13374
GROWTH
a ~EQU ITY
The Tarvaiw Case
|l ~FIllECOPY }
Q X John C. H. Fei
Gstay Ranis
Oxr A WoShirley W. Y. Kuo t
()(frd A C World Bank Research Publication
Of related interest
from Oxford and the World Bank
REDISTRIBUTION
WITH GROWTH
Hollis Chenery, Montek S. Ahluwalia,
C. L. G. Bell, John H. Duloy,
and Richard Jolly
"A major contribution to the literature of
income distribution in less developed
countries." -Journal of Developing Areas
"A rich and instructive contribution for
anyone teaching economic development and
the complex relations between distribution
and growth." -Political Science Quarterly
"Exceptionally valuable analysis of develop-
ment policies . . . Redistribution with
Growth, a model handbook for planners, is
also an extremely useful guide to the state
of the discipline of development economics."
-Journal of Economic Literature
324 pages. Figures, tables, bibliography.
Available in cloth and paper editions.
INCOME INEQUALITY
AND POVERTY:
METHODS OF ESTIMATION
AND POLICY APPLICATIONS
Nanak Kakwani
New techniques, derived from actual data,
analyze problems of size distribution of
income and evaluate alternative fiscal
policies. Both ethical evaluation and
statistical measurement are considered.
The author systematizes existing knowledge
and introduces a number of new findings.
About 320 pages. Figures, bibliography.
Available in cloth edition.
Growth
with
Equity
THE TAIWAN CASE
A World Bank Research Publication
Growth
with
Equity
THE TAIWAN CASE
John C. H. Fei
Gustav Ranis
Shirley W. Y. Kuo
with the assistance of
Yu-Yuan Bian
Julia Chang Collins
Published for the World Bank
Oxford University Press
Oxford UTniversity Press
NEW YORK OXFORD LONDON GLASGOW
TORONTO MELBOURNE WELLINGTON HONG KONG
TOKYO KUALA LUMPUR SINGAPORE JAKARTA
DELHI BOMBAY CALCUTTA MADRAS KARACHI
NAIROBI DAR ES SALAAM CAPE TOWN
(© 1979 by the International Bank
for Reconstruction and Development / The World Bank
1818 H Street, N.W., Washington, D.C. 20433 U.S.A.
All rights reserved. No part of this publication
may be reproduced, stored in a retrieval system,
or transmitted in any form or by any means,
electronic, mechanical, photocopying, recording,
or otherwise, without the prior permission of
Oxford University Press. Manufactured in the
United States of America.
The views and interpretations in this book are the
authors' and should not be attributed to the World
Bank, to its affiliated organizations, or to any
individual acting in their behalf.
Library of Congress Cataloging in Publication Data
Fei, John C. H.
Growth with equity
Includes bibliographical references and index.
1. Income distribution-Taiwan. 2. Taiwan-
Economic conditions. I. Ranis, Gustav, joint
author. II. Kuo, Shirley W. Y., 1930- joint
author. III. Title.
HC430.5.Z915196 339.2'0951'249 79-23354
ISBN 0-19-520115-9
ISBN 0-19-520116-7 pbk.
Foreword
CAN GOVERNMENTS MODIFY POLICIES to produce a more equitable
distribution of the benefits of economic growth? Or must they initiate
more drastic structural changes? These questions are at the heart of
one of the most debated issues in economic development. Most studies
of developing countries indeed show that the rich tend to benefit
more than the poor from rises in national income during the early
phases of economic growth. The experience of Taiwan thus is of par-
ticular interest, because the country has managed to achieve rapid
growth with considerable equity.
This study by Fei, Ranis, and Kuo develops an analytical frame-
work that relates changes in family income to the evolution of its
several components, which are in turn related to development theory.
Application of this method to Taiwan helps to explain the observed
changes in income distribution during two decades of rapid growth.
Circumstances specific to Taiwan naturally played an important part
in this performance. But in speculating about the effects of govern-
ment intervention and the pattern of growth on changes in equity,
the authors identify processes that are relevant both to economic
theory and to economic policy. The authors' catalog of findings
deserves consideration by pessimists who feel the tradeoff between
growth and equity to be inevitable.
This book is one of a series of studies investigating the relations
between growth and distribution in the developing countries-a series
supported by the research program of the World Bank. Other books
in this series include Income Distribution Policy in Developing Coun-
tries: A Case Study of Korea by Irma Adelman and Sherman Robinson,
Public Expenditure in Malaysia: Who Benefits and Why by Jacob
Meerman, Who Benefits from Government Expenditure: A Case Study
v
Vi FOREWORD
of Colombia by Marcelo Selowsky, and Redistribution with Growth by
Hollis Chenery and others. Additional titles forthcoming at this writ-
ing include Models of Growth and Distribution for Brazil by Lance
Taylor and others, Urban Labor Markets and Income Distribution in
Malaysia by Dipak Mazumdar, and Inequality and Poverty in Malay-
sia: Measurement and Decomposition by Sudhir Anand. As in these
other studies, the authors of this book alone are responsible for the
findings. It is the Bank's hope that this series will improve under-
standing of the choices that developing countries have with respect
to growth and the distribution of income. Clearly, the method of
analysis and findings for Taiwan presented here are important
contributions to that understanding.
HOLLIs B. CHENERY
Vice President, Development Policy
The World Bank
Contents
Preface xviii
INTRODUCTION. An Approach to Growth with Equity 1
Framework of Analysis S
Problems of Measurement 6
Problems of Data 10
PART ONE. THE CASE OF TAIWAN 17
1. Historical Perspective 21
The Colonial Legacy 26
Primary Import Substitution, 1953-61 30
Export Substitution, 1961-72 21
2. Economic Growth and Income Distribution, 1953-64 37
Land Reform 38
Agricultural Development during the 1950s 46
The Distribution of Assets and Industrial Growth 50
Effects of Growth on Equity 54
3. Growth and the Family Distribution of Income
by Factor Components 72
Income Inequality and Its Factor Components 75
Growth and the Distribution of Income 83
Empirical Application to Taiwan 90
Impact of Growth on FID: Quantitative Aspects 99
Impact of Growth on FID: Qualitative Aspects 108
Summary and Conclusions 127
4. The Inequality of Family Wage Income 1SO
Empirical Data 182
Analytical Framework 188
vii
viii CONTENTS
Labor Heterogeneity and the Wage Rate:
First-level Analysis 141
Inequality of Income of Individual Wage Earners:
Second-level Analysis 146
Inequality of Family Wage Income: Third-level Analysis 168
Conclusion 193
Appendix 4.1. Data on the Distribution of Family Income
in Taiwan 193
Appendix 4.2. Linear Regression and the Model
of Additive Factor Components 203
5. Income Distribution and Economic Structure 224
The Decomposition Equation 226
Empirical Decomposition by Sectors and Homogeneous
Groups 231
Changes in Income Inequality Associated with
Industrialization and Urbanization 243
Additional Reflections 249
6. Taxation and the Inequality of Income and Expenditure 264
Statistical Data 267
Analytical Framework 270
Decomposition of Family Income after Tax 272
The Impact of Taxation on Income Inequality 279
Future Research 289
Appendix 6.1. Estimation of Indirect Tax 293
7. Relevance of Findings for Policy 308
The Inequality of Family Income 312
The Inequality of Family Wage Income 317
The Inequality of Taxation and Expenditure 321
Future Research 323
PART Two. THE METHODOLOGY OF GINI COEFFICIENT
ANALYSIS 325
8. Basic Concepts 328
Definition of the Gini Coefficient 328
The Gini Coefficient as Related to the Rank Index of Y 330
The Gini Coefficient as the Average Fractional Gap 331
The Pseudo Gini Coefficient 334
9. Testing Hypotheses 338
Testing Hypotheses by Supporting and Contradicting Gaps 340
Gini Decomposition for Hypothesis Testing 342
Net Supporting Gap 343
CONTENTS
Graphic Summary of the Gini and Pseudo Gini Coefficients 346
Correlation Characteristics 348
10. The General and Special Models
of Additive Factor Components 351
Decomposition of G, into Pseudo Factor Ginis 352
Exact Decomposition of G, into Factor Ginis 357
Computation Procedure for Exact Decomposition 359
The Gini Coefficient under Linear Transformation 361
Linear Model of Additive Factor Components 363
Monotonic Model of Additive Factor Components 365
Linear Approximation of Factor Components 367
Linearity Error 369
Approximation of the Monotonic Model 370
11. Applications and Extensions of the Models
of Decomposition 373
Remarks on Chapter Three 374
Renmarks on Chapter Six 375
Additive Factor Components and Growth Theory 376
Income Components with Observation Error 378
Family Income with Negative Components 380
Computation Procedure 383
12. Regression Analysis, Homogeneous Groups,
and Aggregation Error 386
Regression Analysis 386
Family Income Inequality with Homogeneous Groups 394
Gini Error Arising from the Use of Grouped Data 403
Grouping Error in the Analysis of Additive Factor
Components 405
Index 411
Figures
1.1. Ratios of Imports of Nondurable Consumer Goods
to Total Imports and Total Supply, 1953-72 27
1.2. Growth Rate of Real Gross National Product per Capita,
1953-72 28
1.3. Ratios of Savings and Investment to Gross National Product,
1953-72 29
1.4. Ratios of Exports of Primary Goods and Industrial Goods
to Total Exports, 1953-72 SO
Z CONTENTS
1.5. Ratio of Exports to Gross National Product, 1953-72 31
1.6. Ratios of Agricultural and Nonagricultural Employment
to Total Employment, 1953-72 82
1.7. Index Numbers of Real Wages of Males and Females
in Manufacturing, 1953-72 S3
1.8. Index Numbers of Real Wages of Males and Females
in Textiles, 1953-72 S3
1.9. Index Numbers of Real Wages of Males and Females
in Transport and Communications, 1953-72 34
1.10. Gini Coefficients, 1953-72 35
3.1. Gini Coefficients of Total and Factor Incomes, by Model,
1964-72 91
3.2. Factor Shares, by Model, 1964-72 96
3.3. Gini Coefficients of Total Income, by Model, 1964-72 100
3.4. Gini Coefficients of Wage and Property Income, by Model,
1964-72 101
3.5. Ratio of the Wage Share in Nonagricultural Production
to the Property Share, by Model, 1964-72 117
3.6. Ratio of Average Urban Income to Average Rural Income
for Wage and Property Income, 1964-72 118
3.7. Ratio of the Total Income Share of the Top 10 Percent
to That of the Bottom 10 percent, by Model, 1964-72 122
3.8. Ratio of the Wage Income Share of the Top 10 Percent
to That of the Bottom 10 Percent, by Model, 1964-72 123
3.9. Ratio of the Property Income Share of the Top 10 Percent
to That of the Bottom 10 Percent, by Model, 1964-72 124
3.10. Ratio of the Agricultural Income Share of the Top 10 Percent
to That of the Bottom 10 Percent, by Model, 1964-72 125
4.1. The Emergence of Splinter Groups 153
4.2. The Wage Gini and the Explained Portion of the Wage Gini,
by Location, 1966 160
4.3. Percentage Composition of Factor Contributions,
by Location, 1966 162
4.4. Composition of the Contribution of Education
to Explained Inequality, by Location, 1966 163
4.5. Composition of the Contribution of Age
to Explained Inequality, by Location, 1966 165
4.6. Composition of the Contribution of Sex
to Explained Inequality, by Location, 1966 167
4.7. Composition of the Contribution of Family Influence
to Explained Inequality, by Location, 1966 168
4.8. Contribution to Family Wage Income Inequality,
by Labor Grade, 1966 176
CONTENTS xi
4.9. Inequality of Family Ownership of Labor
of Different Grades, 1966 178
4.10. Correlation Characteristics between Total Family Income
and Family Ownership of Labor, 1966 179
4.11. The Economic Weight of Different Grades of Labor, 1966 180
4.12. Weighted Average of the Education Gini Plotted against
the Average Wage Rate, by Level of Education, 1966 182
4.13. Weighted Average of the Education Correlation Characteristic
Plotted against the Average Wage Rate, by Level
of Education, 1966 182
4.14. Weighted Average of the Education Weight Plotted against
the Average Wage Rate, by Level of Education, 1966 183
4.15. Gini Coefficients in Four Cases, Plotted against
the Wage Rate, by Level of Education 188
4.16. Correlation Characteristics in Four Cases Plotted
against the Wage Rate, by Level of Education 189
4.17. Weights in Four Cases Plotted against the Wage Rate,
by Level of Education 189
5.1. Income Distribution for Agricultural, Nonagricultural,
and All Sectors 228
6.1. Contributions to the Inequality of Family Income
after Tax, by Category of Expenditure, 1964-73 272
6.2. Correlation Terms for the Decomposition of Family Income
after Tax, by Category of Expenditure, 1964-73 27S
6.3. Shares for the Decomposition of Family Income after Tax,
by Category of Expenditure, 1964-73 276
6.4. Gini Coefficients for the Decomposition of Family
Income after Tax, by Category of Expenditure,
1964-73 277
6.5. Flows of Income before Tax to Taxes
and Income after Tax, by Family 282
6.6. Contributions to the Inequality of the Tax Burden,
1964-73 284
6.7. Shares for the Decomposition of the Tax Burden,
1964-73 288
6.8. Gini Coefficients of Direct and Indirect Tax, 1964-73 289
8.1. The Lorenz Curve 329
8.2. The Pseudo Lorenz Curve 335
8.3. The Pseudo Lorenz Curve for an Inverse Wage Pattern 337
9.1. Iso Gini Coefficient Contour Lines 347
12.1. Behavior of Indexes of Inequality under Different
Levels of Aggregation 408
Xii CONTENTS
Tables
1.1. Distribution of Land and Owner-Cultivator Households,
by Size of Holding, 1920, 1932, and 1939 28
1.2. Distribution of Farm Families and Agricultural Land,
by Type of Cultivator, 1920-22, 1927-30, and 1939-40 24
2.1. Area and Households Affected by Land Reform,
by Type of Reform 41
2.2. Distribution of Land and Owner-Cultivator Households,
by Size of Holding, 1952 and 1960 42
2.3. Distribution of Farm Families and Agricultural Land,
by Type of Cultivator, 1948-60 48
2.4. Distribution of Agricultural Income, by Factor, 1941-56 44
2.5. Parameters and Indexes of Agricultural Employment,
Production, and Development, 1952-64 46
2.6. Distribution of Industrial Production, by Public
and Private Ownership, 1952-64 51
2.7. Gini Decomposition Analysis Based on Farm Family
Income Stratified by Size of Farm, 1952-67 55
2.8. Multiple Cropping, by Size of Farm, 1952 and 1967 56
2.9. Average Income of Farm Families, by Size of Farm, 1952-67 58
2.10. Distribution of Factor Shares, by Size of Farm, 1952-67 59
2.11. Distribution of Farm Households, Income,
and Factor Shares, by Size of Farm, 1952-67 60
2.12. Off-farm Activity of Farm Families, by Size of Farm, 1960 61
2.13. Composition of Off-farm Employment of "Moved-out"
Workers, by Type of Work, 1963 62
2.14. Establishments in Taiwan, by Location, 1951 and 1961 63
2.15. Gini Coefficients and Factor Shares Based on Income
of Urban Wage and Salary Workers, 1955 and 1959 64
2.16. Measures of the Equity of the Family Distribution
of Income, 1953, 1959, and 1964 66
2.17. Distribution of National Income, by Factor Shares, 1951-72 68
2.18. Gross Domestic Product, Employment, Share of Wages in
Value Added, and Labor Intensity, by Industry,
Various Years 70
3.1. Numerical Example with Three Factor Income Components
and with Total Income Arranged in a Monotonically
Nondecreasing Order 76
3.2. Gini Decomposition by Additive Factor Components, 1964-72 92
3.3. Regression Results for Decile Income Groups, 1964-72 94
CONTENTS xiii
3.4. Comparison of Factor Shares from National Accounts
and Household Surveys, 1952-72 97
3.5. Changes in the Family Distribution of Income
and Their Decomposition, All-households Model, 1964-72 102
3.6. Changes in the Family Distribution of Income
and Their Decomposition, Rural-households Model, 1966-72 104
3.7. Changes in the Family Distribution of Income
and Their Decomposition, Urban-households Model, 1966-72 106
3.8. Gini Coefficients Based on Decile Population Groups
for Urban, Semiurban, and Rural Households, 1964 and 1968 111
3.9. Establishments in Taiwan, by Location, 1951-71 116
3.10. Capital Intensity, by Region and Sector, 1961 and 1971 119
4.1. Relative Wage Rates and Frequency Distribution of Labor,
by Education, Sex, and Job Location, 1966 134
4.2. Relative Wage Rates and Frequency Distribution of Labor,
by Age, Sex, and Job Location, 1966 135
4.3. Wage Parity of Female Workers, by Age and Education, 1966 136
4.4. Numerical Example Corresponding to the Gross-listing
of Information on the Wage Rate and Frequency Distribution
of Workers in Tables 4.20-4.27, by Sex and Level of Education 140
4.5. Numerical Example Classifying Workers into Five Families
and Tracing Wage Income Components to the Membership
Composition of Those Families 141
4.6. Regression Coefficients of Four Explanatory Variables,
by Job Location, 1966 148
4.7. Influence of Total Family Income on Wage Rates,
by Sex and Age, 1966 144
4.8. Distribution of Families, by Job Location
and Total Family Income, 1966 145
4.9. Numerical Example of Regression Analysis
for Five Wage Earners and Two Explanatory Variables 148
4.10. Numerical Example of the Formation
of New Homogeneous Groups with Eight Workers 151
4.11. Numerical Example of the Gap between the Relative Value
of the Education Characteristic for a Privileged Group
and That for a Less Privileged Group 154
4.12. Decomposition Analysis of the Inequality of the Wage Rate,
by Location and Labor Characteristic, 1966 159
4.13. Wage Rates, Family Membership Ginis, and Other Variables
for Thirty-seven Categories of Workers, 1966 172
4.14. The Inequality of Wage Income: Numerical Example of
Uniform Family Size and Homogeneous Family Composition 184
4.15. The Inequality of Wage Income: Numerical Example of
Uniform Family Size and Semihomogeneous Family Composition 187
xiV CONTENTS
4.16. The Inequality of Wage Income: Two Numerical Examples
of Nonuniform Family Size and Homogeneous Family
Composition 191
4.17. The Inequality of Wage Income: Two Numerical Examples
of Descending Family Size and Homogeneous Family
Composition 192
4.18. Size of Sample for DGBAS Surveys, 1964-73 194
4.19. Coding for Characteristics of Individual Wage Earners
and Income-earning Families 200
4.20. Annual Wage Rates of Female Workers, by Age, Occupation,
Job Location, and Level of Education, 1966 204
4.21. Annual Wage Rates of Male Workers, by Age, Occupation,
Job Location, and Level of Education, 1966 206
4.22. Number of Female Workers, by Age, Occupation,
Job Location, and Level of Education, 1966 208
4.23. Number of Male Workers, by Age, Occupation,
Job Location, and Level of Education, 1966 212
4.24. Number of Rural Workers and Average Annual Wage Rate,
by Education, Sex, and Age, 1966 216
4.25. Number of Town Workers and Their Annual Wage Rate,
by Education, Sex, and Age, 1966 218
4.26. Number of City Workers and Their Annual Wage Rate,
by Education, Sex, and Age, 1966 220
4.27. Number of Workers and Average Annual Wage Rate,
by Education, Sex, and Age, 1966 222
5.1. Numerical Example of Income Distribution for Agricultural,
Nonagricultural, and All Sectors 229
5.2. Decomposition Analysis, by Farm and Nonfarm Sectors,
1964-72 282
5.3. Decomposition Analysis, by Degree of Urbanization
in the Six-sector Classification, 1966 and 1972 286
5.4. Decomposition Analysis, by Degree of Urbanization
in the Three-sector Classification, 1966 and 1972 287
5.5. Decomposition Analysis, by Age of Head of Family,
1964 and 1972 2S8
5.6. Decomposition Analysis, by Sex of Head of Family,
1964 and 1972 289
5.7. Decomposition Analysis, by Number of Persons Employed
in Family, 1964 and 1972 240
5.8. Decomposition Analysis, by Educational Level
of Head of Family, 1972 242
5.9. Income Disparities, by Farm and Nonfarm Families,
1964 and 1972 244
CONTENTS xV
5.10. Income Disparities, by Degree of UJrbanization
in the Six-sector Classification, 1966 and 1972 244
5.11. Income Disparities, by Degree of Urbanization
in the Three-sector Classification, 1966 and 1972 245
5.12. Causes of the Reduction in Income Inequality,
by Farm and Nonfarm Sectors, 1964-72 246
5.13. Causes of the Reduction in Income Inequality, by Degree
of Urbanization in the Six-sector Classification, 1966-72 247
5.14. Causes of the Reduction in Income Inequality, by Degree
of Urbanization in the Three-sector Classification, 1966-72 248
5.15. Sources of Income of Farm and Nonfarm Families,
by Decile, 1966 and 1975 250
5.16. Growth of Income of Farm and Nonfarm Families,
by Decile, 1966-75 251
5.17. Gini Index of Land Concentration in Selected Countries,
Comparisons for Various Years 252
5.18. Indexes of the Productivity of Land and Labor
in Agriculture, Taiwan, 1950 and 1955 253
5.19. Relative Tax Burden of Farm and Nonfarm Families,
by Income Range, 1966 and 1975 254
5.20. Average Size of Families, by Income Bracket,
1966 and 1972 256
5.21. Average Size of Farm Families, by Income Bracket,
1966 and 1972 257
5.22. Average Size of Nonfarm Families, by Income Bracket,
1966 and 1972 258
5.23. Income Disparities, by Size of Household, 1966 and 1972 259
5.24. Income Disparities, by Number of Persons Employed
in Family, 1964 and 1972 260
5.25. Causes of the Reduction in Income Inequality, by Number
of Persons Employed in Family, 1964-72 261
5.26. Income Disparities, by Age of Head of Family, 1964 and 1972 262
5.27. Causes of the Reduction in Income Inequality, by Age
of Head of Family, 1964-72 262
5.28. Income Disparities, by Sex of Head of Family, 1964 and 1972 263
5.29. Causes of the Reduction in Income Inequality, by Sex
of Head of Family, 1964-72 263
6.1. Categories of Household Expenditure and Their Indirect
Tax Burden, 1966 268
6.2. Decomposition of the Inequality of Family Income after Tax,
1964-73 274
6.3. Decomposition of the Inequality of Family Income before Tax,
1964-73 280
XVi CONTENTS
6.4. Decomposition of the Inequality of the Tax Burden, 1964-73 286
6.5. Family Income and Expenditure, by Category
and Income Class, 1964 296
6.6. Family Income and Expenditure, by Category
and Income Class, 1966 298
6.7. Family Income and Expenditure, by Category
and Income Class, 1968 SOO
6.8. Family Income and Expenditure, by Category
and Income Class, 1970 302
6.9. Family Income and Expenditure, by Category
and Income Class, 1972 304
6.10. Family Income and Expenditure, by Category
and Income Class, 1973 306
9.1. Numerical Example of Income Fractions, Income Ranks,
and Education Ranks for Five Families 339
10.1. Numerical Example of the Problem of Additive Factor
Components 352
10.2. Gini Decomposition by Pseudo Factor Ginis, 1964-72 354
10.3. Numerical Example of Exact Decomposition
of Gu into Factor Ginis 358
11.1. Numerical Example of Original Income Data 384
11.2. Distributive Shares, Gini Coefficients, and Pseudo Gini
Coefficients for Original Data in Table 11.1 384
11.3. Decomposition Analysis of Original Data in Table 11.1 385
12.1. Numerical Example of Income Data and Regression Terms 391
12.2. Distributive Shares, Gini Coefficients, and Pseudo Gini
Coefficients for Original Data in Table 12.1 392
12.3. Decomposition Analysis of Original Data in Table 12.1 393
12.4. Numerical Example of the Classification
of Families by Education 395
12.5. Numerical Example of the Classification of Seven Families
into Three Homogeneous Groups 400
12.6. Decomposition Analysis of Data in Table 12.5 401
12.7. Numerical Example of the Factor Gini Error
in Grouped Data 406
CONTENTS xVii
Acronyms and Initials
ATP After the turning point
BTP Before the turning point
DGBAS Directorate-General of Budget, Accounting, and Statistics
FID Family distribution of income
GDP Gross domestic product
GNP Gross national product
ICCT Industrial and Commercial Census of Taiwan
JCRR Joint Commission for Rural Reconstruction
LDC Less developed country
NDP Net domestic product
OECD Organization for Economic Cooperation and Development
Preface
THis VOLUME IS DEDICATED to the study of the family distribution of
income in the context of growth. Because the empirical application is
to Taiwan, we quote at the outset a famous observation Confucius
made 2,500 years ago: "Inequality is to be lamented more than
scarcity." More recently, Ricardo had this to say in a letter to
Malthus: "Political economy, you think, is an enquiry into the nature
and causes of wealth-I think it should be called an enquiry into the
laws which determine the division of the produce of industries
amongst the classes who concur in its formation." Ricardo's sentiment
ushered in the classical school's interest in the social problem of
income distribution. Although that interest lapsed for some time, few
today will deny that the persistence of income gaps between wealthy
and poor families probably is the most serious social problem and that
such gaps will continue to be a serious problem as long as there is
scarcity.
It is curious then, despite such universal recognition of the social
importance of the distribution of family income, that modern
economists did not devote serious attention to it until really quite
late: that is, until the post-Keynesian era after the Second World War.
The classical economists focused on the functional distribution of
income and attempted to explain the forces that determine the
division of the national income into various functional distributive
shares. The problem of the equity of income distribution is entirely
different. The phenomenon is explained by the pattern of total income
received by families. That pattern can be summarized by the degree
of inequality of income, as measured by the Gini coefficient or some
other index of inequality. The much more complicated nature of this
problem, as well as the only recently reawakened interest in the fate
of the poorer classes under conditions of growth, were undoubtedly
xviii
PREFACE xiX
responsible for the delayed rebirth of academic and policy interest
in this area.
It is no coincidence that the new concern with the family distribu-
tion of income emerged, after a lag, with the revival of interest in the
study of economic growth-itself a post-Keynesian, postwar phe-
nomenon. The inequality of the distribution of family income must be
traced directly to the inequality in the pattern of family ownership of
the primary factors of production. These factors include physical and
human assets, as well as their compensation. Because growth theory
is primarily concerned with the augmentation of assets-that is,
with capital formation, population growth, and the accumulation of
human capital-the distributional impact of any change in the pattern
of asset ownership can be meaningfully assessed only in the context of
growth. The linkage between the family distribution of income and
the theory of growth, and the conclusions for theory and policy which
can be derived from the inductive examination of the Taiwan
experience, thus constitute the focal points of this volume.
We clearly have not solved the problem. Indeed we shall be
pleased if it is judged that we have somewhat advanced the cause.
Moreover we fully realize that tensions between the political need for
action and the scientific need for a better understanding of behavior
are perhaps more pronounced in the study of income distribution than
in any other area of economics. In fact, researchers are likely to have
to defend themselves against a two-front attack. On one front,
academic and scientific progress demands the formalism of variables
and equations within a deterministic theory based on behavioristic
hypotheses. Such formalism is technically difficult to achieve in this
field, to say the least. On the second front, action-oriented policy-
makers demand to know the implications of research findings with an
unusually high time preference. Consequently researchers run the
risks of having to navigate a narrow course between accusations of
sloppy humanitarianism and those of esoteric irrelevance. We
nevertheless feel that both charges can and must be met.
Academics surely understand that there often exists a pretheoretical
stage in the social sciences-a stage in which inductive evidence is
examined to separate the relevant elements of a problem from the
irrelevant, the essential from the nonessential. Because of the brief
life of research examining the distribution of family income, most
contemporary work cannot, we believe, escape from the grip of the
pretheoretical stage we are in. The present volume is no exception.
Zr PREFACE
Policymakers, on the other hand, sometimes need to be reminded
that good policy is ultimately based on good theory. Although no one
expects a moratorium on policy, planning commissions and aid donors
have little at their disposal to permit them even to rule out absurdities.
Given the many remedies proposed to cure the maldistribution of
income, including fiscal reform, poverty relief, public works, and land
reform, this volume's aim is to begin to fill the vacuum by specifying
some of the things known about the behavioral relations, and
consequently the policy relations, between growth and the distribution
of income.
In short, we are concerned with developing a theory relating income
distribution to growth-a theory which is to be implemented with
statistical data, and a theory from which policy recommendations are
to be deduced. Given the pioneering nature of this area of inquiry, the
task is difficult. The interpretation of results, drawn from imperfect
data, suffers from the absence of a recognized standard of interna-
tional comparison. For example, what is the real significance of, say,
a 2 percent drop in the Gini coefficient over a ten-year period? In
addition, the deduction of policy recommendations, which always is an
art, is particularly difficult at an early phase when the theory still is
highly imperfect. We are aware of these shortcomings, and we
disclaim any notion that our methodology has been perfected or that
definitive policy conclusions can be drawn from it. Our main hope is
that this volume may help to open up a new approach to understand-
ing an important social problem.
We also recognize that all researchers concerned with the distribu-
tion of income face a conceptual difficulty of a basically philosophical
nature. If a Gini coefficient [GQ] is used to measure the degree of
inequality of a pattern of income distribution [Y = (Y,, Y2, . . ., Yn) ],
the underlying implication always is that perfect equality, G, = 0 or
Y, = Y2 = . .. = Y,n represents the social ideal. This implication is
true for all the familiar indexes of inequality which satisfy the axiom
of the desirability of transfer: the axiom that any redistribution from
rich to poor increases social equity. The conceptual difficulty arises
when that axiom is subject to question.
Any modern industrial society, regardless of its organizational
structure, requires a pyramid of positions differentiated by earning
power. There should, for example, be relatively few positions for
doctors and relatively many for unskilled workers. Individuals
differentiated by ability, determination, and other characteristics will
attempt to occupy positions in the pyramid. As a result, in any
PREFACE Xxi
rational society, perfect income equality among individuals cannot
really prevail. Regardless of how positions are allocated to individuals,
the pyramid itself determines a nonzero value for the Gini. This
probably explains why a Gini value below 0.30 is seldom found even
in the most equitable society.
The ideal criterion of equity should thus be the equality of oppor-
tunity to reach for various positions in the pyramid. The major
obstacles in the way of such equality of opportunity are, we believe,
inherent in the genealogical relations of the family system. Even when
markets are perfect and every position is rewarded according to its
productive contribution-that is, even when there are no elements of
discrimination or distortion-not every member of the new generation
has an equal opportunity to reach for these positions. Differences in
family background are the reason. The son of a wealthy black family,
for example, can be expected to earn more than the son of a poor
white family. This inherent inequality of opportunity, whether
caused by variations in inherited assets or educational opportunities,
probably is the principal cause of individual income inequality. Thus
intergenerational, occupational, or class mobility represents the
ultimate test of true equity in a rational society. Income equality
does not.
In this volume we have chosen to study the family distribution of
income as it relates to growth. The choice is based in part on the
belief that a more equal distribution of income across families
increases the equality of opportunity in each generation. For this
reason a lower value or decline in the Gini coefficient will be regarded
as a "good thing." We admit this to be an arbitrary value judgment
on our part. We are content to leave to others, more competent than
we, the unresolved philosophical issues raised in this context.
We would like to thank the World Bank for its financial support
and Montek Ahluwalia, Clive Bell, Hollis Chenery, John Duloy, and
Graham Pyatt for their substantive comments. We are most grateful
for the thorough and perceptive comments of Anthony Atkinson,
who acted as the Bank's outside reader. Others whose constructive
criticisms were appreciated in the course of this effort include Gary
Fields, Mahar Mangahas, and Guy Orcutt. We were beneficiaries of
the cooperation of the Economic Planning Council of Taiwan and the
Economic Growth Center at Yale. Our thanks also go to M. C. Cheng,
M. M. Hsih, T. F. Hsuh, Francoise Le Gall, Regina Liu, and
C. M. Tang for their help in preparing the manuscript, and to
Cheryl Hunt and Paula Saddler for their patience and expert typing.
Zxii PREFACE
Bruce Ross-Larson edited the manuscript for publication. Raphael
Blow prepared the charts, Brian J. Svikhart managed production of
the book, and Kathryn M. Tidyman indexed the text.
JOHN C. H. FEI
GUSTAV RANIS
SHIRLBY Kuo
New Haven, Connecticut
December 1979
INTRODUCTION
An Approach to Growth
with Equity
THE INEQUALITY OF THE DISTRIBUTION OF INCOME AND WEALTH in a
given society has been of concern to man for a very long time.
Economists nevertheless have traditionally focused their attention
more on the functional distribution of income and the determination
of factor prices and shares in the manner of the classical and Austrian
schools. Although the size or family distribution of income (FID) has
not been totally neglected-witness the literature on utopian socialism
and the use of the Lorenz curve-it probably is fair to say that
economists have viewed FID more as a descriptive device. Until quite
recently, it was not successfully integrated with the main body of
analytical economics.'
During the early postwar period, the main social problem every-
where, but especially in the newly independent developing world, was
a concern with growth. The 1950s and 1960s have been characterized,
if unfairly, as being exclusively oriented to growth. Growth was not
quite a religion, but common sense led to one basic assumption: when
the pie is small, policies must be geared to increasing its size, at least
for the time being. The concept of redistribution could not have much
meaning until the pie became much larger.
1. In the first decades of this century, such writers as Cannan and Dalton
were concerned with the measurement of the size distribution of income and its
integration with mainstream economics. Historical hindsight suggests, however,
that their attempt at integration was not very successful. Because the size dis-
tribution of income appears to be a growth-related issue, related to the accumula-
tion of human and physical assets, the chance for successful integration became
real only with the revival of interest in growth after the Second World War.
1
2 INTRODUCTION
In recent years, however, all parties have become increasingly
unwilling to accept the "grow now, redistribute later" package. One
reason for this is a growing reluctance to be generous only to future
generations. But the main reason is the growing skepticism about
whether "later" would ever come. Nevertheless most language in
currency today still relates to redistribution. How is a better measure
of equity to be regained after growth has occurred? How much growth
is to be sacrificed for the sake of better distribution along the way?
This second formulation comes closer to the heart of this volume,
with one proviso: we do not accept the notion that there always has
to be a sacrifice. Consequently it seems more appropriate to address
the extent to which equity can accompany growth from the start, not
to constrain the discourse to the achievement of one objective at the
expense of the other. Of course, the matter may be as much semantic
as it is substantive.
Most economists and policymakers understandably share, at least
implicitly, the assumption of the need for tradeoffs having varying
degrees of severity. Consider the work of Kuznets, Paukert, and
Adelman and Morris.2 On the basis of cross-country cross-sections,
they seem to discern an inverse U-shaped relation between growth
and equity. They conclude that, as income increases from low levels in
a developing society, the distribution of income must first worsen
before it can improve. Two facts support their conclusion. First,
today's less developed countries (LDCS) generally have distributions
which are less equal than those of the rich countries. Second, acceler-
ated LDC growth has most often been accompanied by a worsening of
already unfavorable indexes of equality.
Based on the historical evidence, almost all contemporary LDCS
support the general aura of tradeoff pessimism. Taiwan is one
exception. According to the best data available, Taiwan's family
distribution of income in the 1950s was not very different from the
unfavorable levels most LDCS seem to be prey to in the early years of
2. Simon Kuznets, "Economic Growth and Income Inequality," American
Economic Review, vol. 45, no. 1 (March 1955), pp. 1-28; idem, "Quantitative
Aspects of the Economic Growth of Nations: VIII, Distribution of Income by
Size," Economic Development and Cultural Change, vol. 11, no. 2 (1963), pp.
1-80; Felix Paukert, "Income Distribution at Different Levels of Develop-
ment: A Survey of Evidence," International Labour Review, vol. 108, nos. 2-3
(August and September 1973), pp. 97-124; Irma Adelman and Cynthia Taft
Morris, Economic Growth and Social Equity in Developing Countries (Stanford,
Calif.: Stanford University Press, 1973).
FRAMEWORK OF ANALYSIS S
their transition effort. But that distribution has substantially
improved during two decades of rapid growth. This "deviant" record
should therefore be of interest to academicians and policymakers.
Although no two countries ever are alike, and deviant performance
may be based on special circumstances, an examination of the
relations between growth and equity in a country exhibiting such a
deviant performance can help to isolate the critical elements of that
performance. Only then is it possible to judge whether the underlying
conditions, which seem to have had the effect of virtually eliminating
the usual conflict between these two principal societal objectives in
Taiwan, are sufficient elsewhere to permit somewhat greater optimism.
Such optimism would not be based on the conclusion that achieving
growth with equity is easy. Instead it would be based on the con-
clusion that some of the obstacles are made by man, not nature, and
can thus be removed by changes in policy.
Framework of Analysis
The problem of growth with equity can, we believe, be fruitfully
analyzed in the historical context. During the third quarter of this
century, the less developed world experienced unprecedented growth,
a phenomenon accompanied by a resurgence of interest in the theory
of economic development. We therefore felt that a natural way to
proceed was to construct a framework of analysis that takes advantage
of this new stock of knowledge. In this respect, three dimensions
common to many contemporary growth models are points of departure
for the work of this volume: historical perspective, subphases of
growth, and typological sensitivity.
By historical perspective we mean that the quarter century after
the Second World War can be viewed in most LDCS as a period of
transition between a long epoch of agrarianism and an epoch of
modern growth.8 There in fact are two periods in the history of
3. Latin American countries, for example, started the transition earlier than
most LDCs. For general works on the subject see Simon Kuznets, Modern Eco-
nomic Growth (New Haven: Yale University Press, 1966); John C. H. Fei and
Douglas S. Paauw, The Transition in Open Dualistic Economies: Theory and
Southeast Asian Experience (New Haven: Yale University Press, 1973); and
John C. H. Fei and Gustav Ranis, "Economic Development in Historical Per-
spective," American Economic Review, vol. 59, no. 2 (May 1969), pp. 386-400.
4 INTRODUCTION
economic doctrine when economists have been interested in growth
and income distribution. The first period is the age of the classical
economists-Smith, Malthus, and Ricardo; it dealt with transition
growth in western Europe. The second period is that after the Second
World War; it deals with transition growth in the contemporary
developing world. This setting of transition growth gives the problem
of "growth with equity" its distinctive character. Moreover the
economic content of transition growth includes recognition of the
dualistic structure of most less developed countries: agricultural and
nonagricultural production sectors coexist; the center of gravity
gradually shifts from one to the other. The basic phenomena include
modernizing agriculture, generating an agricultural surplus, ac-
cumulating real capital to provide nonagricultural employment, and
reallocating labor from agricultural to nonagricultural pursuits.
It is convenient and substantively important to divide the overall
phase of transition growth into subphases. These subphases are
related to marked changes in the system's endowment of resources
and in the prevailing package of policies-changes which affect
relative factor prices and shares, as well as the behavior and perfor-
mance of the economy. Because the reallocated labor and the accumu-
lated assets are largely owned by individual families, the phenomenon
of transition growth clearly has important implications for the
distribution of income among families.
To take full advantage of this base of growth theory, an additional
dimension particularly relevant to the analysis of FID must be added:
the spatial perspective. By spatial perspective we mean that a
distinction must be made in the typical LDc between urban families
and rural families, depending on their location and occupational
pursuits. Urban families live in and near the major population centers
and overwhelmingly engage in nonagricultural production. Rural
families are spatially dispersed and derive their income from agri-
cultural and nonagricultural production, the relative proportions of
which depend upon the locational pattern of industries and services.
Thus the separation of rural and urban households is a basic analytical
device used in this volume.
We also find it useful to distinguish among various types of factor
income accruing to families. Wage income and property income are
examples. This separation is essential for our analysis both at the
aggregate and the disaggregate levels. At the aggregate or holistic
level, such a separation makes it possible to trace the inequality of
family income to its various factor components and, in this way,
FRAMEWORK OF ANALYSIS 5
to link that inequality to the theory of development for a dualistic
economy. At the disaggregate level, an intensive search into the
causes of inequality of particular factor components forms a comple-
mentary part of the inquiry.
We must naturally be somewhat selective in choosing the focus for
such disaggregate analysis. A case will be made that the causation of
the inequality of family wage income can be singled out for more
intensive study. The system's labor force usually represents the most
important type of capital distributed among families: human capital.
Moreover, in the course of development, a functionally specialized
modern labor force will gradually be formed out of the more homo-
geneous unskilled labor force of the agrarian epoch. A differentiated
wage structure obtains for this increasingly heterogeneous labor force,
which is differentiated by such characteristics as skill, sex, education,
and age. In addition, the rules of family formation-or the composi-
tion of families with respect to this stratified labor force-also
undergo transformation, depending on the propensity of families and
society to invest in education. It is evident that the inequality of
family wage income, an important component of overall inequality,
can in turn be traced to this pattern of family ownership of differ-
entiated labor, as well as to the differentiated wage structure.
A similar disaggregate study could have examined the ownership
and accumulation of physical capital by families. The usual classifica-
tion of assets suggests that capital assets also are highly hetero-
geneous. The portfolio choice of families appears, however, to be a
much more complex problem that perhaps is less relevant to the
study of family income inequality than its wage counterpart. In any
case, we have not tackled it in this volume.
The role of the public sector also changes in the transition to
modern growth. First and foremost, LDC governments must set the
policy environment for private economic activity through their actions
with respect to foreign exchange, trade, domestic credit, tariffs, and
so on. These actions-whether they work through the market by way
of indirect controls or circumvent the market by way of direct
controls-may be critical for the kind of growth path and the pattern
of income distribution generated. Second, governments directly
participate, at different times and to a greater or lesser extent,
in productive activities through the ownership of public enterprises.
Third, governments act through their tax and expenditure policies to
affect FID after the fact, after the dust of production has settled. In
this volume we attempt to tackle only one of these aspects: taxation.
6 INTRODUCTION
The organization of this volume should be viewed in the foregoing
perspective. We first make an effort to acquaint the reader with the
general story of transition growth and distribution in Taiwan,
especially for the 1950s-a period for which precise FID data either do
not exist or are deficient in quality and sectoral breakdown. Next, we
focus on the period after 1964, when reasonably good and compre-
hensive data become available on income distribution. Our principal
attempt is to forge a more precise link at the aggregate level between
the family distribution of income and the theory of development in a
labor surplus economy. We also attempt to dig more deeply into the
causes of the equity or inequity of income distribution from a number
of related disaggregate perspectives.
The study of FID still is in a pretheoretical stage in which nmuch of
the effort must be directed at examining the empirical evidence. By
sorting out the essential from the nonessential and the relevant from
the irrelevant, it is to be hoped that the relevant and the essential can
then be integrated with the mainstream of economic ideas, especially
those related to development theory. The problems of measurement
and data, two crucial facets of empirical research, thus receive special
attention in this introduction so that readers can maintain their
bearings in the rest of the volume.
Problems of Measurement
How is inequality to be measured? The basic problem is the choice
of an appropriate index of inequality [I(Y)] that can be computed
when the pattern of income distribution [Y = (Y1, Y2, . . . , Y.) ] is
given for n families. Many alternative indexes of inequality are in use,
such as the Gini coefficient [GY], the Theil index, the Atkinson index,
the Kuznets index, and the coefficient of variation. All of them are
reasonable but arbitrary, because none has a conspicuous advantage
over the rest. For reasons spelled out below, we have generally
chosen in this volume to use the Gini coefficient.
All measurements are ultimately motivated by certain theoretical
considerations-or, more appropriately, theoretical intuitions-in the
pretheoretical stage. In our attempt to link the distribution of family
income to growth-the growth of human and physical assets over
time-it is natural to distinguish several types of assets. An example
is the familiar dichotomy between capital [K] and labor [L] in the
mainstream of growth theory. Our basic choice of the additive
PROBLEMS OF MEASUREMENT 7
dimension of income is based on the recognition that this is the only
way to forge the necessary links to development theory.
The pattern of family income [Y = ( Y1, Y2, . . ., Yn) ] is thus seen
to comprise several additive factor components:
MODEL OF ADDITIVE FACTOR COMPONENTS
y = y + y2 + . .+ yr, where
Yi = (Yl, Yi, . . ., Yi). (i = 1, 2, . . , r)
Each factor income component [Fi] corresponds to a particular type
of asset owned by the n families. The formulation of additive factor-
components problems of this type is, with minor exceptions, a central
and unifying theme of this volume. For example, in our attempt to
link FID to growth theory, the two factor components are property
income [EY] and wage income [Ey] for urban households (r = 2).
Agricultural income [Y3] is added as a third component for rural
households (r = 3).4 By letting W = (W1, W2, . . ., W,) represent
the wage income pattern and ir = (71, 7r2, ..., 7rn) the property
income pattern, the pattern of family ownership of the labor force
can be traced to certain demographic rules of family formation, and
the pattern of family ownership of physical assets can be traced to the
rules of saving.
For a more intensive treatment of the wage income component,
the labor force can be stratified by age, sex, education, and other
characteristics. In the model of additive factor components, Y stands
for the pattern of total family wage income; Fi for the wage income
earned by a particular type of labor force, such as adult college-
educated females. The observed structure of wages in part reflects
labor attributes and in part such noncompetitive elements as nepotism
and sex discrimination. Abstractly the problem can again be treated
as a problem of additive factor components.5 In addition to the
differences in human capital dictated by market forces, other differ-
ences are the result of labor market imperfections caused by govern-
ment intervention, oligopoly power, and so on. For one such
4. This formulation is used to forge a link to the dualistic growth model in
chapter three, Growth and the Family Distribution of Income by Factor Com-
ponents.
5. This formulation is used in chapter four, The Inequality of Family Wage
Income.
8 INTRODUCTION
intervention, taxation, the total family income before tax [Y] can be
viewed as the sum of family income after tax [EY] and tax payments
[y2]. Family income after tax can in turn be seen to comprise various
categories of expenditure and savings; tax payments to comprise
direct and indirect taxes.6 Abstractly the problem once again becomes
one of additive factor components.
When the pattern of total income is abstractly formulated as
comprising additive factor components, a natural way to explain the
Gini coefficient of Y[G,] is to trace it to G(Y'), G(Y2), . ., G(yr).
the factor Gini coefficients computed for the r factor components. If:
i=( Yl + Yi + ...+ Yni)/ ( YI + Y2 + ..+ Y.),2
(i = 1,2 . .,r)
the values of i [(UP1, P2, .. . ., XP)] correspond to the r factor income
shares. It then is tempting to design a decomposition formula of the
following type:
G, = 'P1G(Y1) + '2G( Y2) + ... ± 'rG(Yr),
which states that total family income inequality [Ga] is the weighted
average of the factor Ginis [G(Yi)]. It turns out that this is an
approximation relevant only under special conditions. A major
theoretical task of this volume is to design exact and approximate
decomposition formulas of this type.7 The Gini coefficient is thus
used in this volume not because of its greater familiarity or superior
characteristics, but because it has the intrinsic additive property that
makes it convenient for the design of decomposition formulas.
The model of additive factor components differentiates among
various types or sources of income and represents only one kind of
framework for FID analysis. It happens to be the one we find useful for
most of the purposes of this volume. There also are other general
models, such as those which try to differentiate among various types
6. This formulation is used in chapter six, Taxation and the Inequality of
Income and Expenditure.
7. Problems of this type are inherently technical and have therefore been
consolidated in the five chapters constituting part two, The Methodology of
Gini Coefficient Analysis. When the results of that discourse on methodology
are discussed in part one, however, numerical examples and other pedagogical
devices are used to enable the less technically inclined reader to follow the
argument.
PROBLEMS OF MEASUREMENT 9
of income recipient or income-receiving family. For such a model the
pattern of total family income [Y] is abstractly segmented as
follows:
Y = (Yb, Y2, ..., Yn) = (S1, S2, ..., S,), where
SI (Yr, Y2, ..., Yr,), SI = (Yri+i, Yl+2, .. ., Yr,),.
Each subvector ES, (i = 1, 2, . . ., r) ] represents a particular class of
income recipients. For example, when r is 2, S1 and S2 can represent
males and females or, what would be more pertinent to our work,
agricultural households and nonagricultural households. This classifi-
cation suggests that all families within each Si can be referred to as a
homogeneous group. Consequently the abstract framework can be
referred to as a homogeneous group model-or, mathematically, as a
segmentation model. Abstractly an index of inequality can then be
defined on all income recipients [I(Y)], as well as on each homo-
geneous group [I(Si) (i = 1, 2, . . . , r)]. I(Si) is to be called
intragroup inequality. If Yi (i = 1, 2, . . . , r) is the mean value of the
ith group, the income pattern obtained by replacing every Yi by its
group mean becomes:
tR = UP Y, fI, .., 0), (]YI, YI, ..., I2 ,~0 ....I
(Y1, YI2, . . ., Yr)].
While suppressing the intragroup inequality, this equation clearly
brings out the intergroup inequality. Consequently I(R) is called
intergroup inequality. In the homogeneous group approach, the
purpose of any decomposition formula is to trace I(Y) to the inter-
group effect I(R) and the intragroup effect I(S).8
Intrinsically the study of family income distribution is a technically
complicated matter, precisely because of the concern with patterns of
income over families, patterns that are represented by vectors.
Because this volume is principally aimed at the general reader, the
foregoing explanation has been to help identify the contours of part
one, where the methods of analysis are summarized and the empirical
8. This model of homogeneous groups is used only in chapter five, Income
Distribution and Economic Structure. The decomposition of I (Y) into intergroup
and intragroup effects in essence is the analytical technique used in that chapter,
where it also turns out to be more convenient to use the variance as a measure
of inequality, not the Gini coefficient.
10 INTRODUCTION
findings for Taiwan are presented. As noted earlier, the more technical
aspects of decomposition are presented in part two. It is recommended
that general readers turn to this part only after absorbing the
essential ideas in part one.
Problems of Data
In this pretheoretical stage of inquiry, much of the effort must
necessarily be inductive. Consequently the availability and quality of
data become unusually critical issues. The foregoing discussion of the
problem of measurement has already suggested the kind of data
needed for the work of this volume. The model of additive factor
components requires, for example, data on the total family income
pattern [Y] and on the patterns of income components [FY] for all
families involved. All such data must ultimately be based on household
surveys.
For Taiwan in the 1950s, only two surveys gathered data on the
overall distribution of income: one was conducted in 1953; the other
in 1959-60.9 In addition, surveys by the Joint Commission on Rural
Reconstruction (JCRR) for 1952, 1957, 1962, and 1967 contain
information only on farm family incomes.'" Both sets deal with the
total income of these families, not with factor income components;
neither set is of good quality. In 1964, however, the Directorate-
General of Budget, Accounting, and Statistics (DGBAS) began to
conduct household surveys which included information on factor
components, as well as total family incomes." In 1966 the DGBAS
9. Kowie Chang, "An Estimate of Taiwan Personal Income Distribution in
1953-Pareto's Formula Discussed and Applied," Journal of Social Science, vol.
7 (August 1956); National Taiwan University, College of Law, "Report on
Pilot Study of Personal Income and Consumption in Taiwan" (prepared under
the sponsorship of a working group of National Income Statistics, Directorate-
General of Budget, Accounting, and Statistics (DGBAS); processed in Chinese).
10. See Y. C. Tsui and S. C. Hsieh, "Farm Income in Taiwan in 1952," Eco-
nomic Digest Series, no. 4 (Taipei: Joint Council on Rural Reconstruction (JcRR),
1954) and JCRR, Rural Economics Division, "Taiwan Farm Income Survey of
1967-with a Brief Comparison with 1952, 1957, and 1962," Economic Digest
Series, no. 20 (Taipei: JCRR, 1970).
11. DGBAS, Report on the Survey of Family Income and Expenditure, Taiwan
Province, Republic of China, 1964 and subsequent years (Taipei: DGBAS).
PROBLEMS OF DATA 11
broadened the classification to distinguish between rural and urban
households. These data represent the principal data source for the
formal analysis of this volume. The decomposition analysis could thus
be carried out only for the years beginning with 1964; the separation
of urban and rural households, for the years beginning with 1966.12
Even when good household surveys became available after 1964,
specific dimensions of the data needed to be recognized and addressed.
There are problems associated with the randomness of sampling and
the biased nonresponses among sample returns. There are problems
associated with differences between primary and published data-
problems which cause the appearance of a "consolidation error."
There are problems associated with data interpretation, especially in
relation to the imputation of the functional shares and the spatial
characteristics of economic activities. Although these by no means
exhaust all the data problems in this field of inquiry, they are the ones
directly relevant to the theoretical focus of the analysis in this
volume.'3
Data quality
For surveys the DGBAS began to conduct in 1964, a sharp distinction
must be made between the published data and the primary data
contained in the original questionnaires. Only the published data are
available to the public; what is published obviously is severely
constrained by what is viewed as the effective consumer demand for
particular combinations of primary information. As it is, a typical
DGBAS volume contains more than 700 pages of tables, but will
nevertheless disappoint many prospective data users. To illustrate
this point, suppose that workers are classified by sex (male and
female), education (primary, junior high, senior high, professional
12. The city of Taipei originally was part of Taiwan Province and was in-
cluded in the overall DGBAS surveys. Since 1968 Taipei has been reclassified as a
special municipality; the Taipei City government, not DOBAS which is a pro-
vincial organization, has accordingly carried out the same household surveys.
For comparability we have merged the two sets of data by adding, for each in-
come bracket, both the families and incomes of those living in the city of Taipei.
13. For example, the issues of life-cycle income and family lineage are among
the dimensions of FID analysis not addressed. To have formally treated these
issues would have raised even more severe problems of data constraints.
12 INTRODUCTION
school, and college), and age (subdivided into nine age groups).
These three characteristics alone imply the existence of 90 kinds of
labor-180 if rural and urban households are distinguished. Such an
exhaustive cross-listing can be conveniently preserved only in coded
tapes, not in published data.'4
There is no question in our minds that the DGBAS surveys were
based on competently drawn and stratified random samples. Even
when samples are random, however, a frequent problem is the
underresponse of certain groups, such as wealthier families. The
conscientiousness of DGBAS personnel and the good attitude of
respondents to questionnaire surveys nevertheless give us a high
degree of confidence."' In addition, we know of no reason to suspect
differences in the quality of the data over time. We are, moreover,
mainly concerned with interpreting the changes rather than the
precise levels of, say, the Gini coefficients.
It should also be noted that even if the information reported by the
households is perfect, the data may not give the functional income
distribution as the economist would like to have it. In urban family
enterprises, for example, it is difficult to differentiate between the
entrepreneurial income of an owner-operator and his income as a
skilled laborer. The problem is even more serious in a family farm,
where there is less functional specialization. For the urban sector,
DGBAS made its best effort to "impute" family income to the proper
functional share, leaving only a small unallocated "mixed income"
category. For the agricultural income of the rural families, no such
imputation was made by the DGBAS or us. Consequently agricultural
income is a mixed category that includes all property and wage
income. For the spatial dimension, which also is important in the
study of FID, the DGBAS data give the breakdown by "farm" and
"nonfarm" households. We have taken these respective categories to
14. Published DGBAs data are used in chapters two, three, and five; coded
DGBAs data in chapters four and six. Because a complete description of the data
available to us should also focus on the design of questionnaires, the years of
availability, and the absolute and relative sizes of sampies, we discuss these
matters in an appendix to chapter four, where the original coded data are used
for the first time. The use of published DGaAs data is discussed as it is deployed.
15. For analysis of this issue see Shirley W. Y. Kuo, "Income Distribution
by Size in Taiwan Area-Changes and Causes," in Income Distribution, Employ-
ment, and Economic Development in Southeast and East Asia, 2 vols. (Tokyo:
Japan Economic Research Center, 1975), vol. 1, pp. 80-146.
PROBLEMS OF DATA 13
be proxies for "spatially dispersed rural households" and "spatially
concentrated urban households."16
The quality of data must be judged in the context of the problems
indicated. The inferences we derive from the data must be open to the
criticism that conclusions should not be sensitive to small variations.
On the whole, we feel that the quality of data in Taiwan favorably
compares with that in other LDCS; we are quite confident that our
findings are robust in this sense. We nevertheless recognize that the
quality of data of this kind is such that stronger statements are not
admissible. We therefore refrained from applying refined econometric
tests in any of our applications.
Data aggregation
Another problem is the consolidation issue associated with pub-
lished data. Suppose there are n = 5,000 families. The published
tabulation of the pattern of total family income [(Yi, Y2, . . ., Y,)]
must then be in the form of decile or other income groups. By using
such a tabulation, FID analysis tends to underestimate the degree of
income inequality, because some intragroup inequality is inevitably
suppressed. In the published DGBAS data, the number of income classes
varies between 23 and 32; that represents a high degree of consolida-
tion of sample survey returns for 3,000 to 6,000 families. Moreover
the demand for international comparability required a somewhat
higher degree of consolidation.17 Because of this consolidation, trends
in the Gini coefficients over time once again become more meaning-
fuil than the absolute magnitudes.
16. One survey year, 1968, contains in addition to the farm and nonfarm
breakdown a locational breakdown into urban, semiurban, and rural residence.
Because we are basically interested in the broad locational distinctions of urban
residence in relation to rural residence, semiurban workers can thus belong to
either the urban type of household or the rural. For 1968 the breakdown shows
that about 80 percent of nonfarm households and more than 95 percent of farm
households directly correspond to our urban (nonfarm) and rural (farm) sectors
(households). In the absence of ideal data, we thus have confidence that the
results of our empirical research give a relatively accurate picture of the effect
of growth on FID in a dualistic economy.
17. In chapter three we tried to preserve the possibility for international
comparisons by reprocessing our data to conform to the decile grouping con-
vention of the World Bank. See for example Shail Jain, Size Distribution of
Income (Washington, D.C.: World Bank, 1975).
14 INTRODUCTION
Using grouped data for the analysis of additive factor components
is a new and important problem. It is new in its application to the
particular methodology used by us and thus is not dealt with in the
existing literature.'8 It is important because everyone is using grouped
data and the international comparisons based on those data. We
admit that this volume raises these and associated problems
without being able to resolve them. They are shared by virtually all
researchers now investigating income distribution, and this gives us
some comfort. The fact that we lean heavily on the interpretation of
changes in Ginis over time, not on the interpretation of the absolute
levels of Ginis at different times, gives us additional comfort.
Consequently our quantitative conclusions, like those of others,
must be read with these qualifications in mind.
We should add, moreover, that these problems are being tackled
on at least two fronts. On the theoretical front, considerable progress
is being made by Graham Pyatt at the World Bank, Fei and Ranis at
Yale, and Chow and Chen at the Academia Sinica in Taiwan. On the
statistical front, ungrouped or computerized data are now becoming
available in Taiwan-data which will enable us to implement the
theory and determine just how much difference the extent of aggrega-
tion makes to the results. We believe this to be an exciting new area
of future research, but one that will take considerable time to sort
out.'9
Data interpretation
The effort to tackle the relations between equity and growth, the
main objective of this volume, involves matters of theory and the use
of data to implement the theory. For the theory we have, in the main,
chosen to introduce a method of decomposition by additive factor
components. For the data we have used the Gini coefficient to
describe the level and changes in the pattern of equity. In any such
formulation, there always is the problem of interpreting "significant"
or "insignificant" changes in magnitudes. Neither the theoretical
formulations nor the data provide a firm basis for such judgments.
18. See for example Joseph L. Gastwirth, "The Estimation of the Lorenz
Curve and Gini Index," Review of Economics and Statistics, vol. 54, no. 3 (Au-
gust 1972), pp. 306-16.
19. The outline of these issues is fully presented in chapter twelve.
PROBLEMS OF DATA 15
These judgments can be arrived at only in reference to some con-
sensual convention or standard derived over many years of research
and observation. Such a consensus exists, say, for per capita income
and population growth; it does not yet exist for measures of the equity
of income distribution. The experience with international and inter-
temporal comparisons on national income and population growth
does permit judgments about the significance or insignificance of
changes to be made with some confidence. In the realm of the Gini,
however, we do not yet have a similar experience. Our description of
change thus reflects more of our own judgments, which cannot as yet
be checked against an agreed-upon convention.2T As more empirical
work, especially in international comparisons, accumulates in this
relatively new field, we will be in a better position to make qualitative
statements. Meanwhile the reader is asked to take our own judgments
about the significance of quantitative results with a grain of salt.
20. We especially wish to thank Tony Atkinson for bringing this point home
to us.
PART ONE
The Case of Taiwan
IN CONTEMPORARY LDCS the issue of growth with equity must be
viewed in the historical context of attempts by these countries to
make the transition from their agrarian heritage to the epoch of
modern growth. In analyzing equity during this transition, a frame-
work is developed to link the distribution of family income to the
store of growth theory which has been accumulating over the last
quarter of a century. Central to this framework is a decomposition
technique which makes it possible to trace the inequality of family
income to various components of factor income and to various
groups of income recipients. This approach, we believe, reflects the
needs of the current pretheoretical stage of analysis and permits the
systematic processing of data accumulated in recent years.
Chapters one and two outline the case of Taiwan in the context of
transition growth in the open, dualistic, labor-surplus economy. The
crucial phenomenon for focus is the relatedness between the realloca-
tion of domestic labor from agricultural to nonagricultural activities
and the pattern of foreign trade. Upon examination, postwar develop-
ment seems to be marked off by well-defined subphases of transition
growth: a subphase of primary import substitution in the 1950s and a
subphase of primary export substitution in the 1960s. Toward the
end of the 1960s, the condition of labor surplus seems to have become
gradually exhausted, as marked by substantial increases in unskilled
real wages. Analysis of the family distribution of income (FID) over
the entire period of transition must be related to this background.
Chapter two concentrates on an analysis of distribution during the
subphase of import substitution, for which the inadequacy of data on
income distribution does not permit a fully rigorous analysis. Sub-
17
18 THE CASE OF TAIWAN
sequent chapters analyze the distribution of income during the
1964-72 period, for which the data are much better.
In chapter three a dualistic model is used; it contains rural and
urban sectors, each with a number of households. With such a model,
the impact of growth on the equity of FID over time is measured by
the Gini coefficient [Gj] and analyzed by a method of additive factor
Gini decomposition. According to this method, the impact of growth
on the equity of FID is traced, both quantitatively and qualitatively,
to three causal factors: a reallocation effect, a functional distribution
effect, and a factor Gini effect. Each effect is explained and related as
closely as possible to the theory of development. The functional
distribution effect captures changes in the functional distribution of
income-that is, the relative shares accruing to capital and labor.
The reallocation effect captures changes in the share of agriculture in
total income and the extent to which the center of gravity in the
dualistic economy has, or has not, shifted. The factor Gini effect
captures the impact of changes in the inequality of factor income-
that is, the inequality of wage income [G.], property income [G,],
and agricultural income [G0] taken separately. Development theory
within the context of the dualistic economy can adequately explain
only the impact of the reallocation effect and the functional distribu-
tion effect on G, over time. To increase understanding of the factor
Gini effect, which the empirical work of this volume indicates may be
quantitatively important, a fuller inquiry into the causation of the
inequality of particular important factor incomes is required.
Chapter four accordingly concentrates on the causation of the
inequality of family wage income, which is the largest component of
family income. At least two nonconventional aspects of modernization
or development enter into this analysis. First, the formation of a
modern labor force leads to recognition of the growing importance of
labor heterogeneity as workers are stratified by such attributes as age,
sex, and educational attainment. Second, the rules of family formation
regulate the composition of family ownership of various types and
qualities of labor. In this effort at disaggregate analysis, the competi-
tive and discriminatory elements in the wage structure are analyzed
by means of a multiple correlation analysis. On the basis of this
information, as well as that relating to family membership and
formation, a first-cut determination of the basic causes of wage
income inequality among families is attempted. The model of additive
factor components is used in this chapter as well.
Chapter five further analyzes the inequality of total family income,
THE CASE OF TAIWAN 19
but disregards the functional additive components of family income
and classifies the income-receiving families by various criteria. For
example, (Yi, Y', Y3), (Yi2, Y", Y", Y4), (Yl, Y2, Y3) represents the
classification of ten families into three homogeneous subgroups.
Whenever such a classification or segmentation is attempted, the
inequality of total family income can be traced to an intergroup
inequality effect and an intragroup inequality effect. Substantively
three explanatory classifications are used: farm and nonfarm families;
the degree of urbanization of the families; and characteristics of the
head of household, such as age, sex, and educational standard. This
chapter thus attempts to throw additional light on the causes of
income inequality by pointing to differences in family attributes as
causation factors.
Chapter six examines inequality in the disposition of family
income. If Y = (Y1, Y2, . . . , Y.) is the pattern of family incomes
before tax, then the family income pattern after tax [V = (VI, V2,
...,I V,)] will be different because of the payments of direct tax
[(T ., T, T])] and indirect tax [(Ti, T2, . .. , T) ]. The degree
of inequality of family income before tax EGa] and after tax [Gv]
may also be different, depending upon the progressiveness of direct
and indirect taxes. One issue with very obvious policy implications is
the impact of taxation on the equality of FID after taxes. The pattern
of family income after tax [V] is after all only a means to family
economic welfare. That income will in turn be disposed of by the
families in various ways, leading to various patterns of family
consumption [C' = (Ct, C2, ..., C')9] and saving ES = (S, S2,
Sn) ]. The inequality of family income after tax EG[] will thus
lead to inequality of family savings and family expenditure on
education and other consumption categories, depending on the ways
in which incomes are disposed of. A second issue studied in this
chapter is the relation of the inequality of expenditure [G (Ci)] and
saving [EG] to the inequality of family income after tax [EG]. The
inequality of family investment in physical and human capital may
be regarded as the primary causes of the persistence of family income
inequality over the longer run. Persistence of the inequality of family
consumption in particular consumption categories, such as housing or
other items of conspicuous consumption, indicates the existence of
class distinctions and points to possible targets for additional con-
sumption taxation calculated to reduce the social impact created by
family income inequality. The model of additive factors components
is again used in this chapter.
20 THE CASE OF TAIWAN
Chapter seven summarizes the principal analytical findings and
presents the policy conclusions that can be derived from these
findings. As stated earlier, a fully deterministic theory of the distribu-
tion of income-one that is behaviorally specified-frankly is still
beyond reach. We nevertheless believe that we have pointed out some
directions that future work might take at the aggregate and dis-
aggregate levels. Meanwhile there is no possibility of a moratorium on
policy for those wanting to ameliorate existing or potential conflicts
between strategies for growth and equity. Thus, although our
analysis is by no means complete or comprehensive, we feel it
important at this stage to try to derive the main conclusions for
policy.
Part two is devoted to a systematic derivation of the various
decomposition formulas and equations used in part one. There are
two reasons for postponing the discussion of technical issues. First, by
gathering most such matters into one part, it is easier for the interested
reader to appreciate the relatedness of the various methods used in
this volume, to each other and to other contributions in the literature.
Second, the less technically inclined reader can absorb the main
argument of the early chapters without the periodic intrusion of
an undue amount of technical detail.
CHAPTER 1
Historical Perspective
THE BROAD OUTLINES of Taiwan's social and economic development
during the postwar period are relatively well known. Although there
is no unanimity concerning the transferability of this experience to
other nations, there is general agreement that Taiwan's success is
rare among less developed countries (LDCS). Two of Taiwan's achieve-
ments in the years after 1953 are particularly notable: extremely
rapid rates of economic growth were accompanied by improvements
in the family distribution of income; unemployment, or under-
employment, was virtually eliminated by the end of the 1960s. This
success may in part be attributed to the legacy of the Japanese
colonial era. The Japanese left behind an excellent physical and
human infrastructure upon which Taiwan could later build growth
in agriculture and industry. Moreover the influx of high-level man-
power from the mainland more than compensated for the with-
drawal of Japanese human resources after the war. As a result of
these and other factors facilitating reconstruction, all output in-
dicators in 1953 were roughly back to their prewar levels. The
difference was that the economy, poised for takeoff, was engaged in
purposive national development.
The Colonial Legacy
Patterns of colonial investment and resource flows in Taiwan
had features recognizable in most LDCS: the colony supplied the
colonizing country with primary products, in this case sugar and
rice; in return, the colonizing country supplied the colony with
21
22 HISTORICAL PERSPECTIVE
manufactured consumer goods.' Until the Second World War altered
Japanese priorities, there was little encouragement of domestic
industry beyond the processing of agricultural goods for export and
the construction and operation of utilities required to support this
processing. Somewhat less typical, however, was that Japanese
colonial activity in Taiwan focused on food production. This focus
led to the maintenance and expansion of an extensive, well-distrib-
uted irrigation system and to the organization of an islandwide
network of farmers' associations and cooperatives.
The Japanese, in their occupation of Taiwan from 1895 to 1945,
sought to develop the colony into an agricultural supplier for Japan.
All government activities during this period were directed toward
this goal. At the same time Taiwan received a substantial inflow of
physical, human, and institutional capital from Japan, and eco-
nomic growth was considerable. Between 1910 and 1945 the popu-
lation increased by 58 percent, net domestic product by 178 percent,
agricultural production by 133 percent, industrial production by
267 percent, and export volume by 361 percent. Agriculture, which
dominated the economy, was in turn dominated by rice and sugar
cane. During 1935-37 rice accounted for 53 percent of the total
value of agricultural output; sugar cane for 15 percent. The Japa-
nese strongly encouraged the production of both crops, which to-
gether constituted 72.7 percent of Taiwan's total exports during
1930-39. During 1906-40 the production of rice grew at an annual
rate of 2.7 percent; the production of sugar cane, at 4.5 percent.
To encourage agricultural production the Japanese undertook a
variety of projects to develop the physical, human, and institutional
infrastructure of rural areas. They built an efficient and inexpensive
system of railroads and rural roads to facilitate the transport of
rural production. They brought in massive quantities of fertilizer
from Japan and introduced new farming techniques to increase the
productivity of the land. They constructed an extensive irrigation
system: between 1910 and 1942 the area of land under irrigation
increased from 227,000 hectares to 545,000 hectares; the total area
under cultivation increased from 519,000 hectares to 837,000 hect-
ares. Even with that increase in the total area under cultivation,
1. Discussion of the colonial period is largely based on Samuel P. S. Ho, Eco-
nomic Development in Taiwan: 1860-1970 (New Haven: Yale University Press,
1978).
THE COLONIAL LEGACY 23
Table 1.1. Distribution of Land and Owner-Cultivator Households,
by Size of Holding, 1920, 1932, and 1939
Average
Distribution of Distribution size of
owner-cultivator households of land holding
Size of (percent) (percent) (chia)
holding
(chia), 1920 1932 1939 1920 1920
0-0.5 42.7 38.4 43.2 5.7 0.24
0.5-1 21.4 20.9 20.9 8.7 0.72
1-2 17.5 18.7 17.2 13.9 1.42
2-3 7.1 8.1 7.4 9.7 2.45
3-5 5.7 6.7 5.6 12.3 3.81
5-10 3.7 4.5 3.7 14.1 15.50
Over 10 2.1 2.7 2.0 35.8 1.
Total (chia) 405,181b 340,674 431,366 721,252
- Not applicable.
Source: Samuel P. S. Ho, Economic Development in Taiwan: 1860-1970 (New
Haven: Yale University Press, 1978).
a. One chia is equal to 0.97 hectare or 2.47 acres.
b. Because of the poor quality of the survey for 1920, this figure is generally
considered to be too high.
the index of multiple cropping rose from 115.1 for 1911-15 to 125.3
for 1941-45. The Japanese also set up farmers' associations to give
farmers advice on modern agricultural practices and rural credit
cooperatives to provide agricultural finance. Health and education
received considerable attention as well: the average life span rose
significantly during the colonial period; the literacy rate rose from 1
percent in 1905 to 27 percent in 1940.
The distribution of farm families and farmland by size of holding
did not change very much in the twenty years before the Second
World War (table 1.1). Nor did the distribution of families and
land by type of cultivator change very much (table 1.2). It may
thus be inferred that the distribution of land in 1945, when Japanese
rule came to an end, probably was not very different from that
during 1920-39. The poorest 40 percent of households (with less
than 0.5 chia) owned less than a tenth of the land; the wealthiest
2 percent (with more than 10 chia) owned more than a third of
24 HISTORICAL PERSPECTIVE
Table 1.2. Distribution of Farm Families and Agricultural Land,
by Type of Cultivator, 1920-22, 1927-30, and 1939-40
Item and type of cultivator 1920-22 1927-80 19S9-40
Total farm families 385,277 411,377 429,939
Distribution of families (percent)
Owner 30.3 29.1 32.0
Part-owner 28.9 30.7 31.2
Tenant 40.8 40.2 36.8
Distribution of land (percent)
Owner 41.9 43.8 43.7
Tenant 58.2 56.2 56.3
Total agricultural land (hectares)a 670,567 762,289 827,886
Source: Ho, Economic Development in Taiwan.
a. Total area surveyed.
the land. The pattern of tenancy reveals further inequity: about
40 percent of households were landless tenant households; they
worked almost 60 percent of the cultivated land.
Industrial activity during the colonial period also deviated from
the typical colonial pattern. First, rather than serving mainly to
facilitate primary exports to Japan, industry in Taiwan focused
heavily on industries which either used the output of the agricultural
sector or provided inputs to that sector. A survey of industrial
activity in 1930 indicates that food processing accounted for 64
percent of registered factories, 55 percent of factory employment,
and 76 percent of gross value of factory production. Sugar was by
far the most important commodity; its share in total factory pro-
duction during the 1930s was about 50 percent. The chemical and
ceramic industries accounted for about 10 percent of total produc-
tion. Both industries used raw materials readily available in Taiwan
and were linked to the agricultural sector, which used by-products
of sugar processing. Most of Taiwan's colonial industry thus was a
direct extension of agriculture.
In 1940 Taiwan had 8,940 factories which employed 128,000
THE COLONIAL LEGACY 2
workers. The vast majority of factories employed fewer than five
workers and were establishments processing food, primarily rice.
The capitalization of firms reflects the same pattern of small-scale
operations: in 1936 the six largest firms accounted for 80 percent of
paid-up capital. There was, in addition, a sizable handicraft sector,
which accounted for 25 percent of manufacturing employment. To
meet the power demands of the infant industrial sector, the Japanese
invested heavily in power generation. Between 1926 and 1941 the
capacity for power generation increased by 700 percent to levels
that were reached again only in 1954 after the reconstruction of
wartime damage.
The Japanese controlled most of this infant industrial sector in
Taiwan, partly because of initially restrictive regulations regarding
capital ownership and partly because of the lack of accumulated
wealth by Taiwanese. In 1929 the Japanese owned three-fourths of
all paid-up capital in industry. The larger joint-stock companies
engaged in manufacturing accounted for 60 percent of total paid-up
capital. The Japanese also owned sizable shares of commerce, mining,
and unspecified limited partnerships. In contrast, Taiwanese capital
was concentrated in traditional industries based on agriculture; these
industries accounted for only 3 percent of total paid-up capital.
Taiwanese ownership of businesses not based on agriculture was
mainly in handicrafts, commerce, and traditional transport. Most
of these businesses, such as rice mills and noodle factories, were
small-scale operations. In all, the Taiwanese owned less than 10
percent of the joint stock in larger scale operations and 22 percent
of the paid-up capital in industry.
The objectives and actions of Japanese colonial rule in Taiwan
were similar to those applied in most other colonies. The Japanese
implanted a typical triangular mode of operation and segmented
the domestic economy into two distinct sectors: a modern sector
oriented toward exports, and a large, backward sector oriented
toward traditional agriculture. For most colonies such segmentation
led to the formation of two mutually exclusive enclaves having
little or no interaction. But this pattern did not evolve in Taiwan
for three reasons. First, the export commodities were agricultural
in origin and were produced by the land-based peasant class. Second,
modernization of the agricultural sector occurred without the intro-
duction of the plantation system. Third, industrialization had its
roots in agriculture, and the linkages between the industrial and
26 HISTORICAL PERSPECTIVE
agricultural sectors were extensive and close. This high degree of
integration and interaction between the economy's two domestic
sectors greatly facilitated postcolonial development in Taiwan.
Primary Import Substitution, 1953-61
The beginning of a country's effort to make the transition from
colonialism to modern growth is customarily assigned to the year
of its political independence. Taiwan became independent of Japan
in 1945 and mainland China in 1949, but 1953 is more appropriately
regarded as the initial year of its transition. An economic system
independent of the mainland economy did not begin to emerge
until late 1949. The Taiwanese economy did not recover from the
damage caused by allied bombing during the Second World War,
or from the cutoff of such vital agricultural inputs as fertilizer, until
about 1951. Nevertheless the influx of talented officials, managers,
and entrepreneurs from the mainland minimized problems asso-
ciated with replacing the Japanese colonial presence. By the time
government promulgated the first four-year plan in 1953, Taiwan
possessed an unusually good physical and institutional infrastructure,
especially in agriculture. It also had a solid base of human resources
to go along with the more common features of a surplus of labor on
limited arable land.
The first subphase of transition growth, common to virtually all
developing countries, is primary, or first-stage, import substitution.
It is characterized by the diversion of traditional export proceeds
away from further expansion of the colonial enclave and toward
investment intended to replace previously imported industrial con-
sumer goods by domestically produced consumer goods. Primary
import substitution proceeded at a rapid pace in Taiwan. It was
aided by the customary package of diverse policies aimed at en-
couraging the emergence of a class of industrial entrepreneurs and
by a good dosage of natural import substitution made necessary by
the severe disruption of Taiwan's traditional trading channels.
Whether defined in horizontal or vertical terms, this subphase came
to an end in Taiwan by the late 1950s or early 1960s (figure 1.1).
The policies Taiwan chose during the 1950s to effect the desired
redirection of resources seem quite standard. Deficit financing by
government and substantial rates of inflation accompanied the
PRIMARY IMPORT SUBSTITUTION, 1953-61 27
Figure 1.1. Ratios of Imports of Nondurable Consumer Goods to Total
Imports and Total Supply, 1953-72
Labor surplus Labor scarcity
20 Primary import Primary export econdary import and
substitution substitution export substitution
10 -\\_
5 _ \\ _ _ - ,lIT¢//(M, + D,)
O1 I I I I I I I I I I I I I I I I I I
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
lff, = imports of nondurable consumer goods
M = total imports
Af, + D, = total supply
Source: Kuo-shu Liang and Ching-ing Hou Liang, "Exports and Employment
in Taiwan" (paper read at Conference on Population and Economic Development
in Taiwan, December 29, 1975-January 3, 1976, Academia Sinica, Institute of
Economics, Taipei; processed).
classic syndrome of overvalued exchange rates and import licensing.
Close examination nevertheless reveals substantial differences from
the classic syndrome, and these differences suggest that Taiwan's
primary import substitution was mild in relation to that in other
countries. Although agriculture was squeezed both directly and by
way of international trade to help finance industrialization, it was not
as relatively disadvantaged as is normal. The agricultural sector
received favorable attention during the 1950s, primarily through
major land reforms and the allocation of additional investment to
rural infrastructure. Agriculture's terms of trade never dropped below
96 (1952 = 100) in the 1950s. This accomplishment is remarkable by
any standard. Even interest rates, which normally are very low or
negative in real terms during this subphase, were reasonably high
after a reform in the mid-1950s. Interest rates, in addition to gen-
erating savings, thus performed an allocative function.
Taiwan's overall economic growth was good during the 1950s
28 HISTORICAL PERSPECTIVE
Figure 1.2. Growth Rate of Real Gross National Product
per Capita, 1953-72
Labor surplus Labor scarcity
10 Primary import Primary export
8 substitution substitution
Secondary import
; 6 and export
-substitution
4-
2 -
I I l I I I I I I I I I I I Il I I I I
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
Sources: Directorate-General of Budget, Accounting, and Statistics (DGBAS),
National Income of the Republic of China (Taipei, 1975); Economic Planning
Council, Taiwan Statistical Data Book (Taipei, 1975).
(figures 1.2 and 1.3). Despite formidable pressures of population
growth, real per capita income rose at an average rate of almost 3
percent a year. As would be expected, the growth of nonagricultural
output was rapid-8.7 percent a year. Although a high rate of in-
crease of agricultural output would not be expected, that output
in Taiwan grew at the average rate of 5.5 percent a year during
this decade. Saving rates, fluctuating in the vicinity of 10 percent,
were also respectable. In addition, the pattern of industrial growth,
featuring technological choices that were compatible with Taiwan's
comparative advantage and output mixes that were abnormally
intensive in labor, led to annual rates of nonagricultural labor ab-
sorption of more than 3 percent. Foreign capital, mainly U.S. aid,
also was important. It initially helped to stabilize the economy
and subsequently enabled purchases of overhead capital and in-
dustrial producer goods beyond those procurable with Taiwan's
earnings from primary exports alone.
Much of Taiwan's initial success can be attributed to the relative
mildness and flexibility of its regime of primary import substitution.
This subphase inevitably runs out of steam as domestic markets
PRIMARY IMPORT SUBSTITUTION, 1953-61 29
Figure 1.3. Ratios of Savings and Investment to Gr oss
National Product, 1953-72
Labor surplu.s Labor scarcity
40 - Primary import Primary export Secondary import and
substitution substitution export substitution
30-
' 20 -
10 _ SIG7NP
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
I = investment
S = savings
Source: DGBAS, National Income of the Republic of China (Taipei, 1975).
for nondurable consumer goods are exhausted. Domestic markets in
Taiwan reached that point of exhaustion by the late 1950s. Taiwan
did not, however, move into secondary or backward-linkage types
of import substitution, as is typical. Instead Taiwan shifted the
strategy for industrial development from the domestic market to
international markets. The economy's industrial entrepreneurs
were of good quality to start with. By cutting their teeth in the
domestic market, they matured sufficiently to compete abroad
and to find new markets for their labor-intensive industrial con-
sumer goods.
The story of the policy reforms adopted in Taiwan to accommo-
date export-led industrial expansion during the late 1950s and early
1960s is well documented. Chief among these reforms were the move
toward a unified and realistic exchange rate, the relaxation of ex-
change controls, the reduction in the rate of effective protection,
and the continuing modification of interest rates. Government
promulgated nineteen major reforms in 1960 alone.2 Intended to
increase production, liberalize trade, and establish a more realistic
2. For a detailed account see Neil H. Jacoby, U.S. Aid to Taiwan (New York:
Frederick A. Praeger, 1966), pp. 85-103.
30 HISTORICAL PERSPECTIVE
set of relative factor prices, these reforms helped to usher in a rad-
ically different pattern of resource allocation during the second
subphase of economic transition: primary export substitution.
Export Substitution, 1961-72
Several indicators reflect the change in direction of resource flows
in Taiwan and the ensuing change in the structure of production.
During the subphase of primary import substitution, the system
continued to rely mainly on its land-based primary exports, supple-
mented by foreign aid, to finance industrial growth. But the re-
versal was dramatic as industrial exports based on unskilled labor
increasingly substituted traditional primary exports. By 1972 they
accounted for more than 80 percent of total exports, compared
with 10 percent in 1952 and 50 percent in 1962 (figure 1.4). Equally
Figure 1.4. Ratios of Exports of Primary Goods and Industrial Goods
to Total Exports, 1953-72
Labor surplus Labor scarcity
100i- Primary import Primary ezport Secondary import and
substitution substitution export substitution
80 -
G 60 -
P- 40-
20 -
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
Ei = exports of industrial goods
E, = exports of primary goods
E = total exports
Source: Economic Planning Council, Taiwan Statistical Data Book (Taipei,
1975).
EXPORT SUBSTITUTION, 1961-72 31
Figure 1.5. Ratio of Exports to Gross National Product, 1953-72
Labor surplus Labor scarcity
40 Primary import Primary export Secondary
substitution substitution import and
30 - export
substitution
20-
~~ ~EIGNP
10 -
C I I I I I l I I l l I l I I I I I I I
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
E = exports
Sources: Same as for figure 1.2.
dramatic was the increase in the trade orientation of this relatively
small, open economy. With exports growing at rates of more than
30 percent by the end of the 1961-72 period, the export ratio ad-
vanced to nearly 40 percent (figure 1.5). Nor has it since slowed
down: Taiwan's export ratio today is more than 50 percent, one of the
highest in the world. Furthermore the industries that grew fastest
during the 1960s were such light consumer goods as textiles and
such intermediate goods as electronics. Both were internationally
competitive because of the use of technologies extremely intensive
in unskilled labor. Concurrently the productivity of agricultural
labor-supported by earlier investments in rural infrastructure, an
increasingly favorable policy environment, and new technologies
and crops-increased at 6.6 percent a year during the 1960s, com-
pared with 4.9 percent during the 1950s. These gains kept the prices
of foodstuffs low, despite the pattern of rapid industrialization, and
prevented a premature sharp rise in real wages.
Because of all these developments, rates of absorption of non-
agricultural labor doubled from 3 percent in the 1950s to more than
6 percent in the 1960s. Despite high, if declining, rates of population
growth, the reserve of surplus labor in Taiwan was virtually ex-
hausted by the end of the 1960s. As would be expected, the propor-
tion of the labor force in agriculture continuously declined during
the 1950s and 1960s. But even the absolute size of the agricultural
S2 HISTORICAL PERSPECTIVE
Figure 1.6. Ratios of Agricultural and Nonagricultural Employment
to Total Employment, 1953-72
Labor surplus Labor scarcity
8s Primary import Primary export Secondary import and
substitution substitution export _substitution
~~~~~ 60 ~ ~ ~ ~ ~ ~ ~ n/
40-
La,,
20 -
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
Lna = nonagricultural employment
L. = agricultural employment
L = total employment
Source: Shirley W. Y. Kuo, "A Study of Factors Contributing to Labor
Absorption in Taiwan, 1954-71" (paper read at Conference on Population and
Economic Development in Taiwan, December 29, 1975-January 3, 1976, Academia
Sinica, Institute of Economics, Taipei; processed).
work force began to decline after 1965 (figure 1.6). By about 1968
the rapid pace of labor reallocation had led to the end of labor
surplus and the beginning of labor scarcity. The rapid rise in real
wages of unskilled workers, most closely proxied by the wage series
for female textile workers, indicates this transition (figures 1.7, 1.8,
and 1.9).
By returning to the aggregate indicators of performance, it can
be seen that per capita growth rates, which were respectable during
the subphase of primary import substitution, accelerated to new
levels and reached almost 10 percent during the subphase of primary
export substitution (see figure 1.2). This performance was achieved
despite the virtual termination of concessional foreign assistance
and its only partial replacement by private capital from abroad.
Booming industrial exports, along with continuing and expanding
agricultural surpluses, provided ample fuel for the economy's rapid
progress. The domestic saving rate also indicates a regime of sub-
stantially more rapid growth during the 1960s (see figure 1.3). The
EXPORT SUBSTITUTION, 1961-72 S3
Figure 1.7. Index Numbers of Real Wages of Males and Females in
Manufacturing, 1953-72
(1964 100)
Labor surplus Labor scarcity
200- Primary import Primary export Secondary import and
substitution substitution export substitution
U 150 _
; 100 Females
50 _- le
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
Sources: Taiwan Provincial Government, Department of Reconstruction,
Report of Taiwan Labour Statistics, 1958, 1963, 1969, and 1973.
Figure 1.8. Index Numbers of Real Wages of Males and Females in
Textiles, 1953-72
(1964 100)
Labor surplus Labor scarcity
200- Primary import Primary export Secondary import and
;, 15C substitution substitution export substitution
-~150-
,100 Females
5CMales
50
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
Sources: Same as for figure 1.7.
S4 HISTORICAL PERSPECTIVE
Figure 1.9. Index Numbers of Real Wages of Males and Females in
Transport and Communications, 1953-72
(1964 = 100)
Labor surplus Labor scarcity
200 Primary import Primary export /
substitution substitution
15 Males .. , , Secondary import and
c 100 _ export substitution
P-4 _--,,~~~Females
50 _
O I I I I I I I I I I I I I I I I I I I - '
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
Sources: Same as for figure 1.7.
rate virtually doubled between the 1950s and the 1960s and reached
a prodigious 30 percent in 1972 to make Taiwan a net exporter of
capital. Such effective functioning of financial, commodity, and
labor markets during the 1960s was in part the result of the stabi-
lization achieved with the help of policy reforms adopted early in
that decade.3
The scarcity of unskilled labor after 1968 indicates that Taiwan's
economic development was heading into a new subphase charac-
terized by the need for higher levels of skills and greater capital
intensity. But that subphase-which might be called secondary
import and export substitution and which Taiwan had fully entered
by 1973-is part of another story.' This volume is mainly concerned
with a developing economy's pattern of income distribution as it
3. Note the contrast between a 9 percent average annual rise in the con-
sumer price index (cPI) during the 1950s and a modest 2 percent average annual
rise during the 1960s.
4. Because of the substantial cyclical noise in the data for 1973 and subsequent
years, the statistical series and the analysis in this book generally have been
terminated in 1972, the last year of the fifth four-year plan. Extreme inflation
accompanied the economic boom of 1973; inflation persisted during the inter-
national recession of 1974 and most of 1975.
EXPORT SUBSTITUTION, 1961-72 35
Figure 1.10. Gini Coefficients, 1953-72
Labor surplus Labar scarcity
¢ 0.60 Primary import Primary export Secondary import and
substitution substitution export substitution
n 0.50
E 0.40 -
0.30 -
1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972
Source: Shirley W. Y. Kuo, "Income Distribution by Size in Taiwan Area-
Changes and Causes," in Income Distribution, Employment, and Economic
Development in Southeast and East Asia. 2 vols. (Tokyo: Japan Economic Research
Center, 1975), vol. 1, pp. 80-146.
makes its way to the turning point when accelerated labor-intensive
growth has mopped up underemployment.
The pattern of income distribution in Taiwan for the 1953-72
period is summarized by Gini coefficients in figure 1.10.1 Although
the observations for 1953 and 1959 are based on a small sample of
low quality, the overall pattern indicates that the reduction of
income inequality was substantial. Even if the two observations
for the decade of import substitution are disregarded, the low levels
of the Gini coefficient after 1964, when the data become much more
reliable, and the generally downward trend between 1964 and 1972
are both striking. The distribution of income appears to have im-
proved over the entire 1964-72 period, as it very clearly does after
the advent of labor scarcity in about 1968. The pattern after 1968
would be consistent with the views of Lewis and the findings of
Kuznets, Adelman, and Morris that equity can be expected to
5. The purpose here is to present a brief overview of trends in the distribution
of income in Taiwan. Detailed analysis of this pattern, especially for the 1964-72
period, is a principal subject of this volume and is reserved for subsequent
chapters, particularly chapter three.
36 HISTORICAL PERSPECTIVE
improve along with growth once real wages rise in a sustained fash-
ion after commercialization. The really interesting question raised
by the relations between growth and equity in Taiwan is this: Why
was the Gini coefficient virtually constant during the period of
extremely rapid growth before commercialization began in 1968?
The answer clearly could be of great interest to other LDCS because
most of them still are a long way from conditions of labor scarcity.
Two problems are of greatest policy relevance to them: whether
the conflict between growth and equity can be eliminated, or at
least mitigated, before basic conditions of labor surplus can be
brought to an end; and how this conflict might best be eliminated or
mitigated. It would be small comfort for policymakers in these
countries to have to conclude that economic growth is compatible
with an improved distribution of income only after real wages have
begun to rise consistently for neoclassical reasons.
CHAPTER 2
Economic Growth
and Income Distribution, 1953-64
DESPITE CONSIDERABLE WARTIME, DESTRUCTION, the physical and
institutional infrastructure established under colonial rule in Taiwan
was instrumental in the rapid growth of agriculture during the
1950s. The irrigation system, which extended over more than half
of Taiwan's cultivated area, proved valuable in ensuring the equi-
table distribution of benefits of green-revolution technology. Linkages
between agriculture and the rural-based food-processing industry
led to a marked spatial dispersion of economic growth. This pattern
later enabled the provision of substantial nonagricultural employ-
ment to farmers. Progress in public health and education during
the colonial period provided the basis for a highly productive labor
force in both agriculture and industry. In addition, the overwhelm-
ingly Japanese ownership of manufacturing enterprises contributed
to a more equal distribution of income in two ways: it reduced the
concentration of industrial assets in private Taiwanese hands in the
period immediately after independence; and it provided a source of
industrial assets that could be distributed as compensation to land-
owners under the program of land reform. The preconditions for
rapid economic growth and an improved distribution of income thus
were considerably more favorable in Taiwan than in the typical
developing country.
This chapter probes the reasons for the apparent absence of a
conflict between growth and equity in Taiwan, especially during the
1950s. Even if the level of the Gini coefficient, based on poor data
for the 1950s, must be viewed with several grains of salt, it prob-
87
38 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
ably is true, contrary to the experience in most LDCS, that the fam-
ily distribution of income (FID) substantially improved during the
subphase of primary import substitution in Taiwan.' The following
sections examine the distribution of assets and the conditions of
production during this period, first in agriculture, then to a limited
extent in nonagriculture. The chapter concludes with a discussion
of inferences about the course of FID in the 1950s and early 1960s.
In subsequent chapters the superior detailed data available after
1964 enable more rigorous analysis of the interplay of economic
growth and FID duiing the subphase of export substitution, both
before and after commercialization.
Land Reform
The land reform that government instituted between 1949 and
1953 probably was the most important factor in improving the
distribution of income before the beginning of the subphase of
export substitution in the early 1960s.2 Although much of the re-
form took place before 1952, the year for which sample data on the
distribution of income first exist, it continued to have its impact
well into the 1950s. The reform thus remained an important factor
in explaining improvements in FID during that decade.
Land reform was initiated for several reasons. Although the
Japanese had developed a substantial agricultural infrastructure in
Taiwan, they paid relatively little attention to the distribution of
land (see tables 1.1 and 1.2 in chapter one). Given the large class
of tenants, competition for the scarce land was so fierce that the
average lease was less than one year. As a result, rents often were
equal to 50 percent of the anticipated harvest, especially in the
1. Kowie Chang, "An Estimate of Taiwan Personal Income Distribution in
1953-Pareto's Formula Discussed and Applied," Journal of Social Science, vol.
7 (August 1956); National Taiwan University, College of Law, "Report on
Pilot Study of Personal Income and Consumption in Taiwan" (prepared under
the sponsorship of a working group of National Income Statistics, DGBAS; proc-
essed in Chinese).
2. Discussion of land reform draws heavily on Samuel P. S. Ho, Economic
Development in Taiwan: 1860-1970 (New Haven: Yale University Press, 1978)
and Chao-Chen Chen, "Land Reform and Agricultural Development in Taiwan"
(paper read at Conference on Economic Development of Taiwan, June 19-28,
1967, Taipei; processed).
LAND REFORM 39
more fertile regions. Contracts frequently were oral; rent payments
had to be made in advance; no adjustments were made for crop
failures. These conditions and practices left the typical tenant
helpless in any dispute with his landlord. The record of landlord
abuse and the need to meet the food demands of postwar Taiwan-
which, in addition to its own increased population, included hun-
dreds of thousands of mainland Chinese-laid the groundwork for
reform.3 In addition, the principle of land ownership by the tiller,
although never receiving much attention, had always been part of
the ideology of the Chinese Nationalists. The loss of the mainland
and the social unrest threatening in Taiwan made the redistribution
of wealth a particularly important issue for government. Land
reform was also considered to be an essential ingredient of agricultural
growth and economic recovery. Moreover, it could be imposed by a
government free of obligations and ties to the landowning class.
Government's conception of land reform was broad. Strengthen-
ing farmers' associations and other elements of organizational and
financial infrastructure in rural areas was considered to be important.
Moreover the repair of physical infrastructure, started as soon as
Taiwan was retroceded to China and almost completed by 1952,
increased the effect of land reform on both growth and equity. But
the main component of the successful reorganization of the agricul-
tural sector clearly was the three-pronged package of land reform:
the program to reduce farm rents, the sale of public lands, and the
land-to-the-tiller program.
The first step taken to promote agricultural incentives and output
was to reduce farm rents and thereby to increase the share of tenant
farmers in crop yields. Promulgated in 1949, this program had five
basic provisions: first, farm rents could be fixed at no more than
37.5 percent of the anticipated annual yield of the main crops;
second, if crops failed because of natural forces, tenant farmers
could apply to local farm-tenancy committees for a further reduc-
tion; third, tenant farmers no longer had to pay their rent in ad-
vance; fourth, written contracts and fixed leases of three to six
years had to be registered; fifth, tenants had the first option to
purchase land from its owners. The reform affected about 43 per-
cent of the 660,000 farm families, 75 percent of the 410,000 part
3. In 1945 and 1946, 640,000 mainlanders moved to Taiwan. Kuang Lu,
"Population and Employment," in Economic Development of Taiwan, ed. Kowie
Chang (Taipei: Cheng Chung Books, 1968), p. 532.
40 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
owners and tenants, and 40 percent of the 650,000 hectares of private
farmland. Prices of farmland immediately dropped: paddy field
prices by 20 percent; dry field prices by more than 40 percent by
December 1949 and a further 66 percent by 1952.4 Equally impor-
tant, the requirement for written contracts and the fixing of standard
reduced rents enabled tenants to benefit from their own increased
efforts for the first time. This incentive was a primary ingredient
of the sustained increase in Taiwan's agricultural productivity
during the early 1950s. With higher yields and lower rents, the
average income of tenant farmers rose by 81 percent between 1949
and 1952.5 These rising incomes enabled tenants to purchase land
put up for sale by their landlords; about 6 percent of private farm-
land changed hands.
Given the success of the program to reduce farm rents, govern-
ment decided to accelerate the program initiated in 1948 to sell
public land to tenant farmers. Formerly owned by the Japanese,
about 170,000 hectares of public land, or about 25 percent of Tai-
wan's arable land, were suitable for cultivation. Taiwan Sugar
Corporation owned most of this land and leased part of it to tenant
farmers. The program gave priority in land purchases to cultivators
of public land and landless tenants. The size of parcels was limited
according to predetermined fertility grades, and the average size
was 1 chia. Selling prices were 2.5 times the value of the annual
yield of the main crops; payments in kind were set to coincide with
the harvest season over a ten-year period. In all, 35 percent of Tai-
wan's arable public land was sold during 1948-53; 43 percent during
1953-58.
With government setting the example of returning land to the
tiller, the stage was set for the most dramatic component of the
three-pronged package: the compulsory sale of land by larndlords.
This program stipulated that privately owned land in excess of
specified amounts per landowner had to be sold to government,
which would resell that land to tenants.6 The purchase price was
set at 2.5 times the annual yield of the main crops. Landlords were
paid 70 percent of the purchase price in land bonds denominated
4. Chen Cheng, Land Reform in Taiwan (Taipei: China Publishing, 1961),
p. 310.
5. Cheng, Land Reform in Taiwan, p. 309.
6. Individual landowners were allowed to retain three chia of medium-grade
land. Anthony Y. C. Koo, The Role of Land Reform in Economic Development-
A Case Study of Taiwan (New York: Frederick A. Praeger, 1968), p. 38.
LAND REFORM 41
in kind and 30 percent in industrial stock of four public enterprises
previously owned by the Japanese. The selling prices and conditions
of repayment were the same as those provided in the sale of public
lands. This third program had a dual objective. The new owner-
cultivators were encouraged to work harder because they would
benefit from any increases in agricultural output. The landlords,
deprived of the privilege of living comfortably off the land, were
encouraged to participate in the industrial development of Taiwan
through ownership of four large-scale industrial enterprises. Between
May and December of 1953, tenant households acquired 244,000
hectares of farmland, or 16.4 percent of the total area cultivated in
Taiwan during 1951--55.
Effects of land reform on the distribution of assets
Tables 2.1, 2.2, and 2.3 summarize the extent of land reform and
its importance for the redistribution of wealth in Taiwan. Because
Table 2.1. Area and Households Affected by Land Reform,
by Type of Reform
Type of reform
Reduction Sale of Land-to- Total
of farm public the-tiller redistri-
Item rents land program bution,
Area affected
(thousands of chia) 256.9 71.7 193.6 215.2
Farm households
affected (thousands) 302.3 139.7 194.9 334.3
Ratio of cultivated
area affected to
total areab (percent) 29.2 8.1 16.4 24.6
Ratio of farm households
affected to total farm
households (percent) 43.3 20.0 27.9 47.9
Note: Figures may not reconcile because of rounding.
Source: Samuel P. S. Ho, Economic Development in Taiwan: 1860-1970 (New
Haven: Yale University Press, 1978), p. 163.
a. Comprises land distributed under the sale of public land and the land-to-the-
tiller program.
b. Total area is the total area cultivated in 1951-55.
42 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.2. Distribution of Land and Owner-Cultivator Households,
by Size of Holding, 1952 and 1960
Distribution of
owner-cultivator Distribution Average size
households of land of holding
Size of (percent) (percent) (chia)
holding
(chia)a 1952 1960b 1952 1960b 1952 1960b
0-0.5 47.3 20.7 9.9 5.2 0.23 0.30
0.5-1 23.3 45.9 15.1 30.5 0.72 0.81
1-2 16.9 15.3 21.1 19.3 1.39 4.58
2-3 5.7 14.8 12.3 30.3 2.42 2.50
3-5 3.9 2.7 13.2 10.2 3.79 4.58
Over 5 3.4 0.6 28.4 4.6 10.14 9.10
Total
(chia) 611,193 776,002 681,154 948,738 - -
- Not applicable.
Note: Table 1.1 in chapter one gives comparable figures for the prewar period.
Source: Ho, Economic Development in Taiwan.
a. One chia is equal to 0.97 hectare or 2.47 acres.
b. Includes only individual farm households; excludes public and private
commercial farms, which all are larger than 10 chia and account for about 6
percent of total land and less than 0.1 percent of the number of holdings.
of the reform, the distribution of land holdings dramatically changed
between 1952 and 1960. The rising share of families owning medium-
sized plots of land ranging from 0.5 to 3 chia reflects this change:
their share increased from 46 percent in 1952 to 76 percent in 1960.
The largest rise was in the share of families owning between 0.5
and 1 chia. What is even more dramatic, the average size of holdings
in all categories of less than 5 chia increased. The combined share
in total land of families owning less than 3 chia increased from 58
percent in 1952 to 85 percent in 1960. The proportion of land culti-
vated by tenants fell from 44 percent in 1948 to 17 percent in 1959.
The proport,ion of tenant farmers in farm families fell from 38 per-
cent in 1950 to 15 percent in 1960.
Although government compensated landlords for the land they
were forced to give up, this compensation was only 2.5 times the
standard annual yield; market values of land ranged between 5 and
LAND REFORM 43
Table 2.3. Distribution of Farm Families and Agricultural Land,
by Type of Cultivator, 1948-60
Item and type of cultivator 1948 1950 1953 1955-56 1959-60
Total farm families n.a. 638,062 n.a. 732,555 785,592
Distribution of families
(percent)
Owner n.a. 36.0 n.a. 59.0 64.0
Part-owner n.a. 26.0 n.a. 24.0 21.0
Tenant n.a. 38.0 n.a. 17.0 15.0
Distribution of land
(percent)
Owner 55.9 n.a. 82.9 84.9 85.6
Tenant 44.1 n.a. 17.1 15.1 14.4
n.a. Not available.
Note: Table 1.2 in chapter one gives comparable figures for the prewar period.
Sources: Family distribution from Ho, Economic Development in Taiwan; land
distribution from Chen Cheng, Land Reform in Taiwan (Taipei: China Publishing,
1961).
8 times the annual yield. The exercise thus represented a substantial
redistribution of wealth. The total value of wealth redistributed as
a result of this price difference was equivalent to about 13 percent
of Taiwan's gross domestic product (GDP) in 1952.7 Furthermore
bonds used to reimburse landowners paid an interest rate of only 4
percent, substantially less than the prevailing market rates. Be-
cause of the landlords' lack of experience in nonagricultural matters,
most landlords did not place much value on the 30 percent of their
compensation received as industrial stocks. They promptly sold the
stocks at prices far below value. Most of their proceeds went to
consumption; some went to investments in small businesses. The
majority of landlords thus ended up being not much better off than
the new owner-cultivators.8
7. Ho, Economic Development in Taiwan, p. 166.
8. T. Martin Yang, Socio-Economic Results of Land Reform in Taiwan (Hono-
lulu: East-West Center, 1970).
44 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.4. Distribution of Agricultural Income, by Factor, 1941-56
(percent)
Property
Year Land Capital Labor
Before land reform
1941 52.20 11.48 36.32
1942 51.99 11.44 36.57
1943 45.65 10.04 44.31
After land reform
1953 37.39 8.23 54.38
1954 38.05 8.37 53.58
1955 38.19 8.40 53.41
1956 36.28 7.98 55.74
Source: S. C. Hsieh and T. H. Lee, "Agricultural Development and Its Contri-
butions to Economic Growth in Taiwan," Economic Digest Series, no. 17 (Taipei:
JCRR, 1966).
Through the reduction of rents and the redistribution of assets,
the land reform had a marked effect on the functional distribution
of income. Between 1941 and 1956 the combined share of property
in total agricultural income fell from 63.7 percent to 44.3 percent
(table 2.4). The sharp reduction in the share of property income
was thus accompanied by a broader distribution of that income.
Two investigators estimated the shares of farm income by recipient
before the land reform, using the 1936-40 average, and after the
land reform, using the 1956-60 average.9 According to these esti-
mates, the share of cultivators in farm income increased from 67
percent to 82 percent; the share of government and public institu-
tions, which received repayments from new landowners, increased
from 8 percent to 12 percent; but the share of landlords and money-
lenders declined from 25 percent to 6 percent.
9. T. H. Lee and T. H. Shen, "Agriculture as a Base for Socio-Economic
Development," in Agriculture's Place in the Strategy of Development, ed. T. H.
Shen (Taipei: JCRR, 1974), p. 300.
LAND REFORM 45
Reorganization of institutional infrastructure
The institutional infrastructure of Taiwan's agriculture was
extensively reorganized and improved during the 1950s. The farmers'
associations and credit cooperatives, set up by the Japanese to
facilitate agricultural extension programs and rice procurement, were
top-down institutions dominated by landlords and nonfarmers. As
a result, most farmers did not directly benefit from them. In 1952
government consolidated those institutions in multipurpose farmers'
associations restricted to farmers and serving their interests. In
addition to the original function of agricultural extension, the activi-
ties of farmers' associations expanded to include a credit depart-
ment, which accepted deposits from farmers and made loans to
them, and to provide facilities for purchasing, marketing, ware-
housing, and processing.'0 The associations thus became clearing-
houses for farmers, who controlled and maintained them and viewed
them as their own creatures.
The other major institutional reform affecting agriculture during
the 1950s was the establishment of the Joint Commission on Rural
Reconstruction (iCRR) by the U.S. Congress in 1948. Its main
functions were to allocate U.S. aid, provide technical assistance, and
help the Taiwanese government plan and coordinate programs for
agricultural extension, research, and experimentation. Thus, while
the farmers' associations provided the much-needed organizational
structure at local levels and facilitated the efficient flow of
agricultural surpluses to the industrial sector, the JCRR was a major
catalyst. It funded and initiated many innovations in farming
techniques, and it introduced new crops and new markets. For
10. Deposits of the credit divisions of farmers' associations increased from
about NT$100 million to NT$2,700 million by the end of 1965. Loans increased
commensurately. (At the time of writing, the new Taiwan dollar was equal to
about US$0.025.) Wen-Fu Hsu, "The Role of Agricultural Organizations in
Agricultural Development" (paper read at Conference on Economic Develop-
ment of Taiwan, June 19-28, 1967, Taipei; processed). Also during this period,
credit became available to farmers from the ScRR, government-owned banks, and
government agencies and monopolies. Between 1949 and 1960 the proportion of
farm loans provided through the organized money market rose from 17 percent
to 57 percent. Ho, Economic Development in Taiwan, pp. 179-80.
46 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
example, the JCRR was behind the introduction of asparagus and
mushroom cultivation, which led to the highly successful production
and export performance of those commodities in the 1960s.
Agricultural Development during the 1950s
Land reform alone could not solve the primary constraint facing
Taiwan's agriculture: the shortage of land for a rapidly growing
agricultural population. Although an ever-increasing number of
farmers left agriculture to live and work in Taiwan's expanding
urban areas, the population pressure on farmland was severe, espe-
cially during the early 1950s. The agricultural population rose from
4.3 million in 1952 to 5.8 million in 1964, an increase of 33 percent.
During the same period the total area of cultivated land remained
nearly fixed, culminating in a decline of the average size of holding
from 1.29 hectares per family to 1.06 hectares (table 2.5). Taiwan
Table 2.5. Parameters and Indexes of Agricultural Employment,
Production, and Development, 1952-64
Item 1952 1956 1960 1964
Agricultural population
(thousands) 4,257 4,699 5,373 5,649
Agricultural employment
(thousands) 1,792 1,806 1,877 2,010
Cultivated land (thousands of
hectares) 876 876 869 882
Cropped land (thousands of
hectares) 1,506 1,537 1,595 1,658
Percentage of agricultural
population in total population 52.4 50.0 49.8 46.1
Hectares of cultivated land
Per farm family 1.29 1.17 1.11 1.06
Per capita on farm 0.21 0.19 0.16 0.16
Per agricultural employee 0.49 0.48 0.46 0.44
AGRICULTURAL DEVELOPMENT DURING THE 1950s 47
Table 2.5 (Continued)
Item 1952 1956 1960 1964
Indexes
Agricultural population 100.0 110.4 126.2 132.7
Agricultural employment 100.0 100.1 104.7 112.2
Total agricultural production 100.0 121.0 142.8 178.7
Agricultural crop productiona 100.0 116.8 132.1 159.7
Output of crops and livestock 100.0 121.4 139.1 168.5
Agricultural crop production
per worker 100.0 115.4 126.1 142.4
Man-days of labor 100.0 104.1 111.5 116.9
Agricultural crop production
to man-days of labor 100.0 112.2 118.8 136.6
Man-days of labor to
employment 100.0 104.0 106.5 104.2
Fixed capital 100.0 107.5 116.6 133.6
Working capital 100.0 151.5 169.7 240.2
Multiple cropping 171.9 175.5 183.6 188.0
Diversificationb 3.54 4.07 4.01 5.75
Sources: Parameters of land and population and indexes of production from
Economic Planning Council, Taiwan Statistical Data Book, 1975, pp. 47-51;
indexes of labor man-days, output of crops and livestock, working capital, and
fixed capital from Ho, Economic Development in Taiwan, p. 245; index of diversifi-
cation from Shirley W. Y. Kuo, "Effects of Land Reform, Agricultural Pricing
Policy, and Economic Growth on Multiple Crop Diversification in Taiwan," in
Economic Essays, vol. 4 (Taipei: National Taiwan University, Graduate Institute
of Economics, November 1973); other indexes from calculations by the authors.
a. Excludes forestry, fishing, and livestock.
b. The diversification index is calculated for 181 different crops by the formula:
1/2 (value of each product/value of total products)2.
overcame these pressures in three ways: by the achievement of sub-
stantial increases in agricultural productivity at the intensive mar-
gin; by the diversification of agricultural production into more
profitable crops; and by the part-time reallocation of labor to non-
agricultural activities, including off-farm employment for many
members of agricultural families.
The growth of the agricultural sector during the 1950s was im-
pressive. The real net domestic product (NDP) by agricultural
48 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
origin increased by about 80 percent during the 1952-64 period, or
at an average rate of 5 percent a year, even though agriculture's
share in NDP declined, from 36 percent to 28 percent. Because the
agricultural population increased by only a third, an agricultural
surplus was assured. Although this 5 percent annual increase in net
output during the subphase of import substitution is considerably
smaller than that of the industrial sector, it still is an impressive
figure by any international standard of comparison. It is even more
impressive when two additional factors are considered: the natural
fertility of the soil is low; the land frontier on the mountainous
island already had essentially been reached. The growth in agri-
cultural output could only be called dramatic. Between 1952 and 1964
total agricultural production, including forestry, fishing, and live-
stock, rose by 78 percent, with the production of crops alone rising
by 59.7 percent (see table 2.5). These production increases were
primarily the result of increased yields in traditional crops, but
they were also the result of the introduction of new crops. While
the yields of such traditional crops as rice increased 50 percent,
the yields of relatively new specialty crops, such as cotton and
fruits, increased more than 100 percent."
Fixed capital in agriculture expanded by about 34 percent between
1952 and 1964 (see table 2.5). Much of this expansion was in irriga-
tion and flood control facilities, which deteriorated during the war
and were rebuilt and expanded during the 1950s. Farm buildings
and other structures were added to and improved. The water buffalo
was gradually replaced by small tillers and other small mechanical
devices. Working capital increased even more dramatically than
fixed capital, growing by 140 percent between 1952 and 1964 (see
table 2.5). The continuous introduction of new seed varieties, re-
sponsive to intensive fertilizer applications, and the gradual reduc-
tion in fertilizer prices and government restrictions enabled Tai-
wan's total fertilizer use to grow by 91 percent over the same period.'2
As livestock production grew by nearly 120 percent, more and more
commercial feeds were imported. Further increases in working
capital included widespread use of pesticides, a major postwar
innovation which helped to reduce high losses caused by disease
and insects.
11. Economic Planning Council, Taiwan Statistical Data Book, 1975 (Taipei,
1975), pp. 48, 53-55.
12. Taiwan Statistical Data Book, 1975, p. 58.
AGRICULTURAL DEVELOPMENT DURING THE 1950s 49
Technology change, introduced mainly by such government-
supported research agencies as the JCRR, clearly was a significant factor
in generating the increased agricultural output.'3 In 1960 Taiwan
had 79 agricultural research workers for every 100,000 persons
active in agriculture, compared with 60 in Japan, 4.7 in Thailand,
1.6 in the Philippines, and 1.2 in India."4 The research agencies
successfully introduced new strains of rice and sugar and such new
crops as asparagus and mushrooms, as well as pesticides, insecti-
cides, and new agricultural tools and machinery. In the Hayami-
Ruttan terminology, most of the technology change was of the
chemical variety, not the mechanical.'"
Taiwan's impressive success in agriculture can thus be attributed
to many factors. Although the purpose of this volume is not to
analyze these factors in detail, their relation to the distribution of
income nevertheless is relevant to the argument here. Given the
physical and organizational improvement of the environmental
infrastructure and the pervasive package of land reform, farmers
had the incentives and the tools to improve their situation during
the subphase of primary import substitution, which usually dis-
criminates against agriculture. Moreover the technology change
seemed to be of a type that generally used labor and saved land
and capital. Although the number of persons employed in agricul-
ture increased by 12 percent between 1952 and 1964, the number
of man-days increased by 17 percent (see table 2.5). Consequently
the number of working days per worker steadily increased. In 1965
the average worker had 156 days of farm employment, compared
with 90 days in 1946 and 134 days in 1952.'6 As a result, the number
of working days per hectare of land increased from approximately
170 in 1948-50 to about 260 in 1963-65.17
13. Ho estimated that 44.9 percent of the growth of agricultural output during
1951-60 can be attributed to changes in total factor productivity, 10.3 percent
to increases in crop area, and 34.7 percent to increases in working capital. Ho,
Economic Development in Taiwan, pp. 147-85.
14. Ho, Economic Development in Taiwan, p. 178.
15. Yujiro Hayami and Vernon W. Ruttan, Agricultural Development in
International Perspective (Baltimore: Johns Hopkins University Press, 1971),
passim.
16. You-tsao Wang, "Agricultural Development," in Economic Development
of Taiwan, ed. Kowie Chang, p. 176.
17. W. H. Lai, "Trend of Agricultural Employment in Post-war Taiwan"
(paper read at Conference on Manpower in Taiwan, 1972, Taipei; processed).
50 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Larger labor inputs to the cultivation of traditional crops and the
diversification into new crops resulted in more intensive cultivation
of land. Between 1952 and 1964 the multiple-cropping index in-
creased from 171.9 to 188; the diversification index increased from
3.54 to 5.75 (see table 2.5). The shift toward such labor-intensive
crops as vegetables and away from the complete dominance of the
traditional crops of rice and sugar was continuous. As an indication
of the labor intensity of vegetable cultivation, the cultivation of one
hectare of asparagus requires 2,900 times the labor input of the
cultivation of one hectare of rice.
Despite the substantial increase in the absorption of labor in
agriculture between 1952 and 1964, rural underemployment con-
tinued during the 1950s and has been estimated at about 40 percent.18
The smaller, poorer farms were especially unable to generate suffi-
cient income or to keep the entire family fully employed. This pat-
tern led to a small amount of net physical migration out of the
agricultural sector, estimated at less than one percent annually
during the 1950s. Mostly, however, farmers increasingly sought
off-farm employment in the rapidly growing rural industrial sector.
Consequently underemployment did not develop into as serious a
problem as in most other LDCS.19 The pattern of agricultural growth
and the participation in that growth by rich and poor farmers were
the basic ingredients of the dramatic improvement in the distribu-
tion of income in Taiwan during the 1950s.
The Distribution of Assets and Industrial Growth
What can be said about the distribution of assets outside agri-
culture during this period? Obviously much less, but broad patterns
nevertheless are indicative. The 56.6 percent share of the public
sector in industrial output in 1952 characterized the Taiwanese
economy in the early 1950s (table 2.6). This pattern was mainly
18. The estimation difficulties here are well known, and the authors do not
place much confidence in these numbers;
19. Ho, Economic Development in Taiwan, p. 158. Ho derived his figures from
S. F. Liu, "Disguised Unemployment in Taiwan Agriculture" (Ph.D. disserta-
tion, University of Illinois, 1966) and Paul K. C. Liu, "Economic Development
and Population in Taiwan since 1895: An Overview," in Essays on the Population
of Taiwan (Taipei: Academia Sinica, Institute of Economics, 1973).
THE DISTRIBUTION OF ASSETS AND INDUSTRIAL GROWTH 51
Table 2.6. Distribution of Industrial Production, by Public
and Private Otwnership, 1952-64
(percent)
Electricity,
gas,
Total Manufacturing Mining and water
Year Public Private Public Private Public Private Public
1952 56.6 43.4 56.2 43.8 28.3 71.7 100.0
1953 55.9 44.1 55.9 44.1 24.4 75.6 100.0
1954 52.7 47.3 49.7 50.3 32.5 67.5 100.0
1955 51.1 48.9 48.7 51.3 28.5 71.5 100.0
1956 51.0 49.0 48.3 51.7 26.5 73.5 100.0
1957 51.3 48.7 48.7 51.3 26.3 73.7 100.0
1958 50.0 50.0 47.2 52.8 24.2 75.8 100.0
1959 48.7 51.3 45.2 54.8 22.6 77.4 100.0
1960 47.9 52.1 43.8 56.2 24.2 75.8 100.0
1961 48.2 51.8 45.3 54.7 18.8 81.2 99.9
1962 46.2 53.8 42.3 57.7 19.6 80.4 98.6
1963 44.8 55.2 40.6 59.4 19.1 80.4 99.7
1964 43.7 56.3 38.9 61.1 20.5 79.5 98.8
Source: Economic Planning Council, Taiwan Statistical Data Book, 1975, p. 75.
a consequence of the Chinese takeover of Japanese assets at the
end of the Second World War. In addition, before the evacuation
from the mainland, the Nationalist government dismantled and
shipped industrial equipment, such as textile spindles, and in some
cases entire enterprises to Taiwan. Firms under public ownership
were initially plagued with typical problems: inefficiency, over-
staffing, rigid pay structures, and bureaucratic interference. Mean-
while small firms and simple equipment characterized the private
sector. As late as 1961, 31 percent of all manufacturing establish-
ments employed fewer than ten workers.20 All industry was ham-
pered by the shortage of foreign exchange.2'
This situation undoubtedly was favorable to the equity of the
20. Ho, Economic Development in Taiwan, p. 597.
21. Council on U.S. Aid, Industry of Free China, vol. 1, no. 4 (1954).
52 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
initial distribution of industrial assets. Because private ownership
of capital was not on a large scale, entrepreneurs generally were
not in a position to gain monopolistic control of industries or to
accumulate great wealth from property income. In the private
sector the small size and labor intensity of firms was favorable to
the share of workers. Profits of the larger, more capital-intensive
firms went to government, not to private entrepreneurs.
During the early 1950s government began transfering the four
public enterprises under its control to private ownership: Taiwan
Cement Corporation, Taiwan Pulp and Paper Corporation, Taiwan
Industrial and Mining Corporation, and Taiwan Agriculture and
Forestry Development Corporation. This transfer was not easily
accomplished. Government had difficulty finding buyers because of
the lack of accumulated private wealth and entrepreneurial exper-
tise and because of the poor track records of these enterprises. In
1953 a large portion of government assets was nevertheless trans-
ferred as partial payment to landlords under the land-to-the-tiller
program. As a result of this transfer and such other factors as the
increasingly rapid growth of private industry, the government-
owned share of total industrial production fell to 43.7 percent in
1964 (see table 2.6). Industries remaining in the public sector in-
cluded utilities, railroads, shipbuilding, and iron and steel. Thus,
despite the substantial drop in government ownership, the public
control of assets continued to be important, particularly in the
most capital-intensive industries, in which growth is least favorable
to the distribution of income.
Taiwan's industrial growth during 1952-64 was impressive: NDP
grew at the average annual rate of 7 percent; the industrial sector at
the average annual rate of 11 percent. By 1964 the real NDP of the
industrial sector was more than 250 percent higher than in 1952;
that sector's share in total NDP rose from 18 percent to 28 percent.
Most of this growth was the result of the emergence of the manu-
facturing subsector: its share in NDP grew from only 11 percent in
1952 to more than 20 percent in 1964.22 The concentration on food
processing and textiles, as well as on other industries that typically
predominate during the subphase of primary import substitution,
continued to be heavy.
22. Taiwan Statistical Data Book, 1975, p. 28.
THE DISTRIBUTION OF ASSETS AND INDUSTRIAL GROWTH 53
The reorientation of industrial output between the late 1950s
and early 1960s is also reflected in the changing composition of
imports and exports. Although total imports in constant prices
more than doubled during the 1952-64 period, the share of imports
of consumption goods in total imports rapidly declined from 20
percent to 6 percent. In constant prices those imports in 1964 were
slightly below their 1952 level. Imports of raw materials for agri-
culture and industry kept pace with the growth of total imports.
But imports of capital goods, such as machinery and electrical and
transport equipment, almost quadrupled. This growth reflected
the twin efforts to shift industrial activity away from the
narrow domestic market toward wider international markets and
to provide the physical infrastructure needed for that shift. Even
though government policy was to reduce imports in the 1950s, total
imports doubled during 1952-64. This expansion reflected the need
to fuel import substitution during the 1950s, as is evidenced by
the growth of imports of capital goods by about 20 percent a year
before 1960.23 Imports of raw materials, which were growing steadily
at 8 percent a year during the 1950s, started to grow at 11 percent a
year in response to the new opportunities of the export-substitution
era. This policy of accelerated imports of raw materials, combined
with the use of unskilled labor, was at the heart of the drive that
followed for expanding labor-intensive industrial exports.
As would be expected in any developing economy, imports con-
tinued to outstrip exports throughout the 1952-64 period in Taiwan.
Exports in constant prices nevertheless quadrupled. Moreover, as
noted earlier, industrial exports increased by a phenomenal 2,800
percent and dramatically changed the composition of exports. The
share in total exports of agricultural and related exports declined
from 92 percent to less than 60 percent in only twelve years; the
share of industrial exports went up fivefold, from 8 percent to 40
percent. Industrial production and export growth during this period
was concentrated in the textile, leather, and wood and paper in-
dustries. Most of the increase occurred between 1960 and 1964: that
is, after changes in policies and factor endowment ushered in the
subphase of export substitution.
23. See Carlos F. Diaz-Alejandro, "On the Import Intensity of Import Sub-
stitution," Kyklos, vol. 18, no. 3 (1965).
54 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Effects of Growth on Equity
Information about the family distribution of income (FID) in
Taiwan is meager before 1964, when the Directorate-General of
Budget, Accounting, and Statistics (DGBAS) began to conduct regular
surveys. One investigator conducted sample surveys of overall in-
come distribution for 1953 and 1959.24 The JCRR conducted sample
surveys of the income of farm families in 1952, 1957, 1962, and
1967.25 The Economic Planning Council conducted surveys of a
very limited sample of urban wage and salary workers in 1955 and
1959.26
Rural FID
Farm families have three types of income: the income from agri-
cultural activities [Ya], a merged return to property (mainly land)
and labor, is preponderant; it is augmented by wage income [Y-]
and property income [YT] from rural industry and services. Table
2.7 gives the Gini coefficients of total income and factor income
and the distributive shares of factor income components for 1952,
1957, 1962, and 1967.21 In the following analysis, average farm-size
groupings are used as a proxy for average income-size groupings,
which are not available. Because the data are grouped into only a
few intervals based on farm size, the resulting Gini coefficients
undoubtedly are lower than if there had been more intervals. Never-
24. Chang, "Estimate of Personal Income Distribution in 1953;" National
Taiwan University, "Report on Pilot Study."
25. JCRR, "Taiwan Farm Income Survey of 1967-with a Brief Comparison
with 1952, 1957, and 1962," Economic Digest Series, no. 20 (Taipei: JCRR, 1970).
26. Economic Planning Council, "Family Income and Expenditure Survey of
Wages and Salaries by Income Class, Taiwan Province" (Taipei, n.d.; proc-
essed in Chinese); idem, "Family Income and Expenditure Survey of City Con-
sumers, Taiwan Province" (Taipei, n.d.; processed in Chinese).
27. The following notation will be adhered to throughout this volume in
tables and text: the Gini coefficient of income from all sources is G,; the Gini
coefficients for (merged) agricultural income, rural industry wage income, and
rural industry property income respectively are G., G,, and G,; the distributive
shares, or weights, of these kinds of income accruing to farm families respectively
are O., O, and XT.
EFFECTS OF GROWTH ON EQUITY 55
Table 2.7. Gini Decomposition Analysis Based on Farm Family
Income Stratified by Size of Farm, 1952-67
Percentage changea
1952- 1957- 1962-
Item 1952 1957 1962 1967 57 62 67
Gini coefficients
Wage income [G.] n.a. 0.0631 0.0862 0.0823 n.a. 37 -6
Property income
[Gr] n.a. 0.1662 0.0604 0.1116 n.a. -64 31
Agricultural
income [G.] n.a. 0.3499 0.3641 0.3225 n.a. 4 -12
Total income [G,] 0.2860 0.2335 0.2126 0.1790 -18 -9 -14
Distributive shares
Wage income [,0] 0.0580 0.2339 0.1969 0.2522 303 -16 24
Property income
[01] 0.1630 0.1342 0.2124 0.1639 -18 58 -36
Agricultural
income [0.] 0.7790 0.6320 0.5908 0.5840 -19 -7 -1
n.a. Not available.
Sources: 1952 from Y. C. Tsui and S. C. Hsieh, "Farm Income in Taiwan in
1952," Economic Digest Series, no. 4 (Taipei: JCRR, 1954); 1957, 1962, and 1967
from JCRR, "Taiwan Farm Income Survey of 1967-with a Brief Comparison
with 1952, 1957, and 1962," Economic Digest Series, no. 20 (Taipei: JCRR, 1970).
a. For 1952-67 the change in G, was -37 percent, of which 1952-57 accounted
for -18 percent, 1957-62 for -7 percent, and 1962-67 for -12 percent; the
changes in distributive shares were 335 percent for wage income, 0.6 percent for
property income, and -25 percent for agricultural income.
theless it still is possible to observe significant trends in movements
of the Gini coefficient of total income after 1952 and the Gini coeffi-
cients of factor income after 1957.25
Throughout the 1952-67 period the Gini coefficient of total in-
come [G,] declined by a remarkable 37 percent; it declined by 18
28. To the extent that the ranking of family income differs from, and is poorly
proxied by, the ranking of family farm size, the Gini coefficient in table 2.7 tends
to underestimate the true inequality of income. The authors have no way of
checking the degree of this underestimation. The other issue addressed basically
is the error introduced when families are grouped by income ranges, a problem
fully discussed in chapter twelve.
56 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
percent during 1952-57 alone, the heart of the subphase of import
substitution. As import substitution ran out of steam because of
the limitations of domestic markets, the pace of decline slowed
down; the decline for 1957-62 was only 7 percent. Interestingly
enough, the decline of the Gini coefficient picked up speed again
after the policy reforms of 1960-61 got the new era of export sub-
stitution under way. The decline for 1962-67 was 12 percent. This
figure is similar to the decline of 11 percent for 1964-68 obtained
from superior DGBAS data. Hence, the trend of these results, if not
the magnitude, would seem to be fairly reliable.
The data for factor income components indicate that the distribu-
tion of agricultural income and wage income worsened between
1957 and 1962; that of property income improved. After export
substitution got under way, however, the distribution of property
income worsened; that of agricultural and wage income improved.
What are the reasons for these patterns of the Gini coefficients of
factor income over time?
One reason is the increase in multiple cropping. The multiple-
cropping index of farms smaller than 0.5 chia was about 25 percent
higher than that for farms larger than 2 chia (table 2.8). This in-
verse relation between farm size and multiple cropping indicates
that the poorer families cultivated their land more intensively,
Table 2.8. Multiple Cropping, by Size of Farm, 1952 and 1967
(single cropping = 100)
Index of
multiple cropping
Size of farm
(chia) 1952 1967
Less than 0.5 227 216
0.5-1 214 206
1-1.5 204a 197
1.5-2 204a 193
2-3 184b 190
More than 3 184b 161
Average 198 197
Sources: Same as for table 2.7.
a. The 1952 average for farms of 1-2 chia applies to both categories.
b. The 1952 average for farms larger than 2 chia applies to both categories.
EFFECTS OF GROWTH ON EQUITY 57
either by introducing additional harvests in rice or adding high-
valued, and usually more labor-intensive, secondary crops. The
marked decline of the agricultural Gini [Ga] between 1962 and 1967
coincides with the introduction of mushrooms, asparagus, and
other important secondary crops. This pattern implies that poorer
farmers could take more advantage of this type of product-oriented
technology change in agriculture.
A second reason is that the high distributive share of agricultural
income significantly declined, from 78 percent in 1952 to 58 percent
in 1967; the share of nonagricultural income increased from 22
percent to 42 percent (see table 2.7). The increase in the share of
wage income from 6 percent to about 25 percent is particularly
noteworthy. These figures testify to a rapid reallocation of labor
from agricultural to nonagricultural sources of income for the average
farm family. The speed of this reallocation may be explained in a
variety of ways. First, the phenomenon is closely associated with
the pattern of industrial dispersion, which is an inmportant feature
of industrialization in Taiwan. The rapid increase in the share of
wage income may thus be traced to the rapid growth of rural in-
dustries, which provided employment to members of rural families.
Second, associated with transition growth are certain institutional
changes germane to commercialization and the functional specializa-
tion of tasks traditionally performed by members of farm households
under family farming. For example, the replacement of the son as
farm-to-market transporter by a transport firm, which hires the
same son as a wage earner, reduces agricultural income and in-
creases wage income. Much functional specialization of this type
must have taken place during the transition, especially because of
the spatial dispersion of nonagricultural production activities. But
to adduce more about this important problem would require a
different set of data and a more refined analytical design.
A third reason for the movements in the Gini coefficients of factor
income is the greater importance of off-farm wage income to poorer
families than to wealthier families, at least when farm size is used
as a proxy for income class (tables 2.9, 2.10, and 2.11). As the size
of the farm increases, the share of nonagricultural income decreases.
This pattern reflects the greater ability of poorer farmers to take
advantage of nonagricultural income opportunities. For example,
farm families holding less than 0.5 chia in 1957 earned a remarkable
61.9 percent of their income from nonagricultural activities; wage
income accounted for 41.4 percent of their total income. In contrast,
68 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.9. Average Income of Farm Families, by Size
of Farm, 1952-67
(1952 N.T. dollars)
Average income
0-0.5 0.5-1 1-2 2-4 Average
Year and type of income chia chia chia chia size farm
1952
Total income 3,765 5,097 8,010 14,653 7,361
Wage income n.a. n.a. n.a. n.a. 427
Property income n.a. n.a. n.a. n.a. 1,200
Agricultural income n.a. n.a. n.a. n.a. 5,734
1957
Total income 5,015 6,873 9,481 16,606 8,613
Wage income 2,278 1,940 1,695 2,146 2,011
Property income 825 1,140 1,021 2,030 1,160
Agricultural income 1,912 3,793 6,765 12,430 5,443
1962
Total income 5,655 7,937 11,144 17,629 9,682
Wage income 2,355 1,890 1,565 1,775 1,906
Property income 1,835 1,883 2,229 2,462 2,056
Agricultural income 1,465 4,163 7,351 13,392 5,720
1967
Total income 9,920 10,754 15,302 24,962 13,727
Wage income 4,247 3,369 2,928 3,061 3,475
Property income 2,262 1,643 2,426 3,218 2,262
Agricultural income 3,411 5,742 9,946 18,684 7,990
n.a. Not avai:able.
Note: At the time of writing, the new Taiwan dollar was equal to about
US$0.025.
Sources: Same as for table 2.7.
the shares of nonagricultural income in total income were 44.8
percent for families holding 0.5 to 1 chia, 28.7 percent for families
holding 1 to 2 chia, and 25.2 percent for families holding more than
2 chia. For these families the shares of wages in total income respec-
tively were 28.2 percent, 17.9 percent, and 12.9 percent. Thus off-
farm income, particularly wage income, clearly was an important
EFFECTS OF GROWTH ON EQUITY 59
Table 2.10. Distribution of Factor Shares, by Size of Farm, 1952-67
Factor share
0-0.5 0.5-1 1-2 2-4 Average
Year and type of income chia chia chia chia size farm
1952
Wage income n.a. n.a. n.a. n.a. 0.0580
Property income n.a. n.a. n.a. n.a. 0.1630
Net agricultural
income n.a. n.a. n.a. n.a. 0.7789
1957
Wage income 0.4142 0.2823 0.1788 0.1292 0.2338
Property income 0.2045 0.1658 0.1077 0.1223 0.1342
Net agricultural
income 0.3813 0.5519 0.7135 0.7485 0.6320
1962
Wage income 0.4164 0.2381 0.1404 0.1007 0.1969
Property income 0.3245 0.2373 0.2000 0.1397 0.2123
Net agricultural
income 0.2591 0.5246 0.6596 0.7597 0.5908
1967
Wage income 0.4281 0.3133 0.1913 0.1226 0.2522
Property income 0.2280 0.1528 0.1586 0.1289 0.1638
Net agricultural
income 0.3438 0.5339 0.6501 0.7485 0.5840
Note: For each size category in each year, the sum of the shares of wage,
property, and net agricultural income is 1.0000.
Sources: Same as for table 2.7.
FID equalizer because it constituted a greater share of total income
for the poorer farm families.
Data on the extent of off-farm activity by farm families in 1960
give further support to this notion (table 2.12). Less than 50 per-
cent of farm households engaged in full-time farming in 1960. What
is more relevant, the percentage engaged in full-time farming gen-
erally increased with farm size. Among farm families with less than
0.5 hectares, only 30 percent engaged in full-time farming, and 35
60 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.11. Distribution of Farm Households, Income,
and Factor Shares, by Size of Farm, 1952-67
0-0.5 0.5-1 1-2 2-4
Item chia chia chia chia
1952
Total income 0.1535 0.1869 0.2367 0.4229
Households 0.3000 0.2700 0.2176 0.2124
1957
Total income 0.1752 0.2134 0.2936 0.3177
Wage income 0.3410 0.2581 0.2249 0.1759
Property income 0.2140 0.2629 0.2348 0.2884
Agricultural income 0.1057 0.1864 0.3316 0.3763
Households 0.3010 0.2675 0.2668 0.1648
1962
Total income 0.1596 0.2358 0.3352 0.2693
Wage income 0.3377 0.2853 0.2392 0.1378
Property income 0.2438 0.2634 0.3158 0.1770
Agricultural income 0.0700 0.2094 0.3743 0.3463
Households 0.2732 0.2876 0.2912 0.1479
1967
Total income 0.2193 0.2269 0.2943 0.2595
Wage income 0.3710 0.2808 0.2224 0.1257
Property income 0.3036 0.2104 0.2830 0.2030
Agricultural income 0.1296 0.2081 0.3286 0.3337
Households 0.3037 0.2896 0.2640 0.1427
Note: For each row the sum of the entries is 1.0000.
Sources: Same as for table 2.7.
percent had some kind of side income. In contrast, among farm
families with more than 5 hectares, 61 percent were full-time farm-
ers, and fewer than 10 percent had side incomes.29
29. The greater capacity of the richest farmers-that is, those with the largest
holdings-to engage in nonagricultural rural activities as investors might ex-
plain why they again had somewhat higher nonagricultural participation rates;
the greater necessity of the poorest farmers-that is, those with the smallest
holdings-to take advantage of opportunities by offering their labor services
probably explains their high participation.
EFFECTS OF GROWTH ON EQIUITY 61
Table 2.12. Off-farm Activity of Farm Families,
by Size of Farm, 1960
(percent)
Farm
Farming Farming Sideline workers
Size of farm as only as main as main with
(hectares) activity activity activity sidelines
Less than 0.5 30.1 26.7 43.2 34.8
0.5-1 55.6 35.4 9.0 17.9
1-2 65.2 31.7 3.1 11.9
2-3 67.3 30.8 1.9 9.3
3-5 66.5 31.5 2.0 8.5
More than 5 61.4 35.9 2.7 8.6
Total 49.3 30.9 19.8 20.0
Source: Ho, Economic Development in Taiwan, p. 157.
A 1963 study by the JCRR examined the character of such off-farm
employment (table 2.13). This study found that 61 percent of men
who found employment off their own farns were seasonal workers;
of these, nearly 80 percent worked in farming, presumably at har-
vest times. This study also found that 23.5 percent of men who
found employment off their farms were commuters who lived on
farms but held regular off-farm jobs. Of these commuters, 41 per-
cent held jobs in factories or mining; most of the rest worked in
small enterprises, in communication and transport, or as public
officials and teachers. The remaining 15.5 percent of men finding
off-farm work were long-term employees, living away from the
farm but retaining a close budgetary connection with their farm
homes. Long-term workers held roughly the same kinds of job as
commuters, but more worked as clerks and in factories, and fewer
worked in mining. Of women finding off-farm work, a greater per-
centage worked as commuters and long-term employees; fewer were
seasonal workers. Employment patterns were roughly the same
for women as for men, but a somewhat higher percentage of women
worked in factories and handicrafts. The study also found that
off-farm employment varied considerably from region to region,
depending upon the proximity of industrial areas and the avail-
ability of factory work, other nonfarm employment, and jobs in
the service trades. Industry grew not only in the big cities, but in
62 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.13. Composition of Off-farm Employment
of "Moved-out" Workers, by Type of Work, 1963
(percent)
Seasonal Long-term
Commutersa workersb employees'
Type of work Male Female Male Female Male Female
Farming 1.6 2.1 79.6 80.1 2.5 2.0
Mining 14.4 10.5 3.9 3.5 2.1 1.5
Factory labor 27.1 31.9 3.1 4.2 30.5 29.1
Small enterprise 9.0 6.8 - - 6.6 5.2
Clerks 1.1 2.1 - - 12.8 11.9
Public officials and
teachers 27.5 24.1 - - 21.1 18.0
Communication and
transport 7.6 6.0 - - 7.9 5.8
Handicrafts 1.6 7.0 0.9 1.3 5.0 5.5
Carpenters and
plasterers 4.4 3.3 3.4 2.8 4.1 2.9
Other 5.7 6.2 9.1 8.1 7.4 18.1
All workers surveyed 23.5 35.0 61.0 41.1 15.5 23.9
- Not applicable.
Source: Y. C. Tsui and T. L. Lin, "A Study on Rural Labor Mobility in
Relation to Industrialization and Urbanization in Taiwan," Economic Digest
Series, no. 16 (Taipei: iCRR, 1964), pp. 12-16.
a. Commuters are persons regularly traveling back and forth from their farm
home and receiving a monthly salary.
b. Seasonal workers are persons temporarily working for others during their
leisure time and receiving daily wages.
c. Long-term employees are persons who leave their farm home and work
rather permanently in cities or other places. They nevertheless have close connec-
tions with their farm home-for example, by remitting earnings. For convenience,
students living away from home, military servicemen, and dependents of long-term
employees are included in this category.
previously rural areas as well. At times, rural roadbuilding and
other construction projects were important sources of off-farm
employment in many areas.3R
Table 2.14 shows the distribution of the growth of establishments
30. JcRR, Rural Progress in Taiwan (Taipei: JcRR, 1955), pp. 83-85.
EFFECTS OF GROWTH ON EQUITY 63
Table 2.14. Establishments in Taiwan,
by Location, 1951 and 1961
Growth in Percentage
number of distribution
Number of establish- of
establish- ments, establishments
ments, 1951-61b
Locationa 1951 (percent) 1951 1961
Cities 2,959 419.8 24.2 21.5
Semiurban cities 1,235 395.2 10.1 8.5
Semiurban prefectures 2,876 490.1 23.6 24.4
Rural prefectures 2,024 562.2 21.5 25.6
Mixed urban, semiurban,
and rural prefectures 2,517 458.0 20.6 20.0
All Taiwan 12,211 472.3 100.0 100.0
Note: See table 3.9 in chapter three for figures to 1971.
Source: Industrial and Commercial Census of Taiwan (IcCT), General Report,
1971 Industrial and Commercial Census of Taiwan and Fukien Area, 7 (?) vols.
(Taipei: ICCT, 1972), vol. 1, table 6.
a. Based on DGBAS definitions in 1964.
b. Based on number in operation at the end of the year.
in urban, semiurban, and rural areas, based on 1964 DGBAS defini-
tions. Although some semiurban areas may have been rural in 1951,
this table nevertheless gives an idea of the spatial distribution and
growth of industrial establishments. It reveals that the distribution
of establishments in Taiwan was fairly well dispersed in the early
1950s and that the growth of establishments was fairly uniform
into the 1960s. Throughout the 1951-71 period the distribution of
establishments did not become concentrated in any one area, espe-
cially in such large urban centers as Taipei City and Kaohsiung
City, where heavy concentrations might have been expected. This
spatially dispersed growth pattern enabled farm families almost
anywhere in Taiwan to move easily into rural industries that were
intensive in labor.
What are the conclusions to be drawn? As a result of rapidly
increasing agricultural productivity, Taiwan was able to feed itself
and to finance a policy of import substitution on its way to rapid
industrialization and successful export substitution. There were
64 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.15. Gini Coefficients and Factor Shares Based on Income
of Urban Wage and Salary Workers, 1955 and 1959
Item 1955 1959
Gini coefficients
Total income [Gy] 0.3964 0.3960
Wage income [G.] 0.4210 0.4176
Other income [G,] 0.3162 0.2958
Distributive shares
Wage income f+,] 0.7637 0.8196
Other income [f,] 0.2363 0.1804
Sources: 1955 from Economic Planning Council, "Family Income and Ex-
penditure Survey of Wages and Salaries by Income Class, Taiwan Province"
(Taipei, n.d.; processed in Chinese); 1959 from idem, "Family Income and
Expenditure Survey of City Consumers, Taiwan Province" (Taipei, n.d.; pro-
cessed in Chinese).
three main reasons for this success: the early initiation of land
reform, government's subsequent support of agriculture, and the
dispersed pattern of nonagricultural growth. The distribution of
the income of farm families thus improved as a combined result of
the initial distribution of assets and the availability of off-farm
employment for poorer rural families, particularly the employment
opportunities that stemmed from the policy reforms instituted
around 1960.
Urban FID
Evidence on the distribution of income for nonfarm or urban
families during 1953-64 is much sketchier than that for rural fam-
ilies. Hence the results necessarily are less conclusive. Only two
studies investigated the distribution of urban wage income alone
during the 1950s, and these give some indication of a slight improve-
ment. The first is a study of wage and salary income for 1955; the
second, a study of city consumers for 1959.3' If it is assumed that
the wage and salary class and the city consumers are roughly com-
parable categories, comparison of the Gini coefficients derived from
31. Economic Planning Council, "Family Income and Expenditure Survey of
Wages and Salaries by Income Class, Taiwan Province;" idem, "Family Income
and Expenditure Survey of City Consumers, Taiwan Province."
EFFECTS OF GROWTH ON EQUITY 65
these two surveys may be attempted (table 2.15). The basic con-
clusion, drawn mainly from the more reliable figures on wage in-
come, must be that the urban FID changed very little. At best it
improved only slightly, but it certainly contributed much less than
rural FID to the overall increase in equity.
Overall FID
The pattern of overall FID for 1953, 1959, and 1964 shows a strik-
ing improvement by almost every measure (table 2.16). In 1953
the Gini coefficient was 0.56, which is comparable to patterns of
income distribution now prevailing in Brazil and Mexico. By 1964
the Gini coefficient dropped to 0.33, a level comparable to that of
the best performers anywhere.32 This substantial decline in overall
32. The quality of the data, particularly for the 1950s, is suspect. Calculation
of total personal income in 1953, by aggregating the product of average family
income and the number of households in each income group, gives a figure 20
percent lower than that of the national accounts data. A similar calculation
found that the 1953 data underestimated the total family income given in the
national accounts data by 16.7 percent, but that the 1959 data overestimated
total family income by 15.3 percent. The 1964 DGBAS data were found to under-
estimate total family income by only about 5 percent.
Although more than half of Taiwan's population in 1953 was in agriculture,
84 percent of the 1953 sample group came from the more urbanized and indus-
trialized areas; 58 percent of that group lived in Taiwan's four largest cities. If
rural income was better distributed than urban income, as was seen earlier, any
overweighting of urban income may have resulted in a low estimate of total
personal income and a high estimate of the Gini coefficient. In turn, although
DGBAS data for 1964 did not include an appropriate number of families with
income exceeding NT$200,000, the downward bias in the Gini probably is too
small to be of much importance. Nevertheless the survey results for the 1950s
must be accepted with caution.
With respect to the underestimation of FID inequality-the 1964 Gini coeffi-
cient based on decile groups is 0.328-households with income exceeding
NT$200,000 accounted for only 0.1 percent of the population and 1.15 percent
of total income. Even if the income share of these households is increased by 1
percentage point, which almost doubles their income share, and if the 1 percent
loss is equally assigned to the first nine decile groups, the Gini coefficient increases
by only 3.1 percent to 0.3307. The increase really is not that large. To give an
idea of the effect of the underestimation of the Gini coefficient, again for the
1964 data, suppose the income share of the top decile group to be increased by
2, 3, and 4 percentage points. Then the Gini coefficients respectively rise by
6.2 percent, 9.3 percent, and 12.4 percent to 0.3406, 0.3505, and 0.3604. Thus
the smaller the population, income share, underestimation of the wealthiest
households, or any combination of these elements, the smaller the downward
bias of the Gini coefficient.
66 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.16. Measures of the Equity of the Family Distribution
of Income, 1953, 1959, and 1964
Item 1958a 1959b 1964C
Distribution of income by percentile
of households (percent)
0-20 3.0 5.7 7.7
21-40 8.3 9.7 12.6
41-60 9.1 13.9 16.6
61-80 18.2 19.7 22.1
81-95 28.8 26.3 24.8
96-100 32.6 24.7 16.2
Mean income per household
(N.T. dollars in 1972 prices) 22,681 31,814 32,452
Per capita GNP in market prices
(N.T. dollars in 1972 prices) 6,994 8,629 10,875
Ratio of income share of top 10
percent to that of bottom 10
percent 30.40 13.72 8.63
Gini coefficient 0.5580 0.4400 0.3280
Sources: 1953 from Kowie Chang, "An Estimate of Taiwan Personal Income
Distribution in 1953-Pareto's Formula Discussed and Applied," Journal of
Social Science, vol. 7 (August 1956), p. 260; 1959 from National Taiwan University,
College of Law, "Report on Pilot Study of Personal Income and Consumption in
Taiwan" (prepared under the sponsorship of a working group of National Income
Statistics, DGBAS; processed in Chinese), table A, p. 23; 1964 from DGBAS, Report
on the Survey of Family Income Expenditure, 1964 (Taipei: DGBAS, 1966); Shirley
W. Y. Kuo, "Income Distribution by Size in Taiwan Area-Changes and Causes,"
in Income Distribution, Employment, and Economic Development in Southeast and
East Asia, 2 vols. (Tokyo: Japan Economic Research Center, 1975), vol. 1,
pp. 80-146.
a. Data are based on a sample of 301 families, or a sample fraction of 2/1,000.
b. Data are based on a sample of 812 families, or a sample fraction of 4/1,000.
c. Data are based on a sample size of 3,000 families, or a sample fraction of
14.6/1,000.
FID during the 1950s can be traced primarily to the rapidly improv-
ing rural FID, as noted earlier, and secondarily to the distribution
of nonagricultural income, which probably did not worsen and
may even have slightly improved.
EFFECTS OF GROWTH ON EQUITY 67
As will be more fully and rigorously explained in chapter three,
the pattern of industrial growth can affect the family distribution
of income through changes in the functional distribution of income.
For example, if the wage share goes up because of the adoption of
a labor-intensive growth path, the distribution of income will im-
prove, assuming that wage income is better distributed than prop-
erty income, which it generally is. If the wage share declines be-
cause of technological changes that save labor and deepen capital,
the distribution of family income will worsen. Between 1951 and
1954, the early period of import substitution, the share of wage
income in total income sharply increased from 40.7 percent to 46.2
percent (table 2.17). In ensuing years that share was fairly stable,
at least until the onset of policies of export substitution again in-
creased the wage share in the 1960s, especially after commercializa-
tion. Given the distortion of relative prices usually accompanying
import substitution, Taiwan's achievement of a stable wage share
is significant. The chief reasons for this performance are that factor
prices were more distorted before 1954 than subsequently and that
import substitution policies were relatively mild.
If a stable or improving wage share is one precondition for the
improved distribution of nonagricultural income, the adoption of a
labor-intensive growth path is another. Table 2.18 shows the dis-
tribution and growth of the branches of manufacturing in which
most nonagricultural growth took place. The data indicate that
growth in Taiwan during the 1950s was not focused on the highly
capital-intensive industries, as is typical in many LDCS. In fact, the
most labor-intensive branches of industry grew at rates well above
average. The share in total industrial value added of the seven
industries most intensive in labor rose from 10.9 percent in 1954 to
17.6 percent in 1961. The large textile and apparel industry, which
still was more labor-intensive than the average for all industry,
grew at a slower rate; the tobacco industry, the least labor-intensive,
became smaller. In addition, manufacturing in Taiwan was much
more labor intensive than in the typical LDC, such as West Pakistan.
The labor-intensive bias of manufacturing, the good distribution
of industrial assets, the pattern of growth and spatial dispersion of
the nmore labor-intensive industries, the relatively mild price dis-
tortions-all these factors served to improve the overall distribution
of nonagricultural income, or at least prevent its worsening. This
performance, together with the rapidly improving rural FID, paved
the way for the substantial decline observed in overall FID during
68 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.17. Distribution of National Income,
by Factor Share, 1951-72
National TVage Property Agricultural
income incomea incomeb income
Year (hundreds of thousands of N. T. dollars)
1951 10,527 4,287 2,636 2,980
1952 14,653 6,250 3,470 4,208
1953 19,542 7,911 4,789 6,096
1954 20,761 9,600 5,240 5,171
1955 24,684 11,309 5,816 6,374
1956 28,079 13,188 6,147 6,961
1957 32,409 14,903 7,490 7,957
1958 35,921 16,614 8,353 8,585
1959 41,592 18,781 10,248 9,684
1960 50,828 23,107 11,083 12,969
1961 57,012 26,089 13,178 14,061
1962 61,524 29,182 14,756 14,114
1963 70,603 32,918 18,028 14,688
1964 84,570 39,085 19,803 18,555
1965 91,559 44,036 20,809 19,385
1966 101,967 49,642 24,069 20,373
1967 118,046 58,873 29,647 20,241
1968 136,074 69,770 32,817 21,231
1969 152,795 79,564 37,119 20,484
1970 179,195 93,534 45,763 22,269
1971 204,816 112,115 54,592 21,421
1972 241,320 132,416 61,323 23,688
Note: Although nonagricultural income is functionally classified into wage and
property income, agricultural income is not. This explains why the shares here
and later in this volume may add up to something slightly less than one and
reflects the unimputed mixed income of urban family unincorporated enterprises
and professionals. The consistent decline of the share of agricultural income
throughout these years reflects a familiar type of structural change in the transition
and will be more formally analyzed in chapter three. The reversal from the trend
during 1954 and 1955 is a short, noncyclical phenomenon related to the slack in the
economy immediately after the Korean War.
Sources: DGBAs, National Income of the Republic of China, 1969 and 1974.
a. Wages, salaries, and income of professions.
b. Property income and income of other incorporated enterprises.
EFFECTS OF GROWTH ON EQUITY 69
Distributive shares Relative
of national income share of
wage and
Wage Property Agricultural property
income income income income
[0o] 11[4r] [1a] [a/r] Year
0.4072 0.2504 0.2841 1.627 1951
0.4265 0.2368 0.2872 1.740 1952
0.4048 0.2451 0.2153 1.652 1953
0.4624 0.2524 0.2491 1.832 1954
0.4582 0.2356 0.2582 1.944 1955
0.4697 0.2189 0.2479 2.146 1956
0.4598 0.2311 0.2455 1.990 1957
0.4625 0.2325 0.2390 1.989 1958
0.4516 0.2464 0.2320 2.072 1959
0.4546 0.2180 0.2552 2.085 1960
0.4576 0.2311 0.2466 1.980 1961
0.4743 0.2398 0.2294 1.978 1962
0.4662 0.2553 0.2080 1.826 1963
0.4622 0.2342 0.2194 1.974 1964
0.4810 0.2273 0.2117 2.116 1965
0.4868 0.2360 0.1998 2.063 1966
0.4987 0.2511 0.1715 1.986 1967
0.5127 0.2411 0.1560 2.127 1968
0.5207 0.2429 0.1341 2.144 1969
0.5249 0.2568 0.1250 2.044 1970
0.5421 0.2640 0.1036 2.053 1971
0.5487 0.2541 0.0982 2.159 1972
the 1950s. It is not possible to say more than this. The meager
quantity and quality of data for the 1950s, especially for factor
income, preclude formal decomposition analysis of the type under-
taken in subsequent chapters. Instead the estimates should be
viewed as orders of magnitude that might explain the marked ten-
dency for the value of the Gini coefficient to decline between 1953
and 1964. But even if the magnitude of FID levels and changes must
70 ECONOMIC GROWTH AND INCOME DISTRIBUTION, 1953-64
Table 2.18. Gross Domestic Product, Employment, Share of Wages
in Value Added, and Labor Intensity, by Industry, Various Years
Percentage Percentage
distribution Real distribution Employ-
of GDP in GDP in of ment in
manufacturing 1961 employment 1961
(1954 = (1954=
Industry& 1954 1961 100) 1954 1961 100)
Furniture 0.85 1.14 249.3 2.01 2.63 187.9
Metal products 1.36 3.06 416.9 4.64 4.53 140.8
Transport
equipment 1.70 2.84 311.4 5.92 6.29 153.0
Electrical machinery 1.36 2.26 307.6 1.67 2.93 252.2
Printing 3.22 4.41 255.2 3.39 2.94 124.6
Machinery 1.36 2.72 371.1 4.21 3.71 126.6
Rubber 0.91 1.19 244.0 1.74 1.51 124.9
Leather 0.30 0.29 177.0 0.47 0.33 100.0
Wood 3.91 4.88 231.8 5.75 5.91 147.8
Nonmetallic mineral
products 5.88 8.10 256.2 9.65 8.82 131.5
Textiles and apparel 24.26 14.86 114.0 21.92 20.91 137.2
Food 26.84 26.51 183.8 20.66 19.86 138.2
Basic metals 1.94 4.14 396.7 2.06 2.45 171.0
Chemicals 10.98 9.27 158.5 5.74 6.97 174.9
Beverages 0.39 0.58 273.0 1.25 1.99 228.7
Paper 2.59 3.53 264.4 2.11 3.04 206.6
Petroleum 3.73 6.16 307.3 1.10 1.24 162.5
Tobacco 6.00 2.69 83.5 1.58 1.21 110.1
Total manufacturinge 100.00 100.00 186.5 100.00 100.00 143.2
n.a. Not available.
Sources: GDP figures from DGBAS, National Income of the Republic of China, 1969; employ-
ment and labor intensity figures from ICCT, 1961 Industrial and Commercial Census; wage
figures from Mo-huan Hsing, Taiwan and the Philippines-Industrialization and Trade
Policies (London: Oxford University Press for the OECD Development Centre, 1971).
a. Ranked by labor intensity in 1954.
b. Number of employees per hundred thousand N.T. dollars.
c. Includes a miscellaneous category equal to 2 percent of total manufacturing.
be taken with a grain of salt, the evidence that a substantial im-
provement occurred during the 1950s is conclusive. This improve-
ment occurred against the background of an unusually good initial
EFFECTS OF GROWTH ON EQUITY 71
Share of wages in value added
Taiwan West Labor
Pakistan, intensity
1952 1957-60 1965-68 1967-68 in 1954b Industrya
n.a. n.a. n.a. n.a. 165.95 Furniture
81.7 63.4 60.7 31.1 122.10 Metal products
Transport
n.a. n.a. n.a. n.a. 84.66 equipment
58.3 70.7 49.0 29.3 79.18 Electrical machinery
n.a. n.a. n.a. n.a. 77.82 Printing
n.a. n.a. n.a. n.a. 59.96 Machinery
n.a. n.a. n.a. n.a. 57.64 Rubber
n.a. n.a. n.a. n.a. 55.96 Leather
71.1 63.7 80.9 43.6 55.39 Wood
Nonmetallic mineral
61.2 60.6 56.0 19.9 49.00 products
63.1 53.8 51.3 34.6 44.53 Textiles and apparel
81.1 43.5 58.4 19.1 28.97 Food
n.a. n.a. n.a. n.a. 22.90 Basic metals
55.4 49.6 42.6 19.0 19.76 Chemicals
n.a. n.a. n.a. n.a. 18.35 Beverages
70.3 58.1 60.0 52.4 13.48 Paper
n.a. n.a. n.a. n.a. 9.44 Petroleum
n.a. n.a. n.a. n.a. 7.57 Tobacco
n.a. n.a. n.a. n.a. 35.91 Totalmanufacturinge
distribution of assets, the relatively mild regime of import substitu-
tion, the efficient use of abundant labor, and the early attention to
the rural sector-all of which must have contributed to equity.
Furthermore the general liberalization of the economy under the
reforms of the early 1960s could only serve to reinforce these trends.
More precise analysis linking growth and income distribution never-
theless had to await the superior data that began to become avail-
able in 1964.
CHAPTER 3
Growth and the Family Distribution
of Income by Factor Components
THE DETAILED HOUSEHOLD SURVEY DATA available after 1964 make
it possible to move beyond the descriptive treatment of the 1950s
and early 1960s to a more analytical assessment of the relations
between growth and the family distribution of income (FID) for the
1964-72 period. As mentioned earlier, the total income pattern of n
families [Y = (Y1, Y2, ... , Y,)] has a finite number [r] of factor
income components [Wi = (Wi, W2, ... , W') (i = 1, 2, ..., r)].
Total income [Y] is the vector sum of such factor income compo-
nents [Wi] as wage, property, and transfer income. When the
labor force is heterogeneous-differentiated by age, sex, skill, and
level of education-the wage component is in turn the additive
sum of a number of homogeneous wage-income components. If
some index of the inequality of total income is adopted-say, the
Gini coefficient [G,]-it is possible, in addition, to adopt factor
Gini coefficients EGJ] that describe the inequality of distribution
of factor income. That index of inequality of total income [GJ] can
be decomposed into indexes of the inequality of various factor
income components [Gj] and traced to tbem.
These factor income components can be of several types, depending
on the way their inequality relates to and influences the inequality of
total income. One type of income, what we label as type one income,
is distributed less equally than total income; its share increases as the
total income of families increases. Another type of factor income,
type two income, is distributed more equally than total income; its
share decreases as the total income of families increases. A third type
72
GROWTH AND FID BY FACTOR COMPONENTS 73
of income, type three income, decreases absolutely in magnitude as
the total income of families increases; this is unlike type one and
type two incomes, which increase absolutely as the total income of
families increases. Property income typically is a type one income;
wage income a type two income; and transfer income a type three
income. Because transfer income is insignificant in Taiwan, the
empirical analysis of this chapter focuses only on the first two types
of income. It should be emphasized that decomposition of income
inequality by source or type of income considerably differs from
decomposition by type of income recipient, which is far more common.
The purpose here is to introduce a basic decomposition equation
that links the inequality of total income [Ga] to the inequality of
factor incomes [Gi] and to their shares in total income [44]. In
essence that equation states that the inequality of total family income
is the weighted sum of the inequalities of the factor incomes, uwith one
proviso-that negative signs are attached to the type three incomes.
The reason is that type three income contributes not to inequality,
but to equality. Because type three income does not enter into the
analysis of this chapter, the basic decomposition equation is of the
following form: G, = rkGi + 02G2 + . . . + kr,Gr. That equation is then
applied to the substantive problem of this chapter: analyzing the
relations between growth and FID.1
Two recognizable phenomena accompany the successful develop-
1. For a systematic derivation of the decomposition equations used in this
chapter, see chapter ten of part two. A self-contained derivation of the same
set of equations is in the appendix to John C. H. Fei, Gustav Ranis, and Shirley
Kuo, "Growth and the Family Distribution of Income," Quarterly Journal of
Economics, vol. 92, no. 1 (February 1978), pp. 17-53. Other decomposition
efforts in the literature include the following: N. Bhattacharya and B. Maha-
lanobis, "Regional Disparities in Household Consumption in India," Journal of
the American Statistical Association, vol. 62, no. 317 (March 1967), pp. 143-61;
V. M. Rao, "Two Decompositions of Concentration Ratio," Journal of the Royal
Statistical Society, series A, vol. 132, pt. 3 (1969), pp. 418-25; F. Mehran, "De-
composition of the Gini Index: A Statistical Analysis of Income Inequality,"
(Geneva: International Labour Organisation, n.d.; processed); Mahar Mangahas,
"Income Inequality in the Philippines: A Decomposition Analysis," World Em-
ployment Programme Working Papers, Population and Employment Working
Paper, no. 12 (Geneva: International Labour Organisation, 1975); and Graham
Pyatt, "On the Interpretation and Disaggregation of Gini Coefficients," Eco-
nomic Journal, vol. 86 (June 1976), pp. 243-55. With the exception of Rao,
these articles deal with decomposition by homogeneous groups, not by additive
income components.
74 GROWTH AND FID BY FACTOR COMPONENTS
ment of a dualistic developing economy: labor is gradually reallo-
cated from agricultural to nonagricultural activities; changes in
technology and the accumulation of capital affect the absorption
of labor and the functional distribution of income. Within this
developmental framework the disaggregation of total income L7]
into agricultural and nonagricultural income [Ya and Y,] and the
disaggregation of nonagricultural income into wage and property
income [Y, and Y.] enable analysis of the relations between growth
and FID. Changes in the inequality of total income [G,] over time
can thus be examined in relation to changing patterns of growth.
Specifically the decomposition equation introduced in this chapter
enables attributing the changes in G, over time to three effects: a
reallocation effect, a functional distribution effect, and a factor Gini
effect.
The reallocation effect captures the change in the inequality of
income caused by changes in the share of agricultural income in total
income. A declining share of agricultural income indicates the shift
from agricultural to nonagricultural activities-that is, the extent to
which the center of gravity has shifted in a dualistic economy. How
does this shift affect the distribution of income? It depends, of course,
on whether agricultural income is distributed more equally or less
equally than total income. If agricultural income is a type one income,
less equally distributed than total income, its declining share would
contribute to the equality of total income. If it is a type two income,
its declining share would contribute to the inequality of total income.
The functional distribution effect captures the change in the in-
equality of income caused by changes in the relative share of wage
and property income. Because wage income typically is a type two
income, more equally distributed than total income, it would be
expected that any increase in labor's relative share would contribute
to the equality of total income. Analogously an increase in the share
of the less equally distributed property income would contribute to
the inequality of total income. The factor Gini effect captures the
change in the inequality of total income caused by changes in the
inequality of the various factor income components. In essence
the equality of total income increases when the equality of a type one
or type two factor income component increases. The opposite is true
for a type three component.
The first section of this chapter summarizes the technique for
decomposing total income inequality into factor income inequality.
The second section uses this technique to formulate the problem of
INCOME INEQTJALITY AND ITS FACTOR COMPONENTS 75
the effects of growth on FID. The third section presents historical
data for the 1964-72 period in Taiwan. The fourth and fifth sections
respectively trace the quantitative and qualitative effects of groVth
on FID.
Income Inequality and Its Factor Components
At first glance it may seem intuitively appealing to regard total
income inequality [Gd] as the sum of the weighted factor Ginis
[E0Gj] where the weights [Ei] are the distributive shares of factor
income in total income. Such a decomposition nevertheless is likely
to be misleading. For example, if transfer income [YN] is concen-
trated among poor families, and especially if the welfare budget is
large, the distribution of YN will contribute to the equality of total
income, not to its inequality. In addition, other components of
factor income can differ in other ways in their relation to the overall
distribution of income. The methodological contribution of this
chapter centers on the design of a correct decomposition equation
that is sensitive to different types of factor income components
and that enables tracing changes in GQ over time to changing shares
of factor income components. This equation is rigorously developed
in chapter ten.
Let the pattern of total income of n families [Y] be the sum of r
nonnegative factor income components [We]:
(3.1a) 1' (Y1, Y2, .... , Y-);
(3.1b) Y= W + W2 + .. + Wr;
(3.1c) Wi= (Wi, 4. Win) > 0; (i = 1, 2, ...,r)
(3.1d) s = Wi/Y, where (i = 1, 2, . . .r, )
(3.1e) Y = (Y1 + Y2 + ... + Y.)/In,
(3.1f) W7 = (W1I + W21 + ... + Wf)/n, and
(3.1g) k1 + ±2 + *+ r = 1L
The values of 4i are the distributive shares of the factor income
components in national income.
In the numerical example given in table 3.1, where n = 5 and
r = 3, the three factor income components are wage income [Wj],
property income [7rj], and transfer or welfare income [Nj]. Notice
76 GROWTH AND FID BY FACTOR COMPONENTS
Table 3.1. Numerical Example with Three Factor Income Components
and with Total Income Arranged in a Monotonically
Nondecreasing Order
Wage Property Transfer Total
Item incomel incomes income- income
Income patternb Wj ri N, Yj
Family 1 3 (2) 0 (1) 8 (4) 11 (1)
Family 2 1 (1) 0 (2) 12 (5) 13 (2)
Family 3 17 (5) 2 (3) 0 (3) 19 (3)
Family 4 15 (4) 8 (4) 0 (2) 23 (4)
Family 5 9 (3) 25 (5) 0 (1) 34 (5)
Total factor income 45 35 20 100
Factor share [oil 0.45 0.35 0.20 1.00
Factor or total Gini
[Gi] 0.3912 0.6628 0.6400 0.2239
Estimated income
pattern, *o fr lv Yj
Family 1 5.79 (1) -2.96 (1) 8.18 (5) 11.00 (1)
Family 2 6.50 (2) -0.75 (2) 7.25 (4) 13.00 (2)
Family 3 8.64 (3) 5.89 (3) 4.46 (3) 19.00 (3)
Family 4 10.07 (4) 10.32 (4) 2.61 (2) 23.00 (4)
Family 5 14.00 (5) 22.50 (5) -2.50 (1) 34.00 (5)
Total factor income 45 35 20 100
Factor share [oi] 0.45 0.35 0.20 1.00
Factor or total Gini
[Gi] 0.1777 0.7083 0.5202 0.2239
Source: Constructed by the authors.
a. The ranks of families are indicated in parentheses.
b. From original data.
c. Estimated by linear approximation.
in this table that total family income [Yj] is arranged in a mono-
tonically nondecreasing order, satisfying:
(3.2) 0 t< yn < Y2 < ... < Yc (n i g
and that thpe rank index of each factor incorne component is given.
INCOME INEQUALITY AND ITS FACTOR COMPONENTS 77
A highly positive rank correlation is assumed between total income
and property income; a highly negative rank correlation between
total income and transfer income. This pattern gives rise to an
intuitive notion: although the unequal distribution of property
income contributes to the inequality of total income, the unequal
distribution of transfer income contributes to the equality of total
income. The typological distinction among income components is
emphasized in this section.
Heuristically the total Gini coefficient defined on Y can be esti-
mated in the following manner2:
(3.3a) GV = V- , where
[0.2239 = 0.2800 - 0.0561]
(3.3b) G2@ = OWG. + OXG, - kNGN.
E0.2800 = (0.45) (0.39) + (0.35) (0.66) - (0.20) (0.64)]
The estimator Gini E[] is the weighted average of the factor Gini
coefficients; the distributive shares [Ei] defined in equation (3.1d)
constitute the system of weights. Notice that a negative sign is
assigned to the transfer income term [ENGN]. This assignment
conforms to the idea that certain components of income-those
having a large distributive share (tN in this case) and a distribution
that is more unequal than that of total income (GN in this case)-
contribute to the equality of overall Y and reduce the value of G0.3
In the numerical example the error of estimation [0] is 0.0561, and
the degree of overestimation [O/Gj] is about 20 percent. Notice
that if a negative sign had not been attached to transfer income-
that is, if the following alternative estimator [GV] had been used-
the error of estimation would have been larger:
(3.4a) GV = GV + E, where
E0.2239 = 0.5360 - 0.3121]
2. The numbers in brackets under equations (3.3a) and (3.3b) are based
on the numerical example in table 3.1.
3. The rule about whether a plus or minus sign should be attached to certain
types of factor income is presented below. As can readily be seen from the nu-
merical example, the intuitive idea is that a minus sign should be attached to
the transfer income because it has a negative rank correlation with total income.
The more formal analysis of rank correlations is presented in chapter nine of
part two.
78 GROWTH AND FID BY FACTOR COMPONENTS
(3.4b) G, = O.G. + O.GY + kNGN.
[0.5360 = (0.45) (0.39) + (0.35) (0.66) + (0.20) (0.64)]
For the numerical example the error of estimation associated with
G, is 0.3121, and the degree of overestimation [E/G,] is more than
100 percent in this case.
Return to the general case of equation (3.1) and fit a system of
r linear equations to the original data by the method of least squares:
(3.5a) Wi = bi + atY, where (i = 1, 2, ... ,r)
(3.5b) b + b2 + ..+ b = 0 and
(3.5c) a, + a2 + ...+ ar = 1.
These linear approximations give this chapter its methodological
character.4 Applying them to the numerical example gives:
(3.6a) X = -15.143 + 1.1071 Y;
[property income on Y]
(3.6b) W = 1.857 + 0.3571Y;
[wage income on Y]
(3.6c) N = 13.286 - 0.4643Y.
[transfer income on Y]
The factor income components can then be classified into types
by the signs of the regression coefficients [ai] and the regression
constants [bij.5
For type one income:
(3.7a) ai 2 0, bi < 0; (a, = 1.1071, b,, = 15.143)
for type two income:
(3.7b) ai > 0, bi > 0O (a. = 0.3571, b,= 1.875)
4. It should be emphasized that these regression relations are used for purely
descriptive purposes; they are devoid of the usual behavioristic connotations
associated with regression lines in economics. Notice that the combination of
equation (3.1b) with the ordinary least-squares method directly implies equa-
tions (3.5b) and (3.5c).
5. Because the n pairs (W', Y,), (W2', Y2), . . ., (W,, Y.) are nonnegative,
ai and bi cannot both be negative.
INCOME INEQUALITY AND ITS FACTOR COMPONENTS 79
for type three income:
(3.7c) ai < 0, bi > 0. (aN = -0.4643, bN = 13.286).
As will be shown below, type one income is distributed less equally
than total income and concentrated among rich families; type two
income is distributed more equally than total income. The distin-
guishing characteristic of type three income (typically welfare income)
is that it decreases absolutely as the family is wealthier. This explains
why a minus sign is assigned to the transfer income term [ONGN]
in the decomposition of the estimator Gini [v] in equation (3.3b).
Transfer income is a type three income and may be viewed as an
income distribution equalizer.
A generalization of equation (3.3b) is the basic decomposition
equation used in this chapter:
(3.8a) Gy = Gv- B, where
(3.8b) G, = H, + H2 - H3, where
(3.8c) H1 = 'fi1G1 + ±2G2 + ... + 4tXrGn1
(summation over r1 type one incomes)
(3.8d) H2 = Or,+lG,1+2 + ... + 0r,Gr2, and
(summation over r2 - r1 type two incomes)
(3.8e) H3 = On+1Gn2+2 + . . + O,G.
(summation over r - r2 type three incomes)
The usefulness of equation (3.8b) clearly depends on the small
size of the error term Ee]. To investigate 0, first decompose Y into
r factor income components constructed with the aid of the linear
regression lines of equation (3.5a):
(3.9a) Y= W+ W2 + ... + W. ;
(3.9b) ri=(*W f2 * * *sW); (i = 1, 2, . ,r)
(3.9c) W bi + ajYj; (i =1, 2, ...,r; j = 1, 2, ...,n)
(3.9d) 4i = (W + i ± .+. . + W+ 3/n2.
=(WI' + W' + ...W,) /nY = WVi/Yf
[see equations (3.1e) and (3.1f) ]
The decomposition of Y into estimated patterns of factor income
80 GROWTH AND FID BY FACTOR COMPONENTS
is shown in the bottom part of table 3.1. [Notice that the values of
oi remain unchanged, which verifies equation (3.9d).] Applying
the approximation equation (3.8) to the estimated patterns of
factor income gives:
(3.10a) G, = &,- 0, where
[0.2239 = 0.2239 - 0]
(3.10b) 0 = 0 and
(3.10c) G, = O.tGz + ,G; - ONGN.
[0.2239 = (0.45) (0.178) + (0.35) (0.708) - (0.20) (0.520)]
Thus the error term [0] in equation (3.8a) vanishes when the linear
relation between total income [Y] and each factor income compo-
nent [EW] is perfect: that is, when equation (3.5) is satisfied. The
following theorem can now be stated:
THEoREM 3.1. G, = l71 + H2 - i3, where
(a) 1 = f1G(W') + ... + <1G(WVl)
(b) H2 = 01+1G(I"+') + ... + 012G(W*r), and
(C) ff = -r2+iG(172+1) + ... ± k0G(Wf).
Comparing equation (3.8) and theorem 3.1 shows that the error
term [0] in equation (3.8) can be interpreted as a nonlinearity
error. It tends to be small or negligible when the linear correlations
between total income [Y] and the factor income components [Wi]
are nearly perfect: that is, when the correlation coefficients for type
one income and type two income approach one and those for type
three income approach minus one. In fact the existence of such
high correlations is sufficient for the applicability of the basic de-
composition equation (3.8). The major task remaining in this section
is to show how theorem 3.1 can be derived. We begin with the fol-
lowing theorem, which is rigorously proved in chapter ten:
THEOREM 3.2. For type one income and type two income:
(a) G(*i) = (aiAk0)G, = (aiffY/Wi)G.,
and for type three income:
(b) G(W1) = -(ai/4i)G, = -(al/Wi)G, -.
The theorem states that the Gini coefficients of the estimated pat-
INCOME INEQUALITY AND ITS FACTOR COMPONENTS 81
terns of factor income can be obtained by multiplying the Gini
coefficient of total income by the elasticity of the regression lines of
equation (3.5) at their mean points. The term ai/oi is the elasticity
of the regression lines of equation (3.5) at their mean points [Y,
Wi] as defined in equations (3.1e) and (3.1f). Notice that for type
three income a negative sign is assigned to the right-hand side of
theorem 3.2(b) because the Gini coefficients of estimated factor
income [G(1I)] and of total income [G,] and the shares of esti-
mated factor income in total income [0i] are nonnegative. Theorem
3.2 can be verified by substituting values from the numerical example.
For property income:
(3.11a) 0.708 = (1.107/0.35)0.2239, which implies that
a,G, = 0,G(t) or (1.107) (0.2239) = (0.35) (0.708);
for wage income:
(3.11b) 0.178 = (0.357/0.45)0.2239, which implies that
awG,, = O,G(W) or (0.357) (0.2239) = (0.45) (0.178);
and for transfer income:
(3.11c) 0.520 = (-0.464/0.20)0.2239, which implies that
aNG, = -,G(19) or (-0.464) (0.2239) =
- (0.20) (0.520).
Now use theorem 3.2 to prove theorem 3.1. When the implied equali-
ties of equations (3.11a), (3.11b), and (3.11c) are added, equation
(3.10c) is obtained by using equation (3.5c). Thus theorem 3.1 is
obtained in the general case when all r terms aiG, are added. This
result shows that theorem 3.1 follows from equation (3.11). Theorem
3.2 can now help to illuminate the difference between type one
income and type two income. Making use of the relation, Wi =
bi + aiY, rewrite theorem 3.2(a) as follows:
For type one income:
(3.12a) G(Wi) = b + Gu, which implies that G(Wi) > Gv,
bi < ai;
because ai > 0 and b, < 0;
82 GROWTH AND FID BY FACTOR COMPONENTS
for type two income:
(3.12b) G(Wi) a +y GY , which implies that G(Wi) < Gv
because ai > 0 and bi > 0.
Thus type one income is distributed less equally than total in-
come, and type two income is distributed more equally than total
income, as can be readily verified by equations (4.9a) and (4.9b).
This pattern is borne out by comparison of the factor Gini coeffi-
cients in the numerical example with the overall Gini coefficient of
0.224: the factor Gini of property income, a type one income, is
0.708; that of wage income, a type two income, is 0.178. Further-
more equation (3.5a) shows that the share of income attributable
to the ith factor is:
(3.13) Wi/Y = bi/Y + ai.
Because the regression constants for type one income are less than
zero (bi < 0), the share of factor income increases with total in-
come. Similarly, because the regression constants for type two
income are greater than zero (b1 > 0), the share of factor income
decreases with total income. Property income typically is type one
income: wealthier families have absolutely and relatively more of
such income than poorer families. Wage income typically is type
two income: wealthier families have absolutely more but relatively
less of such income than poorer families. Type one, two, and three
incomes, as summarized in the summation terms [H1, H2, and H3]
in equation (3.8), thus represent decreasing contributions to in-
equality.
When there is no type three income-that is when r equals r2-
equation (3.8) has a special case:
(3.14a) GC, = 'kiGI + ¢2G2 + ... + trGr - 0;
(3.14b) 0 > 0.
As is shown in chapter ten, the nonlinearity term [0] always is
nonnegative-that is, the estimator Gini [0,] always slightly
overestimates the true Gini [G,,]. In the empirical application of
these formulations to Taiwan, only this case is used because of the
virtual absence of type three income. The general case of equation
(3.8) nevertheless is methodologically more interesting than this
special case because it can take into account factor incomes that
GROWTH AND THE DISTRIBTJTION OF INCOME 88
contribute to the equality of FID, as well as those that contribute
to its inequality.
Growth and the Distribution of Income
Students of income distribution of course are interested in the
forces determining the inequality of income [G,] at any given time,
but even more in what may occasion changes in G, over time. The
approximation equation (3.14a) derived in the preceding section
can be used to analyze two types of forces that affect the value of
G, over time, assuming that there is no type three income and that
the nonlinearity error is small. First assume a simple one-sector
economy in which the two factor income components (r = 2) are
capital [K] and labor [L] and the respective distributive shares of
those components are 4,. and O.. This simple version of equation
(3.8) then reduces to:
(3.15a) G 4, = XGX + .G., where
(3.15b) k. + 0k = 1.
Differentiating equation (3.15a) with respect to time t gives:
(3.16a) dG,/dt = D + B, where
(3.16b) D = (Gw - G,)dq5/dt and
[functional distribution effect]
(3.16c) B = ,,(dGW/dt) + 4,,(dG./dt).
[factor Gini effect]
Equation (3.16a) attributes the causation of changes in G, over
time to two distinct types of growth-relevant effects. The functional
distribution effect [D] describes the change in G, caused by changes
in the relative shares of capital and labor. The factor Gini effect
[B] describes the change in Gu caused by the net effect of favorable
or unfavorable changes in the factor Gini coefficients. In this simple
world the change in G, may thus be traced in part to changes in
the functional distribution of income and in part to changes in the
patterns of family ownership of labor, capital, land, and so on.
Examination of equation (3.16b) reveals that when wage income
is distributed more equally than property income (that is, when
G,, < G,.) a change in the functional distribution in favor of labor,
indicated by a rise in the distributive share of wage income in total
84 GROWTH AND FID BY FACTOR COMPONENTS
income [E]J, will always serve to improve FID. In fact this relation
establishes the necessary condition for the notion, usually accepted
uncritically, that any change in favor of labor's share in income
necessarily improves FID.
This analysis of the direction of change in the distributive shares
of factor income components can be integrated with development
theory. In a developing economy such as Taiwan's, two historical
periods can be distinguished in addition to the periods of primary
import substitution and primary export substitution: the period
before commercialization when labor still was in excess supply; the
period after commercialization, or the turning point, when surplus
labor has been fully absorbed into productive employment. For
these two periods the following relations help to link FID directly
to the forces of growth:
RELATrON 3.1. Before the turning point, when the real wage ap-
proaches constancy, ,, increases only when the degree of the labor-using
bias of innovation (in the manner of Hicks) overwhelms the innovation-
intensity effect.6
RELATION 3.2. After the turning point, when the real wage is flexible,
k. increases only when there is capital deepening or when innovations
are biased in a labor-using direction.
The growth equation relevant to analyzing the direction of change
of the distributive share of wage income [X] after the turning point
is:
(3.17) = (1 -w)n,L -1 + BL-
The term 77, denotes the rate of change of any x per unit of time.
The term e is the elasticity of substitution; K/L is the capital-labor
ratio; BL is the degree of Hicksian labor-using bias of innovation.
This equation can be derived from normal analysis of aggregative
production functions.7
6. John R. Hicks, Theory of Wages (New York: St. Martin's Press, 1963),
ch. 5.
7. For a fuller exposition and derivation of both these equations, see chapter
three (especially table 1 and the appendix to that chapter) in John C. H. Fei
and Gustav Ranis, Development of the Labor Surplus Economy: Theory and
Policy (Homewood, Illinois: Richard D. Irwin, 1964). The term e used in this
chapter coincides with the more conventional definition in the literature, but is
the reciprocal of the definition used in the volume just mentioned.
GROWTH AND THE DISTRIBUTION OF INCOME 85
If equation (3.17) is substituted in equation (3.16b), the func-
tional distribution effect becomes:
(3.18a) D = [EO(G- - GC)dkw/dt]/ckw (= 0.(G. -Gg),.)
(3.18b) = *.(G. - Gr)E(1 - w)( -1) flEIL, + BL].
Equation (3.18b) shows that, when wages are upwardly flexible
after the turning point, FID improves under two conditions: when
technology change is biased in a labor-using direction (that is,
when BL is greater than zero); when there is overall capital deepen-
ing (that is, when f,lL is greater than zero). The reason is that the
functional distribution effect definitely is favorable (D < 0) only
under these conditions. These conditions are the necessary condi-
tions for an improvement in labor's share (see equation [3.17]).8
Nevertheless, as long as the supply of labor still is unlimited and
the real wage consequently is nearly constant, equation (3.17)
reduces to the following special form9:
(3.19a) 1,j. = BLE - J(1 - f), which implies that
8. This statement is true for the "normal" case of production complemen-
tarity-that is, when e < 1. For the case of production substitutability-that is,
when e > 1-it is true when there is capital shallowing (i7KlL < 0) instead of
capital deepening.
9. When 71. is zero, the rate of labor absorption is:
rlL = 'I + (BL + J/ELL)
(see Fei and Ranis, Development of the Labor Surplus Economy, ch. 3). Substi-
tuting:
SielL = -(BL + J)/ELL
in equation (3.17) gives:
W.etO - (4'r/eLL) (i (B + J) + B)
which can be reduced to equation (3.18) with the help of e = /1ELr (see page
85 in the work just cited). By comparing equations (3.18) and (3.20) it can be
seen that the behavior of 4,, is caused by different types of forces before and
after the turning point. This difference is traced basically to the fact that em-
ployment before the turning point is causally determined by capital accumula
tion through labor absorption. After the turning point, capital and labor are
symmetrical, and the real wage is endogenously determined.
86 GROWTH AND FID BY FACTOR COMPONENTS
(3.19b) qA, > 0 if and only if BL > J -
with --1 > 0.
Combining equation (3.19a) with equation (3.16b) gives the fol-
lowing form to the functional distribution effect before the turning
point:
(3.20) D (G-G)[BLE - J(1 - e)].
Consequently, as long as labor is unlimited, FID is improved and Gv,
is reduced when equation (3.19) holds: that is, when technology
change in the commercialized sector is sufficiently biased in a labor-
using direction to overcome J, the innovation-intensity effect.'"
Thus, for a labor surplus economy, a high innovation-intensity
effect [J] and a high degree of Hicksian labor-using bias of innova-
tion [BL] always contribute to the elimination of unemployment
and the coming of the turning point. The distribution of income
may nevertheless get worse when the intensity effect [J (1/e - 1)]
overwhelms BL. This result would be reflected in a decline in the
distributive share of wage income [Ew] and a rise in the inequality
of total income [G,]. After the turning point a higher value of BL,
combined with capital deepening, contributes to the improvement of
FID. This result would be reflected in a decline in G,, an increase
in BL, and an increase in flK/L, the rate of capital deepening. Whether
these conditions are met determines whether the Kuznets hypothesis
about the inverse U-shaped time path of Gv, is valid. In sumrnmary:
RELATION 3.3 When d4./dt > 0, the functional distribution effect is
favorable to FID (D < 0) if and only if G.D < G_.
What about the factor Gini effect [B]? A negative B, which
would contribute to growing FID equity, can be caused by a change
in the patterns of asset ownership of capital, labor, or both. The
10. In the normal case of production complementarity, a high innovation
intensity leads to more labor absorption and a lower KIL ratio, decreasing labor's
share. Thus a high BL contributes both to employment objectives and FID objec-
tives; a high J contributes to the first objective, but not the second. In the "less
normal" case of production substitutability, a high J and a high B, would con-
tribute both to the elimination of unemployment and to the improvement of
FID.
GROWTH AND THE DISTRIBUTION OF INCOME 87
pattern of family ownership of capital becomes more equal over
time (that is, dG,,/dt is less than zero) when lower income families
acquire capital assets faster than wealthier families do, as might
occur because of higher saving rates or favorable inheritance laws
or because of land or capital reform. The pattern of family owner-
ship of labor becomes more equal over time (that is, dG,/dt is less
than zero) when lower income families acquire more skilled labor
because of their expenditure on education or because of govern-
ment's provision of education to them. In summary:
RELATION 3.4. The factor Gini effect is favorable to FID (B < 0)
when there is a net improvement in the equity of the distribution of
any factor income (other than a type three income).
One additional source of real-world complexity must be accommo-
dated when the foregoing relations are applied to a dualistic LDC,
such as Taiwan. This complexity can be traced to the dualistic
locational aspect of families and production activities and to the
importance of agricultural income. Urban families primarily receive
income from nonagricultural production, that is, from wage and
property income from urban industry and services. Rural families
usually receive income from both agriculture and nonagriculture,
that is, merged wage and property income from agriculture and
wage and property income from rural industry and services. This
additional complexity in the real world is the motivation for treating
the whole economy in accord with three models: urban households,
rural households, and all households. The decomposition equation
(3.16) can be directly applied to urban households. But because
the models of all households and rural households also have the
additional and important source of agricultural income, the analysis
of these two groups must be modified. It is substantially enriched
in the process.
For nonagricultural production the functional distributive shares
of wage and property income will be explicitly treated as above;
income from agriculture will not, however, be functionally distin-
guished. This treatment is based on two considerations, the first
practical, the second theoretical. First, in the farm-family type of
agricultural activity, property and wage income can be disentangled
only by using highly artificial procedures of imputation. Second,
the essence of development in the dualistic economy is the gradual
reallocation of resources, particularly labor, from agricultural to
nonagricultural activities. A declining distributive share of agri-
88 GROWTH AND FID BY FACTOR COMPONENTS
cultural income in total income [¢a] is a proxy for this reallocation.
Now modify equation (3.15a):
(3.21a) C,, = t.GW + 40aG, where 44 = 44 + ± ; X: ± «a = 1;
(3.21b) GC = 44G. + 4GC,
where 4' = 4/44; 44 = 44/44; 44 + 44 = 1.
The two functional distributive shares in the nonagricultural sector
are 44 and 44; the Gini coefficient of all nonagricultural income is
GC. Differentiating the inequality of total income [CG] with respect
to time t gives:
(3.22a) dGC/dt = R + D + B, where
(3.22b) R = (GC - G)da/dt;
[reallocation effect]
(3.22c) D = (GC - Gr) (doI/dt)4O; and
[functional distribution effect]
(3.22d) B = (dGC/dt)Oa + (dCW/dt)o4 + (dCr/dt)o_
[factor Gini effect]
The functional distribution effect, which reflects the importance
of capital intensity and technology change, can now be summarized
by using the shares of wage and profit income from all nonagri-
cultural activity [E4 and 44]. Equation (3.21b) indicates that these
shares move in the same direction as the distributive share of wage
income [O.] in total income. Thus the entire foregoing discussion
of the one-sector case continues to hold in the more complex case.
The factor Gini effect remains unchanged, but it now includes
agricultural income. What is new is the addition of the reallocation
effect [R], which reflects the continuous shift of the economy's
center of gravity from agriculture to nonagriculture. A decline in
the distributive share of agricultural income in total income is a
proxy for this shift. Notice that when such reallocation takes place
over time, the distributive share of agricultural income in total
income declines over time (d44/dt is less than zero). Thus the im-
pact of the reallocation effect on the equity of distribution of total
income [G,] in equation (3.22b) depends upon the sign of the
term, GC - GC: that is, on whether the inequality of agricultural
GROWTH AND THE DISTRIBUTION OF INCOME 89
income is greater or less than the inequality of nonagricultural
income. When agricultural income is a type two income-that is,
when the inequality of agricultural income [Ga] is less than the
inequality of total income [G,]-the inequality of nonagricultural
income [G.] must be greater than G,. Hence the term, Ga -G,
would be negative. As a result, R would be greater than zero, which
means that the reallocation effect would cause the overall equity of
income distribution to worsen. Conversely, when agricultural in-
come is a type one income-that is, when the inequality of agri-
cultural income [Ga] is greater than the inequality of total income
[G ]-it is more of a disequalizer of FID than nonagricultural income.
Hence, the term, G. - G., would be positive. As a result, R would
be less than zero, which means that the reallocation effect would
help to improve overall FID. In summary:
RELATION 3.5. When d(a/dt < 0, the reallocation effect is favorable
to FID (R < 0) if and only if Ga > G,.
Changes in the inequality of total income [Ga] may thus be traced
to three forces. The first is the continuous reallocation of labor from
agricultural to nonagricultural activities, proxied by the decline of
the share of agricultural income in total income as the economic
center of gravity shifts from agriculture to nonagriculture. The
second is the changing impact of the functional distribution of
income as traced to such factors as capital accumulation, technology
change, and population growth. The third is the impact of changes
in factor income distribution as traced to abrupt changes in asset
structure arising from land reform and inheritance laws and to
gradual changes arising from different patterns of private and public
saving for the formation of physical and human capital. For the
first two forces the link of growth theory to FID is quite direct. For
the third force the relation of traditional economic analysis to FID
is more indirect and complicated.
Decomposition equation (3.22), by capturing the effects of these
three forces, provides a framework for analyzing the impact of
growth on FID in a typical developing economy. It enables us to
make qualitative statements about the direction of the impact of a
selected pattern of growth on the distribution of income. Moreover
it enables us to make quantitative statements about the relative
importance of various effects as they contribute to changes in in-
come inequality over time.
90 GROWTH AND FID BY FACTOR COMPONENTS
Empirical Application to Taiwan
Sample survey data on household income in Taiwan-collected
by the Directorate-General of Budget, Accounting, and Statistics
(DGBAS) for 1964, 1966, 1968, 1970, 1971, and 1972-have been
processed in accord with the analytical framework presented in the
foregoing section.'" The following assumptions were made in trans-
forming the raw data into a simplifying three-model framework.
First, a category of unallocable miscellaneous income was ignored,
as was the agricultural income of urban families. Both were quanti-
tatively small. Second, no account was taken of intersectoral pay-
ments, such as the inclusion in rural wage income of the urban
income of farmers' daughters. Isolating such payments in the data
was impossible. Third, as pointed out before, agricultural income
[Ya] was not functionally disaggregated into wage and property
shares. For farm-family agriculture, such a separation would have
entailed a rather arbitrary imputation procedure.
Table 3.2 summarizes the results for all households, urban house-
holds, and rural households. Figures 3.1 and 3.2 provide a graphic
depiction of these time series. Table 3.3 gives the results of linear
regressions for the three models." Comparison of factor shares
emanating from the DGBAS surveys and the national income ac-
counts shows that differences generally are quite small: around 2.5
percent (table 3.4). Consequently the survey data used here are
fairly reliable as a source of data on income distribution.
The regression coefficients [at] and constants [bi] indicate the
following findings:
FINDING 3.1a. For all three models property income was a type one
income and wage income was a type two income.'3 Hence G,. < G, < G,.
11. DGBAs, Report on the Survey of Family Income and Expenditure, 1964,
1966, 1968, 1970, 1971, and 1972.
12. For reasons already cited, the values of ai do not quite add up to 1; the
values of bj to zero. Regressions are based on grouped data classified into decile
population groups.
13. The exception is property income of rural households in 1968: when using
deciles, it marginally was a type two income; when using more intervals, it was
a type one income.
EMPIRICAL APPLICATION TO TAIWAN 91
Figure G.1. (ini Coefficients of Total and Factol Incomes, by M1odel,
1964-72
All households
Cr,. ... - - -
0.4 -
G, -_
0.2-
0.1 [' ---------- -
0.1~ ~ ~ ~~~~ I I o
Urban households
0.4 J _ _ _ _
0.3
0.2
0.1
_lI I I I
Rural households
0.4 -
0.3
0.2 Gr - - - - - - - - - - - _.
0.1 Before turning point After turning point
1964 1966 1968 1970 1971 1972
-Total income - -Property income --- lWage income ---- Agricultural income
Source: Table 3.2.
92 GROWTH AND FID BY FACTOR COMPONENTS
Table 3.2. Gini Decomposition
by Additive Factor Components, 1964-72
Model and variable Notation 1964 1966 1968
All households
Total Gini Gv 0.3208 0.3226 0.3260
Wage Gini G 0 0.2365 0.2697 0.2932
Property Gini G, 0.4487 0.4104 0.4598
Agricultural Gini Ga 0.3543 0.3410 0.1817
Wage sharea 0. 0.4324 0.4760 0.5066
Property share 0, 0.2401 0.2557 0.2777
Agricultural share 0a 0.2754 0.2118 0.1523
Estimated total Gini G, 0.3218 0.3230 0.3278
Nonlinearity error o= - G 0.0009 0.0004 0.0019
Degree of overestimation D, = O/G, 0.0029 0.0013 0.0058
Urban households
Total Gini Gv 0.3288 0.3236 0.3296
Wage Gini Gw n.a. 0.2797 0.2732
Property Gini G, n.a. 0.4193 0.4246
Wage sharea Xw 0.5729 0.5925 0.5673
Property share X, 0.3225 0.3218 0.3366
Agricultural share ka 0.0374 0.0217 0.0288
Estimated total Gini n.a. 0.3244 0.3304
Nonlinearity error 0 = G,-Gv n.a. 0.0008 0.0009
Degree of overestimation D, = I/G, n.a. 0.0026 0.0026
Rural households
Total Gini G,, 0.3080 0.3200 0.2842
Wage Gini 0w n.a. 0.1933 0.1880
Property Gini Gr n.a. 0.3344 0.2775
Agricultural Gini Ga n.a. 0.3534 0.3372
Wage sharea 0. 0.2134 0.2016 0.3227
Property share 0> 0.1115 0.1000 0.0994
Agricultural share ¢. 0.6468 0.6595 0.5263
Estimated total Gini Gv n.a. 0.3221 0.2862
Nonlinearity error fl = -G,, n.a. 0.0021 0.0020
Degree of overestimation D, = 0/G, n.a. 0.0065 0.0069
n.a. Not available.
Sources: Calculated from DGBAS, Report on the Survey of Family Income and
Expenditure, 1964, 1966, 1968, 1970, 1971, and 1972.
a. The relative shares do not quite add up to 1 because the merged category of
EMPIRICAL APPLICATION TO TAIWAN 93
1970 1971 1972 Notation Model a-ad variable
All households
0.2928 0.2950 0.2897 Total Gini
0.2775 0.2730 0.2604 G. Wage Gini
0.4278 0.4268 0.4235 G, Property Gini
0.0655 0.1109 0.1105 G. Agricultural Gini
0.5454 0.5974 0.5895 w Wage sharea
0.2558 0.2417 0.2577 0r Property share
0.1307 0.1015 0.1027 0. Agricultural share
0.2939 0.2961 0.2907 G Estimated total Gini
0.0011 0.0011 0.0010 f = G ,-Gv Nonlinearity error
0.0036 0.0036 0.0033 D, = 0/Gv Degree of overestimation
Urban households
0.2794 0.2794 0.2813 Gv Total Gini
0.2328 0.2403 0.2349 G,, Wage Gini
0.3689 0.3992 0.3874 G, Property Gini
0.6016 0.6500 0.6335 0. Wage sharea
0.3022 0.2680 0.2975 4, Property share
0.0292 0.0262 0.0235 4. Agricultural share
0.2803 0.2865 0.2832 Gv Estimated total Gini
0.0009 0.0017 0.0019 0 Gv - Gv Nonlinearity error
0.0034 0.0059 0.0068 Dv = O/G, Degree of overestimation
Rural households
0.2772 0.2907 0.2844 Gv Total Gini
0.2042 0.2207 0.2378 Gw Wage Gini
0.3607 0.3370 0.3477 G, Property Gini
0.3138 0.3178 0.2983 0G Agricultural Gini
0.3602 0.3572 0.4226 4. Wage sharea
0.1029 0.1224 0.1072 0, Property share
0.4869 0.4523 0.4230 4a Agricultural share
0.2789 0.2917 0.2847 Gv Estimated total Gini
0.0017 0.0010 0.0003 0 = G0 - Gy Nonlinearity error
0.0063 0.0035 0.0009 Dv = 0/Gv Degree of overestimation
mixed incomes, which constitute less than 10 percent of the total, was neglected.
In addition, the share of agricultural income in the total income of nonfarm
households is uniformly small, which conforms to the assumption about the
income of urban households.
94 GROWTH AND FID BY FACTOR COMPONENTS
Table 3.3. Regression Results for Decile Income Groups, 1964-72
Model and variable Notation 1964 1966 1968
All households
Slope a,,, 0.292 0.375 0.435
a,r 0.364 0.344 0.411
a, 0.296 0.215 0.070
Constant b, 4.191 3.382 2.907
b, -3.694 -2.971 -5.415
b0 -0.608 -0.098 3.358
Correlation coefficient r, 0.979 0.992 0.995
r,, 0.988 0.992 0.993
r, 0.992 0.991 0.902
Urban households
Slope a, n.a. 0.474 0.452
a,. n.a. 0.440 0.440
Constant bw n.a. 4.038 5.139
b,. n.a. -4.033 -4.590
Correlation coefficient r,, n.a. 0.987 0.994
n.a. 0.993 0.998
Rural households
Slope a, n.a. 0.123 0.183
a,. n.a. 0.107 0.099
a, n.a. 0.712 0.637
Constant b,, n.a. 2.538 4.469
b,. n.a. -0.224 0.005
b. n.a. -1.688 -3.552
Correlation coefficient rw n.a. 0.974 0.918
r,, n.a. 0.989 0.996
r, n.a. 0.998 0.997
n.a. Not available.
Sources: Same as for table 3.2.
FINDING 3.1b. For rural households agricultural income was a type one
income. Hence Ga > G,,.
FINDING 3.1c. For all households agricultural income was a type one
EMPIRICAL APPLICATION TO TAIWAN 95
1970 1971 1972 Notation Model and variable
All households
0.495 0.524 0.511 a, Slope
0.391 0.369 0.387 a,
0.025 0.035 0.035 aa
2.326 3.829 4.722 b. Constant
-6.333 -6.729 -7.922 b,
4.987 3.508 4.094 bn
0.995 0.992 0.996 r, Correlation coefficient
0.995 0.992 0.996 r,
0.828 0.950 0.951 ra
Urban households
0.474 0.525 0.518 aw Slope
0.422 0.394 0.417 a.
6.605 7.025 7.478 bw Constant
-6.168 -7.108 -7.682 b,
0.988 0.993 0.997 r, Correlation coefficient
0.991 0.992 0.999 r,
Rural households
0.238 0.234 0.321 aw Slope
0.149 0.149 0.146 a,
0.551 0.503 0.448 aa
4.318 5.043 5.021 bw Constant
-1.629 -1.083 -1.894 b,
-2.276 -2.078 -1.250 b,
0.960 0.928 0.973 r, Correlation coefficient
0.958 0.991 0.974 r,
0.998 0.993 0.998 r,
income before 1968 (Ga > Gv) and a type two income after 1968 (Ga
< GU).14
14. This reversal of type is a complicated phenomenon related to the rapid
decline of the relative importance of the merged agricultural income and the
very rapid decline of the Gini coefficient of agricultural income.
96 GROWTH AND FID BY FACTOR COMPONENTS
Figure 3.2. Factor Shares, by Model, 1964-72
All households
0.6 - _
0.5 _
0.4
0.3 -~~
0.2 - _
0.1 B ---------------
L I l I
Urban households
0.6 -
0.5-
0.4-
0.3 +…- - -.-. - -
0.2-
Before turning point After turning point
0.1
Rural households
0.6-
0.5 --- - - - - - - - - -
0.4 --
0.3 -
0.1…---- -- --
1964 1966 1968 1970 1971 1972
- - Property income --- Wage income - Agricultural income
Source: Table 3.2.
EMPIRICAL APPLICATION TO TAIWAN 97
Table 3.4. Comparison of Factor Shares from National Accounts
and Household Surveys, 1952-72
Share of Share of Share of
wage income property income agricultural income
House- House- House-
hold National hold National hold National
Year surveys accounts surveys accounts surveys accounts
1952 n.a. 0.4488 n.a. 0.2491 n.a. 0.3021
1957 n.a. 0.4910 n.a. 0.2468 n.a. 0.2622
1962 n.a. 0.5027 n.a. 0.2542 n.a. 0.2431
1964 0.4561 0.5047 0.2532 0.2557 0.2905 0.2396
1966 0.5045 0.5276 0.2710 0.2558 0.2245 0.2165
1968 0.5409 0.5635 0.2965 0.2650 0.1626 0.1715
1970 0.5860 0.5789 0.2738 0.2832 0.1403 0.1378
1971 0.6350 0.5960 0.2570 0.2902 0.1079 0.1139
1972 0.6205 0.6090 0.2713 0.2820 0.1082 0.1089
n.a. Not available.
Note: Because of differences in definitions, the category of transfers and
miscellaneous income has a different meaning for the two sources. To facilitate
comparability of the factor shares for wage, property, and agricultural income, the
shares in this table are based on a total income that excludes this category.
Sources: Calculated from DGBAS, National Income of the Republic of China,
1967 and 1974; and idem, Report on the Survey of Family Income and Expenditure,
1964, 1966, 1968, 1970, 1971, and 1972.
FINDING 3.1d. For all three models there was no type three income.15
(Notice that this finding follows from findings 3.la, b, and c.)
Thus the special case equation (3.14a) may be used rather than the
general case equation (3.8) for all three models. Notice also that
the error term [O] in table 3.2 always is nonnegative, verifying
expression (3.14b), and that the degree of overestimation [D,]
15. To be precise, a category of so-called transfers, small enough to be ne-
glected, does show up, but it does not decrease absolutely with total family in-
come, as is required for a type three income. This is not to claim that a negligible
volume of type three income could not be detected at some more disaggregated
level.
98 GROWTH AND FID BY FACTOR COMPONENTS
never exceeds 1 percent in any of the three models.'" Consequently
the nonlinearity error can safely be ignored in the empirical analysis.
As would be expected, the Gini coefficient of property income is
larger than the Gini coefficient of total income; the Gini coefficient
of wage income is smaller than the Gini coefficient of total income.
Furthermore finding 3.1a implies that, as households get wealthier,
the share of wage income decreases and the share of property income
increases [see equation (3.13)]. This pattern leads to the generally
consistent straddling of the total Gini curve by the two factor Gini
curves in figure 3.1.17
Findings 3.1b and 3.1c imply that the curve for the agricultural
Gini income lies above the curve for the total Gini for rural house-
holds; the opposite generally is true for all households (figure 3.1).
Thus the share of agricultural income in the total income of rural
households increased with total family income: that is, it was a
type one income. Consequently income from nonagricultural rural
sources, such as rural industry and services, served as an important
FID equalizer because it constituted a larger share of the income of
poor rural families than of rich rural families [see equation (3.13)].
The same relation was true for all households before 1968. But for
all households after 1968 the share of agricultural income began to
decrease with total family income: that is, it became a type two
income. Wealthier families began to derive a larger proportion of
their income from property income than from agricultural income
(see finding 3.1a). Consequently agricultural income became an
income equalizer: any decline in its distributive share would have
resulted in a worsening of FID. The comparative magnitudes of the
factor Gini coefficients of findings 3.1a, 3.1b, and 3.1c then lead to
the following conclusions:
FINDING 3.2a. The functional distribution effect: In all models a
change in the functional distribution of income in favor of labor-that
is, d¢,,/dt > 0 equivalent to d,0'/dt > 0-improved the equity of
overall FID (see relation 3.3 and finding 3.1 a).
16. This supports the linearity specification.
17. The reader might recall that this relation was established for the expected,
not the actual, pattern of factor income. But in view of the almost uniformly
high correlation coefficients in table 3.3, a high degree of linearity is indicated,
and the relation G. < G,, < G,. is seen to be valid for the actual factor Ginis
as well.
IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 99
FINDING 3.2b. The reallocation effect: A decrease in the share of
agricultural income-that is, doa/dt < 0-contributed to the greater
equity of FID for:
* rural households before and after 1968 (see relation 3.5 and finding
3.1b)
* all households before 1968 (see relation 3.5 and finding 3.lc).
It contributed to the greater inequity of FID for all households after 1968
(see relation 3.5 and finding 3.lc).
These findings considerably simplify the analytical task in the
next section.
Impact of Growth on FID: Quantitative Aspects
With GNP growing at more than 10 percent a year, the 1960s were
a period of extremely rapid growth in Taiwan. In addition, the
levels of the overall Gini coefficient were unusually low. They held
in the 0.30 range between 1964 and 1968 and substantially declined
thereafter. The substantial decline, particularly in percentage terms,
of the Gini coefficient after the turning point when wages began to
rise markedly thus seems to reinforce our independent finding that
Taiwan reached the end of its labor surplus condition around 1968.18
Such a pattern is consistent with the views of Lewis, Kuznets, and
others. But what is much more interesting and not in keeping with
the conventional wisdom, the Kuznets effect was almost completely
avoided during the period of rapid growth before 1968.
The analytical tools developed earlier in this chapter are used
here to assess the reasons for the quantitative behavior of the Gini
coefficients for rural, urban, and all households. In other words,
the general decomposition equation (3.22) is used to trace changes
in the Gini coefficients over time to three "causative" factors: the
reallocation effect, the functional distribution effect, and the factor
Gini effect. Tables 3.5, 3.6, and 3.7 in this section summarize the
results. Because of the natural break apparent in the direction of
changes in the Gini coefficients around 1968, that year divides the
1964-72 period into two subphases: before the turning point (BTP),
18. John C. H. Fei and Gustav Ranis, "A Model of Growth and Employment
in the Open Dualistic Economy: The Cases of Korea and Taiwan," Journal of
Development Studies, vol. 11, no. 2 (January 1975), pp. 32-63.
100 GROWTH AND FID BY FACTOR COMPONENTS
Figure 3.3. Gini Coefficient of Total [ncome, by Mlodel, 1964-72
- All households
0.36 - - -Urban households
--------Rural households
0.34 -
0.32 G, - -
0.30 -
0.28 -
0.26-
Before turning point After turning point
0.24 _
l l I I I_ _ i_ _ I _ I
1964 1966 1968 1970 1971 1972
Source: Table 3.2.
and after the turning point (ATP). The magnitudes and percentages
of change in the Gini coefficients are shown for each of the three
models, as are the estimated total changes in G, based on decomposi-
tion equations (3.16) and (3.22). These results make it possible to
deduce the relative quantitative contributions of the reallocation
effect [R], the functional distribution effect [D], and the factor
Gini effect [B]. For a graphic summary see figures 3.3 and 3.4, and
3.5 and 3.6 in the next section.
FINDING 3.3a For all households there was a moderate deterioration
of FID before 1968 (+0.0052 or +1.6 percent for 1964-68) and a
significant improvement after 1968 (-0.0363 or -11.1 percent for
1968-72) .'9
19. In this section, all percentage changes of Ginis refer to actual changes; all
percentage changes of effects refer to their percentage contributions toward the
total estimated changes in G,,.
IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 101
Figure 3.4. Gini Coefficients of Wlage and Property Incomle, by Model,
1964-72
Before turning poiiit After turning point
~~All households
0.50 _ ---Urban households
------ Rural household-s
0.40 -
0.35 -
0.30 -
0.25 -
0.20 ------ - - --- -- -------I
1964 1966 1968 1970 1971 1972
Source: Table 3.2.
FINDING 3.3b For rural households there was a significant improve-
ment of FID before 1968 (-0.0358 or -11.2 percent for 1966-68) and
virtually no deterioration after 1968 (+0.0002 or +0.1 percent for
1968-72).
FINDING 3.3c. For urban households there was virtually no deteriora-
tion in FID before 1968 (+0.0060 or +1.9 percent for 1966-68) and a
significant improvement after 1968 (-0.0480 or -14.6 percent for
1968-72).
The absolute magnitude of a "significant" change is about ten times
larger than a "moderate change," as is apparent in figure 3.1. For a
"significant" change the quantitatively dominant causative factors
are to be determined. For a "moderate" change it is to be deter-
mined whether that change is the result of the stability of all causa-
102 GROWTH AND FID BY FACTOR COMPONENTS
Table 3.5. Changes in the Family Distribution of Income
and Their Decomposition, All-households Model, 1964-72
Percentage
Total changea changes
Nota-
Variable tion 1964-68 1968-72 1964-68 1968-72
Total Gini 0, 0.0052 -0.0363 1.6 -11.1
Reallocation effect R - - - -
Functional distribution
effect D
Factor Gini effect B
Agricultural Gini Ga -0.1726 -0.0712 -48.7 -39.2
Nonagricultural Gini G. 0.0389 -0.0422 12.8 -12.0
Property Gini GO 0.0111 -0.0363 2.5 -7.9
Wage Gini 0,D 0.0567 -0.0328 24.0 -11.2
- Not applicable. See note a.
Source: Calculated from table 3.2.
a. Actual changes in G,,, G(,, G,, G,, and G.. The changes do not equal the sum of the
three effects for three reasons: decomposition equations (3.16) and (3.22) do not include the
quantitatively small, unallocable category of miscellaneous income (for urban households a
small amount of agricultural inconme is also neglected); there is a small nonlinearity error
there is a need to make discrete approximations to continuous changes.
tive factors or the result of the offsetting effects of positive and
negative causative factors. Concentrating first on the all-households
model in table 3.5, the major quantitative finding is:
FINDING 3.4. For all households the (net) factor Gini effect was the
dominant causative factor of change in total G, both before and after
1968.
* Before 1968 the highly favorable agricultural Gini effect (-0.0475
or -183 percent) overwhelmed the highly unfavorable nonagri-
cultural Gini effect (+0.0272 or +105 percent) to cause the
slight worsening of G, (+ 0.0052 or +1.6 percent for 1964-68).
* After 1968 the still favorable agricultural Gini effect (-0.0108 or
-30 percent) reinforced the newly favorable nonagricultural Gini
effect (-0.0267 or -75 percent) to cause the significant improve-
ment of G, (- 0.0363 or - 11.1 percent for 1968-72).
IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 103
Percentage
distribution of
Total estimated changeb estimated changeb
Nota-
1964-68 1968-72 1964-68 1968-72 tion Variable
-0.0259c -0.03560 lOOC lOOC G2, Total Gini
-0.0052 0.0084 -20 24 R Reallocation effect
Functional distribution
-0.0004 -0.0065 -2 -18 D effect
-0.0203d -0.0375d -78d -105d B Factor Gini effect
-0.0475 -0.0108 - 183 -30 Ga Agricultural Gini
0.0272e -O0.0267e 105e - 75e Gz Nonagricultural Gini
0.0027 -0.0101 10 -28 G, Property Gini
0.0245 -0.0166 95 -47 G,,, Wage Gini
b. Based on decomposition equations (3.16) and (3.22). Consequently the values generally
differ slightly from those for actual changes and in rare instances may even change sign.
c. Equal to the sum of the three effects.
d. Equal to the sum of changes in the agricultural and nonagricultural Ginis.
e. Equal to the sum of changes in the property and wage Ginis.
Investigation of the possible causes for the pattern of changes in
the overall Gini coefficient leads to the conclusion that the nonagri-
cultural Gini EGz] followed a pronounced inverse U-shaped pattern.
That is, the actual G. rose by 12.8 percent in the four years before
the turning point and declined by 12 percent in the four years after
the turning point. It nevertheless was consistently overwhelmed by
the combination of a highly favorable agricultural Gini effect, a
moderately favorable reallocation effect, and a slightly favorable
functional distribution effect. The result was that the Gini coeffi-
cient of total income [G5] increased by a mere 1.6 percent before
1968. After the turning point that signaled the end of the labor
surplus condition, the nonagricultural Gini effect became highly
favorable and was reinforced by the still highly favorable agricul-
tural Gini effect and an even more favorable functional distribution
effect. These effects overwhelmingly offset the unfavorable realloca-
tion effect. The reason is that once a lot of labor had been reallocated
104 GROWTH AND FID BY FACTOR COMPONENTS
Table 3.6. Changes in the Family Distribution of Income
and Their Decomposition, Rural-households Model, 1966-72
Total changes Percentage changes
Nota-
Variable tion 1966-68 1968-72 1966-68 1968-72
Total Gini Gy -0.0358c 0.0002 -11.2e 0.1
Reallocation effect R - - -
Functional distribution
effect D
Factor Gini effect B - - - -
Agricultural Gini Oa -0.0162 -0.0389 -4.1 -11.5
Nonagricultural Gini GD -0.0310 0.0509 -12.9 24.3
Property Gini G,r -0.0569 0.0702 -17.0 25.3
Wage Gini G,. -0.0053 0.0498 -2.7 26.5
- Not applicable. See note a to table 3.5.
Note: It should be recalled that the data do not permit a detailed factor decomposition
for rural households for 1964. Consequently the decomposition results are for 1966 onward.
Source: Calculated from table 3.2.
a. See note a to table 3.5.
by 1968, agricultural income switched from being a type one income
for all households to a type two income. Consequently the weight
of agriculture was reduced, and it no longer served as an FID equalizer.
The result was that FID showed a highly significant improvement:
the overall G, declined by 11.1 percent in the short span of four
years. The combination of these effects led to the very mild Kuznets
effect observed for the overall time pattern of G,.
All this evidence implies that the Kuznets effect is a complex
phenomenon that needs to be disaggregated. In its extreme form, it
really is relevant only to the nonagricultural sector. In countries
where agricultural activity is important-as it is in Taiwan and in
most LDCs-growth does not necessarily conflict with equity, even
before the turning point has been reached.20
20. This observed, mild, overall Kuznets effect could also be examined in
relation to the partially offsetting time patterns of the Ginis, taken separately,
of urban and rural households (see figure 3.3 below). Before the turning point
IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 105
Percentage
distribution of
Total estimated changeb estimated changeb
Nota-
1966-68 1968-72 1966-68 1968-72 tion Variable
-0.0367d -0.0120d lOod lOOd Gu Total Gini
-0.0151 -0.0133 -41 -111 R Reallocation effect
Functional distribution
-0.0041 -0.0013 -11 -11 D effect
-0.0175e 0.0026e -48e 22e B Factor Gini effect
-0.0107 -0.0205 -29 -171 Ga Agricultural Gini
-0.0068f 0.0231f -19f 193f G. Nonagricultural Gini
-0.0057 0.0070 -16 59 G,. Property Gini
-0.0011 0.0161 -3 134 Gt Wage Gini
b. See note b to table 3.5.
c. Comparable figures for 1964-68 are -0.0238 and -7.7 percent.
d. Equal to the sum of the three effects.
e. Equal to the sum of changes in the agricultural and nonagricultural Ginis.
f. Equal to the sum of changes in the property and wage Ginis.
FINDING 3.5. For rural households the favorable reallocation effect had
a quantitative significance almost equal to or greater than that of the
factor Gini effect.
, Belfore 1968 the favorable reallocation effect (-41 percent) rein-
forced the favorable factor Gini effect (-48 percent) to cause the
significant improvement of GQ (-0.0358 or -11.2 percent for
1966-68).
* After 1968 the highly favorable reallocation effect (-111 percent)
overwhelmed the unfavorable factor Gini effect (+22 percent) to
cause the very modest deterioration of Gr, (+0.0002 or -0.1
percent for 1968-72).
the favorable FID trend for rural households tends to offset the slightly unfavor-
able FID trend for urban households; after the turning point the opposite is true.
This approach relates more to the method of segmentation of total family in-
come by homogeneous groups, as suggested by Theil-a method which is more
difficult to link directly to growth-related phenomena. Henri Theil, Statistical
Decomposition Analysis (Amsterdam: North-Holland, 1972).
106 GROWTH AND FID BY FACTOR COMPONENTS
Table 3.7. Changes in the Family Distribution of Income
and Their Decomposition, Urban-households Model, 1966-72
Total changea Percentage changea
Nota-
Variable tion 1966-68 1968-72 1966-68 1968-72
Total Gini a7, 0.0060c -0.0480 1 .9c -14.6
Reallocation effect R - -
Functional distribution
effect D - - - -
Factor Gini effect B
Agricultural Gini - - -
Nonagricultural Gini G, -0.0007 -0.0460 -0.2 -14.0
Property Gini Gr 0.0053 -0.0372 1.3 -8.8
Wage Gini Gw -0.0065 -0.0383 -2.3 -14.0
- Not applicable. See note a to table 3.5.
Note: It should be recalled that the data do not permit a detailed factor decomposition
for urban households for 1964. Consequently the decomposition results are for 1966 onward.
Source: Calculated from table 3.2.
Thus the reallocation effect is quantitatively most important for
rural households simply because of the greater share of agricultural
income in the total income of those households. The favorable
impact of the reallocation effect (-41 percent) before the turning
point was consistently reinforced by the factor Gini effect (-48
percent) and the functional distribution effect (-11 percent). The
consistently favorable impact of all three effects thus gave rise to
a substantial improvement in rural FID before the turning point:
the inequality of rural income [Gv] declined by 11.2 percent during
1966-68. For the 1968-72 period after the turning point, the non-
agricultural Gini increased by 24.3 percent; the agricultural Gini
declined by 11.5 percent. This pattern reduced the importance of
the factor Gini effect to 22 percent, but by this time it was unfavor-
able to FID. It nevertheless was overwhelmed by the increased im-
portance of the still favorable reallocation effect (-111 percent)
and the still favorable functional distribution effect (-11 percent).
Consequently there was almost no worsening of rural FID. The
inequality of rural income (G,,) increased by only 0.1 percent.
IMPACT OF GROWTH ON FID: QUANTITATIVE ASPECTS 107
Percentage
distribution of
Estimated changeb estimated changeb
Nota-
1966-68 1968-72 1966-68 1968-72 tion Variable
0.0013d -0.0442d 100d 100d G, Total Gini
- - - - R Reallocation effect
Functional distribution
0.0035 -0.0100 269 -23 D effect
-0.0022e -0.0342e - 169e -77e B Factor Gini effect
- - - G, Agricultural Gini
-0.0022 -0.03421 -169f -77f Gz Nonagricultural Gini
0.0017 -0.0125 131 -25 0 G,, Property Gini
-0.0039 -0.0217 -300 -49 GC, Wage Gini
a. See note a to table 3.5.
b. See note b to table 3.5.
c. Comparable figures for 1964-68 are -0.0008 and 0.2 percent.
d. Equal to the sum of the two effects.
e. Equal to the nonagricultural Gini.
f. Equal to the sum of changes in the property and wage Ginis.
FINDING 3.6. For urban households the functional distribution effect
had a quantitative significance greater than or almost equal to that of
the factor Gini effect.
* Before 1968 the highly unfavorable functional distribution effect
(+269 percent) overwhelmed the moderately favorable factor Gini
effect (-169 percent) to cause the m.oderate worsening of Gv
( + 0.0060 or + 1.9 percent for 1966-68).
- After 1968 the moderately favorable functional distribution effect
(-23 percent) reinforced the favorable factor Gin-i effect (-77
percent) to cause the significant improvement of G' (-0.0480 or
-14.6 percent for 1968-72).
Analysis of the pattern of urban FID alone shows that the time pat-
tern of the functional distribution effect reflects the time pattern
of the inequality of urban income [G2]. The functional distribution
effect is important to the pattern of distribution of urban household
income because, as seen in the foregoing discussion, the main forces
108 GROWTH AND FID BY FACTOR COMPONENTS
affecting changes in the share of nonagricultural income in the total
income of urban households are capital deepening and technology
bias and intensity. The highly unfavorable functional distribution
effect before the turning point was softened by the very favorable
factor Gini effect, which moderated any worsening of urban FID.
The net result was that the inequality of urban income [Gu] in-
creased by only 1.9 percent during 1966-68. With the exhaustion
of surplus labor after the turning point, the functional distribution
effect became favorable to urban FID. The newly dominant and
still favorable factor Gini effect (-77 percent) reinforced the newly
favorable functional distribution effect (-23 percent). Consequently
urban FID tremendously improved. The inequality of urban income
[Ou] declined by 14.6 percent. These time trends lead to a time
pattern of urban FID that is slightly inverse U-shaped.
The reader may have noted some diffidence in the interpretation
of the empirical evidence in this section. The reasons are these:
Slight changes in the magnitude of the Gini coefficient do not war-
rant stronger statements in the absence of statistically designed
tests of significance. In the pioneering field of analyzing the dis-
tribution of income, reliable methods for assessing the significance
of variations in data do not yet exist. It must thus be candidly
admitted that quantitative findings rely for some of their strength
on qualitative findings based on heuristic judgments about their
significance in relation to growth.
Impact of Growth on FID: Qualitative Aspects
In this section the findings about the impact of growth on FID
are further analyzed and interpreted in relation to the reallocation
effect, the functional distribution effect, and the factor Gini effect.
First the changes in the total and sectoral Gini coefficients are
described. Then the impact of the reallocation effect, functional
distribution effect, and factor Gini effect on these underlying phe-
nomena are further analyzed on the basis of findings in the pre-
ceding section. The theoretical underpinnings of this analysis are
discussed in chapter eleven.
The pattern of Gini coefficients over time
The following statements can be made about the behavior of
the Gini coefficients for all households, rural households, and urban
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 109
households during the 1964-72 period:
FINDING 3.7a. For all households G, increased slightly between 1964
and 1968, but consistently and markedly declined thereafter.
FINDING 3.7b. For urban households Gu showed the same time pattern
as that for all households, but was slightly more pronounced.
FINDING 3.7c. For rural households G' significantly declined between
1964 and 1968, but remained relatively constant thereafter.
These observations underscore the arrival of the turning point in
the family distribution of income at some time around 1968. We
consider this conclusion to be highly significant in the light of our
previous work on Taiwan: as was indicated in chapter one, the
period around 1968 was independently established as something of a
landmark in Taiwan's development path.21 That year marked the
end of labor surplus and the beginning of labor scarcity. It is interest-
ing to note, for all households and urban households, that the dis-
tribution of income improved once conditions of labor scarcity
arrived and real wages began to rise sharply. Of greater importance,
however, is the observation that FID did not worsen very much for
any of the three models, even during the period of unusually rapid
growth in the early and mid-1960s. As already noted, the Kuznets
effect is a complex phenomenon mainly relevant to the nonagri-
cultural sector. Examination of the comparative magnitudes of the
urban and rural Gini coefficients provides additional insights about
this phenomenon.
The comparative magnitudes of total
and sectoral Gini coefficients
How do the sectoral Gini coefficients for rural and urban house-
holds compare with the total Gini coefficient for all households?
FINDING 3.8a. Before the turning point the urban Gini [G ] was
greater than the overall Gini [G5], which was greater than the rural
Gini [Gv].
21. See Fei and Ranis, "Model of Growth and Employment," and Mo-huan
Hsing, Industrialization and Trade Policies: The Case of Taiwan (London: Ox-
ford University Press for the OECD Development Centre, 1971).
110 GROWTH AND FID BY FACTOR COMPONENTS
FINDING 3.8b. After the turning point the overall Gini [G5] was
greater than the rural Gini [GQ], which generally was greater than the
urban Gini [Gu].
Finding 3.8a implies that industrialization was more rapid in urban
centers. Consequently the extent of urban dualism was greater than
its rural counterpart before the turning point: the concentration of
assets was more substantial; the variations in the scale of production
and heterogeneity of labor were wider. Furthermore, despite the
substantial inequality of the distribution of agricultural income
among rural households, the inequality of rural income [G6] was
less than the inequality of urban income [EG ]. This pattern suggests
that modernization and nonagricultural activity had not yet reached
rural areas in a big way.
After the turning point-that is, by 1971-the inequality of
rural income [EG] became larger than the inequality of urban in-
come [EG6] (see figure 3.3a). Finding 4.17 thus implies that rural
areas caught up with urban areas in their degree of modernization
and their concomitant rise in structural dualism and FID inequality
just when the effect of urban dualism on FID was declining.22
Additional data on the inequality of income [G,] for all house-
holds in 1964 and 1968, broken down by urban, semiurban, and
rural location, can be used to explore further this issue of how and
when modernization occurred (table 3.8) .23 For all households in
both years, the results show that the inequality of urban income
was greater than the inequality of semiurban income which, in
turn, was greater than the inequality of rural income. In addition,
the inequality of nonfarm income in the three locations was greater
than the inequality of farm income. This evidence implies that, in
22. Because the sectoral Ginis in figure 3.3 are smaller than the total Gini,
intrasectoral income inequality is less than intersectoral inequality. In the ter-
minology of the Theil index, the large G% is the result of the strength of inter-
group income variations, not intragroup income variations. See Theil, Statistical
Decomposition Analysis.
23. The rural and urban breakdowns, available only for these two years,
refer to the precise location of households and therefore are not exact equivalents
of the "rural" and "urban" categories, which earlier were used generally and
which include small amounts of semiurban dwellers. The urban households are
almost exclusively nonfarm households, as are the great majority of semiurban
households. Most rural households are farm households. Also see finding 3.2.
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 111
Table 3.8. Gini Coefficients Based on Decile Population Groups
for Urban, Semiurban, and Rural Households, 1964 and 1968
Percent-
age
Share of Share of Gini change
households income coefficient in Gini
Category of coefficient,
household 1964 1968 1964 1968 1964 1968 1964-68
Non!farm and
farm households
All households 1.0000 1.0000 1.0000 1.0000 0.3208 0.3259 1.59
Urban households 0.3000 0.3243 0.3473 0.4348 0.3185 0.3230 1.41
Semiurban
households 0.3435 0.3245 0.3381 0.2852 0.3175 0.3119 1.76
Rural households 0.3565 0.3332 0.3146 0.2800 0.3115 0.2940 -5.62
Nonfarm
households
All households 1.0000 1.0000 1.0000 1.0000 0.3288 0.3296 0.24
Urban households n.a. 0.4819 n.a. 0.5625 n.a. 0.3259 n.a.
Semiurban
households n.a. 0.3119 n.a. 0.2732 n.a. 0.3135 n.a.
Rural households n.a. 0.2063 n.a. 0.1643 n.a. 0.3022 n.a.
Farm households
All households 1.0000 1.0000 1.0000 1.0000 0.3080 0.2842 -7.73
Urban households n.a. n.a. n.a. n.a. n.a. n.a. n.a.
Semiurban
households n.a. 0.3519 n.a. 0.3214 n.a. 0.2817 n.a.
Rural households n.a. 0.6088 n.a. 0.6303 n.a. 0.2863 n.a.
n.a. Not available.
Note: The urban, semiurban, and rural categories of household are based on the
classification used by the DBGAS in its household surveys. The categories are not
to be confused with the categories "urban" and "rural" (which include semiurban
dwellings) used elsewhere in this volume.
Sources: Calculated from DGBAS, Report on the Survey of Family Income and
Expenditure, 1964 and 1968.
moving from urban to semiurban to rural areas, the degree of mod-
ernization and the inequality of FID decrease. Thus modernization
probably occurs first in the largest urban centers and then slowly
permeates semiurban and rural areas.
Because the original urban-households model includes a small
proportion of semiurban and rural households, the results given in
112 GROWTH AND FID BY FACTOR COMPONENTS
table 3.8, disaggregated into urban, semiurban, and rural house-
holds, can also be used to refine the test of the relevance of the
Kuznets hypothesis to the nonagricultural sector. Between 1964
and 1968 the GQ for urban households worsened; that of rural house-
holds improved. Further comparison shows that the change in the
GD for urban households, which earned all their income from non-
agricultural sources, was much larger than that for all nonfarm
households. Thus the observed worsening of the overall GQ was
mostly the result of the Kuznets effect of modern urban nonagri-
cultural activity on FID. Nevertheless, even where FID worsened
because of the Kuznets effect, that worsening was so mild as to be
insignificant. The nonfarm Gini increased by 0.24 percent; the
purely nonagricultural urban Gini increased by 1.41 percent. But
this worsening of urban FID was ameliorated by corresponding
improvements in the semiurban Gini and the rural Gini. Conse-
quently the Kuznets effect on the overall G, was very mild. This
pattern suggests two conclusions. First, the more that nonagricul-
tural activity is urban-centered, the more the Kuznets effect is
significant. Second, where agricultural activity is important and
industrialization is decentralized, as they are in Taiwan, growth
need not conflict with FID, even before the turning point.
Throughout the eight years under observation, the level of the
Gini coefficient is unusually favorable, certainly by LDC standards,
and it appears that things really do not have to get worse before
they can get better. Because this result flies in the face of much
general empirical evidence for postwar LDcs, as well as the theo-
retical arguments of Lewis, Kuznets, and others, it should be of
considerable interest to see what emerges from an attempt to dig a
little deeper into the causation of changes in FID with the help of
tools developed earlier in this chapter. In summary, our evidence
does support the existence of a close relation between growth and
FID, with marked improvements in FID after the turning point, as
we might have suspected, but without any marked deterioration
before, as we might not have suspected. We will now explore these
issues further, with particular attention to the three types of effects
we have identified.24
24. The mildness of the Kuznets effect, coupled with the low level of G, by
international standards, was a major motivation for this study. See for example
Hollis Chenery and others, Redistribution with Growth (London: Oxford Uni-
versity Press, 1974).
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 11I
The reallocation effect
As already noted, the shift of the economic center of gravity
from agricultural to nonagricultural activities, a reallocation effect
proxied by the declining share of agricultural income in total in-
come, clearly is a critical feature of development in the dualistic
economy.
FINDING 3.9. For rural households and all households the distributive
share of agricultural income [4a] consistently declined throughout the
entire period.
The speed of this shift, whether measured by income generated or
labor force, accelerated during the phase of export substitution that
began in about 1961.25 During the 1960s Taiwan's nonagricultural
labor force increased by a remarkable 80 percent, compared with a
rise of 35 percent during the 1950s. The agricultural labor force
increased by only 5 percent during the 1950s and 4 percent during
the 1960s. In the latter decade the agricultural labor force was
partly reallocated to (absorbed by) labor-intensive, export-oriented
industries and services in the cities, but partly also to spatially
dispersed rural industries and services, which rapidly emerged as an
additional source of income for rural families.
By the end of the 1960s the share of agricultural labor in the
labor force had declined from about a half to only a third. In addi-
tion, and of considerable importance, those remaining in the agri-
cultural labor force spent more and more of their time on nonagri-
cultural activities. By 1964, when the DGBAS surveys began, rural
industries and services already were important sources of rural
family income. They subsequently assumed an even larger role.
In 1964 the combined share of rural wage and property income
[or + r] in the total income of rural families [YrI was 33 percent;
in 1972 it was 53 percent.26
25. Such labor reallocation is well proxied by O.. Although the agricultural
labor force has not substantially increased since the beginning of the 1950s, the
increase in the total labor force caused the share of the agricultural labor force
to decline tremendously. See Shirley W. Y. Kuo, "A Study of Factors Contribut-
ing to Labor Absorption in Taiwan, 1954-1971" (paper read at the Conference
on Population and Economic Development in Taiwan, December 29, 1975-
January 2, 1976; processed).
26. This increase is quite remarkable by any international LDC standard. The
relative importance of nonagricultural rural activity can also be seen in its value
114 GROWTH AND FID BY FACTOR COMPONENTS
The steady rise in the nonfarm income of farm families began in
the 1950s. The JCRR surveys of farm-family income conducted be-
tween 1952 and 1967 show a continuous rise in the distributive
share of nonfarm income in total family income from 22 percent
in 1952 to 37 percent in 1957, 41 percent in 1962, and 42 percent
in 1967.27 Moreover the proportion of farm families who considered
themselves to be part-time farmers rose from 52 percent in 1960
to 68 percent in 1965 and 72 percent in 1970.28 By 1968 rural by-
employment had become the dominant form of rural labor realloca-
tion and the dominant source of rural family income. Although the
total agricultural labor force remained relatively constant, the
share of agricultural income in total income continued to decline
rapidly.
Even during the 1950s this steady rise of the share of nonfarm
income had considerable importance as an equalizer of rural FID. The
surveys of farm-family income conducted by the JCRR show that the
poorest families, proxied by those with the least land (less than
0.5 chia), earned 62 percent of their total income from nonfarm
sources in 1957, 74 percent in 1962, and 66 percent in 1967. Corre-
sponding figures for the wealthiest families, proxied by those with
the most land (more than 2 chia), were 25 percent in 1957, 25 per-
cent in 1962, and 26 percent in 1967.29 In addition, cross-sectional
evidence for 1967 indicates that the proportion of families who
considered themselves to be part-time farmers increased as farm
added, which averaged about 20 percent of that of urban industry during the
period. See International Labour Organisation (ILO), "Sharing in Development:
A Programme of Employment, Equity and Growth for the Philippines," in
Special Paper no. 9 on Medium-Scale and Small-Scale Industry (Geneva: ILo,
1974), pp. 539-68.
27. JCRR, "Taiwan Farm Income Survey of 1967-with a Brief Comparison
with 1952, 1957, and 1962," Economic Digest Series, no. 20 (Taipei; JCRR, 1970);
idem, "A Summary Report of Farm Income of Taiwan in 1957 in Comparison
with 1952," Economic Digest Series, no. 13 (Taipei: JCRR, 1959). Because of
differences in definitions, the values of the shares differ somewhat from those
of the DGIBAs household surveys for the nearest years, 1966 and 1967. The trend
nevertheless is unmistakable.
28. Taipei Provincial Government, Committee on the Census of Agriculture,
Report of the Census of Agriculture, 1960, 1965, and 1970.
29. Further disaggregation also shows for poorer families that relatively more
of that nonfarm income is wage income, not property income. See below for
more on the functional distribution of nonagricultural income. JCRR, "Taiwan
Farm Income Survey of 1967."
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 115
size decreased-from 51 percent of families having more than 2 chia
to 84 percent of families having less than 0.5 chia.80
The seeds for this rapid shift in the economic center of gravity
were planted in the 1950s, when locationally dispersed rural indus-
tries began to grow and meet the need and desire for supplementary
farm income. Table 3.9 shows the growth and distribution of the
number of establishments between 1951 and 1971 grouped into
cities, semiurban cities, semiurban prefectures, rural prefectures,
and prefectures that are a mixture of urban, semiurban, and rural
according to definitions adopted by the DGBAS for the household
survey in 1964. This table reveals not only that the initial distribu-
tion of nonagricultural establishments was remarkably dispersed in
Taiwan, but that growth rates also were quite evenly distributed
from 1951 onward.3' This table also shows that rural areas enjoyed
the highest growth rate over the entire period, a remarkable con-
trast with the performance of most LDCS.
Male labor in rural infrastructure and female labor in home-based
handicrafts oriented toward the domestic market exemplified the
early forms of nonfarm income. But with the accelerated growth
and industrialization of the urban sector and with the new export
orientation of government policies in the 1960s, modernization
slowly permeated the rural sector. The previously unorganized
small handicrafts were organized into small factories, which increas-
ingly modernized in response to export demand.32 This industrializa-
tion of the rural sector was accompanied by substantial growth in
agricultural productivity, especially when high-yielding varieties
were superimposed on an already productive and research-oriented
agricultural sector. With agricultural productivity rising, farmers
could spend more time on nonagricultural activities. Taiwan's
experience thus shows that fostering a spatially dispersed industriali-
zation pattern, in addition to being beneficial for growth, is a prac-
tical way to improve FID for rural households.
30. Derived from the JCRR farm-family income in Y. H. Yu, "Economic Analy-
sis of Full-time and Part-time Farms in Taiwan" (Taiwan Provincial Chung
Hsing University, 1969; processed).
31. For example, the three largest cities combined went from 24 percent to
26 percent of total establishments over the twenty-year period. This is in sharp
contrast with the growth of establishments in Thailand or the Philippines.
32. Mo-huan Hsing, Relationship between Agricultural and Industrial De-
velopment in Taiwan during 1950-59 (Taipei: icmu, 1960); Edward S. Kirby,
Rural Progress in Taiwan (Taipei: JCRR, 1955).
116 GROWTH AND FID BY FACTOR COMPONENTS
Table 3.9. Establishments in Taiwan, by Location, 1951-71
Number Growth in number of establishmenteb
of estab- (percent)
lishments
Locationa 1951 1951-61 1961-68 1968-71 1951-71
Cities 2,959 419.8 854.2 1,164.3 2,438.3
Semiurban cities 1,235 395.2 755.7 903.4 2,054.3
Semiurban prefectures 2,876 490.1 877.0 861.1 2,228.2
Rural prefectures 2,024 562.2 1,063.6 915.6 2,541.4
Mixed urban, semiurban,
and rural prefectures 2,517 458.0 804.7 766.8 2,029.5
All Taiwan 12,211 472.3 884.5 931.0 2,287.8
Source: Industrial and Commercial Census of Taiwan (ICCT), General Report, 1971
Industrial and Commercial Census of Taiwan and Fukien Area, 7 (?) vols. (Taipei: IccT,
1972), vol. 1, table 6.
a. Based on DGBAs definitions in 1964.
b. Based on number in operation at the end of the year.
What, then, can be concluded about the reallocation effect?
FINDING 3.10a. For rural households the reallocation of labor from
agricultural activity to rural industries and services improved FID
equity throughout the entire period (see finding 3.2b, finding 3.5, and
relation 3.5).
FINDrNG 3.10b. For all households the reallocation of labor from
agricultural to nonagricultural production improved FID equity before
the turning point and worsened FID equity after the turning point (see
finding 3.2b, finding 3.4, and relation 3.5).
The functional distribution effect
Turn now to the functional distribution effect, which is caused
by variations in the ratio of the wage share in nonagricultural pro-
duction to the property share [EW/OT] and hence is a proxy for labor
intensity. The time paths of that ratio for all three models are given
in figure 3.5.
FINDING 3.1 la. The relative share ratio [EO/0,] was higher for rural
industries than for urban industries.
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 117
Distribution of establishnents
(percent)
1951 1961 1968 1971 Location,
24.2 21.5 22.8 25.8 Cities
10.1 8.5 8.6 9.1 Serniurban cities
23.6 24.4 23.7 22.9 Semiurban prefectures
21.5 25.6 25.7 23.9 Rural prefectures
Mixed urban, semiurban
20.6 20.0 19.2 18.3 and rural prefectures
100.0 100.0 100.0 100.0 All Taiwan
Figure 3.5. Ratio of the Wage Share in Nonagricultural Production to
the Property Share, by Model, 1964-72
Before turning point I After turning point
4.0 - All industries
. --- Urban industries
-------Rural industries ,
3.5-
3a0 - g
2.5-
2.0 - -- ---½' - --&
1964 1966 1968 1970 1971 1972
Source: Calculated from table 3.2.
118 GROWTH AND FID BY FACTOR COMPONENTS
Figure 3.6. Ratio of Average Urban Income to Average Rural Income
for Wage and Property Income, 1964-72
Before turning point After turning point
- - - Property income
------- Wage income / -
4 -
3~~~
- -t/r \ /
0 ---.-. 7~--- - -- -- - -- -- -
2
1964 1966 1968 1970 1971 1972
Source: Calculated from table 3.2.
FINDING 3.11b. In both rural and urban industries X. exceeded 4,r-
that is, or /oJr > +Xue/0 > 1.
Finding 3.11a implies that industrial and service activities, under
normal conditions of substitution-inelastic production functions,
are more capital intensive in urban areas than in rural areas.3" Figures
compiled from the 1961 and 1971 censuses of industry and com-
merce substantiate the thesis that the ratio X,/+,, is a good proxy
for labor intensity (table 3.10). The results indicate, for almost
33. If p is the wage-profit or factor-price ratio applying to both sectors-that
is, there are no factor-price distortions-and if K and K* respectively are the
capital-labor ratios for rural and urban nonagriculture, the inequality in finding
3.1la implies that p/K* > p/Kr or K* > K*. That is, for the same p, the capital
per worker in urban industries is larger, which is the conventional definition of
relatively high capital intensity.
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 119
Table 3.10. Capital Intensity, by Region and Sector, 1961 and 1971
Fixed assets per employee
(thousands of N.T. dollars) Ratio of Ratio of
all Taiwan five largest
Five Rural to rural cities to
All largest prefect- prefect- rural
Year and sector Taiwan citiesa uresb ures prefectures
1961
Manufacturing 48.35 45.13 49.97 0.97 0.90
Construction 37.64 58.65 19.93 1.89 2.95
Utilities 629.94 618.34 664.28 0.95 0.93
Trade 28.85 40.15 21.08 1.37 1.91
Services 61.91 98.00 26.30 2.95 4.67
1971
Manufacturing 96.09 124.57 63.71 1.51 1.96
Construction 32.43 52.99 11.45 2.83 4.62
Utilities 1,865.79 2,149.79 388.96 4.80 5.52
Trade 66.70 79.47 50.71 1.32 1.57
Services 127.27 180.57 43.43 2.93 4.58
Sources: ICCT, General Report, Industrial and Commercial Census of Taiwan,
1961 and 1971; figures for 1971 were compiled by Samuel Ho, Economic Develop-
ment of Taiwan: 1860-1970 (New Haven: Yale University Press, 1978).
a. The five cities are Taipei, Taichiung, Kaoshiung, Keelung, and Tainan.
b. The rural prefectures are Miaoli, Taichiung, Changhwa, Nantou, Yunlin,
Chiayi, Tainan, Kaoshiung, and Pengtung.
every category of nonagricultural activity in both years, that the
capital per employee was higher for urban areas (the five largest
cities) than for all Taiwan and for rural areas. Moreover the two
marginal exceptions, manufacturing and utilities in 1961, can be
easily explained. First, sugar refining, which is large in scale, inten-
sive in capital, and located in rural areas, played a substantial role
in total manufacturing in 1961. If that and other such processing
are excluded from manufacturing, the general pattern holds. Second,
the capital intensity of utilities in 1961 was apparently affected by
the installation of the country's largest power plant in rural Nantou
Prefecture in that year.
Finding 4.22 indicates that the Gini coefficient of wage income
[G,] always received a heavier weight than that of property income
[G,] (see figure 3.5). Moreover:
FINDING 3.12a. For urban industries and services, the time path of
120 GROWTH AND FID BY FACTOR COMPONENTS
0u/0' was mildly U-shaped-that is, it decreased before the turning
point in 1968 and increased thereafter.
FINDING 3.12b. For rural industries and services, the time path of
./4r increased, except for one year.
The explanation of these findings can be based on growth theory
(see relations 3.1 and 3.2). Given the relative stability of real wages
before 1968, relation 3.1 implies that small-scale rural industries
and services responded more to the stimulation of low wages in the
adoption of labor-using technology than did the large-scale urban
industries and services, which tend to concentrate on a higher in-
tensity of innovation (see the growing divergence in figure 3.5).
Thus, contrary to the arguments of Lewis and others, labor's share
[E.] can rise because of rapid increases in the total number of em-
ployees and the number of hours worked per employee, even during
the phase when labor supply is unlimited and wages are more or
less constant. This conclusion also implies that the more active
promotion of labor-using technology could lead to a more favorable
impact of growth on FID, even on urban FID, before the turning
point.
After the turning point, the ratio of the wage share to the prop-
erty share [+w/,l generally increased in both sectors. According to
relation 3.2, rapidly rising real wages accompanied by capital deep-
ening caused that increase, which was somewhat more pronounced
in the urban sector. In summary, the impact of the functional dis-
tribution effect on FID can be stated as follows:
FINDING 3.13a. Before the turning point the strong labor-using bias of
technology change in rural industries contributed to FID equity for
rural households, and the weak labor-using bias of technology change
in urban industries made a modest contribution to FID equity for urban
households.
FINDING 3.13b. After the turning point capital deepening and the
labor-using bias both contributed to FID equity for all three models.
The factor Gini effect
The factor Gini effect, defined in equations (3.16c) and (3.22d),
captures the impact of changes in the factor Gini coefficients of
wage, property, and agricultural income on the overall Gini coeffi-
cient [G,,]. What are the comparative magnitudes of the factor Gini
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 121
coefficients in each of the three models? What are the longer term
or trend characteristics of these Gini coefficients? What are the
shorter term or transition characteristics of these Gini coefficients
and their impact on G,? The findings related to these questions
will be discussed first for wage and property income, then for agri-
cultural income.
In general:
FINDING 3.14a. Every Gini in the set (Ge,, Gu, GW) < any Gini in
the set (GT, Gu, GT).
FINDING 3.14b. In the set (G,, Gu, (Ur,), GU < G, and Gr < G,,,;
in the set (GT, G', G'), Gu < G. and G" < GT.
FINDING 3.14c. G", < G: and G < G.
The economic significance of finding 3.14a-that every wage Gini
generally was less than every property Gini-is that it strengthens
the intrasectoral conclusion of finding 3.1a. Not only was the in-
equality of wage income [G.] less than the inequality of property
income [G,]; the inequality of rural wage income [G;1,] was less
than that of rural property income [Gr ], and the inequality of urban
wage income [Gu,] was less than that of urban property income
[Gu]. Thus it again is evident, more concretely now, that the un-
equal distribution of property ownership contributed far more to FID
inequality than its small distributive share might imply; wage
income, which had by far the largest distributive share, contributed
less to FID inequality than its share might imply. This conclusion
can be further illustrated by figures 3.7, 3.8, and 3.9, which show
the relative income shares of the highest 10 percent of the popula-
tion to the lowest 10 percent. The results indicate that the ratio of
property shares was about double the ratio of total incomes and
treble the ratio of wage shares.
The economic explanation of finding 3.14b-that sectoral Gini
coefficients for wage and property income were less than total Gini
coefficients for wage and property income-resides in the substantial
gap in average wage and profit income between the rich and poor
groups of a segmented population. A numerical example can illumi-
nate this gap. Suppose in the extreme that the incomes of three
low-income rural families and three high-income urban families are
(Yr, Y-) = (1, 1, 1) (10, 10, 10). Then the Gini coefficients for
both rural households and urban households are zero, but the Gini
coefficient for all households is very large. Thus the inequality for
122 GROWTH AND FID BY FACTOR COMPONENTS
Figure 3.7. Ratio of the Total Incomne Share of the Top 10 Percent to
That of the Bottom 10 Percent, by MlJodel, 1964-72
Before turniing point After turning point
6 -/, <--
-All households
- - -Urban households
5 -Rural households
4 - I II I I I I I
1964 1966 1968 1970 1971 1972
Source: Calculated from DGBAS, Report on the Survey of Family Income and
Expenditure, 1964-72.
all households necessarily is greater than the inequality for urban
and rural households alone. This pattern is also illustrated in figures
3.8 and 3.9, where the ratios of relative income shares of property
and wage income generally are less for urban households and rural
households than for all households.
The economic explanation of finding 3.14c-that rural Gini
coefficients of wage and property income were less than urban Gini
coefficients of wage and property income-is this: during most of
the 1964-72 period, urban structural dualism, with its more sub-
stantial concentration of assets and wider variation in the scale of
production, was more pronounced than its rural counterpart. More-
over the degree of labor force heterogeneity, based on education,
skill, age, and sex, was greater in urban areas than in rural areas.
This pattern led to a more unequal distribution of wage income in
urban areas than in rural areas. By 1972, however, the urban wage
Gini fell below the rural wage Gini, implying two patterns demon-
strated earlier in this section. First, rural dualism related to the
gradual modernization of rural industry may have been catching up
IMPACT OF GROWTH ON FID: QUALITATIVE ASPECTS 123
Figure 3.S. Ratio of the Wage Income Share of the Top 10 Peicent to
That of the Bottom 10 Percent, by Model, 1964-72
8 _ Before turning point After turning point
7-
6-
5 _ Alll households
- - -Urban householdzs
--------Rural households
4
3 r
1964 1966 1968 1970 1971 1972
Source: Samie as for figure 3.7.
with urban dualism just when urban dualism was beginning to
decline. Second, modernization may thus be said to have pene-
trated the larger urban centers first and to a greater extent and
to have permeated the smaller towns and, rural areas only later.
The foregoing findings also provide an insight into the time pat-
terns of the wage and property Gini coefficients of rural and urban
households after the turning point (see figure 3.4):
FINDING 3.15a. The gap between the total wage Gini [G,] and the
sectoral wage Ginis [Gw, and Gr] tended to narrow, as did the gap
between the total property Gini [C-,,] and the sectoral property Ginis
[G,u and Gr].
FINDI11G 3.15b. The gap between G' and GU tended to narrow, as did
the gap between G, and Gu.
FINDING 3.15c. Thus (G,, Gu, Gr) tended to converge to a higher
"limiting value" than (G., Gu, GW), which also were converging (see
findings 3.14a, 3.15a, and 3.15b).
124 GROWTH AND FID BY FACTOR COMPONENTS
Figure 3.9. Ratio of the Property Income Share of the Top 10 Percent
to That of the Bottom 10 Percent, by Model, 1964-72
Before turning point After turning point
20
\ All households
_ - --- Urban households
1964 1966 1968 1970 1971 1972
S-urce: Same as for figure 3.7.
The pattern of intersectoral gaps described in findings 3.15a and
3.15b reinforces the notion expressed in finding 3.14c that the dif-
ference in the economic forces affecting rural and urban industries
tends to become less significant after the turning point, however
pronounced that difference may have been eaxlier. That is, there is
IMPAC1r OF GROWTH ON FID: QIUALITATIVE ASPECTS 125
Figure 3.10. Ratio of the Agricultural Income Share of the Top 10
Percent to That of the Bottomii 10 Percent, by Mlodel, 1964-72
12 - Before turning point After turning point
- All households
10 R ------ Rural households
6
4-
2-
- I I I I I I I I -
1964 1966 1968 1970 1971 1972
Source: Same as for figure 3.7.
a tendency toward convergence as rural industrialization catches up
with urban industrialization. Consequently these gaps are transi-
tional characteristics encountered in the earlier stages of transition
growth. Finding 3.15c nevertheless suggests that the gap between
the property Gini and the wage Gini, identified in finding 3.14c,
tends to persist after the turning point. This pattern suggests that
such a gap is a permanent feature of any economy.
FINDING 3.16. There was a consistency between the patterns of wage
and property Ginis both before and after 1968.
FINDING 3.16a. For rural households there was an overall U-shaped
pattern: Ga, and G' slightly declined before 1968 and significantly
increased thereafter.
126 GROWTH AND FID BY FACTOR COMPONENTS
FINDING 3.16b. For urban households there was an overall mildly
inverse U-shaped pattern: Gu, and Gu stayed constant or slightly in-
creased before 1968 and consistently declined thereafter.
FINDING 3.16c. For all households there was an overall inverse U-shaped
pattern: G,,, and G,, slightly rose before 1968 and consistently declined
thereafter.
This consistency of behavior of the Gini coefficients of wage income
and property income for each model is, in the opinion of the au-
thors, the result of intrasectoral structural dualism. That is, in both
urban and rural industries, some large-scale units hiring higher
quality labor and receiving higher rates of return coexist with smaller
scale units hiring unskilled labor and receiving lower rates of return.
The more pronounced this structural dualism is, the higher are the
values for the Gini coefficients of wage income and property in-
come. If the time pattern of these Gini coefficients is inverse U-
shaped, as it is for urban industries and for the whole economy
(findings 3.16b and 3.16c), an initial increase in structural dualism
in both gives way to its gradual elimination after the turning point.
Finding 3.16a implies that dualism in rural industries initially is
less pronounced than, and only later catches up with, the dualism in
urban industries.
Findings 3.16a, 3.16b, and 3.16c facilitate the following summary
statement about the impact of the nonagricultural factor Gini
effect-that is, the factor Gini coefficient of wage and property
income combined [G.j--on Gu, for the three models (also see tables
3.5, 3.6, and 3.7):
lmpact of
nonagricultural Gini on: Before 1968 After 1968
FINDING 3.17a. G, for all households Very Very
unfavorable favorable
FINDING 3.17b. Gy, for rural households Slightly Very
favorable unfavorable
FINDING 3.17c. Gv, for urban households Slightly Very
favorable favorable
Finally, in examining the agricultural Gini effect traced by the
curve of the Gini coefficient of agricultural income [G.], it can be
concluded that:
SUJMMARY AND CONCLUSIONS 127
FINDING 3.18. The factor Gii effect caused by agricultural income was
always favorable-that is, it was favorable for the rural-households and
all-households models both before and after 1968 (see table 3.8).
Thus the distribution of agricultural income among rural families
was consistently becoming more equal over time and favorably
contributing to overall FID.
Summary and Conclusions
In this chapter a technique for the decomposition of Gini coefficients
was developed to enable forging causal links between growth and
the distribution of income in a developing country. It was shown that
distribution, as measured by the Gini coefficient [Gj, is very much
affected by the particular forces of growth that a country experiences.
In Taiwan, for example, the turning point signifying the exhaustion
of surplus labor brought about a marked difference in the behavior
of the Gini coefficient. In analyzing the causation of the change in
G, and attempting to relate that change to growth, it helps to recog-
nize that family income has a number of factor components which
differ in type and in their impact on overall equity. The time path
of G, affected by growth, can then be analyzed to determine the
quantitative and qualitative impacts of three main effects: the
reallocation effect, which captures changes in the share of agricul-
tural income in total income; the functional distribution effect,
which captures changes in the relative shares of property income
and wage income; and the factor Gini effect, which captures changes
in the inequality of factor income components. The quantitative
and qualitative findings emerging from such analysis seem to support
the notion that historical subphases of growth are relevant to the
distribution of income as well.
It is self-evident that governments of most LDcS, despite their
limited fiscal capacity, can directly affect the distribution of in-
come through taxes and transfers. But the main inference to be
drawn from the findings here is that a change in the growth path is
likely to be the most effective method of tackling the maldistribution
of income. The experience of Taiwan-with unusually low levels of
Gini coefficients, with an unusually mild Kuznets effect over time,
and with no significant transfers through welfare payments-bears
128 GROWTH AND FID BY FACTOR COMPONENTS
out our conviction that significant and sustained changes in FID
equity are mainly achievable through the modification of the basic
forces underlying the pattern of growth-at least in the nonsocialist
mixed economy. The findings for Taiwan also enable us to draw a
number of more specific conclusions.
For all households the findings demonstrate that the Kuznets
effect, whatever trace of it remained, was caused mainly by the
nonagricultural factor Gini effect-an effect which nevertheless can
be substantially, if not totally, overcome by other forces. It is not
surprising that reaching the turning point unambiguously benefits
the overall distribution of income along with the objective of growth.
What is surprising and important, the functional distribution of
income, even before the turning point, does not necessarily make
things worse, and the agricultural factor Gini effect substantially
contributes to making things better. Early concentration on agri-
cultural productivity thus provides additional income to rural
families, encourages nonagricultural activity in rural areas, and
increases the capacity of agriculture to equalize FID. At the same
time, labor's share can rise because of increases in labor intensity,
not because of rapidly rising wages. Under such conditions, the
conflict between growth and the distribution of income can be
eliminated, even before the turning point.
For urban households equity probably cannot substantially
improve until after the turning point, when the unfavorable impact
of the functional distribution effect is reversed. The reason for this
is that urban FID reflects the overall Kuznets pattern, but does not
benefit from the ameliorating effects of agricultural income. The
most dependable way to ensure consistency between growth and
distribution for urban households is to advance the coming of the
turning point by instituting vigorous programs for balanced growth
and reallocation. Even before the turning point, much can be ac-
complished by selecting a relatively labor-intensive path for urban
industry.
For rural households the favorable trend of FID before the turning
point is essentially derived from two sources. One is the beneficial
contribution of the agricultural Gini coefficient, which shows a
consistent and sustained pattern of decline. The other is the un-
usually dispersed pattern of the location of Taiwanese industry, a
pattern which benefits the relatively poor rural families. As members
of rural families, particularly poor rural families, shift to rural
SUMMARY AND CONCLUSIONS 129
industries, the share of wage income rapidly rises and the share of
agricultural income rapidly declines.
Especially surprising is the finding of a rising wage share before
the turning point for rural households and all households. It runs
counter to the experience of most contemporary LDCS and to the
arguments of Lewis, Kuznets, and Marxist and dependency theo-
rists.34 All these observers share one view: As growth really begins
to get under way, distribution must worsen as the shares of rent and
profit income rise. The presumed reasons are that the rich in both
sectors accumulate more assets than the poor and that the shift
from rural to urban activities increases the relative size of the sector
demonstrating the more unequal distribution of income. This argu-
ment apparently neglects the possibility, demonstrated by Taiwan,
that rent reductions in agriculture and a change in the relative
position of workers can simultaneously occur and enable FID to be
improved by the combination of a rising functional distribution of
wage income and a falling agricultural income Gini overcoming all
else. Consequently the Kuznets effect applies not at all to rural
households in Taiwan and only slightly to urban households and
all households.
The analysis of this chapter clearly indicates the need to focus
more attention on the wage share and the causes for its pattern of
distribution. Although the reallocation effect and the functional
distribution effect can be linked to certain familiar notions in growth
theory, that level of formal analysis does not exist to guide attempts
to explain the important factor Gini effect. Efforts to link the factor
Gini effect more fully to growth, by examining the causes of the
heterogeneity of human and physical capital, would thus seem to
deserve a higher priority. Our effort to examine causes of the heter-
ogeneity of human capital is described in chapter four.
34. See William R. Cline, "Distribution and Development," Jounal of De-
velopment Economics, vol. 1 no. 4 (February 1975), pp. 359-400.
CHAPTER 4
The Inequality
of Family Wage Income
THREE INTERRELATED FORCES associated with economic development
are the primary causes of the inequality of family wage income:
the industrialization of economic activity, the differentiation of
the labor force, and the alteration of rules governing family forma-
tion. The distribution of wage income, the largest component of
national income and family income, is thus influenced by forces
quite different from those influencing the distribution of property
and transfer income. As capital is accumulated and technology
becomes more advanced, the structure of industry rapidly changes.
One aspect of this changing structure is the growing demand for a
more diversified labor force. Industry not only becomes more sen-
sitive to the distinction between skilled and unskilled labor; it de-
mands a wider variety of workers having different attributes. At
one end of the spectrum industry requires accountants, managers,
lawyers, and doctors; at the other end, uneducated female workers.
Consequently, when an LDC economy modernizes, the labor force
is differentiated into various homogeneous groups which can be
identified by the different combinations of labor attributes they
embody. The attributes of sex, age, and education are the most
prominent.
The differentiation of the labor force thus is largely a response to
changing industrial demand. That demand, coupled with the supply
of labor in various homogeneous groups, determines the structure
of wage rates at any given time. But the pricing of labor is both
rational and irrational. Market forces operate to reward workers
according to their productive contributions-that is, according to
130
THE INEQUALITY OF FAMILY WAGE INCOME 181
their respective marginal productivities. Concomitantly institutions
discriminate against women and favor the members of wealthier
families to reward workers of the same age and educational qualifi-
cations differently. Thus different wage rates prevail for different
homogeneous groups of workers for both rational and irrational
reasons.
For societies in which the family is the basic labor-owning unit,
the basic determinants of the structure of total family wage income
are the size of the fanmily and the labor attributes of its members.
These determinants are in turn influenced by such factors as fertil-
ity patterns, family decisions to invest in education, and the transi-
tion from extended to nuclear families. Population growth, in addi-
tion to resulting in a larger and increasingly heterogeneous labor
force, influences and is influenced by these same determinants.
In the process of economic development, then, economic forces
determine the wage rates of workers as individuals; demographic
and sociological forces determine the grouping of these workers into
families. The impact of economic development on demographic
variables thus manifests itself in the patterns of family formation,
patterns which naturally affect family wage income.
To describe the heterogeneity of Taiwan's labor force, empirical
data for 1966 is presented in this chapter.' That presentation includes
descriptions of the wage structure, the classification of labor attri-
butes, and the frequency distribution of workers according to that
classification. The data are then analyzed at three levels. The first
level investigates the extent to which the inequality of wage rates
can be explained by various labor attributes. The second examines
the causes of inequality of wage income for groups of individual
wage earners. The third studies the causes of inequality of the dis-
tribution of wage income among families. Certain statistical tech-
niques are used at each level of analysis. At the first level the sta-
tistical technique is the familiar linear regression method. At the
1. In the introduction a sharp distinction was drawn between published and
unpublished DGBAs data. In this chapter use is made of the original unpublished
data. For this reason the procedures adopted in the course of processing and
coding the data from the original household survey are explained in detail in
appendix 4.1 to this chapter. Only one year, 1966, has been singled out for in-
tensive study: it is a high-quality early year; the emphasis here is essentially
cross-sectional; and the requirements of manual coding and computerization are
very substantial.
132 THE INEQUALITY OF FAMILY WAGE INCOME
second and third levels the technique is based on decomposition
equations for the model of additive factor components. But unlike
the preceding chapter, which used linear approximations for purposes
of decomposition, the general case of an exact decomposition is used
here. Although these equations are mathematically derived in part
two of this volume, their meaning and applicability are explained
in this chapter for the benefit of the general reader who may not be
rnathematically inclined.
Empirical Data
The labor force in a developing country typically is rather homo-
geneous before the transition to modern growth gets under way.
During the transition the labor force tends to become more and
more differentiated and heterogeneous. Although this heterogeneity
has many facets, only the five most important characteristics, or
variables, are examined here: sex, age, education, job location, and
occupation. The sex variable has two values: female and male. The
age variable has four values: under 25, 25-45, 45-60, and over 60.
The education variable has five values: primary school or less,
junior high school, senior high school, technical school, and uni-
versity or more. The location variable has three values: rural,
town, and city. The occupation variable has six values: public em-
ployee or serviceman, specialist or professional, service employee,
commercial self-employee, manual laborer, and agricultural employee.
When labor is classified according to the foregoing criteria, there
result 720 types of labor or homogeneous groups. The purpose here
is to analyze the impact of this heterogeneity of the labor force upon
the degree of wage income inequality. Thus the data inputs required
for this analysis consist of the wage rates and frequency distri-
butions of the workers in each homogeneous group. Based on a
sample survey of 2,777 workers for 1966, the average annual wage
rate and the frequency distribution of workers are presented in
tables 4.20-4.23 in an appendix to this chapter. In addition, these
tables have been disaggregated to show separately the wage rates
and frequency for rural workers in table 4.24, town workers in
table 4.25, city workers in table 4.26, and all workers in table 4.27.
The complexity and multidimensionality of issues associated with
the inequality of wage income are evident even when only five labor
characteristics are selected for analysis. Furthermore such a cross-
EMPIRICAL DATA 133
listing of data, essential for applying the model of additive factor
components, seldom is available in published form. And because
the pattern of family ownership of the heterogeneous labor force
underlies the inequality of family wage income, the family affiliation
of workers is needed in addition. To provide a sense of the order of
magnitudes associated with each labor characteristic, the sex, educa-
tion, and age characteristics will be described for the whole economy
by suppressing the location dimension. Relevant to all locations,
these will be referred to as overall characteristics. The sex, education,
and age characteristics will also be separately described for each
location-that is, for rural areas, towns, and cities.
Overall characteristics
Of the 2,777 workers covered in the 1966 survey, about 75 percent
had completed only their primary education (table 4.1). Junior
and senior high school graduates accounted for another 20 percent.
With respect to sex, the completion of primary school significantly
demarked the educational attributes of workers. Although the female
percentage of graduates was higher than the male percentage for
the lowest educational group, it was lower than the corresponding
male percentage for all other educational groups. The figures reveal
the expected pattern: fewer female workers than male workers re-
ceived higher education. Because shortages of technical workers
are generally regarded as a bottleneck for economic development,
the low proportion, only 1.3 percent, of graduates of technical schools
should also be noted.
When the wage rate of each educational group is expressed as a
multiple of that of the primary school group, it is seen that junior
high school and university were the most important steps for up-
grading the earning power of workers. Three years of junior high
school brought about a more than doubling of the wage rate; three
additional years of senior high school brought about practically no
further improvement. The wage index for junior high school was 2.2
(primary school = 1); that for senior high school was 2.32. Another
two years of technical school led to an improvement in the wage
index to 2.95. But university education brought about a really
significant improvement to 4.18. It seems that solid economic rea-
soning justified both the strong pressure on high school graduates
to pass the college entrance examination and the popular feeling that
those who did not enter college were failures.
134 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.1. Relative Wage Rates and Frequency Distribution
of Labor, by Education, Sex, and Job Location, 1966
(percent)
Junior Senior Techni- Univer-
Primary high high cal sity or
Item school school school school over Total
All workers
Percentage distribution 73.93 8.46 12.45 1.33 3.83 100.00
Female 82.59 7.10 8.50 0.97 0.84 100.00
Male 70.90 8.94 13.84 1.46 4.86 100.00
Relative wage rate
(primary school = 1.00) 1.00 2.22 2.32 2.95 4.18 1.85
Rural workers
Percentage distribution 89.20 4.65 5.15 0.50 0.50 100.00
Relative wage rate
(rural areas = 1.00) 1.00 1.00 1.00 1.00 1.00 1.00
Town workers
Percentage distribution 70.40 9.81 14.80 1.06 3.93 100.00
Relative wage rate
(rural areas = 1.00) 1.54 1.01 1.08 0.91 1.21 1.71
City workers
Percentage distribution 63.59 10.29 16.36 2.64 7.12 100.00
Relative wage rate
(rural areas = 1.00) 2.64 2.74 1.39 0.97 1.80 2.98
Sources: Tables 4.20-4.27 appended to this chapter.
More than half the workers were in the 25-45 age group (table
4.2). The under-25 age group accounted for a quarter of workers; the
rest were mainly allocated to the 45-60 age group. When the corres-
ponding percentages of female and male workers are compared, the
contrast between the lowest group-that is, the under-25 group-and
the other groups once again shows the significance of the influence of
the sex characteristic. Although the percentage of female workers was
much higher than the percentage of males in the youngest group,
it was lower than that for males in all the other age groups. As would
be expected, female workers retire from the labor force at a much
earlier age than their male counterparts because of their role in the
family.
EMPIRICAL DATA 135
Table 4.2. Relative Wage Rates and Frequency Distribution of Labor,
by Age, Sex, and Job Location, 1966
Under Over
25 25-45 45-60 60
Item years years years tyears Total
All workers
Percentage distribution 24.70 53.84 19.30 2.16 100.00
Female 44.71 44.71 9.75 0.84 100.00
Male 17.73 57.02 22.63 2.62 100.00
Relative wage rate
(under 25 = 1.00) 1.00 2.24 2.79 2.13 2.04
Rural workers
Percentage distribution 28.14 55.15 15.20 1.51 100.00
Relative wage rate
(rural areas = 1.00) 1.00 1.00 1.00 1.00 1.00
Town workers
Percentage distribution 22.32 55.10 18.48 2.45 100.00
Relative wage rate
(rural areas = 1.00) 1.36 1.68 2.03 1.06 1.71
City workers
Percentage distribution 24.93 50.40 22.30 2.37 100.00
Relative wage rate
(rural areas = 1.00) 1.79 3.14 3.11 3.10 2.98
Sources: Tables 4.20-4.27 appended to this chapter.
When the wage rate of each age group is expressed as a multiple of
that of the youngest group, it is seen that the gain in the wage rate
was most significant for those in the 25-45 age group and much less
significant for the 45-60 age group. The wage index for the 25-45
age group was 2.24 (under 25 = 1); that for the 45-60 age group
was 2.79; that for the over-60 age group was 2.13. The reward
for experience therefore manifested a strong trend toward diminishing
return. The probable reasons for this are that "age" is a poor proxy
for experience and that the advantage of experience gained with
136 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.3. Wage Parity of Female Workers,
by Age and Education, 1966
(male wage rate = 1)
Level of education Under 25 25-45 45-60 Over 60 Total
Primary school 0.7099 0.4077 0.3779 0.4937 0.4235
Junior high school 0.7903 0.5272 0.5307 - 0.4638
Senior high school 0.9304 0.7958 1.0115 - 0.7215
Technical school 1.4468 0.7533 - - 0.7253
University or over 1.0292 0.6372 0.5651 - 0.5798
All levels 0.7688 0.4244 0.4228 0.2984 0.4170
- Not applicable.
Soutrce: 'Table 4.27 appended to this chapter.
higher age is offset by other disadvantages of "aging" for workers
over 60.
The foregoing data reveal that female workers were heavily allo-
cated to age and educational groups that received low pay. The
concentration of females in low-paying jobs may have been the result
of their free choice to join and to leave the labor force early. There
may also have been institutional discrimination in the availability of
jobs for female workers. Wage discrimination is less disputable
(table 4.3). For all groups the wage rate for females was substantially
less than half that for males. Female workers were at a disadvantage
in every educational group. -Moreover discrimination was higher for
the low educational categories, which absorbed almost 90 percent of
female workers. The wage rate for females having primary education
was 42 percent of that of their male counterparts; that for females
having junior high school education, 46 percent. Discrimination
against female workers also prevailed for every age group, and the
severity of discrimination increased with age. Consequently, elderly
women with little education were apt to be most disadvantaged;
young women with higher education, least disadvantaged.
Locational characteristics
The concentration of less educated workers in the rural sector
was high (see table 4.1). Primary school education significantly
demarked the job-location characteristic. The proportion of this
EMPIRICAL DATA 137
group was highest in the rural areas and lowest in cities-89.2
percent compared with 63.6 percent. For all other educational
categories the opposite was true: the proportion of high-education
graduates was greatest for the cities and lowest for the rural areas.
In educational attainment, labor in a tradition-bound rural economy
is an inferior homogeneous group. With the rural areas, towns, and
cities respectively characterized by increasing degrees of moderni-
zation and urbanization, modernization brought about labor hetero-
geneity in a particular sense: the formation of a superior homoge-
neous educational group. Although this conclusion is based upon a
cross-sectional study, it can and should be verified by the analysis
of time series in the future.
When the wage rate of each locational group is expressed as a
multiple of the rural wage rate for each educational group, the most
significant gaps prevail between city workers on the one hand and
town and rural workers on the other. For the two lowest educational
groups, the wage rate for city workers was almost three times that
of rural workers. For higher educational groups, the wage disparities
were less. For the technical school groups, city workers had practi-
cally no advantage.
Turning to the age characteristic, it can be seen that the rural
sector provided more employment opportunities for younger workers
than cities did. The proportions of rural workers in the under-25 and
25-45 age groups respectively were 28.1 percent and 55.2 percent;
those of urban workers, 24.9 percent and 50.4 percent. For workers
over 45 the town and city offered increasingly greater opportunities.
Modernization therefore seems to lengthen the working life. Because
older workers had a higher earning power than their younger coun-
terparts, modernization appears to lead to the formation of a superior
wage-earning group much in the manner that education does (see
table 4.2).
For all age groups, workers in towns and cities received higher
wage rates than rural workers. But this disparity was not as great
for young workers as it was for all other age groups. For those in
the under-25 age group, the wage indexes of town and city workers
respectively were 1.36 and 1.79 (rural workers = 1). The reason
for this pattern may be that young rural workers were more willing
than old workers to migrate to large cities, a propensity that would
result in a smaller wage gap in the youngest age group.
Job location thus represents a significant dimension for the analy-
sis of inequality in the distribution of wage income. For this reason
138 THE INEQUALITY OF FAMILY WAGE INCOME
the three locations are separately treated in the remainder of this
chapter.
Analytical Framework
The analysis of the inequality of wage income thus comprises
three distinct types, or levels, of problems: at the first level the prob-
lem is to determine the impact of labor heterogeneity on the wage rate;
at the second, the causes of the inequality of wage income among
homogeneous groups of individual workers; at the third, the causes
of the inequality of family wage income. It should be perfectly clear
that the focus of this chapter, indeed this entire volume, is the
inequality of family wage income. Although the first two levels of
analysis may be of interest in their own right, they are discussed in
this chapter primarily to lay the foundation and constitute the
input for the third level of analysis.
The association of various dimensions of labor heterogeneity with
the magnitude of the wage rate perhaps is one of the most popular
methods for studying the inequality of wage income. For example,
the familiar earnings-function approach uses a linear regression
model in which the wage rate is regressed on various labor force
characteristics; which are represented by natural and dummy varia-
bles.2 The purpose of this technique is to estimate regression coeffi-
cients that can be interpreted as quantified causes of the inequality
of the wage rate. The regression coefficients of the wage rate on such
characteristics as age, sex, and educational attainment represent
the premiums associated with these characteristics-that is, the
extra wage income additively accruing to workers having different
combinations of values for these characteristics.
This earnings-function technique has nothing to do with the in-
equality of wage income in the sense used in this volume. Inequality
here refers to the degree of inequality of income for a group of income
recipients [W = (WI, W2, . . . , W,)] as measured by the Gini
2. See Jacob Mincer, Schooling, Experience, and Earnings (New York: Na-
tional Bureau of Economic Research, distributed by Columbia University Press,
1974) and Sherwin Rosen, "Human Capital: A Survey of Empirical Research,"
in Research in Labor Economics, ed. Ronald G. Ehrenberg (Greenwich, Ct.:
JAI Press, 1977), vol. 1, pp. 3-39.
ANALYTICAL FRAMEWORK 13.9
coefficient [Gm]. The earnings-function technique is concerned nei-
ther with the pattern of wage income [W]j nor with its degree of in-
equality [Gm]. Nevertheless the earnings function used at the first
level of analysis provides certain research inputs required at the
second and third levels. With this technique such demographic char-
acteristics of labor as sex, age, and educational attainment can be
additively associated with such economic magnitudes as wage income.
Given the basic purpose of this chapter, which is primarily directed
at the analysis of wage income inequality for homogeneous groups
of individual workers and for families, only a rather naive version
of such an earnings function is used here. It can clearly be improved
as an input to this work. Methodologically, however, it should be
obvious that the primary interest here is with the way an earnings-
function technique can be combined with the additive factor-com-
ponents technique, not with the perfectibility of the earnings function
itself. The analytical design used in combining these two techniques
is discussed more fully in an appendix to this chapter.
At the second level of analysis workers are treated as individuals
and all information on their family affiliation is still suppressed.
Given the pattern of wage income of individual workers [W =
(W1, WT2, . . , W.)] and the degree of wage income inequality
EGQg, the crucial analytical task at the second level is to determine
the extent to which each of the labor characteristics accounts for
Gw. At the first level of analysis the wage-rate inequality attributable,
for example, to the sex characteristic is traced to such rational forces
as differences in worker productivity and to such irrational forces as
sex discrimination. The second level of analysis addresses the same
set of socioeconomic forces, but attempts to assess their impact
on the degree of inequality of wage income [Gm], not on the wage
rate. This analysis will be formulated as an additive factor-com-
ponents problem and make use of the earnings-function results
from the first level of analysis.
Analysis of the inequality of family wage income at the third
level requires information on the family affiliation of workers. The
technique for this analysis can be illustrated with a simple model
examining two labor characteristics, sex and education (table 4.4).
The data in this table correspond to the cross-listing of information
on the wage rate and frequency distribution of workers in appendix
tables 4.20-4.23; they also provide all the information needed for
analysis at the second level. For analysis at the third level, the ten
workers in table 4.4 are classified into five families to show total
140 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.4. Numerical Example Corresponding to the Cross-listing
of Information on the Wage Rate and Frequency Distribution
of Workers in Tables 4.20-4.27, by Sex and Level of Education
Inter-
Low mediate High
Item education education education
Wage Rate
Female workers 2 5 10
MA'ale workers 3 7 15
Number of Workers
Female 1 4 1
Male 2 1 1
Note: W = (2, 3, 3, 5, 5, 5, 5, 7, 10, 15)
Source: Constructed by the authors.
family wage income [Y] and to trace the wage income components
to the membership composition of families (table 4.5). The six
grades of labor in this table correspond to those in table 4.4. The
pattern of total family wage income [Y = (5, 8, 10, 15, 22) ] results
in a Gini coefficient [GJ] of 0.2733. This illustrative numerical
example indicates the way the analysis of G,, will be formulated as
an additive factor-components problem at the third level.
The total family wage income obviously depends on family size-
that is, on the number of wage earners owned by the family-as
well as membership structure. A column in table 4.5 describes the
pattern by which workers of a particular grade are distributed
among the families. It is apparent that the unevenness of this dis-
tribution can be a major cause of the inequality of family wage
income. A family with high wage income would be expected to "own"
more high-grade workers, such as college-educated males, than
would a family with low wage income. In addition, the membership
composition of families, described by the sex, age, and educational
attainment of their members, is determined by the rules of family
formation. These rules are affected by a host of sociodemographic
factors, including the institution of marriage, the patterns of repro-
duction, and the properties of nuclear families in transition. Thus
the third level of analysis encounters wholly new factors which are
LABOR HETEROGENEITY AND THE WAGE RATE 141
Table 4.5. Numerical Example Classifying Workers into Five
Families and Tracing Wage Income Components
to the Membership Composition of Those Families
Low Intermediate High
education education education
Total
wage Fe- Fe- Fe-
Family income male Male male Male male Male
Familv 1 5 0 0 5 0 0 0
Family 2 8 2 6 0 0 0 0
Family 3 10 0 0 0 0 10 0
Family 4 15 0 0 15 0 0 0
Family 5 22 0 0 0 7 0 15
Note: The pattern of family wage income is given by Y = (5, 8, 10, 15, 22),
and the resulting Gini coefficient is 0.2733.
Source: Constructed by the authors with data from the numerical example of
table 4.4.
not encountered at the first two levels of analysis and which are
traditionally treated by such other disciplines as sociology and
demography. Because this area of inquiry is relatively new for
economists, we will be content to speculate about the way the prob-
lem can be formulated in future research efforts.
Labor Heterogeneity
and the Wage Rate: First-level Analysis
Multiple regression analysis is used to analyze the impact of labor
heterogeneity on the wage rate. Let W be the wage rate, and let
XI, X2, . . ., XI be the explanatory variables. A regression equation
can then be specified as follows:
(4.1) W = a + aix + a2X2 +... + arxr +
where a is a random error term. The r explanatory variables [xei]
represent the various characteristics that define the heterogeneity
of the labor force. The purpose of the regression analysis is to esti-
mate the coefficients [ai] that measure the quantitative impact of
142 THE INEQUALITY OF FAMILY WAGE INCOME
each labor dimension upon the wage rate under the assumption of
independence.
In applying the regression analysis to the data for 1966 (see
appendix tables 4.20}4.23), the regression equation is specified as:
(4.2) W = a. + aix, + a2X2 + a3x3 + a4X4 + 5.
In addition to the variables representing sex [xi], education EX2],
and age [EX], an additional variable [X4] represents the total income
of the family to which a given wage earner belongs.8 The reason for
using such a variable is to determine whether a wealthy family can
exercise undue influence to secure a higher wage rate for its mem-
bers. Equation (4.2) will be applied separately to each of three job
locations: rural areas, towns, and cities.
The explanatory variables [xi] can be assigned a range of values.
The sex variable [Ex] takes on the value of zero for females and 1
for males; the coefficient a1 thus measures the male premium. The
education variable [x2] takes on values that correspond to the
years of formal education completed (6, 9, 12, 14, or 16). The co-
efficient a2 thus measures the education premium and corresponds
to the market value of one additional year of formal education. The
age variable [Ex] takes on values that correspond to an ordinal
ranking of age as a proxy for the contribution of experience to wage-
earning power (1, 2, 3, or 3).4 The coefficient a3 thus measures the
age premium and corresponds to the value of experience in earning
power. Total family income [Z4] is measured in thousands of new
Taiwan dollars.5 The coefficient a4 thus measures the nepotism
premium associated with undue family influence on the earning
power of its members.
This model was applied to the primary data in appendix tables
4.20-4.23. It is apparent from the sample sizes that the regression
coefficients are very significant (table 4.6). In cities, where the
average wage rate in 1966 was NT$19,831, the male premium was
3. See schedule 4.5 in appendix 4.1 to this chapter for the coded form used
to assemble data on total family income.
4. Notice that the over-60 age group is assigned a rank of 3, or the same as that
assigned to the 45-60 age group. This choice was made after experimentation with
several alternative rankings for the four age groups: (1, 2, 3, 1.5), (1, 2, 3, 2),
(1, 2, 3, 2.5), and (1, 2, 3, 3). The last ranking was selected because it leads to
the highest value of the coefficient of determination (R2 = 0.5).
5. At the time of writing, the new Taiwan dollar was equal to about US$0.025.
LABOR HETEROGENEITY AND THE WAGE RATE 143
Table 4.6. Regression Coefficients of Four Explanatory Variables,
by Job Location, 1966
Regression coefficient
Nota-
Item tion Rural area Town City
Constant a. -10.8977 -12.1360 -18.8349
(-12.2398) (-12.2728) (12.2333)
Sex al 3.3770 5.2287 7.3493
(8.4366) (9.0333) (7.3777)
Education a2 1.4522 1.5537 1.5089
(12.9158) (17.7580) (11.3366)
Age a3 1.7635 2.8801 6.2734
(6.2578) (7.6676) (10.4305)
Total family
income a4 0.0841 0.0800 0.1757
(7.1972) (6.9843) (9.3398)
Sample size 796 1,223 758
Note: Values in parentheses are t scores. The following values have been
assigned to characteristics:
Xi = (female, male) = (0, 1)
X2 = (primary school, junior high school, senior high school, technical
school, university) = (6, 9, 12, 14, 16)
X3 = (under 25, 25-45, 45-60, over 60) = (1, 2, 3, 3)
X4 = (total family income in thousands of N.T. dollars)
Source: Calculated from tables 4.20-4.27 appended to this chapter.
NT$7,349, the age premium was NT$6,273, and the education
premium was NT$1,509. For earning power, one year of formal
education was therefore equivalent to about four to five years of
informal education or experience, as measured by a simple gain in
age. Being female was equivalent to the disadvantage of having
almost five years less formal education.
The locational specifications of rural area, town, and city represent
an increasing degree of penetration by the forces of modernization
into socioeconomic life. It appears, moreover, that the attributes
of labor were probably evaluated (priced) with more sensitivity
144 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.7. Influence of Total Family Income on Wage Rates, by Sex
and Age, 1966
(thousands of N.T. dollars)
Female Male
25-45 45-60 25-45 45-60
Item years years years years
Without family income effect-
Senior high school 11.8187 18.0921 19.1680 25.4414
Technical school 14.8365 21.1099 22.1858 28.4592
University or over 17.8543 24.1277 25.2063 31.4770
With family income effect
Senior high school 13.5757 19.8491 20.9250 27.1984
(29.3887) (35.6621) (36.7380) (43.0114)
Technical school 16.5935 22.8669 23.9428 30.2162
(32.4065) (38.6799) (39.7558) (46.1292)
University or over 19.6113 25.8847 26.9606 33.2340
(35.4243) (41.6977) (42.7736) (49.0470)
Ratio of the wage rate
influenced by high
family income to that
influenced by low
family incomeb
Senior high school 2.1611 1.7967 1.7557 1.5814
Technical school 1.9530 1.6915 1.6604 1.5233
University or over 1.8063 1.6109 1.5865 1.4758
Note: Values in parentheses are t scores. Higher education is taken to be a
proxy for higher wage income.
Source: Calculated from tables 4.20-4.27 appended to this chapter.
a. Computed from equation (4.2) by setting the variable for total family
income equal to zero.
b. Values for total family income of NT$100,000 and NT$10,000 were sub-
stituted into equation (4.2) to examine the effects of family income on the wage
rate.
in the commercialized milieu of large cities than in the traditional
rural communities. The male premium of 7.35 in cities was more
than double that of 3.38 in rural areas. Either male workers in
cities had a higher productive power or, more likely, the discrimina-
tion against women was greater. For the age characteristic the dif-
ference between cities and rural areas was even greater. The age
LABOR HETEROGENEITY AND THE WAGE RATE 145
Table 4.8. Distribution of Families, by Job Location
and Total Family Income, 1966
Number of families
Total family income Rural
(N.T. dollars) area Town City
Less than 10,000 28 46 7
10,000-15,000 70 94 28
15,000-20,000 85 133 46
20,000-25,000 68 114 65
25,000-30,000 48 94 64
30,000-40,000 52 104 87
40,000-50,000 30 51 59
50,000-60,000 8 35 29
60,000-70,000 13 16 23
70,000-80,000 6 11 6
80,000-100,000 7 8 10
More than 100,000 2 6 8
Source: Tables 4.20-4.27 appended to this chapter.
premium of 6.27 in cities was more than triple that of 1.76 in rural
areas. For the education characteristic the difference between cities
and rural areas was not significant. It would appear that rural areas
are less sensitive than cities in their pricing of age and sex attributes
of workers, but equally sensitive in pricing educational attributes.
In a society in which families have a long tradition of playing a
prominent social role, family influence would be expected to be
significant in securing better paid positions for its members. The
nepotism coefficient [a4] measures the extent of the influence of
total family income on the wage rates of family members. The
nepotism premium of 0.18 in cities was more than double that of
0.08 in towns and rural areas. A better view of the quantitative
significance of nepotism in cities can be provided by examining
higher wage-income groups, proxied by educational attainment,
for which family influence would be expected to be strong (table
4.7). The values in the first part of this table do not take into ac-
count the influence of family income; they were computed from
equation (4.2) by setting the variable for total family income [Z4]
146 THE INEQUALITY OF FAMILY WAGE INCOME
equal to zero. The values in the second part of this table do take
into account the influence of family income. Because the vast ma-
jority of city families receive total income ranging from NT$10,000
to NT$100,000 (table 4.8), these two values were substituted into
equation (4.2) to examine the effects of family income on the wage
rate. The ratios of the wage rate influenced by high family income
to the wage rates influenced by low family income are given in the
third part of table 4.7. It can be seen that the wage rates a very
wealthy family can secure for its members are at least 50 percent
higher than those a very poor family can secure for its members.
Given the value of the regression coefficient a4 of 0.1757, the nepotism
premium was worth approximately NT$1,800 a year, or NT$150
a month, for every increase of NT$10,000 in total family income.
Inequality of Income
of Individual Wage Earners: Second-level Analysis
The regression analysis revealed the impact of various dimensions
of labor quality on the wage rate. This section investigates causes
of the degree of inequality of wage income for a group of individual
wage earners. The method of analysis is based on the application of
the following decomposition equation to the data for 1966:
(4.3) G. = 4qR1G1 + 02R2G2 + . . . + 40/,RrGr + A.
In this equation the Gini coefficient of the wage rate [EG], or the
wage Gini, measures the degree of inequality of wage income. Notice
when the wage rate is calculated on an annual basis that the wage
rate is the same as wage income. The r terms on the right side repre-
sent the various dimensions of labor quality. In this analysis r is
equal to 4. The four terms stand for sex, education, age, and total
family income and correspond to the four variables of regression
equation (4.2). The aim of the decomposition analysis is to assess
the quantitative impact, or contribution, of the various labor char-
acteristics on G,. The term A will be referred to as the rank-weighted
error term.
Every term OiRiGi in equation (4.3) is the product of three fac-
tors. The factor Gi measures the degree of inequality of a particular
attribute or characteristic and will be called the labor characteristic
Gini. The factor 4i measures the share of inequality contributed by
INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 147
a characteristic and will be called the labor characteristic weight.
The factor Ri measures the correlation between the values of labor
characteristics and wage income and will be called the labor correla-
tion characteristic. Before the empirical analysis, each factor will be
precisely defined and given an economic interpretation with the
aid of a numerical example.6
Labor characteristic Gini
Suppose that five wage earners have wage income [we] as shown
in the numerical example of table 4.9. The sex, educational attain-
ment, and wage income of these workers constitute the primary
data in this numerical example.7 The sex variable [X1] takes on the
value of zero for females and 1 for males. The education variable
[EX] takes on the value of 1 for low education, 2 for intermediary
education, and 3 for high education (the terms low, intermediary,
and high conform to usage in Taiwan). Wage income is measured
in thousands of new Taiwan dollars. When there are n families, this
data can be summarized by vector notation:
(4.4a) W = col(w1, W2, ... , Wn) and
[wage pattern]
(4.4b) Xi = col(xil, i2 . . x Zi.)- (i =- 1, 2, . . ., r)
[labor characteristic pattern]
For any nonnegative column vector [Y = col( Yl, Y2, ... , Yn)]
the Gini coefficient [Gd] can then be computed from the following
equation':
(4.5a) 0 O for O < Ol < a, and
(4.7g) aG/aI0 < 0 for al < 01 < 1.
When plotted against 01, G is an inverse U-shaped curve that takes
on a maximum value of a, at 01 (figure 4.1). Therefore al is the
critical value of 0G marking off the two phases of G. The maximum
value of G, when 01 is equal to al, is given by:
(4.8) G = 2a-1.
In figure 4.1 the emergence of a privileged splinter group out of a
homogeneous labor force is represented by movement along one
154 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.11. Numerical Example of the Gap between the Relative Value
of the Education Characteristic for a Privileged Group and
That for a Less Privileged Group
(values of s)a
V2 for privileged group
Twelve
Nine years years Fourteen Sixteen
Six years (junior (senior years years
VI for less (primary high high (technical (university
privileged group school) school) school) school) or over)
Six years
(primary school) 0 0.200 0.333 0.400 0.455
Nine years
(junior high school) - 0 0.143 0.217 0.280
Twelve years
(senior high school) - - 0 0.077 0.143
Fourteen years
(technical school) - - 0 0.666
Sixteen years
(university or over) - - - 0
- Not applicable.
Source: Constructed by the authors.
a. s = V* -V*.
of the curves from the point U, where 0o is equal to 1, to the left
toward the origin, where ol is equal to zero. This movement indicates
that the fraction of labor in the underprivileged group [01] is de-
clining. Consider the level of education as an illustration. The value
of s between two education characteristics is given in table 4.11,
where the years of education are indicated in the headings. For
example, the value of s is 0.2 between junior high school, for which
/2 is 9, and primary school, for which VI is 6. Starting from the
point U in the curve relevant to an s of 0.2 in figure 4.1, a turning
point is reached at point T. Thus popularization of junior high
school education will first cause the inequality [Gi] to increase to a
maximum of 0.10, at which point the proportion of workers with
junior high school education has increased to about 45 percent. Notice
when the value of s is higher-such as the s of 0.45 between uni-
versity and primary education-that popularization of higher
education will raise the labor characteristic Gini much faster-in
INEQUALITY OF INCOME OF INDIVIDIUAL WAGE EARNERS 155
this example to a peak value of 0.24 at point T'. But the turning
point [T'] will arrive sooner, when about 38 percent of workers
have university education.
The emergence of an underprivileged splinter group out of a
homogeneous labor force is represented by movement along one of
the curves from the origin, where 01 is equal to zero, to the right
toward the point U, where 01 is equal to 1. This movement indicates
that the fraction of labor in the underprivileged group is increasing.
The entry into the labor force of females and young workers under
25 are typical instances of this pattern. When such an inferior group
is formed, inequality precedes equality, just as for the formation of
a superior group. But when an inferior group is formed, a higher
value of s will not only cause the labor characteristic Gini to in-
crease faster, but will also postpone the turning point to a higher
value of 01. The skewness of these curves shows the basic asymmetry
between the formation of privileged and underprivileged groups.
Notice when the value of the sex characteristic is indexed by zero
for females and by 1 for males that the value of s for sex is the maxi-
mum-that is, it is equal to 1. Equation (4.6g) then is reduced to
a limiting and special case in which G is equal to 01, a relation repre-
sented by the 450 line OA. Therefore the sex Gini is precisely the
fraction of female workers in the labor force; it continuously increases
with increasing rates of female participation.
It can be seen from the foregoing discussion that the labor char-
acteristic Gini EGi] measures inequality in a special sense. Whether
a homogeneous group is inferior or superior, a low value of Gi means
that the number of workers in that group is either very small and
socially insignificant or very large and common. The first instance
would be indicated by a small 01; the second by a large 01. A low
Gi also means that the superiority or inferiority of the homogeneous
group is not very pronounced, which would be indicated by a small
s. Vague as it might seem, the values of Gi consequently measure
certain properties of a group of workers-properties which common
sense would regard as underlying causes of inequality.
Labor characteristic weight
The labor characteristic Gini EGi] measures the degree of non-
homogeneity of labor. Whether Gi is a principal cause of inequality
of wage income depends upon the influence of that characteristic
156 THE INEQUALITY OF FAMILY WAGE INCOME
on the wage rate. Suppose that the male premium [a,] is zero-that
is, there is no difference between the male and female wage rates.
Then sex cannot be a principal cause of inequality of wage income,
regardless of the magnitude of Gi. The labor characteristic weight
[E1] measures the relative wage-earning power associated with a
labor characteristic. Notice that the regression coefficients [ai] of
equation (4.1) are computed from the primary data for the wage
pattern [W] and the labor characteristic pattern [Xi] of equation
(4.4). The primary data for the wage pattern [W], the sex charac-
teristic pattern [X1], and the education characteristic pattern [X2]
in table 4.9 lead to the following regression equation:
(4.9a) W = a. + aizx + a2x2 + 8, where
(4.9b) a. = -1, a1 = 2, and a2 = 3.
When the r values of Xi are substituted into the regression equation
(4.1), a column of error terms [86 = col(61, 82, . . . , an] is deter-
mined.
(4.10a) W = a + aix + a2X2 ... + arXr + 5,, where
(4.10b) a. = col(a., a0, . .. , a0) and
(4.10c) 61 + .2 + * * * + an = 0
The computation of 6, for the numerical example in table 4.9 ap-
pears in the right-hand columns. Notice when the regression coeffi-
cients are estimated by the method of least squares that the sum of
all values of bi is zero (see equation [4.10c]). Because of this prop-
erty the mean values of all column vectors in equation (4.10a) have
the following relations:
(4.11a) W = a. + aljl + a2t2 + ... + asxt, where
(4.1lb) W = (W1 + W2 + . .. ± W.)/n and
(4.11c) xi = (Zil + Xi2 + Xi3 + ... + xn)/n, and
a.
(4.11d) 1 = + 1 + 2... + 'T, where
(4.11e) oi = ajiv/iB. (i = 1, 2, . r. , )
In equation (4.1lb) W is the mean wage income; in equation (4.11c)
xi is the mean value of the ith characteristic. For example, if x2 is
measured in years of formal education, then X2 is the average years
INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 157
of education for the n workers. The labor characteristic weights
[0j] are defined in equation (4.11e). Because the product of the
education premium and the average years of education [aiti] repre-
sents the average contribution of education to the wage rate, the
education characteristic weight is a measure of this contribution as
a fraction of the average wage rate. For a typical term 4iRiGi in
equation (4.3), it can thus be seen that a labor characteristic Gini
[Gi] cannot make a heavy contribution to the inequality of wage
income unless the labor characteristic weight [Ei] is large."
The values of the labor characteristic weights are given in table
4.9: ol is 0.125; 02 is 1.03125. When a higher value of a variable
[xe] corresponds to higher earning power, the regression coefficient
[ai] is positive. Consequently the values of 4i are nonnegative. It
can nevertheless be seen from equation (4.11d) that the r values of
(i do not form a system of weights unless the regression constant
[a0] is equal to zero. Because a. is negative in the numerical example,
the values of oi add up to more than 1. The rank-weighted error
term [A] in equation (4.3) is defined as follows:
(4.12a) A = (j.11. + i262 . ± jaJ.)/ I, where
(4.12b) ji = i/(l + 2 + ... + n) and (i = 1, 2, ...,n)
(4.12c) l + i2 ... + j,, = 1.
The values of ji in equation (4.12b) are relative ranks used as a
system of weights. Therefore A is the rank-weighted error expressed
as a fraction of the average wage [W]. It measures the impor-
tance of the error term in equation (4.3). In view of equation (4.10c)
A can be positive or negative. The computation of A as being equal
to 0.0047 is shown in table 4.9.
Labor correlation characteristic
The contribution of a labor characteristic, such as education or
sex, to the inequality of wage income depends not only on the labor
characteristic weight [+X] and the labor characteristic Gini [Gi],
11. Notice that (Xi, W) is a mean point on the regression line. Thus 4. is the
elasticity of w with respect to X, at the mean point. To illustrate: 2 for educa-
tion is the percentage increase in the average wage rate when the average num-
ber of years of education increases by 1 percent.
158 THE INEQUALITY OF FAMILY WAGE INCOME
but also on the extent to which the values of a characteristic are
correlated with wage income. Assume that the pattern of wage
income of five workers is W = col(10, 12, 18, 25, 30) and the years
of formal education are given by two alternatives, X2 = col(6, 6,
9, 12, 14) and X2 = col(14, 9, 12, 6, 6). For the first alternative,
workers with higher income receive a higher education-that is, W
and Xl are highly and positively correlated. For the second alter-
native, the opposite is true. Workers with higher income receive a
lower education-that is, W and X22 are negatively correlated. The
higher income in the second alternative is the result of such other
labor characteristics as sex and age; education in fact contributes
to the equality of wage income, not to its inequality.
Observe that the value of the labor characteristic Gini [EG] is the
same for X2 and X22. Thus the impact of education on the inequality
of wage income depends not only on the labor characteristic Gini
[G], but also on the correlation characteristic [Ri]. Other things
being equal, a high positive value of Ri indicates that the ith char-
acteristic contributes more to the inequality of wage income than to
its equality. If Ri is negative, the ith characteristic contributes to
equality, not to inequality Esee equation (4.3)].
When the primary data are given for a particular labor charac-
teristic according to equations (4.4a) and (4.4b), the labor correla-
tion characteristic is computed as follows:
(4.13a) Ri = Ri(W, xi) = 0i/lG, where
(4.13b) 0i = 2ui/n - (n + 1)/n, where
(4.13c) i% = r(xill/si) + r2(xi2/si) + ... + rn(xin/s8), where
(4.13d) Si = xi1 + xi2 + . . . + xin
and ri is the wage income rank of the ith worker. The computation
or RJ and R2 is indicated in table 4.9. Note that the education char-
acteristic has a perfect rank correlation with wage income, giving
R2 a value of 1. In general the labor correlation characteristic ERi]
is that fraction of the labor characteristic Gini [Gi] which can be
explained by the variation of wage income or the correlation char-
acteristic between W and X,.12
12. In part two Ci is referred to as the pseudo Gini coefficient, and R, is the
ratio of the pseudo Gini coefficient to the Gini coefficient. See chapters eight
and nine in part two.
INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 159
Empirical analysis
Decomposition equation (4.3) was applied to the data for 1966
(table 4.12). The decomposition was carried out separately for
rural areas, towns, and cities to yield the labor characteristic weights
[Es], the labor characteristic Ginis [G3I, and the correlation charac-
Table 4.12. Decomposition Analysis of the Inequality of the Wage Rate,
by Location and Labor Characteristic, 1966
Variable Notation Rural area Town City
Labor characteristic weight
Sex Oi 0.3536 0.3486 0.3123
Education 02 1.4952 1.1167 0.6564
Age 03 0.5025 0.5360 0.7092
Family income 04 0.1979 0.1421 0.2151
Labor characteristic Gini
Sex GI 0.3304 0.2363 0.2190
Education G2 0.8092 0.5584 0.5506
Age G3 0.5816 0.5798 0.5622
Family income G4 0.5020 0.4820 0.4404
Labor correlation
characteristic
Sex R1 0.6338 0.8819 0.6932
Education R2 0.1036 0.3281 0.3382
Age R3 0.1850 0.4129 0.3131
Family income R4 0.9693 0.5477 0.4301
Contribution term
Sex ,R1G1 0.0740 0.0726 0.0474
Education k2R2G2 0.1253 0.2046 0.1222
Age 413R10 0.0541 0.1283 0.1248
Family income 04R4G4 0.0963 0.0375 0.0407
Wage Gini G. 0.6108 0.5434 0.4876
Explained wage Gini 0G 0.3497 0.4430 0.3351
Rank-weighted error term A 0.2611 0.1004 0.1525
Sources: Calculated from tables 4.20-4.27 appended to this chapter.
160 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.2. The Wage Gini and the Explained Portion of the
Wage Gini, by Location, 1966
1.0 _
430.5 _ 43 peren
0.5 ppercent percent 10.48 31
p~ercent
82
7Bercent 69
percent ~~~~~~percent
Rural Town City
area
2Wage (Gini [G] Explained portion of the wage Gii [Gi ]
Source: Table 4.12.
teristics [Ri]. The factor contribution terms [0&RjGj] measure the
contribution of various labor attributes to the degree of inequality
of wage rates. At the bottom of table 4.12 are shown the Gini coeffi-
cient of the wage rate [GIj, the sum of the four factor contribution
terms [Gi], and the rank-weighted error term [A] which is equal
to G. minus OG. Figures 4.2 and 4.3 graphically summarize the
essential information in this table.
The shaded areas in figure 4.2 represent the explained wage Gini
[&T-1-that is, that portion of the wage Gini that can be explained
by the four characteristics traced in this analysis. The shaded and
unshaded areas together represent the wage Gini EGW]. It can be
seen that the inequality of the wage rate [Gm] consistently declines
from 0.61 for traditional rural areas to 0.54 for semimodern and
semirural towns and 0.49 for modern cities. These magnitudes
indicate, at least for 1966, that modernization was not accompanied
by the increased wage inequality which the Kuznets hypothesis
INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 161
would suggest. The explained wage Gini [O.] accounted for 57
percent of the wage Gini [Gm] for rural areas, 82 percent of that
for towns, and 69 percent of that for cities. The rank-weighted error
terms respectively accounted for 43 percent, 18 percent, and 31 per-
cent of the wage Gini. In other words, the influence of sex, educa-
tion, age, and family income can explain only about 70 percent of
the causes of wage-rate inequality. In this analysis 30 percent can-
not be accounted for by these characteristics."3 By comparing rural
areas, towns, and cities, an inverse U-shaped pattern can be ob-
served in the proportion of the explained inequality [&G,,GJ. That
proportion rises from 57 percent to 82 percent and then declines to
69 percent. Such a pattern suggests that other, unidentified causes
of the inequality of wage rates are more pronounced in rural areas
and large cities than in towns. In towns, however, sex, education,
age, and family influence together constitute a set of causal factors
which can adequately explain the inequality of wage rates. The
following analysis concentrates on this explained portion of wage-
rate inequality-that is, it concentrates on G., not on G,.
The percentage contributions of sex, education, age, and family
income to explained wage-rate inequality [GW] are shown in figure
4.3. The education characteristic, with a simple average of 39 per-
cent for the three locations, makes the largest contribution. The age
characteristic contributes 28 percent, the sex characteristic 17 per-
cent, and the family-influence characteristic 16 percent. Thus educa-
tion and age characteristics together account for about two-thirds
of the explained inequality of the wage rate.
Because the productivity of workers with varying educational
qualifications and experience (proxied by age) is different, the
contribution of these two characteristics to wage-rate inequality
can be viewed as rational or warranted. In contrast, the produc-
tivity differences of workers of different sex and family background
are not as apparent. The contribution of these two factors to in-
equality, unrelated as they are to productivity, can thus be viewed
as irrational or unwarranted. The substantial volume of unwar-
ranted causes, which accounted for about one-third of the explained
inequality, suggests that institutional discrimination against women
13. The unexplained portion of G,. could be further reduced by considering
an additional dimension of the quality of labor, the job or occupational charac-
teristic.
162 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.3. Percentage Composition of Factor Contributions,
by Location, 1966
100
;:4SH~~~~~~~~4
-'50
28
O , .'.,-. '9 ' . 111
Rural Town OiLy
area
Sex (decreasing) [01R,G,] Education (inverse U-shaped) [E2R2G2]
EAge (increasing) [k3RaG3] gFamily income (U-shaped) tk4R4G4]
Source: Table 4.12.
and in favor of members of wealthy families was important in labor
markets. Institutional discrimination declined from 49 percent for
rural areas to 26 percent for cities. In other words, institutional
discrimination was about twice as strong in rural areas as it was in
cities. This evidence thus supports the assumption that moderniza-
tion tends to reduce the discrimination against females and mem-
bers of poorer families. Notice moreover that family influence was
relatively more important than sex discrimination in rural areas,
but that this ranking was reversed in cities. It seems that moderni-
zation removes the bias of family influence faster than that of sex
discrimination.
The contribution of the education characteristic to wage-rate
inequality [&E] was 36 percent for rural areas, 46 percent for towns,
and 36 percent for cities. It thus exhibited something of an inverse U-
shaped pattern. The age characteristic, with values of 15 percent
for rural areas, 29 percent for towns, and 39 percent for cities, never-
INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 163
Figure 4.4. Composition of the Contribution of Education to Explained
Inequality, by Location, 1966
1.5 130O
1.12
1.0 1
08S1
0.65
0.5 -
area
~~Educatzon Gun [02] Education correlation Education weight
....to .... .... Scharacteristic [R,] [(]
Source: Table 4.12.
theless presented an unmistakable increasing pattern. Age and
experience together accounted for more wage-rate inequality in
cities than in rural communities. In the following discussion an
attempt will be made to explain why these two warranted charac-
teristics of age and education exhibited such a pattern. Then the
other two characteristics will be discussed.
THE CONTRIBUTION OF EDUCATION TO INEQUALITY. The data
underlying the analysis of the contribution of education [X2R2C,]
to wage-rate inequality [Gm] is graphically summarized in figure 4.4.
164 THE INEQUALITY OF FAMILY WAGE INCOME
Based on the survey results for 1966, the education Gini [G2] was
0.81 for rural areas, 0.56 for towns, and 0.55 for cities. The educa-
tion weight [02] was 1.50 for rural areas, 1.12 for towns, and 0.65
for cities. These declining values associated with increased urbanity
reflect the high number of educated workers in cities. Both 02 and
G2 contributed to the reduction of 02R2G2 for semiurban and urban
areas. Education's contribution to overall wage-rate inequality
exhibited an inverse U-shaped pattern for the three locations pri-
marily because R2 increased as both 42 and G2 declined. The correla-
tion characteristics [R2] were 0.10 for rural areas, 0.33 for towns,
and 0.34 for cities. In other words, the wage rate was correlated
with educational qualifications to a much higher degree in cities
than in rural areas. The economic interpretation of this evidence is
that the wage rate in cities reflects formal educational qualifications
of workers with a higher degree of sensitivity than it does age, sex,
and other unspecified characteristics. This pattern is precisely what
would be expected in a commercialized urban environment in which
labor markets tend to be somewhat more perfect.
THE CONTRIBUTION OF AGE TO INEQUALITY. As was seen in figure
4.3, the contribution of age [03R]Gs] to inequality [O.] was least in
rural areas and greatest in cities. Although the age Gini was about
0.57 for the three sectors, the weighted correlation characteristic
[43R3] was larger in cities than in rural areas, mainly because the
correlation of age with wage income ER3] was much higher in towns
(figure 4.5). This evidence indicates that older workers, who as-
sumedly were more experienced than their younger counterparts,
participated much more in the urban work force than in the rural.
The value of q53R3 was about 0.22 for both towns and cities. But the
contribution of age to inequality was greater in cities than in towns-
0.39 compared with 0.29-primarily at the expense of the contribu-
tion of education, which was greater in towns than in cities-0.46
compared with 0.36. Thus age and experience began to overtake
education as the most important factor contributing to the inequality
of the wage rate in the cities. The reason probably is that work
experience counted for relatively more in the industrial complexes
of large cities.
By comparing rural areas and urban areas, three tendencies can
be detected in the two warranted characteristics of education and
age. First, the education Gini was lowest in cities and highest in
rural areas, but the age Gini was highest in cities and lowest in rural
INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 166
Figure 4.5. Comnposition of the Contribution of Age to Explained
Inequality, by Location, 1966
1.0
0.71
0.58 0-M 0.54 0X56
Rural Town Ct
area
4ge correlatin
j:Age Girni [0,] ~characteri,stic ER,] WAge weight [4o]
Soure:. Table 4.12.
areas. This pattern means that, when workers with higher formal
education become more abundant, the experienced worker begins
to gain in importance. In figure 4.1 the rural, town, and city situa-
tions for the education Gini are represented by the points R', T',
and C' on the increasing portion of the inverse U-shaped curve
(remember that the formation of a privileged group is indicated by
movement from the point 01 to the left toward the origin). Thus,
when the labor force is modernizing, the development of education
attributes precedes that of experience attributes. Although the age
characteristic still contributes to inequality, the education charac-
teristic begins to contribute to equality. Second, the education
weight [+2] was lowest in cities and highest in rural areas, but the
age weight [¢3] was highest in cities and lowest in rural areas. Con-
sequently, during modernization, age begins to count more heavily
than education in production. Third, the correlation characteristic
166 THE INEQUALITY OF FAMILY WAGE INCOME
[R3] was higher in semiurban and urban areas than in rural areas.
This evidence suggests that the better developed labor market is
more sensitive in rewarding both education and experience in the
commercialized milieu of large cities.
THE CONTRIBUTION OF SEX TO INEQUALITY. As already seen,
institutional discrimination, particularly that against women, was
weaker in cities than in rural areas. The sex contribution term
[EOR0Gl] was 0.074 for rural areas and 0.047 for cities (see table
4.12). Of the factors of this term, the sex Gini [Ga] really is equiva-
lent to the female participation rate. The sex correlation charac-
teristic R,1] represents the correlation between the wage rate and
the maleness of workers. For example, if the pattern of the wage
rates for five workers is given by ($10, $20, $35, $50, $100) and
the sex of these workers is given by (0, 0, 0, 1, 1), the highly posi-
tive correlation [E1] means that male workers get the better paid
jobs. Conversely, if the sex pattern of these workers is given by
(1, 1, 0, 0, 0), the negative correlation reveals that females get the
better paid jobs. A high value of R1 therefore is equivalent to job-
availability discrimination: that is, the more a job pays, the less
it will be available to females. The sex weight [E1] reflects the male
premium in the wage structure: the higher the value of 41, the
higher the degree of discrimination against women.
The contribution of sex to inequality was about the same for
towns and rural areas. The reason for this pattern is that the higher
urban R1 canceled the lower urban G1. More concretely, the female
participation rate in towns, proxied by a G0 of 0.23, was lower than
that in rural areas, proxied by a G1 of 0.33 (figure 4.6). At the same
time, men were getting more of the better paid jobs in towns, proxied
by an R1 of 0.88, than in rural areas, proxied by an R1 of 0.63. In
cities, all three factors work in the relative favor of female workers.
Compared with their counterparts in towns, female workers in cities
had a slightly lower participation rate, obtained more of the better
paid jobs, and benefited from a lower male premium.
THE CONTRIBUTION OF TOTAL FAMILY INCOME TO INEQUALITY. As
with sex discrimination, the wage-rate favoritism for members of
wealthier families was lower in urban areas than in rural areas. The
family-influence contribution term [E4Rf44] was 0.096 for rural
areas, 0.037 for towns, and 0.041 for cities. The family-influence
INEQUALITY OF INCOME OF INDIVIDUAL WAGE EARNERS 167
Figure 4.6. Composition of the Contribution of Sex to Explained
Inequality, by Location, 1966
1.0
0.88
0.69
0.63
0.5-
0.33 0.353.8 0.31
0.23 ~~0.22
oLA
Rural Town City
area
,,Sex correlation
E]Sex Gini EGI] characteristic X IR, Sex weight [o,'
Source: Table 4.12.
Gini [G4] simply is the Gini coefficient measuring the degree of
inequality of total family income. The family-influence weight
['4] measures the wage advantage of members of relatively wealthy
families: the higher the value of 04, the greater the wage-rate dis-
crimination. The family-influence correlation characteristic [R4]
measures the extent to which wealthy families can secure better
paid jobs for their members through nepotism. In effect it is a mea-
sure of job-availability discrimination. In 1966 total family income
was distributed most equally in cities and least equally in rural
areas. The family-influence Gini [G4] was 0.44 for cities, 0.48 for
towns, and 0.50 for rural areas (figure 4.7). It would also appear
that the market mechanisms associated with increasing urbanity
gradually weaken the role of special influence in the award of high-
salary jobs to workers. The correlation characteristic associated with
168 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.7. Coinposition of the Contribution of Family Influence to
Explained Inequality, by Location, 1966
1.0- 0.96
o 4
0.5- 0_44 0_43
Rural Town City
area
Family influence Family influence correlation Family influence
LGini [G4] E characteristic FR4] t weight [E0]
Source: Table 4.12.
family influence [R4] was 0.96 for rural areas, 0.54 for towns, and
0.40 for cities. These factors help explain the decline of nepotism as
a form of institutional discrimination in the commercialized milieu
of urban areas.
Inequality of Family Wage Income:
Third-level Analysis
If a family has more workers or family members with higher
wage-earning power, it will clearly tend to have a higher total wage
income. Assume that there are r types of worker with a pattern of
wage rates given by (wi, w2, . .. , wr). Suppose further that there
are n families. Then let the pattern of total family wage income of
these families be denoted by W = col(W1, W2, ... , W.). Suppose
INEQUALITY OF FAMILY WAGE INCOME 169
that the ith family has xij workers of the jth type. Then:
(4.14a) W = w1X1 + w2X2 + . . . + wrXr, where
(4.14b) Xi = CoI(xli, X2i, . .. , xi) and (i = 1, 2, ... , r)
(4.14c) WI < W2 < ... < W. .
The column vector Xi stands for the pattern according to which
the workers of the ith type are distributed among the n families.
Notice in expression (4.14c) that the n families are arranged in a
monotonically increasing order: in total wage income, the first
family is the poorest, the last family wealthiest. Let G. denote the
Gini coefficient of the distribution of wage income [W] and measure
the degree of inequality of family wage income. Make use of a de-
composition equation of the following form:
(4.15) G. = 0¾R1G1 + ±2R2G2 + ... + 0,RrGr.
In equation (4.15) G. measures the degree of inequality of total
family wage income. The term 4iRiGi will be referred to as the
contribution of workers of the ith type to inequality.
The Gini coefficient EG[] of the labor characteristic vector EXi]
measures the inequality of distribution of workers of the ith type
among families. It will be referred to as the family membership
Gini of the ith type. The term 4i is defined as follows:
(4.16a) W = wltl + w2x2 + . WrXr, where
(4.16b) W = (W1 + W2 ± ...+ + W.)/n and
Xi= (Xli + X2i + ... + x.i) /n, and
(4.16c) 1 = 1+ + 0± . + 4¾, where
(4.16d) 4¾ = w,.ttW. (i = 1, 2, ... ., r)
In equation (4.16b) W is the average wage income of families, and
z, is the number of workers of the ith type per family. Thus 4¾ is
the fraction of wage income per family earned by workers of the
ith type. Call this fraction the wage income weight.
The degree of family wage-income inequality [Gw] can also be
affected by the correlation characteristic between W and Xi. Suppose
there are five workers with a pattern of Ph.D. membership given
by (0, 0, 1, 2, 1). As would be expected, these highly paid workers
are concentrated among the wealthy families: that is, the correlation
between W and Xi is high and positive. If the pattern of Ph.D.
170 THE INEQUALITY OF FAMILY WAGE INCOME
membership were instead given by (1, 1, 2, 0, 0), the family mem-
bership Gini would be the same, but the negative correlation be-
tween W and Xi would obviously contribute to the equality of
family wage income, not to its inequality. When the wage rates of r
types of worker are arranged in a monotonically increasing order
given by (w, < W2 < ... < wr), the first type of worker is the
lowest paid and the last type of worker is the highest paid. With
such a pattern, the low-paid workers would be expected to be con-
centrated among the poor families, leading to a negative correlation
between W and Xi; the high-paid workers would be expected to be
concentrated among the wealthy families, thus leading to a positive
correlation between W and Xi.
Empirical analysis
For purposes of empirical analysis at the third level, forty types
of workers can be identified for the regression equation (4.2). The
number 40 is the product of the number of values assumed by the
sex, education, and age characteristics. Sex has two values: M for
male, and F for female. Education has five values: L for primary
school; I for junior high school; H for senior high school; T for
technical school; and U for university or over. Age has four values:
i for under 25; 2 for 25-45; 3 for 45-60; and 4 for over 60. Thus
the combination of attributes embodied by a homogeneous group of
workers can, for example, be denoted by Ml1LI, which would indicate
male workers under 25 having primary school education, or FT3,
which would indicate female workers aged 45-60 and having tech-
nical school education. To simplify the analysis, the family influence
variable is not used here.
Wage rates for the various types of workers in 1966 were computed
from the following equation:
(4.17a) w = a. + a1x1 + a2x2 + a3x3, where
(4.17b) a, = 13.61, a1 = 5.277, a2 = 1.512, a3 = 3.486 and
(4.17c) x1 = (0, 1), x2= (6, 9, 12, 14,16), X3 = (1, 2, 3, 3).
[sex] [education] [age]
The values of the regression coefficients [ai] in equation (4.17b)
were computed as the average of the rural, town, and city coeffi-
cients of table 4.6, weighted by the sample sizes indicated there.
INEQUALITY OF FAMILY WAGE INCOME 171
When the values of xi in equation (4.1 7c) are substituted into
equation (4.17a), the wage rates [wi] can be computed (table 4.13).
Notice that the wage rate for females under 25 with primary educa-
tion (FL1) becomes negative. The reason is that the term repre-
senting the influence of total family income [a4x4] in equation (4.2)
has been omitted from equation (4.17a). Notice also that the wage
rates in table 4.13 are arranged in a monotonically increasing order.
And because three categories contain no workers (Ff4, FH4, and
FT4), there are thirty-seven wage rates, not forty. The lowest paid
workers were females with primary education under 25 (FL1); their
wage rate [w,] was -3.212. The highest paid workers were males
with university education aged 45-60 (MU3); their wage rate [w37]
was 20.557.
For each category the family membership Gini EGj] reveals the
degree of inequality of family ownership of the workers of the ith
type. For example, suppose that there are five families and the
ownership pattern of female workers with university education aged
25-45 (FU2) is given by (0, 0, 1, 2, 2). The two poorest families
own no workers in this category; such workers are concentrated
among wealthy families. The family membership Gini shows the
degree of inequality of the ownership pattern of workers. For each
category, Ri is the correlation characteristic between the ownership
pattern and total family wage income. A high and positive Ri indi-
cates that the ownership of workers of this type is concentrated in
families with higher total wage income; a negative Ri, in families
with lower total wage income.
To compute the wage income weight [4i] for every category, the
following procedure was used. An estimated pattern of total family
wage income pattern [W = col(Wl, W2, .. , W,)] was computed
from equation (4.14a) to yield:
(4.18a) W = z1XI + 722X2 + ... + I%VVX37,
(4.18b) W = Wl1t + iV2 2+. + .. ±w1X37, and
(4.18c) 1 = 01 + 02 + ... + 037, where
(4.18d) i = wix,/W.
In this estimation the wage rates given by (wii, iiV2, .. ., 137) are
first estimated from the regression coefficients in table 4.6. Thus
the estimated wage income pattern [WV] differs from the actual
pattern. The term oi represents the wage income per family earned
172 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.13. Wages Rates, Family Membership Ginis, and Other Variables
for Thirty-seven Categories of Workers, 1966
Male
Level of education Nota- Under 25 25-45 46-60 Over 60
and variable tion years years years years
Primary school (ML1) (ML2) (ML3) (ML4)
Wage ratea Wi W4 = W=o = W187
2.065 5.551 9.037 9.037
Family membership
Gini 0 0.125 0.110 0.030 0.340
Correlation
characteristic R -0.080 -0.636 0.667 -0.674
Mean of x 0.164 0.426 0.154 0.016
Wage income weight s 0.039 0.272 0.160 0.017
Contribution term ORO -0.0039 -0.019 0.0032 -0.0009
Junior high school (MI1) (MI2) (MI3) (M14)
Wage rate wi W9 = wV6 = Us25 = W24 =
5.521 9.007 12.493 12.493
Family membership
Gini a 0.372 0.380 0.350 0.730
Correlation
characteristic R 0.194 0.655 0.886 0.425
Mean of x 0.021 0.078 0.023 0.001
Wage income weight 4 0.013 0.081 0.033 0.001
Contribution term bRG 0.0009 0.0202 0.0102 0.0003
Senior high school (MH1) (MH2) (MH3) (MH4)
Wage rate wi W15 = W23 = W32 = W31 =
8.977 12.463 15.949 15.949
Family membership
Gini G 0.350 0.380 0.543 0.880
Correlation
characteristic R -0.266 0.942 0.996 0.318
Mean of x 0.027 0.108 0.039 0.0004
Wage income weight q0 0.028 0.155 0.072 0.001
Contribution term ORO -0.0026 0.0555 0.0389 0.0003
Technical school (MT1) (MT2) (MT3) (MT4)
Wage rate wi W21 = W28 = W35 = W34 =
11.281 14.767 18.253 18.253
INEQUALITY OF FAMILY WAGE INCOME 173
Female
Under 25 25-45 45-60 Over 60 Nota- Level of education
years years years years tion and variable
(FLI) (FL2) (FL3) (FL4) Primary school
W1 = W3 = W8 = W7 = Wi Wage ratea
-3.212 0.274 3.760 3.760
Family membership
0.130 0.190 0.280 0.660 G Gini
Correlation
-0.769 -0.842 -0.9253 -0.764 R characteristic
0.196 0.147 0.0361 0.005 x Mean of x
0.073 0.005 0.016 0.002 ( Wage income weight
0.0073 -0.0008 -0.0042 -0.0010 fRG Contribution term
(Fli) (F12) (F13) (F14) Junior high school
w2 w6 = w13 = - wi Wage rate
0.244 3.730 7.216
Family membership
0.240 0.670 0.770 - G Gini
Correlation
0.838 0.910 -0.088 - R characteristic
0.018 0.012 0.001 - x Mean of x
0.0005 0.005 0.001 - k Wage income weight
0.0001 0.003 -0.0001 - cRG Contribution term
(PHI) (FH2) (FH3) (FH4) Senior high school
W5 = W12 - W20 = - wi Wage rate
3.700 7.186 10.672
Family membership
0.400 0.680 0.680 - G Gini
Correlation
0.645 0.985 0.206 - R characteristic
0.017 0.012 0.003 - x Mean of x
0.007 0.010 0.004 - c Wage income weight
0.0018 0.0067 0.0006 - ORG Contribution term
(FT1) (FT2) (FT3) (FT4) Technical school
Wii = wig = W26 = - W; Wage rate
6.004 9.490 12.948
(Table continues on the following pages)
174 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.13 (Continued)
Male
Level of education Nota- Under 25 25-45 45-60 Over 60
and variable tion years years years years
Family membership
Gini G 0.780 0.702 0.850 0.970
Correlation
characteristic R 0.218 0.944 0.953 1.000
Mean of x 2 0.002 0.009 0.004 0.0004
Wage income weight 0 0.003 0.015 0.008 0.001
Contribution term sRG 0.0005 0.0099 0.0065 0.001
University or over (MU1) (MU2) (MU3) (MU4)
Wage rate wi W27 = Ws3 = W37 = W36 =
13.585 17.071 20.557 20.557
Family membership
Gini G 0.846 0.630 0.569 0.870
Correlation
characteristic R 0.366 0.968 0.967 0.840
Mean of x 0.002 0.030 0.018 0.002
Wage income weight q 0.003 0.059 0.043 0.005
Contribution term pRG 0.0009 0.0360 0.0237 0.0037
- Not applicable.
Sources: Calculated from tables 4.20-4.27 appended to this chapter.
a. In thousands of N.T. dollars; i is the wage rank.
by workers of the ith type expressed as a fraction of the estimated
average family income [EWJ]. The values of 4i add up to one. For
all thirty-seven categories, the contribution of workers of the ith
type to inequality was 0.2060 (see table 4.13). This value is the
Gini coefficient of total family wage income [EOT] for the estimated
wage pattern [EW] of equation (4.18a) .14 The values of oi, Ri, and
OiRiGi are plotted against the wage rate in figures 4.8-4.11.
In figure 4.8 the contribution of the thirty-seven grades of labor
[FiRiGi] to the inequality of total family wage income [GE] is
14. We are not concerned in this section with the difference between the true
G, and G,,-that is, with the unexplained portion of G,, measured by G.,, -G.
INEQUALITY OF FAMILY WAGE INCOME 175
Female
Under 25 25-45 45-60 Over 60 Nota- Level of education
years years years years tion and variable
Family membership
0.780 0.890 0.930 - G Gini
Correlation
-0.474 0.787 0.752 - R characteristic
0.001 0.002 0.0004 - x Mean of x
0.001 0.002 0.001 - 4 Wage income weight
-0.0004 0.0014 0.0007 - 4RG Contribution term
(FU1) (FU2) (FU3) (FU4) University or over
W14 = W22 = W30 = W29 M wi Wage rate
8.758 12.244 15.730 15.730
Family membership
0.850 0.820 0.920 0.960 G Gini
Correlation
0.804 0.915 1.000 0.903 R characteristic
0.002 0.004 0.0013 0.0004 t Mean of x
0.002 0.006 0.002 0.001 4 Wage income weight
0.0014 0.0045 0.0018 0.001 4RG Contribution term
measured on the vertical axis. The grade of a particular type of
labor corresponds to its rank in the wage-rate structure and is mea-
sured on the horizontal axis. The nine types of labor below the hori-
zontal axis-that is, those having a negative 4iRiGi-contribute to
equality, not to inequality. They constitute the so-called marginal
labor force: the poorly educated male and female workers who are
either very young and have little work experience or are very old
and near retirement. The exception to this characterization is the
category of poorly educated male workers aged 25-45 (ML2) who
constitute the bulk of the unskilled labor force.
The dotted horizontal line aa' divides the types of workers who
contribute to inequality into two groups. Those above the line
essentially are male workers in their prime age-that is, 25-60. The
exceptions are highly educated females in their prime age (FU2
and FH2)-that is, 25-45. This group, which can be referred to as
176 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.8. Contribution to Family Wage Income Inequality, by
Labor Grade, 1966
0.015 - MH2
MH3
*MU2
M U3
M12
MI3 MT2
0.010
MU1
FH2 MT3
* a
MTi
0.005 _
a ~~~~~~~* FU2
FI2 MLS MI4 MH4 M a'
* MU4
a FHI . FUI FT2 IT4
Mu PU. FH3 PT3 FUM4
FII **U
. F13 10 15
FL4 * FT1 Wage rate [wi]
* MH1 (thousands of N.T. dollars)
MLI
* FL3 . ML4
-0.005 -
FL1
*FPI,
-o.oiLa
Source: Table 4.13.
the prime age group, makes a heavy contribution to inequality. It
accounts for more than 100 percent of the inequality of family wage
income (0.2135/0.2060 = 1.036). Its contribution adds up to more
INEQUALITY OF FAMILY WAGE INCOME 177
than 100 percent because the marginal labor force contributes to
equality.
Given the foregoing conclusion, a sharp distinction can be drawn
between two issues which are sometimes confused: the degree of
inequality of family wage income; the welfare of the marginal labor
force. Government relief or welfare measures-for example, minimum
wage legislation-may represent attempts to help the marginal
labor force, but they do little to resolve the basic inequality of
family wage income. In other words, even if the welfare problem
were solved, the degree of inequality of total family wage income
would remain essentially unchanged. The reason for this outcome
is that the inequality of family wage income is a condition that
centers mainly around workers in the prime age group.
The correlation between the wage rate, or labor grade, and its
contribution to inequality is significant and positive (see figure 4.8).
It can be imagined that the labor force in a traditional society is
homogeneous and that the wage rate is low. Industrialization then
brings about wage increases as the labor force begins to be differ-
entiated. The impact of such modernization is mainly directed at
the prime labor group. The emergence of high-grade laborers and
the increase in their number represent the major causes of family
wage-income inequality.
The positive correlations in figures 4.9 and 4.10 explain the posi-
tive correlation between Wi and &iRiGi. First, the positive correla-
tion between the wage rate [We] and the degree of inequality of
family ownership of workers of various grades [Gi] in figure 4.9
means that low-grade laborers are more evenly distributed among
families than are laborers of higher grades. Put differently, as the
higher grade laborers come into being, they are acquired by a mi-
nority of families. Second, the positive correlation in figure 4.10
between the wage rate [Wi] and the degree of correlation between
total family wage income and family ownership of labor [Ri] sug-
gests that the laborers of higher grades are acquired by wealthy
families that have a higher total wage income. The inequality of
family ownership of high-grade laborers thus rnust be regarded as
the most imnortant cause of family wage-income inequality.
Economic development can affect the inequality of family wage
income through another set of factors which are purely economic.
Consider this example. The mean values of the number of workers
of various grades per family are denoted by xi (see table 4.13). If
N is the total number of families-N is equal to 2,379 in table 4.13
178 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.9. Inequality of Family Ownership of Labor of
Different Grades, 1966
FU 4 MT4
1.00 - FT3 . 0
FT2 * FU3 MT MU4
FUl ~FU2 * MT3
FUI. * MT1 * 'MUl MH4
0
7U FH2 FH3 *M14 .MT2
0 AT
LJ*MU2 MU3
0
3 0.50 MH3
o M12 MH2
M13
0 I
5 10 15 20
Wage rate [wi]
(thousands of N.T. dollars)
Source: Table 4.13.
-then the number of workers of various grades supplied by families
to industry is denoted by Nxi, where i = 1, 2, .. ., 37. Industrial
demand, labor supply, and discrimination determine the structure
of the wage rates [W] which in turn determines the structure of
wage income weights [Ei(:
(4.19) (, .. . ., £37) = (WIXI/W, W2X2/W7 .V . , W37X37/W).
[see equation (4.16d)]
The structure of wage income weights thus reflects demand and
supply for various grades of labor for the whole country.
The values of 4i are plotted against the wage rate in figure 4.11.
These wage income weights measure the contribution of the various
grades of labor to the inequality of family wage income, as traced
INEQUALITY OF FAMILY WAGE INCOME 179
Figure 4.10. Correlation Characteristics between Total Famiily Incomie
and Famnily Otnership of Labor, 1966
FH2 BH2 FU3. MHS MT4 MU3
1.0 H
*FI2 FU2 .: MT2' . M2 MTS
Fll ~~FUi M13 FU4M4
* Fll * FT2 *FT3 MU4
* FHI
M12
m 0.5 _M14
* MU1 .MH4
FHS- *MT1
C
C
I I I.
5 *FI3 10 15Wage
ao ~ ~ ~~~~~~~~~~~aerate [wi]
-~ * (thousands of N.T. dollars)
Ml *MHl
*FT1
-0.5 -
ML2 *ML4
FL1 MLl .L4
' FL2
*oFL3
-1.0_
Source: Table 4.13.
to their respective economic importance arising from their large
size, high wage, or both. In this sense, workers in the prime age are
all economically important, as is seen from the fact that the values
of ki are relatively high for them. As a general rule, these workers
contribute heavily to inequality. There nevertheless are two excep-
tions: low-educated males in their prime age (ML2 and ML3).
They are economically important because of their large numbers,
but they do not contribute heavily to inequality because they are
180 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.11. The Economic Weight of Different Grades of Labor, 1966
0.20
MIL2
ML3
Pt¢0. 1 - H
O.1C _
FLI
* FL1 . MI2 MHS *MTSH
*MU2
0.05 MLI MMUS
MH1
FL3 MI1 F AIML4 FU2 MT2 FUS
FII FHI * FH2 TFS U U
*FL2S :FIFT1 FT2,FHS MUI AMH4T41.MU4
0 FL4 5 FIS t1 oTMI4\ 15a 20
FUl MT1 FTS FU4
Wage rate [wi]
(thousands of N.T. dollars)
Source: Table 4.13.
mnore evenly distributed among families. As a result, family owner-
ship of highly educated, prime-age workers contributes most to the
inequality of family wage income.
Family size and composition
The inequality of family wage income is related in part to such
economic causes as the demand for, and the supply of, labor having
different characteristics, in part to such demographic causes as the
INEQUALITY OF FAMILY WAGE INCOME 181
rules governing the formation of families having different member-
ship compositions. Thus the foregoing empirical analysis of the
causes of inequality of family wage income merely scratches the
surface of complex economic and demographic phenomena. Con-
sider some aspects of demographic phenomena. The sex composition
of a family is influenced by institutions of monogamous and polyg-
amous marriage and by biological laws of reproduction. The age
composition of a family is influenced by rules governing the forma-
tion of nuclear families, the age at first marriage for males and
females, the age at which couples start a new family, and the sup-
port of aged parents and grandparents.'5 The educational composi-
tion of a family is influenced by that family's investment in the
education of its members. What is needed, then, is a positive theory
of family formation that can more satisfactorily explain the inequal-
ity of wage income. By positive is meant a theory based on tested
and systematized experience, not on speculation.
To illustrate the kind of theory required, this discussion concen-
trates on the educational dimension of the labor force. Note that
education is the most important labor characteristic influencing the
inequality of family wage income.
For each educational attribute the weighted averages of oi, Ri,
and Gi (weighted, that is, by sample size) from table 4.13 are plot-
ted against the weighted average of the wage rates [wi] in figures
4.12, 4.13, and 4.14.16 When the educational qualifications of labor
increase from primary education, for which the wage rate [wi] was
3.32, to university education, for which the wage rate was 17.5, the
distribution of the family ownership of labor becomes more unequal
-that is, Gi increases with education in figure 4.12. At the same
time, the ownership of high-quality labor is more concentrated in
the high wage-income families-that is, Ri increases with education
15. The rules governing the formation of families with respect to sex and
age are obviously linked. For example, if a female marries at an earlier age than
a male, both the age and sex structure of the family would be affected. More-
over different societies have different rules governing the extent to which the
young and old establish their own households or stay on as members of the
nuclear household. These differences introduce the possibility of bias in all Gini
measures.
16. For each variable in table 4.13 the weights are X,/S:, 2`2/8s} ... X Xr/:xy
where sr = XI + x2 + . . . + Zr. In words, the weights represent the percentage
of the labor force for the various types of labor in each educational category.
182 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.12. Weighted Average of the Education Gini plotted
against the Average Wage Rate, by Level of Education, 1966
1.00 _
Gini coefficient [Gj] 0.,819
0.75 0.6-549
0.5 - 0.3851
0.25 - 0.1 260
Primary 5 Junior 10 Senior Technical University 20
school high high school (w5 = 17.5)
(w, = 3.3) school school (w4 = 14.1)
(w2 = 7.6) (w3 = 11.6)
Wage rate [wi]
Source: Table 4.13.
Figure 4.13. Weighted Average of the Education Correlation
Characteristic Plotted against the Average Wage Rate,
by Level of Education, 1966
Correlation characteristic [Ri]
0.9933
1.00 007713 _ A
0.077597 0
0.546 __
0.25 - 0617 y
Primary 5 Junior 10 Senior Technical University 20
school high high school (ws = 17.5)
(w, = 3.3) school school (W4 = 14.1)
(W2 = 7.6) (w3 = 11.6)
Wage rate [wi]
Source: Table 4.13.
INEQUALITY OF FAMILY WAGE INCOME 183
Figure 4.14. Weighted Average of the Education Weight Plotted
against the Average Wage Rate, by Level of Education, 1966
0.150 0.1432
0.125 - Weight [*i]
0.100 \
0.075 4
0.050 I 0.0436
0.025F 0.0094I0.005s
0 Primary 5 Junior 10 Senior Technical University 20
school high high school (W5 = 17.5)
(w, = 3.3) school school (W4 = 14.1)
(*2 = 7.6) (W3 = 11.6)
Wage rate [wi]
Source: Table 4.13.
in figure 4.13. The pattern of the wage weight [0&] is U-shaped-
that is, 4i decreases and then increases with education in figure 4.14.
In addition to the issue of how much every term uiRiGi con-
tributes to inequality when the patterns above are empirically
given, the theoretical issue is how these patterns are determined in
the first place. Families may or may not have different numbers of
wage earners. When all families have the same number of workers,
the size characteristic is uniform; otherwise it is nonuniform. Simi-
larly the educational qualifications of workers in individual families
may or may not be the same. When all workers in individual fam-
ilies have the same educational qualifications, the composition
characteristic is homogeneous; otherwise it is nonhomogeneous.
Four cases will be examined here: uniform size and homogeneous
composition; uniform size and semnihomogeneous composition;
nonuniform size and homogeneous composition; descending size and
homogeneous composition. These four cases indicate the analytical
issues in a theory which explains the patterns of ckj, Ri, and Gi in
relation to wi for various labor characteristics.
184 THE INEQUALITY OF FAMILY WAGE INCOME
THE UNIFORM-HOMOGENEOUS CASE. It is assumed for the uniform-
homogeneous case, the simplest of the four cases, that there are
ten families and that every family owns three workers (table
4.14). The first five families own only low-education workers;
three families own only medium-education workers; two families
own only high-education workers. Thus, of the thirty workers,
Table 4.14. The Inequality of Wage Income: Numerical Example
of Uniform Family Size and Homogeneous Family Composition
Family composition
(number of members)
Medium High Total
Low educa- educa- wage
Family number and variable education tion tion income
Family 1 3 0 0 60
Family 2 3 0 0 60
Family 3 3 0 0 60
Family 4 3 0 0 60
Family 5 3 0 0 60
Family 6 0 3 0 90
Family 7 0 3 0 90
Family 8 0 3 0 90
Family 9 0 0 3 165
Family 10 0 0 3 165
All families 15 9 6 900
Workers per family [xi] 1.5 0.9 0.6 -
Wage rate [WOi 20 30 55 -
Wage share [0j] 0.333 0.300 0.367 -
Gini [Gj] 0.500 0.700 0.800 -
Pseudo Gini [0G] -0.500 0.300 0.800 -
Correlation characteristic [Ri] -1.000 0.429 1.000 -
Wage Gini [G.] - - - 0.217a
- Not applicable.
Source: Constructed by the authors.
a. G7D = otAzG + lO.R-G.G + 4ehRhGh
= 0.333 X -1.000 X 0.500 + 0.300 X 0.429 X 0.700 + 0.367
X 1.000 X 0.800.
INEQUALITY OF FAMILY WAGE INCOME 185
fifteen have low education, nine have medium education, and six
have high education. The average number of workers [Xi] of the
first type per family is 1.5; that of the second type 0.9; that of the
third type. 0.6. The proportionality of these numbers reflects in-
dustrial demand. For example, the fifteen workers of the first type
might be skilled or unskilled workers; the nine workers of the second
type might be white-collar workers; the six workers of the third
type might be engineers. The pyramiding pattern of the supply of
workers having certain educational attributes, given by (x1 > x2 >
X3), shows that industry generally absorbs fewer highly educated
workers than it absorbs lowly educated workers. The pattern of the
wage rate for the three types of workers is ascending: the hypo-
thetical wage rate is $20 for workers with low education, $30 for
those with medium education, and $55 for those with high education,
that is, (wi < w2 < W3). The pattern of the values of the wage share
is U-shaped: q1 is 0.33; 02 is 0.30; Oa is 0.37 (see figure 4.17 below).
The empirically observed U-shaped pattern of 4i in figure 4.14
reflects the pyramiding pattern of worker numbers and the ascend-
ing pattern of the wage rate for higher educational qualifications.
After the grade of technical education, the curve turns up because
the effect of increasing wages overwhelms the effect of diminishing
numbers. This U-shaped pattern of the wage share [:+] over the
wage rate for increasing educational qualifications clearly is the
result of the economics of industrial demand and supply. The pat-
tern of family ownership of labor essentially is irrelevant. A positive
theory of industrial supply and demand therefore underlies the
explanation of the pattern of Oi in the sense that they constitute
the economic forces determining the diversity of wage rates as well
as the numbers of workers receiving different levels of wage income.
For the uniform-homogeneous case the values of the Gini coeffi-
cient [Gi] reveal an increasing pattern when plotted against the
wage rate for workers having increasing educational qualifications:
the hypothetical Gini coefficient is 0.50 for low education, 0.70 for
medium education, and 0.80 for high education. This increasing
pattern is the result of the pyramiding pattern of the mean number
of workers of a particular educational grade per family [xi] and the
labor force's uniform size characteristic and homogeneous composi-
tion characteristic. Under the assumptions implicit for the uniform-
homogeneous case, workers with low education are more equally
distributed among families than are workers with high education,
simply because more workers are in the low-education category.
186 THE INEQUALITY OF FAMILY WAGE INCOME
The empirically observed pattern of the Gini coefficient [Gi] in
figure 4.12 bears this relation out, except for the dip for university
education, which will be explained later.
To determine the rank correlation characteristic [Ri] for the
uniform-homogeneous case, the total wage inconme of families is
used. The hypothetical values of Ri in table 4.14 show an increasing
pattern: R1 is -1; R2 is 0.43; R3 is 1. This increasing pattern directly
results from the ascending pattern of the wage rate for higher edu-
cational qualifications and the labor force's uniform size charac-
teristic and homogeneous composition characteristic. Under the
assumptions for this case, high-income families own highly educated
workers, a situation which leads to a high correlation between total
wage income and the pattern of family ownership of labor; low-
income families own lowly educated workers, a situation which
leads to a low correlation between total wage income and the pat-
tern of family ownership of labor. This conclusion is borne out by
the empirically observed pattern of Ri in figure 4.13.
The uniform-homogeneous case thus can adequately explain all
the observable patterns of the causes of the inequality of total wage
income, which causes are summarized in figures 4.12, 4.13, and 4.14. Its
real meaning is that the family is insignificant as a unit of labor
ownership, as it will always be when the assumptions of the uniform-
homogeneous case are satisfied. If family affiliation is completely
disregarded and the Gini coefficient is computed for the thirty
workers as individuals, the value of Gi becomes 0.217. Such a Gini
coefficient measures the inequality of the wage rate and corresponds
to the second level of analysis in the earlier sections of this chapter.
Observe that this inequality of the wage rate is exactly the same as
the inequality of family wage income. This equivalence indicates
that a theory of the inequality of the wage rate is tantamount to a
theory of the inequality of family wage income. Thus, for the edu-
cation characteristic, the theory of the inequality of family wage
income is almost completely economic and only slightly demographic:
that is, the impact of education on family wage income is deter-
rnined by the forces of labor supply, industrial demand, and institu-
tional discrimination, not by the forces of family formation.
THE UNIFORM-SEMIHOMOGENEOUS CASE. For the uniform-semi-
homogeneous case it is assumed that all families have the same
number of workers. With respect to the composition characteristic,
however, the behavioristic hypothesis is that the family unit exerts
INEQUALITY OF FAMILY WAGE INCOME 187
Table 4.15. The Inequality of Wage Income: Numerical Example
of Uniform Family Size and Semihomogeneous Family Composition
Family composition
(number of members)
Medium High Total
Low educa- educa- wage
Family number and variable education tion tion income
Family 1 3 0 0 60
Family 2 3 0 0 60
Family 3 3 0 0 60
Family 4 2 1 0 70
Family 5 2 1 0 70
Family 6 1 2 0 80
Family 7 1 2 0 80
Family 8 0 2 1 115
Family 9 0 1 2 140
Family 10 0 0 3 165
All families 15 9 6 900
Workers per family [xi] 1.5 0.9 0.6 -
Wage rate [Wil 20 30 55 -
Wage share [0i] 0.333 0.300 0.367 -
Gini [Gi] 0.447 0.500 0.767 -
Pseudo Gini [Gi] -0.447 0.233 0.767 -
Correlation characteristic [Ri] -1.000 0.466 1.000 -
Wage Gini [G.] - - - 0.202a
- Not applicable.
Source: Constructed by the authors.
a. G. = kiRiG, + (mR,.G. + OhRhGh
= 0.333 X -1.000 X 0.447 + 0.300 X 0.466 X 0.500 + 0.367
X 1.000 X 0.767.
pressure on all its members to acquire about the same level of educa-
tion (table 4.15). The homogeneous case manifests the extreme
form of such pressure. Here that pressure is more mild, and the
education of family members is restricted to adjacent levels of
attainment. Because the total number of workers for each level of
attainment is the same as in the previous case, the values of the
188 THE INEQUALITY OF FAMILY WAGE INCOME
Figure 4.15. Gini Coefficients in Four Cases Plotted
against the Wage Rate, by Level of Education
r .00 A Nonuntform homogeneous case Uniform homogeneous case
0.75 -___
0.50
a0 7'k
Descending homogeneous case
0.25 Unform semihomogeneous case
w, = 20 W2 = 30 Ws = 55
(L) (M) (H)
Wage rate [wi]
Sources: Tables 4.14-4.17.
wage share [E] are unchanged. The economic aspect for the deter-
mination of 4i therefore is the same in both cases.
The Gini coefficient and the correlation characteristic maintain
the same increasing pattern in the uniform-semihomogeneous case
as in the uniform-homogeneous case. The values for these variables
are plotted against the wage rate in figures 4.15 and 4.16. Note in
these figures that the only apparent impact of the semihomogeneous
case is to make the distribution of workers more equal for each
educational category-that is, for every category Gi is lower in
this case than in the homogeneous case. Thus the uniform-semi-
homogeneous case probably provides a better explanation of the
empirical reality observable in the patterns of figures 4.12, 4.13,
and 4.14.
What then produces that decline in the Gini coefficient for workers
with university education in figure 4.12? The Taiwanese greatly
value a university education. Moreover, the policy of government
for higher education enables persons from all classes of society to
obtain a university degree. As a result, workers with a university
education tend to be more equally distributed among families than
workers with technical education.
INEQUALITY OF FAMILY WAGE INCOME 189
Figure 4.16. Correlation Characteristics in Four Cases Plotted
against the Wage Rate, by Level of Education
Uniform homogeneous case
m1.00
Uniform semihomogeneous case \ -
0.75 -
.4 U.b- 0 ; Nonuniform homogeneous case
0.25 w,= 20 I
W2 =30 W3 55
-0.25 - T (M) (H)
<-0.50 //4sX Wage rate [wi]
o-0.75 \
C) -0.75Descending homogeneous case
- 1.00
Sources: Tables 4.14-4.17.
Figure 4.17. Weights in Four Cases Plotted against the Wage Rate,
by Level of Education
0.40 - All cases
''0.30 - A
f 0.20
be
0.10
w1 ==20 W2 =30 W3 55
(L) (M) (H)
Wage rate [wi]
Sources: Tables 4.14-4.17.
190 THE INEQUALITY OF FAMILY WAGE INCOME
THE NONUNIFORM-HOMOGENEOUS CASE. For the nonuniform-
homogeneous case it is assumed that the number of workers is
different for families, but that the educational qualifications of all
workers in a family are the same. Once again, the values of 'i are
unchanged so that the other aspects of differences between this case
and the uniform-homogeneous case can be concentrated on. What
differs is that total family wage income no longer is in a monoton-
ically increasing order (table 4.16). The reason for this change is
that large families with low-grade workers can earn more wage
income than small families with high-grade workers. For each
educational category the distribution of workers among families is
more unequal than in the two preceding cases (see figure 4.15).
What also differs is that the pattern of the correlation characteristic
[Ri] significantly changes: for the low-education category Ri is
higher than in the preceding cases; for the high-education category
it is lower (see figure 4.16). As with the uniform-semihomogeneous
case, the nonuniform-homogeneous case is a more realistic explana-
tion of the observed patterns in figures 4.12-4.14 than is the uniform-
homogeneous case.
THE DESCENDING-HOMOGENEOUS CASE. For the descending-homo-
geneous case it is assumed that the educational qualifications for
all workers in a family are the same, but that the number of workers
differs in accord with the impact of a new behavioristic hypothesis:
families with low-grade workers tend to be larger than those with
high-grade workers. Under this assumption the ranking of families
by total wage income is completely reversed (table 4.17). Both the
Gini coefficient [Gi] and the correlation characteristic ERi] decline
as the educational level of workers increases. The observed empirical
reality of figures 4.12 and 4.13 contradicts these patterns. Yet, in
figure 4.13, Ri is positive for even the lowest level of education-a
fact that is inconsistent with the assumptions of the first three cases.
This evidence suggests that the behavioristic hypothesis of this
case must, at best, be operating mildly. It may thus be concluded
that the economic model of the uniform-homogeneous case provides
the main explanatory framework for empirical reality and that the
demographic forces of family formation of the other cases can only
serve to moderate this basic pattern.
The similarity of patterns in the numerical examples and the
INEQUALITY OF FAMILY WAGE INCOME 191
Table 4.16. The Inequality of Wage Income:
Two Numerical Examples of Nonuniform Family Size
and Homogeneous Family Composition
Family composition
(number of members)
Low Medium High Total
education education education wage income
Family number Exam- Exam- Exam- Exam- Exam- Exam- Exam- Exam-
and variable ple 1 ple 2 ple 1 ple 2 ple I ple 2 ple I ple 2
Family I 1 1 0 0 0 0 20 20
Family 2 2 2 0 0 0 0 40 40
Family 3 3 3 0 0 0 0 60 60
Family 4 4 0 0 2 0 0 80 60
Family 5 5 4 0 0 0 0 100 80
Family 6 0 0 2 3 0 0 60 90
Family 7 0 5 3 0 0 0 90 100
Family 8 0 0 4 0 0 2 120 110
Family 9 0 0 0 4 2 0 110 120
Family 10 0 0 0 0 4 4 120 220
All families 15 15 9 9 6 6 900 900
Workers per
family [si] 1.5 0.9 0.6 -
Wage rate [Wi] 20 30 55 -
Wage share [W] 0.333 0.300 0.367 -
Gini [Gi 0.633 0.744 0.833 -
Pseudo Gini [Gj] -0.180 0.278 0.767 -
Correlation
characteristic
[Ri] -0.284 0.374 0.921 -
Wage Gini [G.] - - - 0.304a
- Not applicable.
Source: Constructed by the authors.
a. = G=RIG, + 4urnRm.G + 4hRhGh
= 0.333 X -0.284 X 0.633 + 0.300 X 0.374 X 0.744
+ 0.367 X 0.921 X 0.833.
observed evidence does not imply that the examples explain the
evidence. A more rigorous explanation requires an abstract for-
mulation of the ideas embedded in the numerical examples. The
effort here has been restricted to pointing out the kind of behav-
192 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.17. The Inequality of Wage Income:
Two Numerical Examples of Descending Family Size
and Homogeneous Family Composition
Family composition
(number of members)
Low Medium High Total
education education education wage income
Family number Exam- Exam- Exam- Exam- Exam- Exam- Exam- Exam-
and variable ple I ple 2 ple I ple 2 ple 1 ple 2 ple I ple 2
Family 1 5 0 0 0 0 1.5 100.0 82.5
Family 2 5 0 0 0 0 1.5 100.0 82.5
Family 3 5 0 0 0 0 1.5 100.0 82.5
Family 4 0 0 3 0 0 1.5 90.0 82.5
Family 5 0 0 3 3 0 0 90.0 90.0
Family 6 0 0 3 3 0 0 90.0 90.0
Family 7 0 0 0 3 1.5 0 82.5 90.0
Family 8 0 5 0 0 1.5 0 82.5 100.0
Family 9 0 5 0 0 1.5 0 82.5 100.0
Family 10 0 5 0 0 1.5 0 82.5 100.0
All families 15 15 9 9 6.0 6.0
Workers per
family [x,] 1.5 0.9 0.6 -
Wage rate [Wi] 20 30 55
Wage share [fi] 0.333 0.300 0.367 -
Gini [Gj] 0.700 0.600 0.600 -
Pseudo Gini [0G] 0.700 0.100 -0.600 -
Correlation
characteristic
[Ri] 1.000 0.143 -1.000 -
Wage Gini [G.] - - - 0.043,
- Not applicable.
Source: Constructed by the authors.
a. G. = nRzGi + mRmGm + O6hR)Gh
= 0.333 X 1.000 X 0.700 + 0.300 x 0.143 X 0.700 + 0.367 X
-1.000 X 0.600.
ioristic hypotheses that need to be made and tested about the rules
of family formation if future analysis of the inequality of family
wage income is to be improved.
DATA ON THE DISTRIBUTION OF FAMILY INCOME 193
Conclusion
In this chapter an attempt has been made to demonstrate that
the analysis of the inequality of wage income can be traced to the
nonhomogeneity of the labor force and the membership composition
of families. The complexity of the problem required a multidimen-
sional cross-listing of data. It also required the conceptual separation
of inequality into several levels: the inequality of wage rates, in-
dividual wage income, and family wage income. It further required
the design of a special analytical framework that combined the
regression technique with the additive factor-components tech-
nique to process the data at each level. Finally, it required the
formulation of new behavioristic hypotheses in areas tangential to
traditional economic analysis, such as demography and sociology.
At the pretheoretical stage which characterizes this work to date,
much effort has gone into the measurement of inequality as an
inductive device to examine empirical evidence, rather than into
deductive reasoning. This effort should, in turn, help to identify
pertinent behavioristic hypotheses which will be needed to determine
the inequality of income distribution in the theoretical context of a
formal model. Here, only a modest beginning has been made in
the formulation of an analytical framework that incorporates the
techniques of data generation and processing and the rudiments of
theoretical ideas and hypotheses. Clearly, much work remains to
be done.
Appendix 4.1. Data on the Distribution
of Family Income in Taiwan
By standards of developing countries, statistical data on the
distribution of family income in Taiwan is quite satisfactory. Since
1964 there has been a major effort to collect such data on a large
scale. This effort has led to the annual publication of reports on the
survey of family income and expenditure-reports which constitute
the main source of published data.17 This data, collected by the
17. DGBAS, Report on the Survey of Family Income and Expenditure.
194 THE INEQIUALITY OF FAMILY WAGE INCOME
Directorate-General of Budget, Accounting, and Statistics since
1964, will be collectively referred to as DGBAS data. In 1970 the
collection of data for the municipality of Taipei became the responsi-
bility of the Bureau of Budget and Statistics of the municipal
government of Taipei.
Primary data
The DGBAS data is based on information contained in the primary
questionnaires (schedules 4.1-4.4). These elaborate questionnaires
consist of some 750 questions set up in 750 cells and are to be filled in
for every family interviewed. The questions cover such topics as
composition of household population, general status of family
equipment, current family income, current family expenditure, family
capital income and expenditure, agricultural capital income and
expenditure, and a detailed breakdown of family consumption
expenditure. The sample size-that is, the number of families inter-
viewed-and the sample size as a fraction of the population appear
for various years in table 4.18. The number of families interviewed
was 3,000 in 1964; it increased to about 6,000 by 1973.
Based on the processing of the primary questionnaires, a typical
DGBAS annual report contains about 700 pages of tables. The informa-
tion in these tables provides a much broader coverage than is
necessary for most studies of the distribution of family income.
Table 4.18. Size of Sample for DGBAS Surveys, 1964-73
Percentage
of
Year Families population
1964 3,000 0.146
1966 3,000 0.132
1968 3,000 0.126
1970 3,600 0.160
1972 5,730 0.204
1973 5,790 0.202
Sources: DGBAS, Report on the Survey of Family Income and Expenditure,
various years.
Schedule 4.1 Record of Family Interview on Income
and Expenditure, Page One, 1966
Stratum Cluster |Household A f th Occupation f the Number Con-
OO* flu. no* incom~Ae ha of the ~ch head Seh Huehl
no.i|o.| o.fncomeof head of of ns mptio Savings
househlb oold ld household PoPulaton esn xed
b. seb Id ~ ~ mplye itnec
Name of Hsien Hsiang Vill ge .in Household
household head Address_ Town _ Li
City Road _ Section_ .AlDey T..Lne_No._
Distric.t RStreet _
Occupation essential second Amount of
e o 3f 2t i n N h h asinine ort is S
o ;; s , -4 2 ment he holds ment he holds expendi- income .:: S
a ~ ~ Sx -
- ~~~~~oo _ i ~~~~~~f~Theilol . itiLi
_ 5, F _ _ _ I I I I I iti
r:.g;] S 2 ] | [ ; 1 ~~~~~~~~~et'abi h- x
Day BadrNumber | Monthly cost|
Relatianship Lodger boarder Bore ofrs onh Annual of free meals|
} to the | ~~~~~~pending charge charge f for relstives,|Rsa}
Sexseod adult amoont amount workers, and
SexAge Sex Age Sex t Age men Bervants
s Domestic|- - | | | |
t servants l- - - - -Lg Day Boa- , Number Monthly cost
| fW |_|_|_|_|_|_l co,es-totl nd susac
= Ruainens.- ding e a e-_-e-_R_ark
D employces - -|=|=|=|=|=
1 Farm
employees -I-I_I_I_I_1 -1 1 1-
.9 Relatives _____ _ _ _I_ _ _ _ _ __I_ _
S.arce: msa-, Reporl on the Srreey of Family Ixcome and Bope-dilore, 1966.
195
Schedule 4.2. Record of Family Interview on Income
and Expenditure, Page Two, 1966
Electrical Television sets: Electric fans: Radio: Air conditio.ers:
erluipsema H-Roushold - -W" -m
HEi equipmehn reorigerat: Pick-up: Electric cooker: Washn
Ice box: Sewing machines: Camera: T aest
appliance __ _ _ __ _ _ _ __ n -so e
Transport t.bc"
O E equi pment Motor bicycle: Bicycles: Pedicab: Sedan:
Cultural uuage | Newspaper: Magazine:
Income amount
Name Kinds Periodical income
oa of and - - T Otker Amount retained Amount for
> income ofu Total Monthly (including for personal use ily consumption
=_ maker incoe or Annual temporary
_ 8CO quartsrly income)
Ei X
A ~~~~~~~~~~Amount yearly
.= El Item |nkCi°ndm1 YtiemrenY o°f each 1 income Item | Injome Yearly of each income
I time, total ~~~~kind times ltime totsl
n e ~~~~~~~~~~~~~~~Interest
Net | _ -_-
Ei operating Investment
m.Icome___
Tranafers from
§ _________ ______ hounehold
._ Net proton- Transfers from
2 sional income government
Net T~~~~~~~~~~reansfero frmm
c agncNueltural l | | enterprise | 1 I
agricultural Transfers from
V ______ l abroad
R Rent Others
_ _ , ~~~~~~~~~~~~~~~~~~Expendi ture l
amount
Item Illustrations of various items Monthly Yea Remarks
| quarterly total
Total I I
_Riee l (omitted)
F a Floure
s Sweet potato _ _ _____
O ) e l | Other cereals
-n Subsidiary food
lo MIlk
w Condiment
Eating out
-- l ;Dinners for festivals
Marriages, births, birthdays,
to ( funerals, and feasts
|4 |Noaleoh oli l
A Nlcoholic
S Tobacco
Scoree: Same as for schedule 4.1.
196
Schedule 4.3. Record of Family Interview on Income
and Expenditure, Page Three, 1966
_ Expenditure
I ~~~~~~~~~amount
Flour Item Illustrations of various items MonthlY Remarks
__ __ _ __ _ __ __ _ _ _ __ __ _ __ _ __ __ __._ quarterly | ot
Total
Monetary service | (omitted)
r 3 Education and research
: Marriages, births, birthdays,
.S and funerals
aZ Other
c c 8 Interest
c Taxes
Total
To households
To government _
c To enterprwses
3 To abroad
Agricultural productive
expeniditure
Flour Item Illustrations of varioss Ateres Total |Pemar}s| Capital
Total
Drawing from deposits (omitted)
E Mutual savings and capital _ _ _
o o; Loan repayment ____
Borrowinig _ _ _ _ _ _ _
Sales of land
5 Sales of houses
w; Purohases on credit
Other capital in^ome
El Total
Deposits._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
- a Payment to mutual aaviugs
8 and msurance
Repayment of loan
Purchases of land _ l_ l
S Purchases of houses
) Repayment for purchases on
credit
Other capital expenditure __ _ ___
8J_ = $3 1 Agricultural income
Agricultural expenditure
8 Name of the respondent The survey takes--minutes
; The abode belongs to The cooperation of this househ9ld .
Conductor: Enumerator: Survey date:
Source; Same as for sehedule 4.1.
197
Schedule 4.4. Record of Family Intervieiv on Incoine
and Expenditure, Page Four, 1966
Stratum Cluster , Househod Age of th, Occ"P&ton~ Se- f th, Number Consu-
no 0n. no. Income hehasd oOf| of the rehead d....hld f 'lpern iexen Savigs
Expenditure
amount
Flour Item Illustrations of -fious items Monthly | Yealy emak
quarterly |total
TotalI
*o Ma.'s clothing (omitted)
rQ0 Woman's clothing
-^& Child's clothing
°a Jewelry, ornaments, and
o miscellane ous
T otal
= > Rent | Actual
c f I~~mputed
=o House repairnng and
f installation
Water ch.,ge
Total
Eleetticity bill
^= Charcoal
Coal
= Liquid fuel|
G. faSouel
Plant wastes
Oth-rl
E a Furniture .d equipment =
a =. Textiles
A - ppliances for kitchen and _ _
Other
= Total
o Domestic senants
=o& Other household operation
o expenres
=, Total
=c Persnal careml
Hair d-essi.g and bath
g E | Medical and health expesaes
lTotalll l l
e 1Purnhases of pemsnal
8 transport equipment
f =,|Operation of persontal
8 x rnprt equipment
< S|Purchared tran.po,tatiou
:E. °l Others
= lTotal l
° E Recreation
t B l'ooks, newspapers, magazines,|
u and sationmerYll l
Other recreation
Sou,-e Same as for schedule 4.1.
198
DATA ON THE DISTRIBUTION OF FAMILY INCOME 199
Nevertheless the framework underlying the design of these tables is
not specifically suited to the analytical study, such as that in this
chapter, of causes of the inequality of family income. Consequently
we had to return to the primary questionnaires to obtain the cross-
listing of information needed for this chapter.
Analytical cross-listing of data
For the joint project of Yale's Economic Growth Center and
Taiwan's Economic Planning Council, the cross-listing of data is
given by the coded family-income data form-to be referred to as the
coded form (schedule 4.5). There are fifty-one cells in this form. From
the information contained in the primary questionnaires of the
DGBAS data, all cells are filled in for every family; every family has
one card. These coded forms are preserved in cards (for 1966 in
computer cards) for almost all 24,120 families covered in table 4.18.
The coded form contains two basic types of information: wage and
nonwage income. There are three kinds of nonwage income: property
income from interest, rent, and investment; mixed income from
agricultural, business, and professional activities; and transfer income.
Mixed income is a mixture of wage and property income. It occurs
primarily because the family and the production unit coincide-for
example, a family-operated farm, a family business, or a dentist's
office-making it impossible to separate the wage and property
components of income paid by the production unit to the family.
Transfer income consists of government transfer or welfare payments;
it accounts for less than 1 percent of total family income.
The coded form contains the following information on wage income
for every wage earner: sex, age, education, occupation, job location,
number of wage earners, and total income earned by each wage
earner. Total family income (for example, NT$53,647 in schedule 4.5)
is the sum of total wage income (NT$23,800), total property income
(NT$3,600), total mixed income (NT$26,247), and transfer income
(0). The coded form also contains information on family location,
family type, and the year surveyed.
For this chapter, use was not made of the information on nonwage
income, but all information relevant to the analysis of wage income
was coded (table 4.19). Five characteristics are indicated in that
table for individual wage earners and two characteristics for every
wage-earning family. Each characteristic may be thought of as a
200 THE INEQUALITY OF FAM1ILY WAGE INCOME
Table 4.19. Coding for Characteristics of Individual Wage Earners
and Income-earning Families
Value of characteristic
Characteristic 2 2 3
Individual wage
earners
Sex Female Male
Age Under 25 25-45 45-60
Education Primary school Junior high Senior high
(six years) school (nine school (twelve
years) years)
Occupation Public employee Specialist or pro- Service employee
or serviceman fessional
Job location Rural village Township City
Income-earning
families
Family type Farm Nonfarm
Value of characteristic
Family location 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
County
- Not applicable.
Source: Constructed by the authors.
variable that takes on one of a finite number of values. The sex
variable can be coded either as female (1) or male (2). The age
variable assumes one of four possible values: under 25 (1), 25-45 (2),
45-60 (3), or over 60 (4). The education variable takes on one of five
values corresponding to the gradation of the formal education system:
primary school (1), junior high school (2), senior high school (3),
technical school (4), or university (5). Intuitively the characteristics
just mentioned are most significant among the various factors relevant
to the analysis of wage income inequality.
DATA ON THE DISTRIBUTION OF FAMILY INCOME 201
Value of characteristic
4 6 6 Characteristic
Individual wage
earners
- - - Sex
Over 60 - Age
Technical school University (six- - Education
(fourteen years) teen years)
Commercial self- Manual laborer Agricultural Occupation
employee employee
- - - Job location
Income-earning
families
Family type
Value of characteristic
17 18 19 20 21 Family location
Municipality
The occupation variable has six values: government employee and
serviceman (1), specialist or professional (2), service employee of
business establishments (3), commercial self-employee (4), manual
laborer (5), and agricultural employee (6). The classification of
labor according to this criterion corresponds to the homogeneous
groups within a "working class." The variable for job location has
three values: rural village (1), township (2), and city (3). The
variable for "family type" classifies a family as a farm (1) or non-
farm (2) family. The definition of farm family adopted by the
DGBAS is based on one of five possible criteria of agricultural activi-
202 THE INEQUALITY OF FAMILY WAGE INCOME
Schedule 4.5. Coded Form for Data on Family Income,
with Sample Entries
Year Family Family Total Total Total Transfer Total
Year lation type wage property mixed income family
income income income income
1973 01 2 23,800 3,600 26,247 0 53,647
Wage income
Wage earner 1 2 3 4 5 6
Wage income 9,600 1,000 7,200 6,000
Sex 1 1 1 1
Age 1 1 3 1
Education 2 1 1 1
Occupation 3 6 6 6
Job location 1 1 1 1
Nonwage income
Property income Mixed income
Interst icome Rent Invest- Agricul- Business Profes- Transfer
Interest income income . ment tural income sional income
income income income
0 3,600 0 26,247 0 0 0
Note: See table 4.19 for values assigned to characteristics.
Source: Constructed by the authors.
MODEL OF ADDITIVE FACTOR COMPONENTS 203
ties.18 The "farnily location variable" has twenty-one values cor-
responding to the administrative districts of Taiwan.'9
Thus, in the coded forms (schedule 4.5), individual wage income
earners are coded according to the five "individual wage earner's
characteristics" of table 4.19. At the same time, families are coded
according to the two "family characteristics" of that table. The
cross-listing of the data in this way constitutes the primary input of
our analysis of wage income inequality (tables 4.20-4.27). It should
be apparent that the identification of these characteristics is essen-
tially guided by an intuitive notion of what is relevant to the analysis
of wage income inequality.
Appendix 4.2. Linear Regression and the Model
of Additive Factor Components
The method we have designed for the analysis of wage income
inequality is built on a combination of the technique of linear
regression and the technique of additive factor components. For
expository convenience the analytical design has been presented in
chapter four with the aid of numerical examples. The two techniques
can also be stated abstractly-that is, independent of their empirical
applications. The linear regression technique can be stated as follows:
(4.20) y = ao + aix, + a2X2 + . ..± + arxr,
where y is regressed on r explanatory variables [xi]. If there are n
empirical observations, this gives:
(4.21) (Yiy Xil, Xi2) ... Zir)X(i)= 1 2,. .., n)
With the aid of expression (4.21) the regression coefficients aj
(j = 0, 1, 2,..., r) can be estimated. The data input required for
18. These criteria are cultivating an area of 0.2 hectares, raising more than
three pigs of not less than sixty kilograms each, raising more than one buffalo,
raising more than one hundred poultry, and yearly sales of agricultural products
of more than NT$6,000. A "fishing family" is similarly defined by the number
of fish-catching and fish-growing activities.
19. The twenty-one districts comprise sixteen counties-Taipei, Ilan, Taoyuan,
Hsinchu, Miaoli, Taichung, Changhwa, Nantou, Yunlin, Chiayi, Tainan, Kaoh-
siung, Pingtung, Taitung, Hwalien, and Penghu-and five municipalities-
Keelung, Taichung, Tainan, Kaohsiung, and Taipei.
204 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.20. Annual Wage Rates of Female Workers, by Age, Occupation,
Job Location, and Level of Education, 1966
(N.T. dollars)
Under 25 years 25-45 years
Level of education Rural Rural
and occupation area Town City area Town City
Primary school
Public employee - 6,160 9,533 4,950 60,300 7,500
Specialista - - 2,568 - - -
Service employeeb 4,050 6,363 4,746 7,008 7,180 6,186
Commercial self-employee - - 8,200 16,640 4,400 18,400
Manual laborer 5,015 5,859 6,265 4,035 5,796 8,180
Agricultural employee 2,502 1,630 9,600 2,602 3,035 11,400
Junior high school
Public employee - 13,060 10,620 12,540 20,500 12,100
Specialist 4,800 7,000 - - - -
Service employee - 5,850 7,800 - 8,400 -
Commercial self-employee - 3,500 - 0 11,650 -
Manual laborer 5,820 7,115 8,150 - 5,676 -
Agricultural employee 6,000 - - 3,200 7,800 -
Senior high school
Public employee 12,922 10,196 11,010 8,566 16,076 20,413
Specialist - - - - -
Service employee - - - - - -
Commercial self-employee - 7,470 16,710 - - 23,375
Manual laborer - - - - 5,300 -
Agricultural employee - - - - - -
Technical school
Public employee - - 20,500 - - 20,866
Specialist - - - - - -
Service employee - - 12,000 - - -
Commercial self-employee - - - - - 21,400
Manual laborer - - - - -
Agricultural employee - - - - - -
University or over
Public employee 17,908 - - - 10,050 -
Specialist - - - - - -
Service employee - - - - - -
Commercial self-employee - - - - - 43,200
Manual laborer - - - - - -
Agricultural employee - - - - - -
- No entry.
Source: DGBAs, Report on the Survey of Family Income and Expenditure, 1966.
MODEL OF ADDITIVE FACTOR COMPONENTS 205
45-60 years Over 60 years
Rural Rural Level of education
area Town City area Town City and occupation
Primary school
- 12,222 3,900 - - - Public employee
- - - - - Specialist,
- 5,100 6,685 2,700 4,332 - Service employeeb
- - - - - - Commercial self-employee
8,550 5,783 5,600 - - 7,800 Manual laborer
2,894 3,580 - 2,800 - - Agricultural employee
Junior high school
13,661 - - - - - Public employee
- - - - - - Specialist
- 9,900 - - - - Service employee
- - - - - Commercial self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
Senior high school
- 29,703 24,080 - - - Public employee
- - - - - Specialist
- - - - - Service employee
- 26,695 33,000 - - - Commercial self-employee
- = - - - - Manual laborer
- - - - - - Agricultural employee
Technical school
- - - - - Public employee
- - - - - Specialist
- - - - - Service employee
- - - - - - Commercial self-employee
- - - - - - Manual laborer
- - - - - Agricultural employee
University or over
- 1L8,600 - - - - Public employee
- 30,000 - - - Specialist
- - - - - - Service employee
- - - - - - Commercial self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
a. Includes professionals.
b. Includes servicemen.
206 THE INEQUALITY OF FAMILY WAGE LABOR
Table 4.21. Annual Wage Rates of Male Workers, by Age, Occupation,
Job Location, and Level of Education, 1966
(N.T. dollars)
Under 25 years 25-45 years
Level of education Rural Rural
and occupation area Town City area Town City
Primary school
Public employee 10,590 8,104 15,900 20,721 18,017 17,256
Specialista - - - - - -
Service employeeb 3,103 5,852 8,871 12,300 14,175 15,627
Commercial self-employee - 7,540 15,000 8,325 3,186 21,287
Manual laborer 9,015 7,573 7,082 12,470 14,365 19,034
Agricultural employee 3,248 3,107 2,250 5,239 5,292 22,900
Junior high school
Public employee - 11,736 12,750 19,319 18,487 21,901
Specialist - - - - - -
Service employee 41,000 7,600 7,600 - 8,840 16,985
Commercial self-employee 6,000 7,750 14,000 - 11,000 28,000
Manual laborer 1,070 9,710 12,033 14,750 1,475 9,540
Agricultural employee 4,500 1,500 4,800 5,200 11,875 -
Senior high school
Public employee 11,635 10,881 11,160 19,177 22,404 22,404
Specialist - - - - 32,760 -
Service employee 1,600 19,200 11,280 9,600 17,935 32,230
Commercial self-employee - 12,000 13,166 19,814 14,711 25,500
Manual laborer - 11,200 12,900 - 12,961 23,133
Agricultural employee - - - 4,200 7,300 -
Technical school
Public employee - - - 21,264 21,230 32,546
Specialist - 4,095 - 46,800 - -
Service employee - - - - -
Commercial self-employee - 8,100 21,500 - 24,260 -
Manual laborer - - - - - -
Agricultural employee - - - - - -
University or over
Public employee - - 17,400 25,500 27,479 25,584
Specialist - - - - 12,600 -
Service employee - - - - - 90,600
Commercial self-employee - - - 12,600 41,500 56,671
Manual laborer - - - - - -
Agricultural employee - - -
- No entry.
Source: Same as for table 4.20.
MODEL OF ADDITIVE FACTOR COMPONENTS 207
46-60 years Over 60 years
Rural Rural Level of education
area Town City area Town City and occupation
Primary school
16,616 21,803 22,803 11,942 7,959 8,070 Public employee
- 7,200 - - - - Specialist,
1,800 8,614 17,722 - - 10,400 Service employeeb
24,045 22,966 30,554 25,184 8,190 16,800 Commercial self-employee
10,161 13,606 19,367 2,600 8,757 12,440 Manual laborer
5,593 5,239 5,931 3,800 5,142 - Agricultural employee
Junior high school
23,982 20,585 28,492 - - - Public employee
- - - - - - Specialist
- 12,550 18,650 - - - Service employee
4,000 24,345 36,675 - 29,200 - Commercial self-employee
- 16,000 30,300 - - 57,360 Manual laborer
3,000 5,925 - - - - Agricultural employee
Senior high school
26,960 22,783 32,054 - 17,975 26,100 Public employee
- - - --- Specialist
- 3,000 - - - - Service employee
- 29,566 16,382 - - 42,200 Commercial self-employee
- 14,200 28,953 - - - Manual laborer
- - - - - - Agricultural employee
Technical school
- 44,853 32,600 - - - Public employee
- - 7,200 19,100 - - Specialist
- - - - - - Service employee
- - - - - - Commercial self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
University or over
- 33,475 52,226 - - 56,418 Public employee
- 16,800 56,610 - - - Specialist
- - 37,400 - - - Service employee
- 34,150 34,600 - - - Commercial self-employee
- - 33,300 - - - Manual laborer
- - - - - - Agricultural employee
a. Includes professionals.
b. Includes servicemen.
208 THE INEQUALITY OF FAMILY WAGE LABOR
Table 4.22. Number of Female Workers, by Age, Occupation,
Job Location, and Level of Education, 1966
Under 25 years 25-45 years
Level of education Rural Rural
and occupation area Town City area Town City
Primary school
Public employee - 2 3 1 1 2
Specialista - - 1 - - -
Service employeeb 4 8 15 6 13 20
Commercial
self-employee - - 1 1 1 1
Manual laborer 18 45 41 9 30 20
Agricultural employee 82 40 1 100 58 4
Junior high school
Public employee - 5 4 2 3 2
Specialist 1 1 - - - -
Service employee - 2 3 - 1 -
Commercial
self-employee - 1 - - 3 -
Manual laborer 2 8 4 - 4 -
Agricultural employee 1 - - 1 1 -
Senior high school
Public employee 32 10 3 31 11 8
Specialist - - - - - -
Service employee - - - - - -
Commercial
self-employee - 5 4 - - 4
Manual laborer - - - - 3
Agricultural employee - - - - -
Technical school
Public employee - - 1 - - 3
Specialist - - - - - -
Service employee - - 1 - - -
Commercial
self-employee - - - - - 2
Manual laborer - - - - - -
Agricultural employee - - - - - -
MODEL OF ADDITIVE FACTOR COMPONENTS 209
45-60 years Over 60 years
Rural Rural Level of education
area Town City area Town City and occupation
Primary school
- 2 1 - - - Public employee
- - - - - - Specialista
- 1 7 1 2 - Service employeeb
Commercial
- - - - - - self-employee
4 11 3 - - 1 Manual laborer
20 10 - 2 - - Agricultural employee
Junior high school
1 - - -- - - Public employee
- - - - - - Specialist
- 1 - - - - Service employee
Commercial
- - - - - - self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
Senior high school
- 2 2 - - - Public employee
- - - - - - Specialist
- - - - - - Service employee
Commercial
- 1 2 - - - self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
Technical school
- - - - - - Public employee
- - - - - - Specialist
- - - - - - Service employee
Commercial
- - - - - - self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
(Table continues on the following pages)
210 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.22 (Continued)
Under 25 years 25-45 years
Level of education Rural Rural
and occupation area Town City area Town City
University or over
Public employee 1 - - - 2
Specialist - -
Service employee - - - - - 1
Commercial
self-employee - - - - - -
Manual laborer - - - - - -
Agricultural employee -
- No entry.
Source: Same as for table 4.20.
a. Includes professionals.
b. Includes servicemen.
expression (4.21) can be written as column vectors:
(4.22a) Y = col(y1, Y2,..., y,.)
(4.22b) Xi = Col(Xli, X2V,..., Xi) (i = 1, 2,..., n)
With the aid of the estimated regression equation, this gives:
(4.23a) Y = A. + a1X1 + a2X2 +.. . + a,X, + 0, where
(4.23b) A. = col(a0, aO,... a) and
(4.23c) 6 = col(Oi, 02, ... Xt),
and where 6i is the difference between yi and yi, as estimated from
regression equation (4.20) for the ith observation.
It can now be clearly seen how equation (4.23a) may be viewed as
an abstract problem of additive factor components. An application of
the general decomposition technique for such a problem immediately
leads to:
(4.24) G5 = klR,G(X,) + 02R2G(X2) +. . . + 4r,RG(Xr)
+ OeReG(0),
where ci is the share, Ri the correlation characteristic, and G(Xi) the
MODEL OF ADDITIVE FACTOR COMPONENTS 211
45-60 years Over 60 years
Rural Rural Level of education
area Town City area Town City and occupation
University or over
- 1 - - - - Public employee
- - 1 - - - Specialist
- - - - - - Service employee
Commercial
- - - - - - self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
Gini coefficient of Xi. The causation of G, can thus be traced to
the various quality dimensions emphasized in the regression equa-
tion.20 The methodological innovation of this chapter thus resides in
the combination of the linear regression technique with the additive
factor-components technique. For this combination to work, the
additive property of the Gini coefficient is essential-that is, it
underlies equation (4.24). Moreover the additive property of the
linear regression equation (4.20) is equally essential. For example,
in the earnings equation in chapter four, the wage rate is assumed
to be additively determined and traced to various dimensions of the
quality of the labor force. The linearity of the regression is not
essential for the combination of the two techniques. The combination
still is possible when the regression equation is nonlinear, and this
possibility indicates a direction in which the method can be
generalized.
20. Because of the technical complexities, full treatment of the decomposition
analysis for the problem of additive factor components is postponed to part two.
Notice, however, that the term associated with OeRoG (6) in equation (4.24)
arises from the error term [9] in equation (4.23a). To the extent that the error
term is small-that is, to the extent that the multiple linear correlation in the
regression analysis of equation (4.21) is high-the influence of this term in
equation (4.24) similarly is small. One proviso is intuitively obvious: to the ex-
tent that the regression analysis is imperfect, we cannot hope to explain in-
equality fully.
212 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.23. Number of Male Workers, by Age, Occupation,
Job Location, and Level of Education, 1966
Under 26 years 26-46 years
Level of education Rural Rural
and occupation area Town City area Town City
Primary school
Public employee 3 9 2 13 60 32
Specialista I - - - - -
Service employeeb 4 9 7 5 17 20
Commercial
self-employee - 1 2 2 9 18
Manual laborer 19 50 72 46 121 112
Agricultural employee 74 43 4 202 154 3
Junior high school
Public employee - 5 2 7 28 19
Specialist - - - - - -
Service employee 2 2 1 - 3 7
Commercial
self-employee 1 2 1 - 2 4
Manual laborer 1 13 3 4 10 10
Agricultural employee 3 2 1 7 4 -
Senior high school
Public employee 4 4 1 13 66 34
Specialist - - - - 1 -
Service employee 1 1 1 1 7 3
Commercial
self-employee - 1 6 8 17 16
Manual laborer 2 2 - 6 9
Agricultural employee - - - 2 2 -
Technical school
Public employee - - - 2 7 10
Specialist - 1 - 1 - -
Service employee - - - - - -
Commercial
self-employee - 1 1 - 1 -
Manual laborer - - - - - -
Agricultural employee - - - - - -
MODEL OF ADDITIVE FACTOR COMPONENTS 213
46-60 years Over 60 years
Rural Rural Level of education
area Town City area Town City and occupation
Primary school
10 23 23 2 4 3 Public employee
- - - - - - Specialist"
1 7 9 - - 1 Service employeeb
Commercial
2 3 7 1 1 2 self-employee
10 51 43 2 8 5 Manual laborer
63 54 6 3 12 - Agricultural employee
Junior high school
2 12 9 - - - Public employee
- - - - - - Specialist
- 2 2 - - - Service employee
Commercial
1 1 3 - 1 - self-employee
- 1 2 - - - Manual laborer
1 2 - - - - Agricultural employee
Senior high school
6 35 20 - 2 1 Public employee
- - - - - - Specialist
- 1 - - - - Service employee
Commercial
:-: 3 4 - - 1 self-employee
- 1 3 - - - Manual laborer
- - - - - - Agricultural employee
Technical school
- 3 1 - - - Public employee
- 1 1 - - Specialist
- - - - - - Service employee
Commercial
- - - - - - self-employee
- - - - - - Manual laborer
- - - - - - Agricultural employee
(Table continues on the following pages)
214 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.23 (Continued)
Under 25 years 25-45 years
Level of education Rural Rural
and occupation area Town City area Town City
University or over
Public employee - - 1 2 23 19
Specialist - - - - 1
Service employee - - - - - 2
Commercial
self-emplovee - - - 1 4 7
Manual laborer - - - - - -
Agricultural employee -
- No entry.
Source: Same as for table 4.20.
a. Includes professionals.
b. Includes servicemen.
When abstractly stated, the method can be applied to other
problems as well-for example, to the analysis of the inequality of the
distribution of family property income [GJ. The total family
property income [y] can, as in equation (4.20), first be regressed on a
number of explanatory variables [xi] representing particular types of
assets, such as urban land, physical capital, and bonds, or the "class"
affiliation of the family, such as that of the entrepreneurial class,
the professional class, or the class of skilled workers. The regression
results can then be combined with the model of additive factor
components to trace the inequality of family property income to the
unequal distribution of the ownership of assets, to the class affiliation
of families, or to both.
The crude earnings function used in chapter four obviously does
injustice to an approach which has received a good deal of professional
attention of late.2' In this chapter we have somewhat downgraded the
21. Among the shortcomings of the earnings function used in chapter four,
the following may be mentioned: the ambiguity of age as a proxy for experience;
the inadequacy of total family income as a proxy for family influence; the inter-
pretation of G6. when x is an ordinal-for example, when education is measured
by low, medium, and high, not by years of education; the lack of effort to com-
pare our conclusions, such as those on returns to education, with other, inde-
pendent studies.
MODEL OF ADDITIVE FACTOR COMPONENTS 215
45-60 years Over 60 years
Rural Rural Level of education
area Town City area Town City and occupation
University or over
- 14 16 - - 3 Public employee
- 1 1 - - - Specialist
- - 1 - - - Service employee
Commercial
- 2 1 - - - self-employee
- - 1 - - - Manual laborer
- - - - - - Agricultural employee
earnings-function approach. This approach by itself, used for the first
level of analysis in our design, really is insufficient for the analysis of
income inequality. It becomes significant for such analysis only after
it is combined with the model of additive factor components. The
argument in this appendix thus suggests that the regression approach
can play a significant role in the analysis of income inequality when
it is imbedded in a framework involving the model of additive factor
components.
216 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.24. Number of Rural Workers and Average Annual Wage Rate,
by Education, Sex, and Age, 1966
Number of workers
Junior Senior Techni- Univer-
Primary high high cal sity or
Sex and age school school school school over Total
Female 248 8 6 1 263
Under 25 years 104 4 3 - 1 112
25-45 years 117 3 3 - - 123
45-60 years 24 1 - - - 25
Over 60 years 3 - - - - 3
Male 462 29 35 4 3 533
Under 25 years 100 7 5 - - 112
25-45 years 268 18 24 3 3 316
45-60 years 86 4 6 - - 96
Over 60 years 8 - - 1 - 9
Both sexes 710 37 41 4 4 796
Under 25 years 204 11 8 - 1 224
25-45 years 385 21 27 3 3 439
45-60 years 110 5 6 - - 121
Over 60 years 11 - - 1 12
- No entry.
Source: Same as for table 4.20.
MODEL OF ADDITIVE FACTOR COMPONENTS 217
Annual wage rate
Junior Senior Techni- Univer-
Primary high high cal sity or
school school school school over Total Sex and age
3,114 8,048 10,745 - 17,908 3,495 Female
2,997 5,610 12,923 - 17,908 3,489 Under 25 years
3,079 9,427 8,567 - - 3,368 25-45 years
3,837 13,661 - - - 4,230 45-60 years
2,767 - - - - 2,767 Over 60 years
6,864 13,385 18,164 27,107 26,367 8,222 Male
4,559 14,653 9,628 - - 5,416 Under 25 years
7,387 12,813 17,742 29,776 26,367 8,875 25-45 years
7,791 13,741 26,961 - - 9,237 45-60 years
8,209 - - 19,100 - 9,419 Over 60 years
5,554 12,731 17,078 27,107 24,252 6,660 Both sexes
3,762 11,365 10,864 - 17,908 4,453 Under 25 years
6,077 12,330 16,723 29,766 26,367 7,332 25-45 years
6,928 13,725 26,961 - - 8,203 45-60 years
6,724 - - 19,100 - 7,756 Over 60 years
218 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.25. Number of Town Workers and Their Annual Wage Rate,
by Education, Sex, and Age, 1966
Number of workers
Junior Senior Techni- Univer-
Primary high high cal sity or
Sex and age school school school school over Total
Female 224 30 32 - 3 289
Under 25 years 95 17 15 - - 127
25-45 years 103 12 14 - 2 131
45-60 years 24 1 3 - 1 29
Over 60 years 2 - - - - 2
Male 637 90 149 13 45 934
Under 25 years 112 24 8 2 - 146
25-45 years 361 47 99 8 28 543
45-60 years 139 18 40 3 17 217
Over 60 years 25 1 2 - - 28
Both sexes 861 120 181 13 48 1,223
Under 25 years 207 41 23 2 - 273
25-45 years 464 59 113 8 30 674
45-60 years 163 19 43 3 18 226
Over 60 years 27 1 2 - - 30
- No entry.
Source: Same as for table 4.20.
MODEL OF ADDITIVE FACTOR COMPONENTS 219
Annual wage rate
Junior Senior Techni- Univer-
Primary high high cal sity or
school school school school over Total Sex and age
4,633 9,636 12,422 - 2,900 6,103 Female
4,127 8,495 9,288 - 5,322 Under 25 years
4,932 11,230 13,767 - 10,050 6,531 25-45 years
5,374 9,900 22,034 - 18,600 7,709 45-60 years
4,333 - - - - 4,333 Over 60 years
9,946 13,339 19,771 24,587 30,320 13,026 Male
5,763 9,109 12,141 6,098 - 6,667 Under 25 years
10,814 13,370 19,288 21,609 28,951 13,675 25-45 years
11,617 18,018 22,583 44,853 32,574 16,270 45-60 years
6,872 29,200 17,975 - - 8,462 Over 60 years
8,564 12,414 18,475 24,857 29,231 11,390 Both sexes
5,012 8,855 10,280 6,098 - 6,041 Under 25 years
9,508 12,935 18,604 21,609 27,691 12,286 25-45 years
10,698 17,591 22,544 44,853 31,797 16,612 45-60 years
6,684 29,200 17,975 - - 8,187 Over 60 years
220 THE INEQUALITY OF FAMILY WAGE INCOME
Table 4.26. Number of City Workers and Their Annual Wage Rate,
by Education, Sex, and Age, 1966
Number of workers
Junior Senior Techni- Univer-
Primary high high cal sity or
Sex and age school school school school over Total
Female 121 13 23 7 2 166
Under 25 years 62 11 7 2 - 82
25-45 years 47 2 12 5 1 67
45-60 years 11 - 4 - 1 16
Over 60 years 1 - - - - 1
Male 361 65 101 13 52 592
Under 25 years 87 8 10 1 1 107
25-45 years 175 40 62 10 28 315
45-60 years 88 16 27 2 20 153
Over 60 years 11 1 2 - 3 17
Both sexes 482 78 124 20 54 758
Under 25 years 149 19 17 3 1 189
25-45 years 222 42 74 15 29 382
54-60 years 99 16 31 2 21 169
Over 60 years 12 1 2 - 3 18
- No entry.
Source: Same as for table 4.20.
MODEL OF ADDITIVE FACTOR COMPONENTS 221
Annual wage rate
Junior Senior Techni- Univer-
Primary high high cal sity or
school school school school over Total Sex and age
6,766 12,772 20,471 19,700 36,600 10,040 Female
6,081 8,953 14,267 16,250 - 7,413 Under 25 years
7,794 33,780 21,401 21,080 43,200 12,527 25-45 years
6,136 - 28,540 - 30,000 13,229 45-60 years
7,800 - - - - 7,800 Over 60 years
15,998 37,725 24,393 29,751 43,998 22,577 Male
7,389 11,000 12,724 21,500 17,400 8,383 Under 25 years
18,489 46,061 23,784 32,547 38,000 25,213 25-45 years
20,071 29,022 29,388 19,900 51,862 26,805 45-60 years
11,856 57,360 34,150 - 56,419 25,019 Over 60 years
13,680 33,566 23,665 26,233 43,724 19,831 Both sexes
6,845 9,815 13,360 18,000 17,400 7,962 Under 25 years
16,225 45,476 23,398 28,724 38,180 22,988 25-45 years
18,523 29,022 29,279 19,900 50,821 25,519 45-60 years
11,518 57,360 34,150 - 56,419 24,063 Over 60 years
222 TIHE INEQUALITY OF FAMILY WAGE INCOME
Table 4.27. Number of Workers and Average Annual Wage Rate,
by Education, Sex, and Age, 1966
Number of workers
Junior Senior Techni- Univer-
Primary high high cal sity or
Sex and age school school school school over Total
Female 593 51 61 7 6 718
Under 25 years 261 32 25 2 1 321
25-45 years 267 17 29 5 3 321
45-60 years 59 2 7 - 2 70
Over 60 years 6 - - - - 6
Male 1,460 184 285 30 100 2,059
Under 25 years 299 39 23 3 1 365
25-45 years 804 105 185 21 59 1,174
45-60 years 313 38 73 5 37 466
Over 60 years 44 2 4 1 3 54
Both sexes 2,053 235 346 37 106 2,777
Under 25 years 560 71 48 5 2 686
25-45 years 1,071 122 214 26 62 1,495
45-60 years 372 40 80 5 39 536
Over 60 years 50 2 4 1 3 60
- No entry.
Source: Same as for table 4.20.
MODEL OF ADDITIVE FACTOR COMPONENTS 22
Annual wage rate
Junior Senior Techni- Univer-
Primary high high cal sity or
school school school school over Total Sex and age
4,433 10,186 15,303 19,700 21,635 6,058 Female
4,141 8,292 11,118 16,250 17,908 5,217 Under 25 years
4,624 13,564 16,388 21,080 21,100 6,570 25-45 years
4,891 11,781 25,752 - 24,300 7,728 45-60 years
4,128 - - - - 4,128 Over 60 years
10,647 21,961 21,211 27,161 37,314 14,529 Male
5,833 10,492 11,848 11,232 17,400 6,786 Under 25 years
11,342 25,728 20,594 27,984 33,114 15,479 25-45 years
12,943 22,201 25,460 34,872 43,000 18,280 45-60 years
8,361 43,280 26,063 19,100 56,419 13,834 Over 60 years
8,724 19,406 20,201 25,749 36,426 12,388 Both sexes
5,045 9,500 11,468 13,239 17,654 6,052 Under 25 years
9,667 24,033 20,024 26,656 32,533 13,566 25-45 years
11,666 21,680 25,485 34,872 19,100 25,749 45-60 years
7,853 43,280 26,063 19,100 56,419 12,863 Over 60 years
CHAPTER 5
Income Distribution
and Economic Structure
THE CAUSES OF THE INEQUALITY of family income were explicitly
traced in earlier chapters to additive factor-income components.
In this chapter a more aggregate view is taken by deemphasizing
additive factor components and concentrating on the structure of
total family income. This aggregate view facilitates tracing the
inequality of family income to various homogeneous categories
of income recipients. Such analysis is hardly revolutionary. Kuznets's
classical study, inquiring whether inequality in the distribution of
family income increases in the course of industrialization and ur-
banization, emphasized sectoral and locational dimensions.' Sub-
sequent studies by other investigators have done the same. In this
chapter, too, sectoral and locational dimensions constitute the two
focal points of an analysis that will be formulated as an abstract
model of homogeneous groups. As part of this analysis, the inequality
of family income will be examined in relation to family attributes.
The income gaps between families in different sectors and locations
are an important and dynamic economic force that causes the urbani-
zation of the population and the shift of farm workers to nonfarm
activities. If labor were completely mobile, the income gaps would
tend to be small. But the mobility of labor is often impeded by such
factors as traditional ideologies and social systems, particularly
during the early stages of economic development. Consequently it
1. Simon Kuznets, "Economic Growth and Income Inequality," American
Economic Review, vol. 45, no. 1 (March 1955), pp. 1-28.
224
INCOME DISTRIBUTION AND ECONOMIC STRUCTURE 225
never is perfect. Because it is imperfect, part of the labor force
remains in the lower productivity sectors and causes the gaps in
income to widen between sectors.
In Taiwan the income gap between farm and nonfarm families
widened during 1964-72 because farm income was growing at a
slower rate than nonfarm income. The income gap between rural
and urban sectors also widened. But despite these widening gaps
between sectors, the inequality of income significantly declined at
the national level. How could this have happened? How could the
inequality of income decline for the entire country as the inequality
of income increased between farm and nonfarm families? This chapter
probes the reasons for that reduction in the inequality of family
income by using a sectoral decomposition formula that measures two
main effects: the inequality within sectors, and that among sectors.
The root causes of the inequality of family income will thus be
explained by analyzing an intersectoral effect and an intrasectoral
effect.
The intersectoral effect, constituted by a family-weight effect
and an income-disparity effect, is caused by changes in the shares
of different sectors in the total number of families and in total family
income. The family-weight effect is caused by changes in the weights
of sectors as measured by the percentages of families in each sector.
When an economy develops and labor is reallocated, the modern
sectors expand while the more traditional sectors shrink. This shift
of family weights among sectors has an effect on the distribution
of income. In contrast, the income-disparity effect is caused by
changes in the income parities among sectors. The gap of average
family income between two sectors principally arises from produc-
tivity differences. Because of the differences in the technology used
in agricultural and nonagricultural production, labor productivity
usually is higher and growing more rapidly in the modern sector
than in the traditional sector. That, too, has an effect on the distri-
bution of income.
The intrasectoral effect is caused by changes in the inequality
of income within each sector and is explained by numerous causative
elements. Its principal cause, however, is the heterogeneity of families
arising from differences in the ownership of assets and differences
in the ownership of labor embodying particular characteristics.
Thus, within each sector, it is possible to identify a number of social
groups or classes of families based on the various types and quan-
tities of physical and human assets owned by families. A group will
226 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
be referred to as a homogeneous group. The heterogeneity of families
in a sector can then be described by the coexistence of homogeneous
groups.
This chapter is principally devoted to a study of the proximate
causes of the reduction in the inequality of income in Taiwan. First,
an equation for decomposition will be presented. Second, an attempt
will be made to decompose national income according to classifica-
tions of income recipients by sector and homogeneous group. The
sectoral classifications are based on farm and nonfarm activity and
on the degree of urbanization, proxied by rural, semiurban, and
urban residence. The group classifications are based on the number
of persons employed per family and on the age, sex, and educational
background of the head of family. Third, changes in the inequality
of income over time will be analyzed in relation to industrialization
and urbanization through the divergence in the income-relative,
which is the ratio of the sectoral share in total income to the sectoral
share in total households, and through the decomposition of income
recipients into homogeneous groups. Fourth, demographic factors will
be examined, and the causes of inequality identified in relation to
the size and composition of families. The reduction in the inequality
of income over time will be linked to changes in the size of families,
the number of employed members per family, and the age, sex, and
educational background of the head of family. Here, again, changes
will be analyzed through the divergence in the income-relative for
various sectors and the decomposition of income recipients into
homogeneous groups.
The analysis of the intrasectoral and intersectoral effects will
show that the reduction in the inequality of income within the non-
farm sector was the essential cause of the nationwide reduction in
the inequality of income. That is, the favorable intrasectoral effect
for the nonfarm sector more than compensated for the adverse
intersectoral effect and made it possible for the inequality of income
to be reduced across the entire country. The findings, based on the
analysis of intragroup and intergroup effects, indicate the importance
of demographic and economic forces in reducing the inequality of
income among families in Taiwan.
The Decomposition Equation
Kuznets used agricultural and nonagricultural family weights, as
well as intersectoral and intrasectoral inequalities, to analyze the in-
THE DECOMPOSITION EQUATION 227
terrelations between changes in the economic structure and the
distribution of income.2 Swamy decomposed the coefficient of varia-
tion in the two-sector model.' The decomposition in this chapter
follows this general line of reasoning, but is generalized to n sectors.
The decomposition formula should separately identify the intra-
sectoral and intersectoral effects that contribute to overall income
inequality. For this purpose, it helps if the inequality indicator of the
whole economy can be explained in relation to such measures as the
proportions of farm and nonfarm families, the mean incomes of the
two sectors, and the indicators of income inequality of the two sec-
tors. As an inequality indicator, the coefficient of variation is con-
venient for this purpose.'
Now consider the whole economy [w] to comprise a farm sector
[a] and a nonfarm sector [n]. In the example of figure 5.1, the three
sectors [w, a, and n] are represented by the three frequency distri-
butions corresponding to the data in table 5.1. This example illus-
trates the type of data needed in this chapter.
When there are two groups of income recipients (agriculture and
nonagriculture) and k income classes, the variances for agriculture
[Va], nonagriculture [Vs], and the whole economy [EV,] are defined
as follows:
b, k
(5.1a) Va = L Pa(Yi - Ya),, Vn E Pi(Yi -
V.c =E Pj(Y -j )2, where:
i=l
(5.1b) f = i + fn; (i =1, 2, . ,k)
E class frequency for whole economy 1
as sum of group frequencies ]
k ~~~~~k
(5. 1c) fa fai f f f = fa + fn;
i=l i=l
2. Kuznets, "Economic Growth and Income Inequality."
3. Subramanian Swamy, "Structural Changes and the Distribution of Income
by Size: The Case of India," Review of Income and Wealth, vol. 12, no. 2 (June
1967), pp. 155-74.
4. It will be shown in chapter twelve that if the Gini coefficient were used
for homogeneous group decomposition, a third term-for a crossover effect-
would appear in addition to the intersectoral and intrasectoral effects. Conse-
quently the coefficient of variation is used in this chapter to simplify the analysis.
228 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Figure 5.1. Income Distribution for Agricultural, Nonagricultural,
and All Sectors
6( _
60-
f a = agricultural sector
n = nonagricultural sector
50
0 40
20
1)
D 30 L ---I
1 2 3 4 5 6 7 8
Income EY]
Source: Table 5.1.
(5.1d) h,, = ff, h. = fn/f; (h. + h. 1
Egroup family shares]
(5.1e) pai = faj/jf pn =fi'lfn, Pi = haP'j + h.P,.;
(i 1,02, )
k k A;
pai = ) EPi = 1) (EPi 1)
rrelative class frequencies]
k k ~~~~~~~~~~~k
(5-1f) Ya.= iy,i Y. pyn i, Yi,. = piyi
1 2- 3i_16
[incom means] = hy + h[yY
by equation (5.1e).
THE DECOMPOSITION EQUATION 22.9
Table 5.1. Numerical Example of Income Distribution
for Agricultural, Nonagricultural, and All Sectors
Number of Number of
households households Number of
in agri- in nonagri- households
Income Income Midpoint cultural cultural in all
group range income sector sector sectors
[i] [Y.] [fa] [fnd Ef = faS±fn
1 0.5-1.5 1 6 2 8
2 1.5-2.5 2 30 25 55
3 2.5-3.5 3 17 31 48
4 3.5-4.5 4 10 26 36
5 4.5-5.5 5 6 24 30
6 5.5-6.5 6 4 13 17
7 6.5-7.5 7 2 4 6
All groups - - 75 125 200
- Not applicable.
Source: Constructed by the authors.
It can be readily shown that:
(5.2a) Vt = A + B, where
(5.2b) A = haVa + hnVn and
(5.2c) B = ha(yw - ya)2 + hn(Y. - y.)2.
In equation (5.2b) A is the weighted average of the group variances
[V0 and Vn]; the group family shares [ha and h.] are the weights.
In equation (5.2c) B is the variance of all households when, for
each group, total income is redistributed such that every household
receives the mean income of the group [Ya and y.]. The coefficients
of variation for the two groups [Ia and I,,] and for the whole econ-
omy [Il] are defined as follows:
(5.3) I. = V .Iw/yw, Ia = V-V/Ya, and I. = /y.
Substituting these definitions in equation (5.2) gives:
(5.4a) I', = h.U2I2 + h0U'In + ha(l - Ua)2 + hn(l - U0)2,
where:
(5.4b) Ua = ya/yut and U, = y./yu.
230 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
In equation (5.4b) U0 and Up express the mean income of each
group as a fraction of the mean income of the whole economy. Be-
cause the object of this analysis is to assess the separate effects on
I,L of the variation of the group family shares [h. and h.], the group
coefficients of variation [Ia and I.], and the group income parities
[U, and U.], it is not convenient to use Ua and U.. The reason is
that the family shares [ha and h.] enter into the definition of Yw
in equations (5.1e) and (5.1f). The group income parities are defined
as follows:
(5.5a) Za = Ya/Y and Z. = ya/y, where
(5.5b) y = (ya + Y.)/2.
These equations express the individual group means as a parity of
the simple arithmetic average of the group means. Then:
(5.6a) U = Fa(Za, Z., h., ha) = Za(Z. + Z.)/2(h.Z0 + hnZn)
and
(5.6b) Un = F (Z, Z., ha, ha) = Zn(Za + Z.)/2(haZa + hnZn)
by equations (5.4b), (5.5a), and (5.1f).
These equations show that U. and U. are functions of Z,, Z0, h.,
and hn. When Ua and U. in equation (5.5) are substituted in equation
(5.4a):
(5.7) IW = f(Ia, In, ha, h., Z., Za).
That is, I. is a function of I,, I,, h,, ha, Z., and Z.. If there are m
groups of income recipients, equation (5.7) can be readily general-
ized as:
(5.8) IW= f(I,, I2, ...,Ij,..Im; h,h2,..., hj, hm;
ZI) Z27 ... p Zip ... J Zm).
1i is the coefficient of variation; h, is the family share; Z, is the
income parity of the jth group. Treating these variables as func-
tions of time, I. can be differentiated with respect to time to give:
(5.9a) dt = R + D, where
(5.9b) >l jdt
(5.9b) R = asectnald d
al181 dt
rintrasectoral effectj
EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 231
(5.9c) D = W + P, where
[intersectoral effect]
(5.9d) W = (t-' = O) and
j_,_ ah3 dt j- dt/
[family-weight effect]
(5.9e) p = Z dZ
aZi dt
[income-di8parity effect]
Empirical Decomposition by Sectors
and Homogeneous Groups
The decomposition equation (5.4a) can be applied to decompose
the nationwide coefficient I, for various kinds of sectoral classi-
fication. This application is part of the strategy in this chapter of
seeking additional causal relations by way of an essentially inductive
methodology. Because the Taiwanese economy is dualistic, the
nationwide coefficient of variation will first be decomposed into
coefficients for the farm and nonfarm sectors. This nationwide co-
efficient will also be decomposed into sectors classified by varying
degrees of urbanization. Because the age, sex, and educational level
of the family head are attributes that affect family income, the
same decomposition equation will then be applied to the classifica-
tion of these families according to each of these factors. It will also
be applied to groups based on the number of persons employed per
family. In summary, the decomposition equation will be applied to
the following sectoral and group classifications:
* Farm and nonfarm economic activity (two sectors)
* Degree of urbanization (six sectors and three sectors)
* Age of family head (six groups)
. Sex of family head (two groups)
* Educational level of family head (six groups)
* Persons employed per family (seven groups)
For each decomposition the information needed is the coefficient of
variation for the jth sector or group [I;], the proportion of families
in the jth sector or group [hj], and the ratio of the income per family
232 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.2. Decomposition Analysis, by Farm
and Nonfarm Sectors, 1964-72
Variable and sector Notation 1964 1966 1968
Total Gini G 0.3282 0.3301 0.3348
Sectoral Gini
Farm sector G, 0.3153 0.3264 0.2916
Nonfarm sector G2 0.3363 0.3315 0.3383
Total coefficient I 0.7493 0.7073 0.7939
Sectoral coefficient
Farm sector 11 0.6524 0.6658 0.5952
Nonfarm sector 12 0.8035 0.7244 0.8109
Sectoral family
fraction
Farm sector hi 0.3959 0.3093 0.3154
Nonfarm sector h2 0.6041 0.6907 0.6846
Sectoral family
income parity
Farm sector ZA = yi/y 0.9888 0.9735 0.8350
Nonfarm sector Z2 = y2/y 1.0112 1.0265 1.1650
Estimated coefficient 7 0.7490 0.7087 0.7956
Error e = I-I -0.0003 0.0014 0.0017
Percentage error
(percent) D e/I X 100 -0.04 0.20 0.21
Sources: Calculated from DGBAS data (Taiwan Province and Taipei City
combined) for various years.
of sector or group j to the average income per family of all sectors or
groups EZ, = (y1/y) ].
The results of each decomposition are shown in tables 5.2 through
5.8. The maximum error of estimation of equation (5.4a), expressed
as a percentage of the original coefficient, is 1.69 percent among the
seventeen estimates; the average error of estimation is 0.24 percent.
EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 233
1970 1971 1972 Notation Variable and sector
0.2991 0.3006 0.2953 G Total Gini
Sectoral Gini
0.2828 0.2974 0.2907 GI Farm sector
0.2852 0.2916 0.2876 02 Nonfarm sector
0.6120 0.6194 0.6021 I Total coefficient
Sectoral coefficient
0.5734 0.6218 0.6061 I, Farm sector
0.5822 0.6007 0.5857 I2 Nonfarm sector
Sectoral family
fraction
0.3091 0.2363 0.2588 hi Farm sector
0.6909 0.7637 0.7412 h2 Nonfarm sector
Sectoral family
income parity
0.8075 0.8464 0.8644 Z, = yi/y Farm sector
1.1925 1.1536 1.1356 Z2 = Y2/Y Nonfarm sector
0.6115 0.6199 0.6032 I Estimated coefficient
-0.0005 0.0005 0.0011 e = I-I Error
Percentage error
-0.08 0.08 0.18 D = E/I X 100 (percent)
In all these tables the values of the sectoral and group Gini coeffi-
cients [Gi] and the Gini coefficient for all families [G] are shown for
purposes of comparison.
Farm and nonfarm sectors
It is interesting to compare the results shown in table 5.2 with the
income inequalities, family fractions, and family income parities of
234 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
the DGBAS farm and nonfarm sectors used in chapter three. According
to table 5.2 the situation in Taiwan over the 1964-72 period shows
the following:
* The inequality of the distribution of income was less within the
farm sector than within the nonfarm sector before 1971 and
slightly greater in 1971 and 1972.
. The weight of the farm sector in the total declined.
* The per family income of the nonfarm sector was higher than
that of the farm sector.
. The income distribution of the farm and nonfarm sectors im-
proved, but the speed of improvement was less for the farm
sector than for the nonfarm sector. The farm sector, which
earlier showed less inequality than the nonfarm sector, showed
more in 1972.
These results, using segmentation rather than additive-components
decomposition, are comparable to those obtained in chapter three.
Degree of urbanization
Because of the importance of industrialization and urbanization
in economic growth, the effect of urbanization on the distribution of
income should be explored. This effect can be brought out more
clearly with the help of the sectoral decomposition equation. The
necessary data were compiled from the original questionnaires of the
DGBAS surveys for 1966 and 1972. This compilation is divided into
two parts. One model of six sectors is based on a county classification;
another model of three sectors is based on a city-town-village classi-
fication. The six-sector classification is based on the degree of ur-
banization defined by a cluster of ratios: population to area, non-
agricultural employment to area, nonagricultural wage to area,
nonagricultural value added to area, government expenditure to
area, nonagricultural capital to labor, nonagricultural wage to labor,
nonagricultural value added to labor, nonagricultural employment to
population, and agricultural products to total products. The three-
sector classification is based on the definitions for urban, semiurban,
and rural areas given by the DGBAS and used in chapter four.
The two classifications have their respective merits and demerits.
The six-sector classification has the merit that many economic
indicators are available at this level, so that the characteristics of
urbanization can be identified and analyzed in relation to these
EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 235
indicators. That six-sector classification nevertheless deemphasizes
the geographic or locational dimension; for this reason a town may
well be included in a rural area. The three-sector classification is
separated by smaller units and brings out more clearly the underlying
characteristics of urbanization. But its usefulness for economic
analysis is limited because not even the information on value added
is available by this classification.
To identify the relations between urbanization and income distri-
bution, the income data based on the city-town-village classification
were compiled from the original questionnaires for 1966 and 1972.
Tables 5.3 and 5.4 give the results of the six-sector and three-sector
classifications and show the following for those two years:
. The inequality of the distribution of income within the more
urban sectors was not necessarily worse than that within the
less urban sectors.
* The proportion of families in the most urban sector in the total
increased, while that of the least urban sector declined over time.
* The per family incomes of the more urban sectors generally
were higher than those of the less urban sectors.
* Income inequality within a sector improved for every sector
over time.
Age of family head
Table 5.5 indicates that the inequality of income distribution for
each age category declined between 1964 and 1972. Moreover there
seems to have been a tendency toward somewhat greater inequality
for the higher age groups. As would be expected, earning power
increased with age until age 60 and then declined.
Sex of family head
The percentage distribution of female and male family heads in
each income bracket shows that females make up a majority of
family heads in the two lowest income groups; there are none in the
highest income group. Thus the presence of female heads of house-
holds is associated with poverty. In Taiwan, as elsewhere, job op-
portunities for females have generally been far from equal to those
for males. The jobs offered to women are also relatively less important,
and thus provide lower incomes. Although a female's earning power
236 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.3. Decomposition Analysis, by Degree of Urbanization
in the Six-sector Classification, 1966 and 1972
Variable and sector Notation 1966 1972
Total Gini G 0.3237 0.3018
Sectoral Gini
Most urban sector G1 0.3146 0.3052
Second urban sector G2 0.3066 0.2776
Third urban sector G1 0.2928 0.2566
Fourth urban sector G4 0.3325 0.2730
Fifth urban sector Gs 0.3183 0.2876
Most rural sector G6 0.3321 0.2924
Total coefficient I 0.6610 0.6290
Sectoral coefficient
Most urban sector h1 0.6405 0.6406
Second urban sector 12 0.6380 0.5499
Third urban sector 1, 0.5745 0.5016
Fourth urban sector 14 0.6869 0.5455
Fifth urban sector I5 0.6665 0.5848
Sixth urban sector 1 0.6593 0.6202
Sectoral family fraction
Most urban sector h, 0.2122 0.2195
Second urban sector h2 0.0952 0.1431
Third urban sector h3 0.1469 0.1917
Fourth urban sector h4 0.3111 0.2259
Fifth urban sector h5 0.1150 0.1496
Sixth urban sector h6 0. 1196 0.0702
Sectoral family income parity
Most urban sector Z y = Yi/y 1.1481 1.3740
Second urban sector ZI = Y2/y 1.1073 1.1374
Third urban sector Z3 = yl/y 0.9095 0.9893
Fourth urban sector ZI = y4/y 0.8993 0.8424
Fifth urban sector Z5 = Y6/y 1.0219 0.8677
Sixth urban sector Z6 = /Y 0.9138 0.7890
Estimated coefficient I 0.6620 0.6297
Error = I-1 0.0010 0.0007
Percentage error (percent) D e/I X 100 0.15 0.11
Note: The total Gini coefficient and the coefficient of variation differ from
those in tables 5.2 and 5.5-5.8 because the ones used here are directly calculated
from the original questionnaires.
Sources: Calculated from the original questionnaires of the DGBAS surveys.
EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 237
Table 5.4. Decomposition Analysis, by Degree of Urbanization
in the Three-sector Classification, 1966 and 1972
Variable and sector Notation 1966 1972
Total Gini G 0.3237 0.3018
Sectoral Gini
Urban sector G, 0.3134 0.2974
Semiurban sector G2 0.3182 0.2719
Rural sector G3 0.3316 0.2800
Total coefficient I 0.6610 0.6290
Sectoral coefficient
Urban sector I1 0.6505 0.6182
Semiurban sector I2 0.6432 0.5433
Rural sector 13 0.6684 0.5628
Sectoral family fraction
Urban sector hi 0.2826 0.3798
Semiurban sector h2 0.4137 0.3434
Rural sector h3 0.3037 0.2768
Sectoral family income parity
Urban sector Zi = yi/y 1.1278 1.2632
Semiurban sector Z2 = Y2/Y 0.9245 0.9223
Rural sector Z3 = YJ/y 0.9477 0.8145
Estimated coefficient I 0.6615 0.6291
Error = I-I 0.0005 0.0001
Percentage error (percent) D e/I X 100 0.08 0.02
Note: Same as to table 5.3.
Sources: Same as for table 5.3.
on average is less than that of a male, the data compiled by sex of
head of household distort the real earning power of a female (table
5.6). In the ordinary family, the husband's name is registered as the
head of his family, which results in the large proportion of male
heads in the total. For the distribution of income, a family headed
by a female has broader implications than its literal meaning. Such
a family is most likely to be headed by a single woman or a widow;
238 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.5. Decomposition Analysis, by Age of Head of Family,
1964 and 1972
Variable and age Notation 1964 1972
Total Gini G 0.3282 0.2953
Sectoral Gini
Under 20 years GI 0.3289 0.2645
20-30 years G2 0.3131 0.2875
30-40 years 03 0.2995 0.2672
40-50 years G4 0.3227 0.2817
50-60 years G5 0.3401 0.3150
Over 60 years G6 0.4107 0.4038
Total coefficient 1 0.7493 0.6021
Sectoral coefficient
Under 20 years I, 0.6280 0.5122
20-30 years I2 0.7867 0.5840
30-40 years 13 0.6364 0.5434
40-50 years I4 0.8244 0.5798
50-60 years I, 0.6933 0.6287
Over 60 years I6 0.8407 0.7971
Sectoral family fraction
Under 20 years hi 0.0083 0.0090
20-30 years h2 0.1136 0.0956
30-40 years h3 0.3274 0.2916
40-50 years h4 0.3181 0.3582
50-60 years h, 0.1721 0.1839
Over 60 years h6 0.0605 0.0617
Sectoral family income parity
Under 20 years Z, y,/y 0.6388 0.7758
20-30 years Z2 Y2/Y 0.9437 0.9577
30-40 years Z3 y3/y 0.9893 0.9862
40-50 years Z4 - y4/y 1.0833 1.0876
50-60 years Z= y6/y 1.2130 1.1681
Over 60 years Z= Y6/Y 1.1318 1.0245
Estimated coefficient I 0.7519 0.6029
Error e = I - I 0.0026 0.0008
Percentage error (percent) D = elI X 100 0.35 0.13
Sources: Same as for table 5.2.
EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 239
Table 5.6. Decomposition Analysis, by Sex of Head of Family,
1964 and 1972
Variable and sex Notation 1964 1972
Total Gini G 0.3282 0.2953
Sectoral Gini
Male G, 0.3245 0.2899
Female G2 0.3575 0.3617
Total coefficient I 0.7493 0.6021
Sectoral Coefficient
Male 1, 0.7591 0.5953
Female I, 0.7511 0.7239
Sectoral family fraction
Male h, 0.9235 0.9327
Female h2 0.0765 0.0673
Sectoral family income parity
Male ZA = yi/y 1.1173 1.0722
Female Z2= =Y/Y 0.8827 0.9278
Estimated coefficient I 0.7620 0.6039
Error e= I-I 0.0127 0.0018
Percentage error (percent) D E/I X 100 1.69 0.30
Sources: Same as for table 5.2.
in the absence of a male spouse, the number of working persons in
the family may be less than that in a family with a male head. These
factors, when added to the lower earning power of the female, make
the income parity of female-headed households lower than that of
male-headed households.
Number of persons employed per family
The number of persons employed per family is considered to be an
important factor affecting family income and its distribution. The
240 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.7. Decomposition Analysis, by Number of Persons Employed
in Family, 1964 and 1972
Variable and number employed Notation 1964 1972
Total Gini G 0.3282 0.2953
Sectoral Gini
None GI 0.4889 0.4297
1 G2 0.3213 0.2877
2 G3 0.3232 0.2805
3 G4 0.2968 0.2949
4 Gs 0.3158 0.2740
5 G6 0.2655 0.2415
6 or more G7 0.2785 0.2682
Total coefficient I 0.7493 0.6021
Sectoral coefficient
None I, 1.0472 0.8999
1 I2 0.7316 0.6102
2 I3 0.7018 0.5645
3 14 0.5962 0.5892
4 is 1.0119 0.5719
5 I, 0.5497 0.4777
6 or more I7 0.5348 0.4942
conclusions from the decomposition effort are summarized in table
5.7.
. Income generally increased as the number of persons employed
increased, which can be observed by comparing the income
parity of each category.
* Income inequality seems to have had a slight tendency to
decline as the number of employed rose; the category, zero
persons employed, had the widest income inequality.
Educational level of family head
As already seen with respect to the explanation of the distribution
of the wage share in chapter four, the effect of education on the level
and distribution of income is crucial. The data reveal that illiterates
EMPIRICAL DECOMPOSITION BY SECTORS AND HOMOGENEOUS GROUPS 241
Table 5.7 (Continued)
Variable and number employed Notation 1964 1972
Sectoral family fraction
None h, 0.0140 0.0185
1 h2 0.3929 0.4218
2 h3 0.2760 0.3220
3 h4 0.1464 0.1206
4 h6 0.0895 0.0686
5 h6 0.0434 0.0295
6 or more h7 0.0378 0.0190
Sectoral family income parity
None Z = yi/y 0.5818 0.6121
1 Z2= Y21Y 0.8129 0.8228
2 Z3 = y3/y 0.8816 0.9104
3 Z4= Y4/Y 0.9167 1.0947
4 Zs = Y /y 1.0964 1.0606
5 Z6= Y6/y 1.1460 1.1121
6 or more Z7= y7/y 1.5646 1.3873
Estimated coefficient 1 0.7552 0.6037
Error e = I - I 0.0059 0.0016
Percentage error (percent) D = e/I X 100 0.79 0.27
Source: Same as for table 5.2.
had the least earning power (table 5.8). They were followed in
ascending order by graduates of primary school, junior high school,
and senior high and vocational school. The highest income could
generally be earned by college graduates, not by graduate school
graduates. The relation between wealth and higher levels of educa-
tion is known not to be close.5 Although educational attainments
up to a point are required for obtaining higher incomes, a person's
income-earning ability does not seem to be monotonically related to
5. Shirley W. Y. Kuo, "Income Distribution by Size in Taiwan Area-Changes
and Causes," in Income Distribution, Employment and Economic Development in
Southeast and East Asia, 2 vols. (Tokyo: Japan Economic Research Center,
1975), vol. 1, pp. 80-146.
242 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.8. Decomposition Analysis, by Educational Level of Head
of Family, 1972
Variable and educational level Notation 1972
Total Gini G 0.2820
Sectoral Gini
Graduate school graduate GI 0.1852
College graduate G2 0.2438
Senior high school graduate GS 0.2547
Junior high school graduate G4 0.2521
Primary school graduate G, 0.2769
Illiterate G6 0.3059
Total coefficient I 0.5651
Sectoral coefficient
Graduate school graduate II 0.3450
College graduate 12 0.4725
Senior high school graduate Ih 0.5132
Junior high school graduate 14 0.5062
Primary school graduate I, 0.5627
Illiterate 16 0.5895
Sectoral family fraction
Graduate school graduate h, 0.0011
College graduate h2 0.0706
Senior high school graduate h3 0.1607
Junior high school graduate h4 0.1301
Primary school graduate h5 0.5141
Illiterate h6 0.1234
Sectoral family income parity
Graduate school graduate Z= yi/y 1.1247
College graduate Z2 Y2/Y 1.1840
Senior high school graduate Z3= yS/y 1.1458
Junior high school graduate Z4 = y4/y 0.9626
Primary school graduate ZA = y/y 0.8505
Illiterate Z = Y6/Y 0.7324
Estimated coefficient I 0.5635
Error e=I-I -0.0016
Percentage error (percent) D = c/I X 100 -0.28
Source: Calculated from DGBAS data. Only 1972 data for Taiwan Province is
available.
CHANGES IN INCOME INEQUALITY 243
education beyond a certain income level. What is more interesting,
the equity of income distribution tends to be higher for the more
educated groups.
Changes in Income Inequality Associated
with Industrialization and Urbanization
During the 1964-72 period, as already seen, overall income in-
equality significantly declined. But with farm-family income growing
less rapidly than nonfarm-family income, the income gap between
the two kinds of family widened. In addition, the income gaps among
family groups in different locations, classified by the degree of urbani-
zation, widened during the same period. The widening gap caused
by industrialization and urbanization can be observed through
changes in income disparities, an indicator suggested by Kuznets,
in sectors classified by farm and nonfarm families and by different
degrees of urbanization.6
Disparities in the shares of farm and nonfarm families increased
from 1964 to 1972, indicating increasing inequality between the two
sectors (table 5.9). The respective divergence of the income-relative
from unity in each sector also shows increasing inequality. Income
disparities by degree of urbanization show that the widening was
mainly caused by the most urban and rural sectors (tables 5.10 and
5.11). Levels and trends in income differences among the sectors
reveal that per family income was rising at a higher-than-average
rate in the nonfarm sector and the most urban sector. In contrast,
per family income was rising at a lower-than-average rate in the
farm sector and the most rural sector.
How, then, was more equity generated for the whole economy?
In an attempt to answer this question, equation (5.9) was used to
determine intrasectoral and intersectoral effects for the 1964-72
period.7 The intersectoral effect will be further divided into a family-
6. Simon Kuznets, "Demographic Components in Size Distribution of Income,"
in Income Distribution, Employment and Economic Development in Southeast and
East Asia, vol. 2, pp. 389-472.
7. In earlier chapters 1968 was identified as the turning point for growth and
distribution. In this regard separate causal analyses should be made for the
1964-68 and 1968-72 subperiods. We nevertheless restrict ourselves to the
entire 1964-72 period because the data required for the separate analysis of
causal subperiods are lacking. For example, data on urbanization can be used
only for 1966 and 1972.
244 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.9. Income Disparities, by Farm and Nonfarm Families,
1964 and 1972
Share of Share of Disparity
income families in shares Income
(percent) (percent) (percentage points) relativea
Type of
family 1964 1972 1964 1972 1964 1972 1964 1972
Farm
families 39.1 21.0 39.6 25.9 -0.5 -4.9 0.99 0.81
Nonfarm
families 60.9 79.0 60.4 74.1 0.5 4.9 1.01 1.07
All families 100.0 100.0 100.0 100.0 1.0b 9.8b 1.00 1.00
Sources: Same as for table 5.2.
a. The ratio of the share of income to the share of families.
b. The sum of the absolute values.
Table 5.10. Income Disparities, by Degree of Urbanization
in the Six-sector Classifcation, 1966 and 1972
Share of Share of Disparity
income families in shares Income
(percent) (percent) (percentage points) relative,
Degree of
urbanization 1966 1972 1966 1972 1966 1972 1966 1972
Most urban 24.6 29.3 21.2 21.9 3.4 7.4 1.16 1.34
Second
urban 10.7 15.8 9.5 14.3 1.2 1.5 1.13 1.10
Third
urban 13.5 18.4 14.7 19.2 -1.2 -0.8 0.92 0.96
Fourth
urban 28.3 18.5 31.1 22.6 -2.8 -4.1 0.91 0.82
Fifth
urban 11.9 12.6 11.5 15.0 0.4 -2.4 1.03 0.84
Most rural 11.0 5.4 12.0 7.0 -1.0 -1.6 0.92 0.77
All sectors 100.0 100.0 100.0 100.0 10. 0b 17.Sb 1.00 1.00
Sources: Same as for table 5.3.
a. The ratio of the share of income to the share of families.
b. The sum of the absolute values.
CHANGES IN INCOME INEQUALITY 245
Table 5.11. Income Disparities, by Degree of Urbanization
in the Three-sector Classification, 1966 and 1972
Share of Share of Disparity
income families in shares Inconw
(percent) (percent) (percentage points) relative
Degree of
urbanization 1966 1972 1966 1972 1966 1972 1966 1972
Urban 32.2 46.9 28.2 38.0 4.0 8.9 1.14 1.23
Semiurban 38.7 31.0 41.4 34.3 -2.7 -3.3 0.93 0.90
Rural 29.1 22.1 30.4 27.7 -1.3 -5.6 0.96 0.80
All sectors 100.0 100.0 100.0 100.0 8.0b 17.8b 1.00 1.00
Sources: Same as for table 5.3.
a. The ratio of the share of income to the share of families.
b. The sum of the absolute values.
weight effect and an income-disparity effect. The change in the
nationwide inequality depends on the sum of these effects and can-
not be explained by any single one.
Causes traced to the farm-nonfarm decomposition
The intrasectoral and intersectoral effects calculated for the farm
and nonfarm sectors are shown in table 5.12.
* Because of the reduction in internal inequality within both the
farm and nonfarm sectors, the favorable intrasectoral effect con-
tributed to the reduction in income inequality. The farm sector
contributed 7 percent to the intrasectoral effect; the nonfarm
sector 93 percent.
* The intersectoral effect, constituted by the adverse family-
weight effect and the adverse income-disparity effect, was
adverse to the distribution of income. The family-weight effect
contributed 26 percent to the intersectoral effect; the income
disparity effect 74 percent. That is, the change in the
weights of farm and nonfarm family numbers and the widening
of the income gap between the two sectors adversely affected
the distribution of income. The magnitude of adverse effects,
expressed as a percentage of the absolute value of the total
change, was 18.1 percent.
246 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.12. Causes of the Reduction in Income Inequality, by Farm
and Nonfarm Sectors, 1964-72
Intra- Inter- Family Income
Total sectoral sectoral = weight + disparity
effect effect, effect effect effect
[2 aI-.dIl 1 aL. .dAl h F al. dZ
Sector [i] IY ali dJ + Lj a dtj
Both sectors -0.1457 -0.172 7 0.0270 0.0057 0.0213
Percentage
of total
effect -100.0 -118.5 18.5 3.9 14.6
Farm sector - -0.0117 (-6.8) - 0.0512 0.0115
Nonfarm
sector - -0.1610 (-93.2) - -0.0455 0.0098
- Not applicable.
Note: Positive coefficients represent effects which act to increase income in-
equality; negative coefficients, those which act to reduce income inequality.
Source: Calculated from table 5.2.
a. The figures in parentheses indicate the percentage composition of the in-
trasectoral effect.
The decomposition of the intrasectoral and intersectoral effects
shows that the essential cause of the reduction in income ine-
quality in Taiwan was the reduction in income inequality within
the nonfarm sector. That is, the reduction in intrasectoral
inequality within the nonfarm sector more than compensated
for the adverse intersectoral effect and made possible the re-
duction in income inequality for the total economy.
Causes traced to the urbanization decomposition
The causes of the overall reduction in income inequality related to
the degree of urbanization are examined next (table 5.13). The
following intrasectoral and intersectoral effects were observed:
- The reduction in internal inequality within each of the six
sectors contributed most to the reduction in income inequality.
The rate of contribution to the reduction in income inequality
of the total economy was 183.7 percent. The reduction in intra-
CHANGES IN INCOME INEQUALITY 247
Table 5.13. Causes of the Reduction in Income Inequality, by Degree
of Urbanization in the Six-sector Classification, 1966-72
Intra- Inter- Family Income
Total sectoral sectoral = weight + disparity
effect effect' effect effect effect
r[tu a1 sl r2] d, Praldh,k| + 2 aIwdZj]
Sector [ I ] lhdt I l oh1 dt j L,aZidtJ
All sectors -0.0332 -0.0610 0.0278 -0.0066 0.0344
Percentage
of total
effect -100.0 -183.7 83.7 -19.9 103.6
Most urban - -0.00003 (0.0) - -0.0018 0.0259
Second urban - -0.0118 (-19.4) - -0.0175 0.0004
Third urban - -0.0091 (-14.9) - -0.0181 -0.0042
Fourth urban - -0.0282 (-46.2) - 0.0267 0.0047
Fifth urban - -0.0091 (-14.9) - -0.0110 0.0040
Most rural - -0.0028 (-4.6) - 0.0151 0.0036
- Not applicable.
Note: Positive coefficients represent effects which act to increase income in-
equality; negative coefficients, those which act to reduce income inequality.
Source: Calculated from table 5.3.
a. The figures in parentheses indicate the percentage composition of the in-
trasectoral effect.
sectoral inequality compensated for the adverse intersectoral
effect and thus significantly contributed to the reduction of
income inequality for the whole economy.
. The fourth urban sector made the highest contribution to the
intrasectoral effect, recording 46.2 percent of the total. Other
important contributions came from the second, third, and fifth
urban sectors; their contribution rates ranged from 14.9 percent
to 19.4 percent. The most rural sector contributed 4.6 percent;
the most urban sector contributed nothing. This seems to indi-
cate that the income inequality was reduced much more within
a semiurban area than within either the most urban or the most
rural area.
* The intersectoral effect was unfavorable to the reduction of
income inequality. Combining the family-weight effect and the
income-disparity effect, the total adverse contribution was 83.7
percent.
248 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.14. Causes of the Reduction in Income Inequality, by Degree
of Urbanization in the Three-sector Classification, 1966-72
Intra- Inter- Family Income
Total sectoral sectoral = weight + disparity
effect effect' effect effect effect
[ a .il 2d al-.dh,1 + [2 aI_ dZj]
Sector I i L j al; dt I ahi dt LaZi dt
All sectors -0.0334 -0.0679 0.0345 0.0049 0.0296
Percentage
of total
effect -100.0 -203.3 103.3 14.7 88.6
Urban - -0.0151 (-22.2) - -0.0279 0.0179
Semiurban - -0.0296 (-43.6) - 0.0245 0.0002
Rural - -0.0232 (-34.2) - 0.0083 0.0115
- Not applicable.
Note: Positive coefficients represent effects which act to increase income in-
equality; negative coefficients, those which act to reduce income inequality.
Source: Calculated from table 5.4.
a. The figures in parentheses indicate the percentage composition of the in-
trasectoral effect.
. The change in the weights of family numbers had a moderately
favorable effect on the reduction of income inequality for the
total economy.
. The widening income gaps among the six sectors adversely
affected the distribution of income. The magnitude of the ad-
verse income-disparity effect, expressed as a percentage of the
absolute value of the total change, was 103.6 percent.
Another observation for the effects of urbanization on the dis-
tribution of family income is based on the three-sector classification
of cities, towns, and villages. Causes of reduction in income inequality
observed by this three-sector classification are presented in table
5.14. Essentially the results are the same as those observed with
the six-sector classification.
. The favorable intrasectoral effect more than compensated for
the adverse intersectoral effect.
* The contribution by the semiurban sector to the intrasectoral
effect was largest; that by the urban sector, smallest.
ADDITIONAL REFLECTIONS 249
The intersectoral effect was adverse to the reduction of income
inequality. Based on this city-town-village classification, the
change in the family weight had a slightly adverse effect on the
change in income equality.
In summary, the intersectoral income gap widened during the
course of industrialization and urbanization in Taiwan, but intra-
sectoral inequality was reduced more than enough to compensate
for the adverse intersectoral effect. This performance confirms that
decentralization of economic development may contribute substan-
tially to the reduction of income inequality.
Additional Reflections
Rapid economic growth in Taiwan during the 1964-72 period
raised the average income of households in every bracket and led to
absolute increases in the welfare of all income groups. What are
the policies that seem to have contributed to TI'aiwan's success in
reducing income inequality during a period of rapid growth? Many,
to be sure. But some of the more important and obvious policies are
the following: the pursuit of a labor-intensive and outward-looking
growth path; early land reform; the reduction in the collection of a
hidden tax on rice; and reductions in the relative tax burden of
farmers and the poor. Moreover, the size and composition of families
moved in a direction favorable to a reduction of income inequality.
The causal interrelations among these and other factors still are far
from clear and require further analysis.
The importance of rural by-employment
As noted in chapter three, a distinguishing characteristic of Tai-
wan's farm-family income is that it has a substantial component of
nonagricultural income. The proportion of nonagricultural income in
farm income was 34.1 percent in 1964 and 53.7 percent in 1975.
How did the composition of nonagricultural income relate to differ-
ent levels of farm income? The lower the income level, the bigger
the proportion of nonagricultural income (table 5.15). In 1975 the
lowest 80 percent of families received more than half their income
from nonagricultural sources. About 98 percent of nonfarm income
260 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.15. Sources of Income of Farm and Nonfarm Families,
by Decile, 1966 and 1976
(percent)
Composition of total family income
1966 1975
Nonfarm Nonfarm
Farm families families Farm families families
Non- Non- Non- Non-
Agri- agri- Agri- agri- Agri- agri- Agri- agri-
cultural cultural cultural cultural cultural cultural cultural cultural
Decile, income income income income income income income income
1 54.7 45.3 2.9 97.1 33.9 66.1 2.1 97.9
2 55.3 44.7 2.8 97.2 37.3 62.7 2.0 98.0
3 57.3 42.7 3.0 97.0 39.0 61.0 2.1 97.9
4 61.0 39.0 2.4 97.6 40.6 59.4 1.9 98.1
5 64.3 35.7 1.8 98.2 43.1 56.9 1.6 98.4
6 65.5 34.5 2.4 97.6 44.4 55.6 1.9 98.1
7 68.5 31.5 1.7 98.3 46.0 54.0 1.8 98.2
8 70.1 29.9 2.2 97.8 48.4 51.6 2.7 97.3
9 70.2 29.8 2.3 97.7 50.8 49.2 1.9 98.1
10 67.6 32.4 1.8 98.2 52.4 47.6 2.4 97.6
All
deciles 65.9 34.1 2.2 97.8 46.3 53.7 2.1 97.9
Sources: Calculated from DGBAS, Report on the Survey of Family Income and
Expenditure, 1966 and 1975.
a. Arranged from lowest to highest income.
was from nonagricultural activities. Thus the role of agricultural
income in nonfarm household income was negligible.
During the 1964-75 period the real income of both farm and non-
farm families considerably increased in every income bracket. The
increase was much higher in the lower income groups than in the
higher income groups (table 5.16). For the nonfarm sector, the lowest
decile had a 368 percent increase in income; the highest decile a 199
percent increase. For the farm sector, the lowest decile had a 235
percent increase in income; the highest decile had only a 17 percent
increase. Furthermore, the increase of nonagricultural income
brought about the increase in total farm-family income.
The higher growth rates of income from nonagricultural activities
ADDITIONAL REFLECTIONS 251
Table 5.16. Growth of Income of Farm and Nonfarm Families,
by Decile, 1966-75
(percent)
Farm families
Total
Agri- Nonagri- income of
Total cultural cultural nonfarm
Decilea income income income families
1 235 107 388 368
2 251 137 392 335
3 238 130 382 315
4 232 121 406 303
5 228 120 423 298
6 213 112 405 290
7 202 103 417 278
8 185 97 392 262
9 182 104 367 240
10 170 110 297 199
All deciles 199 110 372 261
Sources: Same as for table 5.15.
a. Arranged from highest to lowest income.
among the lower-income family groups give additional support to
the notion that two main factors were responsible for the good overall
performance: the relatively rapid rate of employment generation
for members of the lower income groups initially; the change in their
wages subsequently. During the period under observation, rapid
labor absorption finally eliminated rural unemployment or under-
employment. Newcomers and unemployed individuals were mainly
absorbed by the nonagricultural sector, particularly by light manu-
facturing industries. Thus unskilled labor was efficiently used. As
the economy grew, such labor became relatively more scarce, until
wage rates of unskilled labor finally were rising more rapidly than
those of skilled labor. Undoubtedly the early and rapid absorption
of unskilled labor substantially contributed to the rise in relative
incomes of the lower income families, both urban and rural. Indus-
trial decentralization clearly contributed to this labor absorption and
was an essential factor contributing to the reduction of overall in-
come inequality.
252 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.17. Gini Index of Land Concentration in Selected
Countries, Comparisons for Various Years
Decline
in Gini
Gini Gini index
Country Year index Year index (percent)
Colombia 1960 0.864 1969 0.818 5.32
India 1953-54 0.628 1960-61 0.589 6.14
Mexico 1930 0.959 1960 0.694 27.64
Philippines 1948 0.576 1960 0.534 7.26
Taiwan 1952 0.618 1960 0.457 26.08
United Arab
Republic 1952 0.810 1964 0.674 16.74
Source: Hung-Chao Tai, Land Reform and Politics (Berkeley: University of
California Press, 1974), p. 310, reproduced in Yung Wei, "Modernization Process
in Taiwan: An Allocative Analysis," Asian Survey, vol. 16, no. 3, (March 1976),
pp. 249-69.
Effects of land reform
Income inequality is naturally related to initial conditions. That
is, it is related to the original distribution of such assets as land,
capital, and educational training, which provide rents, dividends,
interest, and salaries. The inequality usually is much more severe in
asset holdings than in income. For these reasons, measures to dis-
tribute assets more equally may be important for a more equal
distribution of income.
Table 5.17 shows the Gini index of land concentration in selected
countries. The Gini index for Taiwan was 0.618 in 1952, before
land reform had its full effect, and 0.457 by 1960.8 Taiwan's land
reform, already discussed in chapter two, resulted in smaller scale
farming. Landholdings of more than three hectares constituted 42
percent of the total cultivated area before land reform, but only 23
percent after its implementation. Landholdings of one hectare or
less, which originally constituted 25 percent of the total area, increased
to 35 percent. The smaller average size farms in turn brought about
a more intensive use of labor and of multiple-cropping practices.
8. Yung Wei, "Modernization Process in Taiwan: An Allocative Analysis,"
Asian Survey, vol. 16, no. 3 (University of California Press, March 1976), pp.
249-69.
ADDITIONAL REFLECTIONS 258
Table 5.18. Indexes of the Productivity of Land and Labor
in Agriculture, Taiwan, 1950 and 1955
Land Land Labor Labor
Year area productivity inputs productivity
1950 100.0 100.0 100.0 100.0
1955 100.7 121.5 107.6 113.2
Source: T. H. Lee, "Impact of Land Reform on the Farm Economy Structure,"
(n.p., n.d.).
After the land reform, farmers had a freer choice of crops. As
owner-cultivators, they were under no obligation to produce rice for
rental payments. Thus the land reform tended to reduce the share of
rice and to increase the share of other such crops of higher value
as livestock and poultry. Moreover labor productivity increased
more slowly than land productivity during 1950-55, indicating the
labor-using bias of technological change in agriculture (table 5.18).
Reduction in the collection of the hidden tax on rice
For market control, all commercial activities of farmers' associa-
tions and private rice dealers in Taiwan were subject to government
supervision. Control of rice not only stabilized the supply and price
of rice, but also generated considerable revenue for government.
A hidden tax on rice was imposed through land taxes, compulsory
rice purchases, a rice-fertilizer barter system, and the payment for
land in kind. All these taxes were levied by government purchases
at lower-than-market prices. The revenue from these hidden taxes
was important: it exceeded total income tax collections every year
before 1963, but declined gradually after 1964 and rapidly after
1969, especially in comparison with the income tax. This rapid re-
duction in the collection of the hidden tax on rice undoubtedly
contributed to the more even distribution of income over time.
Relative reduction in the tax burden of farm families
The ratio of the tax burden of farm families to that of nonfarm
families was 1.73 to 1 in 1966; it declined to 0.35 to 1 by 1975 (table
5.19). Even more noteworthy is that the reversal from farm families
having a heavier to a lighter tax burden than nonfarm families was
more pronounced for the lower income brackets. A cross-sectional
254 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.19. Relative Tax Burden of Farm and Nonfarm Families,
by Income Range, 1966 and 1975
Ratio of tax burden of farm
families to that of nonfarm
Income range families
(thousands of
N.T. dollars) 1966 1975
Less than 10 3.92
10-20 3.60 0.85
20-30 3.22 1.16
30-40 2.59 1.39
40-50 1.67 1.34
50-60 2.07 1.12
60-70 2.02 0.95
70-80 1.42 0.83
80-90 1.31 0.82
90-100 0.68 0.60
100-150 0.68 0.49
150-200 1.17 0.56
More than 200 - 0.19
All income ranges 1.73 0.35
-Not applicable.
Sources: Calculated from DGBAS, Report on the Survey of Family Income and
Expenditure, 1966 and 1975.
analysis of the relation of taxes to distribution is discussed in the
next chapter.
Changing size and composition of families
In chapter four on the inequality of family wage income, the
causes of inequality were related to the size and composition of
families. Some additional inductive evidence is cited here to support
that analysis. These observations are based, however, on total family
income, not on family wage income.
How can the reduction in income inequality during the 1964-72
period be traced to changes in the size of families, the number of
employed per family, the age of the family head, and the sex of the
family head? Because the income gap widened between the farm
and nonfarm sectors, it is desirable to keep the two sectors separate,
lest the positive and negative demographic effects of each sector act
ADDITIONAL REFLECTIONS 255
to compensate each other. But because of the lack of sectorally
separated data for demographic effects on the distribution of in-
come, these effects are observed in a combined framework that
takes into account the whole economy. The income disparities by
the number of employed, by age, and by sex are calculated. The
causes of the reduction in the income inequality are also identified,
based on the decomposition equation for each classification. All
statistical results are shown in tables 5.20-5.29 appended to this
chapter.
During 1966-72 the average family sizes for the total economy,
farm families, and nonfarm families all declined.9 The variance of
family size also declined for each kind of family. The reduction of
family size and its variance thus increased the homogeneity of family
composition, a pattern that may have contributed to the reduction
of income inequality. When the income disparity by size of family is
calculated for the total economy, the results show that income dis-
parities between various sizes of families considerably narrowed
during the period. The disparities were mostly reduced by changes
in the incomes of one-person families and of the family group of ten
persons or more.
The income disparities by number employed per family also de-
clined. The greatest reduction of disparities occurred in family groups
with the larger numbers of employed. Using the same decomposition
formula to calculate the three effects, it is found that all of them
contributed to the reduction of overall income inequality. The
family-weight effect contributed 1.3 percent; the income-disparity
effect 5.9 percent; the intrasectoral effect 92.8 percent.
The income disparities by age of family head slightly declined.
The reduction mainly resulted from the groups of under 20, 50-60,
and over 60. The income disparities classified by sex of family head
also declined. The per family income share of female-headed families
rose during the period. The decomposition analysis shows that,
whereas all effects contributed to the reduction in income inequality,
the intrasectoral effect was dominant.
In brief, when families are classified by size or composition, a
reduction in income disparities is observed between groups in every
case. The intrasectoral effect was dominant in each of the three
cases. A favorable intersectoral effect is also observed in every case,
9. The year 1966 is observed because of the inadequacy of the relevant DGBAS
data for 1964. We are grateful to Professor Kuznets for pointing this out.
256 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
but its magnitude was not large. This suggests that changes in the
size and composition of families must have contributed to the re-
duction of income inequality. The picture is not clear, however,
because many of these changes were in turn the result of economic
growth and by no means exogenous. Because interrelations between
demographic change and economic growth are close, the intrasec-
toral reduction in income inequality observed in the demographic
classification must have been caused by a large number of economic
factors that are still too complicated to be unraveled here. More
theoretical work, departing from the preliminary inductive evidence
gathered in this chapter, is required.
Table 5.20. Average Size of Families,
by Income Bracket, 1966 and 1972
1966a /972b
Average Average
Income bracket number of Deviation number of Deviation
(thousands of persons in from the persons in from the
N. T. dollars) family mean family mean
Less than 10 2.0 -3.9 1.2 -4.5
10-20 4.4 -1.5 2.7 -3.0
20-30 5.5 -0.4 4.4 -1.3
30-40 6.5 0.6 5.2 -0.5
40-50 7.9 2.0 5.5 -0.2
50-60 8.4 2.5 5.9 0.2
60-70 7.2 1.3 6.1 0.4
70-80 8.8 2.9 6.4 0.7
80-90 8.2 2.3 6.9 1.2
90-100 8.2 2.3 6.5 0.8
100-200 9.3 3.4 7.5 1.8
More than 200 4.2 -1.7 7.0 1.3
All brackets 5.9 - 5.7
-Not applicable.
Note: The average sizes of family in the same income brackets may not be
directly comparable for the two years because of a possible escalation in the income
level in each bracket during the period.
Sources: Calculated from DGBAs, Report on the Survey of Family Income and
Expenditure, 1966 and 1972.
a. For 1966 the variance divided by the square of the mean is 0.0747.
b. For 1972 the variance divided by the square of the mean is 0.0330.
ADDITIONAL REFLECTIONS 257
Table 5.21. Average Size of Farm Families,
by Income Bracket, 1966 and 1972
1966& 1972b
Average Average
Income bracket number of Deviation number of Deviation
(thousands of persons in from the persons in from the
N.T. dollars) family mean family mean
Lessthan 10 3.2 -4.0 2.0 -4.5
10-20 5.5 -1.7 3.2 -3.3
20-30 6.7 -0.5 5.0 -1.5
30-40 7.8 0.6 6.1 -0.4
40-50 8.8 1.6 6.7 0.2
50-60 9.7 2.5 7.0 0.5
60-70 9.1 1.9 7.6 1.1
70-80 11.6 4.4 8.2 1.7
80-90 9.5 2.3 8.8 2.3
90-100 11.8 4.6 9.1 2.6
100-200 13.9 6.7 10.1 3.6
More than 200 - - 9.9 3.4
All brackets 7.2 - 6.5 -
Not applicable.
Note: The average sizes of family in the same income brackets may not be
directly comparable for the two years because of a possible escalation in the
income level in each bracket during the period.
Sources: Same as for table 5.20.
a. For 1966 the variance divided by the square of the mean is 0.0709.
b. For 1972 the variance divided by the square of the mean is 0.0583.
258 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.22. Average Size of Nonfarm Families,
by Income Bracket, 1966 and 1972
19668 1972b
Average Average
Income bracket number of Deviation number of Deviation
(thousands of persons in from the persons in from the
N. T. dollars) family mean family mean
Less than 10 1.6 -3.7 1.1 -4.2
10-20 3.8 -1.5 2.0 -3.3
20-30 5.0 -0.3 3.7 -1.6
30-40 6.0 0.7 4.7 -0.6
40-50 7.4 2.1 5.1 -0.2
50-60 7.8 2.5 5.5 0.2
60-70 6.5 1.2 5.7 0.4
70-80 7.5 2.2 5.8 0.5
80-90 7.4 2.1 6.5 1.2
90-100 7.3 2.0 6.1 0.8
100-200 7.1 1.8 6.9 1.6
More than 200 4.2 -1.1 6.1 0.8
All brackets 5.3 - 5.3 -
- Not applicable.
Note: The average sizes of family in the same income brackets may not be
directly compaxable for the two years because of a possible escalation in the income
level in each bracket during the period.
Sources: Same as for table 5.20.
a. For 1966 the variance divided by the square of the mean is 0.0828.
b. For 1972 the variance divided by the square of the mean is 0.0357.
ADDITIONAL REFLECTIONS 259
Table 5.23. Income Disparities, by Size of Household, 1966 and 1972
Share of Share of Disparity
income households in shares Income
Number of (percent) (percent) (percentage points) relative,
persons in
household 1966 1972 1966 1972 1966 1972 1966 1972
1 2.6 1.4 6.6 3.3 -4.0 -1.9 0.39 0.42
2 4.3 2.8 5.4 4.2 -1.1 -1.4 0.80 0.67
3 5.8 7.8 7.7 9.3 -1.9 -1.5 0.75 0.84
4 9.7 12.5 11.5 13.7 -1.8 -1.2 0.84 0.91
5 14.0 20.9 15.3 21.2 -1.3 -0.3 0.92 0.99
6 14.5 19.5 14.8 19.3 -0.3 0.2 0.98 1.01
7 16.2 13.7 14.9 12.6 1.3 1.1 1.09 1.09
8 10.3 9.0 9.4 7.6 0.9 1.4 1.10 1.18
9 6.8 4.8 5.6 3.9 1.2 0.9 1.21 1.23
10 or more 15.8 7.6 8.8 4.9 7.0 2.7 1.80 1.55
All house-
holds 100.0 100.0 100.0 100.0 20.8b 12.6b 1.00 1.00
Sources: Same as for table 5.20.
a. The ratio of the share of income to the share of households.
b. The sum of tl - absolute values.
260 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.24. Income Disparities, by Number of Persons Employed
in Family, 1964 and 1972
Share of Share of Disparity
Number of income families in shares Income
persons (percent) (percent) (percentage points) relative,
emrployed in
family 1964 1972 1964 1972 1964 1972 1964 1972
None 1.2 1.2 1.8 1.8 -0.6 -0.6 0.67 0.67
1 37.3 37.9 42.2 42.2 -4.9 -4.3 0.88 0.90
2 27.9 32.0 29.1 32.2 -1.2 --0.2 0.96 0.99
3 11.8 14.4 11.1 12.1 0.7 2.3 1.06 1.19
4 11.5 8.0 S.9 6.9 2.6 1.1 1.29 1.16
5 5.2 3.6 4.0 2.9 1.2 0.7 1.30 1.24
6ormore 5.1 2.9 2.9 1.9 2.2 1.0 1.76 1.53
All families 100.0 100.0 100.0 100.0 13.4b 10.2b 1.00 1.00
Sources: Same as for table 5.2.
a. The ratio of the share of income to the share of families.
b. The sum of the absolute values.
ADDITIONAL REFLECTIONS 261
Table 5.25. Causes of the Reduction in Income Inequality, by Number
of Persons Employed in Family, 1964-72
Intra- Inter- Family Income
Total sectoral sectoral = weight + disparity
Number of effect effect, effect effect effect
persons 2 aI,dI [ al. dhj] + r2 dl,1dZ
emfployeld [2] , 2 tJ,d: S ,ajd
in family P3] i W iT I L oh, dtJ L aZ-j -dl
All categories -0.1532 -0.1422 -0.0110 -0.0020 -0.0090
Percentage
of total
effect -100.0 -92.8 -7.2 -1.3 -5.9
None - 0.0015(-1.0) - -0.0002 -0.0002
1 - -0.0395 (-27.8) - -0.0096 -0.0011
2 - -0.0371 (-26.1) - -0.0175 -0.0012
3 - -0.0010 (-0.7) - 0.0103 0.0008
4 - -0.0577 (-40.6) - 0.0022 -0.0024
5 - -0.0031 (-2.2) - 0.0070 -0.0002
6 or more - -0.0023 (-1.6) - 0.0058 -0.0047
- Not applicable.
Note: Positive coefficients represent effects which act to increase income
inequality; negative coefficients, those which act to reduce income inequality.
Source: Calculated from table 5.7.
a. The figures in parentheses indicate the percentage composition of the in-
trasectoral effect.
262 INCOME DISTRIBUTION AND ECONOMIC STRUCTURE
Table 5.26. Income Disparities, by Age of Head of Family,
1964 and 1972
Share of Share of Disparity
income families in shares Income
Age of (percent) (percent) (percentage points) relative,
head of
family 1964 1972 1964 1972 1964 1972 1964 1972
Under 20 0.5 0.7 0.8 0.9 -0.3 -0.2 -.63 0.78
20-30 10.1 8.7 11.4 9.6 -1.3 -0.9 0.89 0.91
30-40 30.6 27.3 32.7 29.2 -1.1 -1.9 0.94 0.93
40-50 32.6 36.9 31.9 35.8 0.7 1.1 1.02 1.03
50-60 19.7 20.4 17.2 18.4 2.5 2.0 1.15 1.11
Over60 6.5 6.0 6.0 6.1 0.5 -0.1 1.08 0.98
All families 100.0 100.0 100.0 100.0 6 4b 6.2b 1.00 1.00
Sources: Same as for table 5.2.
a. The ratio of the share of income to the share of families.
b. The sum of the absolute values.
Table 5.27. Causes of the Reduction in Income Inequality, by Age
of Head of Family, 1964-72
Intra- Inter- Family Income
Total sectoral sectoral = weight + disparity
effect effectV effect effect effect
Age of 2 al.dIj F aI,.dh1l+[, aI. dZ7l
head of Fli dtI [7.- 11z2
family I, ] L dt L hj dt I L, aZ; dt J
All families -0.1487 -0.1474 -0.0013 0.0034 -0.0047
Percentage
of total
effect -100.0 -99.1 -0.9 -2.3 -3.2
Under 20 - -0.0004 (-0.3) - -0.0002 -0.0009
20-30 - -0.0174 (-11.8) - 0.0057 -0.0003
30-40 - -0.0220 (-14.9) - 0.0144 0.0003
40-50 - -0.0898 (-60.9) - -0.0123 0.0002
50-60 - -0.0144(-9.8) - -0.0040 -0.0018
Over 60 - -0.0034 (-2.3) - -0.0002 -0.0022
- Not applicable.
Note: Positive coefficients represent effects which act to increase income
inequality; negative coefficients, those which act to reduce income inequality.
Source: Calculated from table 5.5.
a. The figures in parentheses indicate the percentage composition of the in-
trasectoral effect.
ADDITIONAL REFLECTIONS 263
Table 5.28. Income Disparities, by Sex of Head of Family,
1964 and 1972
Share of Share of Disparity
income families in shares Income
(percent) (percent) (percentage points) relative,
Sex of head -
of family 1964 1972 1964 1972 19641 1972 1964 1972
Male 93.9 94.1 92.3 93.3 1.6 0.8 1.02 1.01
Female 6.1 5.9 7.7 6.7 -1.6 -0.8 0.79 0.88
All families 100.0 100.0 100.0 100.0 3.2b 1.6b 1.00 1.00
Sources: Same as for table 5.2.
a. The ratio of the share of income to the share of families.
b. The sum of the absolute values.
Table 5.29. Causes of the Reduction in Income Inequality, by Sex
of Head of Family, 1964-72
Intra- Inter- Family Income
Total sectoral sectoral weight + disparity
effect effecta effect effect effect
Sex of r al dI,1 al[ dh, r aLo dZ,1
head of F1 2 2 _+1 2-
family L.i iof dtj J L ah, dt j X oZ, dt
All families -0.1597 -0.1576 -0.0021 -0 .0007 -0.0014
Percentage
of total
effect -100.0 -98.7 -1.3 -0.4 -0.9
Male - -0.1561 (-99.0) - -0.0032 -0.0006
Female - -0.0015 (-1.0) - -0.0025 -0.0008
- Not applicable.
Note: Positive coefficients represent effects which act to increase income
inequality; negative coefficients, those which act to reduce income inequality.
Source: Calculated from table 5.6.
a. The figures in parentheses indicate the percentage composition of the in-
trasectoral effect.
CHAPTER 6
Taxation and the Inequality
of Income and Expenditure
A TYPICAL FAMILY'S TOTAL INCOME [y] is the sum of several income
components, such as wage income [w], property income [7r], and
transfer income [n]. It also is the sum of various additive expendi-
ture components, such as spending for food and clothing [cl], hous-
ing [c21, and education [cD], payments of direct tax [ti] and indirect
tax [t2], and savings [s]. Thus:
(6.1a) y =w + r + n;
(6.1b) y= C + C2 + C3 + tl + t2 +S.
According to equation (6.1b), y is total family income before tax.
If there are n income-receiving families, column vectors can be
used to describe the structures of family income and expenditure:
(6.2a) Y = Cl + C2 + C3 + T, + T2+ S, where
(6.2b) Y = col (Yi, Y2, .. ),
(6.2c) ci = col (cil c,2, . . . v ci)X (i = 1, 2, 3)
(6.2d) T7 = col (til, t., tin), and (i = 1, 2)
(6.2e) S = col (S1, S2, . . . -
Thus Y is the structure of family income, Ci is the structure of
consumption of the ith commodity, Ti is the structure of tax pay-
ments, and S is the structure of savings.
When the family income structure [Y] is given, economists can
apply the familiar theory for determining the various consumption
264
TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE 265
structures [Ci] and tax structures [Ti]. For example, the various
consumption structures [Ci] are determined by consumption func-
tions measuring the propensities to consume the commodity ci
when y is given; family savings [8] are a residual. The structure
of direet tax payments [T1] is related to the structure of total family
income [Y] through rates of income tax. The structure of indirect
tax payments [T2] is related to the various consumption structures
through the rates of sales tax and commodity tax imposed upon
various commodities. This chapter is not concerned, however, with
the theory for the determination of Ci and Ti. They are assumed to
be given and are the points of departure for the analysis here.'
Total family income Ey] clearly is the means by which to obtain
family welfare; the various consumption categories Eci] and family
savings [s] are the ends. The inequality of family income, measured
for example by the Gini coefficient [G (Y)], thus is tantamount to
the inequality of the means to obtain family welfare. The inequality
of family income [G(Y)] is important, then, only because it ulti-
mately leads to the inequality of consumption [G(Ci) l and savings
[G(S) ]-the two measures focused upon in this analysis.
The structures of family savings [S] and family expenditure on
education [C3] respectively represent family investment in physical
and human resources. The inequality of these investment patterns
in one year, measured by G(S) and G(C3), leads to the inequality
of total family income in subsequent years. Thus the inequality of
family income persists mainly because the inequality of family
investment persists.
The inequality of the various family consumption patterns, meas-
ured by G(C1) and G(C2), can indicate the economic welfare of
families in the narrow sense. In a poor, underdeveloped economy
with a consumption standard not far above the subsistence level,
the inequality of the consumption of a basic food item corresponds
to the inequality of family welfare. In wealthier countries, however,
some items are consumed because they are conspicuous. For such
items of conspicuous consumption as clothing and housing, a large
G(Ci) indicates a sharp distinction in status or among classes. For
this reason a large G(Ci) is expected to be positively correlated
with G(Y), suggesting that the inequality of total family income
1. The outline of how such deterministic theories might be formulated is dis-
cussed at the end of this chapter.
266 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
leads to the inequality of conspicuous consumption. In the present
state of knowledge, it is not known whether the designation of a
particular commodity as "conspicuous" bears any relation to cultural
traits. For purposes of analysis the expenditure on housing [C3] has
been separated as a special category of consumption. This separation
is based on the intuition that housing expenditure in Taiwan is
conspicuous insofar as it is more unequal among income-receiving
families than expenditure for food and clothing-a hypothesis that
can be refuted by the empirical finding that G(C2) does not signifi-
cantly differ from G(C1).
The inequality of the tax structure, measured by G( T1) and
G(T2), indicates the primary impact of taxation on the inequality
of family income. Equation (6.2a) can be rewritten as:
(6.3a) V = Cl + C2 + C3 + S, where
family family spending
income = on consumer + family spending
after goods [ on housing J
-tax ii
+ [family spending family 1
on education Isavings]
(6.3b) V =Y-T1- -T2 and
family family
income income | payments of] [payments ofl
after before I [direct tax J Lindirect tax]
Ltax -Ltax i
(6.3c) Y = V + T1 + T2.
family 1 family
income income + payments of 1 [payments of]
before after Ldirect tax J indirect tax J
-tax L tax z
In the foregoing equations the column vector V = col (V1, V2, ...
Vn) stands for the structure of family income after tax-that is,
for the structure of net income. When the structure and inequality
of family income before tax are given, the inequality of the tax
structure [G(T ) and G(T2)] determines the inequality of income
after tax [G(V)]. The relations among G(Y), G(V), and G(Tj)
will be indicated more clearly as the analysis unfolds.
STATISTICAL DATA 267
In summary, the analysis of the inequality of family expenditure
has three purposes: to study the inequality of investment, to study
the patterns of consumption, and to study the inequality of taxation
-all in relation to their separate impact on the inequality of family
income. Having explained the economic significance of this analysis,
the discussion now proceeds to introduce the statistical data and the
analytical framework. The empirical analysis using this framework
will be undertaken in the final two sections.
Statistical Data
The statistical data used in the empirical analysis are for 1964,
1966, 1968, 1970, 1972 and 1973 (see tables 6.5-6.10 in appendix 6.1
at the end of this chapter). Each table presents the following data:
the income classes for total family income; the number of families
and the total family income for each income class; the expenditure
on housing [C2] and education [Ca], the expenditure on all other
consumption [cl], the direct tax [t,] and indirect tax [t2j; and the
family savings [s]. When the families are grouped into classes, the
underlying assumption is that all families within the same class
receive the same family income and spend the same amount for
each category of consumption.2
The main source for these tables is the DGBAS data, which give a
fairly detailed classification of family expenditure.3 For 1966 the
classification contained sixteen major categories as well as detailed
subcategories (table 6.1). In all, it had sixty-four items.4
As applied to appendix tables 6.5-6.10, housing expenditure [C2]
includes the categories for rent and water charges and for furniture,
furnishings, and household equipment; these items are indicated
by an asterisk in table 6.1. Educational expenditure [C3] includes
2. The tendency with such a procedure is to underestimate the inequality of
all expenditure components that do not have a high positive correlation with
the structure of total family income. This difficulty can be avoided only when
use is made of the original data-that is, when families are not grouped-rather
than published data, which groups families into classes. The original data is in
the original DGBAS questionnaires (see the tables appended to chapter four).
3. See appendix 4.1 to chapter four for the sample sizes and other details of
the DGBAS data.
4. For different years the DGBAS classifications differ slightly.
268 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
the categories for personal and medical care and for recreation and
amusement, as well as the subcategory of miscellaneous consumption
expenditure for education and research; these items are indicated
by a double asterisk in table 6.1. Therefore c3 is a proxy for invest-
ment in human resources; c2 for conspicuous consumption. Obvi-
ously the judgments involved in such definitions of these variables
Table 6.1. Categories of Household Expenditure
and Their Indirect Tax Burden, 1966
Indirect
tax burden
Category (percent)
Food 4.10
Beverages and tobacco 42.85
Clothing and other personal effects 5.60
Rent and water charges* 0.54
Rent 0.50
House repairs and installation 0.50
Water charges 1.78
Fuel and light 11.39
Furniture, furnishings, and household equipment* 5.93
Furniture and furnishings 2.41
Textile furnishings 5.60
Appliances for kitchen and bathroom 10.68
Other 10.68
Household operation 3.84
Personal and medical care** 6.59
Personal care n.a.
Barber and bath shop services n. a.
Medical and health expenses n.a.
Transport and communication 7.00
Recreation and amusement** 1.73
Recreation n.a.
Books, newspapers, magazines, and stationery n.a.
Other n.a.
STATISTICAL DATA 269
Table 6. 1 (Continued)
Indirect
tax burden
Category (percent)
Miscellaneous consumption expenditure 18.59
Financial services n.a.
Education and research** n.a.
Marriages, birthdays, and funerals n.a.
Other n. a.
Interest
Taxes
Household tax
House tax
Land value tax
Land tax
Land value improvement tax
Land value added tax
Inheritance tax
Bicycle license tax
Income tax
Other
Gifts and other transfer expenditure
Savings
d Indicates items of housing expenditure [c2].
** Indicates items of educational expenditure [ca].
Not applicable.
n.a. Not available.
Source: DGBAS, Report on the Survey of Family Income and Expenditure, 1966.
are a priori. For example, the expenditure for fuel and light is ex-
cluded from conspicuous consumption [C2] because it is for cooking.
The direct tax [t1] in the appendix tables includes all ten items
in the category for taxes in table 6.1. In addition to these direct
tax payments, families pay indirect tax when consumption expendi-
tures are made. Because the DGBAS data are based on household
surveys, the consumption expenditures listed under the various
categories in table 6.1 include indirect taxes. A separate procedure
was used to estimate the indirect tax payments [t2], which have
270 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
been subtracted from the DGBAS data to give family consumption
expenditures exclusive of indirect tax payments [cl, c2, and c3]. The
procedure for this computation is explained in appendix 6.1.
Analytical Framework
It can be seen from equations (6.3a) and (6.3c) that both V and
Y are vector sums of a number of components. Thus the inequality
of total family income [G( Y) ] and of family income after tax [G( V) ]
can be decomposed into factor components according to the follow-
ing equations5:
(6.4a) G(V) = RIeGc + RG2 + o3R3G3 + O.R.Gs;
inequality
of family [effect on effect on
income = consumption + housing
after expenditure expenditure
tax ]
[effec on [effect1on
+ educational + [ on
expenditure]
(6.4b) G(Y) = r + OtMG + 4RtGt±
inequality
of family [effect on 1 effect on1 r effect on 1
income = after-tax + o +
before ~ [ income [direct tax indirect tax
tax
Each effect is the product of a weight term [+X], a correlation term
[Ril, and a Gini term [GJ.
The terms GI, G2, Ga, and G. are the Gini coefficients of the struc-
tures of consumption [CJ and savings [S] in equation (6.3a)-that
is, GC = G(Ci) and G0 = G(S). Therefore G0 and G. respectively
measure the inequality of family investment in human and physical
resources. Similarly G, and G, respectively measure the inequality
of family expenditure on other consumption and housing consump-
5. The equations are directly obtained by applying equation (10.5) in chapter
ten to equations (6.3a) and (6.3c). Notice in equation (6.4) that G(V) = G..
ANALYTICAL FRAMEWORK 271
tion. The terms G1 and G2 respectively measure the inequality of
payments by families for direct and indirect tax.
The terms RI, R', R', and RS measure the correlation of the vec-
tors C1, C2, C3, and S with the vector of V. High and positive values
of R3 and R. indicate that human and physical investments are
heavily concentrated among wealthy families. A high and positive
value of R' means that expenditure on housing is very sensitive to
the level of total family income and suggests that housing is an
item of conspicuous consumption.
The terms RD, R', and R' express the correlations of the vectors
V, Ti, and T2 with the vector Y. R, would be expected to be close
to 1 because any rationally designed tax system should not overtly
disturb the rankings of families in the structure of income [Y]-
that is, families should have the same rank before and after their
tax payments. For a progressive direct tax, R' would be expected
to be high and positive, indicating that tax payments become pro-
gressively higher as total family income increases. For a regressive
indirect tax, R2 would be expected to be negative and close to -1,
indicating that the heavier tax burden falls upon low-income families.
Equation (6.4b) can be rewritten as:
(6.5) G(V) = (1/,BR,)G(Y) - (¶1Rj11/R,)G1- (o2R2/p,B)G2.
When the inequality of family income [G (Y)] is given, equation
(6.5) shows the impact of taxes on family income after tax. A high
and positive R1, which would be associated with a progressive tax,
contributes to the equality of family income after tax. A negative
Ri, which would be associated with a regressive tax, contributes to
the inequality of family income after tax.
The weight terms [¢i] in equations (6.4a) and (6.4b) are defined
as follows. Let X be the mean value of any vector X. Then equa-
tions (6.3a) and (6.3c) imply that:
(6.6a) V= 01 + 02 + C3 + S = - T1 - T2;
(6.6b) t0 = 01/V, 2 = C2/'V, C = 03/V, 0. = S/V; and
(6.6c) 4,, = V/Y, 44 = T1/j, 44 = T2/V; where
(6.6d) + e + is + 4. = 1 and
(6.6e) k8 + 1 + 02 1.
In equation (6.6b) 44 is the consumption expenditure of the ith
type expressed as a fraction of total family income excluding taxes;
272 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
4, is the fraction of average savings in average family income after
tax, or the average propensity to save. In equation (6.6c) 0, is the
ratio of income after tax to income before, or including, tax; Ot is
the total tax payment of the ith type expressed as a fraction of
income including tax.
Decomposition of Family Income after Tax
The results of the decomposition according to equation (6.4a) of
the Gini coefficient of family income after tax [G(V)] are presented
in table 6.2. The time series in this table are graphically represented
in figures 6.1-6.4. Figure 6.1 shows the time series of G(V) and
that of the four contribution terms [OiRiGi]. The once-for-all decline
of G(V) indicates that the distribution of family income after tax
was generally becoming more equal in this ten-year period. The
Figure 6.1. Contributions to the Inequality of Family Income
after Tax, by Category of Expenditure, 1964-73
0.4 Inequality of family income after tax
0.3 -
Consumption expenditure
-< _--.- - __ XI
0.2
Housing expenditure Savings
o.1 - - ------ ------
0 c I - Educational expenditure
0 ~R 3G3
1964 1966 1968 1970 1972 1973
Source: Table 6.2.
DECOMPOSITION OF FAMILY INCOME AFTER TAX 273
Figure 6.2. Correlation Terms for the Decomposition of Family
Income after Tax, by Category of Expenditure, 1964-73
RI Consumption expenditure Educational expenditure R3
1.00 _- _ -
0.98 - \ R2 Housing '
expenditure -
* 0.96 _
/ R, Savings
t 0.94 \ /
V
0.92 -
0.90
0 1964 1966 1968 1970 1972 1973
Source: Table 6.2.
expenditure on food, clothing, and other consumer goods accounted
for about 50 percent of the inequality of family income after tax
[G(V)]; educational expenditure accounted for about 10 percent.
Savings and expenditure on housing respectively accounted for
16 percent and 23 percent. The contrast is sharp between the two
consumption components. The term for housing expenditure shows
an increasing trend; that for other expenditure a decreasing trend.
No increasing or decreasing trend could be detected for the two
investment components. The difference between them is that the
curve for the savings term is mildly U-shaped and that for the
education term is inverse U-shaped. In the following discussion the
behavior patterns for consumption and investment are separately
explained.
Consumption
The values of the correlation terms for consumption expenditure
[Rc] and housing expenditure [Re] are very close to the unit value
(figure 6.2). The higher the family income is after tax, the higher
274 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.2. Decomposition of the Inequality
of Family Income after Tax, 1964-73
Item Notation 1964 1966 1968
Shares
Other expenditure +1 0.6744 0.6559 0.6478
Housing expenditure 02 0.1211 0.1425 0.1567
Educational expenditure 03 0.0897 0.0924 0.1039
Savings 0. 0.1149 0.1092 0.0916
Gini coefficients
Other expenditure Gf 0.2598 0.2736 0.2550
Housing expenditure G2 0.3462 0.3481 0.3582
Educational expenditure GC3 0.3587 0.3804 0.3751
Savings Gs 0.7363 0.5908 0.8843
Correlation terms
Other expenditure Ro 1.0000 1.0000 0.9945
Housing expenditure R2 0.9948 0.9977 0.9983
Educational expenditure Rc 0.9967 0.9979 0.9979
Savings Rs 0.9921 0.9983 0.9240
Effects
Other expenditure . f/4RfGf 0.1752 0.1795 0.1643
Housing expenditure k9RWG2 0.0417 0.0495 0.0560
Educational expenditure OM-G3 0.0321 0.0350 0.0389
Savings -O8R8G. 0.0839 0.0644 0.0748
Composition of effects (percent)
Other expenditure 52.6 54.7 49.2
Housing expenditure 12.5 15.1 16.8
Educational expenditure 9.6 10.7 11.6
Savings 25.3 19.5 22.4
Gini coefficient of income
after tax G, 0.3329 0.3284 0.3340
Sources: Calculated from tables 6.5-6.10 appended to this chapter.
the family expenditure is for both types of consumption. Thus
the effect of the variation of the correlation characteristic can be
neglected-that is, it can be assumed that Rl and R' are equal to
1- and the analysis can concentrate on 4i and Gi.
The share of consumption expenditure [E] exhibits a decreasing
trend; the share of housing expenditure [E] an increasing trend
DECOMPOSITION OF FAMILY INCOME AFTER TAX 275
1970 1972 1973 Notation Item
Shares
0.6521 0.6150 0.6000 O Other expenditure
0.1407 0.1619 0.1620 42 Housing expenditure
0.1185 0.0870 0.0812 (PC Educational expenditure
0.0887 0.1361 0.1568 0) Savings
Gini coefficients
0.2304 0.2343 0.2319 Gi Other expenditure
0.3220 0.3256 0.3534 G2 Housing expenditure
0.3300 0.3299 0.3478 G3 Educhtional expenditure
0.6915 0.5134 0.5335 G, Savings
Correiation terms
0.9974 1.0000 1.0000 R' Othet expenditure
1.0000 1.0000 1.0000 R2 Housing expenditure
0.9988 0.9994 0.9994 R3 Educational expenditure
0.9806 1.0000 0.9989 R, Savings
Effects
0.1498 0. 1441 0.1391 oIeRGl Other expenditure
0.0453 0.0527 0.0573 2 R21G2 Housing expenditure
0.0391 0.0287 0.0282 scRlGc Educational expenditure
0.0601 0.0699 0.0836 O4sR,G. Savings
Composition of effects (percent)
50.9 48.8 45.1 Other expenditure
15.4 17.8 18.6 Housing expenditure
13.3 9.7 9.2 Educational expenditure
20.4 23.7 22.1 Savings
Gini coefficient of income
0.2943 0.2954 0.3082 G, after tax
(figure 6.3). Because the increase of family income was rapid during
this ten-year period, the foregoing trends reveal that the family
housing expenditure is income-elastic and other family expenditure
is income-inelastic. This pattern is consistent with expectations
based on the conventional theory of consumer behavior.
The inequality of the distribution of family expenditure on hous-
276 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
F1igure 6.3. Shares for the Decomnposition of Famnily Income after
Tax, by Category of Expenditure, 1964-73
0.7 Consumption expenditure
f1 ~~~~~~~~4
0.5
0.3
Housing expenditure Savings
2 _-- -------
0. I~~~~~~~~~~~~~~~
0. 1 C_ =_ __ _
Educational expenditure
0 1 1 I I
1964 1966 1968 1970 1972 1973
Source: Table 6.2.
ing [G'] was much greater than that of family expenditure on other
consumption [EG] (figure 6.4). Thus the expenditure on housing,
more than that on other consumer goods, distinguished the class of
wealthy families and therefore took on the character of conspicuous
consumption. This was true despite the rapid growth of family
income over the period. It may be concluded that the difference in
the income elasticity of demand for housing and for other consump-
tion expenditure mainly explained the long-run declining trend of
0jRlG, and the long-run increasing trend of O'R'G2 seen in figure 6. 1.
Investment
It can be seen from the correlation characteristics in figure 6.2
that educational expenditure and savings were highly correlated
with family income after tax. Even the lowest value of R., registered
DECOMPOSITION OF FAMILY INCOME AFTER TAX 277
Figure 6.4. Gini Coefficients for the Decomitposition of Famlily Income
after Tax, by Category of Expenditure, 1964-73
0.8 _
G, s / " Savings
N,~~~~
-0.6-
Educational expenditure
0
0.4 -
G2 --
Housing expenditure
0.2 Consumption expenditure
O I I I I l I I I I
1964 1966 1968 1970 1972 1973
Source: Table 6.2.
in 1968, is 0.9024. Thus the correlation characteristic can again be
neglected, enabling concentration upon 'i and G,.6
The shares of expenditure on education [06] and savings [+8]
both present a constant time trend, fluctuating around 10 percent
over the ten-year period (see figure 6.3). Families therefore spent
about the same percentage of their income on investment in human
resources and on physical resources. Notice that the movements of
4. and X4 always are in the opposite direction. When (A. moves up-
6. That all values of Ri in figure 6.2 are close to 1 should come as no surprise.
It simply means that wealthier families spent more on each of the items.
278 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
ward, O moves downward, and vice versa. The reason is that when
families decide to spend more on education-as they did, for exam-
ple, before 1970-they saved relatively less. Conversely, when they
spent less on education-as they did, for example, after 1970-they
saved more. Together the two curves seem to indicate a constant
propensity to "save" of about 20 percent up to 1972. In 1973 the
sum of i, and 0, increased to 24 percent. It remains to be seen
whether this was indicative of a new, increasing trend.
Finally the inequality of savings [G8] and the inequality of educa-
tional expenditure [Gc] were consistently greater than the inequality
of housing expenditure [Gc] and the inequality of consumption
expenditure [GO]. Consequently the inequality of family income
after tax led more to the inequality of investment (in education or
savings) than to the inequality of consumption. The fact that the
inequality of investment in one year leads to the inequality of in-
come in subsequent years in part explains the persistence of the
inequality of family income over time.
It should be observed that the inequality of family saving was
much greater than the inequality of family expenditure on educa-
tion. As pointed out earlier, the percentages of income applied
to education and savings were approximately the same at around
10 percent for earlier years (see figure 6.3). Thus the inequality of
investment in physical resources is more responsible than the in-
equality of investment in human resources for the persistent in-
equality of family income. In arriving at this conclusion, it should
be borne in mind that government spends heavily on public educa-
tion-both on education up to the nine-year level, which became
compulsory in 1968, and on higher education. This expenditure is,
in principle, very equally distributed among the families benefiting
from this policy. The education policy thus has greatly reduced the
role of private expenditure on education as a causal factor in con-
tributing to the inequality of family income over time.
It should also be noticed that there is a long-run declining trend
of G. over time. This means that as family income increases, the
low-income families begin to save proportionately more of their
income than high-income families. The persistence of such a time
trend implies that the inequality of investment in physical resources
in the future will contribute less to the inequality of family income
than it has in the past. For this reason the distribution of family
income in Taiwan can be expected to continue improving.
THE IMPACT OF TAXATION ON INCOME INEQUALITY 279
The Impact of Taxation on Income Inequality
The results of the decomposition of the inequality of family in-
come EG(Y)] according to equation (6.4b) appear in table 6.3.
The primary purpose of the decomposition is to show whether pay-
ments of direct and indirect tax contributed to the equality of
family income after tax. The ratio of the Gini coefficient after tax
[G.] to the Gini coefficient before tax [G,] shows that there was no
significant difference between G. and G, in all the years examined-
that is:
(6.6) G, _ G,
It can thus be concluded for this ten-year period that the direct
impact of taxation on the distribution of family income was neutral
and that it brought about neither greater equality nor greater in-
equality. It follows that the cause of the near-equivalence of G, and
G0, in the past should be investigated and that future measures
should be introduced so that tax policy can contribute more to the
equality of family income. As a first step in this investigation, it
should be determined whether the taxation system in Taiwan satis-
fies certain minimum requirements for being "reasonable."
Is Taiwan's system of taxation reasonable?
The impact of taxation is graphically represented by the flow
chart in figure 6.5. The income before tax EY = (yr, Y2, y3)] is re-
ceived by the families [(fl, f2, f3)]; from this income, families make
tax payments [T = (tl, t2, t3)] which constitute the structure of
the tax burden. That tax burden [T] is the sum of the direct tax
burden [T1 = (t1, t4, t,)] and the indirect tax burden [T2 = (t,
2, 3)]. What remains is family income after tax [V = (Vl, V2, V3)].
The near-equivalence of G, and G0, in expression (6.6) implies that
the tax burden [T] causes no difference between the degree of
inequality in before-tax income [Y] and after-tax income [V]. Thus:
(6.7a) Y = V + T, where
(6.7b) T = T, + T2.
280 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.3. Decomposition of the Inequality
of Family Income before Tax, 1964-73
Item Notation 1964 1966 1968
Shares
Income after tax f 0.9341 0.9277 0.9189
Direct tax f 0.0268 0.0122 0.0139
Indirect tax 2 0.0591 0.0601 0.0672
Gini coefficients
Income after tax GD 0.3329 0.3284 0.3340
Direct tax GI 0.4381 0.5208 0.5902
Indirect tax GI 0.2605 0.3229 0.2945
Correlation terms
Income after tax R. 0.9988 1.0000 0.9997
Direct tax Rf 0.9781 0.9965 0.9949
Indirect tax R' 0.9724 0.9913 0.9891
Effects
Income after tax 0,R,G, 0.3106 0.3047 0.3068
Direct tax 0IRIGGl 0.0029 0.0064 0.0082
Indirect tax 4R4G24 0.0150 0.0192 0.0196
Inequality of income before tax G, 0.3285 0.3303 0.3346
Ratio of inequality of income
before tax to that of income
after tax G,/IG 1.0133 0.9942 0.9982
Sources: Calculated from tables 6.5-6.10 appended to this chapter.
When total family incomes are arranged in a monotonically non-
decreasing order, any rationally designed tax system should satisfy
the following conditions:
(6.8a) Y < Y2 < ... < Yn,
which implies that:
(6.8b) V1 < V2 < ... < V.,
[no reversal of rank]
THE IMPACT OF TAXATION ON INCOME INEQUALITY 281
1970 1972 1973 Notation Item
Shares
0.9234 0.9154 0.9176 ct Income after tax
0.0112 0.0150 0.0146 oi Direct tax
0.0654 0.0695 0.0678 021 Indirect tax
Gini coefficients
0.2943 0.2954 0.3082 GD Income after tax
0.5450 0.5758 0.5830 Of Direct tax
0.2559 0.2423 0.2485 G21 Indirect tax
Correlation terms
1.0000 0.9983 1.0000 R, Income after tax
0.9989 1.0000 1.0000 Rf Direct tax
0.9984 0.9992 1.0000 RI Indirect tax
Effects
0.2718 0.2699 0.2828 ORXG, Income after tax
0.0061 0.0086 0.0085 ti4RfGf Direct tax
0.0167 0.0168 0.0168 021R21G2 Indirect tax
0.2946 0.2953 0.3081 G, Inequality of income before tax
Ratio of inequality of income
before tax to that of income
0.9983 1.0003 1.0003 G1/G, after tax
(6.8c) t1< t, < . .. < tn,
fminimum progressiveness
[mLnm°f direct tax
(6.8d) t G, .
The neutrality of taxation observed in expression (6.6) implies that
the conditions of expression (6.12) were not satisfied. The conditions
associated with expression (6.6) and equation (6.11a) immediately
show that:
(6.13) G, = GV = GT.
In other words, the taxation system in Taiwan did not bring about
a more equitable distribution of income because the total tax burden
was distributed with the same degree of inequality as income before
tax. The time paths of GT and G, are shown in figure 6.6. The curve
THE IMPACT OF TAXATION ON INCOME INEQUALITY 285
for GC is very close to the curve for GT, and they become closer over
time. This verifies the conditions stated in equation (6.13).
The equivalence of GC and GT can be analyzed from another angle.
Assume a hypothetical marginal tax rate of m:
(6.14) dT/dY = m, where m < 1.
Whenever the total family income increases by one dollar, the
additional total tax payment is m dollars. The average tax rate for
all families is given by:
(6.15) rT = (tl + t2 + .. + tn)/(Y1 + Y2 + + Yn) -
Under the assumptions of equation (6.14) GT and GC satisfy the
following equation8:
(6.16) GT = (m/OT) GC1.
The equivalence of GT and G, shown in equation (6.13) immedi-
ately implies that:
(6.17) m = kT.
Equation (6.17) indicates the equivalence of the average and mar-
ginal tax rates. This equivalence means that the total tax burden is
such that the same percentage of family income is collected as taxes
from all families, regardless of their income. Thus, despite the reas-
onable properties of Taiwan's system of taxation, the overall tax
burden was highly regressive according to a modern standard.
Analysis of the burden of taxation
The total tax burden is the sum of the direct and indirect tax
burdens (see equation [6.7b]). The inequality of the tax burden
CGT] is traced in turn to the direct and indirect tax burdens. Apply-
ing the decomposition formula to equation (6.7b) gives:
(6.18a) GT = 04RCG1 + O'R,G,, where
(6.18b) +' = 44/4T, 02 = O/4T, and
(6.18c) 4i' + 02 = 1.
8. See theorem 12.2 in chapter twelve. Notice that if the taxation system is
reasonable, the value of m must lie between zero and 1-that is, 0 < m < 1.
Thus, according to theorem 12.2, the tax payment T corresponds to a type one
or type two income when m is a positive fraction.
286 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.4. Decomposition of the Inequality
of the Tax Burden, 1964-73
Item Notation 1964 1966 1968
Shares
Direct tax 1 0.1031 0.1687 0.1713
Indirect tax 04 0.8968 0.8312 0.8286
Effects
Direct tax fGt 0.0451 0.0878 0.1011
Indirect tax 02,G 0.2336 0.2683 0.2440
Composition of effects
(percent)
Direct tax 16.2 24.7 29.3
Indirect tax 83.8 75.3 70.7
Gini coefficient
of tax burden GT 0.2787 0.3561 0.3451
Error term (GT - Gy)/Gy 0.1515 0.0781 0.0313
Sources: Calculated from tables 6.5-6.10 appended to this chapter.
In equation (6.18b) tl and o2 are the percentages of direct and
indirect taxes in total taxes. In equation (6.18a) R' and R' are the
correlation characteristics of T1 and T2 with T. The reasonable
property associated with the expressions of (6.8) implies that9:
(6.19a) R' = R2 = 1.
Hence:
(6.19b) GT= 'Gt + ±'G2'.
9. The condition of minimum progressiveness of total tax in expression (6.8e)
implies that Y and T have a perfect rank correlation; the conditions of minimum
progressiveness of direct and indirect tax in expressions (6.8c) and (6.8d) imply
that T, and T2 also have a perfect rank correlation with Y. Therefore T, and
T2 have a perfect rank correlation with T. The economic interpretation is that
as a higher income family pays more in total taxes, it also pays more in direct
and indirect taxes.
THE IMPACT OF TAXATION ON INCOME INEQUALITY 287
1970 1972 1973 Notation Item
Shares
0.1462 0.1775 0.1771 44 Direct tax
0.8537 0.8224 0.8228 42 Indirect tax
Effects
0.0796 0.1022 0.1032 'GC Direct tax
0.2184 0.1992 0.2044 4202 Indirect tax
Composition of effects
(percent)
26.7 33.9 33.6 Direct tax
73.3 66.1 66.4 Indirect tax
Gini coefficient
0.2980 0.3014 0.3076 CT of tax burden
0.0115 0.0206 0.0016 (T - GC/CG, Error term
The results of the decomposition of GT according to equation (6.19b)
are given in table 6.4. According to equation (6.19b) the values of
GT in this table are the sums of the values of 'G/C and C'Gf. The
shares of direct and indirect taxes in the share of total taxes are
defined as in equation (6.18b); the values of GC and GC were taken
from table 6.3. The time patterns of these variables are graphically
represented in figures 6.6-6.8.
Indirect taxes contributed much more than direct taxes to the
inequality of taxation [GT] (see figure 6.6). Direct taxes on average
accounted for 27 percent of GT; indirect taxes for 73 percent. There
nevertheless was a long-run declining trend for the indirect tax
contribution and an increasing trend for the direct tax contribution.
Thus, although the indirect tax contribution was quantitatively
important, that importance relative to the direct tax contribution
declined.
The two relative tax shares E[4, and 44] maintained a constant
time trend over the ten-year period (figure 6.7). The indirect tax
share [E4] was much greater than the direct tax share [E4]. The
288 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Figure 6.7. Shares for the Decomposition of the Tax Burden, 1964-73
1.0 _
0.8 _ _2
0.6 - Burden of indirect tax
0.4 -
Burden of direct tax
0.2 /
1964 1966 1968 1970 1972 1973
Source: Table 6.4.
average value of the indirect tax share was 84 percent; that of the
direct tax share 16 percent. Thus the quantitative importance of
the indirect tax contribution indicated in figure 6.6 was entirely
the result of the importance of indirect tax as a source of govern-
ment revenue.
The burden of indirect tax payments was much more evenly
distributed than the burden of the progressive direct tax payments
(figure 6.8). Over the ten-year period, the average value of Gf was
0.54; that of G' 0.27. Moreover the inequality of the burden of
direct taxes exhibited a long-run increasing trend; that of indirect
taxes a long-run declining trend. These patterns conform to those
observed in figure 6.6.
It can be seen from the foregoing analysis that the canceling of
the quantitatively less important and more progressive direct tax
payments by the quantitatively more important and regressive
indirect tax payments brought about the neutrality of the total tax
burden. For tax policy to be an instrument for improving the dis-
tribution of income after tax, one practical method is to shift the
reliance of government from indirect taxes to direct taxes. The
reason is that the progressive features of taxation are built into
direct taxes. The curve for the inequality of the indirect tax burden
FUTURE RESEARCH 289
Figure 6.8. Gini Coefficients of Direct and Indirect Tax, 1964-73
Direct tax
0.6 -
0.4 G Indirect tax
G2t
0.2
O0 I I I I I I I I
1964 1966 1968 1970 1972 1973
Source: Table 6.4.
[Gf] in figure 6.8 shows a long-run decline-a decline which is not
favorable to the equality of income distribution. To reverse this
trend the tax rates should be increased for commodities likely to be
consumed by families in higher income brackets. In addition to
promoting the equality of family income, such a policy would en-
courage higher saving rates which, in turn, would contribute to
economic development.
Future Research
This study of the inequality of family expenditure provides only
a partial picture of the inequality of family welfare. There are four
reasons for this. First, by concentrating only on the expenditure by
families, this study neglects the impact of government expenditure
on family welfare. Second, it relies on household surveys for tax
data, not on agencies collecting taxes. Third, it does not take full
advantage of the household data that is available. Fourth, the
method adopted for this study lacks the basis of a positive, deter-
ministic theory.
The failure to take government expenditure into account is the
major deficiency of this chapter. Family expenditure constitutes
only part of the aggregate demand for gross national product. For
290 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
example, the taxes paid by families are spent by government on
various programs. Because many families benefit from such public
expenditure, the analysis of the inequality of family welfare is
incomplete without considering its impact.10 But assigning this
expenditure to households, or classes of households, is not easy. The
reason is that unemployment compensation or welfare payments
to needy families, which could be calculated with relative ease,
are not that important in developing countiies. In contrast, public
expenditure on health and education is very important. Generally,
however, the benefits that families derive from public expenditure
must be imputed. Because this expenditure both substitutes and
supplements private expenditure in similar categories, it can and
should, to the extent possible, be imputed in future studies. Primary
data on the administration of government programs for health and
education will be needed for this purpose.
Because of this study's exclusive reliance on data based upon
household surveys, certain issues arose which should be resolved in
future research. For one thing, the payments of direct and indirect
tax reported by families obviously differ in magnitude from those
collected. Moreover the calculation of the indirect tax burden, out-
lined earlier in this chapter, is only a crude approximation. Satis-
factory analysis of the burden of indirect tax, which is quantitatively
more important than the burden of direct tax, requires a more
adequate framework for the analysis of the shifting incidence of the
indirect tax burden in the context of general equilibrium. In addition
to data from household surveys, other primary data for the fiscal
operations of government will be needed.
Despite these requirements for additional data, not even existing
data were used to the fullest extent. The wealth of data on family
expenditure, such as that detailed in the classification for consump-
tion expenditure in table 6.1, has not been adequately explored. If
these data were used more fully, the inequality of family expenditure
on consumption could be calculated at a more disaggregated level
to provide a firmer grasp of the meaning of the inequality of welfare
associated with family consumption.
How have these deficiencies affected the results? The failure to
incorporate government expenditure probably resulted in an over-
10. There is, moreover, no consideration of hidden taxes, such as those im-
posed through the rice and fertilizer exchanges.
FUTURE RESEARCH 291
estimation of the inequality of family welfare. The failure to incor-
porate the undistributed profits of corporations and other similar
items probably led to an underestimation of the inequality of savings
and income. The failure to examine household data at a more dis-
aggregated level of detail probably obscured some underlying trends.
Nevertheless a start has been made. The intent here was to show
how the basic theory of decomposition presented in this volume
might be applied to the inequality of additive expenditure com-
ponents, just as it was applied to the inequality of additive income
components.
Finally a word on theory. The method of decomposition used in
this chapter basically is empirical. It lacks the foundation of a
positive deterministic theory. Therefore one direction for future
research into the inequality of expenditure and savings would be to
construct a positive deterministic theory based on assumptions
about consumer behavior. A theory of this type would not be as
difficult to construct, at least conceptually, as that which would
apply to some other areas of the analysis of income inequality-for
example, to the determination of the inequality of wage income,
as posited in chapter four. One possible approach to such a formula-
tion is now discussed.
Deterministic theories of the inequality of consumption and
taxation are relatively easy to formulate because conventional
economic theory has already provided some of the foundations.
Abstractly a functional relation is postulated:
(6.20) y = f(x).
For example, f(x) represents a consumption function when x stands
for income and y stands for consumption. Alternatively f(x) repre-
sents a tax function when x stands for income and y stands for tax
payments. A special case of equation (6.20) is represented by a
linear function:
(6.21) y = b + ax,
which represents a linear consumption or other function. To see
how equation (6.20) is related to inequality analysis involving
patterns in vectors Y = (Yl, Y2, . .. , y.) and X = (xl, x2, . . .), x)
for n families, use the following definition:
DEFINITION 6.1. The vector Y is an f-transformation of X if yi =
f (xi) (i = 1, 2, ... ., n).
292 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
A linear transformation gives the following theorem'1:
THEOREM 6.1. GY = (a/s) GD, where 4 = y/.
The same language can be used to describe equation (6.21) as a
type one, two, or three transformation, depending upon the signs
of b and a [see equation (3.7) in chapter three]. When equation
(6.21) is interpreted as a consumption function for a particular
commodity, a type three commodity (with a < 0) is an "inferior"
good. Similarly a type one commodity is a "superior" good, such
that the percentage of income spent on this commodity increases
with income [see equation (3.13) in chapter three]. In all cases,
theorem 6.1 provides information on the inequality of consumption
[G,] as related to the inequality of income [EG,] [see equation (3.12)
in chapter three]. Precisely the same classification and interpretation
can be given when equation (6.21) is interpreted as a tax function:
For example, a type three tax is in fact a subsidy which declines with
the level of income.
When the transformation function (6.20) is nonlinear, theorems
similar to 6.1 cannot be readily deduced. For example, for a pro-
gressive system of income tax, the transformation function becomes:
(6.22a) y = b + tx'/2, with
(6.22b) dY = tx for t > 0,
dx
when the marginal tax rate [dy/dx] is a linear function of income
Ex]. When the tax payment pattern [Y = (Yl, Y2, ...), yj] is a
transformation of the income pattern [X = (xl, X..., xv)] by
equation (6.22a), it is not easy to relate the inequality of the tax
burden [G1,] to the inequality of income distribution [G]. The
primary reason for this is that the nonlinearity of equation (6.22a)
is not amenable to the linearity property of the Gini coefficient.
The difficulty, however, is technical rather than conceptual. What
needs to be done is to search for another inequality index-one
other than the Gini coefficient-that satisfies certain "multiplica-
tive" properties. This points the direction future research efforts
should probably take to deal with deterministic theories on the
problems encountered in this chapter.
11. This theorem was proved as equation (3.12) in chapter three, where a/0
is the elasticity of the linear regression line at the mean point.
ESTIMATION OF INDIRECT TAX 293
Appendix 6.1. Estimation of Indirect Tax
The procedure for computing the indirect tax payments of house-
holds uses information contained in input-output flow matrices. Let
the prices of the n commodities be denoted by the row vector
P' = (pi, p2,.. . , pn). Let A = (aij) be the n X n coefficient matrix,
and let W' = (wI, W2,. . ., w.) and T' = (t1, t2,. . ., tn) be the values
added and indirect tax payments per unit of output for the industries.
Then:
(6.23) P' = P'A + W' + T',
where, for C' = P'A = (ce, C2,. . ., cn ), the element ci stands for the
intermediary factor cost per unit output of the ith industry. It
follows that:
(6.24a) P' W'E + T'B, where
(6.24b) B = (I - A)-'
is the Leontief inverse matrix. By using the two-industry case as an
illustration, the input-output flow table becomes:
Intermediary inputs
Final Total
Item Industry 1 Industry 2 demand output
Industry 1 ppX,Y plX,2 ply, p,X,
Industry 2 p2X21 p2X22 p2Y2 p2X2
Value added w,X, w2X2
Indirect tax T, = tlXI T2 = t2X2
- Not applicable.
In the table Xij, Yi, and Xi respectively are interindustry flows,
final demand, and total output in physical units. For any base year
a monetary input-output flow table contains all the numbers in such
cells. Thus the indirect tax rates [ti] are estimated by:
(6.25) ti = TilXi = (Ti/Xipi)pi, (i = 1, 2,..., n)
where Ti and Xipi are the marginal entries in the table. If the unit of
measurement for output is normalized so that pi = 1, then equation
294 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
(6.25) reduces to:
(6.26) ti = TilXipi, (i = 1, 2,..., n)
which can be estimated from the marginal entries. The rates of tax
burden, given by (b6, b2,..., bn), are defined by having bi be the
amount of indirect tax payment for every dollar spent on the ith
commodity or, equivalently, for every normalized unit of commodity
purchased. Thus:
(6.27) bi = t,. (i = 1, 2,..., n)
This procedure of estimation is based on the assumption that all
purchasers of a commodity pay the indirect taxes-that is, all indirect
tax burdens are shifted to the consuming public.
By using input-output tables for 1966, the average values of the
indirect tax burden [(b1, b2,. . ., b,)] were calculated for the various
consumption categories.12 The rates of tax burden were revised
whenever input-output tables were available for years other than
1966. These rates were then applied to the DGBAs data for the various
categories of family consumption to obtain the structure of indirect
tax payments given in tables 6.5-6.10, beginning on page 296.
12. Economic Planning Council, Interregional Input-Output Tables, Taiwan
Area Republic of China, 1966. (Taipei, n.d.).
296 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.5. Family Income and Expenditure,
by Category and Income Class, 1964
(thousands of N.T. dollars)
Number of Total family All other Housing
Income class families income expenditure expenditure
(N.T. dollars) [N] [Yd] [C1] [02]
Lessthan 6,000 22,288 97,612 74,206 12,938
6,000-8,000 45,294 318,829 247,062 39,524
8,000-10,000 51,046 458,795 365,144 54,750
10,000-12,000 86,994 955,018 794,188 107,260
12,000-14,000 113,596 1,471,883 1,117,165 160,293
14,000-16,000 130,132 1,960,103 1,492,311 200,924
16,000-18,000 132,289 2,244,952 1,556,775 241,157
18,000-20,000 140,916 2,664,356 1,937,333 237,670
20,000-22,000 153,857 3,226,015 2,343,125 346,986
22,000-24,000 144,511 3,325,103 2,243,790 372,368
24,000-26,000 127,975 3,194,728 2,206,247 341,771
26,000-28,000 140,916 3,793,958 2,511,383 451,987
28,000-30,000 105,687 3,061,453 2,084,927 354,635
30,000-32,000 79,805 2,469,080 1,614,334 280,026
32,000-34,000 78,367 2,586,469 1,699,524 320,036
34,000-36,000 76,210 2,664,522 1,681,692 285,621
36,000-38,000 63,268 2,335,582 1,473,956 242,951
38,000-40,000 43,138 1,684,054 1,032,257 223,682
40,000-45,000 100,654 4,248,315 2,625,497 504,021
45,000-50,000 73,334 3,467,577 1,976,334 400,296
50,000-55,000 50,327 2,631,650 1,510,906 365,021
55,000-60,000 44,576 2,558,480 1,470,207 295,625
60,000-65,000 30,915 1,930,572 1,027,877 233,646
65,000-70,000 21,569 1,447,266 763,400 201,672
70,000-75,000 17,255 1,242,817 658,269 189,453
75,000-80,000 13,660 1,054,572 604,423 127,617
80,000-90,000 20,131 1,687,238 902,263 191,357
90,000-100,000 13,660 1,293,438 646,044 79,978
100,000-150,000 23,006 2,819,096 1,319,552 316,022
150,000-200,000 4,314 722,397 359,226 77,929
200,000-300,000 1,438 345,660 123,723 11,186
More than 300,000 719 394,943 77,529 9,256
Total income 2,151,847 64,356,533 40,540,669 7,277,658
Source: DGBAs, Report on the Survey of Family Income and Expenditure, 1964.
ESTIMATION OF INDIRECT TAX 297
Educational
expenditure Direct tax Indirect tax Savings Income class
[C3] [T1] [T2] [S] (N.T. dollars)
7,340 522 8,489 -5,883 Less than 6,000
24,954 1,033 24,921 - 18,665 6,000-8,000
31,370 1,745 45,146 -39,360 8,000-10,000
66,647 3,860 67,929 -84,866 10,000-12,000
102,587 6,640 92,862 -7,664 12,000-14,000
137,658 11,277 121,694 -3,761 14,000-16,000
156,026 15,033 227,912 48,049 16,000-18,000
203,476 12,824 168,031 105,022 18,000-20,000
245,260 25,023 208,803 56,818 20,000-22,000
231,470 19,681 200,723 257,071 22,000-24,000
297,754 15,394 196,947 136,615 24,000-26,000
353,339 15,990 232,621 228,638 26,000-28,000
276,981 19,153 188,234 137,523 28,000-30,000
253,947 13,564 147,725 159,484 30,000-32,000
228,298 16,115 156,895 165,601 32,000-34,000
217,505 15,376 157,477 306,851 34,000--36,000
203,499 13,169 144,727 257,280 36,000-38,000
139,284 10,824 92,619 185,388 38,000-40,000
320,786 24,945 243,601 529,465 40,000-45,000
320,217 28,094 182,970 559,666 45,000-50,000
240,236 29,174 139,923 346,390 50,000-55,000
243,711 22,161 138,547 388,229 55,000-60,000
192,855 9,316 100,311 366,567 60,000-65,000
149,340 8,538 79,668 244,648 65,000-70,000
122,918 15,420 63,072 193,685 70,000-75,000
83,144 4,550 59,945 174,893 75,000-80,000
137,731 18,447 82,962 354,478 80,000-90,000
126,150 13,805 61,651 365,810 90,000-100,000
179,539 38,199 113,025 852,759 100,000-150,000
66,048 4,529 33,494 181,171 150,000-200,000
15,329 936 14,192 180,294 200,000-300,000
15,088 91 6,456 286,523 More than 300,000
5,390,487 435,428 3,803,572 6,908,719 Total income
298 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.6. Family Income and Expenditure,
by Category and Income Class, 1966
(thousands of N.T. dollars)
Number of Total family All other Housing
Income class families income expenditure expenditure
(N.T. dollars) [N] [Yi] [C1] [C2]
Less than 6,000 13,044 62,367 45,999 7,924
6,000-8,000 36,228 273,539 197,469 34,811
8,000-10,000 54,624 533,261 377,014 68,484
10,000-12,000 61,417 710,762 516,788 84,344
12,000-14,000 109,990 1,505,136 1,058,954 175,794
14,000-16,000 112,595 1,761,244 1,222,373 212,237
16,000-18,000 131,632 2,321,090 1,607,048 274,464
18,000-20,000 141,767 2,799,545 1,964,355 340,322
20,000-22,000 165,090 3,570,040 2,421,485 434,864
22,000-24,000 137,202 3,254,517 2,153,717 459,149
24,000-26,000 138,421 3,511,997 2,349,874 466,070
26,000-28,000 122,909 3,407,384 2,212,159 467,090
28,000-30,000 125,897 3,693,025 2,432,312 449,887
30,000-32,000 101,761 3,228,045 2,081,560 428,139
32,000-34,000 81,221 2,732,158 1,712,836 358,813
34,000-36,000 75,132 2,671,424 1,726,170 344,376
36,000-38,000 73,454 2,770,170 1,707,057 401,896
38,000-40,000 55,910 2,194,434 1,330,121 302,788
40,000-45,000 118,578 5,214,635 3,145,169 710,392
45,000-50,000 84,411 4,135,582 2,432,101 556,068
50,000-55,000 73,255 3,958,065 2,326,276 549,979
55,000-60,000 56,536 3,328,065 1,904,726 523,617
60,000-65,000 49,381 3,145,084 1,792,069 455,654
65,000-70,000 27,181 1,861,423 939,498 258,880
70,000-75,000 23,948 1,774,913 1,021,464 191,537
75,000-80,000 18,563 1,464,804 763,174 195,764
80,000-90,000 26,928 2,358,611 1,167,754 311,798
90,000-100,000 16,646 1,640,462 805,344 266,784
100,000-150,000 33,140 3,943,986 1,908,467 474,443
150,000-200,000 9,833 1,711,977 750,419 189,974
More than 200,000 4,341 957,819 457,922 116,412
Total income 2,281,035 76,495,564 46,549,674 10,112,754
Source: DGBAS, Report on the Survey of Family Income and Expenditure, 1966.
ESTIMATION OF INDIRECT TAX 299
Educational
expenditure Direct tax Indirect tax Savings Income class
[C3I [T1] [T,] IS] (N.T. dollars)
3,849 817 3,536 242 Less than 6,000
20,401 669 14,122 6,067 6,000-8,000
34,570 2,861 35,335 14,997 8,000-10,000
50,756 5,482 46,193 7,199 10,000-12,000
104,107 11,253 93,755 61,273 12,000-14,000
121,609 13,860 106,626 84,539 14,000-16,000
163,236 16,630 137,731 121,981 16,000-18,000
204,125 20,184 165,739 104,820 18,000-20,000
268,183 27,898 218,141 199,469 20,000-22,000
244,487 27,596 185,825 183,743 22,000-24,000
264,690 25,475 205,756 200,132 24,000-26,000
260,988 27,035 201,686 238,426 26,000-28,000
303,707 36,810 221,112 249,197 28,000-30,000
284,319 25,316 196,888 211,823 30,000-32,000
224,592 21,328 223,391 191,198 32,000-34,000
242,185 28,019 162,461 168,213 34,000-36,000
269,747 27,251 170,517 193,702 36,000-38,000
179,888 30,077 133,288 218,272 38,000-40,000
514,604 64,918 317,467 462,085 40,000-45,000
432,182 59,208 258,465 394,558 45,000-50,000
369,419 54,757 230,930 426,704 50,000-55,000
312,544 33,614 206,249 347,315 55,000-60,000
325,390 36,066 197,792 338,113 60,000-65,000
169,672 24,776 107,799 360,798 65,000-70,000
200,324 25,797 112,163 223,628 70,000-75,000
109,913 18,154 85,716 292,083 75,000-80,000
227,136 49,345 131,922 470,656 80,000-90,000
140,639 36,321 92,269 299,105 90,000-100,000
313,797 87,404 207,176 952,699 100,000-150,000
100,353 45,234 78,058 547,939 150,000-200,000
94,423 49,033 46,328 175,701 More than 200,000
6,558,835 933,188 4,594,436 7,746,677 Total income
800 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.7. Family Income and Expenditure,
by Category and Income Class, 1968
(thousands of N.T. dollars)
Number of Total family All other Housing
Income class families income expenditure expenditure
(N.T. dollars) [N] [YI] [C1] [C2]
Less than 6,000 8,717 35,623 54,197 9,683
6,000-8,000 11,883 84,843 59,334 11,651
8,000-10,000 24,464 216,705 145,623 42,804
10,000-12,000 48,397 543,308 366,065 83,187
12,000-14,000 40,271 528,317 370,345 74,419
14,000-16,000 72,769 1,103,666 789,980 152,426
16,000-18,000 103,715 1,806,929 1,275,112 242,767
18,000-20,000 119,195 2,290,129 1,733,917 299,601
20,000-22,000 123,418 2,605,688 1,853,384 319,900
22,000-24,000 112,758 2,603,833 1,792,427 296,260
24,000-26,000 134,010 3,386,270 2,364,914 445,470
26,000-28,000 106,404 2,875,279 1,904,022 354,415
28,000-30,000 128,242 3,751,380 2,510,261 538,790
30,000-32,000 133,719 4,192,962 3,284,440 542,595
32,000-34,000 87,112 2,881,135 1,820,324 469,365
34,000-36,000 89,516 3,148,092 2,022,361 454,944
36,000-38,000 79,764 2,966,426 1,851,886 397,883
38,000-40,000 79,784 3,126,891 1,937,608 435,450
40,000-45,000 168,012 7,243,895 4,677,913 1,055,272
45,000-50,000 152,750 7,244,441 4,491,360 1,067,183
50,000-55,000 125,936 6,651,426 3,798,543 995,421
55,000-60,000 81,178 4,692,924 2,675,855 768,522
60,000-65,000 69,395 4,367,069 2,404,218 695,035
65,000-70,000 53,806 3,636,707 1,987,697 613,914
70,000-75,000 42,780 3,096,804 1,798,128 517,994
75,000-80,000 27,902 2,164,001 1,150,017 344,747
80,000-90,000 42,728 3,760,734 1,880,158 585,319
90,000-100,000 32,712 3,078,102 1,673,003 430,228
100,000-150,000 41,821 5,318,524 2,264,500 803,367
150,000-200,000 14,725 2,549,714 1,078,425 375,230
200,000-300,000 10,902 2,835,251 1,051,300 376,549
More than 300,000 3,831 1,581,337 296,235 79,433
Total income 2,372,616 96,368,405 57,363,552 13,879,824
Source: DGBAS, Report on the Survey of Family Income and Ezpenditure, 1968.
ESTIMATION OF INDIRECT TAX 301
Educational
expenditure Direct tax Indirect tax Savings Income class
[C3] [T1] [T21 [S] (N.T. dollars)
3,783 248 4,682 -36,971 Less than 6,000
7,360 584 6,529 -615 6,000-8,000
12,643 505 15,628 -498 8,000-10,000
42,658 3,119 43,213 5,066 10,000-12,000
41,352 3,873 38,978 -650 12,000-14,000
86,052 5,022 82,809 -12,623 14,000-16,000
135,314 12,142 134,300 7,294 16,000-18,000
175,764 14,610 135,355 -69,188 18,000-20,000
233,165 14,958 191,661 -7,380 20,000-22,000
234,553 16,316 196,667 67,610 22,000-24,000
313,122 26,028 237,262 -526 24,000-26,000
219,181 18,214 197,124 182,323 26,000-28,000
326,565 25,314 263,808 86,642 28,000-30,000
356,717 29,728 389,915 -410,433 30,000-32,000
259,031 26,435 196,544 109,436 32,000-34,000
274,268 28,058 212,945 155,516 34,000-36,000
251,795 15,843 198,418 250,601 36,000-38,000
322,405 32,569 217,924 180,935 38,000-40,000
720,730 77,721 550,087 162,172 40,000-45,000
812,897 91,705 500,460 280,836 45,000-50,000
669,678 100,345 433,001 654,438 50,000-55,000
454,778 81,903 309,853 402,013 55,000-60,000
447,287 55,957 277,947 486,625 60,000-65,000
316,821 45,940 232,206 440,129 65,000-70,000
345,589 47,558 203,802 183,733 70,000-75,000
257,627 21,915 140,840 248,855 75,000-80,000
381,971 90,996 212,303 609,987 80,000-90,000
326,565 76,994 195,231 376,081 90,000-100,000
458,436 117,656 368,717 1,305,848 100,000-150,000
287,372 73,831 117,593 617,263 150,000-200,000
239,649 67,047 114,502 986,204 200,000-300,000
185,709 119,976 53,458 846,527 More than 300,000
9,200,837 1,343,110 6,473,762 8,107,320 Total income
302 TAXATION AND THE INEQIUALITY OF INCOME AND EXPENDITURE
Table 6.8. Family Income and Expenditure,
by Category and Income Class, 1970
(thousands of N.T. dollars)
Number of Total family All other Housing
Income class families income expenditure expenditure
(N.T. dollars) [NJ [YN [CI] [C2]
Less than 6,000 5,072 - 12,852 49,797 8,163
6,000-8,000 13,354 95,173 76,922 15,128
8,000-10,000 11,012 96,943 83,258 14,865
10,000-12,000 14,763 163,810 105,736 22,203
12,000-14,000 26,796 351,231 259,537 45,215
14,000-16,000 41,593 622,151 427,667 79,408
16,000-18,000 50,611 857,590 630,763 92,926
18,000-20,000 64,726 1,225,430 896,503 131,563
20,000-22,000 76,780 1,619,145 1,252,162 194,703
22,000-24,000 67,784 1,560,938 1,380,001 189,467
24,000-26,000 106,759 2,666,382 1,819,552 324,928
26,000-28,000 110,679 2,986,573 1,996,355 341,263
28,000-30,000 96,886 2,798,284 1,859,128 328,274
30,000-32,000 106,133 3,290,549 2,147,211 377,167
32,000-34,000 105,405 3,479,122 2,252,726 415,203
34,000-36,000 105,273 3,686,013 2,417,061 417,609
36,000-38,000 124,543 4,592,604 2,911,929 588,941
38,000-40,000 91,980 3,579,819 2,309,551 462,964
40,000-45,000 205,860 8,707,838 5,442,467 1,128,665
45,000-50,000 181,317 8,564,914 5,264,774 1,117,375
50,000-55,000 118,746 6,221,924 3,728,342 846,048
55,000-60,000 106,340 6,096,172 3,500,004 833,203
60,000-65,000 89,350 5,559,718 3,144,018 811,549
65,000-70,000 69,658 4,688,358 2,566,119 678,630
70,000-75,000 48,114 3,486,654 1,933,123 517,292
75,000-80,000 33,838 2,620,015 1,410,393 356,708
80,000-90,000 44,887 3,794,328 2,088,656 535,956
90,000-100,000 42,926 4,050,229 2,165,341 566,552
100,000-150,000 56,607 6,670,916 3,348,734 814,693
150,000-200,000 18,849 3,132,936 1,470,198 444,447
200,000-300,000 7,032 1,636,277 655,435 143,279
More than 300,000 731 256,802 112,018 35,818
Total income 2,244,404 99,145,986 59,705,481 12,880,205
Source: DG3AS, Report on the Survey of Family Income and Expenditure, 1970.
ESTIMATION OF INDIRECT TAX 0S0
Educational
expenditure Direct tax Indirect tax Savings Income class
[Cal [T,] [T2] [S] (N.T. dollars)
10,286 630 4,581 -86,309 Less than 6,000
13,793 484 6,415 - 17,569 6,000-8,000
10,007 518 7,598 - 19,303 8,000-10,000
14,176 578 13,254 7,863 10,000-12,000
29,495 1,432 32,809 - 17,257 12,000-14,000
84,065 3,656 46,702 -19,347 14,000-16,000
70,077 3,555 68,627 - 8,358 16,000-18,000
108,784 7,046 67,150 14,384 18,000-20,000
134,379 8,717 115,912 -86,728 20,000-22,000
142,500 10,633 108,313 -269,976 22,000-24,000
254,516 10,143 191,926 65,317 24,000-26,000
284,275 17,310 210,269 137,101 26,000-28,000
290,619 15,191 197,540 107,532 28,000-30,000
296,876 17,255 223,875 228,165 30,000-32,000
367,080 22,297 242,746 179,070 32,000-34,000
392,666 23,438 261,728 173,511 34,000-36,000
455,356 24,614 308,055 303,709 36,000-38,000
405,405 30,559 237,839 133,501 38,000-40,000
933,292 70,214 609,660 523,540 40,000-45,000
958,163 75,199 582,127 567,276 45,000-50,000
729,562 50,299 411,696 455,977 50,000-55,000
716,513 60,621 400,311 585,520 55,000-60,000
681,695 74,324 360,647 487,485 60,000-65,000
569,761 73,659 297,041 503,148 65,000-70,000
409,049 42,954 221,380 362,856 70,000-75,000
325,179 44,690 173,506 309,539 75,000-80,000
464,104 53,525 243,317 408,770 80,000-90,000
475,541 71,795 258,012 512,983 90,000-100,000
701,009 174,798 282,320 1,349,362 100,000-150,000
307,215 72,385 187,506 651,185 150,000-200,000
176,982 34,843 94,094 531,644 200,000-300,000
37,841 12,424 15,007 43,694 More than 300,000
10,850,261 1,109,786 6,481,963 8,118,290 Total income
304 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.9. Family Income and Expenditure,
by Category and Income Class, 1972
(thousands of N.T. dollars)
Number of Total family All other Housing
Income class families income expenditure expenditure
(N.T. dollars) [N] [Yd] [C1] [C2]
Less than 10,000 11,418 93,232 58,129 16,820
10,000-15,000 24,575 314,301 207,526 46,255
15,000-20,000 63,724 1,128,238 778,304 142,963
20,000-25,000 106,913 2,443,578 1,615,347 313,822
25,000-30,000 157,288 4,312,587 2,886,558 562,800
30,000-35,000 216,839 7,044,936 4,653,777 924,673
35,000-40,000 248,665 9,371,680 5,990,899 1,256,042
40,000-45,000 252,387 10,720,908 6,735,904 1,509,213
45,000-50,000 248,324 11,790,427 7,246,380 1,689,363
50,000-55,000 200,652 10,555,480 6,360,216 1,523,170
55,000-60,000 186,462 10,721,843 6,359,583 1,515,719
60,000-65,000 148,420 9,271,515 5,415,123 1,412,963
65,000-70,000 136,792 9,215,939 5,291,237 1,374,419
70,000-75,000 122,339 8,838,724 5,008,457 1,397,870
75,000-80,000 94,762 7,332,131 4,104,498 1,117,977
80,000-85,000 76,330 6,303,236 3,381,900 966,197
85,000-90,000 68,550 6,003,608 3,262,912 883,129
90,000-95,000 55,417 5,109,051 2,645,938 841,060
95,000-100,000 36,458 3,554,360 1,821,546 554,000
100,000-150,000 236,255 27,872,800 14,163,585 4,552,994
150,000-200,000 52,057 8,879,408 3,843,180 1,400,525
200,000-300,000 21,966 5,076,387 1,902,820 635,211
More than 300,000 4,864 1,746,755 674,682 220,433
Total income 2,771,457 167,701,124 94,408,501 24,857,618
Source: DGBAS, Report on the Survey of Family Income and Expenditure, 1972.
ESTIMATION OF INDIRECT TAX 805
Educational
expenditure Direct tax Indirect tax Savings Income class
[C3] [TI] [T2] [S] (N.T. dollars)
7,026 173 5,906 5,178 Less than 10,000
21,176 1,142 27,758 10,444 10,000-15,000
81,909 3,487 93,935 27,640 15,000-20,000
162,080 9,157 196,920 146,252 20,000-25,000
305,916 20,589 340,636 196,088 25,000-30,000
466,922 35,873 543,905 419,786 30,000-35,000
677,383 48,909 717,500 680,947 35,000-40,000
745,254 77,828 812,416 840,293 40,000-45,000
894,649 91,681 879,792 988,562 45,000-50,000
864,473 103,121 834,234 870,266 50,000-55,000
888,558 123,214 773,020 1,061,749 55,000-60,000
701,356 118,086 661,359 962,628 60,000-65,000
753,610 118,826 658,866 1,018,981 65,000-70,000
721,286 112,321 619,651 979,139 70,000-75,000
621,313 92,842 529,684 865,817 75,000-80,000
561,288 96,570 420,132 877,149 80,000-85,000
554,572 94,819 412,853 795,323 85,000-90,000
448,308 98,609 338,819 736,317 90,000-95,000
326,160 66,582 245,080 540,992 95,000-100,000
2,393,664 655,079 1,748,797 4,358,681 100,000-150,000
685,128 285,057 495,164 2,170,354 150,000-200,000
357,276 158,975 225,048 1,797,057 200,000-300,000
123,588 110,673 74,946 542,433 More than 300,000
13,362,895 2,523,613 11,656,421 20,892,076 Total income
306 TAXATION AND THE INEQUALITY OF INCOME AND EXPENDITURE
Table 6.10. Family Income and Expenditure,
by Category and Income Class, 1973
(thousands of N.T. dollars)
Number of Total family All other Housing
Income class families income expenditure expenditure
(N.T. dollars) [N] [Yd [CI] [C2]
Lessthan 10,000 4,706 32,729 43,155 7,396
10,000-15,000 13,142 173,702 177,907 33,372
15,000-20,000 33,413 601,385 453,219 93,377
20,000-25,000 63,584 1,447,121 981,868 181,356
25,000-30,000 93,436 2,579,618 1,713,159 310,933
30,000-35,000 147,877 4,789,163 3,262,488 579,117
35,000-40,000 187,831 7,061,009 4,485,162 872,249
40,000-45,000 178,633 7,591,085 4,904,235 978,339
45,000-50,000 228,614 10,845,636 6,885,053 1,410,873
50,000-55,000 202,529 10,634,583 6,796,902 1,420,303
55,000-60,000 185,412 10,645,307 6,578,248 1,467,923
60,000-65,000 185,849 11,572,819 7,158,236 1,587,324
65,000-70,000 157,879 10,606,557 6,284,235 1,537,840
70,000-75,000 142,171 10,291,020 5,992,513 1,536,800
75,000-80,000 125,281 9,703,135 5,604,665 1,432,037
80,000-85,000 109,654 9,039,353 5,171,099 1,485,437
85,000-90,000 104,333 9,110,737 5,134,329 1,385,537
90,000-95,000 77,403 7,141,273 3,975,464 1,075,972
95,000-100,000 68,908 6,701,063 3,619,996 1,039,971
100,000-150,000 383,675 45,830,233 23,269,023 7,566,972
150,000-200,000 98,356 16,631,725 7,470,937 2,763,891
200,000-300,000 45,401 11,113,270 4,350,321 1,746,133
More than 300,000 20,425 8,997,359 3,024,034 1,162,432
Total income 2,858,512 213,140,882 117,336,248 31,675,584
Source: DGBAs, Report on the Survey of Family Income and Expenditure, 1973.
ESTIMATION OF INDIRECT TAX 307
Educational
expenditure Direct tax Indirect tax Savings Income class
[CW] [Tl] [T2] [S] (N.T. dollars)
1,881 251 7,368 -27,322 Less than 10,000
24,357 1,119 19,208 -82,261 10,000-15,000
55,311 2,445 53,914 56,881 15,000-20,000
94,660 6,286 118,565 64,386 20,000-25,000
144,763 12,082 214,482 184,199 25,000-30,000
300,236 20,666 376,728 249,928 30,000-35,000
431,468 39,025 557,565 675,540 35,000-40,000
514,269 39,233 573,203 581,806 40,000-45,000
696,253 65,314 794,873 993,270 45,000-50,000
679,973 77,628 784,418 875,359 50,000-55,000
716,455 79,408 773,263 1,030,010 55,000-60,000
813,520 87,733 861,387 1,064,619 60,000-65,000
822,757 100,674 783,415 1,077,636 65,000-70,000
772,428 120,361 728,338 1,140,580 70,000-75,000
766,824 106,504 707,480 1,086,625 75,000-80,000
646,411 123,319 627,028 986,059 80,000-85,000
735,645 125,243 634,321 1,095,662 85,000-90,000
553,968 99,321 494,723 828,825 90,000-95,000
616,227 99,808 475,210 849,851 95,000-100,000
3,835,007 811,851 2,982,699 7,364,681 100,000-150,000
1,382,955 427,850 995,448 3,590,643 150,000-200,000
807,556 285,697 549,114 3,374,448 200,000-300,000
475,088 390,255 337,190 3,608,360 More than 300,000
15,880,012 3,122,073 14,449,940 30,669,025 Total income
CHAPTER 7
Relevance of Findings for Policy
THE ULTIMATE PURPOSE of the examination of Taiwan's development
experience, indeed any country's development experience, should be
more than simply attempting to understand what happened during
a specified period. It should be to distill conclusions that may be
relevant to other developing societies and to determine special
features that are likely to be irrelevant elsewhere. We consequently
have tried to illuminate the possibilities, at various levels of aggre-
gation and analysis, for minimizing the conflict between growth
and equity. Readers may nevertheless expect a listing of policy
recommendations that stem from such an analysis. Thus, even
where our work is preliminary and tentative, which it generally
is, we will at least indicate the kinds of policy conclusions that
seem to be supported by the empirical findings.
Before proceeding to such a listing, however, two general pre-
cautions are necessary. One has to do with the extent to which
policy is based on sound theory or on a combination of vaguely
conceived relations and good intentions. The other has to do with
the extent to which analysis of the distribution of income is purely
economic or intertwined with other disciplines.
Postwar growth has been associated with the observed general
worsening of the distribution of income in most developing coun-
tries. This pattern has elicited strong protests: "Growth has failed.
Governments must resort to direct, even radical actions to correct
the situation." The actions proposed usually include land and fiscal
reform, public works programs, and major packages of poverty
relief and welfare. But what is the basis for the contention that the
primary strategy of growth has failed and that direct intervention
308
RELEVANCE OF FINDINGS FOR POLICY 309
is required to fix up FID after the fact? All too frequently the evidence
is little more than a crude correlation between high rates of growth
and worsening indexes of income inequality.
It is easy to sympathize with the humanitarian instincts, and to
honor the political instincts, that propel observers to the conclusion
that radical change is required. But the general absence of underlying
positive analysis is open to question. Consider medicine. After many
years of basic research and the accumulation of substantial knowledge,
a sure cure for cancer still has not been found. Yet few experts favor
declaring a "war on cancer" if that means abandoning a step-by-step
scientific approach to the problem. Similarly it would be unwise to
reject the basic accumulated tool kit of economics, to claim that
growth does not work without specifying alternative growth paths,
or to raise false hopes by stating that a "quick fix" is possible and has
been worked out analytically. To do any of these things would
probably impede the cause, not advance it.
Accumulated economic theory must provide a framework that
enables economists and planners to differentiate the relevant from
the irrelevant and to rule out logical absurdities. Such a framework,
to be achieved through the traditional mixture of deductive and
inductive analysis, is a prerequisite for understanding the relations
between distribution and growth-and thus for knowing what to
do about them. True, such a framework is only now beginning to
emerge. Although still inadequate, it is the best we have, and it
can be improved in the future. The policy implications listed in
this chapter should therefore be interpreted in this context. They
have been developed within the limits of existing theory and method,
and much additional work is required to corroborate or refute them.
A second general precaution is related to the realization that a
society's modernization involves, in addition to economic elements,
important noneconomic elements relevant to the problem at hand.
For example, inductive evidence and deductive logic may indicate
that institutional discrimination against women in the labor force
is relevant to wage income inequality (see chapter four). Although
this finding may decidedly be relevant to policy, we find it difficult,
as economists, to go beyond the stylized prescription that such
discrimination should be removed, and we leave to others the task
of designing an appropriate action program. In fact, policies rele-
vant to the family distribution of income seldom are purely econo-
mic. Many interdisciplinary complexities relate to such issues as
nepotism, family formation, and imperfections in educational
310 RELEVANCE OF FINDINGS FOR POLICY
access. If some of the policy conclusions cited below seem terse
and barren, the excuse is that we have followed a natural tendency
to appeal to a division of labor among social scientists.
Here, as elsewhere, good policy should be based on good theory.
The analysis of determinants of the family distribution of income
still is at an early, largely inductive, and pretheoretical stage. In the
introduction we tried to explain the overall framework of reasoning
adopted to guide the work of this volume. Our findings and their
relevance for policy are presented following the same pattern.
At the aggregate level, the most important, if general, policy
conclusion which may be derived from our work is this:
* It is possible for economic growth to be compatible with an
improved distribution of income during every phase of the
transition from colonialism to modern growth.
Taiwan's experience demonstrates that if assets are not distributed
too unequally, a growth path initially based on a flexible version of
primary import substitution, followed by the timely reduction of
the veil between a changing endowment and relative factor and
commodity prices, can yield this result. True, few other developing
countries have the same combination of a relatively favorable initial
distribution of assets and a willingness to deploy the market
mechanism effectively over time. But the experience in Taiwan
does not support those who argue that because tinkering with rela-
tive prices did not work in the 1950s and 1960s, we must now reach
for the radical medicine bottle. Nor does it support the argument
that the market solution at every step of the way will, in the pres-
ence of powerful landed or industrial interests, yield the desired
complementarity between the objectives of growth and equity.
What it does support is the conclusion that, given initial conditions
that are not too unfavorable, such complementarity can be achieved
by affecting the basic growth path, not by following what may be
called a secondary or mop-up strategy through direct interventions
by government. That is, such complementarity can be achieved by
following a different primary strategy of transition growth.
The basic thesis of this volume then is that an equitable level of
FID can come about mainly through the kind of economic growth
which is generated and hence that FID policy should center on growth-
related policies. This thesis is in turn predicated on the idea that
economic growth is typologically and historically sensitive. In other
words, the transition to modern growth is an historical event charac-
RELEVANCE OF FINDINGS FOR POLICY 311
terized by meaningful subphases. Furthermore, because of inherited
economic, geographic, and institutional characteristics, different LDCS
will undergo this transformation by following different patterns or
subphases. Thus the policy focus elaborated here would not neces-
sarily be relevant for types of countries very different from Taiwan-
for example, countries large in size, rich in oil, or having a surplus
of land. Mioreover any suggestions relevant to policy must be sensi-
tive to the particular subphase that a country has reached in the
transition to modern growth. In this volume we have concentrated
on Taiwan as a successful example. The transferability of policy
suggestions to other countries must be strictly based on the under-
standing that good FID policy, along with growth policy, must be
sensitive to typological and historical considerations.
Much can be said about what is unique or not unique in any
particular experience and the consequent applicability or inapplica-
bility to other countries. As was pointed out at the outset, no coun-
try's experience can ever be fully transferred. Taiwan unquestion-
ably had some unique advantages: its initial endowment of human
resources, its cultural heritage, its early colonial experience, its
strong support by the United States. But some popular notions
about the large quantitative role played by U.S. foreign aid early,
and private investment later, are factually incorrect.1 Moreover
Taiwan also had some substantial disadvantages not shared by
many other contemporary LDCS: its initially unfavorable man-land
ratio, its heavy population pressure over time, its felt need to spend
a large part of its resources on national defense, its growing inter-
national diplomatic isolation. We recognize, when all is said and
done, that readers will have to determine for themselves what is
unique in, or transferable from, the Taiwan experience. We believe
that many elements from the analysis in this volume, and the policy
conclusions derived therefrom, have relevance in other contexts.
As was pointed out earlier, the postwar transition to modern
growth in Taiwan moved from the initial subphase of primary im-
port substitution into that of export substitution in the early 1960s.
By means mainly of a labor-intensive export drive, a landmark of
transition growth appeared in about 1968, when the economy's
1. Although aid may have been of strategic importance in encouraging the
important policy changes of 1961, public and private foreign capital contributed
less than 6 percent of cumulative investment during the 1953-72 period.
312 RELEVANCE OF FINDINGS FOR POLICY
labor-surplus condition ended and real wages began to increase at
an accelerated rate. Thus any respectable analysis of the essential
growth phenomenon in such a labor-surplus, dualistic economy
must explore the reallocation of labor from the agricultural sector
to the nonagricultural sector and the changing pattern of the func-
tional distribution of income. That changing pattern, measured by
the relative size of the wage and property income shares, is brought
about by changes in wage rates, factor endowment, and technology.
The impact of growth on FID can be examined from three view-
points: that of all families, that of urban families (receiving wage
and property income), and that of rural families (receiving agri-
cultural income as well as wage and property income). We naturally
are interested in the relations between growth and equity for the
entire population. We nevertheless found it useful, for both analytical
and policy reasons, to focus first on the underlying sectoral level.
The Inequality of Family Income
The first specific empirical findings emanating from our analysis
were these:
. For all households and urban households, virtual constancy
in FID before 1968-the turning point marking off labor sur-
plus from labor scarcity-gave way to significant improvement
thereafter.
• For rural households, significant improvement before 1968 gave
way to virtual constancy thereafter.
These empirical findings support our basic thesis that FID equity
indeed is a growth-sensitive phenomenon, as can be seen from the
fact that, for urban and rural sectors separately and for the economy
as a whole, this turning point demarcates markedly different phases
of both growth and FID performance. Furthermore the transition
involves the transformation of an agrarian economy into an indus-
trial economy. Our findings indicate that the favorable impact of
growth on FID in that context must occur in the relatively more
dominant sector of the economy-that is, in agriculture before
1968 and in nonagriculture thereafter-if growth is to have a con-
sistently favorable effect on FID over time. The unusually high
priority Taiwan attached to the agricultural sector-to land reform,
THE INEQUALITY OF FAMILY INCOME 313
infrastructural investments, and relative prices before commer-
cialization-represents an example of the selection of the correct
policy focus from the points of view of both growth and distribution
in this general historical perspective.
Analysis of the underlying causes of this aggregate performance
can be conducted by identifying a reallocation effect which captures
changes in the relative size of the agricultural and nonagricultural
sectors, a functional distribution effect which captures changes in
the relative shares of wage and property income, and a factor Gini
effect which captures changes in inequality of distribution of a
particular component of family income. What policy implications
can be derived from this tripartite division of the causes of inequality?
The main implication is that different types of policy are required
to deal with the first two effects, which can be more directly related
to analysis in the context of growth theory, than with the third.
Thus it becomes important to know something about the relative
quantitative significance of the three effects as causes of overall FID
equity. The empirical findings, more specific than those related to
the degree of income inequality, once again support the general
thesis that the nature of economic growth determines much of FID
in both sectors of the dualistic economy.
. For urban households the functional distribution effect, wvhich
was highly unfavorable before 1968 and favorable after 1968,
was a dominant cause of FID performIance.
* For rural households the reallocation effect, which was favor-
able both before and after 1968, was a dominant cause of FID
performance.
The phenomena related to growth here are not only relevant but
dominant as explanatory causes of changes in the family distribu-
tion of income. As summarized in the foregoing findings, the differ-
ence between urban households and rural households is an important
growth-relevant phenomenon. For the urban sector the accumula-
tion of capital and human assets is at the heart of the industriali-
zation effort. For this reason the functional distribution effect is a
dominant cause of FID. For the rural sector, in contrast, the re-
allocation of labor from agricultural to nonagricultural production
represents a much more crucial development issue. Consequently
the reallocation effect turns out to be a dominant cause of FID per-
formance. The implications of these findings help in the identifica-
tion of the proper policy focus. For the urban sector the wage rate,
314 RELEVANCE OF FINDINGS FOR POLICY
factor endowment, and technology choice-all elements affecting
the functional distribution of income-are the dominant policy
issues related to FID. For the rural sector the growth of rural-based
industries and services alongside a productive agricultural sector,
and the additional employment opportunities thus offered to rural
households, are the dominant policy issues.
To see more precisely how these growth-relevant forces affect FID,
we first concentrated on rural families, which receive both agri-
cultural and nonagricultural income.
* For rural families agricultural income consistently was less
equally distributed than nonagricultural income-that is,
Ga > GO.
. Over time, agricultural income became more equally distri-
buted-that is, Ga declined.
. Rural families received a surprisingly large and increasing
share of income from rural industries and services, which were
increasingly labor-using-that is, ka declined and O/O in-
creased.
As an economy modernizes, analysis of the equality of income dis-
tribution for rural families involves issues quite different from those
affecting urban families. The main reason is the importance of
agricultural production. Two central issues here are the equality of
the distribution of agricultural income, which is the dominant in-
come component for traditional rural societies, and the increase
in the equality of the distribution of nonagricultural income asso-
ciated with the growth of rural industries during the transition to
modern growth. The foregoing empirical findings for rural areas
show that the distribution of income from the traditional agricul-
tural base is more unequal than that of the new income associated
with rural-based industrialization.
Worldwide concern about inequality in the distribution of agri-
cultural income in rural communities has led to the laudable ad-
vocacy of direct government interference with the market mechanism
where productive assets in agriculture (mainly land) are highly
unequally distributed. In Taiwan early land reform, followed by
increases in multiple cropping and the cultivation of new crops by
the poorer (smaller) farmers, caused agricultural income to become
significantly more equally distributed over time. That experience
seems to indicate that land reform is an important input. But if
the distribution of agricultural income is to be improved when
THE INEQUALITY OF FAMILY INCOME 315
agricultural growth is rapid, a fairly equal distribution of landed
assets is also required, and the "right" growth-oriented policies must
follow such reform.
How did the favorable reallocation effect cited earlier work to
bring about a more equitable distribution of income for rural families
over time? Because nonagricultural income was more equally dis-
tributed than agricultural income, the growth of rural industries and
services made a substantial contribution to FID equity. Furthermore,
when compared with urban industries, rural industries were found to
be much more "labor using" (increasingly so over time). Thus the
steady increase of opportunities in rural by-employment available to
members of rural families, especially the poorer ones, greatly con-
tributed to the complementarity of growth and FID. All these factors
lie behind the reallocation effect's being a dominant factor con-
tributing favorably to FID equity.
The basic policy implication of the foregoing empirical findings
for rural households is relevant to industrial location. As was pointed
out in chapter three, nonagricultural income has always been an
important component of rural family income in Taiwan. Given the
spatially dispersed pattern of industrial location, the growth of
rural-based industries and services offered new opportunities for
employment and investment. These opportunities made it possible
in later years for nonagricultural income to overwhelm agricultural
income and become the most important source of rural family in-
come. All the advantages of such a decentralized pattern of industrial
location-for example, those related to agricultural modernization
arising from direct contact with industrial activity to avoiding the
costs associated with labor dislocation and transport, and to re-
ducing urban congestion and social overhead expenditure-need not
be elaborated here. But the development of rural industries and the
abandonment of the all-too-frequent incenitives for urban concen-
tration and agglomeration must be emphasized as prime policy
recommendations emerging from our work. It is interesting to note,
moreover, that most of the workers migrating from agriculture to
nonagriculture were part-time or commuting farmers who were
readily available for agricultural tasks at peak harvest time.
Advocacy of a spatially dispersed pattern of industrial location
provides a good example of the typological sensitivity re-
quired in policymaking. The pattern that emerged in Taiwan
was largely the result of such demographic and geographic features
as high population density, such topological features as the location
316 RELEVANCE OF FINDINGS FOR POLICY
of principal ports and mountain ranges, and such historical fea-
tures as the transport and energy networks established during the
Japanese period. That pattern was also the result of government
policies to equalize the cost of industrial energy and fuel through-
out the island and to provide additional rural infrastructure as needed
-policies which did not succumb to the normal subsidization and
artificial encouragement of industrial agglomeration in urban areas.
Consequently, competitive market forces yielded a dispersed pat-
tern of industrial location and a labor-intensive output mix. Rela-
tive to these forces, economies of scale played a minor role. When
these basic demographic and geographic conditions are not met-as,
for example, in the Philippines-and when, moreover, governments
pursue policies intended to give special encouragement to large-
scale, capital-intensive industry-as, for example, in Thailand and
the Philippines-a centralized pattern of urban industrialization
results. FID equity can be improved only in the context of a growth
policy that is typologically sensitive.
How did the functional distribution effect work to affect FID
equity among urban households? First, the operation of the observed
funtional distribution effect further supports the thesis that equity
is a growth-sensitive phenomenon. As the conditions of labor sur-
plus gave way to those of labor scarcity after 1968, the impact of
the functional distribution effect on FID changed from being un-
favorable to favorable. The reason is this. Only when labor becomes
a scarce commodity, as evidenced by the sharp increase in the real
wage, does the functional distribution effect become favorable. Two
empirical findings explain more precisely the essential behavior of
the functional distribution effect on urban FID.
For urban households property income was more unequally
distributed than wage income.
The share of wage income declined relative to the share of
property income before 1968 and gained at the expense of
property income after 1968.
Because property income was more unequally distributed than wage
income, the functional distribution effect was unfavorable or favor-
able depending upon whether the labor share was falling-as it was
before 1968-or rising-as it was after 1968. Before 1968 the real
wage was relatively stable because of the continued surplus of labor.
The urban family's share of wage income declined slightly, mainly
because employment opportunities were not expanding at a pace
THE INEQUALITY OF FAMILY WAGE INCOME 317
significantly greater than the rate of capital accumulation. That was
in turn caused by the relatively weak labor-using bias of technology
in urban industries. When the surplus of labor was exhausted after
1968, the increase in the real wage and the rapid increase of capital
per worker (capital deepening) led to the expected increase in the
wage share relative to the property share. In this way the functional
distribution effect became favorable to FID after the turning point
for conventional reasons.
For the entire 1964-72 period, and disregarding additive factor
components as in chapter five, it appears that overall income in-
equality declined mainly because of a reduction in inequality in the
urban sector over time. This occurred despite the existence of a
widening income gap between the urban and rural sectors. The
declining trend in income inequality can be attributed to the rapid
rate of labor absorption in light manufacturing industries, which were
competitive in international trade before the turning point, and to
the more conventional rise in wages thereafter.
It often is said that growth in the 1960s and 1970s has failed to
produce a more equitable distribution of family income. This state-
ment has led, directly or indirectly, to the conclusion that radical
government intervention is required to transfer assets from rich
to poor, or at least to effect redistribution after the fact. The find-
ings here, based on the analysis of the relations between growth
and FID in Taiwan, indicate that the frequent conclusion in favor of
continuous direct government intervention is not necessarily war-
ranted. A relatively favorable initial distribution of assets clearly
helped in Taiwan. But the major accomplishment of substantially
eliminating the conflict between growth and FiD before the turning
point was the result of three basic policies: the early attention to
agriculture; the mild version of import substitution followed by
thorough-going export-oriented industrialization; and the decen-
tralization of industrial operations.
The Inequality of Family Wage Income
For the more disaggregate analysis of the inequality of family
wage income, our conceptual framework recognized the formation
of a heterogeneous labor force as crucial in industrialization. Differ-
ences in education, age, sex, and family income characterize that
heterogeneity. Distinctions were drawn among three types of issues
318 RELEVANCE OF FINDINGS FOR POLICY
and reflected at three levels of analysis. At the first level we attempted
to trace the differentiated structure of wage rates to principal char-
acteristics of the labor force. At the second level we attempted
to trace the inequality of individual wage income to the differen-
tiated wage rate structure and the composition of the labor force.
At the third level we attempted to trace the inequality of family
wage income to the membership composition of families. The policy
implications of the findings will be summarized separately for each
of the three levels.
At the first level, the analysis of the differentiated wage struc-
ture, we accepted the convention that differences in wage rates
arising from differences in education and age are justifiable or war-
ranted, but those arising from differences in sex and family influence
are not. We acknowledge that not everyone will necessarily agree
with this convention. The analysis at the first level nevertheless
confirms that:
Overall differences in wage rates reflected a mixture of both
warranted and unwarranted causes.
The policy implications of warranted causes clearly are neutral.
Wage rates are supposed to differ for warranted reasons, and nothing
should be done to influence them. The policy implications of un-
warranted causes are stylized. Institutional discrimination against
females and members of poorer families exists and should be removed.
More significant, of course, is the issue of how stylized policy
conclusions are to be related to growth. Using rural, town, and
city residence as proxies for the increasing degree of industrializa-
tion, it was found that the modern commercialized milieu of large
cities tends to evaluate sex and family influences with more sensi-
tivity than the more tradition-bound milieu of rural communities.
Institutional discrimination thus appears to be a by-product, per-
haps an inevitable by-product, of modernization in its early phases.
But because policy measures clearly affect more than the economic
sphere, caution is required when dealing with wage differences that
can be traced to institutional discrimination.
For the education characteristic, it was found that there was no
significant difference between large cities and rural communities
in evaluating this warranted cause of differences in wage rates.
In other words, the premium for education was about the same
everywhere. Thus, in the more tradition-bound rural communities,
market forces can more or less sensitively value this most important
THE INEQUALITY OF FA-MILY WAGE INCOME 319
labor attribute. The policy implication again is negative or inactive.
Government does not need, for example, to make a special effort
in rural communities to render the labor market more perfect or
to offer special inducement for labor migration to ensure a more
efficient spatial pattern of educated manpower use.
At the second level, the analysis of wage income inequality, the
crucial issue about the relative overall importance of warranted and
unwarranted causes can be addressed.
. Discrimination by sex or family influence is not as quantita-
tively important as discrimination by education or experience
(age).
Together sex and family influence accounted for only 33 percent
of the explained inequality. This type of conclusion provides an indi-
cation of what a policy that is calculated to eliminate institutional
discrimination might accomplish, presumably at some cost.
The findings at the first level of analysis show for differences in
wage rates that labor markets in large cities tend to discriminate
more against females and members of poor families than those in
rural communities. But the composition of the labor force in the
large cities apparently tends to compensate for this inequality.
The findings at the second level of analysis indicate that institu-
tional discrimination accounted for a smaller percentage of wage
income inequality in large cities than in rural communities. In other
words, females and members of poor families tend to get a larger
share of better jobs in large cities. The implication of this finding
for policy is that industrialization can be relied upon, despite the
higher degree of institutional discrimination of wage rates, to bring
about greater equality in the distribution of wage income. This con-
clusion tends to confirm the earlier assertion that policies to eliminate
institutional discrimination should proceed cautiously. With an eye to
future research, it can be added here that the analysis at the first level,
which constitutes the focal point of what can be called traditional
analysis, might give a misleading picture by concentrating only on
institutional discrimination of wage rates. To assess the quantita-
tive significance of institutional discrimination for wage income
inequality, the changing composition of the labor force must also be
known. The empirical findings presented here are a perfect illus-
tration of this crucial point.
At the third level, the analysis of family wage-income inequality,
it was recognized that labor is a very heterogeneous factor of pro-
320 RELEVANCE OF FINDINGS FOR POLICY
duction. Even the crude classification by sex, age, and education
used in this analysis leads to thirty-seven grades of labor. Within
our framework of reasoning, the unequal family ownership pattern-
that is, the unequal composition of family membership by these
grades-lies behind family wage-income inequality. Some "inferior"
grades, such as the poorly educated old female, can be interpreted as
being part of the marginal labor force; some "superior" grades, as part
of the prime labor force.
- The pattern of unequal ownership of the marginal labor force
is a minor problem as far as overall family wage-income inequal-
ity is concerned.
The policy implication is that government relief and welfare mea-
sures may help the marginal labor force, but have little impact
on the basic problem of family wage-income inequality. Such a
conclusion may at least force policymakers to think a little harder
about the likely impact of policy options that seemingly are poli-
tically attractive. A related conclusion may do the same:
* The most important cause of overall family wage-income in-
equality is the pattern of unequal ownership of high-grade
workers.
High grade, it will be recalled, can mean one or a combination of
three attributes: prime age, male, and highly educated. If inequality
is traced, for example, to differences in age and sex ownership-
that is, to the contrast between families having a preponderance of
prime-age males and families having a preponderance of old or very
young females-there is no obvious government policy relevant to
correcting this inequality. Any such policy would have to be very
far-fetched, interfering with rules of family formation by preventing
divorce or the formation of secondary nuclear families.2
The inequality of family ownership of the educated labor force
is a different matter. The thesis of a tendency for the unequal dis-
tribution of the opportunity for higher education to perpetuate the
inequality of family income has many adherents. According to this
2. The low causal effect attributable to age, by itself, gives us some confidence
that the problem of life-time earning relative to observed earning may not be as
serious as is sometimes believed. It was not possible, however, to examine this
potentially important issue more rigorously in this volume.
THE INEQUALITY OF TAXATION AND EXPENDITURE 321
thesis the wealthier families can provide better education, and better
paying jobs, to their members-advantages that conceivably could
be principal causes of family wage-income inequality. The findings
here cast some doubt on this thesis, because as far as education is
concerned the family turns out to be insignificant as the unit of
labor ownership. This means that the degree of inequality of wage
income of, say, 1,000 workers would remain the same, irrespective
of whether the family affiliations of these workers are taken into
consideration.
For Taiwan this finding is not particularly surprising. The im-
perial examination system, institutionalized long ago in traditional
China, continues to hold sway. Rigorous and impartial entrance
examinations are annually held at all levels of formal education.
Because wealthy families do not have the marked special advan-
tages frequently encountered elsewhere, access to educational oppor-
tunities is thus relatively equal for all. Whether such a policy is
feasible for other countries not having a similar cultural bias would
seem to be at the heart of policy discourse in this general area.
The Inequality of Taxation and Expenditure
The analysis in this volume suggests a number of more specific
policy conclusions based on findings related to patterns of taxa-
tion, disposable income, and family consumption. Economists and
noneconomists have traditionally thought of taxes as an easy after-
the-fact method of improving FID if the primary or growth-related
outcome proves unsatisfactory. In this context, there usually is a
secondary strategy concerned with minimizing the so-called dis-
incentive effects of a taxation system that is too progressive.
In Taiwan the system of taxation was found to be reasonable
from the viewpoint of incentives-that is, it was not unduly pro-
gressive or regressive. In fact:
* The distribution of the total tax burden was neutral with re-
spect to its impact on the equity of distribution of family income.
In other words, the degree of inequality of family income before
and after taxes was about the same. The policy implication of this
empirical finding lends further support to the overall conclusion
of this volume: adequate FID performance is mainly the result of an
322 RELEVANCE OF FINDINGS FOR POLICY
appropriate primary-that is, growth-related-strategy. Other work
relating to fiscal impact seems to support this position.' Thus, even
when the fiscal capacity of an LDC is relatively strong, as it is in
Taiwan, direct government intervention after the fact will probably
do little to affect FID performance.4 A second and related finding also
has an obvious implication for policy:
* The total tax burden was neutral because the quantitatively
more important and regressive indirect tax payments canceled
the quantitatively less important and more progressive direct
tax payments.
Thus if the tax system is to be an instrument for bringing about a
more equitable distribution of income, the tax basis should be shifted
to direct taxation from its present overwhelming reliance on in-
direct taxation. This conclusion nevertheless is weakened because
considerations other than equity considerations often prevail. During
most of the period after 1962, Taiwan has been in a growth subphase
of primary export substitution. The dominant phenomenon in this
subphase is the export of labor-intensive goods, such as textiles, in
exchange for the import of mainly producer goods, such as raw
materials and capital goods. With the exhaustion of surplus labor
around 1968 and the rapid increase in real wages subsequently,
there has been a growing consensus that Taiwan now faces the
transition into a sequence of secondary import and export substi-
tution. That sequence aims first at the production, and later at the
export, of those capital-intensive and skill-intensive producer goods
which now are largely being imported.
Given this change, it follows that Taiwan in the near future cannot
hope to continue relying on cheap labor as the basis of its comparative
advantage in foreign trade. The accumulation of skills, technology,
and capital is likely to replace cheap labor and make unprecedented
demands on Taiwan's private entrepreneurial resources. Consequently
the primary emphasis in any future revisions of tax policy is likely to
be on investment incentives, not on equity. For this reason, a shift
3. See for example Jacob Meerman, "Fiscal Incidence in Empirical Studies
of Income Distribution in Poor Countries," AID Discussion Paper, no. 25
(Washington, D.C.: U.S. Agency for International Development, June 1972).
4. The possible redistributive effect of changes in the pattern of government
expenditure, especially for such social services as health and education, is not
dealt with here.
FUTURE RESEARCH 323
from the regressive system of indirect taxation to a more progressive
system of direct taxation may be inappropriate for Taiwan. Instead,
movement toward a more progressive consumption tax, which would
be very heavy on items likely to be consumed by high-income families,
may be more appropriate. Entrepreneurs could still be encouraged to
earn income and required to pay little tax as long as they reinvest
their profits. Another interesting finding relates to expenditure:
* For high- and low-income families the distribution of family
expenditure on housing is significantly more unequal than that
on other consumption.
This finding indicates that a progressive consumption tax on housing,
such as that based on the space or construction cost of residential
units, could be considered as a major component of any proposed
tax reform. Unlike the luxury consumption associated with night
clubs, golf courses, and imported cars, housing is a popular item of
mass consumption. It accounts for a larger portion of household
expenditure than either savings or expenditure on education. Hous-
ing, more than clothing and food, seems to symbolize class dis-
tinctions in the cultural milieu of contemporary Taiwan. If the
experience in other countries is a guide, such class-differentiated
consumption patterns will probably become socially and politically
offensive in Taiwan as well. Consequently the introduction of pro-
gressive consumption taxation conforms well to the relatively egali-
tarian pattern of income and the goals set for the future.
Future Research
We believe that the work of this volume, including the effort to
derive general and specific policy conclusions from it, has demon-
strated the desirability of integrating income distribution with the
general framework of development theory. It also has demonstrated
the complexity attached to many dimensions of the problem-dimen-
sions that still are inadequately understood. We have not, moreover,
even attempted to tackle some other issues, even though we recog-
nize them to be important subjects for future analysis. Further
investigation of the causation underlying the inequality of property
income is one example.
By making a highly selective and inductive effort, we have tried
to contribute to a less ad hoc and more analytical treatment of the
324 RELEVANCE OF FINDINGS FOR POLICY
distribution of family income as a dimension of development. By
pointing out that at least one developing economy could "have its
cake and eat it, too," we hope at least to make the tradeoff pessi-
mists sit up and take notice. We have examined the whys and where-
fores of that experience from a number of directions. We have con-
cluded that the way transition growth is generated largely determines
the levels of transition equity. By so doing we have perhaps con-
tributed to the integrated deterministic theory of income distribu-
tion-a theory which still eludes us-and shed some light on the
direction of policy choices that must be made in the meantime.
What, then, are the implications for future research? Good poli-
cies for income distribution must be based on good theory. The
prime focus of theoretical research must therefore be to attempt to
explain empirically observed realities in order to understand the
causal nexus between growth and equity. At this stage of under-
standing, much of that effort still is inductive. -Much attention still
is paid to gathering, organizing, and processing data in accord with
certain pretheoretical frameworks. The additive factor-components
model and its combination with the linear regression technique illus-
trate the nature of these frameworks. Motivated by theoretical
notions, they require a mathematical design that is broad enough
for application to different types of problems. With more refined
analytical tools, we can hope to separate the quantitatively important
causes of inequality, such as access to educational opportunities,
from the less important causes, such as sex discrimination. The
policy focus could then be aimed at the important causes, and addi-
tional efforts could be directed at a determination of the feasibility
and practicality of various policy options. Moreover it may be
necessary to depart from subject areas familiar to the economist to
those more tangential to traditional analysis. In this volume we hope
merely to have demonstrated that it is feasible to make progress
along these lines.
PART TWO
The Methodology of Gini
Coefficient Analysis
THE SECOND PART OF THIS VOLUME is devoted to a systematic discus-
sion of decomposition procedures and the derivation of decomposition
formulas that use the Giri coefficient [G,] to measure the degree of
inequality of a pattern of income distribution [Y = (Y,, Y2,
... Y.) ].' All decomposition equations used in part one amount to
special cases developed irn this part. All the formulas deduced can be
applied to empirical analyses of the inequality of income distribution,
as will be emphasized through the use of numerical examples that
show the computation procedures involved. This part has five
1. Many authors have worked out and published Gini decomposition for-
mulas. They include, but perhaps are not limited to, the following. N. Bhatta-
charya and B. Mahalanobis, "Regional Disparities in Household Consumption
in India," Journal of the American Statistical Association, vol. 62, no. 317 (March
1967), pp. 143-61. V. M. Rao, "Two Decompositions of Concentration Ratio,"
Journal of the Royal Statistical Society, series A, vol. 132, pt. 3 (1969), pp. 418-
25. Mahar Mangahas, "Income Inequality in the Philippines: A Decomposition
Analysis," World Employment Programme, Population and Employment Working
Papers, no. 12 (Geneva: International Labour Organisation, 1975). Graham Pyatt,
"On the Interpretation and Disaggregation of Gini Coefficients," Economic Jour-
nal, vol. 86 (June 1976), pp. 243-55. Two other authors have published alternative
indexes of inequality: Henri Theil, Economics and Information Theory (Amster-
dam: North-Holland, 1967); Anthony B. Atkinson, "On the Measurement of
Inequality," Journal of Economic Theory, vol. 2 (1970), pp. 244-63. The relatedness
of their contributions to the work of this volume will be indicated where appro-
priate.
325
326 THE METHODOLOGY OF GINI COEFFICIENT ANALYSIS
chapters:
. Basic Concepts
* Testing Hypotheses
* The General and Special Models of Additive Factor Components
* Applications and Extensions of the Models of Decomposition
* Regression Analysis, Homogeneous Groups, and Aggregation
Error
Chapter eight presents an investigation of the alternative definitions
of the Gini coefficient, as well as of the pseudo Gini coefficient, when
Y is given. In chapter nine we formulate a problem of testing hy-
potheses when an observable quality characteristic-such as education
with high, medium, and low values-is associated with variations in
the income levels in Y. The ideas developed in these two chapters are
essential for the analysis in chapters ten, eleven, and twelve.
Chapter ten is concerned with the derivation of decomposition
formulas when Y has a finite number of additive factor components
given by WI = (Wi, W4, ..., Wi), where i = 1, 2,..., p. Its
purpose is to trace G, to G(Wi), the factor Gini coefficients defined
for Wi. In addition to a general model, decomposition formulas are
deduced for a linear model and a monotonic model, which are special
cases of the general model when additional restrictions are postulated
for Wi. Methods of approximation are developed when these restric-
tions are only approximately fulfilled, as often is the case in empirical
work. Two other special cases are developed in chapter eleven. In one
special case the sum of all values of W, in one component Wi is
assumed to be zero, leading to a model of "income components with
observation error." In the other special case several factor components
are assumed to be negative.
In chapter twelve a linear regression equation, estimated by the
method of least squares, is combined with the model of additive
factor components. Also in that chapter the analysis is directed at a
situation in which Y is segmented into a finite number of subvectors:
y = (Y, Y,,y yq),
yi = (yi yi, y ), ( = 1 2 q)
- 1 n2** i n t 2 n* 2
where Yi is interpreted as a homogeneous group. The purpose of this
analysis is to trace G, to G(PY), the intragroup inequality, as well as
to other effects. Finally the question of grouping error is addressed.
THE METHODOLOGY OF GINI COEFFICIENT ANALYSIS 327
In empirical research on the problem of additive factor components,
such as that in chapter three, the "grouped data" that often is used
leads to a "grouping error" in the Gini coefficient. The problem is
investigated as an application of the decomposition equation for
homogeneous groups, and the possibility of future research on this
issue is explored.
CHAPTER 8
Basic Concepts
THE PURPOSE of this chapter is to define the basic concepts used in
this volume and to illuminate them with numerical examples and
figures. First, the Gini coefficient is defined in relation to the Lorenz
curve, as is conventional. Second, two alternative definitions of the
Gini coefficient are presented and proved: one in relation to weighted
income fractions; the other to the average gap between income
fractions. Third, the pseudo Gini coefficient is defined in relation
to the pseudo Lorenz curve, which obtains when incomes are not
necessarily ranked in a monotonically nondecreasing order. These
concepts constitute the foundation for the discourse on methodology
in subsequent chapters.
Definition of the Gini Coefficient
Suppose there are n families with income Yi (i = 1, 2, ..., n)
and compute the income fractions yi:
(8.1a) Y = (Y1, Y2, ... , Y.) > 0,
(8.1b) s, = Y1 + Y2 + . .. + Yn > 0, and
(8.1c) y = (Yi, Y2, . , Y.) = (Y1/sy, Y2/sy, ... , Y./sy), where
(S. 1d) YI + Y2 + ...+ Y. = 1 and
(8.1e) Y < Y2 < ..._< Yn.
In equation (8.1b) s,, is the sum of incomes for all families; in equa-
tion (8.1c) the income fractions [yi] form a system of weights.
828
DEFINITION OF THE GINI COEFFICIENT 829
Figure S. 1. The Lorenz Curve
YD
I I 0/4
----------t ---------- L;7---
X / t~~orenz curve Y .
< <, 4_~~~~~~~~~~~~~Y = -02
source: Constructed bv the autliors.
Notice that family incomes are arranged in a monotonically non-
decreasing order, such that the first family is poorest and the last
family is wealthiest.
The Lorenz curve is a real-valued function defined on (1/n, 2/n,
... , n/n):
(8.2a) Ly (j/n) = Y + Y2 + . Y. .+ (j = 1, 2, n)
For example, when n equals 4:
(8.2b) Y - (Yl, Y2, YS, Y4) = (0.1, 0.2, 0.3, 0.4).
If B denotes the area under the Lorenz curve of the unit square of
figure 8.1, the Gini coefficient is defined as:
(8.3) G,, = (1/2 -B)/(1/2) = -2B.
330 BASIC CONCEPTS
In words, G, is the area above the Lorenz curve inside the triangle
OED, expressed as a fraction of that triangle's area, which is 1/2.
For the numerical example in equation (8.2b) the Gini coefficient
is 0.25. The Gini coefficient, according to its definition in equation
(8.3), is a nonnegative fraction. It takes on extreme values of 1
to represent extreme inequality and zero to represent extreme
equality. For these extremes:
(8.4a) Y, = Y2 = ... = Yn, which implies that G, = 0, and
Eperfect equality]
(8.4b) Y1 = Y2 = ... = Y-, = 0, which implies that G, = 1.
Eperfect inequality]
When equality is perfect, the Lorenz curve coincides with the diag-
onal OD in figure 8.1. When inequality is perfect and n is large,
the Lorenz curve coincides -with the unit square's edge OED.
Because the Gini coefficient of Yi is defined in relation to income
fractions [Y], the following result is elementary:
if:
(8.5a) Z = (kY1, kY2, .. ,Y),
then:
(8.5b) G. = Gy.
In words, if the incomes of all families change by a common multi-
ple, the Gini coefficient will not change.
The Gini Coefficient
as Related to the Rank Index of Y
The intuitive explanation of the geometrically defined Gini coeffi-
cient as a measure of income inequality can be seen from two al-
ternative definitions, the first of which is presented in this section.
THEOREM 8.1. The Gini coefficient of Y, as defined in equation
(8.3), is:
G, = au,b - , where
(a) a = 2/n,
THE GINI COEFFICIENT AS THE AVERAGE FRACTIONAL GAP 881
(b) a = (n + 1)/n, and
(c) U, = XlYl + X2Y2 + ... + XnYn where
(d) Yl < Y2 < Y, which in the general case of n
families is defined as:
(8.9a) S = E (yi - yi) for all i > j.
Using the figures from the numerical example in equation (8.8)
gives:
(8.9b) S, = 0.05 + 0.10 + 0.25 + 0.35 + 0.05 + 0.20 + 0.30
+ 0.15 + 0.25 + 0.10
= 1.8.
A term such as Y4 - Y2 = 0.20 indicates the gap of income fractions
between a wealthy family (the fourth) and a poor family (the
THE GINI COEFFICIENT AS THE AVERAGE FRACTIONAL GAP 333
second) and measures the extent or degree of inequality between
them. In equation (8.9a) the sum of all fractional gaps is S,. The
average fractional gap for n families is Sn/n. When equality is per-
fect, as in equation (8.4a), the average fractional gap [S,/n] obvi-
ously is equal to zero. The following theorem states that the Gini
coefficient is precisely the average fractional gap':
THEOREM 8.2. G, = Sn/n, where S, is defined as in equation (8.9a).
Proof: Take the sum of positive and negative entries of the matrix
on the left-hand side of equation (8.8) separately, which gives:
uv= U- [ny1 + (n -l)Y2 + . .. + lyn] by theorem 8.1(c)
=u - [nyl + nY2 + ... + nyn]
+ EOYI + lY2 + 2y3 + . . . + (n-l )y.]
=u -n + [OY + ly2+ 2y3 + . + (n- )Yn
by equation (8.1d)
=U -n- + (Yl + Y2 + + yn)
+ [Oy1 + ly2+ 2y + ...+ (n- 1)y]
= - n- 1 + u, by theorem 8.1(c)
2u1, - (n + 1)
= n[ (2/n) u - (n + 1) /n] = nG1, by theorem 8.1.
This completes the proof.
The numerical example in equation (8.7) can verify theorems
8.1 and 8.2, which posit that the Gini coefficient can be calculated
as the average fractional gap:
G, = Sn/n = 1.8/5 = 0.36,
1. Bhattacharya and Mahalanobis, in their analysis of regional disparity in
household consumption, give the equivalence of the two definitions of the Gini
coefficient. If, in their model, every region contains exactly one household, their
special case becomes equivalent to the theorem stated here. N. Bhattacharya
and B. Mahalanobis, "Regional Disparities in Household Consumption in India,"
Journal of the American Statistical Association, vol. 62, no. 317 (March 1967),
p. 149.
334 BASIC CONCEPTS
or as a linear function of the rank index of Y:
u, = 1(0.05) + 2(0.10) + 3(0.15) + 4(0.30) + 5(0.40) = 3.9;
G, = (2/5) (3.9) - 6/5 = 0.36.
The Pseudo Gini Coefficient
Let Y = (Y1, Y2, .. . , Y.) be an ine.)me distribution pattern
which is not necessarily monotonically arranged-that is, which
may not satisfy the conditions of expression (8.1e). Now define a
pseudo Lorenz curve as:
(8.10) Lt(j/n) = Y1 + y2 + ...+ yj. (j = 1, 2, ...,n)
For the following numerical example:
(8.11) y = (y', Y2, y3, y4) = (0.2, 0.4, 0.1, 0.3),
the pseudo Lorenz curve is indicated by the curve A'B'C'D' in
figure 8.2. When B denotes the area under the pseudo Lorenz curve,
a pseudo Gini coefficient can be defined in a way similar to equation
(8.3):
(8.12) 1 = 2B.
Notice that the only difference between the Gini coefficient defined
in equation (8.3) and the pseudo Gini coefficient defined here is
this: for G, the terms of the expression Y = (Y1, Y2, . .. , Y.) are
arranged in a monotonically nondecreasing order, thus satisfying the
conditions of expression (8.1e); for G, they are not so arranged.
Theorem 8.1 then rigorously implies:
THEOREM 8.3. The pseudo Gini coefficient of Y is:
G, = -a/-, where
ty = XIYI + X2Y2 + . . . + X,,Y.,
and where a, ,S, and Xi are defined as in theorem 8.1.
The term a, in theorem 8.3 will be referred to as the pseudo u index.
To illustrate, the numerical example in equation (8.11) can be used
to calculate the pseudo Gini coefficient:
(8.13a) u,, = 1(0.2) + 2(0.4) + 3(0.1) + 4(0.3) = 2.5;
(8.13b) Gy = (2/4) (2.5) - 5/4 = 0.
THE PSEUDO GINI COEFFICIENT 335
Figure 8.2. The Pseudo Lorenz Curve
y DI
(Y4 0.3
P s e u d | UsB = 0.4
Pseudo Lorenz curve 0 0)
0 0 ~~~~~Y2 0.4
oLorenz curve)
____________ . = 0.2
0 1/4 2/4 3/4 4/ E
Source: Constructed by the authors.
The pseudo Gini coefficient, as defined, is an abstract, geometrical
concept which will be applied in subsequent chapters.
When an income distribution pattern [Y = (Y1, Y2, ..., )
is not necessarily monotonically arranged, there can be a permuta-
tion [(i1, i2, . . . , in)] of the n integers such that:
(8.14a) y* = (Yj,, Yi2, .. . ,Yi)
satisfies:
(8.14b) Yi, > yi2 > ... >Yf
In words, Y* is a rearrangement of Y into a monotonically non-
decreasing order. For example:
Y* = (0.1, 0.2, 0.3, 0.4)
836 BASIC CONCEPTS
in the numerical example of equation (8.2b) is a rearrangement of:
Y = (0.2, 0.4, 0.1, 0.3)
in equation (8.11).
The difference between the Gini coefficient of Y [G( Y*)] and the
pseudo Gini coefficient [GJ can be defined as a Gini error [E]:
(8.15) E = G(Y*) - 2, Ž 0,
which always is nonnegative. From the numerical examples in equa-
tions (8.2b) and (8.11) it can be seen that:
(8.16) E = G(Y*)- = 0.25 - 0 = 0.25 > 0.
[see equations (8.6b) and (8.13b)]
Equation (8.16) shows that the Gini coefficient is at least as large
as the pseudo Gini coefficient. The Gini error [E] will later be
proved to be nonnegative.
A geometric interpretation of the Gini error is evident from:
(8.17) E (1 - 2B) - (1 - 2B) by equations (8.3) and (8.12)
2(B - B).
Thus the area between the pseudo Lorenz curve and the Lorenz
curve is equal to one-half the value of the Gini error (see figure 8.2).
In that figure the area corresponding to B - B is shaded. In figure
8.3 a pseudo Lorenz curve [A"B"C"D"] is shown for y = (0.4, 0.3,
0.2, 0.1) which is in a reverse monotonic order, that is, a mono-
tonically nonincreasing order. This curve is now rotationally sym-
metrical with the Lorenz curve ABCD from figure 8.1 with respect
to the 45-degree line OD". Thus the shaded area in figure 8.3 is:
B - B = 2A = 2(1/2 - B),
where A is the area between the Lorenz curve and the line OD", and
the Gini error becomes:
(8.18a) E = 2(B - B) = 2(1 - 2B) = 2G(Y*)
by equation (8.3),
which implies that:
(8.18b) G(Y) = -G(Y*) by equation (8.16).
THE PSEUDO GINI COEFFICIENT 387
Figure 8.3. The Pseudo Lorenz Curve for an Inverse Wage Pattern
g ~~~~~~~~~~~~~~~Dt
Pseudo Lorenz curve
for inverse wage pattern
0 1/4 2/ 4 3/ 4 4/4 E
Source: CSonstructed by the authors.
For later reference, this equation can be summarized as:
THXEOREM 8.4. For a monotonically nonincreasing pattern of income
distribution:
0(Y) =
that is, the pseuzdo Gini coeffi:cunt is the negative of the Gini coefficient.
CHAPTER 9
Testing Hypotheses
CERTAIN QUALITY CHARACTERISTICS, denoted by C, can be intui-
tively identified as relevant to the analysis of causes of income
inequality:
(9.1) c = (cl < C2 < ... <
ordinally ranked values
of a quality characteristic
affecting G J
For example, C can represent the sex characteristic and have values
of cl for female and c2 for male; it can represent the education char-
acteristic and have values of cl for low education, c2 for medium
education, and c3 for high education; or it can represent the age
characteristic and have values of ci, where i is the age of the head
of household or income earner. Whenever C is given, the presumption
-that is, the hypothesis-is that its values will affect the levels of
family income. In such a situation the minimum information to be
postulated is that the values [ci] are ordinally ranked attributes
that contribute to the earning power of families. For the ranking in
equation (9.1), cl is assumed to make the least contribution to the
level of family income; cm the greatest contribution. If C is educa-
tion, the values of the education characteristic are assumed to
contribute to higher income levels in an ascending order:
(9.2) cl < c2 < C3.
E low 1< [medium] < high 1
education J - [education -L [education]
Assume that such a quality characteristic as education is given
38
TESTING HYPOTHESES 339
Table 9.1. Numerical Example of Income Fractions, Income Ranks,
and Education Ranks for Five Families
Family Family Family Family Family
Variable 1 2 5 4 5
Income fraction, y, = 0.05 y2 = 0.10 YS = 0.15 y4 = 0.30 y5 = 0.40
Income rank x, =1 X,=2 x, = 3 X4 = 4 4 x = 5
Education rank r, = 5 r2 = 4 r3 = 1 r4 = 2 r6 = 3
Value of education
characteristich CB = H C3 = H cl =L cl = L C2 = M
Source: Constructed by the authors.
a. These values are from the numerical example in equation (8.6a) in chapter
eight.
b. In accord with expression (9.2), cl and L stand for low education, c2 and
M for medium education, and Cs and H for high education.
and that every family receives a value [ci] for that characteristic
[C]. The n families can then be ranked with respect to C (table
9.1). In this table the first family receives the lowest income rank
because it is the poorest; curiously it also receives the highest educa-
tion rank because its income earner has the most education.
When the number of families [n] is large and the number of char-
acteristic values [m] is small, the n families are classified in m
education groups. Families belonging to the same group-that is,
families with tied rank-are arbitrarily assigned a numerical ranking.
In the numerical example, the first two families received the two
highest education ranks: family one's education rank [r,] is 5;
family two's [r2] is 4. The alternative way of assigning ranks to
these two families is: r, = 4; r2 = 5. In general the following per-
mutations of the first n integers can stand for the characteristic
ranking of the n families:
(9.3) r = (ri, r2, . . . ,
and it can be hypothesized that a higher characteristic rank should
lead to a higher income rankl:
HYPOTHESIS 9.1. The relation ri > rj implies that yi > yj or Xi > Xi.
1. Graham Pyatt of the World Bank has presented an ingenious interpreta-
tion of the Gini coefficient as the expected value of a game and demonstrated
the usefulness of that interpretation to socioeconomic problems relevant to
340 TESTING HYPOTHESES
If the characteristic is education, the hypothesis is that higher
education should lead to higher income. Because the first two fami-
lies in table 9.1 are the most educated, and yet the poorest, they
clearly violate this hypothesis. The purpose of this chapter is to
investigate how a hypothesis, such as hypothesis 9.1, can be sys-
tematically tested.
Testing Hypotheses by Supporting
and Contradicting Gaps
Postulate the income fractions [y3, income ranks [Xi], and
characteristic ranks [ri] as follows:
(9.4a) y = (YI, Y2, e , Y.), where y, < y2 < ... < yf/ and
[income fractions] EYi = 1;
(9.4b) X = (Xi, X2, . .. , X.) = (1, 2, .. n)
[income ranks]
(9.4c) r = (ri, r2, . .. , rn), which is a permutation of (1, 2, . . ., n).
[characteristic ranks]
Notice that the pattern of income fractions [y] is arranged in a
monotonically nondecreasing order in accord with the conditions of
expression (8.1e). Consequently the pattern of income ranks [X] is
just the natural order of the first n integers. The pattern of charac-
teristic ranks [r] is a permutation of the first n integers, such that
ri > rj implies that the ith family should have a higher income
than the jth family by null hypothesis 9.1.
When y is given as in equation (9.4a), the nonnegative income
gaps [yi - yj] between all pairs of families can be defined as in
equation (8.8). When Xi and ri are given in addition, these income
income inequality, such as discrimination and migration. The approach adopted
in this chapter is tantamount to an alternative interpretation of the decomposi-
tion of Gini coefficients in relation to testing a null hypothesis about the role of
quality characteristics in the analysis of income distribution equality. This ap-
proach will be adhered to throughout this chapter. Graham Pyatt, "On the
Interpretation and Disaggregation of Gini Coefficients," Economic Journal, vol.
86 (June 1976), pp. 243-55.
TESTING HYPOTHESES BY SUPPORTING AND CONTRADICTING GAPS 341
gaps can be classified into two types: a type that supports the hy-
pothesis; a type that contradicts it. In the numerical example of
table 9.1, the income gap between family one and family three
clearly contradicts the hypothesis. On the other hand, the income
gap between family four and family five clearly supports the hy-
pothesis. Use that numerical example to see how the two types of
gap can be systematically identified, and construct the following
matrix from the characteristic ranks in equation (9.4c):
(9.5) r1 r2 rs r4 r5
ri 0 r2-r1 r3-ri r4-rl r5-r1
r2 0 r3-r2 r4-r2 rT-r2
r3 0 r4-r3 r6-r3 =
r4 0 r- r4
r5 0
0 -1 -4 -8 -2
0 -3 -2 -1
0 1 2.
0 1
0-
An element of this matrix indicates the difference, or gap, between
the characteristic ranks of a pair of families. Because the income
fractions [yi] are monotonically ranked in accord with equation
(9.4b), a negative entry in this matrix indicates that the hypothesis
is contradicted; a positive entry, that it is supported. In the right-
hand matrix, all negative entries are in italics. They indicate all
pairs of families which contradict the hypothesis. [In the matrix of
equation (8.8) the corresponding family pairs are also in italics.]
The other entries indicate the supporting gaps.
Let S+ denote the sum of all supporting gaps and S- the sum of
all contradicting gaps. Formally the definitions of S+ and S- thus
842 TESTING HYPOTHESES
are:
(9.6a) S, = S+ + S-, where
(9.6b) S- = E (yi - yi) Ž 0 for i > j and ri < r,, and
[contradicting gaps]
(9.6c) S+ = E (y -y,) > 0 for i > j and ri > r,.
[supporting gaps]
Equation (9.6a) shows that S&, which is defined in equation (8.9a)
as the sum of all fractional gaps, is partitioned into two nonnegative
components, S+ and S-. Figures from the numerical example of
table 9.1 give:
(9.7a) S, = 1.3 + 0.5 = 1.8, where
(9.7b) S- = 0.05 + 0.10 + 0.25 + 0.35 + 0.05
+ 0.20 + 0.30 = 1.3 and
(9.7c) S+ = 0.15 + 0.25 + 0.10 = 0.5.
In the example, S- is larger than S+, a relation which indeed sub-
jects to doubt the hypothesis that education contributes to income-
earning.
Gini Decomposition for Hypothesis Testing
Theorem 8.2 showed the Gini coefficient to be the average frac-
tional gap [Sd/n]. This definition, or interpretation, is quite inde-
pendent of any quality characteristic [C], as postulated in equation
(9.1). When a quality characteristic [C] and a corresponding char-
acteristic rank [r] are given, the result in equation (9.6) immedi-
ately shows that the Gini coefficient can be decomposed into an
average supporting gap [s+] and an average contradicting gap [s-]:
(9.8a) G, = s+ + s- by equation (9.6) and theorem 8.2, where
(9.8b) s+ = S+/n > 0 and
[average supporting gap]
(9.8c) s- = S-/n > 0.
[average contradicting gap]
NET SUPPORTING GAP 343
The values in equation (9.7) give:
(9.9a) G, = S,/n = 0.36 = s+ + s- = 0.10 + 0.26 = 0.36, where
(9.9b) s+ = S+/n = 0.5/5 = 0.10 and
[average supporting gap]
(9.9c) s- = S-/n = 1.3/5 = 0.26.
[average contradicting gap]
G, can now be interpreted as the "total variation" of yi. Before a
characteristic is introduced, all variations [y. - yj] are unexplained.
After such a characteristic as education or age is introduced, a part
of the variation, corresponding to s+, can be explained by that
characteristic; the other part, corresponding to s-, cannot be ex-
plained by that characteristic. In fact, s- reduces the explanatory
power of s+.
Net Supporting Gap
For testing the hypothesis, it is natural to find out the compara-
tive magnitudes of s+ and s-. If s+ is much larger than s-that is,
if the average supporting gap overwhelms the average contradicting
gap-we would tend to accept such a null hypothesis as 9.1. Thus
it is natural to define a net supporting gap as:
(9.10) N = + -s-,
[net supporting gap]
and to accept the null hypothesis when N is positive, reject it when
N is negative, or regard it as irrelevant when N is close to zero.
The purpose of this section is to show that N is precisely the pseudo
Gini coefficient defined in theorem 8.3 of chapter eight. Recall that a
pseudo Gini coefficient [G( Y)] can be defined for any pattern of
income [Y = (Y1, Y2, ..., Y.)] which is not necessarily mono-
tonically ranked.
When y, X, and r of equation (9.4) are given, the following
weighted ranks can be defined:
(9.lla) u, = ly, + 2y2 + ... + ny.;
[weighted income rank]
844 TESTING HYPOTHESES
(9.llb) u,, = rly1 + r2y2 + ... + rnyn.
[weighted characteristic rank]
Respectively applying theorems 8.1 and 8.3 gives:
(9.12a) Gy = (2/n)u.1 - (n + 1)/n and
[Gini coefficient]
(9.12b) 0, = (2/n)i - (n - 1)/n.
[pseudo Gini coefficient]
To illustrate with figures from the numerical example:
(9.13a) u,, = 1(0.05) + 2(0.10) + 3(0.15)
+ 4(0.30) + 5(0.40) = 3.9;
(9.13b) Q, = 5(0.05) + 4(0.10) + 1(0.15)
+ 2(0.30) + 3(0.40) = 2.6
= 1(0.15) + 2(0.30) + 3(0.40)
+ 4(0.10) + 5(0.05) = 2.6.
Hence:
(9.14a) G. = (2/5) (3.9) - 6/5 = 0.36;
(9.14b) G. = (2/5) (2.6) - 6/5 = -0.16.
Notice that the italicized expression in equation (9.13b) is merely
a rearrangement of the terms of i4-the weighted characteristic
rank of equation (9.llb)-into an ordering by the characteristic
rank. Now the income fractions (yi) are not monotonically arranged.
Thus O;, in equations (9.12b) and (9.14b) indeed is the pseudo Gini
coefficient as defined in theorem 8.3 of chapter eight.
By comparing equation (9.13) with equation (9.7b) it can be
seen that the contradicting gap [S- = 1.3] is the difference between
the weighted income rank [u, = 3.9] and the weighted charac-
teristic rank [4 = 2.6]. This relation may be stated as:
LEMMA 9.1. S_ = U, - UY.
Proof: S- = E (yi - yi) for i > j and ri < r1
= dly- + d2Y2 + . . . + d( y.
= ( Ul - V1 ) YI + ( U2 - V2) Y2 + ...+ ( U. - Vn.) Yn.
NET SUPPORTING GAP 845
It can be seen that the coefficient di of yi is the difference between
ui and vi, where ui is the number of families with an income rank
lower than the ith family and a characteristic rank higher than the
ith family, and where vi is the number of families with an income
rank higher than the ith family and a characteristic rank lower
than the ith family. It is obvious that:
ri = Xi + Vi -Ui,
for in order to compute the characteristic rank [ri] of the ith family
from its income rank [Xi], ui must be subtracted from Xi and v1
must be added to Xi. Thus:
di= -ui = i- ri.
Hence:
SL=(Xi - ri)y, + (;X2 -r2)Y2 + ...+ (X. - r.)y.
= UV - U,,.
This completes the proof.
Lemma 9.1 will now be used to prove the following theorem,
which states that the net supporting gap [N = s+- s-] defined in
equation (9.10) is precisely the pseudo Gini coefficient.
THEOREM 9.1. 0G = S+ - S .
Proof: s- = S,,/n by equation (9.8c)
= l/n[u, - i,,] by lemma 9.1
[((2/n)u, - (n + 1 )/n) - ((2/n)iz. - (n + 1 )/n) ]/2
(G., - G,)/2 by equation (9.12)
(s+ + s - -G,)/2 by equation (9.8a);
s+ + s --G = 2s-.
Thus:
G, = s+ - -.
This completes the proof.
Theorem 9.1 states that the pseudo Gini coefficient is the differ-
ence between the average supporting gap and the average con-
tradicting gap and thus is the net supporting gap. The hypothesis
.346 TESTING HYPOTHESES
is supported when G, is positive-that is, when the supporting gaps
[S+] overwhelm the contradicting gaps [S-]. Similarly the hy-
pothesis is rejected when G0 is negative.
In summary:
(9.15a) GQ = s+ + s-;
(9.15b) Gz, = s+-s-;
(9.15c) G,, = Q + 2s-, or E = G,-G =2s- >O.
Thus the Gini coefficient [G,] is the sum of the average supporting
and contradicting gaps; the pseudo Gini coefficient [G] is their
difference. In addition, the difference between G, and G,, is 2s-,
which always is nonnegative. This proves that the Gini error [E]
is nonnegative, as was stated in equation (8.16).
Graphic Summary of the Gini
and Pseudo Gini Coefficients
It has been shown that the Gini coefficient and the pseudo Gini
coefficient can be defined when the income fractions [y], income
ranks [X], and characteristic ranks [r] of equation (9.4) are given.
The relation between G, and G0, is graphically summarized in this
section.
Let s+ be measured on the horizontal axis in figure 9.1 and s- on
the vertical axis. Because the value of G, lies between zero and one,
all possible combinations of the coordinates (s+, s-) can be repre-
sented by points in the equilateral triangle OAB (OA = OB = 1).
The parallel and negatively sloped 45-degree lines represent iso Gini
coefficient contour lines. Thus all points on the line FF", for exam-
ple, have a Gini coefficient equal to OF. The line AB represents
perfect inequality-that is, G, = 1.
Also in figure 9.1 the 45-degree line OR3 divides the triangle OAB
into two regions: r+ lies below OR3; r- lies above OR3. A point such
as P in the region r+ indicates that the average supporting gap [s+]
overwhelms the average contradicting gap [s-] and hence that
empirical evidence supports a hypothesis such as 9.1. A point such
as Q on or near OR3 indicates that empirical evidence does not sup-
port the hypothesis. A point such as T in the region r- indicates
that empirical evidence contradicts the hypothesis.
The straight lines parallel to OR3 are the equal pseudo Gini con-
tour lines. On the line FF", the value of the pseudo Gini is OF. The
GRAPHIC SUMMARY OF THE GINI AND PSEUDO GINI COEFFICIENTS 347
Figure 9.1. Iso Gini Coefficient Contour Lines
(OA = OB 1)
R6
B
s- 8 Rs~~~~~~~R
Xs+t'~~~~~~~~F
O F' A
Source: Constructed by the authors.
pseudo Gini coefficient is positive in r+ and negative in r?. Further-
more it can be seen that:
(9.16) -1 < (, < 1.
A higher positive value of CT, is represented by a contour line closer
to point A; a higher negative value, by a contour line closer to
point B. A positive value of G, close to 1 would therefore indicate
that the hypothesis is strongly supported; a negative value close to
-1, that the hypothesis is strongly contradicted.
Two extreme cases are to be mentioned:
(9.17a) ri = Xi, which implies that s- = 0 and G, = (;u = s+;
(9.17b) ri = n - (i + 1), which implies that s+ = 0 and
G, = -G, = sr.
348 TESTING HYPOTHESES
The economic interpretation of equation (9.17a) is that the correla-
tion between the income rank [xi] and characteristic rank [ri] is
perfect and positive. In this case the contradicting gap vanishes
and the Gini coefficient equals the pseudo Gini coefficient [see
equations (9.11) and (9.17)]. Points on the horizontal axis OA in
figure 9.1 represent this special case. The economic interpretation
of equation (9.17b) is that the correlation between the income
rank [Ex] and characteristic rank [ri] is perfect and negative. The
supporting gap vanishes, and the pseudo Gini coefficient equals
the negative value of the Gini coefficient. Points on the vertical axis
OB represent this special case (see theorem 8.4).
Correlation Characteristics
Now express the pseudo Gini coefficient as a fraction of the Gini
coefficient:
(9.18a) R = GJGa = + + by equation (9.15);
s+ + s- 1 + s-/s+
In economic terms R is the net supporting gap expressed as a frac-
tion of the "total gap"-that is, as a fraction of the sum of the aver-
age supporting and contradicting gaps. To arrive at another inter-
pretation of R, the ordinary correlation coefficient r(x,y) between
two vectors, x and y, is introduced to define:
(9.19a) r(y,X) = cov(y,X)/o-,or for y = (YI, Y2, . , yn) and
X= (1,2, ...n);
(9.19b) r(y,r) = cov(y,r)/ loa,, for r = (r1, r2, . . . ),
(9.19c) Ur = ax-
Therefore r(y,X) is the ordinary correlation coefficient between the
family income fractions and the income rank [X]; r(y,r) is the
ordinary correlation coefficient between those fractions and the
characteristic rank [r]. Notice that equation (9.19c) is valid be-
cause both terms represent the standard deviation of the first n
integers. In equations (9.19a) and (9.19b) the notation cov(x,y)
CORRELATION CHARACTERISTICS 349
stands for the covariance between x and y. This leads to the follow-
ing theorem:
THEOREM 9.2. R = r(y,r)/r(y,X).
Proof: We know that:
1= /n by equation (8.1d);
r= = (1 + 2 + ... + n)/n = n(n + 1)/2n = (n + 1)/2;
cov(y,r) = E (yi - y) (ri - f) = E yiri -nf
= u- nyr by equation (9.llb)
- n(n + 1)/2n
= - (n + 1) /2 = (n/2) [(2/n)t - (n + 1) /n]
= (n/2) G, by equation (9.12b).
Similarly:
cov(y,X) = (n/2)G5.
Thus:
r(y,r)/r(y,X) = , (n/2)G/aoo]/[(n/2)G)/ow)j by equation (9.19)
= R by equation (9.18).
This completes the proof.
Therefore R can also be considered as a ratio of two ordinary
correlation coefficients-that is, r(y,r) expressed as a fraction of
r(y,X).2 From equation (9.18b) it can be seen that the value of R is
completely determined by the ratio of s- to s+. In figure 9.1 the
radial lines OR1, OR2, ... , OR6 then represent iso R contour lines.
In the region r+, R is positive, and a radial line such as OR1 takes
on a value close to 1. In the region r-, R is negative and a radial
line such as OR6 takes on a value close to -1.
It directly follows from expression (9.16) and equation (9.18)
2. There thus are two alternative interpretations of R as defined in equation
(9.18) and theorem (9.2). Pyatt first suggested the second interpretation in a
private discussion with the authors.
350 TESTING HYPOTHESES
that R lies between 1 and -1. Two types of case-a positive R
and a negative R-can be identified:
(9.20a) -l 0 if and only if 0 < G,, or s+ > s-;
[positive R]
(9.20c) R < 0 if and only if G0 < 0 or s+ < gs.
[negative R]
In words, R is positive if and only if the pseudo Gini coefficient is
positive. When R is positive, the average supporting gap [s+] over-
whelms the average contradicting gap [s-]. The ratio of G, to G,,
is R. Their sum is:
(9.21a) G,, + G , = G(1 + R) = 2s+ > 0,
and their difference is:
(9.21b) G,- = G,(1 - R) = 2s- > 0.
Thus their sum is twice the average supporting gap, or 2s+; their
difference is twice the average contradicting gap, or 2s-. Both are
nonnegative numbers.
So far certain basic ideas have been developed for testing hy-
potheses when the pattern of income of n families is associated with
one ordinal characteristic [C]. This method can be applied to other
related empirical problems of hypothesis testing. But our purpose
is to apply these ideas to the derivation of the various decomposi-
tion formulas used in the earlier chapters of this volume.
CHAPTER 10
The General and Special Models
of Additive Factor Components
As NOTED EARLIER, a situation is frequently encountered in which
family income is the sum of several types of income. Consider the
example used in chapter three with five families and three income
components (table 10.1). In this example the factor income com-
ponents correspond to components of the functional distribution
of income. In another example family income may come from such
sources as industry and agriculture. In short, a components prob-
lem is formed once there is a classification of the sources of income.
Generally, when there are n families and p income components, the
components problem is summarized by:
(10.la) Yi = W + W2 ... + W?; (i = 1, 2, ... ,n)
(l0.lb) Si = Wi + W + ... + W'; (i = 1, 2, .. ,p)
(10.lc) s, = Sl + S2 + + Sp;
(l0.ld) fi= Si/SY;
(10.le) 1 = 01 + (2 + + (P;
(lO.1f) yl < Y2 < ... < Yn-
In equation (10.la) the total income [Yi] of the ith family has p
components. In equation (lO.ld) the values of 4i (i = 1, 2, ... , p)
form a system of weights and correspond to the fraction of the ith
type of income received by all families. It will be assumed that
total family income [Yi] is arranged in a monotonically nonde-
creasing order as in equation (10.lf).
S31
S52 MODELS OF ADDITIVE FACTOR COMPONENTS
Table 10.1. Numerical Example of the Problem
of Additive Factor Components
Family Family Family Family Family
Item 1 2 5 4 5 Total
Wage income 3 1 17 15 9 45
Wage income rank 2 1 5 4 3 -
Property income 0 0 2 8 25 35
Property income
rank 1 2 3 4 5 -
Transfer income 8 12 0 0 0 20
Transfer income
rank 4 5 3 2 1 -
Total income 11 13 19 23 34 100
Total income rank 1 2 3 4 5 -
- Not applicable.
Source: Constructed by the authors.
The components problem can be restated in vector notation:
(10.2a) Y = W + WI2 + ... + WP, where
(10.2b) Y = (Y1, Y2, ... , Y,n) and
[pattern of total income]
(10.2c) Wi = (I W2, . . ., Wi). (i = 1, 2,..., p)
[pattern of the ith factor component]
Denote the Gini coefficient of Y by G(Y) or G,, and the Gini coeffi-
cient of Wi by G(Wi) or Gi. The basic purpose of the approach
using factor income components is to investigate the relations
between the total Gini [Gb] and the factor Ginis [G,].
Decomposition of G, into Pseudo Factor Ginis
When the total income pattern [Y] is monotonically arranged, a
particular factor component [W'] may not be monotonically ar-
ranged (see table 10.1). Thus, to see how the earlier analysis can
DECOMPOSITION OF G,, INTO PSEUDO FACTOR GINIS 35S
contribute to the understanding of the factor components problem,
it is natural to define for each factor component a pseudo factor
Gini [Os] in which the exogenously postulated characteristic [C]
is the total income rank [Xl:
(10.3a) G. = (2/n)ift - (n + 1) /n by theorem 8.3, where
(10.3b) ii = Xw + X2wu + . .. .+ Xnw, where (i = 1, 2, .. ., n)
(10.3c) Xi = i,
(10.3d) w, = WJ/Si, and
(10.3e) w' + w2 + ...+ wn 1
From the discussion in chapter nine and from theorem 9.1 in particu-
lar, it can be seen that the pseudo factor Gini [GE is the net support-
ing gap [N] when the total income rank Di] is used as a quality
characteristic to explain the variation of a factor income component.
This definition of the pseudo factor Gini leads to:
THEOREM 10.1. The Gini coefficient is the weighted average of the
pseudo factor Ginis, that is:
Gyu = OIGI + 02G2 + ...+ OpGr,
where the distributive shares Eri] defined in equation (10.1d) are the
weights.
Proof: By theorem 8.1 (c) the u index of Y is:
U= XIYI + X2Y2 + ... + X.Yn
X r01(W'/S') + 0,(W,/S2) + ... + 0r(Wl'/Sr)]
+ X2[Al(W2/S') + +2(W22/S2) + * * * + kr(WF2P/S)]
+ . .. ± X,n[i(Wn/S1) ± ck2(W2/S2) + ... + 0r(Wp/St)]
[1EX1(W1/S') + X2(W2/sl) + e ± e X(W'/S')]
+ 2E2[X1(W'/S2) + X2(W2/S2) + ... + Xn(Wn/S2)]
+ ... ±+ kE[Mi(Wfp/SP) + X2(W2/SP) + * * * + Xn(Wp/Sv) ]
= Ouil + 02u2 + ... + opfp,u by equation (1O.lb),
where ai is the pseudo u index of the ith factor component [Wi].
354 MODELS OF ADDITIVE FACTOR COMPONENTS
Table 10.2. Gini Decomposition by Pseudo Factor Ginis, 1964-72
Model and variable Notation 1964 1966 1968
All households
Total Gini G, 0.321 0.323 0.326
Pseudo wage Gini Gw 0.237 0.270 0.293
Pseudo property Gini 0.449 0.410 0.459
Pseudo agricultural Gini Ga 0.354 0.341 0.178
Pseudo miscellaneous Gini Gm 0.256 0.302 0.363
Wage share 0.432 0.476 0.507
Property share 0.240 0.256 0.278
Agricultural share q. 0.275 0.212 0.152
Miscellaneous share 'km 0.052 0.057 0.063
Wage correlation R. = GU,/GW 1.000 1.000 1.000
Property correlation R,, = GT/GT 1.000 1.000 0.997
Agricultural correlation R. = Ga/Ga 0.999 1.000 0.979
Urban households
Total Gini G, 0.329 0.324 0.330
Pseudo wage Gini n.a. 0.280 0.273
Pseudo property Gini n.a. 0.419 0.425
Pseudo agricultural Gini Ga n.a. 0.256 0.311
Pseudo miscellaneous Gini Gm n.a. 0.273 0.337
Wage share 0.573 0.593 0.567
Property share 0.323 0.322 0.337
Agricultural share a 0.037 0.022 0.029
Miscellaneous share 'km n.a. 0.064 0.067
Wage correlation Rw = Gw/Gw n.a. 1.000 1.000
Property correlation R, = GW/G, n.a. 1.000 1.000
Agricultural correlation Ra = Ga/Ga n.a. 0.959 0.990
Rural households
Total Gini G, 0.308 0.320 0.284
Pseudo wage Gini n.a. 0.187 0.187
Pseudo property Gini GT n.a. 0.332 0.278
Pseudo agricultural Gini Ga n.a. 0.353 0.337
Pseudo miscellaneous Gini Gm n.a. 0.410 0.365
DECOMPOSITION OF G, INTO PSEUDO FACTOR GINIS 355
1970 1971 1972 Notation Mlodel and variable
All households
0.293 0.295 0.290 Total Gini
0.278 0.273 0.260 Pseudo wage Gini
0.428 0.427 0.424 G1r Pseudo property Gini
0.060 0.107 0.106 Oa Pseudo agricultural Gini
0.354 0.301 0.324 G, Pseudo miscellaneous Gini
0.507 0.545 0.590 Wage share
0.256 0.242 0.258 Property share
0.131 0.102 0.103 e, Agricultural share
0.068 0.060 0.050 'kin Miscellaneous share
1.000 1.000 1.000 R. = Gw/Gw Wage correlation
1.000 1.000 1.000 R,. = GO,/G,. Property correlation
0.910 0.961 0.958 R. = G,/Ga Agricultural correlation
Urban households
0.279 0.279 0.281 Gv Total Gini
0.233 0.240 0.235 Gw Pseudo wage Gini
0.369 0.399 0.387 Gr Pseudo property Gini
0.154 0.247 0.168 Ga Pseudo agricultural Gini
0.329 0.271 0.280 Gm Pseudo miscellaneous Gini
0.602 0.650 0.634 Wage share
0.302 0.268 0.298 Property share
0.029 0.026 0.024 Xv. Agricultural share
0.073 0.058 0.047 'm Miscellaneous share
1.000 1.000 1.000 Rv = GI/Gw Wage correlation
1.000 1.000 1.000 R, = G,/G, Property correlation
0.885 0.906 0.879 R. = Ga/Ga Agricultural correlation
Rural households
0.277 0.291 0.284 Ga, Total Gini
0.204 0.220 0.238 Gw Pseudo wage Gini
0.359 0.337 0.348 G,, Pseudo property Gini
0.314 0.318 0.298 Ga Pseudo agricultural Gini
0.282 0.396 0.434 G, Pseudo miscellaneous GiDi
(Table continues on the following pages)
356 MODELS OF ADDITIVE FACTOR COMPONENTS
Table 10.2 (Continued)
Model and variable Notation 1964 1966 1968
Wage share 0. 0.213 0.202 0.323
Property share ,,. 0.112 0.100 0.099
Agricultural share X 0.647 0.660 0.526
Miscellaneous share Om n.a. 0.039 0.052
Wage correlation R., = G/G,,, n.a. 0.968 0.995
Property correlation R,, = G,./G, n.a. 0.994 1.000
Agricultural correlation R. = Ga/Ga n.a. 1.000 1.000
n.a. Not available.
Note: Compare this table with table 3.2 in chapter three.
Sources: Calculated from DGBAs, Report on the Survey of Family Income and
Expenditure, 1964, 1966, 1968, 1970, 1971, and 1972.
Thus the Gini coefficient of total income [Y] by theorem 8.1 is:
GD = (2/n) uy - (n + 1) /n
= (2/n)E[1fl + 'k2U2 + .. . + pp] -(n + 1)/n
= 01E(2/n)fzi - (n + 1)/n] + 02[(2/n)fi2 - (n + 1)/n]
* ... ± + [(2/n) p - (n + 1)/n] + 4l (n + 1)/n
* 02(n + 1)/n + .. . + op(n + l)/n - (n + 1)/n
= 4P1G1 + 2k2G2 + . . . + ArGr by equations (10.3a) and (10.le).
This completes the proof.
In the model of additive factor components, there is a natural
interpretation of the pseudo Gini coefficient [Gi] as the concentra-
tion ratio, which measures the extent to which the ith factor compo-
nent is concentrated among wealthy families. Despite the attractive-
ness of its economic interpretation and the exactness of its decom-
position, the pseudo Gini coefficient has not been used much in the
empirical work of this volume. The reasons are these. The pseudo
Gini coefficient [G] not only differs from Gi, but is in fact a more
complicated concept. Although the factor Gini coefficient [GJ]
measures the degree of inequality of a factor component by itself,
the pseudo Gini coefficient is definable only in terms of the related-
ness of the pattern of factor income, given by (WI, W,;, .. , '),
EXACT DECOMPOSITION OF G, INTO FACTOR GINIS 357
1970 1971 1972 Notation Model and variable
0.360 0.357 0.423 c. Wage share
0.103 0.122 0.107 (Al Property share
0.487 0.452 0.423 dtJ. Agricultural share
0.050 0.068 0.047 O. Miscellaneous share
0.997 0.998 1.000 R. = 0G, Wage correlation
0.995 1.000 1.000 R,, = G,/GI Property correlation
1.000 1.000 1.000 R. = Ga/Ga Agricultural correlation
to the pattern of total family income, given by (Y1, Y2, ..., Y).
Thus, from the substantive economic point of view, the socioeco-
nomic forces determining Gi are very different from those deter-
mining Gj.
The decomposition equation in theorem 10.1 can nevertheless be
applied in empirical work. Using the same set of data as in table
3.2 of chapter three, the empirical decomposition of the Gini coeffi-
cient of total family income [G,] into the pseudo Gini coefficients
of wage income [GE,J property income [GE], and agricultural in-
come [Ga] is shown in table 10.2. The decomposition of the Gini
coefficient is exact for all three models: all households, urban house-
holds, and rural households.
Exact Decomposition of Gv into Factor Ginis
For each factor component [Wi] a factor Gini [Gj] and a pseudo
factor Gini [GD] can be computed. The correlation characteristic
of the ith factor can then be calculated:
(10.4) Ri = GilGi. (i = 1, 2, ... , p)
[factor correlation characteristics]
Theorem 10.1 immediately leads to:
(10.5) G, = 0uRiGi + 02R2G2 + ... + 4,REG,.
Equation (10.5) will be referred to as the exact Gini decomposition
3S8 MODELS OF ADDITIVE FACTOR COMPONENTS
Table 10.3. Numerical Example of Exact Decomposition
of G, into Factor Ginis
Wage Property Transfer Totao
Variable Notation income income income income
Factor share Oi 0.4500 0.3500 0.2000 1.0000
Factor Gini G. 0.3912 0.6628 0.6400 -
Weighted factor Gini 4,A 0.1760 0.2320 0.1280 -
Total Gini G2 - - - 0.5360
Pseudo factor Gini Gi 0.2308 0.6628 -0.5600 -
Weighted pseudo factor
Gini *.GA 0.1039 0.2320 -0.1120 -
Total Gini G" - - - 0.2239
Average contradicting
gap6 s, 0.0802 0.0000 0.6000 -
Average supporting
gapb s+ 0.3110 0.6628 -0.0004 -
Factor correlation
characteristico Ri 0.5900 1.0000 -0.8750 -
Gini error E - - - 0.3121
Gini decomposition 4.R.Gi; G, 0.1039 0.2320 -0.1120 0.2239
- Not applicable.
Source: Constructed by the authors.
a. s, = (Gi - G) /2.
b. sak = (Gi + G,)/2.
c. Ri = Gi/lG.
formula. It shows that three types of factors affect G,,. If an income
component is positively correlated with total family income
(Re > 0), then this component contributes heavily to total income
inequality when the factor income is unequally distributed (indi-
cated by a large Gj) and when the share of this factor is large (indi-
cated by a large Xi). Conversely, when an income component is
negatively correlated with total family income (Ri < 0), a large
Gi and a large oi indicate that the component contributes to total
income equality.
Table 10.3 uses figures from table 10.1 to give the values for the
factor shares [oi], the pseudo factor Ginis [GJ], the factor Gini
COMPUTATION PROCEDURE FOR EXACT DECOMPOSITION 359
coefficients [Gij, the factor correlation characteristics [Ri], and the
Gini coefficient of total income [Gj]. Table 10.3 also indicates the
decomposition of G, into pseudo factor Ginis according to theorem
10.1 and the decomposition of G, according to equation (10.5).
Notice for transfer income that Ri and Gi are negative. Hence a
large share of transfer income [0i] and a more unequal distribution
of transfer income [Gi] contribute to total income equality.
Computation Procedure for Exact Decomposition
The following values can be computed for an exact decomposi-
tion according to equation (10.5):
(10.6a) Gu = (2/n)u - (n + 1)/n,
[total income Gini]
(10.6b) Gi = (2/n)ui - (n + 1)/n, and (i = 1, 2, ... , p)
[factor Gini]
(10.6c) Gi = (2/n)ui - (n + 1)/n, where (i = 1, 2, ... , p)
[pseudo factor Gini]
(10.6d) u, = l(yi) + 2(Y2) + ... n f(yn) for
Yl < Y2 < ... < Yn,
(10.6e) ui = 1(wj') + 2(w,2) + ... + n(w,') for
wji < wji, < ... < w;, and
(10.6f) Fti = l(wu) + 2(w') + ... + n(w'), where
(10.6g) (w,, w', ... , w') = (Ws/Si, W /SS, ... I, W /Si).
(i = 1, 2, .. p)
Notice when the original data are given as in equation (10.1) or
(10.2) that a factor component [Wi] may not be monotonically
arranged. For the computation of ui and Gi, the elements in (wi,
W2 ... I, w') defined in equation (10.6g), which are not necessarily
in a monotonic order, must be rearranged into nondecreasing order.
That rearrangement is shown in equation (10.6f) by the permuta-
360 MODELS OF ADDITIVE FACTOR COMPONENTS
tion (jl' i2, ... , jn) of the first n integers. For each factor
component:
(10.7a) Gi = sg+ + s,, and (i = 1, 2, ...,p)
(10.7b) Gi = s+ - s by theorem 9.1. (i = 1, 2, *.* ,p)
Consequently, when Gi and G. are first computed, s4+ and s, can be
computed:
(10.8a) St = (Gi + ±G)/2; (i = 1, 2, ...,p)
(10.8b) s. = (GI-G6)/2. (i = 1, 2, ...,p)
The values of st and s- are given in table 10.3.
For an empirical application, the correlation characteristies
R., R,, and R, are indicated for the three models: all households,
urban households, and rural households. Together with the factor
Gini coefficients G., G,,, and Ga indicated in table 3.2 of chapter
three, an exact decomposition of G, can be attempted for all three
models according to the basic decomposition equation (10.5).
Notice that the factor correlation characteristics [Ri] can be
defined by using equation (9.18) and written as:
(10.9) Ri = GilGi = r(wi, X)/r(wi,ri) = (st - s:)/(st± + s).
(i = 1, 2, ... ., p)
In this expression, r(wz,ri) is the correlation coefficient between
factor income fractions [wi] and factor income ranks [ri]; r(wi,x)
is the correlation coefficient between factor income fractions [wi]
and total income ranks [X]. There thus are two interpretations for
the term Ri in the basic decomposition equation: as the correlation
characteristic according to theorem 9.2; as the fractional net sup-
porting gap according to equations (9.18a) and (9.18b).
In the example in table 10.3, where the Gini coefficient of wage
income [Gm] is 0.3912, the average supporting gap [s+]-that is,
the variation of wage income that total family income can explain
-is 0.3110; the average contradicting gap [s-] is 0.0802. These
values lead to a pseudo wage Gini [GE] of 0.2308. Notice that the
property Gini [G,-] of 0.6628 is entirely explained by the supporting
gap (G = G = s+), indicating that the correlation between total
income rank and property income rank is perfect and positive. The
opposite is true for transfer income.
THE GINI COEFFICIENT UNDER LINEAR TRANSFORMATION 361
The Gini Coefficient under Linear Transformation
Let the vectors X = (X1, X2, . . . , Xn) and Y = (Y], Y2, ... ., Yn)
be nonnegative. X is a linear transformation of Y if there is a linear
function:
(10.10) x = b + ay,
where a and b are not both negative, such that:
(10.11) Xi = b + aYi. (i = 1, 2, ...,n)
It is obvious when Y > 0 that the coefficients a and b cannot both
be negative if X is to be nonnegative (X > 0). The following means
can be defined:
(10.12a) X = (X1 + X2 + ... + Xn)/n;
[the mean of X]
(10.12b) Y = (Y1 + Y2 + ... ± Y.)/n;
[the mean of Y]
(10.12c) q5u = (X1 + X2 + ... + X,)/
(Y, + Y2 + . .+ Y,,).
In equation (10.12c) , is the ratio of the mean XV to the mean Y.
The theorem to be proved in this section is:
TEIEOREM 10.2. If X = (X1, X2, ... , X,) is a linear transforma-
tion of Y = (Y1, Y2, ... , Yn) -that is, if Xi = b + aYi for i = 1,
2, ... , n-then:
(a) G(X) = (a/0ry)G(Y) i.f a > 0, and
(b) G(X) = -(a/4.v)G(Y) if a < 0,
where i, = X/Y and where G(X) and G(Y) respectively are the
Gini coefficients of X and Y.
For a geometric interpretation of this theorem, notice that:
(10.13a) X = b + aY,
362 MODELS OF ADDITrVE FACTOR COMPONENTS
which implies that:
(10.13b) (b/X) -1 = -a/0, by equation (10.12c).
Because the elasticity of the linear function in theorem 10.2 is:
(10.14) (dx/dy)(y/x) = al(xly),
it can be seen that a/(X/Y V) = a/O,, is the elasticity of the linear
function at the mean point (X,Y). Thus theorem 10.2 states that
G(X) can be obtained from G(Y) by multiplying G(Y) by the
elasticity at the mean point (X,Y). Theorem 10.2 can be proved as
follows:
Proof: Assume that Y1 < Y2 < ... < Yn. If a > 0 and X1 > X2 >
... > X, then by theorem 8.1:
u. = (1X± + 2X2±+ . . . + nX.)/nX
= [(b -+ aYi) + 2(b + aY2) + ... + n(b + aY.)]/nX
= b(l + 2 + ... + n)/nX + a(nY/nX)u,, by theorem 8.1
= (n + 1)b/2X + au.,,/, by equation (10.12c).
Thus by theorem 8.1:
G(X) = (2/n)[(n + 1)b/2X + au,/O)]- (n + 1)/n
= (a/.,,) (2/n)u% + b(n + 1)/ni- (n + 1)/n
= (a/X) (2/n) u + E(n + 1)/n](b/lf - 1)
= (a/O..) E(2/n) -(n + 1) /n] by equation (10.13b)
= (a/lov)G(Y).
This proves the case for a > 0. If a < 0 and Y1 < Y2 < ... < Y,
the values of Xi are in a reverse monotonic order X1 > X2 > ...
> X,. The above proof implies that G(X) = (a/q.,)G(Y) by
theorem 8.3. Now, however:
O(X) = -G(X) by theorem 8.4.
This completes the proof.
A positive coefficient a in equation (10.10) gives:
THEOREM 10.3. If X = (X1, X2, ... , X,,) is a linear trans-
formation of Y = (Y1, Y2, . .. , Y.) with a positive coefficient a > 0
LINEAR MODEL OF ADDITIVE FACTOR COMPONENTS 363
in x = b + ay, then:
(a) G(X) > G(Y) if and only if a/oz,, > 1 or b < 0, and
(b) G(X) < G(Y) if and only if a/+,,? < 1 or b > 0.
Proof: From theorem 10.2 it can be seen that G(X) Ž G(Y) if
and only if:
a ; 0zv = X/Y = (b + aY)/Y by equation (10.13a), or
aY t b+ aY.
This completes the proof.
The theorem essentially states that b is negative when the function
defined in equation (10.10) is elastic at the rnean point (X,Y), and
that b is positive when the function is inelastic at the mean point
(X,Y). The rest of the proof directly follows from theorem 10.2.
Linear Model of Additive Factor Components
Now consider a special case of the additive factor-components
problem defined in equation (10.1). For this special case, postulate:
(10.15a) wi = bi + aiy, where (i = 1, 2, ... , p)
(10.15b) a + a2 + ...+ a = 1 and
(10.15c) bi + b2 + ... + bp = 0,
such that the ith factor component [Wi = (Wj, W, . . , W) ] is
a linear transformation of the total income pattern EY = (Y1, Y2,
... > Yn)] according to the ith linear function in equation (10.15a).
In other words:
(10.16) Wi = (Wi, Wi, . . .w, I)
= (bi, bi, ..,bi) + ai(Yi, Y2, ...Y).
(i = 1, 2, .. p)
Notice when the restrictions of equations (10.15b) and (10.15c)
are postulated for ai and bi that:
(10.17) Y = WI + W2 + ..+ Wn
so that Y is the sum of all values of Wi, as in equation (10.2).
364 MODELS OF ADDITIVE FACTOR COMPONENTS
This model will be referred to as the linear model of additive factor
components. It is a special case of the general model defined earlier.
Notice in equation (lO.i5a) that some values of as may be nega-
tive. But when ai is negative, bi must be positive (see equation
[10.10]). Thus with no loss of generality the pairs (ai,bi) can be
classified into three types of case.
For a type one component:
(10.18a) as > 0 and bi < 0; (i = 1, 2, ... , q)
for a type two component:
(10.18b) ai > 0 and bi > 0; (i = q + 1, q + 2, . t. ,t)
for a type three component:
(10.18c) ai < 0 and bi > 0. (i = t + 1, t + 2,...,)
Let G, be the Gini coefficient of Wi and G, be the Gini coefficient
of Y. Applying theorem 10.2 gives:
(10.19a) Gi = (aj/1j)G,, or aiGy = iGi, and
(i = 1, 2, . ,t)
(10.19b) Gi = -(ai/4j)G,, or aiG, = -OiGi,
(i= t+ 1,t+2, ...,n)
where 1 0, ... p, are the distributive shares defined in equation
(10.ld). When all the romanized terms in equations (10.19a) and
(10.19b) are added, equation (10.15b) implies that:
(10.20a) G, = H1 + H2 - Hs, where
(10.20b) H1 = 41G1 + 02G2 + ... ± qGq,
Etype one components]
(10.20c) H2 = .q+,Gq+ + 0k+q2Gq+2 + ... + 0,Gt, and
[type two components]
(10.20d) H3 = ¢o+lGt+, + (t+2Gt+2 + .+. . +
[type three components]
Equation (10.20a) is an exact decomposition of G, for the linear
model of this section. Notice that this decomposition equation is a
MONOTONIC MODEL OF ADDITIVE FACTOR COMPONENTS 865
special case of the general decomposition equation (10.5). For this
special case, theorem 10.3 further implies that:
for type one income:
(10.21a) Gi 2 Gv, and (i = 1, 2, .. , q)
for type two income:
(10.21b) Gi < G,. (i = q + 1, q + 2, . ,t)
Thus, in the linear model, a type one factor component is distri-
buted more unequally than Y. A type two factor component is
distributed more equally than Y. A type three factor component
contributes more to income equality the more unequally it is dis-
tributed-that is, when Gi increases, GD decreases.
Monotonic Model of Additive Factor Components
Postulate for the generally defined model of additive factor com-
ponents in equation (10.1) that every factor component [W; =
(Wli, W2, . . , W') ] satisfies:
(10.22a) wi < W_ < ... < W, or
[monotonically nondecreasing conditions]
(10.22b) Wli > Wli > ... 2 Wi-.
[monotonically nonincreasing conditions]
The linear model obviously is a special case of this monotonic model.
When the total income pattern [Y] is monotonically nondecreasing,
a type one or type two income obviously is monotonically nonde-
creasing; a type three income is monotonically nonincreasing.
Applying equations (9.17a) and (9.17b) to Wi in the monotonic
model gives:
(10.23a) Gi = Gi,
when Wi is in a monotonically nondecreasing order, and:
(10.23b) Gi = -0i,
when Wi is in a monotonically nonincreasing order. In the first
case the factor Gini coefficient equals the pseudo factor Gini coeffi-
cient. In the second case it equals the negative value of the pseudo
366 MODELS OF ADDITIVE FACTOR COMPONENTS
factor Gini coefficient. Substituting equations (10.23a) and (10.23b)
in the equation of theorem 10.1 gives:
THEOREM 10.4. In the monotonic model:
G-= U1 - U2, where
(a) Ul = klG1 + q2G2 + ... ±+ ¢tGt and
[monotonically nondecreasing Wi]
(b) U2 = Ot+1Gt+l + O+2Gt+2 + ... + O.Gn.
[monotonically nonincreasing Wi]
In comparison with the general decomposition equation (10.5) it
can be seen in the monotonic model that all values of Ri, the correla-
tion characteristic, equal 1 or -1. Furthermore the decomposition
equation in the linear model (10.20) is a special case of theorem
10.4. In other words, the linear model is a sufficient, but not a neces-
sary, condition for deducing Ri to be 1 or -1.
The monotonic model of this section is useful for empirical appli-
cation because, when total income is monotonically arranged [Y1 <
Y2 < ... < Yn]J it can often be assumed, as a first approximation,
that all factor components [Wi] satisfy the monotonic conditions
of expression (10.22). The primary advantage of the monotonic
model is the simplicity that accrues to theoretical analysis when
all correlation characteristics are assumed to be 1 or -1. Consider
the following numerical example:
(10.24a) (Y1, Y2, Y3) = (20, 30, 50), G, = 0.2;
(10.24b) (W1, W2, W3) = (10, 24, 46), G. = 0.3,
Co = 0.8, (W1 < W2 < W3);
(10.24c) (1n, 72, Ir3) = (10, 6, 4), G, = 0.2,
0, = 0.2, (Xl > Ir2 > m3);
(10.24d) (Yr, Y2, Ya) = (WV, W2T) W I+ (wi, Tr2, Tr3);
(10.24e) G, = 4.G, - 0,WG, = (0.8) (0.3) - (0.2) (0.2) = 0.2.
Notice that the two factor components are not linear transforma-
tions of (Y1, Y2, Y3). Yet theorem 10.4 can be applied because the
monotonic conditions are satisfied. Notice also that a minus sign is
attached to the component (rl, T2, r3) because it is in a monotonic-
ally nonincreasing order.
LINEAR APPROXIMATION OF FACTOR COMPONENTS 367
Linear Approximation of Factor Components
Suppose that Y and Wi (i = 1, 2, .. . , p) are interpreted as
original data and given as in equation (10.2) such that some Wi
is not a linear transformation of Y. In this section the purpose is to
investigate the construction of approximated factor components
[Wi = (WL W2, .. ., Wi) (i = 1, 2, ... , p)] which satisfy the
following conditions:
(10.25a) Y = Wl + W + .. . WP, and
(10.25b) 'i = (Wli + W ± ... + Wi)/nY
= ( +lit+ W2± . .. ±IVD/rt, (i = 1, 2, ... ,n)
where Wi is a linear transformation of Y according to:
(10.25c) wi = bi + aiy, (i = 1, 2, ... , p)
(10.25d) Q1 + Q2 + + Qp = 1,
(10.25e) 61 + b2 + ... + bp = 0, and
(10.25f) Wj = bi + diFY. (i = 1, 2, .. ,p; j= 1, 2, .. ,n)
The vector Wi constructed in this way will be referred to as a linear
approximation of Wi. Condition (10.25a) states that Y, interpreted
as original data, is the additive sum of the linear approximations of
the factor components [Wi]. This condition is ensured by the fact
that Wi is a linear transformation of Y with the conditions postu-
lated in equations (10.25d) and (10.25e). Condition (10.25b) states
that the factor share [0i], originally defined for Wi, remains un-
changed when Wi replaces Wi. With such an approximation, the
original additive factor-components problem, which in equation
(10.2) is stated as:
(10.26) Y = W± + W2 + ... + WP,
is now replaced by a new additive factor-components problem
through a linear approximation.
The primary advantage of the formulation of this new problem is
the theoretical simplification the linear approximation brings about.
If G(Wi) is the Gini coefficient for the approximated factor com-
368 MODELS OF ADDITIVE FACTOR COMPONENTS
ponents (W'), equation (10.20a) immediately implies that:
(10.27a) G, = fl'1 + 22 - Th, where
(10.27b) 121 = 40,G(W') + 02G(W2) + ... + OG(W-)
for type one incomes satisfying di > 0 and bi < 0;
(10.27c) -22 = 0,+1G(WF+l) + 0+2G(*jJf+2) + ... + OsG(#7V)
for type two incomes satisfying di > 0 and bi > 0; and
(10.27d) A, = 0+1,G(Wft+I) + k,+2G(V'+2) + ... + 0,G(*-J)
for type three incomes satisfying di < 0 and bi > 0.
Equation (10.27a) is comparable to the general decomposition
equation (10.5) when the correlation characteristics [Ri] are 1 or - 1.
Furthermore the classification of income into types one, two, and
three, hitherto definable only in the context of the linear model,
becomes applicable. The new decomposition problem thus becomes
simpler and wealthier in economic content.
To proceed with the construction of Wi, the linear function in
equation (10.25c) is treated as a linear regression equation in which
the parameters ai and bi are estimated from the original data for
Y and Wi (i = 1, 2, ... , p) by the method of least squares. Con-
dition (10.26), a property of the original data, ensures that equations
(10.25d) and (10.25e) are satisfied when the method of least squares
is used. When these regression functions are constructed, the esti-
mated factor components [EW (Wi W,..., W) (i = 1, 2,
p) ] are obtained by substituting Yi in the regression equation
(10.25f). To prove equation (10.25b) it can be seen for the ith
regression equation that:
(10.28a) oi = (p, 92, * * *, °n)
= (Wi, Wi, * . ., Wi) - (, W;, . . .W,i);
(10.28b) lk Wi, ..., n)
= (bi, bi, . . ., bi) + ai(YI, Y2, . . ., Yn)
by equation (10.25f);
(10.28c) Of + 62 + *.+ o °=0;
(10.28d) Wli + W2 + . . . + W'= W + 2 + * . . + nW
=ai(Y, + Y2 + . .. + Y.) + nbi.
LINEARITY ERRCR 369
In equation (10.28a) Oi contains all the deviations [EO (j = 1, 2,
. n) ] of W' from the estimated W,. The least-squares method
of estimation implies that the sum of all deviations is zero [equation
(10.28c) ]. Summing both sides of equation (10.28a) directly leads
to equation (10.28d) which shows that the sum of all elements in
Wi, the original data, is the same as the sum of all elements in the
pattern of approximated factor incomes [Wi]. Thus 4i remains
unchanged.
Linearity Error
When the original data are given for Y and Wi (i - 1, 2, ... p),
the method of linear approximation can be used only when every
Wi approximately is a linear transformation of Y. In computing
the regression coefficients [4i and bi] in equation (10.25c), the
correlation coefficients should also be calculated:
(10.29) ri = r(Y,Wi). (i = 1, 2, ... , p)
[correlation coefficients]
The values of ri give an indication of how close the linear approxi-
mation is. It is recommended that the method of the preceding
section be used only when all absolute values of ri are sufficiently
close to 1-that is, only when all values of Wi are nearly perfectly
correlated with Y, whether positively or negatively. When this
condition is not met, the following approximation formula can be
defined by replacing every G(Wi), the factor Gini of the approxi-
mated factor component, by G(Wi), the true factor Gini:
(10.30a) ,, = H1 + H2 - 1, where
(10.30b) 1T = OG(W') + 02G(W2) + ... + .G(Wq),
(10.30c) 122 = 0q+G(Wq+1) + O,q+2G(W12) + ... + OtG(Wt), and
(10.30d) 123 = 0,+1G(Wc+1) + Ot+2G(W'+2) + ***+ ±pG(WI).
When this approximation formula is used, an error term EJ] is
involved. It is the difference between G,, as defined in equation
(10.27), and U,,:
(10.31a) J = U,, - Gv, = JI + J2 - J3, where
(10.31b) Ji = sldl + A2d2 + *.. + dSd,
370 MODELS OF ADDITIVE FACTOR COMPONENTS
(10.31c) J2 = ,+f1d,+ + 0,+2d,+2 + + q¶tdt, and
(10.31d) J3 = 0,+1d,+ + 01+2dt+2 + ... + ,dp, where
(10.31e) di = G(Wi) - G(fVi). (i = 1, 2, .. , p)
In equation (10.31e) di is the difference between the Gini coeffi-
cient of the true factor component and that of the approximated
factor component. Notice in equation (10.28a) that the difference
between Wi and Wi is Oi. When the absolute value of the correlation
coefficient Eri] is close to 1, 9i is close to a zero vector, leading to the
fact that di is close to zero.
By comparing equation (10.30) and theorem 10.4, it can be seen
that the approximation formula can be used even when the absolute
values of the correlation coefficients [ri] are not close to zero. In
other words, the fact that they are close to zero is a sufficient, but
not a necessary, condition. In the monotonic model, G, is equal to
G. Hence the linearity error vanishes-that is, J = 0-even though
di, d2, . . ., d, may not vanish. [For a numerical example see equa-
tion (10.24).] Thus it is recommended in attempts to apply the
linear model to empirical work that checks be made to ensure that
the following conditions are fulfilled:
(10.32) j ri I = I r(Y, Wi) I 1. (i = 1, 2, . . ., p)
In words, the linear correlation coefficient between Wi and Y should
be close to 1 or -1.
Approximation of the Monotonic Model
Suppose that Y and Wi (i = 1, 2, ... , n) are given as in equa-
tion (10.2) and that the monotonic conditions are only approxi-
mately satisfied. If the monotonic model is to be used, the equation
of approximation is:
(10.33) G, = U1 - U2,
where U, and U2 are defined as in theorem 10.4. The difference
between G, and G2, as defined in the exact decomposition equation
(10.5), is the Gini error term:
A
(10.34a) E = G - G,= E1 - E2, where
APPROXIMATION OF THE MONOTONIC MODEL 371
(10.34b) E1 = 5igt + 02g2 + ... + kogt 2 0
for 0 < Ri < 1, and
(10.34c) E2 = ot±lgt+i + ot+2gt+2 + ± * + o,gP > 0
for -1 < R < 0, where
(10.34d) g, = Gj(1 - Rj) and (i = 1, 2, ... , t)
(10.34e) gi = Gi(l - Ri). (i = t + 1, t + 2, ,p)
The term El includes all components [Wi = (Wi, W2, ..., W')]
for which Ri is positive. This condition is interpreted as approxi-
mately satisfying the monotonic increasing condition [Wl' < W2' <
... < WW]. Similarly the term E2 includes all Wi for which Ri is
negative. This condition is interpreted as approximately satisfying
the monotonically decreasing conditions [Wi > W2' > ... > Wi].
It is easy to show that El and E2 in equations (10.34b) and
(10.34c) are nonnegative. The Gini and pseudo Gini coefficients of
a factor component EW?] may be written as they are in equations
(10.7a) and (10.7b):
(10.35a) Gi = st + s; (i = 1, 2, ,p)
[factor Gini]
(10.35b) G=s+s(i= 1, 2, . ,p)
[pseudo factor Gini]
When the total income pattern [Y] is monotonically arranged
[Y1 < Y2 < ... < Yn] for a particular factor component [W' =
(Wli, Wi, , Wi)], the average supporting gap [st] is the sum of
all such terms satisfying (W' - Ws) > 0 for u > v. In other words,
if the total income is higher (Yu > Y~), the factor income is also
higher (W' > WI). Conversely the contradicting gap [s- ] includes
all terms such that the factor income is lower (Wu < W,) if the total
income is higher. Equations (10.34d), (10.34e), (9.12a), and (9.21b)
give:
(10.36a) gi = 2s- (i = 1, 2, ... , t)
when W, < W' < ... < W' is approximately satisfied and:
(10.36b) gi = 2s+ (i = t + 1, t + 2, ...,n)
372 MODELS OF ADDITIVE FACTOR COMPONENTS
when Wi > Wi > ... > Wi is approximately satisfied. The fact
that s- and s+ are nonnegative implies that E1 and E2 are nonnega-
tive, as was to be demonstrated. Furthermore the underlying na-
ture of the error terms is now known. For E1 the error is traced to
the violation of monotonically increasing conditions. For E2 the
error is traced to the violation of monotonically decreasing condi-
tions.
Because E is the difference between two nonnegative terms E1
and E2, it can be seen that G, defined in equation (10.33) can either
underestimate or overestimate the true G,. If all values of Ri are
positive, then E2 vanishes and G, always overestimates G,. This
condition can be stated as:
THEOREM 10.5. If all factor correlation characteristics are positive-
that is, if Ri > 0 for i = 1, 2, . .. , p-then the error of estimation
[E] defined in equation (1 0.34) is:
E = El = 2 (qis- + 02s2 + ..+ fxsp,) 2 °
Hence Gy = OIG1 + k2G2 + ... + G always overestimates Gy.
Furthermore E is twice the weighted sum of contradicting gaps.
When the monotonic model is to be used for empirical work,
equation (10.34) suggests that the following conditions should be
verified after the correlation characteristics [Rij are computed:
(10.37) 1 Ri I - 1. (i = 1, 2, ... ., p)
In words, the absolute values of all Rf should be close to 1 to ensure
that the monotonic conditions are approximately fulfilled.
CHAPTER 11
Applications and Extensions
of the Models of Decomposition
THE CONSTRtUCTION OF A GENERAL MODEL of additive factor com-
ponents in chapter ten led to the exact decomposition equation (10.5).
Construction of the monotonic model, a special case of the general
model, led to the exact decomposition equation in theorem 10.4.
Construction of the linear model, a special case of the monotonic
model, led to the exact decomposition equation (10.20). These three
models can be used both for theoretical purposes and for empirical
applications.
The general model of equation (10.5) is most useful for empirical
applications because of its generality. Precisely for that reason,
however, the monotonic model or the linear model may be preferred
for theoretical purposes. If there are a priori reasons, based on
economic theorizing, for assuming that the monotonic conditions
of expressions (10.22a) and (10.22b) are fulfilled, the monotonic
model should be used. Similarly, if there are a priori reasons for
assuming that the strong linear conditions of equation (10.16) are
fulfilled, the linear model should be used. The monotonic model is
less complicated than the general model, because the correlation
characteristics can be neglected as a first approximation. The linear
model can, in addition, identify three different types of income-
types which help in reasoning about the distribution of income. In
reality, the monotonic and linear conditions can only be approxi-
mately fulfilled. Thus the exact monotonic and linear models are
used for theoretical purposes; the approximation models, for em-
pirical work.
573
374 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION
Remarks on Chapter Three
The approximation of the linear model was applied in chapter
three. Because of the aggregated data, the conditions of equation
(10.32) were judged to be fulfilled: I ri I = I r(Y, Wi) I 1 (ob-
serve the values of r,, r., and r, in table 3.3). For the empirical
application in that chapter, there was no type three income (observe
that the values of a., a,, and a. are positive in table 3.3). Thus the
terms H3 and J3 respectively vanish in the approximation equation
(10.30a) and the error equation (10.31a), which reduce to:
(11.la) u = 1i + 2, and
(11.lb) J = JL + J2.
The value of J is denoted by U in table 3.2 of chapter three. Notice
that because the linear conditions are judged to be fulfilled, the
values of 0 are quite tolerable. The overestimation of the true Gv
by G,, which the positive values of 0 in table 3.2 indicate, is sug-
gested by theorem 10.5: G, -G = X 0.
How do the formulations of chapter three relate to those pre-
sented in chapter ten? In the theoretical derivation of chapter
three, equation (3.3b) is a special case of equation (10.30a): that
is, Gu = ¢OwG. + -GT - OkNGN is a special case of v,, = fll + f12 -
12g. (Notice that the term kNGN corresponds to a type three income.)
Equation (3.5a) is a special case of equation (10.25f): that is, Wi =
b. + aiY is a special case of W# = bi + diY,. The definition of Gu
in equation (3.8b) is the same as in equation (10.30): that is, Gu =
Hi + H2- H3 is the same as G,v = i21 + 122- 123. Nevertheless 0,
which corresponds to J in equation (10.31), was not explicitly dis-
cussed in chapter three. Theorem 3.1 corresponds to equation (10.27):
that is, Gu = 121 + 122 - 3. Theorem 3.2 corresponds to equation
(10.19): that is, G(1i) = (ai/lo)G, = Gi for type one and type
two incomes, and G(47i) = - (ai/¢)G, = Gi for type three income.
The statements in equations (3.12a) and (3.12b) are proved by
equation (10.21): that is, Gi 2 Gu for type one income, and Gi < Gu
for type two income. Equations (3.14a) and (3.14b) are suggested
by theorem 10.5: that is, when there is no type three income, G" =
k1G1 ± t2C2 + .O.. + 0Gr - 0, where 0 > 0, is suggested by Gv =
REMARKS ON CHAPTER SIX 375
0,G, + 02G2 + ... ± 4yG,, where GQ overestimates GQ by an amount
equal to the error term E.
Remarks on Chapter Six
Equations (6.3a) and (6.3c) of chapter six stated that:
(11.2a) V = C= + C2 + C3 + S and
[expenditure model]
(11.2b) Y= V+ T1+ T2.
[tax model]
In the expenditure model the pattern of income after tax [V =
(V1, V2, ... , VT)] is the sum of three consumption components
ECi = (Cil, C6, . . ., Cin) (i = 1, 2, 3)] and a savings component
ES = (si, s2, ... , s)]. In the tax model the pattern of income
before tax EY = (yl, Y2, . . ., y,)] is the sum of V and the patterns
of direct tax payments ET1 = (tll, t12, . . . , tj, )] and indirect tax
payments ET2 = (t2l, t22, . . . , 12)]. For these two models the exact
decomposition equation (10.5) was applied: G, = Z &iRiGi Esee
equations (6.4a) and (6.4b) in chapter six].
The tax model is a good example of the way sound economic
reasoning should guide the choice among decomposition models.
When total income before tax is monotonically increasing E1¾ <
Y, < ... < Y.], any reasonable taxation system should approxi-
mately satisfy the conditions that V, T1, and T2 also are mono-
tonically increasing-conditions described as "no reversal of rank"
and "minimum progressiveness" in equation (6.8) of chapter six.
Thus confidence in this reasoning should have led to the choice of
the monotonic model, not the more complicated general model. As
it turned out, the accuracy of exact decomposition associated with
using equation (10.5) is spurious because all the correlation charac-
teristics [Ri] are close to 1, as would be expected in the first place
(see the values of R., R', and R' in table 6.3 of chapter six).
In the expenditure model, whether Ci should be monotonically
increasing or decreasing is a matter of well-known theoretical specu-
lation in the economic theory of consumption. The pattern of con-
sumption ECi] is expected to be monotonically increasing if the
376 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION
commodity is a noninferior good; it is expected to be monotonically
decreasing if the commodity is an inferior good. For this model it
turns out that the correlation characteristics [Ri] also are close to 1
(see the values of R', Re, R3, and R. in table 6.2). Nevertheless the
general equation (10.5) was used in chapter six, as it should be in
such cases, because the strength of those correlations was uncertain
until the values of Ri were calculated.
Additive Factor Components and Growth Theory
The models of additive factor components have been abstractly
constructed to emphasize that these models can be applied to many
problems once there is a classification of the sources of income. In a
theoretical application, the models must be combined with addi-
tional theoretical notions, economic and noneconomic, to increase
the understanding of the social and economic forces that determine
the equity of family income distribution. When adopting such an
approach, certain behavioristic assumptions usually must be added
to the framework of additive components.
The analysis of equity in relation to growth in chapter three is an
example of such an approach. But in that chapter the linear model
was used as a first approximation: G,, = qwG. + ,G,, - 0. What
if the basic decomposition equation (10.5) had been used instead?
What would have been the added theoretical requirement asso-
ciated with such a generalization? To illustrate with the urban
family case of chapter three:
(11.3) G,, R=w R.G, + R.,,G,r, where fw + + = 1.
Equation (11.3) decomposes C,G into the wage income effect [R.0 G.]
and the property income effect [Rr+pGr. The decomposition now
is exact. This exactness appears to be an advantage, because it now
is unnecessary to worry about an error term in empirical applica-
tions. That advantage is not gained, however, without a cost. The
theoretical requirement becomes greater because of the appearance
of the correlation characteristics [RW, and R,.] in equation (11.3).
When these variables are functions of time, differentiating equa-
tion (11.3) gives:
(11.4a) dGy = Bo + Do + Ro, where
ADDITIVE FACTOR COMPONENTS AND GROWTH THEORY 377
(1 1.4b) Bo = R.or dG + R+ r r dGt
(liAb) BO = ~~~dt dt
Efactor Gini effect]
(11.4c) Do = (RtoG. - RiOG) d-', and
Uunctional distribution effect]
dR_
(11.4d) R° = dt+G. dt+
Ecorrelation effect]
Notice that the terms Bo and Do are direct generalizations of the
factor Gini effect [B] and the functional distribution effect [D] of
equation (3.16) in chapter three. The term R° is a newly added
correlation effect. It indicates the impact of the variation of the
correlation characteristic on total income inequality. It essentially
captures the variations of the ways in which wage and property
income are correlated with total family income: that is, the extent
of exceptions to the rule that wealthier families tend over time to
receive more wage and property income than poorer families. This
simple example shows that at least three types of forces can affect
G, in the process of growth.
The endeavor to link growth theory with income distribution
theory can proceed at the aggregate or disaggregate level. The
framework of reasoning provided by equation (11.3), or equation
(3.16) in chapter three, aims to link them at the aggregate level
and to take advantage of the knowledge accumulated in the more
developed branch of development theory. A good example of this
link is the functional distribution effect; another is the reallocation
effect in the more general a.ll-households model. These effects con-
stitute the focal points of analysis of aggregate growth theory in a
dualistic economy and can now be incorporated into the framework
of FID analysis.
It should be noted that very little is inductively known about
Ro. Even less is known about a positive behavioristic theory of R°.
Thus, by focusing on the special case in chapter three and omitting
RO in the framework of reasoning, heavy costs are not incurred
because not much is to be gained by including R°. This is not to
deny that future advances in understanding R° would be helpful.
378 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION
The obvious advantage of theoretical simplicity in the special
case must be weighed against the disadvantage of imprecise results
traceable to the omission of R°. When aggregated data are used, as
in the analysis in chapter three, O/G, is observed to be uniformly
less than one percent. Thus the precision of analysis is not impaired
by the use of the approximation formula. In fact, the use of equation
(11.3) instead of Gy = ±>G + ,G,. - 0 would have led to an expen-
sive search for spurious accuracy traceable to a factor [RO] about
which not much is known.
By constructing a number of abstract models of additive factor
components as frameworks for theoretical reasoning and empirical
analysis, it has been shown that the choice of appropriate models is
guided not only by the availability of statistical data, but by the
complementary theoretical inputs which are currently or potentially
available.
Income Components with Observation Error
In economic applications total family income [Yi] may be the
sum of several components and an observation error [Di]. Thus:
(11.5a) Yi = Wii + W2i + ...+ Wit + 6i; (i =1, 2, *,n)
(11.5b) 61 + 62 +* + a =0;
(11.5c) s = Y + Y2 + ...Y = S± + S2 + *+ S;
(11.5d) Si = Wl' + W,' + ...+ Win. (i = 1, 2, . ,p)
In vector notation let 6 = (d1, a2, . . ., an). Then:
(11.6a) Y = Wl + W2 + . . . + WP + ±, where
(11.6b) a = (a1, 62, ... * * a
Notice that the sum of all elements in a is zero by construction.
All other vectors-that is, Y and Wi (i = 1, 2, ... , p)-are as-
sumed to be nonnegative. Thus the only difference between equation
(11.5) and the components problem introduced at the beginning
of chapter ten is that one "factor component" may have negative
entries: a. Such a situation may arise, for example, when Y and Wi
are independently estimated in empirical work.
The Gini coefficients G, and Gi (i = 1, 2, ..., p) can be de-
INCOME COMPONENTS WITH OBSERVATION ERROR 879
fined as before. But a Gini coefficient cannot be defined for i be-
cause it contains negative entries. To construct a decomposition
equation, first construct a system of weights and define a weighted
observation error, 6, in the following manner:
(11.7a) ji = i/g, where (i = 1, 2, , n)
(11.7b) g = 1 + 2 + . .. + n = n(n + 1)/n,
(11.7c) 6 = jlbl + j22± .. + nn, and
(11.7d) A = 6/Y, where
(11.7e) Y = (Y1 + Y2 + ... + Y.)/n and
(11.7f) il + i2 + . . . + jn = 1.
Thus (ji, j2, ... , jn) are the "rank weights"; 6 is the rank-weighted
observation error; and A is a expressed as a fraction of the mean
income of all families.
THEOREM 11.1. G, = 0,G, + ± 2G2 + ... + 0,0p + (n + 1) A/n,
where A = / Y.
Proof: UD = (1/s) 2Yi Xi = (1/s,) E Xi(Ww + Wi +
Wij + bi) by equation (11.5)
=(Sl/S) (E XiWV/s1) + (S2/Sy) (E XiXW/s2)
+ ... + (sp/sS) (E XiW-V/s) + (1/sn) E Xiai
- Olfl + 42U2 + . . . + 4),ii + J, where
J = (1/sy) EXi5i = (S./Sy) (X51a/S. + X262/S& + . + X.5/.S.)
= [n(n + 1)/2sj[ji5, + j262 + ... + ji]
by equations (11.7b) and (11.7c)
= (n + 1)a/2Y
= (n + 1) A/2.
Hence:
Gv = (2/n)u% - (n + 1) /n
= (2/n)[U19i + 2u2 + . . . + opiip + (n + 1)A/2- (n + 1)/n
= 0'101 + k2G2 + . .. .+ tpGp + (n + 1) A/n.
This completes the proof.
380 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION
Based on theorem 11.1, equation (10.5) can be modified as:
(11.8a) G, = 4O1RG1 + 02R2G2 + ... + 4,RpG, + (n + 1)A/n,
where:
(11.8b) Ri = ai/Gi and (i = 1, 2, ... , p)
(11.8c) A = S/ = (ji&, + j2a2 ... + jj.)/Y, where
(11.8d) ji = 2i/n(n + 1).
Theorem 11.1 is a direct generalization of the special case of equation
(10.5).
Family Income with Negative Components
In empirical reality the net income of a family may have a nega-
tive component. For example, although gross income has such
positive components as wage income and property income, tax
payments must be subtracted from gross income to obtain net
family income. The following equations formulate this problem
conceptually:
(11.9a) Wi = col(Wl, W2, . . . , Wn) > 0; (i = 1, 2, . . ., p)
(11.9b) Zi = col(Z,i, Z2i, . ., Z') 2 0; (i 1, 2, . . ., q)
(11.9c) 6, = col(i1, 62, . . ., an); ( Ei = 0)
(1 1.9d) Y = Wl + W2 + . ..... + WP - Z' - Z2 . ..... _Z" + 6,
= col(Yl, Y2, .... Yn) > 0;
(11.9e) X = Y +Z' + Z'+ ....... + Zq= TV'+W2 + +...... +WP + 3
col (XI, X2, .. ., X.) 2 0.
Thus Wi stands for the ith positive income component; Zi for the
ith negative income component. Net family income is Y; gross
family income is X. As in the preceding section, 6. stands for a column
vector containing the elements 6i with a zero sum. It is assumed
that gross incomes are arranged in a monotonically increasing order:
(11.10) XI < X2 < ... < Xn.
The purpose of the analysis is to find out the causation factors
FAMILY INCOME WITH NEGATIVE COMPONENTS 381
that explain G,, the inequality of net income. Equation (11.9d)
shows that this problem can be solved by investigating two com-
ponents problems:
(11.11a) X = Y + ZI + Z2 + + Z9;
(11.l1b) X = WI +W' + ... + WP +6
To apply equation (11.8) to these problems, the terms oi, Ri, and
A must be defined. For fi, define:
(11.12a) X = (Xi + X2 + ... + X.)/n,
(11.12b) 2i = (Zli + Z2 + ..+ Z') /n, (i =1, 2, * ,q)
(11.12c) W i=(Wl+ W2+ ...... + W')/n, .. (i =1, 2, ...,p)
(11.12d) Y (Y1 + Y2 + ... + Y.)/n;
(11.13) X = Y + (Z1 + 2 + ... + Zq) by equation (11.9e)
= Wl+fV2+ ... +Wp,
by equations (11.9e) and (11.9c);
(11.14a) 01,= Y/X,
(11.14b) CS = Z4/X, (i = 1, 2, ... , q)
(11.14c) '° = Wi/X, (i = 1, 2, ... , p)
(11.14d) Oi = 0 = Zi/Y, (i = 1, 2, ... , q)
(11.14e) 6, = d,/4v = Wi/Y; (i = 1, 2, . ,p)
(11.15a) 4, + -l + ± + .2 . . + 4 = 1 by equation (11.12b),
(11.15b) + + +w + *w+ ... + ow = 1 by equation (11.12b).
In equation (11.12) the means are defined for all the column
vectors of equation (11.9e), leading to the equalities in equation
(11.13). The relative shares of the two components problems in
equation (11.11) are defined in relation to these means. Observe
that 0b, is net income as a fraction of gross income; 4, is the ith
income component as a fraction of gross income; 0$ is the ith pay-
ment as a fraction of gross income. In equation (11.14) the income
and payment components are expressed as a fraction of net income:
O, and V,. To apply equation (11.8), the following must also be
382 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION
defined:
(11.16a) G. = G(X),
(11.16b) G, = G(Y),
(11.16c) G- G(Zi), (i = 1, 2, , q)
(11.16d) G.= G(W9); (i = 1, 2, ... , p)
(11.17a) ay (y),
(11.17b) G= (i,(i =1, 2, . ,q)
(11.17c) Gs = G(Wi); (i = 1, 2, . . ., p)
(11.18a) R, = 6.1Gy,
(11.18b) R= GJGs, (i = 1, 2, ... , q)
(11.18c) R,' = G, ; (i 1, 2, ... , p)
(11.9) A (jll + j262 + ... + j,bn)/X by equation (11.8c).
In equation (11.16) G, is the Gini coefficient of gross family income;
G,, of net family income; GT, of the ith income component; G., of
the ith payment component. The pseudo Gini coefficients are de-
fined in equation (11.17). Notice that these pseudo Gini coefficients
are defined relative to expression (11.10): the gross income ranking
is used as the exogenous characteristic. The relative correlation
coefficients are defined in equation (11.18); the relative rank-weighted
error term is defined in equation (11.19).
Applying equation (11.8) to the two problems in equation (11.11)
gives:
(11.20a) G. = OR,,GV + zRzGz + OJR?Gz + ... + o,,R,G,
by equation (11.16) and
(11.20b) G. = 0-RI-'Glw + O-R-G- + ... + .pRpGp+ (n-+ 1)A/n
by equations (11.17) and (11.19).
It now is possible to solve for G, and obtain:
(11.21a) Gy = (A+ - A- + E)/R,, where
(11.21b) A+ = 0"R-'Gw + OwRWG2w + ... + oRwGpw 0,
[income effect]
COMPUTATION PROCEDURE 383
(11.21c) A- = OIR'G+ + O +R ± .. + 6'R'GŽ > O, and
[payment effect]
(11.21d) E = (n + 1)A/no,
= [(n + 1)/n]Q(ji6 + j262 + ...+ jb)/9y
by equation (11.19)
E (n + 1) /n] ( ial + j282 + ..+ j. )
[decomposition error] by equation (11.14).
The inequality of net family income [Gd] is therefore decomposed
into an income effect [A+], a payment effect [A-], and an error
term [E]. When an income component is positively correlated
with gross income-that is, when R7 > 0-an unequal distribution
of an income component, indicated by a large G[, contributes to
income inequality. When an income component is negatively cor-
related with gross income-that is, when RX' < 0-an unequal
distribution of an income component contributes to income equality.
The opposite relations are true for the payment effect. When a
payment is negatively correlated with gross income, an unequal
distribution of payment, indicated by a large GW, contributes to
net income equality. The error term [E] tends to be small when
net income accounts for a higher fraction of gross income and 0, is
large.
Computation Procedure
A numerical example will now illustrate the computation proce-
dure for the problem described in the preceding section. For the
five families shown in table 11.1, there are two types of income
(wage and property), two types of payment (tax and transfer),
and an error term. Net income [Yj] and gross income [Xi] are
also given. All families are arranged in a monotonically increasing
order according to gross income, thereby satisfying expression
(11.10). The pseudo Gini coefficients are computed relative to this
family ranking. It should be noted in this example that the rankings
384 APPLICATIONS AND EXTENSIONS OF THE MODELS OF DECOMPOSITION
Table 11.1. Numerical Example of Original Income Data
Nota- Family Family Family Family Family
Variable tion 1 2 5 4 5 Total
Wage income Wl 8 4 12 20 6 50
Property
income W2 0 10 5 15 45 75
Tax
payment Zi -1 -3 0 -4 -7 -15
Transfer
payment Z2 -2 -2 -2 -2 -2 -10
Error term Si 0 1 0 1 -2 0
Net family
income Yi 5 10 15 30 40 100
Gross family
income Xi 8 15 17 36 49 125
Source: Constructed by the authors.
Table 11.2. Distributive Shares, Gini Coe.ticients,
and Pseudo Gini Coefficients for Original Data in Table 11.1
Nota-
Variable tion X Y WI JV Z' Z2
Mean 25 20 10 15 3 2
Distributive share in X oi 1.0 0.8 0.4 0.6 0.12 0.08
Distributive share in Y os - 1.0 0.5 0.75 0.15 0.10
Gini coefficient Gi 0.3296 0.3600 0.3040 0.5333 0.4533 0.0000
Pseudo Gini coefficient (G, - 0.3600 0.0960 0.5066 0.3467 0.0000
Relative correlation R, - 1.0000 0.3158 0.9499 0.7648 0.0000
- Not applicable.
Source: Calculated from table 11.1.
of families according to X and Y are the same. This relation never-
theless is just an accident leading to R, = 1. Thus table 11.1 con-
tains all the primary data needed for the decomposition problem.
The computation procedure is set forth in tables 11.2 and 11.3.
COMPUTATION PROCEDURE 885
Table 11.3. Decomposition Analysis of Original Data in Table 11.1
Nota-
Variable tion Computation Value
Rank-weighted
error term A = o/X = (jib + 1282 + *
+ j5b5)/X
= -(4/15)/25 = -4/3
Income effecta A+ = ,wR,wG,w + 2wRwGw = 0.4279
Payment effectb A- = OVRjGf + ± ORG1 = 0.0519
Decomposition
errorc E = (n + 1)A/noy = -0.0160
Decomposition
analysisd Gy = A+ - A + E
= 0.4279 - 0.0519
- 0.0160 = 0.3600
Relative weight 1 = A+/Gy - A-/GI + E/Gy
= 1.1886 - 0.1446
+ (-0.0440) 1.0000
Sources: Calculated from tables 11.1 and 11.2.
a. See equation (11.20b).
b. See equation (11.20c).
c. See equation (11.20d).
d. See equation (11.20a).
CHAPTER 12
Regression Analysis,
Homogeneous Groups,
and Aggregation Error
THREE ADDITIONAL SUBJECTS require elaboration. The first is the
manner in which regression analysis of variations in family income
can be related to the analysis of additive factor components. The
second is the analysis of the distribution of income by homogeneous
groups of income recipients. The analysis of these groups could be
so construed that the Gini coefficient is decomposed into inter-
group and intragroup effects, as well as a crossover effect. That
crossover effect will be shown to increase as the decisiveness with
which ordinal rankings of groups affect earning power is perverted.
The third subject is the error introduced when grouped data on the
distribution of family income must be used because of the unavail-
ability of primary data. It will be shown that the use of grouped
data leads to the consistent underestimation of the index of inequality
and hence the degree of that inequality.
Regression Analysis
One of the most popular methods used in attempts to explain
the variation of family income is based on a linear regression model
of the following form:
(12.1a) Y = a + b1X' + b2X2 ± ... + bqXg + a, where
(12.1b) Xi > 0.
886
REGRESSION ANALYSIS 387
The family income is to be explained by independent variables
[Xi] which stand for various ordinal characteristics, such as educa-
tion, age, and sex. The term 6 represents a randomly distributed
error term. The basic aim of regression analysis is twofold: first, to
estimate the regression constant a and the regression coefficients
bi; second, to assess the reliability of these estimations once the
observable data of n families are given:
(12.2a) Y = col(Y1, Y2, ...., );
(12.2b) Xi = col(Xfi, X,..., X,) > 0; (i = 1, 2, ...,q)
(12.2c) 0 < yl < Y2 < ... < Yn.
The total incomes of the n families and the values of the indepen-
dent variables are shown as column vectors. Assume that the re-
gression constant a and the coefficients bi are already estimated and
given as a starting point of the analysis-that is, the reliability of
estimation, which is the focal point of traditional regression analysis,
is not a concern. Once the values of equation (12.2) and the regres-
sion coefficients are given:
(12.3a) Y = a, + b6X1 + b2X2 + ... + b,Xq + 6,, where
(12.3b) a, = col(a, a, . . ., a),
(12.3c) 6, = col(61, 62, . . . , 6,), and
(12.3d) 61 + ±2 + *. . + 6. = 0,
and where bi is an error term defined to ensure equality for the
regression equation of the ith family. Notice in equation (12.3d)
that the sum of all values of 6i is zero. It can now be seen that the
vector of total family income is the sum of q + 2 components: the
first component is the constant term a; the last component is the
error term b6; the other q components are the independent variables.
Causation of G,, based on regression analysis
Traditional regression analysis emphasizes the causes of variation
in family income [Y]; it is not concerned with the cause of variation
in the inequality of family income [G,]. Nevertheless, when the
traditional regression analysis is done, it is possible to proceed
with an analysis of G, based on the technique developed in chapter
eleven for factor component analysis. This possibility is seen from
388 REGRESSION ANALYSIS
equation (12.3a), where the Y vector is the additive sum of q + 2
column vectors: that is, Y now has q + 2 components. In particu-
lar, equation (12.3d) shows that equation (11.9) is applicable.
Consequently the decomposition result obtained in equation (11.18)
can be applied.
The sign of the column vector biXi is the same as that of the
regression coefficient. The sign of the column vector a. is the same
as that of the regression constant. Therefore equation (12.3) can
be rewritten in two ways, depending upon whether a. is positive or
negative:
(12.4a) Y = a, + b1X' + b2X2 + .... + b,XP
- (cIZ' + c2Z2+ ... + cqZ) + B. when a, > 0, and
(12.4b) Y = b1X1 + b2X2 + ... + bpXp
- (a + CIZ + C2Z2+ ... + CZq) + 6,
when a, < 0,
where:
(12.4c) bi 2 °, (i = 1, 2, . ,p)
(12.4d) ei < O, (i = 1, 2, . ,q)
(12.4e) Y = col(Yi, Y2, . . , Yn) 2 0,
(12.4f) Xi= col(Xii, . x) > 0,
(12.4g) Z = col(Zi, Z2, ... , Zi) 2 0,
(12.4h) a,= col(a, a,..., a), and
(12.4i) 6,= col(61, 62, .. , 6,) where
(12.4j) 61+ 62 + ±+ . = O.
Use the notation M(X) to denote the mean of the column vector
X. Applying this notation to the column vectors of equations (12.4a)
and (12.4b) gives:
(12.5a) M(Y) = [a + b1M(XI) + b2M (X2) + ,.. + bpM(XP)]
- [cIM(Z') + c2M(Z2) + ... ± c'M(Zq)]
when a > 0,
REGRESSION ANALYSIS 389
(12.5b) M(Y) = [b,M(X1) + b2M(X2) + ... + b,M(XP)]
- Ea + ciM(ZI) + c2M(Z2) + ...
+ cqM(ZQ) when a < 0,
(12.5c) = | a I /M(Y),
(12.5d) = bjM(Xi)/M(Y), and (i = 1, 2, , p)
(12.5e) = ciM(Z) /M(Y) (i = 1, 2, , q)
For the case when a > 0 define:
(12.6a) U = col(Ul, U2, , Un)
q p
= Y + ciZi = a,+ biXi +
i=l i-1
by equation (12.4a),
(12.6b) U = Ui/n
i=l
= Y + CiZli + CZ2± + + CqZQ
=a + big, + b22 + ..+ bpXp, and
(12.6c) X,= YI/U.
For the case when a < 0 define:
(12.7a) U = col(Ul, U2, ... , Un)
= Y+a+cCZI+c2Z2±+ .. CZq
= bX1 + b2X2 + + b,XP,
(12.7b) U = E Ut/n
=Y+ a + C11 + C2Z2 + ..+ cqZ,
= b1X1 + b2X2 + + b± Xp, and
(12.7c) f = Y/U.
The definition of the column vector U corresponds to equations
(11.9c) and (11.9d). Its components, given by (Ul, U2, ... , U.),
are assumed to be arranged in a monotonically increasing order as
390 REGRESSION ANALYSIS
in expression (11.10):
(12.8) U1 < U2 < ... < U,.
All the pseudo Gini coefficients are defined relative to this ranking.
Respectively use the notation G(X) and G(X) to denote the Gini
coefficient and the pseudo Gini coefficient, and define:
(12.9a) G, G(Y),
(12.9b) G(a.) = 0,
(12.9c) G(biXi) = G(Xi) = Gi, (i = 1, 2, ... ,p)
(12.9d) G(ciZi) = G!; (i = 1, 2, . . ., q)
(12.10a) G, = G(Y),
(12.10b) 0(a,) = 0,
(12.10c) G(biXi) = 0Q, (i = 1, 2, ... , p)
(12.10d) G(ciZi) = GZ.; (i = 1, 2, . ,q)
(12.11a) R, =
(12.11b) 4= G/GtI (i =1, 2, ,p)
(12.11c) 4= G'/0i; and (i =1, 2, ...,q)
(12.12a) E = [(n + 1)/n](jibi +±j22 ... + jnan)/Y, where
(12.12b) ji = 2i/n(n + 1).
Notice in equations (12.9) and (12.10) that the Gini coefficient
and pseudo Gini coefficient for the column vector a, obviously
are zero. The Gini coefficient and pseudo Gini coefficient for the
column vector biXi obviously are the same as G(Xi); those for the
column vector ciZi, the same as G(Zi). Hence the regression con-
stant a and the regression coefficients bi and ci are not involved in
the foregoing definitions. They nevertheless are involved in the
definition of the relative shares in equation (12.5c). A direct ap-
plication of equation (11.18) leads to:
(12.13a) G. = (A+ - A- + E) /R,
where R, is defined as in equation (12.11) and where:
(12.13b) A+ = OftRGtx + OW2R + ... ± -RG
(12.13c) A = 0lzRGz + RzGz + ... + 4RG,z and
(12.13d) E = [(n + 1)/n](j51 + j1262 + ... + j.6.) Y.
REGRESSION ANALYSIS S91
Table 12.1. Numerical Example of Income Data
and Regression Terms
Nota- Family Family Family Family Family
Variable tion 1 2 5 4 5 Total Mean
Independent
variables Xl¾ 4 2 6 10 3 25 5
XI 0 2 1 3 9 15 3
zli 1 3 0 4 7 15 3
Net family
income Yi 5 10 15 30 40 100 20
Column
vectors
a= -2 a -2 -2 -2 -2 -2 -10 -2
bi = 2 b1xi' 8 4 12 20 6 50 10
b2 = 5 b,xl 0 10 5 15 45 75 15
cl = -1 clzl -1 -3 0 -4 -7 -15 -3
Estimated
net family
income Yi 5 9 15 29 42 - -
Error term ai 0 1 0 1 -2 0 0
Gross family
income Ui 8 15 17 36 49 125 25
- Not applicable.
Source: Constructed by the authors.
The terms in equations (12.13b) and (12.13c) were defined in
equations (12.5c) and (12.11); those in equation (12.13d), in
equations (12.6), (12.7), and (12.12).
Computation procedure
Table 12.1 gives for five families the family income EYi] and the
values of the three independent variables EX', X2, and Z']. From
this set of data a regression equation of the following form is esti-
mated:
(12.14a) Y = a + b1Xl + b2X2 + c1Z1', where
(12.14b) a = -2, b1 = 2, b2 = 5, c1 = -1.
392 REGRESSION ANALYSIS
Table 12.2. Distributive Shares, Gini Coefficients,
and Pseudo Gini Coefficients for Original Data in Table 12.1
ANota-
Variable tion a Xi X2 Z1 Y U
Net family income
weight [YC/U] -- 4/5
Distributive share in Y oi -2/20 1/2 3/4 -3/20 1/1
Gini coefficient Gi 0.0000 0.3040 0.5333 0.4533 0.3600 0.3296
Pseudo Gini coefficient St 0.0000 0.0960 0.5066 0.3467 0.3600 -
Relative correlation Ri 0.0000 0.3158 0.9499 0.7648 1.0000 -
- Not applicable.
Source: Calculated from table 12.1.
When the values of Xl, X2, and ZV in table 12.1 are substituted
into this equation, the column vectors a, b1xz, b2x2i, and c1x' are
obtained. The sum of those vectors is the estimated value of net
family income EY[J. The error term is the difference between Yi
and Yi. Notice that the sum of the vector 8 is zero. Notice also that
the vectors a and cix. are both negative. The sum of nonnegative
vectors-that is, b1xl., b2,x2, and ai-is shown in the row for gross
family income. The computation of pseudo Gini coefficients is car-
ried out relative to this ranking (table 12.2). Notice that when the
regression analysis is transformed into an income components
problem, it takes on exactly the same numerical value as shown in
table 11.2. Thus the decomposition analysis shown in table 12.3
merely is a repetition of that in table 11.3.
Remarks on chapter four
The analysis of inequality of family wage income in chapter four
was based on the decomposition equation (12.13a) In table 4.6 of
that chapter the regression coefficients a,, a2, as, and a4 are positive;
the regression constant ao is negative. This is a special case of equa-
tion (12.4b) in which the terms Z', Z2, .. ., Z" vanish. Equation
(12.7) reduces to the special case:
(12.15a) U =col (U1, U2, . . . , U,,)
= Y + a. = b1X, + b2X2 + b3X3 + b4X4 + 5,;
REGRESSION ANALYSIS 393
Table 12.3. Decomposition Analysis of Original Data in Table 12.1
Variable Computation Value
Rank-weighted
error term =/Y= (ji+i + J262 +
+ j5b6/Y
= (-4/15)/20 -1/75
Income effecta A+ = PR,Gl + VRl2G2 = 0.4279
Payment effectb A- = OiRiGl + OnRIG. = -0.0519
Decomposition
error0 E = (n + !)A/n = -0.0160
Decomposition
analysisd G, = A+ - A + E
= 0.4279 - 0.0519
- 0.0160 = 0.3600
Relative weight 1 = A+/G -A-I/G, + E/IG
= 1.1886 - 0.1446
+ (-0.0440) = 1.0000
Sources: Calculated from tables 12.1 and 12.2.
a. See equation (12.13b).
b. See equation (12.13c).
e. See equation (12.13d).
d. See equation (12.13a).
(12.15b) U1 < U2 < ... < U. implies that Y, < Y2 < ... < Yn
by expression (12.8);
(12.15c) R, = 1 as Gv = G, in equation (12.11a);
(12.1.5d) , = Y/U = Y/(Y + a) in equation (12.7).
Thus equation (12.13) reduces to the special case:
(12.16a) Gv = (1R1Gi + 02R2G2 + ... + 0,R,G, + E, where
(12.16b) E = ((n + 1)/n) (j161 + j262 + . . . + j.8)/YI.
Equation (12.16a) is the decomposition equation (4.3) in chapter
four. In that chapter 4i is defined in equation (4.11e), Gl in equa-
tion (4.5b), Ri in equation (4.13a), and E = A in equation (4.12a).
394 HOMOGENEOUS GROUPS
In equation (4.18a) W is defined as the sum of the nonnegative
components indicated on the right-hand side. Thus the decomposi-
tion equation (4.15) used in chapter four is the exact decomposition
equation (10.5) of chapter ten.
Family Income Inequality with Homogeneous Groups
In the analysis of family income distribution, one popular ap-
proach is to identify homogeneous groups of income recipients.
For example, the homogeneous groups in the urban sector may be
capitalist families, blue-collar labor families, white-collar labor
families, and civil servant families. For another example, the ho-
mogeneous groups in the rural sector may be landlord families,
owner-cultivator families, and tenant families. When such groupings
of families are accepted, the total family income of n families can
immediately be classified into q mutually exclusive groups:
(12.17a) Xi = col(Xi, X2, .. ., Xin); (i 1, 2, . . ., q)
(12.17b) ni + n2 + . . + n,, = n;
(12.17c) oi = ni/n; (i = 1, 2, ,q)
(12.17d) Si = X + X ... + X+ i; (i = 1, 2, ... ,q)
(12.17e) XS, = Sl + S2 + + S,;
(12.17f) Xi =Silni; (i = 1, 2, ... , q)
(12.17g) oi = Sls/v; (i = 1, 2, . ,q)
(12.17h) 01 + 02 + . . . + 0, = 1.
In equation (12.17c) 9i is the fraction of families in the ith group;
in equation (12.17g) Xs is the fraction of total income earned by the
ith group. The average income in the ith group is given by XS in
equation (12.17f). The value of Xi may be thought of as the income
earned by a typical member of the ith group. Equation (12.17a)
thus contains the primary data of this section.
Intuitive ideas associated with homogeneous groups
When a classification of families is given, the presumption is that
the characteristic of each grouping is decisive in affecting total
family income. More precisely two ideas are implied.
FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS 895
First, there is the presumption that the groups are ordinally
ranked by their income-earning potential. Thus the q groups will
be arranged so that:
(12.18) X1 < X2 < ... _
that is, typical incomes of the members of q groups are arranged in
monotonically increasing order. As a further illustration of this
point, suppose the n families to be cross-classified into six groups
by education and sex (table 12.4). The integers in the six cells in
this table indicate a particular ordinal ranking in which the lowly
educated female contributes least in determining family income and
the highly educated male contributes most. Altogether there are
720 (6!) possible ways to rank these cells ordinally. Ideally the
acceptance of a particular ordinal ranking is the result of theorizing
and constitutes a null hypothesis. In fact, the theorizing is informal,
and the empirical ranking obtained in equation (12.18) thus is
often taken to be indicative of the relative earning potential of the
various groups.
Second, such a group ordering, when given as in expression (12.18),
is decisive in two senses. One sense is that the variation of income
within each group-that is, the variation of family income within
each cell in table 12.4-should not be as great as the variation of
income between the groups. Therefore the notions of intragroup
and intergroup variation in incomes must be separated. The other
sense is that no member of a group should receive an income higher
than any member of a group with a higher ranking. When perversity
is observed, it is to be regarded as evidence contradicting the hypoth-
esis that groupings are decisive in affecting income. As an illustra-
tion of this idea, suppose in an apartheid society that the ordinal
Table 12.4. Numerical Example of the Classification
of Families by Education
Ordinal rank
Low Medium High
Sex education education education
Female 1 2 3
Male 4 5 6
Source: Constructed by the authors.
896 HOMOGENEOUS GROUPS
ranking of white and nonwhite groups may be so decisive that no
member of the nonwhite group receives an income higher than even
the poorest member of the white group. If perversity of order is
observed, the apartheid system will be regarded as incomplete. It
follows that to measure this decisiveness a "crossover effect" should
somehow be measured.
In summary, once family income is classified into homogeneous
groups as in equation (12.17), an intergroup variation [Gr], an intra-
group variation [A], and a crossover effect [C] should be defined.
Intergroup variation
The natural definition of Gr, the intergroup variation, is the Gini
coefficient for the following set of n numbers:
nl n2
(12.19a) R = COI(XI, XZ, . . . , X1; X2, X2, . . .X2;
n,,
***;X9, X,Z , XQ);
(12.19b) S,, = niXl + flX2 ± ... + n,,Xq.
Equation (12.19a) is constructed by replacing every XJ by the
mean of the group [iV] to which it belongs. It is apparent in this
set that there is no intragroup variation, because all families within
each group receive a typical income. If the groups indeed are ho-
mnogeneous and all members within each group cannot be distin-
guished from each other by their income, then equation (12.19a)
represents the income pattern of idealized homogeneous groups. To
define the Gini coefficient for this set, first define the following
numbers:
(12.20) Ci = ni + n2 + ... + ni; C, = 0. (i = 1, 2, ...,q)
where Ci is the cumulative number of families earning a typical
income less than or equal to Xi. The next theorem indicates the
method of computing the Gini coefficient for the pattern of idealized
homogeneous groups indicated by R in equation (12.19a):
THEOREM 12.1. Gr = G(R) = [01(Co + C1 - n)/n]
+ [E2(C1 + C2 - n)/n]
+ . .. *+ E,(C_j + Cq-n)/n]
FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS S97
Proof: Theorem 8.2 gives:
Gr = (Xi - X>) niny/S,n for i > j
= g1X1/Svn + g2X2/S,n + ... + ggXq/Sv,n, where
gi = [ -(Ci-(n - C)]ni.
The reason for this result is that Xi appears Ci-, times as the upper
end in the definition of income gaps and n - Ci times as the lower
end in the definition of income gaps. Thus:
G, = E (Ci_- + Ci - n)niXi/S,n = E (Ci- + Ci -n)i/n.
This completes the proof.
Intragroup variation and the crossover effect
In defining the intragroup variation [A] it is to be noted because
there are q groups that A is by nature a weighted average of the
intragroup variations of q groups. Therefore the intragroup varia-
tion can be heuristically defined as:
(12.21a) A = OlklGl + 02,2G2 + ... + 6q4,GQ, where
(12.21b) Gi = G(Xi). (i = 1, 2, . q. , q)
The intragroup effect [A] is defined to be the weighted average of
the Gini coefficients of the q groups, where the weights are the pro-
duct of the relative group size [Di] and the relative income share
[0.,] respectively defined in equations (12.17c) and (12.17g).
To define the crossover effect [C] it will first be assumed that
the incomes of families within each group are arranged in a mono-
tonically nondecreasing order:
(12.22) X1 < X2 < ... < Xn. (i = 1, 2, * *q)
Each of the n families so ordered will be assigned a natural ranking
(1, 2, . .. , n). In other words, each family will be assigned a lexico-
graphic ranking in the following way:
(12.23) The rank of Xt is Ci-1 + j (lexicographic rank).
(j = 1, 2, . ,ni)
(i = 1, 2, .. q)
398 HOMOGENEOUS GROUPS
This ranking can be illustrated by an example with seven families
and three groups:
(12.24a) (Xl = I < Xl = 3; X1 = I < X2 = 4 < Xs = 7;
X1 = 6 < X2 = 10);
(12.24b) (1, 2; 3, 4, 5; 6, 7);
(12.24c) X1 = 2 < X2 = 4 < X3 = 8.
Thus the families in each group are arranged in a monotonically
nondecreasing order, satisfying expression (12.22). Furthermore it
can be seen from expression (12.24c) that the group means are also
arranged in a monotonically nondecreasing order, thereby satisfying
equation (12.18). The ranks assigned according to expression (12.23)
are indicated in expression (12.24b). In order words, after the
families are arranged in a lexicographic order, expression (12.23)
simply is the first n integers arranged in the natural order. The
ranking may be referred to as a lexicographic ranking conforming
to the group decisiveness. The main idea is that members of the
first group are ranked first, those of the second group second, and
so on.
When the lexicographic ranking of expression (12.23) takes the
place of the characteristic rank [C] of equation (9.1) in chapter
nine, the Gini coefficient [G] of n families is the sum of two terms,
s+ and s-, according to equation (9.18a). In this case the s+ term is
the average of the gaps that support the lexicographic ordering;
the s- term is the average of the gaps that contradict the lexico-
graphic ordering. In the numerical example s- is calculated as
follows:
S- = [(X1- X) + (X3 - X1)]/(7 X 32)
- [(3 - 1) + (7 - 6)]/224 = 3/224.
Notice because of expression (12.23) that a term in s- can only
occur between two members belonging to different groups. Further-
more such a term exists when and only when a member of a lower
income group earns more income than a member of a higher income
group, thus perverting the lexicographic ranking. The s- term may
therefore be referred to as the crossover effect. Formally the cross-
FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS 399
over effect can be defined as:
(12.25) s- = E (Xl- Xi) for all X' > Xi with i < j.
Decomposition of G,
When the primary data on homogeneous groups are given as in
equation (12.17), the intergroup variation [Gr], the intragroup
variation [A], and the crossover effect Es-] can be defined. Now let
G, be the Gini coefficient for the n numbers X, in equation (12.17a).
The basic theorem to be proved is:
THEOREM 12.2. GV = G, + A + 2s-.
The theorem states that the Gini coefficient EG,] can be decom-
posed into an intergroup variation term EGr]J an intragroup varia-
tion term [A], and twice the crossover effect [2s]--.1 All these terms
are nonnegative. As a result, if homogeneous groups are postulated,
the Gini coefficient of all families, when approximated by intergroup
and intragroup effects, always leaves a nonnegative error 2s-]. The
magnitude of this error term is determined by the degree to which
group decisiveness is perverted.
Theorem 12.2 can be illustrated by the numerical example in
equation (12.24a) and tables 12.5 and 12.6, which classify the in-
come of seven families into three homogeneous groups. The means
of the three groups are arranged in a monotonically increasing order.
With the lexicographic ordering, the supporting and nonsupporting
gaps are shown by s+ and s-. The decomposition of G, according
to theorem 12.2 is given in the bottom row.
To prove theorem 12.2 all that is needed is to prove the following
lemma:
LEMMA 12.1. G s+ - s- = A + G,.
1. This three-way decomposition of the Gini coefficient to address the prob-
lem of homogeneous groups was first proved by Bhattacharya and Mahalanobis.
It was rediscovered by Rao and reinterpreted, with simplified proofs, by Pyatt.
Mangahas presented a two-way decomposition corresponding to intragroup and
intergroup effects alone. In chapter five we worked with the variance, not the
Gini coefficient, primarily because of the simplification caused by the disap-
pearance of the GI term for the particular problems tackled there. For the sources
of studies mentioned here see note 1 to the introduction of part two.
400 HOMOGENEOIUS GROUPS
Table 12.5. Numerical Example of the Classification
of Seven Families into Three Homogeneous Groups
Nota- Group I Group 8 Group s
Variable tion [xI] [z2] [XI] Total
Family income x, 1,3 1,4,7 6,10 -
Group frequency ni 2 3 2 7
Group income xi 4 12 16 32
Mean of group income xi 2 4 8 7/32
Relative group frequency Oi 2/7 3/7 2/7 -
Group income share Oi 1/8 3/8 4/8 -
Group Gini coefficient G1 1/4 1/3 1/8 -
- Not applicable.
Source: Constructed by the authors.
By using equation (9.15a) in addition to lemma 12.1, theorem 12.2
can be immediately derived. To prove this lemma, the Gini coeffi-
cients for every one of the q homogeneous groups are defined as:
(12.26a) Gi = G(Xi) = G(X' < X2 < ... < Xn_ )
= (2/ni)ui - (ni + 1)/ni, where (i = 1, 2, ..., q)
(12.26b) ui = (1) (X /Si) + (2) (X'/Si) + ... + (ni) (Xni/Si)
by theorem 8.1.
The pseudo Gini coefficient (G0) takes on the following form:
(12.27a) G, = (2/n) - (n + 1)/n, where
(12.27b) 4t = OIUI + 102U2 + ... + OqUq + C102 + C203 + ...
+ Cq1i4q,
where Ci is defined as in equation (12.20).
q n;
Proof: By theorem 8.3 and letting S, = E X,:
i-I j-I
FAMILY INCOME INEQUALITY WITH HOMOGENEOUS GROUPS 401
Table 12.6. Decomposition Analysis of Data in Table 12.5
Variable Computation Value
Intergroup
variation G, = (Xi- Xj)n,nj/Svn
= (4 - 2)(2)(3) + (8 - 2)(2)(2)
+ (8 - 4)(2)(3) = 230/112
Intragroup
variation A = aiGi = (2/7)(1/8)(1/4)
+ (3/7) (3/8) (1/3)
± (2/7)(4/8)(1/8) = 9/112
Crossover effect s- = (X' - X') + (X' - XI)/(32)(7) = 3/224
Supporting gap s+ = (2+12+4+3+6+1+4+5+9
+3+7+5+9+2+6+3)/
(32)(7)= 81/224
Pseudo Gini
coefficient G= A + G, = S+-S-
= 30/112 + 9/112
= 81/224 - 3/224 = 39/112
Gini coefficient G, = S+ + S- = 81/224
± 3/224 = 84/224 = 21/56
Decomposition of
Gini coefficient Gv = A + G, + 2S-
= 9/112 + 30/112
+ 3/224 = 84/224 = 21/56
Source: Calculated from table 12.5.
ews n2 n,
UV = ,, iXi/Sy± + (C1 i)X2il/S + .+ . + X (Cq-_+i)Xy/&
i=l ~i-I i-I
>;l n2
= , i(X'/S1)01 + E (C1 + i) (X2%/S2) 2 + *
i=l ~~~~i=l
nq
+ X (Cq-i + i) (X./Sq)oq
i=l
- lU± + 02U2+ .+ . + 0Uq + C12 + C243 + ... ±Cq-ic0.
This completes the proof of equation (12.27b).
402 HOMOGENEOUS GROUPS
Substituting equation (12.27b) into equation (12.27a) gives:
2
G, ( (flul + ± 2U2 + ..+ quq)
2
+ - (C1I2 + C203 + ... + Cq,q5q) - (n + 1)/n
Oini [2 Xu_nl + 11 02r2 [ 2-n2 + 1
n ni ni j n Ln2 n2
+ + [ nq2 11 2 X + ]]
n n n n
+ 1 2 + . + n]
+[1n n ...n
_ 01 I + ,n + .+ ,,n
n n n
2
+ - [(Cl0,2 + C203 +. + Cqi4)q)]
n
=1A1G, + .22G 2 . + Oq9qGq + B, where
B n n n2-n n2 + 2C,-n n3 + 2C2-n
n n n
+n, + 2C,- - n
n
± n+(n, - n) + 02(C, + C2 - n) + 03(C2 + C3 - n) +
+ 4)q(Cq-_i + Cq -n)]/n
- Gr by equation (12.26).
Hence:
0, = A + G, by equation (12.21).
This completes the proof of lemma 12.1, which also proves theorem
12.2.
GINI ERROR ARISING FROM THE USE OF GROUPED DATA 403
Gini Error Arising from the Use of Grouped Data
One important problem relevant to the analysis in this volume was
first brought to our attention by Professor Orcutt. As an illustration
of that problem, which is associated with the use of grouped data on
the distribution of family income, assume that an income survey has
been conducted for ten families and that the results are processed
as follows:
(12.28a) (4, 10, 14, 5, 12, 15, 6, 14, 16, 4)
[survey returns]
(12.28b) (4, 4, 5, 6, 10, 12, 14, 14, 15, 16)
[ordered tabulation of primary data]
(12.28c) [(4), (4, 5, 6), (10, 12, 14), (14, 15, 16)]
[partitioned primary data]
(12.28d)
Faamily group
Variable 1 2 3 4
Number
of
families 1 3 3 3
Total
income 4 15 36 45
Mean
income 4 5 12 15
[published frequency distribution]
(12.28e) [(4), (5, 5, 5), (12, 12, 12), (15, 15, 15)]
[grouped data]
The survey returns are first ordered into a tabulation: that is, they
are computerized. Next some partitioning of the ordered tabulation is
selected. In the example here the ten families are classified into four
404 AGGREGATION ERROR
groups according to total income rank. In actual practice a decile
partition is often chosen to enable international comparisons. Then a
frequency distribution is computed. The frequency distribution
presented here indicates the number of families, total income, and
average income for each family group. In reality the number of
families usually is very large, and the final tabulation of the frequency
distribution is the only practical way in which data can be published
and made available to the general user.
When the original survey returns (12.28a) are processed into a
frequency distribution, all intragroup variations are suppressed.
Published data almost always suppress intragroup variations when
the sample size is large. One method a researcher can use to recover
part of the suppressed information for empirical work is by interpola-
tion-that is, by guessing or speculating about the intragroup
variations with the aid of additional assumptions.2 An ideal method,
which we strongly advocate, obviously is to work with primary
data-something which is becoming increasingly feasible in this age
of computerization, but which was not possible for us.3 The purpose
in this section, however, is to investigate the seriousness of this
suppression when the published frequency distribution is used to
calculate the Gini coefficient.
The problem is not serious when grouped data are used for the
computation of mean income. In grouped data every member
belonging to the same group is interpreted as having the same income
as the mean income of the group; those mean values essentially
replace the primary data.4 Suppose the incomes within each group to
be randomly distributed around the group mean. Then the average
income computed from grouped data will not differ much from the
true mean of the primary data. But if grouped data are used to
2. Joseph L. Gastwirth, "The Estimation of the Lorenz Curve and Gini
Index," The Review of Economics and Statistics, vol. 54, no. 3 (August 1972),
pp. 306-16.
3. This method is especially advocated for any future research that involves
the multidimensional cross-listing of data. Our work in chapter four has shown
that the most serious deficiency of published data is the absence of cross-listing,
not the suppression of intragroup variation. Consequently this section, as well as
the interpolation method, may some day have only historical interest in the
analysis of the distribution of family income.
4. This obviously is the only interpretation when the original survey data
are not available and interpolations are not used.
GROUPING ERROR IN THE ANALYSIS OF ADDITIVE COMPONENTS 405
compute the Gini coefficient, or for that matter any reasonable index
of inequality, there will always be an underestimation of the degree of
inequality. In the numerical example the true Gini coefficient
computed from primary data is:
(12.29a) G7 = 0.256;
the Gini coefficient computed from grouped data is:
(12.29b) G, = 0.240.
Thus G, underestimates GT by 0.016. By comparing the grouped
data and primary data it is seen that GQ, when computed from
grouped data, captures only the intergroup effect of G'. Because the
grouped data represent a consecutive partitioning of a monotonically
increasing vector, there is no crossover effect in this case. Equation
(12.21a) can be used to compute the intragroup effect in the numerical
example as follows:
(12.30a) 01 = 0.1, 02 = 0.3, Os = 0.3, 04 = 0.3;
(12.30b) (A = 0.04, 02 = 0.15, 03 = 0.36, 4= 0.45;
(12.30c) GI = 0, G2 = 4/45, G3 = 2/27, G4 = 4/135;
(12.30d) A = (0.1) (0.04)0 + (0.3) (0.15) (4/45)
± (0.3) (0.36) (2/27) + (0.03) (0.45) (4/135)
= 0.016.
That value of A is exactly the amount of underestimation. Thus,
when grouped data are used, there always is a systematic downward
bias in the estimation of the true degree of inequality.
Grouping Error in the Analysis
of Additive Factor Components
When the pattern of total income has factor components, the use
of grouped data presents additional problems, which can be illustrated
by the numerical example in table 12.7. The total income [Yi],
wage income [Wi], and property income [Eri] of six families con-
stitute the primary ungrouped data for this example. Notice that Yi
is the sum of Wi and 1ri. Furthermore, as in the tabulation discussed
at the beginning of the preceding section, the primary ungrouped
406 AGGREGATION ERROR
Table 12.7. Numerical Example of the Factor Gini Error
in Grouped Data
Primary ungrouped data Wage income pattern in
(f = 1)a published data
Total
family Wage Property
Family income income income f = 2 f = 3 f = 6
1 Y1 = 12 10= w1 2 = 7r, 8 25.3 19.2
2 Y2 = 14 6 = w2 8= r2 8 25.3 19.2
3 Y3= 64 60= w3 4= r3 30 25.3 19.2
4 Y4= 70 0 = W4 70 = T4 30 13.3 19.2
5 Y6 = 80 0 = w5 80 = 7r5 20 13.3 19.2
6 Ye = 100 40 = W6 60 = r6 20 13.3 19.2
Source: Constructed by the authors.
a. The symbol f stands for the number of families in each income class.
b. Of the type used for the model of additive factor components in this volume.
data for the six families are ranked according to total income:
Y1 < Y2 < Y3 < Y4 < Y5 < Y6. As a result, the primary data on
wage income [Wj] and property income [ri] are not monotonically
ranked. If the primary data are available, the values of Wi can be
monotonically ranked, as in table 12.7, and used to compute the true
wage Gini [GT(W)]. The same holds for the values of ri.
The published data available to the general reader do not,
however, include the primary ungrouped data. According to the
standard practice of data publication, some integer f is always chosen
so that primary data are consecutively partitioned into classes of
families and that f families are included in each income class. In the
example here, f is a divisor of 6: f = 1, f = 2, f = 3, and f = 6.
The primary data on wage income in table 12.7 correspond to the
case f = 1. The cases f = 2, f = 3, and f = 6 correspond to different
levels of aggregation of wage income patterns and are also given in
table 12.7. Notice the difference between patterns based on published
data, which are monotonically ordered by total income rank, and
those based on primary data, which are monotonically ordered by
GROUPING ERROR IN THE ANALYSIS OF ADDITIVE COMPONENTS 407
Wage income patterns based Property income pattern
on original unpublished based on original
data and ranked by Published grouped datab unpublished data and
wage rank (f = 2) ranked by property rank
Prop-
Total Wage erty
f = 1 f = 2 f = 3 f = 6 income income income f = I f = 2 f = 3 f = 6
0 0 2.0 19.2 13 8 5 2 3 4.6 37.3
0 0 2.0 19.2 13 8 5 4 3 4.6 37.3
6 8 2.0 19.2 67 30 37 8 34 4.6 37.3
10 8 36.6 19.2 67 30 37 60 34 70.0 37.3
40 50 36.6 19.2 90 20 70 70 75 70.0 37.3
60 50 36.6 19.2 90 20 70 80 75 70.0 37.3
wage income rank. At each level of aggregation the group mean
replaces the income of a particular family.
The numerical example's published data on total income [Yi],
wage income EWiJ, and property income [?ri] are grouped for f = 2
in table 12.7. Notice that total income is the sum of wage income and
property income. In other words, the published grouped data satisfy
the basic requirement of the additive factor-components problem:
Yi = Wi + 1ri. The published data in this grouped form customarily
are available only for a limited number of values of f-usually for 15
to 25 family groups. In the early chapters of this book, such as
chapter three, the decomposition analysis is based on the use of
grouped data in this form: following the decile convention, the value
of f is equal to the total number of families divided by ten. Thus,
when primary ungrouped data are not available on tape, researchers
must use grouped data at a particular level of aggregation correspond-
ing to a particular value of f.
The true wage Gini and the pseudo wage Gini can be computed
from the primary data in table 12.7: G,(W) = 0.61; Gt(W) = 0.09.
Based on different levels of aggregation, a set of wage Ginis [G (W, f)]
and a set of pseudo wage Ginis [E(W, f)] can also be computed.
Notice that G,(W) = G(W, 1) and L,(W) = G(W, 1) . In figure 12.1
408 AGGREGATION ERROR
Figure 12.1. Behavior of Indexes of Inequality under Different Levels
of Aggregation
0.8 G(W,1) = 0.61
0.7 - G(W,2). = 0.58
0.6 A A
0.5- (W,s). = 0.41
0.4 _ -G(W,2) = 0.25
0.2 _G(W,1) = 0.09 - G(W,S) = 0.14
0.1- B - ____B
1 4 - --
-0.1 __ /5 6
-0.2- G(W,2) = 0.14 4
-0.3 _ d(wa) = -o_i G(W,6) = G(W,6) 0
-0.4
True wage Gini a- a'
True pseudo wage Gini b- b'
- Wage Gini for wage pattern ranked by total income rank
- - -Pseudo wage Gini for wage pattern ranked by total income rank
--------Wage Gini for wage pattern ranked by wage rank
Source: Calculated from table 12.7.
the values of the true wage Gini [G( W, 1) ] and the true pseudo wage
Gini EG(W, 1)] are respectively indicated by the horizontal lines
aa' and bb'. The values of the wage Ginis at different levels of
aggregation are: G(W, 2) = 0.25; G(W, 3) = 0.14; and G(W, 6) = 0.
The corresponding values of the pseudo wage Ginis are: G(W, 2) =
0.14; G(W, 3) = -0.17; and G(W, 6) = 0. As the data become more
aggregated-that is, as the values of f become higher-G(W, f)
decreases. Thus G(W, f) implies an increasing underestimation of the
true wage Gini as f increases from one. That underestimation is
indicated by the vertical gap, G,(W, 1) - G(W, f), between the
solid curve and the horizontal line aa'. Notice that the pseudo Gini
[EG(W, f) ] behaves more erratically as f increases.
When the wage pattern is monotonically ranked, a different set of
wage Ginis can be computed: G(W, 1)" = 0.61; G(W, 2)m = 0.58;
G(W, 3)m = 0.41; and G(W, 6),,, = 0. These values are indicated in
figure 12.1. Notice in this monotonic case that the underestimation of
GROUPING ERROR IN THE ANALYSIS OF ADDITIVE COMPONENTS 409
the true wage Gini represents the intragroup effect discussed in
conjunction with equations (12.29) and (12.30) .
By comparing the two error terms, it can be seen that G(W, 1) -
O(W, f)m generally is smaller than G(W, 1) - G(W, f) for every f.
The reason is that the wage patterns associated with the second
error are not monotonically ranked. Thus, in addition to the intra-
group effect, there are other sources of underestimation. It should
now be clear that two distinct problems, both associated with the
Gini error, arise from the use of grouped data.
The first problem is related to the size of the Gini error when the
income pattern is monotonically arranged. It has been shown that
this error [G(W, 1) - G(W, f)m] corresponds to the intragroup
effect, which can be calculated when the primary ungrouped data are
available.6 When the primary data are not available, this error can be
estimated by an interpolation method which has already been
developed.7
The second problem is conceptually more complicated. It is
associated with the Gini error [G(W, 1) - G(W, f) ] when a factor
income component is not monotonically ranked. Our discussion
should have made it clear that this constitutes a special problem
which arises when the grouped data are used for the analysis of
additive factor components-that is, when the arrangement of factor
incomes is by total income rank and for this reason is not monotonic.
For this new problem the Gini error is larger than the intragroup
effect, but its precise nature remains to be investigated from a
5. Exchanges with Graham Pyatt of the World Bank indicate that two addi-
tional words of clarification may help to avoid further confusion. First, if only
published grouped data are available, as often is the case, the values of G (W, f)m>
cannot be computed. Second, G(W, f)m is irrelevant to the additive factor-
components method of Gini decomposition. This is true despite the fact that
G(W, f)m is a better approximation of the true wage Gini than is G(W, f) for
each value of f. The reason is that the patterns of wage and property income
must add up to the pattern of total income, as is illustrated by the published
data in table 12.7, if this method is to be applied. But when wage and property
income respectively are monotonically ranked according to wage and property
rank, the patterns of factor income do not add up to the pattern of total income.
6. Of course, it is preferable to use primary data, when available, and thus
avoid this error. The interpretation of this error nevertheless is conceptually
important.
7. See Gastwirth, "The Estimation of the Lorenz Curve and Gini Index."
410 AGGREGATION ERROR
theoretical standpoint.8 Thus the intrinsic interpretation of the error
term, as a property of the primary ungrouped data, remains to be
studied. Furthermore no method has yet been developed, at least to
our knowledge, to estimate upper and lower bounds of this error when
primary data are not available-that is, a method cormparable to the
interpolation method for the simple case when the income pattern is
monotonically arranged.
This second problem is serious for all users who must rely, as we
have in this volume, on published grouped data to implement the
additive factor-components approach. Future research can be expected
to proceed along three fronts: theoretical research on the nature
of the Gini error as a property of ungrouped data; empirical research
using ungrouped data to determine the seriousness of underestimation
associated with each level of aggregation9; the design of interpolation
methods when primary data are not available. The empirical results
in this volume will no doubt require reassessment as further work in
these areas comes to fruition.
8. For certain special cases it can be shown that the Gini error has two com-
ponents: an intragroup effect and a crossover effect. See theorem 12.2.
9. The purpose of that research ultimately is to determine safe levels of ag-
gregation Ef] so that the error falls within tolerable limits.
Index
Additive expenditure components, 264, of, 57, 95n, 128; and reallocation
291. See also Consumption expendi- effect, 18, 113-16; and rural by-
ture; Direct tax payments; Educa- employment, 114, 249-51, 315; as
tion; Food and clothing expenditure; type one or type two income, 74, 89,
Housing expenditure; Indirect tax 94-95, 98, 104
payments; Savings Agriculture, 3; in colonial Taiwan, 22,
Additive factor components. See Addi- 24-26; diversification of, 47; em-
tive factor income components pirical findings and policy conclu-
Additive factor components model, 7, sions for, 312-17; fixed capital in, 48;
18, 19, 133, 324, 373, 376-78; data and industry, 24-26, 27, 37; infra-
requirements of, 10; and earnings- structure in, 45-46; labor force in,
function technique, 139; and linear 31, 113, 114; and nonagricultural
regression equations, 203, 211, 214- income, 115; population in, 46; in
15, 326, 386-94. See also Decomposi- postcolonial Taiwan, 28, 31, 46-50;
tion formulas production in, 225, 226. See also
Additive factor Gini decomposition, 18. Agricultural income; Farm families;
See also Decomposition formulas Land reform; Rural households;
Additive factor income components, Rural family income; Rural industry
7-8, 73n, 224, 291; and decomposi- Agricultural production. See Agri-
tion formulas, 14, 326, 351-57; and culture
grouped data, 14; grouping error, All households, 87, 90, 94-95, 98, 99,
405-10; and growth theory, 376-78 100, 102-04, 128, 312; Gini coeffi-
Adelman, Irma, 2, 35 cient for, 99, 100, 108-12. See also
Age, as labor attribute, 130, 132-37, Rural households; Urban households
142-43, 145, 317, 320; and analytical Analysis, methods of, 17-20
cross-listing of data, 200; and wage- Approximation: equation, 83; of factor
rate inequality, 161, 164-66, 170, components, 367-69; methods of,
171, 175-76, 179-80. See also Family 326, 367-72
attributes Assets, 6-7; capital, 5; distribution of,
Agricultural income, 12, 49, 54, 56, 74, 41-44, 50-53; human, 6-7, 225; in-
87, 90; distributive share of, 57, 88, dustrial, 37; labor, 6-7; physical,
98, 113-16; empirical findings and 6-7, 225; structure of, 89
policy conclusions for, 314-15; as Atkinson, Anthony B., 15n, 325n
factor component, 7; and FID, 98, Atkinson index, 6
104, 126; factor Gini effect and, 18, Attributes. See Family attributes;
88, 102, 103, 106, 127; Gini coefficient Labor attributes
411
412 INDEX
Average contradicting gap, 342-46 Consumer price index (cPi), 34n
Average supporting gap, 342-46 Consumption expenditure, 267, 269-
70, 273-76, 278
Consumption goods, imports of, 53
Consumption structures, 264-65, 267
399n t Consumption taxes, 19. See also Taxes,
399n . ~~~~~~~taxation
Bias of innovation. See Labor-usin taxtio
bias of innovation g Contradicting gap, average, 342-46
hris of i o Council on U.S. Aid, 51n
Bureauil 65BdeadSaisis9 Credit cooperatives, rural, 22-23, 45
Bureau of Budget and Statistics, 194 Crossover effect, 386, 398-99
By-employment, rural, 114, 249-Si, Cyclical noise, 34n
Dalton, Hugh, ln
Cannan, Edwin, ln Data: analytical cross-listing of, 199-
Capital: control of, 25; as factor income 201, 202, 203; computerized, 14;
component, 83; fixed, 48; foreign, 28, DGBAS, 10-13, 54, 56, 65n, 90, 113,
45, 311; working, 48. See also Capi- 115, 131n, 193n, 194n, 234, 255n,
tal-labor ratio; Industrial assets 267-72, 294; on family expenditure,
Capital accumulation, 85n 267-72, 290; grouped, 14, 403-10;
Capital assets, 5 interpretation of, 14-15; primary,
Capital deepening, 84-85, 86, 108, 11-12, 194, 199-201, 202, 403-10;
120, 317 published, 11-12, 13, 131n, 404-10,
Capital goods, imports of, 53 409n; quality of, 11-13, 65n; scarcity
Capital intensity, 52, 118n, 119 of, 54, 69; and underestimation of
Capital-labor ratio, 84, 86-87, 11i8n Gini coefficient, 65n; ungrouped, 14,
Chang, Kowie, iOn, 38n-39n, 54n 403-10; unpublished, 131n, 403-10
Characteristic ranks, 340-42 Data aggregation, 13-14. See also
Chen Chao-Chen, 38n Grouping error
Chenery, Hollis, 112n Decile groups, 13, 65n, 90n
Cheng Chen, 40n Decomposition analysis, 11, 69, 126,
China, mainland, 26 211n, 291, 325. See also Decomposi-
Classical economists, 1, 4 tion formulas; Gini coefficient analy-
Cline, William R., 128n sis; Gini coefficient(s)
Coefficient of variation, 6 Decomposition formulas, 8, 14, 17, 73,
Colonial infrastructure, 37 74, 75, 79, 89, 100, 132, 146, 159; and
Colonial Taiwan, 21-26, 37, 316 additive factor income components,
Commercialization, 84, 86. See also In- 14, 326, 351-67; derivation of, 325-
dustry, industrialization; Modern- 26, 351-72; exact computation pro-
ization cedure for, 359-60; of family income
Commodity tax, 265 after tax, 270-79; for homogeneous
Computerized data, 14 groups, 9, 327, 394-402; of income in-
Consolidation error, 11 equality, 73, 75-83; and linear
Consolidation issue, 13. See also model, 326, 363-65, 373, 374; and
Grouping error monotonic model, 326, 365-66, 373,
Conspicuous consumption, 266, 269, 375-76; sectoral, 226-31; for house-
271, 276 holds, 87
Consumer behavior, 275, 291 Deficit financing, 26
INDEX 413
Degree of overestimation, 77-78, 97 181, 183, 184-91, 200, 317, 318-19,
Demographic factors, and FID, 249-63 320-21. See also Family attributes
Dependency theorists, 128 Elasticity of substitution, 84
Descending homogeneous case, 183, Employment. See By-employment;
190-92 Labor; Labor force; Underemploy-
Deterministic theory, 20, 291-92 ment; Unemployment
Development theory, 3, 7, 18, 84, Error of estimation, 77-78
323-24 Error, nonlinearity, 83, 98, 99
DGBAS. See Directorate-General of Bud- Error term, 97, 211n; rank-weighted,
get, Accounting, and Statistics 146, 161
Diaz-Alejandro, Carlos F., 53n Estimator Gini coefficient, 77, 79
Direct tax burden, 264, 265, 267, 269, Europe, Western, 4
271, 279, 283-89, 290 Exact decomposition computation pro-
Direct taxes, taxation, 19, 279, 286, cedure, 359-60
287, 290, 322-23. See also Taxes, Exchange rates, 27, 29
taxation Expenditure. See Consumption ex-
Directorate-General of Budget, Ac- penditure; Family expenditure;
counting, and Statistics (DGBAS): Housing expenditure
data of, 10-13, 54, 56, 65n, 90, 113, Export-led industrial expansion, 29
115, 131n, 193n, 194, 234, 255n, 267- Export ratio, 31
72, 294 Exports, 30-31, 32, 53
Disaggregate analysis, 5 Export substitution. See Primary ex-
Discrimination. See Wage-rate in- port substitution; Secondary export
equality substitution
Distributive shares, 54n, 75, 77, 87-88;
of agricultural income, 57, 88, 98,
113-16; of factor income compo-
nents, 75, 83-84; of nonagricultural Factor Gini coefficients, 8, 72, 82,
income, 66-67, 88; of property in- 83, 357-59; and factor Gini effect,
come, 87, 88; of wage income, 84, 120-26; of property income, 82,
86, 87, 88 120-26; of wage income, 82, 120-26;
Distributive weights. See Distributive weighted, 77
shares Factor Gini curves, 98
Diversification index, 50 Factor Gini effect, 18, 74, 83, 313; and
Domestic markets, 28-29 agricultural income, 18, 88, 102, 103,
106, 127; and FID, 86-87, 126-29; and
factor Gini coefficients, 120-26; and
Earnings-function technique, 138-39, Gini coefficients, 99-100, 102, 105,
214-15 106, 107, 108; and nonagricultural
Economic Planning Council, 48n, 54, income, 125-26, 127; and property
64n, 199, 294n income, 18
Economic policies, development of, and Factor income components, 4-5, 7, 17,
Taiwan findings, 308-24 54, 75; distributive shares of, 75, 83,
Education, 309-10; of family head, and 84; Gini coefficient of, 55, 56-57, 80-
FID, 240-43; family expenditure for, 81; and growth and FID, 72-129; in-
19, 264, 265, 267-68, 273, 276-78; dex of inequality of, 72, 74; labor
government expenditure for, 290; as and capital as, 83; linear approxima-
labor attribute, 130, 132-37, 139, tion of, 367-69; negative, 326, 380-
142-43, 145, 161, 162, 163-65, 170, 83; with observation error, 326, 378-
414 INDEX
80; and total income inequality, 73; and family ownership, 18; rules of,
rank index of, 77; types of, 72-73 140. See also Family size and com-
Factor income distribution, 89 position
Factor income inequality, 75-83 Family grouping, 55n
Factor income pattern, 98n Family head, attributes of, and sectoral
Factor-price ratio, 118n decomposition equation, 235, 240-43
Factor prices, 1, 4, 30 Family income. See Family distribution
Factor shares, 1, 4, 90 of income; Family wage income; Net
Family affiliation, 130, 139. See also family income; Property income;
Family attributes Total family income; Wage income
Family attributes: and inequality of Family income inequality: empirical
family income, 19, 224-26, 255; and findings and policy conclusions for,
sectoral decomposition equation, 312-17; and savings and consump-
231, 235-40. See also Age; Education; tion, 265; and taxation, 266, 267,
Sex 279-89, 321-23. See also Family dis-
Family consumption patterns, 19. See tribution of income
also Consumption expenditure; Family income structure, 264-65
Family expenditure Family influence, 318, 319. See also
Family distribution of income (FID), Family affiliation
1-3, 4, 5, 6, 34-35, 100-01, 312; and Family investment in physical and
demographic factors, 249-63; as human resources, 265, 267, 268, 270,
descriptive device, 1; and DGBAS 271, 276-78
data, 90-99; and education of family Family lineage, lln
head, 240-43; empirical findings and Family size and composition: and total
policy conclusions for, 310, 312, 314, wage income, 131; and wage-rate in-
315, 316, 317; and factor Gini effect, equality, 180-93, 226, 249, 254-56
86-87, 126-29; and factor income Family type, 201, 203
components, 72-129; and functional Family savings. See Savings
distribution effect, 18, 86, 98, 99-100, Family wage income, 4-5, 130-223; and
103, 106, 107, 108, 116-20, 126-29, differentiation of labor force, 130-38,
313-14, 316-17, and functional dis- 141-46; empirical findings and policy
tribution of income, 67, 89, 312; conclusions for, 317-21; and family
growth and, 7, 17, 18, 72-129; and affiliation, 130, 139; and family form-
land reform, 38, 44, 50; overall, 65- ation, 130, 139, 168-93, 224-26; and
71; and primary import substitution, industrialization, 130; sectoral and
38, 71, 84, 310-11, 317; and realloca- locational dimensions of, 224-63. See
tion effect, 88-89, 99-100, 103, 105, also Wage income
108, 126-29, 313-15; rural, 12-13, Family-weight effect, 225, 231, 243,
54-64, 66, 110, 114, 128, 312; sectoral 245, 247
and locational dimensions of, 224- Family welfare, 265, 289-91
63; and taxation, 19, 272-78, 279-89; Farm sector, 233-34, 245-46. See also
urban, 12-13, 64-65, 107-08, 110, Agriculture; Rural industry
127-28, 312, 313, 314, 316. See also Farmers' associations, 22, 23, 39, 45,
Net income, Property income; Total 253
family income; Wage income Farm families, 19; changing size and
Family expenditure, 19, 264, 267-307 composition of, 254-56; DGBAs defini-
Family farm size, 54, 55n tion of, 201-02; distribution in
Family formation, 309; and distribu- colonial Taiwan, 23; income gap be-
tion of wage income, 131, 168-93; tween nonfarm families and, 225,
INDEX 415
243, 245, 254; reduction in tax bur- technique for, 126, 325, 342-43; and
den of, 253-54; rise of nonfarm factor Gini effect, 99-100, 102, 105,
income of, 112-16; and rural by- 106, 107, 108; of factor income com-
employment, 249-51; and sectoral ponents, 55, 56-57, 80-81; graphic
decomposition formula, 227-31. See summary of, 346-48; and homogen-
also Rural households eous group decomposition, 227n
Farm rents, 39-40 under linear transformation, 361-63;
Farm size and multiple cropping, 56 of nonagricultural income, 88; pat-
Fei, John C. H., 3n, 73n, 84n, 85n, 99n, tern of, over time, 108-09; of prop-
109n erty income, 98, 119, 120-26; for
Female(s); heads of households, 235; rural households, 99, 101, 108-12,
and wage-rate inequality, 131, 136, 120; sectoral, 109-12, 121; semiurban,
143, 145, 161-62, 166, 170, 171, 175; 112; after tax, 279; before tax, 279;
workers, 134-35 and time patterns, 123; of total in-
FID. See Family distribution of income come, 54n, 55-56, 72, 81, 98, 100,
First-stage import substitution. See 103, 108, 109; underestimation of,
Primary import substitution 65n; for urban households, 64-65,
Fixed capital, 48 99, 101, 108-12; of wage income,
Food and clothing expenditure, 264, 64-65, 98, 119, 120-26
273. See also Consumption ex- Government expenditure on health,
penditure education, and family welfare, 289-
Food processing industry, 37 90, 322n
Foreign aid, U.S., 28, 45, 311 Gross domestic product (GDP), 43
Foreign capital, 28, 45, 311 Gross national product (GNP), 99, 289
Foreign trade, 17 Grouped data, 14. See also Grouping
Functional distribution effect, 18, 74, error
83, 85, 88, 313; and FID equity, 86, Grouping error, 326-27, 386, 403-10
98, 99-100, 103, 106, 107, 108, 116- Growth path, labor-intensive, 67, 127,
20, 126-29, 313-14, 316-17; and 249-51, 309, 310. See also Labor-
property income, 313, 316; and urban using bias of innovation
households, 107-08, 313-14, 316-17 Growth theory, 89, 120, 376-78
Functional distribution of income, 1,
12, 44, 67, 89, 127, 312
Functional specialization, 57
Handicraft sector, 25, 115
Hayami, Yujiro, 49n
Gastwirth, Joseph L., 14, 404n, 409n Head of household, characteristics. See
Gini coefficient analysis, methodology, Family head
325-410 Health, government expenditure on,
Gini coefficient(s), 6, 8, 12-15, 18, 35- 290, 322n
36, 37, 54n, 65, 69, 82; additive fac- Hicks, John R., 84n
tor property of, 8; of agricultural Hicksian labor-using bias of innova-
income, 57, 95n, 120-26; for all tion, 84, 85, 86, 108, 120, 253, 317
households, 99, 100, 108-12; al- Hidden taxes, 253, 290n
ternative definitions of, 326, 328-34; Historical perspective, 3-4
as average fractional gap, 331-34; Ho, Samuel P. S., 22n, 38n, 41n, 43n,
causative factors of changes in, 99- 45n, 50n, 51n
116; comparative magnitudes of total Homogeneous case, descending, 183,
and sectoral, 109-12; decomposition 190-92
416 INDEX
Homogeneous group decomposition, 9, Industry, 28, 110, 226; and agriculture,
327, 394-402; and Gini coefficient, 24-26, 27, 37; and changes in income
227n inequality, 243-49; in colonial
Homogeneous labor groups, 150-55 Taiwan, 24-26, 37; decentralized,
Household surveys. See All households; 112, 249, 315-16, 317; and differen-
Data; Rural households; Semiurban tiation of labor force, 130-31, 177;
households; Urban households and distribution of assets, 50-53;
Housing expenditure, 263, 267, 270-71, export-led expansion of, 29; private,
273-76, 278, 323 50, 52; publicly owned, 50-52; and
Hsieh, S. C., 1On sex discrimination, 318-19; urban,
Hsing Mo-huan, 109, 115n 119, 120, 122-23, 124, 128, 316. See
Hsu Wen-fu, 45n also Labor-using bias of innovation;
Human assets, 225 Rural industry
Human capital, 5, 19, 129 Inflation, 26, 34n
Innovation-intensity effect, 84, 86. See
also Labor-using bias of innovation
Imperial examination system, 321 Interest rates, 29
Import licensing, 27 Intergroup inequality effect, 9, 19, 386,
Imports, 53 396-97
Import substitution. See Primary im- International Labour Organisation
port substitution; Secondary import (ILO), 114n
substitution Intersectoral effect: and decomposition
Income. See Agricultural income; formula, 225-31; for degree of urban-
Family distribution of income; ization, 246-49; for farm and non-
Family wage income; Functional dis- farm sectors, 245-46. See also Func-
tribution of income; Nonagricultural tional distribution effect
income; Property income; Total Intersectoral income inequality, 1IOn
family income; Transfer income; Intersectoral payments, 90
Wage income Intragroup inequality effect, 9, 13, 19,
Income classes, 13 326, 386, 397-98
Income components. See Factor income Intrasectoral effect: and decomposition
components formula, 225-31; for degree of urban-
Income-disparity effect, 225, 231, 245, ization, 246-49; for farm and non-
247, 248, 255 farm sectors, 245-46
Income fractions, 328, 340-42 Intrasectoral income inequality, 1iOn
Income gap, farm-nonfarm, 225, 243, Intrasectoral structural dualism, 125
245, 254 Investment patterns, family, 265, 267,
Income ranks, 340-42 268, 270, 271, 276-78
Income-relative, 226, 243
Income shares, relative, 121, 122
Income sources, classification of, 351.
See also Income Jacoby, Neil H., 29n
Indexes of inequality, 6-9 Jain, Shail, 13n
Indirect taxes, taxation, 19, 279, 286, Japan, colonial legacy in Taiwan, 21-
287, 290, 293-94, 322-23. See also 26, 37, 316
Taxes, taxation JCCR. See Joint Commission on Rnral
Indirect tax burden, 264, 265, 267, Reconstruction
269-70, 271, 279, 285-89, 290, 294 Joint Commission on Rural Recon-
Industrial assets, 37 struction (JCCR): data, 10, 45-46, 54,
Industrial exports, 30, 53 61, 62n, 114
INDEX 417
Job location, as labor attribute, 132, 113, 114; rural, 161-68; stratifica-
136-38, 143-45, 159, 160, 161; and tion of, 5, 7, 18; urban, 161-68. See
analytical cross-listing of data, 201 also Labor
Labor-intensive industries, 67, 116,
118, 119, 120
Labor-using bias of innovation, Hick-
Kaohsiung City, 63 sian, 84, 85, 86, 108, 120, 253, 317
Kirby, Edward S., 15n Lai, W. H., 49
Kuo, Shirley W. Y., 12n, 73n, 113n Land reform, 37, 38-46, 249, 252-53,
Koo, Anthony J. C., 40n 312, 314
Kuzoets, Anton, 2. 3n, 4n5 99, 112, 128, Land-to-the-tiller program, 39, 52. See
224, 226, 227n, 243, 255n also and reform
Kuznets effect, 6, 86, 99, 104, 109, 112, Latin America, 3n
127, 151 Least-squares method, ordinary, 78n
LDC. See Less developed countries
Less developed countries (LDc), 2, 4,
5-6, 127
Labor: absorption of, 28, 31, 74, 85, Lee, T. H., 44n
86n, 251, 317; as factor income com- Leontief inverse matrix, 293
ponent, 83; family ownership of, 18, Lewis, W. Arthur, 35, 99, 112, 120, 128
87, 225; male and female, 115; Life-cycle income, lln
mobility of, 224; pricing of, 130; re- Linear approximations, 78, 367-69
allocation of, 17, 32, 47, 57, 74, 113- Linearity error, 369-70
16, 225, 312; scarcity of, 32, 34, 109, Linearity specification, 98n
316-17; surplus of, 17, 31-32, 108- Linear model, decomposition formula,
09, 312, 316-17; unskilled, 30, 34. 326, 363-65, 373, 374
See also Labor force; Wage-rate in- Linear regression equation, 141, 146,
equality; Wage rates 326, 386-94
Labor assets, 6 Linear regression lines, 79, 81
Labor attributes: impact on wage rates, Linear regression method, 90, 131, 138,
131, 132, 133, 135, 136-37, 138, 141- 324
46, 160-68, 318-21; and pattern of Liu, Paul K. C., 50n
wage income of individual workers, Liu, S. F., 50n
139. See also Age; Education; Labor Lorenz curve, 1, 328-30
characteristic Gini; Labor charac- Lu, Kuang, 39n
teristic weight; Labor correlation
characteristic; Quality characteris-
tics; Sex
Labor characteristic Gini, 146-55, 158, Mahalanobis, B., 73n, 325n, 333n, 399n
159 Malthus, Thomas, 4
Labor characteristic weight, 147, 155- Mangahas, Mahar, 73n, 325n, 399n
57, 159 Manufacturing, 24-25, 37, 52, 67, 119.
Labor correlation characteristic, 147, See also Industry; Labor-using bias
157-68, 169, 171 of innovation; Nonagricultural pro-
Labor force: agricultural, 31, 113, 114; duction
differentiation of, 5, 72, 122, 130-38, Marginal labor force, 175, 177, 320
141-46, 146-68; family ownership of, Market mechanism, government inter-
7; formation of modern, 18; homo- ference with, 314
geneous, 150, 153, 155; marginal, Markets, domestic, 28-29
175, 177, 320; nonagricultural, 31, Marxist theorists, 128
418 INDEX
Meerman, Jacob, 322n 56. See also All households; Urban
Mehran, F., 73n households
Mexico, 65 Nonfarm Gini coefficient, 112
Migration, 340n Nonlinearity error, 83, 98, 99
Mincer, Jacob, 138n Nonlinearity term, 82
Minimum progressiveness, 282-83, Nonuniform homogeneous case, 183,
286n 190
Modernization, 110-11, 115, 122-23, No-reversal-of-rank condition, 282, 283
130-31, 137, 177. See also Industry,
industrialization
Monotonic model, decomposition for- Occupation, as labor attribute, 132;
mula, 326, 365-66, 373, 375-76 and analytical cross-listing of data,
Morris, Cynthia Taft, 2, 35 201
Multiple-cropping index, 50, 56-57 Overestimation, degree of, 77-78, 97
Multiple regression analysis, 141. See
also Linear regression method
Paauw, Douglas S., 3n
Paukert, Felix, 2
National income, decomposition of, 75, Personal income, total, 65n. See also
231-43 Total family income
Negative rank correlation, 77n Philippines, 115n, 316
Nepotism, 7, 309 Physical assets, and pattern of family
Nepotism coefficient, 142, 145 ownership, 7, 225
Net domestic product (NDP), 47-48, 52 Physical capital, 5; family investment
Net factor Gini effect, 102 in, 19; heterogeneity of, 129
Net family income, 266, 272-78. See Population growth, 131
also Taxes, taxation. Power generation, in colonial Taiwan,
Net income structure, 266 25
Net supporting gap, 343-45 Primary data, 11-12, 194, 199-201,
Nonagricultural factor Gini effect, 102, 202, 403-10
106, 125-26, 127 Primary export substitution, 17, 30-36,
Nonagricultural income, 87, 98; dis- 53, 56, 63, 84, 113, 311, 322
tribution of, 66, 67; disaggregation Primary import substitution, 17, 26-
of, 74; early forms of, 115; empirical 30, 32, 49, 52, 56, 67, 71, 84, 310-11,
findings and policy conclusions for, 317
314-15; Gini coefficient of, 88; and Private industry, 50
rural by-employment, 114, 249-51, Private land, 40-41
315 Production complementarity, 85n, 86n
Nonagricultural labor force, 31, 113, Production substitutability, 85n, 86n
114 Progressive taxes, taxation, 271, 282,
Nonagricultural production, 28, 37, 283, 288, 322-23
112, 225, 226; and ratio of wage Property income, 4, 7, 56, 72, 73, 74, 75,
share to property share, 116 81, 83, 87, 264; analytical cross-list-
Nonfarm sector, 233-34, 245-46 ing of data on, 199; distributive
Nonfarm employment, 61-62 shares of, 87, 88; as factor compo-
Nonfarm families, 19; income gap be- nent, 7; factor Gini coefficient of, 82,
tween farm and, 225, 243, 245, 254; 120-26; and factor Gini effect, 18;
and sectoral decomposition formula, and functional distribution effect,
227-31; size and composition of, 254- 313, 316; Gini coefficient of, 98, 119,
INDEX 419
120-26; rank correlation between Regressive taxes, taxation, 271, 282,
total income and, 77; rural, 54, 56, 283, 285, 322-23
113; sectoral Gini coefficient of, 121; Relative factor prices, 30
as type one income, 73, 82, 90; as Relative income shares, 121, 122
type two income, 90n Relative share ratio, 116
Pseudo factor Ginis, 352-57 Ricardo, David, 4
Pseudo Gini coefficient, 158n, 326, 328; Rice, hidden tax on, 253
graphic summary of, 346-48; and Rosen, Sherwin, 139n
pseudo Lorenz curve, 328, 334-37 Rural by-employment, 114, 249-51,
Pseudo Lorenz curve, 334-37 315
Public lands, 39, 40. See also Land Rural credit cooperatives, 22, 23, 45
reform Rural dualism, 122. See also Structural
Publicly owned industry, 50-52 dualism
Published data, 11-12, 13, 131n, 404- Rural families. See Family distribution
10, 409n of income; Farm families; Rural
Pyatt, Graham, 73n, 325n, 339n, 340n, households
349n, 399n, 409n Rural households, 4, 12-13, 87, 90, 94,
97, 99, 101, 105, 106, 128; agricul-
tural income and, 314, 315; and FID,
Quality characteristics, 326, 338-50 12-13, 54-64, 66, 110, 114, 128, 224,
Qualty carateritics 32, 33-50 312; Gini coefficient for, 99, 101,
108-12, 120; income sources of, 87;
nonagricultural income of, 112-16,
Ranis, Gustav, 73n, 84n, 85n, 99n, 314, 315; and reallocation effect, 105-
lO9n 06, 313; and reallocation of labor,
Rank correlations, 77 313-14; spatially dispersed, 12-13;
Rank index of factor income compo- surveys of, 10-11. See also Farm
nents, 77 families; Sectoral decomposition
Rank-weighted error term, 146, 161 equation
Rao, V. M., 73n, 325n, 399n Rural industry, 50, 61-63, 113, 114,
Raw materials, imports of, 53 115, 116, 118, 119, 120, 122, 125, 128,
Reallocation effect, 74; and agricul- 315; decentralization of, 315-16, 317;
tural income, 18, 113-16; and FID and property income, 54, 56, 113;
equity, 88-89, 99-100, 103, 105, 108, and wage income, 54, 56, 57-61. See
126-29, 313-15; and rural house- also Industry; Labor-using bias of
holds, 105-06, 313 innovation
Reallocation of labor, 17, 32, 47, 57, 74, Rural unemployment, 50
113-16, 225, 312, 313-14 Rural workers. See Labor force; Job
Real wages, 17, 32, 35, 36, 84, 85, 109, location
120, 312, 316, 317 Ruttan, Vernon W., 49n
Redistribution. See Land reform; Re-
allocation effect
Regression coefficients, 78, 90, 142 Salary income, urban, 64-65. See also
Regression constants, 78, 82, 90 Wage income
Regression equation. See Linear re- Sales tax, 265
gression equations Savings, family, 19, 27, 264, 265, 267,
Regression lines. See Linear regression 273, 276-78, 291
lines Savings rate, 28, 32-33
Regression relations, 78n Savings structure, 264, 265
420 INDEX
Secondary export substitution, 34. See Taiwan Pulp and Paper Corporation,
also Primary export substitution 52
Secondary import substitution, 29, 34. Taiwan Sugar Corporation, 40
See also Primary import substitution Taxes, 5, 8, 19, 127, 279-89, 321-23;
Second World War, 22, 23, 51 burden of, 264, 265, 267, 269, 271,
Sectoral decomposition equation, 225- 279, 283-89, 290, 321-22; com-
31, 233-34 modity, 265, and consumption, 19;
Sectoral property Gini, 123 direct, 19, 279, 286, 287, 290, 322-23;
Sectoral Gini coefficients, 109-12, 121 and expenditure, 264-307, 321-23;
Segmentation model, 9 and FID, 19, 279-89; hidden, 253,
Semiurban Gini coefficient, 112 290n; indirect, 19, 279, 286, 287, 290,
Semiurban households, 110-11, 112 293-94, 322-23; progressive, 271,
Sex, as labor attribute, 130, 132-34, 282, 283, 288, 322-23; reductions in,
135-36, 139, 142-45, 317-20; and 249, 253-54; regressive, 271, 282,
analytical cross-listing of data, 200; 283, 285, 322-23; sales, 265
and wage-rate inequality, 7, 131, Tax payments structure, 264, 265, 266
136, 143, 145, 161-62, 166, 170, 171, Technology, 49, 312. See also Industry;
175, 235, 237, 309, 318, 319, 340n. Labor-using bias of innovation
See also Family attributes Tenant farming, 24, 38-42
Share ratio, relative, 116 Terms of trade, 27
Smith, Adam, 4 Thailand, 115n, 316
Stable wage share, 67 Theil, Henri, 105n, 1iOn, 325n
Structural dualism, 110, 122; intrasec- Theil index, 6, liOn
toral, 125 Total family income, 7, 8, 18-19, 54, 58,
Subphases of transition growth, 3, 4, 65n, 67, 73, 77; definition of, 72; dis-
17, 26. See also Primary export sub- aggregation of, 74; Gini coefficient
stitution; Primary import substitu- of, 54n, 55-56, 72, 74, 81, 98, 100,
tion; Secondary export substitution; 103, 108, 109; and factor income
Secondary import substitution; inequality, 75-83; index of inequal-
Turning point ity of, 72, 74; ranking of, 55n; rank
Sugar refining, 119 correlation between property income
Supporting gap; average, 342-46; net, and, 77; and taxation and expendi-
343-45 ture, 8, 264-307; and wage rates,
Surplus labor, 17, 31-32, 108-09, 312, 142, 145, 146, 161-62, 166-68; of
316-17 rural families, 113-16. See also
Swamy, Subramanian, 227n Family distribution of income; Net
family income; Wage income
Total Gini curve, 98
Taipei City, 1 ln, 63 Total income inequality, decomposition
Taipei Provincial Government, Com- technique for, 75-83
mittee on the Census of Agriculture, Total income pattern, 72
114n Total personal income, 65n
Taiwan, colonial, 21-26, 37, 316 Town workers. See Labor force
Taiwan Agriculture and Forestry De- Transfer income, 72, 73, 75, 77, 78, 79,
velopment Corporation, 52 81, 127, 264; and analytical cross-
Taiwan Industrial and Mining Com- listing of data, 199; as type three
pany, 52 income, 73, 97n
Taiwan Province, lln Transition growth, subphases of, 3, 4,
INDEX 421
17, 26. See also Primary export sub- Urbanization, 19, 226, 234-35, 243-49
stitution; Primary import substitu- Urban-rural model, 18
tion; Secondary export substitution; Utilities, 119
Secondary import substitution; Utopian socialism, 1
Turning point
Tsui, Y. C., iOn
Turning point, 84, 85, 86, 99-108, 109, Wage income, 18, 72, 73, 75, 78, 81, 83-
124, 125, 127, 243n, 311-12 84, 87, 130-223, 264, 309; analytical
Type one income, 72-73, 74, 78-79, 80, cross-listing of data on, 199; and dif-
82, 89, 94-95, 104, 285n ferentiation of labor force, 130-31,
Type three income, 73, 79, 80, 97 132-38, 144-46; distributive share of,
Type two income, 72-73, 74, 78-79, 80, 84, 86, 87, 88; as factor component,
82, 89, 94-95, 98, 104, 285n 7, 72; factor Gini coefficient of, 82,
120-26; and family formation, 130-
31, 139, 168-93; and functional dis-
tribution effect, 313, 316; Gini co-
Underemployment, 21, 50, 251. See also efficient of, 64-65, 98, 119, 120-26;
Labor; Labor force of individual workers, 138, 139, 146-
Unemployment, 251. See also Labor; 68, 318; and industrialization, 130;
Labor force rural, 54, 57-60, 61-62, 113; sectoral
Unemployment compensation, 290 Gini coefficient of, 121; as type two
Ungrouped data, 14, 403-10 income, 73, 74, 90; urban, 64-65.
Uniform homogeneous case; 183, 184- See also Real wages; Wage-rate
86, 188 inequality
Uniform semihomogeneous case, 183, Wage income pattern, 7
186-88 Wage income weight, 171, 178-79
U.S. foreign aid, 28, 45, 311 Wage index, 133, 135
Unpublished data, 131n, 403-10 Wage-profit ratio, 188n
Urban dualism, 110, 122, 123 Wage-rate inequality: age and, 161,
Urban families. See Urban households 164-66, 170, 171, 175-76, 179-80;
Urban family income. See Urban house- and family size and composition,
holds, and FID 180-93, 226, 249, 254-56; sex and, 7,
Urban Gini coefficient. See Gini coeffi- 131, 136, 143, 145, 161-62, 166, 170,
cient of urban households 171, 175, 235, 237, 309, 318, 319,
Urban households, 4, 12-13, 87, 90, 99, 340n
101, 107, 108, 128; capital and assets Wage rates, 131, 312; Gini coefficient
of, 313; decomposition equation for, of, 146; and individual wage earners,
87; and FID, 12-13, 64-65, 107-08, 146-68; and labor heterogeneity, 131,
110, 127-28, 225, 312, 313, 314, 316; 132, 133, 135, 136-37, 138, 141-46,
and functional distribution effect, 160-68, 318-21; regression coeffi-
107-08, 313-14, 316-17; Gini coeffi- cients of, 138
cient for, 64-65, 99, 101, 108-12; in- Wage share, 67, 116, 120, 128
come sources of, 87; property in- Wage structure, 5, 18
come of, 316; spatially concentrated, Wang You-tsao, 49n
12-13; surveys of, 10-11; wage in- Wei, Yung, 252n
come of, 316 Weighted factor Gini coefficient, 75, 77
Urban industry, industrialization, 119, Weighted income fractions, 328
120, 122-23, 124, 128, 316 Welfare, 177, 290
422 INDEX
Welfare income, 75, 79 Yale University, Economic Growth
West Pakistan, 67 Center, 199
Women, and wage-rate inequality. See Yang, T. Martin, 43n
Sex, and wage-rate inequality Yu, Y. H., 115n
Working capital, 48
THE WORLD BANK AND THE YALE ECONOMIC GROWTH CENTER
supported the research leading to the publication of this volume.
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Also from Oxford
and the World Bank
STRUCTURAL CHANGE
AND DEVELOPMENT POLICY
Hollis Chenery
A book that offers both a retrospective
evaluation by the author of his thought and
writing over the past two decades and an
extension of his work in Redistribution with
Growth and Patterns of Development.
Chapters that discuss the structural
characteristics of individual countries or
groups of countries set the stage for a
systematic analysis of the internal and
external aspects of structural change that
affect the design of policy.
A FRAMEWORK FOR POLICY
Economic Growth and Structural Change
Models of the Transition
INTERNAL STRUCTURE
The Process of Industrialization
Substitution in Planning Models
The Interdependence of Investment Decisions
Economies of Scale and Investment over Time
EXTERNAL STRUCTURE
Comparative Advantage and Development
Policy
Development Alternatives in an.Open
Economy: The Case of Israel
Optimal Patterns of Growth and Aid:
The Case of Pakistan
INTERNATIONAL DEVELOPMENT POLICY
Foreign Assistance and Economic
Development
Growth and Poverty in Developing Countries
544 pages. Figures, tables, bibliography.
Available in doth and paper editions.
The World Bank
MUST RAPID ECONOMIC GROWTH lead inevitably to greater inequality
in the distribution of income? No. This book describes how Taiwan
achieved growth with equity between the early 1950s and the early
1970s. It also offers explanations for this performance. The underlying
purpose, however, is to present a general method of analyzing the
behavioral interactions between growth and equity in any developing
economy.
The analytical framework enables the authors to trace changes in
the inequality of total family income over time to changes in the
weights and inequalities of such income components as wage and
property income. This decomposition of income inequality allows the
authors to begin to forge a link between two areas of knowledge that
heretofore have been somewhat isolated: development theory and
the analysis of the size distribution of income.
The principal conclusion for policy is that the most reliable method
of minimizing, or possibly even eliminating, a conflict between growth
and equity is to make better choices about the ways in which output
and income are generated. For example, the favorable performance
of Taiwan is largely attributable to the early attention paid to agri-
culture and to the spatially dispersed and labor-intensive character
of its industrialization. Direct government intervention through tax
and relief measures is likely to be less important than often is assumed.
John C. H. Fei and Gustav Ranis are professors of economics asso-
ciated with the Economic Growth Center at Yale University. Shirley
W. Y. Kuo is a professor of economics at National Taiwan University
and vice-governor of the Central Bank in the Republic of China.
Oxford University Press ISBN O-19-520115-9
Jacket design by Carol Crosby Black