23242 Hinkle January 2001 Montiel Exchange Rate MISALIGNMENT CONCEPTS AND MEASUREMENT FOR ) > DEVELOPING COUNTRIES Io~ rn zr Z ; -- Lawrence E. Hinkle Peter J. Montiel 0 A WORLD BANK RESEARCH PUBLICATION Oxford University Press  Exchange Rate MISALIGNMENT CONCEPTS AND MEASUREMENT FOR DEVELOPING COUNTRIES  Exchange Rate MISALIGNMENT CONCEPTS AND MEASUREMENT FOR DEVELOPING COUNTRIES Lawrence E. Hinkle Peter J. Montiel A WORLD BANK RESEARCH PUBLICATION Oxford University Press Oxford University Press Oxford New York Athens Auckland Bangkok Bogata Buenos Aires Calcutta Capetown Chennai Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris Sao Paulo Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin Ibadan Copyright © 1999 The International Bank for Reconstruction and Development/ THE WORLD BANK 1818 H Street, N.W. Washington, DC 20433, U.S.A. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York, 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in retrieval system, or transmitted, in any form or by any means, electronic, mechani- cal, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Manufactured in the United States of America First printing June 1999 2 3 4 5 03 02 01 00 The findings, interpretations, and conclusions expressed in this study are entirely those of the authors and should not be attributed in any manner to the World Bank, to its affiliated organizations, or to members of its Board of Executive Directors or the countries they represent. The boundaries, colors, and other information shown on any map in this volume do not imply on the part of the World Bank any judgement on the legal status of any territory or the endorsement or acceptance of such boundaries. Library of Congress Cataloging-in-Publication Data Hinkle, Lawrence E., 1944- Exchange rate misalignment : concepts and measurement for developing countries / Lawrence E. Hinkle and Peter J. Montiel. p. cm. Includes bibliographical references and index. ISBN 0-19-521126-X 1. Foreign exchange rates - Developing countries. 2. Foreign exchange administration - Developing countries. I. Montiel, Peter. II. Title. HG3877.H56 1999 332.4'56'091724-DC21 98-52201 CIP Table of Contents Foreword ix Preface xii Acknowledgments xiv About the Authors xvi Acronyms and Abbreviations xvii 1. Exchange Rate Misalignment: An Overview I Peter J. Montiel and Lawrence E. Hinkle The Real Exchange Rate: Concepts and Measurement 4 Determinants of the Equilibrium Real Exchange Rate 10 Methodologies for Estimating the Equilibrium RER: Empirical Applications 14 Policy and Operational Considerations 28 Conclusions 32 Part I: The Real Exchange Rate: Concepts and Measurement 2. External Real Exchange Rates: Purchasing Power Parity, the Mundell-Fleming Model, and Competitiveness in Traded Goods 41 Lawrence E. Hinkle and Fabien Nsengiyumva Common Features of All External Real Exchange Rate Indexes 43 Measurement of the Different RER Concepts: Choosing Appropriate Price or Cost Indexes 72 Comparison of Alternative External RER Measures: Competitiveness and the Terms of Trade 86 Summary and Conclusions 92 Appendix A: International Comparison Programme Exchange Rates 99 Appendix B: The Relationship between Profitability, Competitiveness, and the Different External RERs 105 3. The Two-Good Internal RER for Tradables and Nontradables 113 Lawrence E. Hinkle and Fabien Nsengiyumva The Two-Good Internal RER for Tradables and Nontradables: Concepts and Measurement 116 V vi EXCHANGE RATE MISALIGNMENT The Relationship between the External RER and the Two-Good Internal RER 129 External RERs as Proxies for the Two-Good Internal RER 141 Summary 152 Appendix: Direct Estimation of the Internal RER from National Accounts Data 155 4. The Three-Good Internal RER for Exports, Imports, and Domestic Goods 175 Lawrence E. Hinkle and Fabien Nsengiyumva The Three-Good Internal RERs for Imports and Exports: Concepts and Measurement 176 The Terms of Trade, the Internal RERs for Imports and Exports, and the External RER 186 Summary and Conclusion 201 Appendix A: The Relationship between the Internal RER for Imports, the External RER, and the Terms of Trade 209 Appendix B: An Additional Possible Proxy for the Three-Good Internal RER 212 Part II: Determinants of the Equilibrium Real Exchange Rate 5. The Long-Run Equilibrium Real Exchange Rate: Conceptual Issues and Empirical Research 219 Peter J. Mon tiel Conceptual Issues 220 Empirical Estimation: Industrial Countries 233 Empirical Estimation: Developing Countries 254 Summary 260 6. Determinants of the Long-Run Equilibrium Real Exchange Rate: An Analytical Model 264 Peter J. Montiel The Analytical Framework 266 The Long-Run Equilibrium Real Exchange Rate 274 Long-Run Fundamentals 278 Summary and Conclusions 289 Part III: Methodologies for Estimating the Equilibrium RER: Empirical Applications 7. Estimating the Equilibrium Real Exchange Rate Empirically: Operational Approaches 293 Theodore 0. Ahlers and Lawrence E. Hinkle CONTENTS vii The Relative PPP-Based Approach to RER Misalignment 296 The Trade-Equations Approach: Establishing the Quantitative Relationship between the RER and the Resource Balance 313 Determining the Target Resource Balance 321 Adjusting the Initial Resource Balance 333 Conclusion: Advantages and Limitations of the Trade-Equations Methodology 342 Appendix A: The RER, Trade-Elasticities, Resource Balance Relationship in a Three-Good Framework 345 Appendix B: Representative Estimates of the Income Elasticity of Demand for Imports 354 Appendix C: Formulas for Exchange Rate Appreciation, Depreciation, and Misalignment in Domestic- and Foreign- Currency Terms 356 8. Estimates of Real Exchange Rate Misalignment with a Simple General-Equilibrium Model 359 Shantayanan Devarajan The DLR Model 361 Applying the DLR Model to the Pre-1994 CFA Zone 365 Sensitivity Analyses and Extensions 372 Conclusion 378 Appendix: The DLR Model 380 9. Long-Run Real Exchange Rate Changes in Developing Countries: Simulations from an Econometric Model 381 Nadeem Ul Haque and Peter J. Montiel A Brief Description of the Model 383 Domestic Policy Shocks 391 External Shocks 395 Summary and Conclusions 398 Appendix: An Application to Thailand 402 10. Single-Equation Estimation of the Equilibrium Real Exchange Rate 405 John Baffes, Ibrahim A. Elbadawi, and Stephen A. O' Connell Step One: Modeling the Equilibrium Real Exchange Rate 407 A Brief Detour: Motivating the Single-Equation Approach 418 Step Two: Estimation 425 Step Three: Calculating the Equilibrium Real Exchange Rate 443 Conclusions 451 Appendix A: Conditioning and Weak Exogeneity 456 Appendix B: Data Description 459 Appendix C: Sustainable Fundamentals 461 viii EXCHANGE RATE MISALIGNMENT Part IV: Policy and Operational Considerations 11. The Three Pessimisms: Real Exchange Rates and Trade Flows in Developing Countries 467 Nita Ghei and Lant Pritchett The Import Response to a Real Depreciation 470 Export Demand Pessimism 482 The Export Supply Response to RER Movements 485 Summary and Conclusion 494 12. The Use of the Parallel Market Rate as a Guide to Setting the Official Exchange Rate 497 Nita Ghei and Steven B. Kamin Essential Characteristics of Parallel Exchange Markets 499 A Simple Model of Parallel Exchange Rate Determination 505 Trends in Official and Parallel Real Exchange Rates 522 Summary and Conclusions 532 Appendix: Sensitivity of Results to Choice of Real Exchange Rate 535 13. A Note on Nominal Devaluations, Inflation, and the Real Exchange Rate 539 Nita Ghei and Lawrence E. Hinkle Devaluations, Inflation, and the External RER: the Stylized Facts 544 An Accounting Framework for Determining Consistent Nominal and Relative Prices 552 Conclusion: Advantage and Limitations of the Consistency Framework 570 Appendix: The Accounting Framework for the Two-Good Internal RER 573 References 587 Index Foreword John Williamson Chief Economist, South Asia Region, World Bank The last week has, I suppose, been a fairly typical one for me. Twice during the week I have encountered distinguished economists ana- lyzing important current problems who asked their audience to accept the new faith that exchange rate policy has been hollowed out by capital mobility, leaving nothing coherent between a fixed exchange rate backed up by a currency board on the one hand, and floating rates on the other. One was Barry Eichengreen, discussing the design of a new interna- tional financial architecture at a meeting of the Institute for International Economics. The other was Ernie Preeg, focusing on the outlook for the U.S. economy escaping from its massive current account deficit without a hard landing, in a paper for the Hudson Institute. Interestingly, nei- ther of these analysts ended up by advocating completely freely float- ing exchange rates without any intervention. Eichengreen took it for granted that floating would be "dirty"; as we all know, "dirty floating" is an emotionally biased term invented by ideological floaters in order to try and discredit exchange rate management. Preeg argued that some "disciplines among the three key currencies on central bank interven- tion" will be necessary. If even those who think they have been driven to support floating exchange rates are still taking it for granted that there needs to be some degree of management by the authorities, then two things follow. The first is that there is still a market niche for those of us who try to think about how a system of limited flexibility might best be organized. The other is that there is going to be a continuing need for analysis of where an exchange rate lies in relation to what the authors of this volume call its long-run equilibrium level (the LRER). In the second footnote of the volume the authors gently chastise me for "the somewhat apologetic tone" of my introduction to Estimating Equilibrium Exchange Rates, a vol- ume I edited that set itself a fairly similar task, where I seek to defend the value of this exercise. I am delighted that they feel no need for such a qualification. There is indeed a serious job of work to be done, and the ix x EXCHANGE RATE MISALIGNMENT authors in this volume set about doing it with determination and a high degree of professional competence. Since it seems I am no longer as in- tellectually isolated as I have periodically feared since I began drawing analytical distinctions between different concepts of the equilibrium exchange rate back in 1983, and argued that it was important to try and develop empirical estimates of at least one of those concepts (the one that I termed the "fundamental equilibrium exchange rate," which is roughly equivalent to the LRER of this volume), I promise to be less apologetic in future. Had I been asked to guess ex ante what countries the authors planned to focus most attention on, I cannot imagine that I would have regarded C6te d'Ivoire and Burkina Faso as leading candidates. In f act this choice was driven by operational exigencies in the World Bank in the early 1990s, at a time when people valuing their careers did not talk out loud about the overvaluation of the CFA franc (any more than people with ambitions spoke about the overvaluation of the pound in the British Treasury in 1966). The natural strategy of a conscientious official con- fronted by a gag order that he believes cannot last long is to quietly initiate a research program that will help to sort out the mess when higher authority is forced to face the facts of life. That is what happened here. We should be profoundly thankful that the Bank had employees who were prepared to take the risk of reacting that way. They have ended up by producing a book that has far wider applicability than to the CFA countries, or indeed than just to developing countries. This book will surely become the standard reference on the estimation of equilibrium exchange rates (or, what amounts to the same thing, on exchange rate misalignments). I find it difficult to imagine a world in which it would not be impor- tant to estimate exchange rate misalignments. Imagine that Argentina really does dollarize, and then an asymmetrical shock leaves it in deep and seemingly permanent depression. Estimating the degree of over- valuation would be important not just as an input into the inevitable national debate on whether to recreate a national currency, but also to estimate how large a general wage cut would be needed to create the desirable real devaluation without using the exchange rate. Or consider the problems that confront the East Asian countries today (early 1999), of knowing whether their now-floating exchange rates have undone a sufficient part of the overshooting of late 1997 to make it sensible policy to start rebuilding reserves in a big way. Or it may even be that there will be a role for this type of analysis one day among the G3, if and when a concern to adjust the U.S. current account deficit re-emerges. The material in this volume covers all the important approaches to the estimation of the LRER, from the crudest PPP doctrines (currently FOREWORD xi popularized by The Economist's "Big Mac Index") through to the simula- tions of large macroeconometric models that I have attempted to use and the new approach of using unit-root econometrics to derive esti- mates from a single equation reduced form. I found it particularly inter- esting that, as an empirical proposition, relative PPP works for Burkina Faso. The volume also provides an excellent guide to the quite sophisti- cated literature on different concepts of the real exchange rate, and avoids facile identification of one concept as being "the right one." It warns against all the errors that abound in this field (for example, purporting to explain why devaluation won't work, or claiming that all one needs to do is look at the black-market rate or the Big Mac Index to know what the exchange rate should be). Some people may believe that crises are an inevitable feature of the capitalist system. Others hold that exchange-rate crises will vanish as more and more countries adopt floating exchange rates. I can under- stand adherents of both those views dismissing this book as of no inter- est. But some of us believe that crises can be avoided or at least limited by good economic management, and that having a reasonable idea of where the equilibrium exchange rate lies is an essential requirement for good macro management. Those who share these views will want to see this volume widely used to help policy analysts get a feeling on what can and cannot be said about the equilibrium exchange rate, and so make an important contribution to the improvement of macro management and hence the avoidance of future crises. Preface Exchange rate misalignment has been an important element in most of the exchange rate crises that have plagued the developing world during the last decade, including those in Mexico, East Asia, Russia, and Brazil. The increasing integration of world capital markets has escalated the costs of such crises, and some of them have even threatened the stability of the international financial system. Consequently, a broad consensus has emerged in recent years that the overriding objective of exchange rate policy in developing countries should be to avoid episodes of pro- longed and substantial misalignment - meaning situations in which the actual real exchange rate differs significantly from its long-run equilib- rium value. It was the World Bank's involvement in one such episode of misalignment -that preceding the successful devaluation of the CFA francs in 1994 - that eventually led to this book. Views on how to manage exchange rates in developing countries have recently split into two competing schools of thought. One increasingly common view holds that, in light of the heightened integration of world capital markets and the increased vulnerability of developing countries to exchange rate crises, such countries must adopt extreme exchange rate arrangements. This school of thought sees the only credible policy options as, at one extreme, truly free floating exchange rates, which al- low the unfettered action of markets to determine the exchange rate, or, at the other extreme, currency boards, which permanently fix the exchange rate, or "dollarization," which eliminates the exchange rate altogether. The alternative view holds that for many developing countries a managed exchange rate -possibly in the context of an exchange rate band - remains a potentially superior option. This option permits avoid- ing the extremes of a completely clean float with its dangers of excessive real exchange rate volatility and resulting macroeconomic instability, on the one hand, or currency boards and "dollarization" with their ri- gidities in dealing with large real shocks or domestic banking crises, on the other hand. However, with unrestricted capital flows, the viability of the managed exchange rate option requires the timely detection and measurement of exchange rate misalignment so that the nominal ex- change rate and macroeconomic policy can be adjusted appropriately to Xii PREFACE xiii avoid crises. Thus, having a reasonable idea of where the equilibrium exchange rate lies has become an increasingly important requirement for good macroeconomic management under the managed exchange rate regimes still employed by the vast majority of developing countries. Despite the importance of being able to detect and measure exchange rate misalignment, the economics profession has yet to reach a consen- sus on how to do so. The documentation of the various technical proce- dures for determining equilibrium exchange rates is also widely scat- tered among numerous sources. Hence, this World Bank research study - Exchange Rate Misalignment: Concepts and Measurement for Developing Coun- tries -takes stock of the state of the art. It undertakes a comprehensive review of the conceptual and empirical issues concerning measurement of exchange rate misalignment in developing countries and analyzes in detail the currently available methodologies for estimating the long-run equilibrium exchange rate. The study is designed to provide policy makers and their advisors with a compendium of practical techniques for measuring exchange rate misalignment. In this study we reach the cautiously optimistic conclusion that, al- though economists may not at present know enough to calculate ex- change rate misalignment with great precision, we do know enough to identify cases of serious misalignment and sound clear warning signals. The implication for exchange rate policy is that ignorance about the empirical value of the equilibrium exchange rate cannot be used to clinch arguments for extreme exchange rate arrangements such as completely clean floats, currency boards, and "dollarization." Although in some cir- cumstances other considerations may justify adoption of extreme ar- rangements, we believe that appropriate management of the nominal exchange rate will, for the foreseeable future, remain a key concern of macroeconomic policy in most developing countries. To the extent that it does, the detection and measurement of real exchange rate misalign- ment are likely to employ techniques based on or inspired by those set out in this book. Acknowledgments The initial research that eventually led to this book was motivated by one of the major exchange rate crises that punctuated the last decade in the developing world - the devaluation of the CFA francs in 1994. Most of the members of the study team participated in that initial research, although none of us had any idea at the time that our work would emerge in anything like its current form. As the relevance of our initial research on the misalignment of the CFA francs to other developing countries was highlighted by repeated exchange rate crises elsewhere, analytical techniques used in other countries, and economists experienced with these, were added to the project to complement the initial research and round out the coverage of the study. As project managers and then editors, we were blessed with a par- ticularly competent team of fellow researchers and co-authors. They both made strong individual contributions and provided invaluable com- ments and guidance on the other papers and the project as a whole. The other members of the study team were: Theodore 0. Ahlers, Country Director, Africa Country Department 13, World Bank; John Baffes, Economist, Development Prospects Group, World Bank; Shantayan Devarajan, Research Manager, Development Research Group, World Bank; Ibrahim A. Elbadawi, Senior Economist, Development Research Group, World Bank; Nita Ghei, Economist, Consultant, College Park, Md.; Nadeem Ul Haque, Advisor, IMF Institute, International Monetary Fund. Steven B. Kamin, Senior Economist, Division of International Finance, Board of Governors of the Federal Reserve System, Washington, D.C.; xiv ACKNOWLEDGMENTS Xv Fabien Nsengiyumva, Economist, IMF Institute, International Monetary Fund; Stephen A. O'Connell, Professor of Economics, Swarthmore College, Swarthmore, Pa.; Lant Pritchett, Principal Economist, Resident Mission Indonesia, World Bank. A special note of thanks is also due to John Williamson. John came to the project as a reviewer when the manuscript of the book was first tak- ing shape. His insightful and intellectually demanding comments both shaped the volume and motivated us to push the work farther than we had initially envisaged. Ingrid Ivins provided cheerful, careful, and competent research as- sistance from the first days of the initial work on the CFA francs in 1990 through final completion of this volume in the spring of 1999. Emily Khine, Camille Darmon, and Jagdish Lal tirelessly processed and repro- cessed countless versions of the 13 papers that became the manuscript of this book. The World Bank's Africa Region, Development Research Group, and Poverty Reduction and Economic Management Network provided the financial support for the research. Finally, we would like to dedicate this book as follows: To my father, Lawrence E. Hinkle, M.D., for his lifelong in- terest in research and his support. To my mother, Maria Montiel, for her unwavering support and affection. LAWRENCE E. HINKLE PETER J. MONTIEL WORLD BANK WILLIAMS COLLEGE MAY 1999 About the Authors Lawrence E. Hinkle is Lead Economist in a macroeconomic unit of the Technical Department of the World Bank's Africa Region. From 1991 to 1994, he led the Bank's technical preparatory work for the devaluation of the CFA francs. From 1994 to 1997, while much of the research for this book was carried out, he was a visiting fellow in the macroeconomics division of the World Bank's Policy Research Department. His work at the Bank has been primarily in the areas of adjustment policy, exchange rates, trade, monetary and customs unions. Peter J. Montiel is Professor of Economics and the James Finney Baxter III Professor of Public Affairs at Williams College. He has recently been the Chair of the Center for Development Economics at Williams College and has worked in the Policy Research Department of the World Bank as well as the Research Department of the International Monetary Fund. His research has been in the area of macroeconomic stabilization in de- veloping countries, and his recent work has focused on capital flows and exchange rate policy. xvi Acronyms and Abbreviations ADF augmented Dickey-Fuller ADL autoregressive distributed lag BN Beveridge-Nelson BRER bilateral real exchange rate CFA Communaute Financikre Africaine CGE computable general equilibrium CPI consumer price index DEER desired equilibrium exchange rate DER dual exchange rate DF Dickey-Fuller DLR Devarajan, Lewis, and Robinson DRER desired equlibrium real exchange rate EU European Union FDI foreign direct investment FEER fundamental equilibrium real exchange rate G-7 group of seven GDP gross domestic product HBS Harrod-Balassa-Samuelson HLM Haque-Lahiri-Montiel model ICP International Comparison Programme IFS International Financial Statistics IE Institute of International Economics IMF International Monetary Fund INS Information Notice System LIBOR London interbank offer rate LIDC low-income developing country LRER long-run equilibrium real exchange rate NATREX natural equilibrium real exchange rate NEER nominal effective exchange rate NTB nontariff barrier OECD Organization for Economic Cooperation and Development OLS ordinary least squares PP Phillips-Perron PPP purchasing power parity REER real effective exchange rate xvii xviii EXCHANGE RATE MISALIGNMENT RER real exchange rate SDR standard drawing right(s) SRER short-run equilibrium real exchange rate SSA sub-Saharan Africa UFC unit factor cost ULC unit labor cost UNCTAD United Nations Conference on Trade and Development UNIDO United Nations Industrial Development Organization WPI wholesale price index 1 Exchange Rate Misalignment: An Overview Peter J. Montiel and Lawrence E. Hinkle The collapse of the Smithsonian agreement in March of 1973 marked the end of the Bretton Woods system of fixed exchange rates among the major industrial countries. Initially, many developing countries re- sponded to this event by attempting to sustain their fixed exchange rate parities. Over time, however, the majority of these countries have also moved toward exchange rate arrangements involving more frequent adjustments in nominal exchange rates. Most such arrangements, how- ever, have not left exchange rate determination to the market. Instead, whether in the form of crawling pegs or managed floating, they have invariably featured an important role for the authorities in the setting of nominal exchange rates and thus have led to increased activism in ex- change rate management. Consequently, the question of how to choose the appropriate value of the nominal exchange rate has remained a key concern of macroeconomic policy in developing countries. In this con- text, a broad consensus has emerged in recent years that the overriding objective of exchange rate policy should be to avoid episodes of pro- longed and substantial misalignment-meaning situations in which the actual real exchange rate (RER) differs significantly from its long-run equilibrium value. Unfortunately, following this advice is not as simple as it sounds, even for the most well intentioned policymaker. Leaving aside the sub- stantial difficulties that may arise in setting the actual nominal and real 1. For a description of the evolution of developing-country exchange rate regimes since the collapse of the Bretton Woods system, see Agenor and Montiel (1999). See also Caramazza and Aziz (1998) for a review of experiences with fixed and flexible exchange rate regimes in the 1990s. I 2 EXCHANGE RATE MISALIGNMENT exchange rates on their intended paths, two fundamental issues have to be confronted. The first is defining exactly what is meant by the long- run equilibrium real exchange rate. The second is estimating what the value of this long-run equilibrium rate is for a given country at any moment in time. Neither issue is trivial. Even though exchange rate misalignment is an important concern for policymakers, the economics profession has yet to reach a consensus on precisely what is meant by the long-run equilibrium real exchange rate. And not surprisingly, there- fore, it has provided little systematic guidance on how to measure it.2 Despite the absence of consensus, not only do developing-country policymakers continue to confront these issues on a daily basis, but the urgency of getting this key macroeconomic relative price "right" may be increasing over time, as growing financial integration has arguably escalated the costs associated with real exchange rate misalignment. In the developing-country context alone, recent episodes such as the Janu- ary 1994 devaluation of the CFA francs in West and Central Africa,' the Mexican currency crisis at the end of 1994, the Asian crisis that erupted in mid-1997, and the Brazilian devaluation in January 1999 have served as reminders of the macroeconomic disruptions that can be caused by real exchange rate misalignment. The severe macroeconomic disloca- tions experienced during these episodes suggest that the importance of being able to estimate the degree of misalignment may, if anything, have increased in recent years. This volume arose from one such episode of misalignment. Most of the papers collected here originated in the course of a practical exercise in measuring real exchange rate misalignment at the World Bank. Dur- ing the long dialogue over the degree of overvaluation of the CFA francs, World Bank staff were confronted with the problem of estimating the extent of real exchange rate misalignment in a context where it was im- portant to ensure that the estimates were both theoretically defensible and empirically accurate. Hence, the staff did a considerable amount of analytical work on various methodologies for calculating indexes of the actual real exchange rate and for estimating the value of the long-run 2. An interesting perspective on the evolution of these issues is provided by John Williamson's introduction to his edited book on the topic, Estimating Equi- librium Exchange Rates (1994). The somewhat apologetic tone of that introduc- tion suggests that, in the authors' opinion, the very concept of estimating long- run equilibrium exchange rate needed to be defended within the economics pro- fession. 3. CFA is the abbreviation for Communaut6 Financi&re Africaine. The CFA francs are the currencies of the West and Central African Monetary Unions, which together constitute the CFA zone. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 3 equilibrium real exchange rate. This methodological work focused on the types of analysis that could be carried out relatively quickly with (a) the limited amount and periodicity of data usually available in small African countries (for example, a monthly consumer price index (CPI), standard annual national accounts aggregates, annual export and im- port price indexes, and monthly official and parallel market exchange rates) and (b) the limited staff inputs (for example, one economist and a researcher) that are typically available for work on small developing countries. The staff also directed considerable attention to some empiri- cal problems encountered during this work that are relatively more im- portant in developing than industrial countries, such as unrecorded trade, parallel exchange markets, shifting trade patterns, and large fluc- tuations in export prices. This book is intended to preserve and disseminate this work on mea- suring misalignment because the methodologies that were used are likely to be of practical relevance in many other developing-country applica- tions. The book's objectives are thus to bring this work together, set it in an analytical framework, and complement it with other techniques that- while not employed in the CFA franc context because the operational restrictions described above prevented doing so or because the particu- lar structure of the CFA economies did not make them suitable-might well be applicable in other developing countries. What we hope to achieve is to provide policymakers and their advisers with a compen- dium of practical techniques for estimating equilibrium real exchange rates, as well as to further the development of this area of research by taking stock of the current state of the art. The objective of this first chapter is to present an overview of the book and to place the subsequent chapters in context. The remainder of this overview is divided into five sections, corresponding to each of the four parts of the book, plus a concluding section. Part I of the book considers issues that arise in the definition and measurement of the actual real exchange rate. It is indispensable to treat these first because the choices made in selecting the appropriate actual real exchange rate for a particular application will obviously affect the equilibrium concept relevant to it and also because the reliability of the estimates of the equilibrium exchange rate will clearly depend on how closely empirical proxies can approximate the "true" variable being measured. These definition and measurement issues are reviewed and summarized in the second section of this overview. Part II turns to the long-run equilibrium real exchange rate (LRER) itself. It contains two chapters that provide overviews of existing litera- ture. The first chapter considers conceptual issues that arise in defining the long-run equilibrium real exchange rate and surveys existing 4 EXCHANGE RATE MISALIGNMENT techniques for its empirical estimation. The following chapter sets out an analytical model that synthesizes existing theories about the deter- minants of the LRER. The basic findings of these two chapters are de- scribed in the section below on the determinants of the equilibrium RER. Part III then analyzes in some detail four methodologies for the em- pirical estimation of the long-run equilibrium real exchange rate: a PPP- based approach, a recursive trade-equations approach, and two general equilibrium approaches-one based on structural econometric models and the other on a reduced-form methodology utilizing unit-root econo- metrics. These methodologies are described in the four chapters con- tained in Part III of the book. They are summarized and evaluated in this overview's section on methodologies for estimating the equi- librium RER. Part IV of the book, reviewed below in the section on policy and op- erational considerations, takes up some important related issues. The first chapter in Part IV examines the empirical role of the real exchange rate in promoting external balance, a mechanism that is featured promi- nently in traditional definitions of the long-run equilibrium real exchange rate but the empirical effectiveness of which has sometimes been ques- tioned. The two remaining chapters in Part IV assess the usefulness of the parallel market premium as an indicator of the LRER and describe operational techniques for estimating the magnitude of nominal exchange rate changes required to correct a given real exchange rate misalignment. The overview concludes with a final section presenting our assess- ment of where the enterprise of defining and estimating equilibrium real exchange rates in developing countries currently stands. We find, in brief, that recent developments justify optimism. The three techniques that have traditionally been used for the estimation of equilibrium real exchange rates-based on purchasing power parity, on the trade equa- tions, and on simulations of empirical general equilibrium models- each suffer from particular limitations; but each can be useful under appropriate circumstances. What we have dubbed the reduced-form general-equilibrium approach is a relatively recent technique. Although this method of estimation is not without its own pitfalls, it appears to hold promise of future progress in the empirical estimation of equilib- rium real exchange rates for developing countries. The Real Exchange Rate: Concepts and Measurement The point of departure for estimating the long-run equilibrium real ex- change rate (which we call the LRER) is the measurement of the actual real exchange rate (RER). Unfortunately, this is not a straightforward EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 5 matter. The difficulties are both conceptual and empirical. Multiple con- ceptual definitions of the real exchange rate, drawn from different ana- lytical frameworks and suitable for use in different circumstances, have long complicated the analysis of real exchange rate issues. This multi- plicity poses the problem of how to choose among alternative defini- tions of the real exchange rate. In addition, in the empirical measure- ment of the RER in many developing-country applications one confronts a large number of practical problems that are not often encountered in the case of industrial countries and thus have not been as widely dis- cussed as other more general issues. The first three chapters in Part I of the book take up these definitional and measurement issues in detail. As discussed subsequently in Part IL the development of LRER theo- ries has followed somewhat different lines in industrial- and develop- ing-country applications. Somewhat surprisingly, the differences have extended to the very definition of the RER itself. In the context of industrial countries, economists have focused on the "external" RER for both analytical and empirical purposes. When defined in this manner, the RER is measured as the ratio of the foreign to the domestic values of some broad-based price index such as the CPI or the deflator for gross domestic product (GDP), expressed in a com- mon currency by using the nominal exchange rate to convert the price level in one country into the currency of the other. Unfortunately, mat- ters are complicated by the fact that alternative conceptual frameworks imply alternative choices of price indexes. As a result, even within the external real exchange rate category there exist multiple definitions from which to choose. This multiplicity of concepts would be of little conse- quence if the alternative measures all tended to move together, but they cannot be counted upon to do so-that is, empirically, the choice of price index tends to matter. In the developing-country context, moreover, the RER tends to be defined in two different ways for analytical purposes: either as the rela- tive price of traded goods in terms of nontraded goods, which is re- ferred to in this book as the two-good internal real exchange rate, or as the relative prices of exportable and importable goods in terms of nontraded goods, which are referred to here as the three-good internal real exchange rates. To complicate matters further, despite the analyti- cal preference for the use of internal RER concepts, the external RER tends to be used for empirical purposes in developing-country applica- tions. This practice raises a number of issues. For example, when is it appropriate to use one definition rather than another? What is the rela- tionship between the definitions? Are there specific pitfalls to which practitioners should be alerted in formulating hypotheses using one RER concept and testing them using another as an empirical proxy? The three 6 EXCHANGE RATE MISALIGNMENT chapters in Part I by Hinkle and Nsengiyumva take up these questions, considering each of the three broad definitions of the RER in turn. The External RER Chapter 2, the first chapter in Part I, provides a general summary of conceptual and empirical issues that arise in defining and measuring the external real exchange rate. Three alternative definitions, based on different price indexes, are reviewed; and both their theoretical under- pinnings and empirical counterparts are described. Chapter 2 also pro- vides a critical evaluation of the usefulness of external RER measures in developing countries from a conceptual perspective. On a more practi- cal level, issues such as the choice of weighting schemes in the construc- tion of real effective exchange rate (REER) indexes and alternative de- compositions of such indexes for analytical purposes are also discussed. Finally, particular attention is given to measurement problems that arise with special force in developing countires because of parallel exchange rates, unrecorded trade, and rapidly shifting trade patterns. The three external real exchange rate measures examined are the rela- tive expenditure PPP-based RER, which uses domestic and partner country CPIs; the Mundell-Fleming or aggregate production cost RER, which uses GDP deflators; and the traded-goods RER, which can be constructed using relative unit labor costs in manufacturing, wholesale prices, manufacturing-sector deflators, or export unit values. The CPI- based measure has the important empirical advantage that the domes- tic price data required are widely available on a current basis for most developing countries so that REERs with reasonably comprehensive partner country representation can be computed. The aggregate pro- duction cost RER, in contrast, relies on GDP deflators that are available at much lower frequencies for developing than for industrial countries. This shortcoming also affects some versions of production cost-based RERs for traded goods, such as that based on manufacturing deflators. Both of these cost-based RERs (the aggregate and traded-goods ver- sions) can, in principle, be improved upon as measures of competitive- ness through the use of unit labor cost measures, since these take into account intercountry differences in average labor productivity. How- ever, lack of data on unit labor costs limits the usefulness of such mea- sures in developing countries. 4. However, traded-goods RERs computed using wholesale prices, when these are available, do permit the use of higher-frequency data as discussed in Chapter 2. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 7 A more fundamental problem with the cost-based RERs, however, is that they are based on a concept of competitiveness between domestic and foreign goods that are not perfectly substitutable. For countries with a large share of standardized commodities in their exports, the applica- bility of cost-based RERs may, therefore, be limited. For such countries the relevant concept of competitiveness is not the ability to produce at lower costs and thus sell at lower prices (expressed in a common cur- rency) than other countries producing similar products. Rather, it is the adequacy of domestic incentives to produce goods that are not greatly differentiated from (and thus must sell at similar prices to) those pro- duced by other countries. This difference makes such cost-based con- cepts seriously misleading in the presence of terms-of-trade changes. An increase in the price of domestic exports-which would increase in- ternal incentives to produce such goods-would, for example, show up as an increase in the GDP deflator or wholesale price index (WPI) and thus inaccurately suggest a deteriorating relative cost performance. Cost- based measures are therefore not usually considered to have particular conceptual advantages over expenditure-based measures in the devel- oping-country context. In view of the data availability advantages of the latter, Chapter 2 concludes that for most developing countries the REER computed using domestic and foreign CPIs is the most useful of the various external RER measures. However, both expenditure-based and cost-based external RER mea- sures can be very sensitive to the existence of parallel markets and unre- corded trade, as well as to shifting trade shares and weighting schemes. Calculations for C6te d'Ivoire illustrate the significant difference that such factors can make to estimated REERs. Hence, a variety of measures should be calculated and interpreted together to permit cross-checks, rather than relying on a single measure. Finally, a presentational point noted in Chapter 2, and worth repeat- ing here to avoid subsequent confusion, is that, like nominal exchange rates, all RER measures can be expressed both in foreign-currency terms and inversely in domestic-currency terms. When expressed in foreign- currency terms (that is, in units of foreign currency per unit of domestic currency), an increase in the RER represents an appreciation. However, when the RER is expressed in domestic-currency terms (that is, in units of domestic currency per unit of foreign currency), the inverse is true: an increase in the RER represents a depreciation. Since for some pur- poses it is useful to express RERs in foreign-currency terms and for oth- ers in domestic-currency terms, both versions are widely used in the literature and in this volume. In the interest of clarity, we have noted throughout the text and in the graphs and tables whether the RER is 8 EXCHANGE RATE MISALIGNMENT measured in foreign- or domestic-currency terms, but readers should be alert to shifts between the two measures. The Two-Good Internal RER for Tradables and Nontradables Chapter 3 turns to the two-good internal real exchange rate, the defini- tion of which is based on the familiar Swan-Salter "dependent economy" model and which is in widest use for analytical purposes in the devel- oping-country context. Although the two-good internal real exchange rate has strong analytical appeal, difficulties with this definition arise in practical applications, stemming from the absence of generally avail- able price indexes for "traded" and "nontraded" goods. Chapter 3 de- scribes and evaluates alternative approaches to the construction of such indexes, which differ according to whether they attempt to measure border prices or domestic prices as well as to whether the relative price indexes are expenditure-based or production-based. These may diverge significantly in developing countries. A familiar proxy for the internal RER, based on partner country WPIs as measures of traded-goods prices and the domestic CPI as an indicator of the price of nontraded goods, may be reasonable as long as the terms of trade and commercial policies are stable. When the terms of trade change, the measure is likely to be a better proxy for the internal RER for importables than for exportables. However, as in the case of the external RER, this measure also proves quite sensitive to parallel exchange rates, unrecorded trade, and changes in trade patterns. Hinkle and Nsengiyumva also consider the theoretical and empirical relationships between the external RER and two-good internal RER. This is a particularly important problem in the developing-country context since, as indicated above, analysis of RER issues tends to be formulated using the two-good internal RER concept, while for data availability reasons empirical work tends to rely on the external RER. Conceptually, the relationship between the two measures is well known-the home country's internal RER is a function of its external RER as well as of the internal RER of the foreign country and the relative prices of tradable goods in the two countries. Because of the role of the last two factors, a country's internal and external RERs need not move together. More- over, even if these factors were unchanged, movements in a country's internal RER are likely to be larger than those in its external RER. In Chapter 3, the two measures are compared for a specific country, and the effects on the measured RER of changes in a subset of fundamen- tals-specifically productivity and trade taxes-are analyzed. The chap- ter illustrates the familiar result that faster productivity growth in the traded than in the nontraded sector will cause the internal RER to EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 9 appreciate. Further, it shows that differentially faster productivity growth in the traded-goods sectors of partner countries than in the domestic economy could cause the external RER to depreciate at the same time. A final important caveat noted by Hinkle and Nsengiyumva con- cerns the role of the law of one price. The quantitative relationships be- tween the measured internal and external RERs all depend upon the law of one price holding for tradable goods, a supposition that has been strongly challenged by much recent empirical work on large industrial countries. If the law of one price does not hold or holds only loosely as a long- run tendency, then the effect of exchange rate movements on the internal RER will be muted, the internal and external RERs will diverge, and the external RER will not be a reliable indicator of movements in domestic relative prices. The various caveats articulated in Chapter 3 concerning the relationship between the two RER concepts are relevant for the rest of the book, in which some of the empirical work utilizes the external RER. Chapter 3 thus concludes that, despite its analytical appeal, the two- good internal RER is of limited empirical utility for low-income coun- tries. Data problems make it extremely difficult to measure the two-good internal RER with any accuracy in most countries. In addition, many of these countries experience significant exogenous variations in their terms of trade, which cannot be addressed in a two-good framework. The Three-Good Internal RERs for Exportables and Importables The final chapter in Part I, Chapter 4, considers the three-good internal real exchange rate, which disaggregates tradable goods into exportables and importables and produces two real exchange rate measures- corresponding to the relative prices of exportables and importables, re- spectively, in terms of nontraded goods. Here, the central conceptual issue concerns the choice between a two-good and a three-good frame- work. Chapter 4 analyzes the conditions under which each of these may be appropriate. The three-good framework is strongly advocated for most cases since fluctuations in the terms of trade and commercial policies are often important in developing countries. These shocks tend to move exportable and importable RERs in opposite directions, making a two- good internal RER essentially meaningless. Hence, in most cases, ana- lysts will want to examine the behavior of both the exportables and importables real exchange rates. 5. If for presentational reasons a single RER measure is needed, the price of domestic goods measured in foreign exchange may be used for this purpose as illustrated in Chapter 8. 10 EXCHANGE RATE MISALIGNMENT Overall, the three chapters by Hinkle and Nsengiyumva make the case that for low-income countries, the most useful RER measures are the CPI-based external RERs (or those using unit labor costs if the data are available) and the three-good internal RERs for exportables and importables. The external RER and its components are particularly useful for analyzing the effects of nominal shocks such as nominal ex- change rate movements and foreign and domestic inflation. The three- good internal RERs are useful for measuring the effects on domestic relative prices of real shocks such as changes in the terms of trade and commercial policy. If the law of one price holds for traded goods, it is possible to calcu- late any of the various internal and external RER measures from given values of the others. However, empirically the law of one price holds at best only loosely for traded goods, and (unknown) measurement errors affect the accuracy of all the empirical RER measures. Since inconsisten- cies in the data may pose serious analytical problems in some cases, best practice will typically involve constructing and analyzing several RER measures. In the case of the external RER, these would examine alterna- tive assumptions about trade through parallel markets, unrecorded trade, and trade shares. Similarly, different approaches to the estimation of the three-good internal RERs should be compared to the extent possible in each case. In a number of low-income countries the unavailability of the data required for timely and accurate measurement of the three-good inter- nal and the external RER for traded goods is still a serious analytical constraint. In these cases, improved data collection is a prerequisite for more accurate measurement and analysis of the real exchange rate. Determinants of the Equilibrium Real Exchange Rate In Part II, the book turns to the long-run equilibrium real exchange rate (LRER) itself. The two chapters, 5 and 6, in this part, both by Montiel, are overviews: the first of the existing empirical literature devoted to the estimation of the LRER, and the second of theory linking the LRER to its long-run fundamental determinants. Conceptual Issues and Empirical Research Chapter 5 actually takes up two separate topics. Since it is the first chap- ter in the volume that explicitly considers the question of the definition and measurement of the LRER, its first section is devoted to conceptual issues, examinrng in particular what is meant by the long-run equilibrium EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 11 real exchange rate, before describing how economists have attempted to estimate it. The purpose of this first section is to sort out some con- ceptual problems that have arisen in defining and measuring the LRER. These are of various types, two of which are worth mentioning here. First, some economists question the very notion of distinguishing between the actual RER and its notional equilibrium value, since the actual RER is itself the outcome of the economy's macroeconomic equi- librium. This argument appears to be somewhat confused, however. The distinction between the actual RER and the LRER is not one between disequilibrium and equilibrium, but rather between different types of equilibriums-that is, equilibriums conditioned on different values of macroeconomic variables. The actual RER observed at any moment may be influenced by a variety of factors that may prove to be transitory. These include speculative "bubble" factors, actual values of predeter- mined variables that differ from their long-run values, and transitory movements in both policy and exogenous variables. When at least some of the variables on which the actual "equilibrium" RER depends are unsustainable, the actual RER will tend to change over time, tracing out an equilibrium path. It is possible, then, to think of alternative "equilibrium" RERs, for which the notion of equilibrium is defined over different time horizons. For example, we can distinguish conceptually between the actual RER and a "short-run equilibrium" RER (SRER). The latter refers to the value of the RER that would be observed in the absence of speculative (bubble) factors. This value depends on "short-run fundamentals" such as the actual values of predetermined variables as well as actual and expected future values of policy and exogenous variables. Similarly, we can dis- tinguish between this SRER and a long-run equilibrium RER (LRER). In contrast to the SRER, the LRER is a function of the steady-state values of the predetermined variables and the permanent (sustainable) values of policy and exogenous variables, rather than of the actual values of these variables. Finally, we can also distinguish between the LRER and the "desired" LRER (DRER), which is conditioned on optimal values of the policy variables, permanent values of the exogenous variables, and steady-state values of the predetermined variables. Second, even if one accepts these distinctions and is specifically in- terested in measuring the LRER, a further complication arises in deter- mining the duration of the "long run" that is relevant for policy pur- poses. The traditional definition of the LRER based on the simultaneous attainment of internal and external balance, established by Nurkse (1945), suggests that the long run should be long enough for cyclical effects to have worked themselves out. However, in specifying "external balance" as a situation in which the current account is financed by sustainable 12 EXCHANGE RATE MISALIGNMENT net capital inflows, this definition leaves open the question of whether the long run implies that the economy has reached a steady-state inter- national net creditor position. Alternative definitions of external bal- ance, built on different assumptions about the economy's net external creditor position, are examined in Chapter 5. The second part of Chapter 5 surveys existing methods of estimating the LRER (based on various definitions of "external balance") in both industrial and developing countries. After reviewing evidence on the validity of purchasing power parity (PPP) as a theory of the LRER, ap- plications of three alternative approaches to empirical estimation of the LRER are surveyed: (a) a recursive partial-equilibrium trade-equations approach, (b) an approach based on the simulation of macroeconometric models, and (c) two varieties of reduced-form estimation, a traditional one and one based on unit-root econometrics. Each of these techniques is subsequently described, analyzed, and illustrated in detail in Part III of this book. Thus, the role of this survey is to provide background for the individual estimation techniques to be described later, as well as to explore the relationships among them. An Analytical Model Chapter 6 then presents a theoretical model of the determination of the LRER that is intended to synthesize previous literature on the determi- nants of the LRER. The role of this chapter is to identify the set of vari- ables that may potentially act as long-run fundamentals and to deter- mine the qualitative nature of their influence on the LRER. The vari- ables identified there are domestic supply-side factors, fiscal policy, changes in the international economic environment, and commercial policy. Each of these is discussed in turn below. Domestic supply-side factors. These essentially refer to differences in sectoral productivity growth rates-particularly, the Balassa-Samuelson effect. Traditionally, this effect has been interpreted as arising from faster productivity growth in the traded-goods sector than in the nontraded- goods sector. Differential productivity growth of this type requires an appreciation of the long-run equilibrium value of the internal RER. Fiscal policy. Permanent changes in the distribution of government spending between traded and nontraded goods affect the LRER in dif- ferent ways. Additional tax-financed spending on nontraded goods, for example, creates incipient excess demand in that market, requiring a real appreciation to restore equilibrium. By contrast, tax-financed in- creases in spending on traded goods put downward pressure on the trade balance and require a real depreciation to sustain external balance. Changes in the international economic environment. Changes in an economy's external terms of trade, the flows of external transfers, the EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 13 world inflation rate, and the level of world real interest rates, all may potentially influence the LRER. Improvements in the terms of trade tend to appreciate the equilibrium real exchange rate for importables by im- proving the trade balance and creating excess demand for nontraded goods. Whether the long-run real exchange rate for exportables depreci- ates or appreciates is ambiguous in the theoretical model. Empirically, however, the exportables RER almost always depreciates when the terms of trade improve because the price of exports tends to rise much more than the price of nontraded goods. Increases in the flow of external transfers received also appreciate the equilibrium RER through posi- tive effects on the sustainable current account balance. In the model analyzed in Chapter 6, changes in world inflation affect the equilibrium real exchange rate through effects on transactions costs associated with changes in real money balances. The direction of these effects on the LRER depends on whether such costs are incurred prima- rily in the form of traded or nontraded goods. The absorption of either type of goods by transactions costs effectively reduces their supply. Hence, when transactions costs are incurred in the form of traded goods, an equilibrium real depreciation is required to maintain external bal- ance; but when they are incurred in the form of nontraded goods, an equilibrium real appreciation is required to maintain internal balance. The effects on the LRER of changes in world real interest rates de- pend on the nature of the domestic economy's financial links with the rest of the world. In the analytical model described in this chapter, al- though the domestic economy is financially open, its real interest rate is independent of the world rate in the long run, being determined in- stead by the domestic rate of time preference. In this model, reductions in world real interest rates cause the long-run equilibrium real exchange rate to depreciate. The reason is that lower world interest rates induce capital inflows that reduce the country's net creditor position over time, and the long-run loss of net interest receipts requires a real depreciation to maintain external balance. The opposite result is, however, possible with alternative assumptions about the determination of domestic in- terest rates as explained in footnote 12 below. Commercial policy. Finally, trade liberalization is associated with a long- run depreciation of the equilibrium RER. The effect of liberalization is to switch resources into the nontraded (or non-import-competing) sec- tor. The emergence of incipient excess supply in the nontraded-goods market requires a depreciation of the real exchange rate. The challenge in estimating the LRER, of course, is assessing the quan- titative influence on the LRER-if any-of changes in each of the above variables. Alternative methods of doing so are described in Part III of the book. 14 EXCHANGE RATE MISALIGNMENT Methodologies for Estimating the Equilibrium RER: Empirical Applications The heart of the book is Part III, in which alternative techniques for esti- mating the LRER are presented. Four such techniques-all of them briefly reviewed earlier in the empirical survey-are analyzed individually and illustrated with specific empirical applications in the four chapters, 7 to 10, that make up this part of the book. Chapter 7 focuses on the two estimation techniques that are in widest operational use: the purchas- ing-power-parity (PPP)-based approach and a recursive partial-equilib- rium approach based on adjustments in the economy's external resource balance, which we have dubbed the trade-equations approach. There are two versions of the trade-equations approach in wide use. The first one is a Mundell-Fleming version that takes export volumes to be deter- mined on the demand side of the market; export supply is taken to be perfectly elastic. The second one is a three-good version that takes ex- port demand to be perfectly elastic; export volumes are correspondingly determined on the supply side of the market. Empirical application of the trade-equations approach also involves two analytical tasks-mea- surement of the underlying (or structural) resource balance and deter- mination of a target long-run resource balance-that are common to most other methodologies for estimating the LRER empirically.6 Chapter 7 provides a general overview of the trade-equations approach with an illustration for C6te d'Ivoire. Chapter 8 presents an application of the three-good trade-equations approach, which focuses on the role of one specific "fundamental" (the terms of trade), and applies the technique to a larger group of 12 CFA countries. The last two chapters in Part III analyze the two more explicitly general-equilibrium approaches. Chap- ter 9 describes how simulations of fairly traditional empirical macro- economic models can be used to estimate the LRER in developing coun- tries. Chapter 10 provides a detailed description and two applications of a relatively new approach based on single-equation reduced-form estimation using unit-root econometrics. The following section summa- rizes the findings of each of these four chapters. The Relative PPP-Based Approach The simplest and most venerable technique for estimating the LRER in developing countries, no less so than in industrial countries, is the PPP 6. The term "resource balance" is used throughout this volume to refer to the difference between exports and imports of goods and nonfactor services. It is equal to gross domestic savings less gross investment. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 15 approach. Chapter 7 of Part III, by Ahlers and Hinkle, describes the PPP- based method, as well as the trade-equations method discussed below. The Ahlers and Hinkle exposition is based on an illustration of how the simple PPP method could have been used to estimate the degree of mis- alignment that characterized C6te d'Ivoire prior to the devaluation of the CFA franc. Relative PPP may be applied either broadly to the external RER for all goods or more narrowly to just the RER for traded goods. The ratio- nale for applying relative PPP to traded goods, as an application of the law of one price, is stronger; and this is the standard practice in indus- trial countries. However, lack of data on the RER for traded goods, as in the C6te d'Ivoire example considered in Chapter 7, usually limits one to the use of RER for all goods in developing countries. The use of the relative PPP-based method can be justified in one of two ways. On the one hand, the analyst may simply adopt ex ante the traditional relative-PPP view on the determination of the long-run equi- librium real exchange rate, which essentially takes the LRER to be a constant.7 On the other hand, the LRER may be considered by the ana- lyst to be determined by a broad set of fundamentals, which may turn out ex post to be stationary in a time-series sense for the specific appli- cation at hand. In the first case, the decision to apply the PPP approach would be made before looking at the data. In the second case, the PPP approach would be adopted only after the RER in the country under review passes a test of stationarity. When relative PPP is assumed to hold ex ante, measuring the equi- librium real exchange rate essentially involves removing the effects of nonsystematic transitory shocks. In practice these are eliminated by iden- tifying a base period in which such shocks are believed, on the basis of independent evidence, to have been negligible-a procedure that en- sures that the actual real exchange rate coincided with its equilibrium (PPP) value during that period. Thus the actual real exchange rate in the base period represents the estimate of the equilibrium rate. The nomi- nal exchange rate consistent with the LRER from that moment on can then be calculated by simply adjusting the nominal exchange rate for the cumulative difference between domestic and foreign inflation. The alternative case is that the LRER is interpreted as subject to change in response to changes in underlying fundamentals but turns out em- pirically to be stationary for a particular country. In this case, the stationarity of the RER forces the analyst to take the position that its 7. This is in contrast to the absolute version of PPP, which takes the LRER to be unity. 16 EXCHANGE RATE MISALIGNMENT fundamental determinants are either individually stationary-that is, that the "permanent" values of the fundamentals have not changed dur- ing the sample period, though the fundamentals may have been subject to transitory fluctuations-or that any nonstationary fundamentals must be cointegrated among themselves. In either situation, the LRER can still be measured using a base-year value, though the identification of a suitable base year is more complicated under this interpretation, as ex- plained below. Ahlers and Hinkle refer to the PPP-based method that estimates the LRER using the value of the RER during some base year as the "PPP base-year" approach. It calculates misalignment by simply plot- ting the real exchange rate over time and comparing its value during the period of interest to the corresponding value in the base year in which the real exchange rate was judged to be at its long-run equilibrium value. The empirically oriented exposition of the PPP base-year approach by Ahlers and Hinkle is particularly appropriate because in this meth- odology everything depends on the identification of a suitable base year. As mentioned above, how the base year is chosen depends on whether the rationale underlying the procedure is a simple ex ante relative PPP- based one or a more sophisticated one in which the real exchange rate is driven by stationary fundamentals. In the simple PPP case, the "inde- pendent evidence" of equilibrium referred to previously is likely to con- cern the behavior of a particular outcome variable, such as the resource balance. In contrast, from the "stationary fundamentals" perspective, the base year chosen should be a recent year in which the actual ex- change rate is believed to have been close to its equilibrium value be- cause all the fundamentals were close to their sustainable values. This requirement makes the application of the PPP methodology more complicated in the latter case. As explained in the survey of empirical estimation in Chapter 5, the set of fundamentals to be considered in choosing a base year may in- clude both exogenous and policy variables. In assessing the behavior of the exogenous variables, the analyst may look, for example, for terms of trade that are reasonably close to their likely long-run trend levels and for capital flows that are consistent-in amount and terms-both with the likely long-term availability of capital and the country's debt-servicing capacity. For assessing the permanence of the policy stance, the relevant criteria may involve the attainment of growth, investment, and infla- tion targets during various years over the sample period. A common problem in selecting appropriate base years is that, be- cause of policy shortcomings and external constraints, years in which exogenous variables were at sustainable levels are not always years in which policy variables were at desirable levels. Thus, the choice of a base year tends to call for subjective judgments in determining when EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 17 the real exchange rate was near its long-run equilibrium value. For ex- ample, historically, desirable growth and investment levels have some- times been attained only when the terms of trade were temporarily in- flated or when capital flows were unsustainable. Conversely, sustain- able terms of trade and capital flows have often been associated with undesirable growth and investment outcomes. Hence, in applying the PPP base-year approach under the "stationary fundamentals" interpre- tation, the analyst is often forced to make tradeoffs between the sustainability of exogenous variables and that of policy variables. One way to deal with this problem is to estimate the sustainable val- ues of the fundamentals on the basis of their sample means or, in the trend-stationary case, as their trend values within the sample. In effect, this procedure amounts to estimating the LRER as the sample mean or the trend value of the RER within the sample, rather than as the particu- lar value of the RER in a specified base year. This procedure can be re- ferred to as the PPP average or trend approach. Ahlers and Hinkle also illustrate this alternative method of estimating the LRER in applications of the PPP-based method. Empirically, a large appreciation of the RER relative to its trend value in a short period of time is one of the most reliable statistical indicators of misalignment and a potential exchange rate crisis. The relative PPP-based approach, however, has one severe limita- tion: if the RER is nonstationary, its equilibrium value will be affected by changes in the fundamental variables that determine it. If these fun- damentals are subject to permanent changes, and the evidence suggests that they usually are, then techniques for estimating the long-term value of the equilibrium exchange rate must take these changes into account. In other words, estimates of the LRER must depend on the estimated permanent changes in the fundamentals. The Trade-Equations Approach The PPP-based approach described above was originally motivated by the relative-PPP theory of exchange rate determination. Similarly, the trade-equations methodology is also based on a venerable analytical tool in open-economy macroeconomics-in this case, the partial-equilibrium "elasticities" approach to exchange rate determination. This methodol- ogy is based on the notion that the primary macroeconomic role of the real exchange rate is to influence the resource balance through expendi- ture-switching mechanisms. It is more sophisticated than the simplest interpretation of the empirical PPP approach in that it acknowledges that the equilibrium real exchange rate is not necessarily constant. Ahlers and Hinkle describe and illustrate the trade-equations ap- proach as well as the relative-PPP approach. As mentioned previously, 18 EXCHANGE RATE MISALIGNMENT there are two standard versions of the trade-equations approach. The version most commonly used in industrial countries is based on the Mundell-Fleming production structure. In this framework, complete spe- cialization in the production of one good by both the domestic and for- eign countries (each country's own GDP) makes export supply func- tions perfectly elastic, while the domestic and foreign goods are taken to be imperfect substitutes in demand. Export and import quantities are consequently both demand-determined, and the real exchange rate ex- erts its effect on the trade balance through its influence on the domestic demand for imports and on the external demand for the country's ex- ports. This perspective is typically adopted for industrial countries, as well as for some developing countries whose exports are dominated by differentiated manufactured goods. The alternative version is usually applied to developing countries in which exports are instead dominated by undifferentiated primary products. In this case, it is more appropri- ate to consider export demand as being infinitely price-elastic and to recognize a finite export supply elasticity.' The quantity of exports is thus determined by the elasticity of export supply In both versions of the trade-equations approach, the resource bal- ance will in general depend on the real exchange rate as well as other variables. For given values of the latter, the "equilibrium" value of the real exchange rate must be that which generates the "equilibrium" value of the resource balance-that is, that value of the resource balance that is consistent with balance of payments equilibrium. Given a target for external reserves and an exogenously determined volume of net resource flows (net capital inflows plus net interest receipts plus net transfers), the equilibrium value of the resource balance is determined. Alterna- tively, for fully creditworthy countries in which capital markets can be assumed to provide the financing required to cover a resource deficit, a sustainable or trend saving-investment balance can be projected sepa- rately and assumed to determine the equilibrium resource balance. In either case, the equilibrium value of the real exchange rate can then be calculated from the required change in the initial resource balance for given initial values of exports and imports if the relevant import and export demand or supply elasticities are known. The three key empirical requirements for implementing the trade- equations approach are: (a) estimates of the elasticity of exports and im- ports with respect to the real exchange rate; (b) methods for determin- ing a target resource balance to be used in the analysis; and (c) tech- niques for estimating the effects on the initial resource balance of 8. Conceptually, this approach implies supposing that the home country pro- duces at least one other type of good besides the exportable good. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 19 variables that affect it, other than the real exchange rate. Empirical esti- mates of the relevant elasticities needed for step (a) are given in Chapter 11 on trade flows and the RER. Steps (b) and (c), which are also required in many applications of the other methodologies discussed subsequently, are analyzed in detail by Ahlers and Hinkle. The specification of the target resource balance, step (b), is often one of the most problematic steps in the empirical estimation of the LRER. A particularly useful contribution of the Ahlers-Hinkle chapter, therefore, is its inclusion of a comprehensive discussion of practical methods for specifying the volume of net capital inflows and reserve accumulation required to derive the target resource balance. The authors describe two polar ways of establishing sustainable capital flows and a target resource balance: one for noncreditworthy countries that must rely entirely on aid flows and the other for creditworthy countries that have full access to credit markets. In the case of noncreditworthy countries-that is, coun- tries that absorb external resources primarily in the form of aid flows- resource balance targets are essentially based on projections of aid avail- ability. Such projections can be derived from independent information (for example, from donor sources) or can be projected on the basis of past history. For countries that are judged creditworthy by international financial markets, a variety of means is available to project sustainable capital flows. These can be based on demand-side or supply-side deter- minants. The former refer to domestic saving-investment balances that are deemed desirable or are otherwise judged sustainable. The latter may be based on debt stocks that are judged compatible with a country's intertemporal budget constraint or on credit allocation rules of thumb used by international lenders. However calculated, an increased inflow of capital permits the accommodation of a larger "equilibrium" resource balance deficit and is thus consistent with a more appreciated value of the equilibrium real exchange rate. As noted above, the resource balance may depend on variables other than the real exchange rate, such as the level and composition of aggre- gate demand, the external terms of trade, and commercial policy. Hence, it is usually necessary to determine the underlying or structural resource balance corresponding to a particular value of the RER by adjusting the actual resource balance in the given year for cyclical, exogenous, and policy changes that affect it. The simplest solution to this problem is to identify a base year, simi- lar to that used in the relative PPP-based approach, in which the actual 9. For a description of the application of this methodology in the context of financial programming exercises, see Khan, Haque, and Montiel (1990). 20 EXCHANGE RATE MISALIGNMENT RER and its fundamental determinants are believed to have been close to their equilibrium levels. This technique is sometimes employed in empirical applications of all of the methodologies for estimating the LRER as explained in Chapters 8 to 10. However, for the reasons explained on pages 16 and 17 above, a suit- able base year may not be available in many cases. Ahlers and Hinkle demonstrate an alternative two-step procedure for taking into account the effects of changes in variables other than the RER that influence the resource balance such as the terms of trade, taxes on international trade, and underutilized productive capacity. First, the initial resource balance is adjusted to reflect the impact of changes in these variables, resulting in an "adjusted" resource balance.10 Second, the required change in the real exchange rate is calculated as that which would cause a change in the resource balance equal to the difference between its adjusted and target values. For example, for a given target resource balance, the achievement of a higher long-run growth target for the economy may require a shift in the composition of aggregate demand from consump- tion to investment. If the import intensity of investment spending ex- ceeds that of consumption, an increase in the share of investment in aggregate demand would increase the resource balance deficit associ- ated with any given real exchange rate. Thus, such a change in the com- position of demand would result in a larger adjusted resource balance deficit. To reconcile the larger projected resource balance deficit with the unchanged projected long-run equilibrium value of capital inflows, a larger real depreciation would be required. Hence, the adoption of a more ambitious long-run growth target would imply a more depreci- ated long-run equilibrium real exchange rate. The second chapter in Part III, Chapter 8 by Devarajan, links the par- tial-equilibrium trade-equations approach with general equilibrium models. Devarajan shows how the trade-equations approach can be ex- tracted from a restricted form of a computable general equilibrium (CGE) model. The particular model on which the Devarajan chapter is based (taken from Devarajan, Lewis, and Robinson (DLR, 1993)) utilizes a three- good framework, with exports, imports, and domestic goods. As indi- cated above, the extension to three goods has important advantages in 10. To the extent that the composition of aggregate demand (for example, between consumption and investment, between private or public expenditure, or between different categories of government spending) affects the resource balance, the change in the real exchange rate required to achieve the target re- source balance target will depend on how the target resource balance is attained. The adjustment procedure suggested by Ahlers and Hinkle also permits taking into account such effects. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 21 developing-country applications. Because of its two-good production structure, the Mundell-Fleming approach cannot distinguish between the terms of trade and the real exchange rate. Thus, it cannot be used to analyze the impact of changes in fundamentals that involve changes in the domestic relative price of exportables and importables, such as the terms of trade and commercial policy. A three-good framework is nec- essary to analyze how the LRER is affected by changes in the relative prices of imports and exports. The particular concern of the Devarajan chapter is to demonstrate how the effects on the LRER of changes in such fundamentals can be handled in this expanded framework." The DLR method is based on three equations: (a) a "transformation function" linking the exports-GDP ratio to the relative price of exports in terms of domestic goods, (b) a "substitution function" relating the imports-GDP ratio to the relative price of imports in terms of domestic goods, and (c) an identity deriving the resource balance-GDP ratio from the export and import ratios. Given a target value for the resource bal- ance, as well as exogenously determined export and import prices, the system can be solved for the equilibrium value of the price of domestic goods and, therefore, for the real exchange rates for exportables and importables. Devarajan's chapter thus illustrates how a general-equilib- rium "fundamentals" approach to the determination of the LRER can be simplified and tailored to a specific application. An attractive feature of this method relative to the more explicitly general equilibrium ap- proaches described below is that it benefits from the primary opera- tional advantage of partial-equilibrium approaches: it requires minimal data and is easy to implement. To illustrate the relative ease with which this methodology can be implemented empirically, the DLR model was applied to the estimation of misalignment in 12 of the 13 countries in the CFA zone on the eve of the devaluation of the CFA franc. Since the CFA countries are special- ized primary exporters, changes in the terms of trade proved to be the dominant influence on the LRER in this case, justifying the focus on this variable. The results indicated a substantial degree of misalignment, averaging 31 percent but varying substantially among the CFA coun- tries, with middle-income countries and oil producers exhibiting the most pronounced degree of misalignment. As we shall see below, these estimates are consistent with those obtained in the subsequent chapter by Baffes, Elbadawi, and O'Connell for C6te d'Ivoire and Burkina Faso, using a single-equation methodology. Both Devarajan and Baffes, 11. Devarajan also shows how the DLR methodology can be applied to exam- ine the effects of changes in other fundamentals conventionally considered in the trade-equations approach in industrial countries such as capital flows. 22 EXCHANGE RATE MISALIGNMENT Elbadawi, and O'Connell find a substantial degree of overvaluation in COte d'Ivoire by 1993. In contrast, the real exchange rate for Burkina Faso is found to be quite close to the LRER estimated under both methodologies. The two operational estimation techniques described in Chapters 7 and 8 impose minimal data requirements, appear to make few demands on empirical knowledge about the structure of the relevant economy, and are computationally straightforward. Thus, they have been the tech- niques of choice for estimating the LRER when research resources are limited or when the context in which estimates of the LRER are needed does not allow time for further research. They remain extremely useful under both sets of circumstances. The Structural General-Equilibrium Approach A key shortcoming of the trade-equations approach, however, is that it may not do enough justice to the general-equilibrium nature of the proccess by which the equilibrium RER is determined. While the de- mand for imports and exports undoubtedly depends on their relative prices in terms of other goods, it also depends on the level and compo- sition of domestic spending (as the "absorption" approach of Alexander (1951) emphasized), as well as on the costs of production of exportables and importables. The problem is that variables such as these and the capital flows that determine the "equilibrium" value of the resource balance are themselves endogenous and thus are determined by the ul- timate fundamentals identified in the discussion above of the long-run equilibrium RER. Consequently, the real exchange rate is deeply em- bedded in the economy's short-run macroeconomic equilibrium. The trade-equations approach, however, employs a recursive partial-equi- librium methodology. Given required changes in an economy's resource balance, it determines new equilibrium values for the RER, imports, and exports but not for other important macroeconomic variables such as government revenue, saving, and investment. Nor does it explicitly al- low for feedback from the RER to the variables determining the target resource balance (capital flows or the saving-investment balance). While rough adjustments can be made for some of the more important income and feedback effects, one would be more confident of the results if they were determined in a complete general-equilibrium framework that takes into account all important macroeconomic interactions in a fully consis- tent manner. Chapters 9 and 10, the two remaining chapters in Part III, implement general-equilibrium methods for detecting empirically the influence of changes in some fundamentals on the LRER. By and large, these chap- ters take a practical approach. Their objective is to estimate the value to EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 23 which a country's RER would tend to converge over time, given sus- tained values of certain "fundamentals," including both policy variables and variables that are exogenous to the economy. It is important to em- phasize that these chapters set a limited task for themselves. They are concerned neither with deriving optimal values of the policy variables, which have been considered necessary for some definitions of the LRER, nor with detailed exploration of the time-series properties of the truly exogenous variables. These restrictions greatly simplify both the con- ceptual and empirical issues and are logically defensible. Both the opti- mal setting of the broad range of policy instruments that may influence the long-run equilibrium real exchange rate and the specification of ap- propriate techniques for decomposing movements in exogenous vari- ables into permanent and transitory components are logically separate from the issue of how particular values of the policy and exogenous variables affect the long-run equilibrium real exchange rate. Thus, Chap- ters 9 and 10 focus on the task of assessing how the value of the LRER is empirically affected by once-and-for-all changes in the values of what- ever subset of these variables is relevant for the particular technique being used. Chapter 9, by Haque and Montiel, adopts a structural general-equi- librium modeling approach. The model employed, taken from Haque, Lahiri, and Montiel (HLM, 1993), is based on a Mundell-Fleming pro- duction structure and assumes a high degree of integration of the do- mestic economy with international financial markets. In that sense, the HLM model is best suited for applications to middle-income develop- ing countries with diversified manufactured exports and an open capi- tal account. The model was estimated with panel data from a large sample of developing countries. Consequently, the simulations produced with the HLM model are intended to be representative of such economies, illustrating the outcomes in a model economy, rather than generating an estimate of the LRER for a specific country. In estimating changes in the LRER using simulations from an em- pirical macroeconomic model, the Haque-Montiel chapter is closely re- lated to the work of Williamson (1994) and others on the estimation of the LRER for industrial countries. However, in addition to being based on a "representative" economy, the simulation exercises in Chapter 9 differ from those conducted by Williamson in two other ways. First, in contrast to the Williamson approach, Haque and Montiel make no at- tempt to identify "desirable" values of the policy fundamentals. Sec- ond, they report "analytic" simulations, consisting of tracing the dy- namic responses of the model economy to permanent shocks adminis- tered to individual fundamental variables, with a view to exploring how such shocks would affect the equilibrium real exchange rate that char- acterizes the new postshock steady state. In such simulations, policy 24 EXCHANGE RATE MISALIGNMENT and external variables are exogenous, and the sustainable trade balance is endogenously determined simultaneously with the LRER. By con- trast, the simulations in Williamson (1994) are "real-time" simulations, which solve for the value of the RER associated with the achievement of internal and external balance targets within a specified policy-relevant period of time. Since the external balance target is specified exogenously and the time frame allowed to attain it will in general be shorter than that required for the model to approach its steady-state configuration, the attainment of such targets in general requires endogenous adjust- ment of policy variables. The simulations in Chapter 9 confirm that nominal variables-namely, the nominal exchange rate and monetary policy-have no effect on the LRER, which is a real variable. This result is a consequence of the model's long-run neutrality to monetary shocks. In contrast, permanent changes in "real" fundamentals do affect the LRER. To complement the exercises conducted in the preceding chapters, the simulations of real shocks by Haque and Montiel analyze the effects of changes in some fundamen- tals not considered there. These are the effects of a permanent change in the world real interest rate and in external demand, considered sepa- rately, as well as a shift in the composition of government spending from foreign to domestic goods. A permanent increase in the world real inter- est rate depreciates the LRER in the HLM model, while increases in both external demand and in government spending on domestic goods cause the LRER to appreciate.12 The Haque-Montiel simulations are used to estimate the elasticity of response of the LRER to permanent changes in the set of fundamentals considered. These results can be used in a number of ways: a. The elasticities themselves can be used directly to estimate changes in the LRER in specific applications when one of the fundamen- tals has changed in a known way, b. The structural parameter estimates of the model can be imposed in a structural model of an actual economy for which the LRER is 12. The qualitative result for the external real interest rate here is the opposite of that derived in the theoretical model in Chapter 6. The reason is that the way that imperfect capital mobility is modeled in the theoretical paper causes the domestic real interest rate to remain unchanged in response to increases in the external rate (since it is determined by the exogenous domestic rate of time pref- erence). The Haque-Montiel model, in contrast, assumes that the domestic inter- est rate is determined by the world interest rate so that the domestic real interest rate rises one-for-one with increases in the world rate. The negative effect of the higher domestic interest rate on the demand for domestic goods causes the LRER to depreciate in the Haque-Montiel model. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 25 to be estimated, and then simulations similar to those of Haque and Montiel can be run using data for that economy c. The model's specification can be used as guidance for actual esti- mation of a similar structural model for the economy in question, and the required simulations can be based on the estimated model. Haque and Montiel illustrate the second of the above possibilities in an application to Thailand. Retaining the estimated representative pa- rameters but using Thai macroeconomic data, they estimate the LRER for Thailand in 1995 on the assumption that the actual and equilibrium real exchange rates coincided in 1991. They find that between 1991 and 1995 the Thai LRER depreciated by 17 percent. Since the actual real ex- change rate depreciated by only about 4 percent over the same time, Haque and Montiel estimate that the baht was overvalued by about 13 percent in 1995. In principle, the general-equilibrium modeling approach illustrated in Chapter 9 is the most attractive method for estimating the LRER. It permits the incorporation of the full range of macroeconomic influences that may potentially affect the LRER and imposes a minimum of restric- tive and possibly erroneous assumptions about the structure of the economy. Two traits argue strongly in favor of this methodology: the richness of the macroeconomic interactions that can be taken into ac- count in estimating the LRER by simulating a fully dynamic aggregate macroeconomic model and the flexibility that this method offers in de- fining alternative versions of the LRER over different time horizons. Moreover, an important feature of this approach for policy purposes is that its structural nature makes transparent the mechanism through which the LRER is determined, at least in principle. This structural general-equilibrium approach, however, is subject to a variety of limitations. Some of these are shared with other approaches. For example, when implemented in "real-time" simulations-which are its most operationally relevant form-the structural general-equilibrium approach relies, like the trade-equations approach, on an exogenous specification of the equilibrium resource balance. More important, the estimation of general-equilibrium macroeconomic models places very strong demands on economic theory, on the power of statistical tech- niques, and on the availability and quality of data. Even in industrial countries, where off-the-shelf models with known track records are of- ten available, doubts about model specification, empirical estimation, and parameter stability have eroded confidence in these models during recent years. With no previous track record, made-to-suit models for individual developing countries with limited data and more frequently changing economic structures and policy regimes confront a higher 26 EXCHANGE RATE MISALIGNMENT hurdle of credibility. Furthermore, the modeling approach has serious operational limitations. In the absence of a previously existing model, it is likely to be very time consuming and expensive to implement. It may thus be more suited to large research projects in countries with long time-series data than to operational applications in most low-income developing countries. For the near future, estimates of the LRER de- rived from simulations of dynamic macroeconomic models should be treated as indicative in developing-country applications and used to supplement and inform other approaches to estimation. The Reduced-Form General-Equilibrium Approach The final chapter in Part III-Chapter 10, by Baffes, Elbadawi, and O'Connell-abandons the specification of structural models, adopting a single-equation reduced-form methodology. It relies on unit-root econo- metrics to measure the effect that potential fundamentals have on the LRER in two CFA franc countries, C6te d'Ivoire and Burkina Faso.13 The attraction of this method is that, like the structural general-equilibrium approach, it incorporates the full general-equilibrium interaction of the fundamentals in a dynamic structure that generates a time series, rather than just a point estimate, for the LRER. Yet, relative to the structural general-equilibrium approach, it places fewer demands on both theory and data. From the perspective of theory, the method requires an appro- priate specification of long-run relationships, but the dynamic structure of the economy does not need to be imposed ex ante. Instead, it is deter- mined entirely by the data. The data required, in turn, are only those that would enter the reduced-form equation for the real exchange rate in a short-run macroeconomic equilibrium model. Structural equations for the economy do not have to be estimated, and data on other short- run endogenous macroeconomic variables are not required. The fundamentals considered by Baffes, Elbadawi, and O'Connell for the two countries in their study include many of those examined in the previous chapters: the terms of trade, trade openness (as a proxy for commercial policy), capital flows, and the composition of domestic ab- sorption (the share of investment in GDP). Interestingly, these variables prove to be nonstationary and cointegrated with the real exchange rate in C6te d'Ivoire but stationary in Burkina Faso. In the case of Burkina Faso, all but the composition of absorption prove to be statistically sig- nificant determinants of the (stationary) real exchange rate. Thus, Burkina Faso provides an illustration of how in certain cases PPP can continue 13. Previous applications of this methodology to developing countries in- clude Elbadawi (1994), as well as Elbadawi and Soto (1994, 1995). EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 27 to provide an adequate representation of the behavior of the LRER, de- spite the role of "fundamentals" in influencing the LRER. As mentioned previously, the key ingredient in reconciling PPP with a fundamentals- driven theory of the LRER is stationarity of the fundamentals, as in Burkina Faso. Baffes, Elbadawi, and O'Connell show how their estimated cointegrating equations can be used to construct estimates of the LRER. Given the estimated cointegrating equation, they utilize a variety of sta- tistical techniques to estimate the permanent values of the fundamen- tals (including employing the actual values, calculating moving aver- ages, and computing Beveridge-Nelson decompositions). In addition, Baffes, Elbadawi, and O'Connell employ counterfactual simulations of the fundamentals, an innovation that can allow these variables to take on out-of-sample values and permits measuring normative as well as positive misalignment. Substituting their estimates of the permanent or sustainable values of the fundamentals into the cointegrating regres- sions, they derive for both countries LRER estimates that can be com- pared with the actual RER to provide measures of misalignment. The results suggest that overvaluation was severe in C6te d'Jvoire in 1993 (approximately 34 percent in domestic-currency terms), just prior to the devaluation of the CFA franc, but that Burkina Faso escaped major episodes of overvaluation during the sample period.4 This finding is consistent with the widely held view that overvaluation was a more serious problem among the middle-income CFA countries than for the low-income countries. As already indicated, the reduced-form methodology has significant advantages over both the traditional PPP and trade-equations ap- proaches, on the one hand, and simulations of general-equilibrium mod- els, on the other. Accordingly, it has begun to receive a substantial amount of attention from researchers as a technique for estimating the LRER in both industrial- and developing-country contexts.5 Because of these advantages, it is a promising avenue for further research. Nevertheless, the methodology is not without its own shortcomings. Chief among these are that the statistical tests involved have low power in small samples and that the dynamic specifications required in some of the statistical techniques employed absorb a large number of degrees of freedom, par- ticularly when a priori exclusion restrictions cannot be imposed on the set of included fundamentals. As a result, estimates of the LRER de- rived using this technique may be fragile. In particular, they may not 14. Devarajan also found only a mild misalignment in Burkina Faso. 15. See the survey of empirical research in Chapter 5. 28 EXCHANGE RATE MISALIGNMENT prove to be robust with respect to the set of included fundamentals or to procedures for selecting the "best" model in circumstances in which the set of potential fundamentals is large and time series are short, as is typically the case in developing countries. Operationally, like the trade- equations and structural general-equilibrium approaches, the procedure usually requires an exogenous specification of the equilibrium resource balance. In addition, use of the reduced-form methodology may be hin- dered not only by inadequate time-series data in low-income countries but also, in crisis situations, by the time-consuming nature of the fairly sophisticated econometric analysis that is involved in implementing it. Policy and Operational Considerations The last part of the book, Chapters 11 to 13, rounds out the analysis of techniques for estimating the LRER by discussing three operational con- siderations. The first has to do with the applicability of the analysis in this book to small low-income countries. All of the approaches to esti- mating the LRER described here rely on the key macroeconomic role of the real exchange rate in influencing the trade balance by allocating demand and supply between traded and nontraded (or foreign and domestic) goods. Many observers, however, question the empirical strength of this influence, particularly for small low-income countries, on the basis of various types of elasticity pessimism. This issue is taken up in Chapter 11, the first chapter in Part IV. The second consideration has to do with countries having dual exchange markets. The question in this case is how much information the parallel exchange rate-which can be observed directly--contains about the LRER that would prevail if the exchange markets were unified. In an extreme case, if the parallel rate is simply taken as revealing the value of the "true" long-run equi- librium real exchange rate, one would circumvent the need to imple- ment any of the techniques described in this book for measuring the LRER in countries with dual exchange markets. The validity of this ap- proach is considered in Chapter 12. The final issue taken up in Part IV is not directly related to the estimation of the LRER but is likely to be of interest in operational attempts to correct misalignment. It concerns how to estimate, in operational applications, the nominal exchange rate move- ment required to eliminate any misalignment identified using one of the previously described techniques for measuring the LRER. Empirical Estimates of Trade Elasticities Chapter 11 by Ghei and Pritchett analyzes a topic that is central to the macroeconomic role of the real exchange rate and therefore that must be addressed in the definition and estimation of the LRER: what effect does EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 29 the real exchange rate have empirically on trade flows and external ad- justment in developing countries? While the role of relative prices in adjusting trade balances has long been a central tenet of open-economy macroeconomics, this tenet has been questioned by "elasticity pessimists" as well as by advocates of "global monetarism." More recently, the ef- fects of real exchange rate changes on the trade balance have also been called into question by sophisticated empirical analysis (see Rose 1990). Since most definitions of the LRER emphasize the role that the RER plays in the simultaneous achievement of internal and external balance, this issue is an important one for this book. Ghei and Pritchett ask whether the empirical effectiveness of the real exchange rate in adjusting the trade balance is sufficiently strong to link "external balance" outcomes to the path of the RER, particularly in small low-income countries, for which "elasticity pessimism" has been most widespread. They further ask how, if the RER does significantly affect trade flows, useful estimates of the relevant elasticities can be obtained even for countries in which notional import demand cannot be observed in the historical data because of the prevalence of foreign exchange ra- tioning. Ghei and Pritchett group reasons for doubting elastic import and export responses under three types of elasticity pessimism regard- ing the elasticity of import demand and export supply in the develop- ing country itself as well as the elasticity of demand for the country's exports in world markets. They find that none of the three pessimisms is justified, even for small low-income countries for which such con- cerns are most often articulated. Along the way, they provide represen- tative values of the relevant elasticities for small low-income countries. These values can be used by practitioners in empirical applications of the trade-equations approach for countries where the accurate estima- tion of such elasticities proves to be impractical. Ghei and Pritchett con- clude that a reasonable range for the aggregate price elasticity of de- mand for imports is -0.7 to -0.9, even for low-income countries, and that elasticities of export supply tend to be in the range of 1.0 to 2.0. Consequently, given the typically high world price elasticity of demand for exports from individual countries, RER movements should gener- ally be expected to have significant effects on trade balances. Using the Parallel Market Premium as an Indicator of Misalignment The frequent use of quantitative restrictions on the availability of for- eign exchange under managed exchange rate systems in many develop- ing countries has in the past given rise to parallel exchange rates as ex- cess demand for foreign exchange spills over into the unofficial market. Since private traders buy and sell foreign exchange at a price that is 30 EXCHANGE RATE MISALIGNMENT freely determined in the parallel market, it is natural to interpret the freely determined exchange rate in the unofficial market as a "shadow" exchange rate-that is, as an indicator of the value that the official ex- change rate would reach if left to market forces and thus as an estimate of the LRER. Chapter 12, by Ghei and Kamin, on the use of the parallel market premium as an indicator of misalignment, emphasizes that there are at least two reasons why this interpretation is not appropriate. First, even if the parallel rate accurately represented the value that a freely floating rate would reach if a unified floating system were in ef- fect, that floating rate would not necessarily equal the LRER at any given moment. The reason is that, as an asset price, the spot value of the float- ing rate would in part depend on its expected future value as well as on the current stock of foreign exchange in residents' hands, both of which are dynamic variables that need not be at their steady-state values for any arbitrarily chosen initial configuration of the economy16 When mac- roeconomic conditions and policies are volatile, as frequently is the case in developing countries with parallel exchange markets, adverse expec- tations may drive the parallel exchange rate to levels much more depre- ciated than the LRER. Second, even when financial markets are tranquil and macroeconomic conditions are close to their average levels, the parallel market exchange rate may still provide a poor approximation of the rate that would pre- vail under a unified float and hence of the LRER as well. As Ghei and Kamin show, the very conditions that may give rise to a parallel market in the first place-an overvalued official exchange rate, combined with foreign exchange rationing to conserve international reserves-may lead to scarcities of and excess demand for foreign exchange in the parallel market. Unless these demands are restrained by other barriers to im- ports, therefore, the parallel market exchange rate is likely to be more depreciated than the equilibrium unified rate and would be even more so under unstable macroeconomic conditions.17 Ghei and Kamin conduct some empirical exercises to evaluate this conclusion. They compare the parallel market exchange rate with esti- mates of the equilibrium unified rate computed using averages of the official rate over long periods in which the exchange market was uni- 16. This point is simply the familiar one that in flexible exchange rate models shocks typically trigger exchange-rate dynamics as in Dornbusch (1976). Note that if under a floating exchange rate regime the market-determined exchange rate were always equal to the LRER, there would be no need to estimate the LRER for major industrial countries during clean floats as in the research on these countries described in the empirical survey in Chapter 5. 17. Montiel and Ostry (1994) reached a similar conclusion. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 31 fied. They find that, consistent with their theoretical analysis, for Latin American countries the parallel rate tended to be substantially more depreciated than their estimate of the equilibrium unified rate, For countries in Africa and South Asia, in contrast, the parallel rate was not significantly more depreciated than the estimated equilibrium unified rate. However, Ghei and Kamin attribute this outcome to special cir- cumstances prevailing in these countries-namely, poorly enforced ex- change controls in African countries and extremely well-enforced im- port controls in Asian countries. Overall, they conclude that under gen- eral conditions the parallel premium is a biased and volatile indicator of misalignment between the official rate and a unified long-run equi- librium exchange rate. Setting the Nominal Exchange Rate The primary purpose of estimating the degree of misalignment, of course, is to move the nominal exchange rate in the direction of equilibrium. As mentioned at the outset, moving the nominal exchange rate to attain a desired path of the actual RER is not a straightforward task. The degree to which a domestic price level response will erode any gains in com- petitiveness achieved through a nominal devaluation, for example, is likely to depend on structural characteristics of the economy such as the nature of the wage-price mechanism, as well as on the nature of the accompanying macroeconomic policies and the initial degree of mis- alignment. Without a complete and reliable structural model of the economy with endogenous nominal variables, ex ante estimates of the real exchange rate change that will accompany a given change in the path of the nominal exchange rate in any given application can only be crude approximations. Nevertheless, such approximations must inevitably be made in the course of exchange rate management since most policy variables are set in nominal terms. In the absence of a macroeconomic model that deter- mines nominal as well as relative prices, two sources of guidance are available on the relative sizes of the nominal and real changes that are likely to follow a devaluation: the experience of other countries that have successfully devalued and the accounting relationships between the nominal and real changes. The last chapter in this book, by Ghei and Hinkle, examines the usefulness of these two sources of information for estimating the change required in the nominal exchange rate when one has already made an estimate of the real change required using one or more of the methodologies discussed above. Both theoretically and empirically any combination of RER realign- ment and inflation is possible after a devaluation-a depreciation, an appreciation, or no change in the RER, accompanied by an acceleration 32 EXCHANGE RATE MISALIGNMENT of the trend inflation rate or a return to predevaluation price trends. The key to a successful devaluation is monetary discipline and appropriate demand management policies. Successful devaluations (that is, those accompanied by appropriate macroeconomic policies) in open develop- ing economies have typically led to a depreciation of the external RER of 30-65 percent of the nominal devaluation in domestic-currency terms. The RER typically depreciates on impact by the full amount of the de- valuation and then gradually appreciates as the domestic price level shifts upward. In successful devaluations, the aggregate price level has generally shifted upwards by 20-55 percent of the nominal devaluation expressed in percentage terms in domestic currency with no increase in the long-term trend inflation rate. Chapter 13 by Ghei and Hinkle describes a simple method for pre- paring "first-pass" estimates of the effects of nominal exchange rate changes on actual RERs in developing countries. The chapter sets out a consistent accounting framework in the form of an eight-equation struc- ture, which can easily be incorporated into a spreadsheet format. This framework can be used to calculate the nominal exchange rate required to achieve a given real exchange rate target, conditional on an assump- tion about the response of domestic nominal wages to the nominal de- valuation or to the change in domestic prices. Alternatively, the frame- work can be used to calculate the real exchange rate adjustment that a given nominal exchange rate would produce, on the basis of assump- tions about the behavior of nominal wages or the degree of pass-through. Although the methodology, not being based on a general-equilibrium model, can provide only first-pass approximations to the nominal changes, it can be a useful tool in the hands of informed analysts. As an illustration of its usefulness, the authors analyze various policy scenarios used to determine the effectiveness of the nominal CFA franc devalua- tion in altering the real exchange rate and compare these with the actual outcome. In short, the accounting framework described in this last chapter de- scribes a simple yet reasonably accurate method for translating a de- sired real exchange rate movement into a required adjustment in the instrument actually controlled by the authorities-the nominal exchange rate. It thus complements the methodologies for measuring real exchange rate misalignment that came before. Conclusions Developing countries that avoid extreme exchange rate arrangements- currency boards and floating rates with purely domestic objectives for monetary policy-need to manage the nominal exchange rate. In doing so, they have long been enjoined to avoid misalignment-that is, the EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 33 emergence of large gaps between the actual real exchange rate and some notion of a sustainable "equilibrium" real exchange rate. Defining and measuring this sustainable equilibrium real exchange rate, however, has not proven to be an easy task, either for practitioners or for research- ers. Unfortunately, the urgency of doing so has not gone away and may even have increased in recent years as the result of increasing financial integration. This book provides a unified overview of the conceptual and empiri- cal problems that arise in defining and measuring the real exchange rate in specific applications. It then explores and illustrates alternative em- pirical methods for measuring the long-run equilibrium real exchange rate. Four distinct approaches to doing so are considered. Although all of these approaches have shortcomings, there are circumstances under which the use of each may be appropriate. Hence, to conclude this over- view, we briefly summarize the main advantages and disadvantages of each approach and describe the situations for which each is best suited. The relative PPP-based approach can be justified as a method of estimat- ing the LRER when the RER is shown to be stationary in a time-series sense. In this case, estimation of the LRER boils down to choosing an appropriate base period consisting of one or more years during which the RER was close to its equilibrium value (the PPP base-year approach) or taking a sample average of the actual RER (the PPP-average or trend approach). However, the applicability of these relatively simple meth- ods is restricted by the empirical observation that real exchange rates in developing countries often prove to be nonstationary. Nevertheless, because of the simplicity of its application and the complexity of alter- native methodologies, the PPP approach is likely to continue to be the only feasible approach for the estimation of misalignment in large multicountry research studies and hence to remain the method of choice for such studies. It is also useful for initial detection of misalignment, particularly in high-inflation countries, and for identification of hypoth- eses for subsequent analysis using more sophisticated techniques. When the RER is nonstationary, this nonstationarity must be the re- sult of nonstationarity in some subset of its fundamental determinants. Estimating the LRER then consists of three steps: identifying the rel- evant set of nonstationary fundamentals, determining their "long-run equilibrium" (sustainable) values, and determining how these funda- mentals are empirically linked to the LRER. The remaining three meth- ods of estimation described in the following paragraphs permit the in- corporation of permanent changes in the fundamentals into the analysis. The trade-equations approach is a well-established estimation technique that allows the estimated LRER to depend on the values taken by fun- damentals. This approach is structural so the determination of the LRER can be understood. It makes use of a small set of behavioral parameters 34 EXCHANGE RATE MISALIGNMENT that are widely estimated and thus readily available, and it is relatively simple to apply. Hence, the trade-equations approach has been the work- horse of empirical analysis and is still widely used by the IMF and oth- ers for industrial as well as developing countries." However, it relies on an ad hoc specification of the trade balance, and its recursive partial- equilibrium framework may ignore potentially important macroeco- nomic interactions. Furthermore, like other methodologies, the trade- equations approach requires often problematic estimates of the under- lying and target resource balances and forecasts of the "permanent" val- ues of potentially volatile fundamental variables such as the terms of trade and private capital flows. Nevertheless, in country applications in which data limitations or time constraints do not permit the implemen- tation of the more sophisticated approaches described below, the trade- equations approach may be the only feasible way of taking into account changes in the fundamentals. Under these circumstances the trade-equa- tions approach, despite its limitations, may be the method of choice. In principle, simulation of empirical general-equilibrium models should dominate other estimation methods. This approach allows the estimated LRER to reflect the full range of known macroeconomic interactions in the economy. Since the entire dynamic path of the RER from its current value to the steady-state (or semisteady-state, if conditioned on some slowly adjusting variable) LRER can be simulated, the approach also provides complete information about the dynamics. The model-based general-equilibrium method, however, suffers from a variety of short- comings. When implemented in the form of "real-time" simulations, it remains dependent, like the trade-equations approach, on an exogenous specification of the equilibrium resource balance and on forecasts of sometimes volatile exogenous variables. Moreover, it places relatively strong demands on economic theory, on the power of statistical tech- niques, and on the availability and quality of data. Made-to-suit models for individual developing countries with limited data and possibly un- stable economic structures are vulnerable to doubts about model speci- fication and parameter stability. Estimates derived from such models may thus fail to command much credibility, particularly when the mod- els on which they are based have no previous track record. For the near future, it is likely that estimates of the LRER derived from simulations of macroeconomic models should be treated as indicative and used to supplement and inform other approaches to estimation. Model simula- tions may be most attractive in applications in which an existing model 18. See, for example, Isard and Faruqee (1998) and Wren-Lewis and Driver (1998). EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 35 has demonstrated its usefulness through an established record of track- ing the macroeconomic performance of a particular economy. Recent developments in unit-root econometrics seem to hold special promise for the estimation of long-run equilibrium real exchange rates. Estimates of the LRER based on cointegrating equations are derived from a single-equation reduced-form approach. This approach follows naturally from the time-series tests for stationarity required to assess the applica- bility of the simple PPP-based approach. Relative to the general-equi- librium models, it places fewer demands on economic theory since the theory required is about long-run relationships, not short-run macro- economic dynamics. Moreover, fewer data (time series) are required since the researcher needs time-series data only for the variables that can be expected to appear in the reduced-form equation for the real exchange rate in short-run macroeconomic equilibrium. For these reasons, the re- duced-form methodology has the potential to significantly advance our ability to generate credible empirical estimates of the LRER in specific country cases. Despite these advantages, it would be premature to suggest that cointegration-based estimation of the LRER should dominate the other techniques under all circumstances. The method shares some of the other approaches' limitations and is subject to others that are specific to it. When net capital inflows are treated as a fundamental, for example, the problematic estimation of a target resource balance is a required input for this approach, just as it is for several others. Even when they are not, an independent method for estimating the "permanent" values of the fundamentals such as the terms of trade is indispensable for the imple- mentation of the reduced-form single-equation approach. Determining the permanent value of these may prove to be as problematic as the estimation of a target resource balance. Moreover, as indicated above, the statistical tests associated with this approach tend to have low power in small samples. They are particularly vulnerable to low degrees of freedom when a priori exclusion restrictions cannot be imposed on the fundamentals or when the time-series data of the country under study is characterized by structural breaks. Thus, while the method may re- quire fewer time-series than general equilibrium models, achieving re- sults of reasonable confidence may only be possible with time series of greater length than may be available in many developing countries. Es- timates of the LRER derived using the reduced-form technique may thus prove to be too fragile to dominate those from the more transparent struc- tural approaches, particularly in policy applications. Nonetheless, the results achieved with the reduced-form method to date, both in the previous research surveyed in Part II of the book as well as in Chapter 10 in Part III, provide justification for additional work 36 EXCHANGE RATE MISALIGNMENT using this approach. More research is also needed comparing the re- sults from the reduced-form methodology with those obtainable from the other approaches set out here. Our hope is that this book will con- tribute to motivating such research. Where, then, do we currently stand in our ability to estimate the LRER in developing countries, and what are the policy implications of the current state of the art? The "true" value of the LRER, of course, is unobservable, even ex post. Thus, we cannot evaluate the various meth- odologies examined in this book in the same manner that theories of nominal exchange rate determination under floating exchange rates are evaluated empirically-that is, by their ability to track the variable be- ing explained in sample or to predict it out of sample. However, other methods of evaluating these techniques are available. Two such meth- ods are described in the survey of empirical work in Chapter 5. First, empirical estimates of the LRER for particular countries can be judged by how well measures of misalignment derived from such estimates are able to replicate historical episodes for which RER misalignment has emerged as the consensus diagnosis ex post. Second, if the notion of the LRER has any meaning, then a current gap between the actual RER and the estimated LRER should have predictive value for (that is, should Granger-cause) the future actual RER. Both of these tests have been met by available techniques for estimating the LRER. Moreover, error-cor- rection equations based on lagged estimates of misalignment from the reduced-form general-equilibrium methodology, as well as on lagged changes in fundamentals, have proved able to explain a substantial part of the variance of the change in the actual RER (a stationary variable) in several applications. Although much has been learned about the estimation of the LRER in recent years, much still remains to be learned. Accurately establish- ing precise targets for a managed exchange rate-for example, for a new pegged rate after a devaluation-is currently beyond the state of the art. Furthermore, if some of the fundamental variables determining the LRER such as the terms of trade or capital flows are completely unpredictable or subject to repeated shock to their "permanent" values, the LRER will also be unpredictable or volatile. More research is also needed on how the results from different methodologies for estimating the LRER are likely to be related to each other in different country cases. Yet, while we may not at present know enough to calculate the LRER in specific applications with great precision, we do know enough to sound warning signals of serious misalignment.9 The implication for 19. For a discussion of the interpretation of apparent misalignments, see Isard and Faruqee (1998), pp. 1-3 and 16-17. EXCHANGE RATE MISALIGNMENT: AN OVERVIEW 37 nominal exchange rate policy is this: except perhaps for periods of large economic dislocations, ignorance about the empirical value of the LRER cannot be used to underpin arguments for extreme exchange rate ar- rangements-for example, currency boards or completely clean floats with only monetary targets-that imply abandoning the management of nominal exchange rates. We hope that the cautiously optimistic tone of this conclusion can be put to the test in future work motivated by the contents of this book.  m r1 3 P  2 External Real Exchange Rates: Purchasing Power Parity, the Mundell-Fleming Model, and Competitiveness in Traded Goods Lawrence E. Hinkle and Fabien Nsengiyumva* The real exchange rate is generally defined in the economic literature in two principal ways: either (a) in external terms as the nominal exchange rate adjusted for price level differences between countries (that is, as the ratio of the aggregate foreign price level or cost level to the home country's aggregate price level or cost level measured in a common cur- rency) or (b) in internal terms as the ratio of the domestic price of trad- able to nontradable goods within a single country. The first of these con- cepts of the RER derives originally from the purchasing power parity (PPP) theory. It compares the relative value of currencies by measuring the relative prices of foreign and domestic consumption or production baskets. Following the terminology adopted by De Gregorio and Wolf (1994), this chapter refers to this RER concept as the external real ex- change rate because it compares the relative prices of baskets of goods produced (or consumed) in different countries. The second concept, the internal RER, captures the internal relative price incentive in a particu- lar economy for producing or consuming tradable as opposed to nontradable goods. The real exchange rate in this case is an indicator of domestic resource allocation incentives in the home economy. To * Ms. Ingrid Ivins provided research assistance in the preparation of this chap- ter. Ted Ahlers developed the original computer spread sheet used for calculat- ing multilateral RER indexes. The authors are grateful to Amparo Ballivian, Shanta Devarajan, Peter Montiel, and three anonymous readers for helpful suggestions and comments on earlier drafts. 41 42 EXCHANGE RATE MTSALIGNMENT distinguish this second concept from the first, this real exchange rate is referred to here as the internal RER. Within each of these two broad RER concepts, there are several alter- native formulations derived from different analytical approaches. There are three primary versions of the external RER. These are based alterna- tively on purchasing power parity theory, on the Mundell-Fleming one composite good model, and on the law of one price and competitive- ness in the pricing of internationally traded goods. Similarly, there are several different definitions of the internal RER based on two-, three-, or multi-good models. The existence of multiple concepts and alternative measures of the RER raises questions concerning the theoretical and empirical relationship among these, the interpretation of differences in their behavior, and the appropriate measure to use in given circumstances. The three chapters in Part I of this book discuss the different theoreti- cal concepts of the RER, their empirical measurement, and the relation- ships among them. This chapter reviews indexes for measuring the ex- ternal RER in developing countries. Measurement of the internal RER and the relationship between the internal and external RERs are dis- cussed in the following two chapters on the two-good and three-good internal RERs. Several different types of problems are encountered in the measure- ment of the external RER. At a conceptual level, one set of problems arises from the multiplicity of theories underlying the external RER. The various theories that have motivated the different definitions of the ex- ternal RER imply the use of different empirical price and cost indexes in computing the external RER. Some theories are also ambiguous as to exactly what baskets and weightings of domestic and foreign goods should be used empirically. These conceptual problems are common to both industrial- and developing-country applications. A second set of problems is practical and empirical. These problems tend to be particularly acute in developing-country applications. Paral- lel foreign exchange markets, substantial smuggling and unrecorded trade, and large shifts in the terms of trade, trade policy, and trade pat- terns create complexities not commonly encountered in measuring the external RER in industrial countries. Moreover, even after one has sorted through the conceptual issues involved in the use of alternative price or cost indexes, it is often difficult to find reasonably exact empirical mea- sures of the desired indexes in developing countries. For many devel- oping countries only the consumer price index (CPI) and the gross do- mestic product (GDP) deflator are available. Hence, the analyst's choice is often limited to these. In light of the above problems, this chapter attempts to describe best practice in the calculation of external RER indexes for developing coun- tries. It has three objectives: EXTERNAL REAL EXCHANGE RATES 43 a. To review and operationalize the definitions of the three principal theoretical concepts of the external RER as a starting point for the subsequent discussion of their empirical measurement; b. To examine important empirical problems that often compli- cate the measurement of the external RER in developing coun- tries; and c. To clarify the interrelationships among the different external RERs. This chapter and the following two are intended as user's guides. They therefore give enough details of the methodologies and calcula- tions that readers who wish to use these indexes can replicate the calcu- lations. Data from Cte d'Ivoire prior to the devaluation of the CFA francs in January 1994 are used to illustrate the calculations. The rest of this chapter is divided into four sections and two appen- dixes. Certain features are common to all external RER indexes, but oth- ers depend upon the particular concept being measured. The next sec- tion discusses those features that are common to all external RER in- dexes. The following section on the measurement of different RER con- cepts then reviews the three principal external RER concepts and exam- ines the methodological issues that are specific to measuring each of these. This is followed by a section comparing the effects of changes in the terms of trade on the three external RERs and their implications for competitiveness. The final section summarizes and concludes. Appen- dix A briefly reviews the International Comparison Programme and the purchasing power parity exchange rates derived from it. Appendix B sets out in more detail the relationship between competitiveness and the different external RERs. Common Features of All External Real Exchange Rate Indexes The concept of the external real exchange rate derives originally from expenditure or purchasing power parity (PPP) theory. Over time, two additional concepts of the external RER developed based on the law of one price and competitiveness in production of traded goods and on the Mundell-Fleming one composite good model or competitiveness in aggregate production costs of all goods. Relative labor costs expressed in foreign currency are a fourth, although somewhat less common, mea- sure of the external RER. To empirically calculate these external RER indexes, four elements are needed: (1) the operational mathematical formulas to be used, (2) appropriate measures of the nominal exchange rate, (3) country weights and the averaging method to be used in computing the multilateral RER, 44 EXCHANGE RATE MISALIGNMENT and (4) empirical counterparts of the price or cost indexes desired theo- retically. The first three elements-the operational formulas, the nomi- nal exchange rate, and the country weights-are common to the various different versions of the external RER. The fourth element, the appro- priate price or cost index, varies with the version of the external RER being constructed. This section reviews the elements that are common to all external RER indexes. Computation of External RERs: Common Formula and Conventions Similar conventions and formulas are used for calculating all of the ba- sic versions of the external RER. The following subsection sets out these conventions, which are used in the remainder of the volume. Readers al- ready familiar with these conventions may wish to skim this subsection. Domestic Versus Foreign Currency Terms Nominal exchange rates and external RER indexes can be measured in domestic-currency terms (units of domestic currency per unit of foreign exchange, E) or in foreign-currency terms (units of foreign exchange per unit of domestic currency, E ). The domestic- and foreign-currency measures are the inverses of each other, as shown in equation 2.1: (2.1) Edc = . The term appreciation (depreciation) is used to refer to an increase (decrease) in the value of the home currency relative to foreign curren- cies. An appreciation corresponds to an increase (or an upward move- ment graphically) in the RER indexes in foreign-currency terms but to a decrease (or a downward movement) in an index in domestic-currency terms since this is the inverse of the index in foreign-currency terms. For some purposes, it is useful to express RER indexes in domestic-currency terms and for others in foreign-currency terms. Both versions are widely used in the literature and are used in this volume. For ease of exposi- tion, most of the equations in this chapter are expressed in domestic- currency terms; but, unless otherwise noted, all graphs are in foreign- currency terms so that an upward movement indicates an appreciation. 1. Appendix C of Chapter 7 on operational approaches to estimating equilib- rium RERs gives formulas for converting appreciations and depreciations in for- eign-currency terms to domestic currency and vice versa. EXTERNAL REAL EXCHANGE RATES 45 The Bilateral RER Irrespective of the price or cost concept employed, the external RER for the home economy can be defined either in relation to one trading part- ner or to an average for all of its main trading partners or competitor countries. In the first case of a pair of countries, it is called a bilateral real exchange rate (BRER). In the second multicountry case, it is called a multilateral real exchange rate, which is also known as a real effective exchange rate (REER), and is calculated as a weighted average. The bilateral RER is the simplest and easiest to calculate of the exter- nal RER indexes. It compares the price of a representative consumption or production basket in the home country with the price of a representa- tive basket in a foreign country measured in the same currency, either domestic or foreign, and indicates the relative value of the domestic and foreign currencies. The bilateral RER is useful both as a bilateral and as a more general indicator of the external RER in cases in which a country belongs to a currency bloc, such as the dollar or the franc zones, or has one dominant trading partner. For these reasons, the bilateral RER has been widely used in empirical work, particularly before the increased availability of high-powered personal computers facilitated the calcula- tion of multilateral RERs. The external bilateral RER index in domestic-currency terms (BRERd) between the domestic economy (d) and a foreign country (f) is given by equation 2.2: E, -Pc (2.2) BRERd = Gd where Edc is the index of the nominal exchange rate, defined as units of domestic currency per one unit of foreign currency. PG and PGd are the foreign and the domestic general or aggregate price indexes, respectively.2 The subscript dc indicates that the RER is defined in domestic-currency terms. A decline in the BRERd, index (which corresponds to a real ex- change rate appreciation) reflects an increase in the price or cost of do- mestic goods and services relative to foreign goods and services. The equivalent definition of the external bilateral real exchange rate index in foreign-currency terms is shown in equation 2.3: (2.3) BRER = E - =Pd 1 fc P, BRERdc 2. To simplify the notation in this chapter, the bases for all indexes are set at 1.00 in the reference period rather than at 100. 46 EXCHANGE RATE MISALIGNMENT Bilateral RERs in relation to the dollar, the two other major currency blocks (the yen, and the DM or the euro), the currency in terms of which a country pegs or manages its exchange rate, and the currency of a country's principal trading partner are often particularly useful for ana- lytical purposes. These bilateral RERs are both as simple to calculate and more broadly representative than the bilateral RERs with smaller trading partners. Table 2.1 illustrates how radically bilateral RERs of developing coun- tries can diverge as a result of movements in the major currencies and the policies of individual countries. It shows the bilateral RERs between C6te d'Ivoire and its competitors, along with weighted averages for coun- try groupings. While C8te d'Ivoire's RER appreciated moderately (by 8-9 percent) from 1985 to 1993 relative to France and European coun- tries as a group and depreciated relative to Japan (by 12 percent), it ap- preciated by 60 percent relative to the dollar, by almost 100 percent rela- tive to the currencies of its non-African developing-country competi- tors, and by more than 400 percent relative to its African competitors. Similarly, figure 2.1 shows the movement of the bilateral RERs between Figure 2.1 The Bilateral RERs Between C6te d'Ivoire and France, Germany, Japan, and the United States, 1980-96 (1985=100) 220 200 ' RER with United States 180 160 'A' RER with 140 A' France 100M 80 60 German I 1980 1982 1984 1986 1988 1990 1992 1994 1996 RER with France - ---- - RER with Germany X RER with Japan --- A--- RER with the United States Note: The RERs were calculated using CPIs and official exchange rates. An upward move- ment represents an appreciation of the RER for C6te d'Ivoire. Source: Computed from World Bank data. Table 2.1 Bilateral Real Exchange Rate Indexes for C6te d'Ivoire Computed Using CPIs and Official Exchange Rates, 1980-96 (1985=100) Adjusted IFS country weights Country % 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 European Countries, 53.9 122.1 116.7 110.1 105.5 102.6 100.0 107.9 111.0 114.4 111.1 107.0 103.9 106.5 109.1 67.6 76.6 76.7 France 25.9 120.2 115.3 111.0 106.9 103.8 100.0 107.0 110.7 115.3 112.6 108.0 106.4 108.4 108.4 67.2 75.5 75.8 Netherlands 5.5 118.9 118.3 106.3 100.7 99.7 100.0 104.9 107.6 112.5 112.6 109.7 106.4 107.2 106.3 65.4 72.0 74.0 Italy 4.4 140.2 131.7 119.7 106.7 101.4 100.0 104.9 107.3 110.7 103.6 98.8 94.5 99.2 115.7 73.4 89.5 81.6 Germany 7.2 120.9 119.6 108.6 100.7 99.7 100.0 105.1 106.9 111.3 109.4 106.4 103.7 104.1 101.2 62.0 68.4 70.8 United Kingdom 6.4 127.6 110.7 105.0 105.6 103.8 100.0 121.6 124.6 121.8 115.9 113.0 105.6 113.4 125.4 77.1 92.0 90.7 Spain 1.9 121.5 115.5 106.9 113.3 103.8 100.0 107.7 111.2 108.0 96.9 90.9 85.9 88.8 100.7 65.1 73.6 72.2 Belgium-Luxembourg 2.7 112.0 111.8 112.5 106.5 103.0 100.0 105.7 107.1 112.5 110.4 105.2 102.2 104.4 104.4 63.4 70.0 72.0 Other Industrial Countries, 20.1 191.9 148.3 131.7 115.1 101.7 100.0 124.1 139.9 138.3 127.9 144.4 132.8 142.5 128.9 79.1 95.9 98.5 United States 9.8 211.3 162.1 135.8 119.9 104.5 100.0 139.6 165.9 172.1 154.9 170.9 160.8 173.4 160.8 100.9 124.7 121.2 Japan 7.0 176.5 138.2 135.2 115.4 102.6 100.0 99.9 105.6 100.2 99.5 117.8 104.1 106.9 88.6 52.0 60.9 70.3 Canada 1.8 198.3 153.0 126.4 108.6 99.5 100.0 139.0 156.6 150.8 130.4 142.5 130.0 150.1 150.3 102.1 127.6 124.9 Australia 1.6 148.3 113.4 102.5 95.6 85.8 100.0 136.3 148.1 133.2 115.6 127.1 121.2 141.3 143.3 84.0 100.7 93.0 (Table continues on next page) (Table 2.1 continued) Adjusted IFS country weights Country % 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 CFA Countries" 2.0 134.6 132.2 125.6 113.8 106.5 100.0 101.8 96.2 101.2 104.0 102.0 103.7 108.1 114.1 106.4 106.8 104.9 Cameroon 2.0 134.6 132.2 125.6 113.8 106.5 100.0 101.8 96.2 101.2 104.0 102.0 103.7 108.1 114.1 106.4 106.8 104.9 African Countries (non-CFA? 12.9 133.1 74.0 59.9 61.2 82.8 100.0 222.3 436.4 403.1 408.1 448.7 449.5 570.1 547.1 297.6 243.6 222.5 C1 Nigeria 6.4 238.0 188.3 169.6 134.9 93.0 100.0 263.8 669.2 527.9 538.2 635.9 680.7 913.1 740.8 288.8 211.5 172.2 Ghana 6.4 74.4 29.1 21.2 27.8 73.7 100.0 187.4 284.6 307.7 309.4 316.7 296.8 355.9 404.0 306.6 280.5 287.6 Developing Countries (excluding AfricaY 11.1 148.8 120.7 104.6 99.4 93.6 100.0 153.6 194.8 200.8 185.6 220.4 212.9 219.5 197.4 123.9 142.4 136.4 Malaysia 4.4 178.1 145.4 123.9 108.2 95.6 100.0 146.9 176.2 192.6 182.8 206.8 197.6 194.8 181.0 113.9 131.8 128.5 Indonesia 2.7 145.3 110.3 93.9 105.2 97.6 100.0 155.2 224.5 230.5 214.5 240.9 228.7 245.8 220.2 135.1 163.3 158.2 Colombia 2.2 147.3 112.8 94.6 88.6 88.7 100.0 163.4 203.9 211.8 203.1 240.0 227.6 238.8 211.4 106.7 122.0 115.2 China 1.8 101.3 95.1 92.1 85.8 89.2 100.0 156.4 190.9 170.7 140.1 203.9 212.0 224.6 191.5 159.9 168.5 154.9 Total' 100.0 138.5 116.2 105.2 99.6 98.7 100.0 126.5 147.2 148.5 142.9 148.0 142.8 152.0 148.5 91.1 100.3 99.2 Note: a. The REERs for the regional groupings have been computed as geometric averages of the bilateral RERs in their constituent countries. Source: Computed from World Bank data. EXTERNAL REAL EXCHANGE RATES 49 the CFA franc, French franc, and the major currency blocks. France, the United States, Germany, and Japan are also C6te d'Lvoire's four largest trading partners and account for one half of the weights in table 2.1. The Multilateral or Effective RER (REER) The multilateral or real effective exchange rate index (REER) is used when multiple trading partners are considered.' It is a weighted external real exchange rate index. The REER is defined in domestic-currency terms as shown in equation 2.4: (2.4) REERdc = EcGiw 1 -=1 Gd1 where m is the number of trading partners or competitors of the home country and H denotes the product of the bracketed terms over the m countries. The geometric averaging method is used where (Did is the ap- propriate weight for each foreign country i (i = 1, ...m) and the sum of weights must equal one, as shown in equation 2.5: (2.5) ,X ' =1. i=1 The equivalent definition of the REER in foreign-currency terms is expressed by equation 2.6 as follows: (2.6) REER = [ ] Gd i=1 PGi REERdc The REER can also be defined as an arithmetic average. Although the arithmetic average is easier to calculate, the geometric averaging tech- nique is used in the above formulations because a geometric index has certain properties of symmetry and consistency that an arithmetic index 3. The term "effective" has two common but different meanings when used to describe exchange rates in the economic literature. Its first meaning is "weighted average," and this is the sense in which the term effective is used here. The sec- ond common meaning of an effective exchange rate is one that includes the ef- fects of tariffs, subsidies, and other charges on the domestic costs of imports and domestic prices of exports. Such exchange rates are referred to in this book as including taxes. The terms bilateral, multilateral, and effective indicate the num- ber of external trading partners to which an RER applies and, therefore, do not apply to the internal RER, which is an indicator of relative internal domestic prices in a particular country 50 EXCHANGE RATE MISALIGNMENT does not. In analyzing RER indexes, one is often interested in determin- ing not only the level of the index at a particular point in time but also the rate at which the RER is appreciating or depreciating over time. In an arithmetic index, the percentage changes between any two dates de- pends upon the reference date used for the index so that rescaling (or rebasing) the index from the original base year equal 100 to a different reference year equal 100 affects the percentage changes in the index. A geometric index, in contrast, gives RER levels for which the percentage change between two dates is not influenced by the choice of the base period and may, therefore, be readily rescaled to have a different refer- ence year equal 100. In addition, an arithmetic index, in effect, gives larger weights to currencies that have appreciated or depreciated to a significant extent relative to the home currency. A geometric average treats depreciating and appreciating currencies in an entirely symmet- ric manner.4 There are two equivalent ways of calculating the real effective ex- change rate. These two methods decompose the components of the REER index differently and provide supplementary empirical information useful in analyzing the evolution of the effective exchange rate indexes. The first method calculates the REER as a geometric weighted average of the bilateral RERs of the home country with each of its main trading partners or competitors. The real effective exchange rate in domestic- currency terms is then given by equation 2.7: (2.7) RER,C = HIBRER< where BRERdc is the bilateral real exchange rate in domestic currency as defined by equation 2.2. The second method calculates the REER as the product of the nomi- nal effective exchange rate and the effective relative price index. Equa- tion 2.4 is then rewritten as equation 2.8: (2.8) REERd = NEERdc EPGf PGd in which: 4. The properties of the geometric averages are discussed further in Brodsky (1982) and Maciejewski (1983). 5. These two methods are shown here only for the real effective exchange rate defined in domestic-currency terms (equation 2.4). They are equally applicable to the REER defined in foreign-currency terms. EXTERNAL REAL EXCHANGE RATES 51 m (2.9) NEER,, = HE" (2.10) EPGf Gd NEERC is the nominal effective exchange rate in domestic-currency terms between the home economy and its trading partners or competitors. EP1 is the geometric weighted average (or effective) foreign aggregate price index for the home country's trading partners. The real effective exchange rate indexes obtained from equations 2.7 and 2.8 are exactly the same, as the two equations are mathematically equivalent. However, the two alternative calculations generate differ- ent statistical information as by-products. Computing the REER as the weighted average of bilateral RERs can provide calculations of bilateral RER indexes for individual countries or subsets of countries. In cases in which a country pegs its exchange rate to or targets it on that of another country, it is often useful to analyze the home country's REER in terms of (a) changes in the home country's bilateral RER with the peg currency caused by differences in inflation rates in the home and peg countries and (b) changes in the home country's REER relative to the bilateral RER with the peg currency caused by in- flation and exchange rate movements in third-country currencies. This relationship is given in equation 2.11: (2.11) REERd = BRER * REER,C 'c BRERd., where BRERdCb is the bilateral RER with the base or target currency. Calculating the REER as the product of the nominal effective exchange rate and the effective relative price index, by contrast, makes possible a separate analysis of the effects of movements in nominal exchange rates and foreign prices as shown in equation 2.8 above.' It also permits a further decomposition of the NEER to express movements in it in terms of changes in the exchange rate between the home currency and its peg currency and in the NEER relative to the peg currency. This decomposi- tion is shown in equation 2.12: (2.12) NEERdc = EdcNEER Edc 6. NEERs for selected developing countries are reported in IFS. 52 EXCHANGE RATE MISALIGNMENT where E.b is the nominal exchange rate with the base or target currency. Such a decomposition is often useful because the pegged rate in equa- tion 2.12 is typically a policy variable or target while the NEER relative to the peg currency is exogenous for the pegging country. The usefulness of these alternative REER decompositions can be il- lustrated with data from Cte d'Ivoire. Figure 2.2, for example, decom- poses its REER into its NEER and effective relative price indexes. It indi- cates that C6te d'Jvoire's relative price performance was actually quite good in the period 1985-93, with its prices falling by 20 percent relative to its trading partners. However, its REER, nevertheless, appreciated by almost 50 percent as a result of the 85 percent appreciation in its NEER. When the home country's currency is pegged, like C8te d'Ivoire's, to another currency, it may be also useful to use equation 2.12 to express the NEER in terms of the bilateral exchange rate relative to the peg cur- rency and the NEER relative to the peg currency This procedure sepa- rates the effects of changes in the peg, a policy variable, from the other exogenous changes in the NEER. For the CFA countries, however, such Figure 2.2 The Nominal Effective Exchange Rate (NEER), Relative Consumer Prices, and REER for C6te d'Ivoire, 1980--93 (1985=100) 190 180 NEER A" 170 - REER 160 A - -A R 150 140, A- 130, 120 - . ,A 110 . . m. 100 A. E- -U- *II 90 A -... A" 80 Relative - . Consumer Prices 70 l i l l i ii l i 1980 1982 1984 1986 1988 1990 1992 1994 1996 - - - - NEER - - a - - Relative Consumer Prices - REER Note: The NEER and REER were calculated using official exchange rates and adjusted IFS country weights. The relative consumer price index is the CPI for Cote d'Ivoire divided by the weighted average of the CPIs for its foreign competitors. An upward movement repre- sents an appreciation of the NEER, REER, or relative consumer prices. Source: Computed from World Bank data. EXTERNAL REAL EXCHANGE RATES 53 a decomposition is not necessary as the pegged rate to the French franc remained at 50:1 for the entire period from 1948 through 1993. Hence, all of the variation in Cte d'Ivoire's NEER during this period was due to exogenous changes in the exchange rate between the French franc and other currencies. It is worth noting, however, that because of different trading patterns, and hence country weights, the NEER for the home currency and that for the peg currency may behave quite differently. Figure 2.3 shows that, while the NEER for France appreciated by about 15 percent in the pe- riod 1985-93, the NEER for C6te d'Ivoire appreciated by 320 percent because of its different trading partners. Hence, C6te d'Ivoire experi- enced a huge nominal appreciation as a result of its peg to the French franc, even though the NEER for the franc itself only appreciated mod- erately. Such divergences can have significant implications for decisions about the appropriateness of maintaining a given peg. Figure 2.3 The Nominal Effective Exchange Rates (NEER)for C6te d'Ivoire and France at Official Exchange Rates, 1980-96 (1985=100) 360- 340-- 320-- 300-- 280-- NEER for n 260-- Cte dIvoire 0 240-- 220-- 200-- 180- . NEER . .r 160 for France 140 -. NEER for C6te d'Ivoire as a 1980 1982 1984 1986 1988 1990 1992 1994 1996 - - * - -NEER for France - -n - NEER for Cote dIvoire -.--NEER for COte d'Ivoire as a percentage of France's NEER Note: The NEERs have been calculated using IFS country weights. An upward movement represents an appreciation of the NEER. Source: Computed from World Bank data. 54 EXCHANGE RATE MISALIGNMENT Similarly, figure 2.4 uses equation 2.11 to express C6te d'Ivoire's REER in terms of its RER relative to the French franc, the peg currency, and the REER between the French franc and the currencies of C6te d'Ivoire's other trading partners. It shows that while C6te d'Ivoire's bilateral RER appreciated by about 10 percent relative to the French franc, C6te d'Ivoire's REER appreciated by an additional 20 percent relative to France's RER because of larger real depreciations by C6te d'Ivoire's trad- ing partners. Determining the Appropriate Nominal Exchange Rate Industrial countries typically have unified exchange rates and curren- cies that are freely convertible for current and most capital transactions. In these circumstances, the single nominal exchange rate truly repre- sents the market price of foreign exchange. In developing countries, however, the situation may be more compli- cated. Although convertible currencies and unified exchange rates are becoming more common, many developing-country currencies are still Figure 2.4 The Bilateral RER with France and the REER for C6te d'Ivoire, 1980-96 (1985=100) 150 REER for 140 C6te d' Ivoire (CIV) 130 120 * *- - - 110 re-- 110 /A' A.. REERfor 100 : CIV/RER *..... ....-with 90 RER with France France 80 A.... 70 60 I I I I II I I I I I I 1980 1982 1984 1986 1988 1990 1992 1994 1996 --RER with France- -REER for CIV/RER with France ---REER for CIV Note: CIV=C6te d' Ivoire. The RER and REER were calculated using CPIs official exchange rates and IFS country weights. An upward movement represents an appreciation of the RER and REER for C6te d'Ivoire. Source: Computed from World Bank data. EXTERNAL REAL EXCHANGE RATES 55 not readily convertible for capital transactions. Sometimes current trans- actions are also subject to exchange controls; and smuggling, unrecorded, and misrecorded trade may be common. Hence, at different points in time there may be a quite significant parallel (or black) market for for- eign exchange in the home country, in some of its major trading part- ners, or both. The coverage and importance of these parallel markets may vary from country to country and from period to period. Under such circumstances, an RER computed using only official nominal ex- change rates could be quite misleading as an economic indicator. When a parallel market exists, a country has, in effect, two external real exchange rates, one for transactions at the official nominal rate and one for transactions at the parallel rate. These two rates may create quite different incentives for different types of activities. Which of the two RERs is the more relevant analytically will depend upon the situation in the country concerned. It may in some cases be desirable to use both these RERs for analytical purposes rather than trying to arrive at a single unique measure of the external RER. Jorgensen and Paldam (1986) argue, however, that an average of the parallel and official rates is usually much more stable and representa- tive than either of the two rates separately. Misalignments in the paral- lel and official rates tend to be in opposite directions (the parallel rate being undervalued when the official rate is overvalued) and policy shocks such as large devaluations often move the two rates in opposite direc- tions. Hence, when a parallel market exists in the home country or its trading partner(s), one possibility for calculating a single representative bilateral RER is to use a weighted average of the official and parallel market nominal exchange rates. The weights should reflect the share of transactions at each rate and corrections should be applied to the paral- lel rate for the extra risks and other costs of transactions in the informal market. In practice, however, it is likely to be quite difficult to obtain the data required to arrive at anything more than reasonable assumptions about the shares of transactions taking place in the official and parallel markets and about the extra costs of transactions at the parallel rate. Parallel foreign exchange markets may exist for the home country or for one or more of its trading partners. When it is the home country that has a parallel market, potentially all of its trade and capital flows with all of its trading partners could be affected by the parallel rate. When it is a major trading partner (or partners) that has a parallel market, the overall analytical problem is less serious; but bilateral trade and capital flows with these countries may still be significantly affected by the par- allel rate. For any given developing country, the effect of parallel rates on the multilateral RER will depend upon both the size of the black market premiums and the weights assigned to countries having parallel 56 EXCHANGE RATE MISALIGNMENT rates. Box 2.1 illustrates the effects of other countries' parallel market rates on the bilateral and multilateral RERs of Cbte d'Ivoire, which itself had a unified exchange rate.' Box 2.1 The Effects of Parallel Markets on C6te d'Ivoire's Bilateral and Multilateral RERs In the case of C6te d'Ivoire, the home currency, the CFA franc, was itself actually freely convertible in the 1980-93 period. However, Nigeria, which was Cte d'Ivoire's second largest trading partner after France in 1993 (accounting for 11 percent of total trade) had an important parallel market that had significant effects on Cte d'Ivoire's bilateral and multilateral RERs. The Bilateral RER. Figure 2.B.1 shows how the official and par- allel exchange rates for the naira and the parallel market premium have varied over time. Figures 2.B.2 and 2.B.3 illustrate the effects of the divergence between the parallel and official exchange rates on the bilateral RER between C6te d'Ivoire and Nigeria. Figure 2.B.2 shows the bilateral RERs calculated using CPIs and the par- allel and official exchange rates. The trends in the official and parallel RERs are quite different in the period 1981-85 when Cte d'Ivoire's official RER depreciated 130 percent while its parallel RER fluctuated moderately but changed little over the period as a whole. The large devaluations of the naira during 1986-87, which substantially reduced the parallel market premium on the naira as shown in figure 2.B.1, then caused C6te d'Ivoire's official RER to appreciate much more strongly than its parallel RER. Varia- tions in the official RER have also been much more pronounced than those in the parallel RER, although the changes in both have been substantial. Thus, transactions taking place in the official and parallel markets have been subject to quite different incen- tives; and the conclusions at which one arrives may depend upon which of the two RERs is used. (Box continues on page 54) 7. For a further discussion of parallel markets and the use of the parallel rate as a guide for setting the official exchange rate, see Chapter 12 by Ghei and Kamin in Part IV of this volume. EXTERNAL REAL EXCHANGE RATES 57 Figure 2.B.1 The Official and Parallel Naira/US$ Exchange Rates and the Parallel Market Premium, 1980-96 2.2 350 a 2.0-- Parallel 1.8.. Exchange 300 1.--Rate 8 ~21.50 0.8 0.6 .. A' Parallel15 0.6 Official Parket 0.4 Exchange Prermum 100 z0.2-- Rae AM 0.0,0 -0.2 ... A'" 0.4i "i I I I I I I 1980 1982 1984 1986 1988 1990 1992 1994 1996 ---Log of Parallel Exchange Rate - - * - - Log of Official Exchange Rate -&--Parallel Market Premium Note: An upward movement represents a depreciation of the naira. Source: PIC's Currency Year Book. Figure 2.B.2 The Bilateral RER Between C6te d'Ivoire and Nigeria Computed Using CPIs at Official, Parallel, and Weighted Average Exchange Rates, 1980-96 (1985=100) 1,000 900-- A 800 700-- RER at . Official 600 Exchange : RER at the Naira's 500-. Rates , - Weighted Average Exchange Rate 400 300 20 'A -A 200 --4... ... --- a--- 100 ... .RER at the Naira s Parallel ExchanRe Rate 0 I 1 1 : 1 I I : I I I I I 1980 1982 1984 1986 1988 1990 1992 1994 1996 e -. RER at the Naira's Parallel Exchange Rate -+-RER at the Naira's Weighted Average Exchange Rate * . - RER at Official Exchange Rates Note: The weighted average is calculated using 36 percent for the official rate and 64 per- cent for the parallel rate based on the adjusted IFS country weights in table 2.3. An upward movement represents an appreciation of the RER for C6te d'Ivoire. Source: Computed from figure 2.B.1 and World Bank data. 58 EXCHANGE RATE MISALIGNMENT (Box 2.1 continued) Figure 2.B.2 also gives a weighted average bilateral RER that was computed using a weight of 0.36 for the official rate and 0.64 for the parallel rate. These weights were based on World Bank staff estimates of the shares of trade taking place at the official and parallel rates.* Because of the shortage of data, these estimated weights are little more than educated guesses that give an idea of what the average bilateral RER might have been. The official, par- allel, and average bilateral RERs give quite different impressions of the magnitude and timing of the appreciation in the measured RER. Which of them is the more representative indicator for trans- actions between C6te d'Jvoire and Nigeria is an empirical ques- tion that depends upon one's assumptions about the relative importance of trade at the official and parallel rates. Hence, de- tailed knowledge of the functioning of any parallel markets is criti- cal for measuring the actual bilateral RER accurately. In cases where both the home country itself and its trading partner have parallel markets, computing a representative bilateral RER may be further complicated; and an understanding of parallel markets becomes even more critical. The Multilateral RER. In addition to Nigeria, five of C6te d'Ivoire's other developing-country competitors appearing in the official weights used in IFS had parallel markets during 1980-93. (These countries were China, Colombia, Ghana, Indonesia, and Malaysia.) Together these six countries accounted for 14.8 per- cent of the country weights used for C6te d'Ivoire in IFS. Figure 2.B.3 illustrates the effect of taking into account parallel markets when measuring real effective exchange rate (REER) and the po- tential sensitivity of the REER to assumptions about parallel ex- change rates. It shows the REER for COte d'Ivoire calculated us- ing both the official and parallel rates for the countries having paral- lel exchange rates. Figure 2.B.3 also gives a weighted average of the * Because of lack of data on the extra costs and risks of transactions in the parallel market, no adjustment for these was made to the parallel rate. (Box continues on next page) EXTERNAL REAL EXCHANGE RATES 59 Figure 2.B.3 The REER for C6te d'Ivoire Computed at Official, Parallel, and Weighted Average Exchange Rates, 1980-95 (1985=100) 140 REER at Weighted Average Exchange Rates 130 .***g/ A. 120 ' REER at Parallel 110 Exchange Rates REER at Official 100 Exchange Rates 90 80 70 : : I I I I I I I I I 1980 1982 1984 1986 1988 1990 1992 1994 - -*- -REER at Official Exchange Rates -9-- REER at Weighted Average Exchange Rates - - * - - REER at Parallel Exchange Rates Note: The REER was calculated using CPIs and IFS country weights. An upward movement represents an appreciation of the REER for C6te d'Ivoire. Source: Computed from PIC's Currency Year Book and World Bank data. (Box 2.1 continued) parallel and official REERs, using weights equal to the estimated shares of recorded and unrecorded trade for Ghana and Nigeria and equal weights for the parallel and official rates for the other countries having parallel markets. While the differences in C6te d'Ivoire's REER are not as pronounced as in the bilateral RER be- tween C6te d'Ivoire and Nigeria (because the six countries with parallel markets account for only 14.8 percent of the total weights in the REER and the parallel market premium was not as large for the other countries as for Nigeria), the use of parallel rates still affects the overall index by as much as 10 percent in a given year. 60 EXCHANGE RATE MISALIGNMENT Multilateral or Effective RERs (REERs): Weighting Schemes, Unrecorded Trade, and Hyperinflation The calculation of multilateral RERs or real effective exchange rates (REERs) presents a number of additional empirical problems beyond those involved in computing bilateral RERs-namely, the choice of a weighting scheme appropriate for a particular country, adjustments for unrecorded trade, and the effects of hyperinflation. Weighting Schemes Unfortunately, the determination of appropriate country weights for use in calculating REERs sometimes poses difficult conceptual and empiri- cal problems, particularly in developing countries. For countries with- out parallel exchange markets and substantial unrecorded or misrecorded trade, actual trade weights can usually be calculated with- out too much difficulty. However, when the intercountry pattern of trade is significantly different for imports and exports, it may be preferable for some analytical purposes to calculate separate REERs for imports and exports rather than, in effect, just averaging these together in a single REER for all trade. In addition, if (a) the home country experiences sig- nificant competition in its export markets from third countries with which it does not trade much directly or (b) its pattern of intercountry trade is at the margin significantly different from the average (for example, non- traditional exports are sold in different markets from traditional com- modity exports), the problem of determining appropriate weights is fur- ther complicated. For countries that have, or whose major trading part- ners have, parallel exchange markets, or significant unrecorded or misrecorded trade, determination of even actual trade weights can be problematic. Furthermore, trade is sometimes denominated in a major currency rather than in the trading partners' currencies (for example, many commodities are priced in U.S. dollars) so that country weights may need to be adjusted to reflect the currency composition of trade rather than its geographic origin and destination. Moreover, patterns of trade are not independent of the bilateral RERs but, rather, are influenced by them. Fixed weight averages become less representative as bilateral RERs and trading patterns change over time, and it is necessary to update country weights periodically. Hence, for calculating REERs, it is desirable to have country weights that reflect reasonably well the structure of trade in the period being analyzed. Fairly recent weights should be used for current policy analysis and represen- tative ones from the past for historical or econometric analysis of time- series data. Using current weighting schemes or Fisher indexes also EXTERNAL REAL EXCHANGE RATES 61 mitigates the problem of changing trade structure but increases the com- plexity of the calculations required. Ideally, it is desirable that, for a given country, the reference period for the weighting scheme for calculating the multilateral RER and the base (or equilibrium) year be the same so that the weights reflect the equilibrium RER. This approach, however, may require different base years for different countries and complicates the computation of a con- sistent set of REER indexes for a group of countries. Hence, when con- sistent REER indexes are needed for groups of countries, it is standard practice to calculate all of them using country weights for the same year. However, it is unlikely that the real exchange rates of all developing countries will be in equilibrium at the same time. Hence, for interpret- ing real exchange rate movements for an individual country its REER is usually "rebased" or rescaled so that it equals 100 in a representative "equilibrium year" for that country. As long as the reference year for the trade weights and the equilibrium year to which the REER index is rebased are reasonably close in time and the trade pattern has not changed significantly in the interim, this practice is satisfactory for most empirical purposes. It does, however, reinforce the desirability of using geometric rather than arithmetic averaging as discussed earlier.' Shares of Direct Trade Several different country weighting schemes are employed in the litera- ture for calculating REERs. The simplest and most transparent way to determine country weightings is to use shares of total direct trade (im- ports and exports) as calculated-for example, from the statistics pub- lished in the IMF's Direction of Trade. This procedure is simple enough to give the analyst many options for the choice of base year and also per- mits calculation of relatively up-to-date trade weights. The IMF, in fact, uses such a simplified procedure of calculating competitiveness weights on the basis of bilateral trade flows for new member countries in which data deficiencies and unstable trade patterns preclude utilization of the more sophisticated weighting methodology discussed below (see Zanello and Desruelle 1997). Since trade patterns can change considerably as a result of changes in bilateral RERs and other factors, the first step in devising a weighting 8. A Fisher index is a geometric average of the indexes calculated using weights of the initial year and of the most recent year. 9. The problem of choosing an appropriate base year for analytical purposes is discussed further in Chapter 7 on operational methodologies for estimating the equilibrium RER. 62 EXCHANGE RATE MISALIGNMENT scheme is to establish an appropriate, up-to-date base year for the coun- try concerned. Table 2.2 illustrates this problem for Cte d'Ivoire. It gives country shares for Cte d'Ivoire's imports, exports, and total trade for 1985, the last reasonable base year before the impact of the shocks of the mid-1980s, and for 1993, the year before the devaluation. A comparison of the movements in the bilateral RERs in table 2.1 and the changes in the trade shares in table 2.2 illustrates how trade shares can change with movements in RERs. In 1985 the dollar peaked relative to the French and CFA francs, after appreciating sharply in the early 1980s, and then began to depreciate. In 1985, C6te d'Ivoire was also hit by a large de- cline in its terms of trade. The trade share figures for 1993 show the considerably different trade pattern that existed by the time of the de- valuation of the CFA franc in January 1994, as the share of Cte d'Ivoire's total trade with other African countries had increased by 16 percentage points in the intervening years while that with industrial countries had fallen correspondingly. Figure 2.5 shows how the REER differs when computed using the different trade weights for 1985 and 1993. At 1985 weights, the REER Figure 2.5 The REER for C6te d'Ivoire Calculated Using 1985, Average 1980-82, and 1993 Total Trade Weights and Old IFS Country Weights, 1980-93 (1985=100) 170 REER at 1993 Total Trade Weights 160 150 REER with Old -. IFS Country Weights REER at 1985 Total 140 Trade Weights 130 A 120 110 REER at Average 1980-82 Total Trade Weights 100 R" 90 II I I I I l I 1980 1982 1984 1986 1988 1990 1992 --o--REER at 1993 Total Trade Weights --*--REER with Old IFS Country Weights REER at Average 1980-82 Total -* REER at 1985 Total Trade Trade Weights Weights Note: The REER has been calculated using CPIs and official exchange rates. An upward movement represents an appreciation of the REER for Cbte d'Ivoire. Source: Computed from World Bank data. Table 2.2 Shares in Percent of C6te d'Ivoire's Exports, Imports, and Total Trade by Country, in 1985 and 1993 Exports (%) Imnports (%) Total trade (%) Counltry, 1985 1993 1985 1993 1985 1993 European countries 65.0 54.9 59.7 50.5 63.0 53.0 France 16.6 16.7 34.3 30.5 22.9 22.4 Other EU 47.3 35.2 22.9 17.5 38.1 27.8 Other European countries 1.2 3.2 2.5 2.5 2.0 2.8 Other industrial countries 13.2 6.8 13.7 7.2 13.4 7.1 United States 11.7 5.8 7.3 4.4 10.2 5.2 Japan 1.0 0.5 5.3 2.7 2.6 1.5 m Other 0.5 0.5 1.1 0.1 0.6 0.4 CFA countries 10.4 18.4 7.3 1.3 9.3 11.3 Other UMOA 9.5 14.1 2.6 0.7 7.0 8.5 UDEAC 1.0 4.3 4.8 0.6 2.3 2.7 Non-CFA African countries 2.3 11.2 12.7 32.4 6.0 20.2 Nigeria 0.6 1.3 11.9 24.4 4.6 11.0 Other African countries 1.7 9.8 0.8 8.0 1.4 9.2 Non-African developing countries 9.1 8.3 6.4 8.3 8.1 8.2 Total developing countries 21.9 37.9 26.4 42.0 23.4 39.7 Source: IMF, Direction of Trade. 64 EXCHANGE RATE MISALIGNMENT appreciated by 32 percent between 1985 and 1993, whereas at 1993 weights it appreciated by 57 percent. The REER using the 1985 base- year weights is appropriate for assessing the misalignment of the RER over the period 1980-93. The 1993 weights, which reflected the then cur- rent structure of trade, should be used to assess the immediate impact of the January 1994 devaluation, however. A developing country may import from and export to different sets of countries. Hence, its export- and import-competing industries may be affected by the bilateral RERs with sets of quite different countries. Figure 2.6 compares the multilateral RERs for C6te d'Ivoire's import and export markets computed using the 1985 trade shares for imports and exports given in table 2.2. It shows that the REER with the countries from which C6te d'Ivoire imports appreciated considerably more (44 percent) than the REER with the countries to which it exports (25 percent). In some cases, it may also be desirable to disaggregate the REERs for imports and exports. For example, an oil exporter may sell its oil and nonoil exports in different markets under different competitive condi- tions. In this case it may be desirable to calculate separate REERs for oil Figure 2.6 The REERs for C6te d'Ivoire's Export and Import Markets Calculated Using 1985 Export and Import Weights, 1980-93 (1985=100) 160 REER at 1985 Import Weights 150 ik 140 REER at 1985 Export Weights 130 120 110 100 90 I 1 : I I1 I 1980 1982 1984 1986 1988 1990 1992 - - u - REER at 1985 Import Weights ----REER at 1985 Export Weights Note: The REER has been calculated using CPIs and official exchange rates. An upward movement represents an appreciation of the REER for Cte d'Ivoire. Source: Computed from World Bank data. EXTERNAL REAL EXCHANGE RATES 65 and nonoil exports. Similarly, a particular country may export nontradi- tional products to markets that are significantly different from those in which it sells its traditional export commodities; or a country's tradi- tional and nontraditional exports may experience quite different move- ments in their terms of trade. In such cases, it may be desirable to com- pute separate REERs for traditional and nontraditional exports in order to give a clearer picture of the incentives for export expansion and di- versification. Third-Country Competition Exports of the home country compete both with domestic production of the same product in its trading partner i and with exports from other countries, which may not trade at all with the home country, selling in the same market in country i. Ideally, competitiveness weights should take into account not only the aggregate trade flows between the home country and its trading main partners but also the effects on these trade flows of competition in export markets from third countries, which are not important direct trading partners of the home country. For example, although COte d'Ivoire has only a small amount of direct trade with Malaysia, both countries export very similar primary products to the United States, which is one of C6te d'Ivoire's major trading partners. Hence, a change in the bilateral RER between the ringitt (Malaysia's currency) and the U.S. dollar is likely to have an impact on C6te d'Ivoire's exports to the United States. Empirically, taking into account competition from third countries is much more difficult than simply allowing for direct trade-as it requires a model of competition in international markets that is not available to most analysts. The only weights incorporating such third-country com- petition available for calculating REERs are those from the IMF's Infor- mation Notice System (INS) used in International Financial Statistics. Table 2.3 shows the original IFS competitiveness weights for C6te d'Ivoire, which were in use at the time the CFA franc was devalued in 1994. These weights were based on data for the period 1980-82. They reflected both the relative importance of C6te d'Ivoire's trading part- ners in direct bilateral trade and competition from third countries." Figure 2.5 compares the REERs for C6te d'Ivoire computed using the original IFS weights and actual trade shares both for the 1980-82 base period used in computing these weights and for 1985. The main differ- ences between the original IFS weights and the actual trade shares are that the IFS gave significantly higher weights to third-country competitors 10. See Wickham (1987) and McGuirk (1987) for a discussion of the original weighting scheme employed by the IMF at that time. 66 EXCHANGE RATE MISALIGNMENT Table 2.3 C6te d'Ivoire: Average 1980-82 Total Trade Weights, Official and Adjusted IFS Country Weights, and 1993 Total Trade Weights Average 1980-82 Old IFS Adjusted old New IFS 1993 total trade country IFS country country total trade weights weights weights weights weights (%) (%) (%) (%) (%) European countries 62.3 56.5 53.9 62.8 53.0 France 30.1 27.2 25.9 21.6 22.4 Netherlands 9.4 5.8 5.5 6.3 5.8 Italy 7.5 4.6 4.4 6.5 5.8 Germany 6.1 7.5 7.2 10.6 6.1 United Kingdom 3.3 6.7 6.4 5.9 2.8 Spain 2.9 2.0 1.9 2.9 3.3 Belgium-Luxembourg 2.2 2.8 2.7 5.8 4.0 Portugal 0.8 n.a. n.a. n.a. n.a. Switzerland n.a. n.a. n.a. 1.8 n.a. Sweden n.a. n.a. n.a. 1.4 n.a. Other European Countries n.a. n.a. n.a. n.a. 2.8 Other industrial countries 12.9 21.1 20.1 23.5 7.1 United States 8.6 10.3 9.8 11.7 5.2 Japan 3.7 7.3 7.0 7.2 1.5 Canada 0.4 1.8 1.8 3.1 0.3 Australia 0.2 1.7 1.6 1.4 0.1 CFA countries 7.8 1.6 2.0 0.0 11.1 Burkina Faso 2.3 n.a. n.a. n.a. 2.9 Mali 2.3 n.a. n.a. n.a. 3.5 Senegal 1.8 n.a. n.a. n.a. n.a. Togo 0.7 n.a. n.a. n.a. 1.0 Niger 0.7 n.a. n.a. n.a. 0.9 Cameroon n.a. 1.6 2.0 n.a. n.a. Gabon n.a. n.a. n.a. n.a. 2.1 Other CFA Countries n.a. n.a. n.a. n.a. 0.7 (Ghana, Brazil, China, Indonesia, Malaysia, Colombia, and Cameroon) and non-European industrial countries (the United States, Japan, Canada, and Australia) and significantly lower weights to the European and other CFA countries than their shares of total trade. Despite these differences in the country weights, the REERs for C6te d'Ivoire calculated using the original IFS weights, average 1980-82 trade shares, and 1985 trade shares actually tracked each other fairly closely. The original IFS competitiveness weights were subsequently updated during 1994-96 for 146 countries using disaggregated world trade data for 1988-90. These new weights are based on separate models of world trade and competition in the markets for nonoil primary products, manu- EXTERNAL REAL EXCHANGE RATES 67 Average 1980-82 Old IFS Adjusted old New IFS 1993 total trade country IFS country country total trade weights weights weights weights weights (%) (%) (%) (%) (%) Non-CFA African countries 3.4 5.7 12.9 0.0 20.2 Nigeria 2.4 2.3 6.4 n.a. 11.0 Morocco 0.6 n.a. n.a. n.a. 0.6 Mauritania 0.2 n.a. n.a. n.a. 0.6 Ghana 0.2 3.4 6.4 n.a. 2.1 Guinea n.a. n.a. n.a. n.a. 2.0 South Africa n.a. n.a. n.a. n.a. 1.0 Zaire n.a. n.a. n.a. n.a. 0.6 Sierra Leone n.a. n.a. n.a. n.a. 0.5 Mozambique n.a. n.a. n.a. n.a. 0.5 Other African countries n.a. n.a. n.a. n.a. 1.3 Non-African developing countries 13.7 15.1 11.1 13.7 8.2 Algeria 2.1 n.a. n.a. n.a. n.a. Taiwan (China) 1.6 1.3 0.0 1.3 1.2 Venezuela 4.4 n.a. n.a. n.a. n.a. Saudi Arabia 1.4 n.a. n.a. n.a. n.a. Pakistan 1.0 n.a. n.a. n.a. n.a. Thailand 0.6 n.a. n.a. n.a. 1.3 Brazil 1.4 4.8 0.0 4.2 0.9 China 0.9 1.5 1.8 2.0 1.1 Indonesia 0.3 2.2 2.7 1.3 0.3 Malaysia n.a. 3.6 4.4 1.9 0.4 Colombia n.a. 1.8 2.2 1.7 n.a. Korea n.a. n.a. n.a. 1.4 n.a. Poland n.a. n.a. n.a. n.a. 0.7 Tunisia n.a. n.a. n.a. n.a. 0.5 Other developing countries n.a. n.a. n.a. n.a. 1.8 Total developing countries 24.9 22.4 26.0 13.7 39.5 Source: IMF. factures, and, where significant, tourism. The choice of the 1988-90 base period was a compromise between the use of up-to-date information, on the one hand, and comprehensive coverage, on the other. The meth- odology and data used to compute the new weights are described in Zanello and Desruelle (1997).n Even the new competitiveness weights 11. As explained in Zanello and Desruelle (1997), in the updating, a some- what different weighting system-based on data for 1989-91-was employed for calculating the REERs using unit labor costs in manufacturing for 17 indus- trial countries rather than the system for calculating weights for computing REERs using CPIs for all countries, which is discussed above. 68 EXCHANGE RATE MISALIGNMENT are, unfortunately, not readily available to all analysts; may be out of date for some countries; and are difficult for others to update or adjust for such factors as unrecorded trade and shifting trade patterns. The updating of the IMF's competitiveness weights was finalized af- ter most of the REER calculations and analysis reported in this chapter had been completed, and the new weights were not used in the REER indexes shown in most of the graphs and tables. For illustrative pur- poses, figure 2.7 compares the REERs computed with the original IFS weights, the new IFS weights, and 1993 trade shares. If the new IFS weights were actually the correct ones to use, then the measure of the REER actually used at the time of the devaluation was off by 20 percent because of incorrect weights; and the adjustments made by Bank and Fund staff for unrecorded trade (see below) only made matters worse, increasing the error by another 20 percent. However, the new weights themselves raise some puzzling questions, for example: should neigh- boring African countries really have been given a zero competitiveness Figure 2.7 The REER for C6te d'Ivoire Computed with New and Old IFS Country Weights, Adjusted IFS Country Weights, and 1993 Total Trade Weights, 1980--93 (1985=100) 180 REER with Adjusted 170 REER with 1993 IFS Country Weights Total Trade Weights 160 150 REERwithOldIFS *.. u 140 Country Weights . - - 130 120 110 REER with New IFS Country Weights 100 .... 90 I I I 1980 1982 1984 1986 1988 1990 1992 -a-- REER with New IFS Country Weights --- REER with Old IFS Country Weights -*- - REER with Adjusted IFS Country Weights -*- REER with 1993 Total Trade Weights Note: The REER has been calculated using CPIs and official exchange rates. An upward movement represents an appreciation of the REER for C6te d'Ivoire. Source: Computed from World Bank data. EXTERNAL REAL EXCHANGE RATES 69 weight despite a trade share of 31 percent in 1993 (table 2.3)? Was the REER fully 40 percent less appreciated than 1993 trade shares indicated? Unrecorded Trade Another practical complication that may be important for some SSA and other low-income countries is the existence of a significant amount of unrecorded trade through parallel markets. Such unrecorded trade is likely to be greater the higher are tariffs and nontariff barriers to official trade and the greater is the parallel market premium. In such cases, some adjustments may be required to all weighting schemes that are based on the official direction of trade statistics. Any adjustments for unrecorded trade should be consistent with the treatment of parallel market exchange rates discussed previously. For example, in calculating adjusted REER indexes for the CFA coun- tries, the original IFS weights for Ghana and Nigeria were revised up- ward for some countries to take into account the high level of unre- corded trade with these two countries that is not reflected in the official trade statistics. Thus, as shown in table 2.3, for C6te d'Ivoire the weight for Ghana was increased from 0.034 to 0.064 and that for Nigeria from 0.023 to 0.064 to allow for unrecorded trade. Figure 2.8 illustrates the possible effects of an adjustment for unrecorded trade on the REER. It shows that the REER appreciated by almost twice as much between 1985 and 1993 with the adjusted weights (50 percent) as with the unadjusted ones (28 percent). Use of the parallel exchange rates for the unrecorded trade reduces the difference to 10 percent, however. Hyperinflation Once the country weights have been determined, the calculation of the REER as a geometric weighted average of the bilateral RERs (shown in equation 2.7 above) is straightforward. However, a possible additional complication may arise in calculating separate NEER and effective price indexes as components of the REER (as in equation 2.8 above). If any of the trading partners-even those with small country weightings in the home country's index-are experiencing hyperinflation, including these countries in the calculation may distort the separate NEER and effective relative price indexes. The only practical way to get around this prob- lem and arrive at analytically useful NEER and relative price indexes is to delete the hyperinflation countries and adjust the weights for the re- maining countries accordingly. The REER index itself, in contrast, will not be distorted because hyperinflations are usually accompanied by offsetting hyperdevaluations. Hence, the REER indexes calculated in- cluding and excluding countries experiencing hyperinflation can be com- 70 EXCHANGE RATE MISALIGNMENT Figure 2.8 The REER for C6te d'Ivoire Computed Using IFS Country Weights and Adjusted IFS Country Weights, and Official and Weighted Average Exchange Rates, 1980-93 (1985=100) 160 REER with Adjusted IFS Country REER with Adjusted IFS Country Weights 150 Weights and Official ER m' .. and Weighted. 140Average ER 130 120 110 REER with IFS Country 10- R Weights and Official ER 90- 80 - 70 - 60 I Ill llI l 1980 1982 1984 1986 1988 1990 1992 1994 1996 --REER with IFS Country Weights and Official Exchange Rates (ER) --- - REER with Adjusted IFS Country Weights and Official ER REER with Adjusted IFS Country Weights and Weighted Average ER Note: An upward movement represents an appreciation of the REER for C8te d'Ivoire. Source: Computed from World Bank data. pared to see if the adjustments to the country weights necessary to cal- culate separate NEER and relative price indexes are reasonable. For example, Brazil, which experienced hyperinflation in the 1980s, was assigned a weight of .048 in the old IFS competitiveness weights for C6te d'Ivoire. Figure 2.9, which compares the NEER and relative price indexes for C6te d'Ivoire computed with and without Brazil, shows how even one such hyperinflation country can distort these indexes. C6te d'Ivoire's NEER including Brazil appreciated by 220 percent between 1985 and 1993, whereas without Brazil it appreciated by only 45 per- cent. Similarly, C6te d'Ivoire's price level relative to its competitors de- clined by 60 percent if Brazil is included but by only 10 percent if it is excluded. The behavior of C6te d'Ivoire's REER index, on the other hand, was relatively little affected by the inclusion or exclusion of Brazil. The Choice of Appropriate Country Weights Hence, in addition to actual recorded trade flows, the choice of appro- priate country weights may be affected by a number of additional fac- EXTERNAL REAL EXCHANGE RATES 71 tors, including parallel foreign exchange markets, unrecorded trade, and changing patterns of trade. Other relevant factors may include third- country competition in export markets, the pricing of trade in major currencies rather than in the trading partners' currencies, and hyperinflations-hyperdevaluations in competing countries. In addition, in some cases, it may be useful analytically to calculate separate REERs for imports and exports when the factors affecting these differ signifi- cantly. Given the analytical complexity of making systematic adjustments for all of the above factors and the shortage of empirical data needed for doing so, the choice of appropriate country weights may in some cases be as much art as science. Different (reasonable) weighting systems can affect measurement of the REER by as much as 25 percent in a particu- lar year. Hence, the choice of weights may call on the analyst for sub- stantial judgment as empirical accuracy may be a matter of knowing which factors are important (and which are not) in a specific case and making the most reasonable adjustments for the important factors with Figure 2.9 The NEER, Relative Prices, and Expenditure-PPP REER at Old IFS Country Weights for C6te d'Ivoire with and without Brazil, 1980-96 (1985=200) 320 300-- 280.- NEER with 260-- Brazil 0 240 220 200 NEER without 180- Brazil 160- Relative Prices with Brazil 20 i il I I I I 11 1980 1982 1984 1986 1988 1990 1992 1994 1996 --- Expenditure-PPP REER with Brazil -- Relative Prices with Brazil -x- Relative Prices without Brazil -i- NEER with Brazil --- Expenditure-PPP REER without Brazil ---NEER without Brazil Note: An upward movement is an appreciation. Source: Computed from World Bank data. 72 EXCHANGE RATE MISALIGNMENT the limited empirical information available. It is also important to check the sensitivity of the REER index to alternative weighting schemes. While the task of determining appropriate weights may seem daunting, arriv- ing at reasonably accurate and up-to-date weights for one small coun- try is inherently simpler than determining a consistent set of general- equilibrium weights for all countries. Measurement of the Different RER Concepts: Choosing Appropriate Price or Cost Indexes All three of the primary versions of the external RER are widely used in empirical applications. The computational formulas and conventions, nominal exchange rates, and country weighting schemes discussed above are common to all of these. The differences among the measures result primarily from using different foreign and domestic price indexes in their calculations.2 Since the different versions of the external RER are based on different types of price indexes, empirical measures of them will be similar only if the price indexes are. If these price indexes always moved in parallel, the choice between the indexes might make little prac- tical difference in determining the change in the external RER. How- ever, as discussed below, for a given country the different types of price indexes, and the corresponding measures of the external RER, may dif- fer significantly because of changes in the terms of trade, trade policy, or productivity. Unfortunately, changes in these factors, particularly the terms of trade and trade policy, tend to be much larger in developing countries than in industrial ones, magnifying the differences between different external RER measures. In constructing external RER indexes, similar types of price indexes should be used for both the home country and its foreign competitors, with the type of index depending upon the theoretical concept being used. Thus, it is not conceptually consistent, in calculating an external RER, to use a consumption price index for the home country and a pro- duction price index for its competitors because the resulting ratio would be based neither on expenditure price nor on production cost parity. Similarly, it would be inconsistent to compare a value-added deflator for one country with a final product price index for another. This section discusses the choice of appropriate price or cost indexes for measuring each of the three primary versions of the external RER. 12. The statistical problems involved in the construction of price indexes are not discussed in this chapter. See Maciejewski (1983) for an extensive discussion of statistical issues. EXTERNAL REAL EXCHANGE RATES 73 The following three subsections take up, in turn, the empirical indexes needed for measuring the expenditure-PPP, Mundell-Fleming, and traded-goods versions of the RER. The Expenditure-PPP External RER Purchasing power parity, the oldest theory of the equilibrium exchange rate, may be applied to the prices of all goods, as discussed here, or only to the prices of traded goods, as discussed below in the subsection on the external RER for traded goods. There are two versions of PPP: abso- lute and relative. Since both versions are concerned with purchasing power, they employ expenditure price rather than production cost in- dexes. However, the two versions use different baskets of goods; abso- lute PPP requires standardized baskets whereas relative PPP requires representative ones. Absolute PPP The original absolute form of PPP theory holds that the equilibrium nominal exchange rate between two currencies is equal to the ratio of the actual domestic and foreign prices of an identical standardized bas- ket of goods in the home and foreign countries as shown in equation 2.13: (2.13) Edc - Ad where P and P are the actual domestic- and foreign-currency prices of the standardized basket of goods.13 Note that absolute PPP both deter- mines an equilibrium nominal exchange rate and implies that the real exchange rate in equation (2) equals one. Because, among other things, of the shortage of data on the actual costs of standardized baskets of goods in different countries, absolute PPP has not been much used empirically." Recently, however, in order 13. See Rogoff (1996). If the baskets of goods are not identical in two coun- tries, the nominal exchange rate cannot be uniquely determined as the ratio of the cost of the baskets in the two currencies because the cost of the baskets will in general depend upon their composition. Absolute PPP is theoretically unattrac- tive in that a standardized basket of goods will not be representative of the ex- penditure patterns in two countries unless they have identical consumption pat- terns. (See Officer 1982). Absolute PPP is also sometimes referred to as "strong PPP."1 14. The Economist's "Big Mac Index" is, as noted in appendix A, a simple one- good absolute PPP nominal exchange rate and is the most commonly encoun- tered example of the empirical use of absolute PPP. 74 EXCHANGE RATE MISALIGNMENT to make possible more accurate comparisons of income and consump- tion levels across countries, a large research effort known as the Interna- tional Comparison Programme (ICP) was carried out to price standard- ized baskets of goods in different countries. From the comparative pur- chasing power parity indexes derived under the ICP, implicit nominal PPP exchange rates can be calculated as the relative cost of the stan- dardized basket of goods in the countries being compared. These ICP exchange rates have been used in a few multicountry studies as esti- mates of the equilibrium nominal exchange rate and are discussed further in appendix A. Relative PPP In its relative form, PPP holds that the nominal exchange rate is propor- tional to the ratio of the domestic and foreign price levels as expressed by equation 2.14: (2.14) Ed PG" k where k is a constant.3 Relative PPP in equation 2.14 implies that the real exchange rate in equation 2.2 is a constant. Conceptually, for the expenditure version of relative-PPP external RER price indexes should be comprehensive, representative expenditure-based indexes including both traded and nontraded goods.16 Because of the ready availability of consumer price indexes for representative baskets of goods for most countries, the relative expenditure-PPP version of the external RER has been extensively used empirically. Unless other- 15. Because k is an arbitrary constant, rather than a specific number, the "prices" in equations 2.2 and 2.14 may be either actual prices or indexes. The value of k will depend upon which of these is used but will still be constant. Relative PPP is also sometimes referred to as "weak PPP," and some formulations of it allow k to follow a time trend. 16. The representative baskets should include both traded and nontraded goods in whatever proportions they are actually purchased in the domestic and foreign economies. Use of a standardized but arbitrary basket in calculating the relative-PPP version of the RER would require an improbable behavioral as- sumption-that households and firms in both countries know the composition of this standardized basket and value currencies accordingly rather than in terms of their actual expenditure patterns. Even the use of representative baskets of goods in measuring expenditure PPP could, however, be problematic if the com- position of these baskets tends to change systematically over time because of the demand and supply factors discussed in Chapter 5. EXTERNAL REAL EXCHANGE RATES 75 wise specified in this volume, the term PPP always refers to relative expenditure PPP. References to absolute PPP are explicitly identified as such. The consumer price index (CPI) is usually broadly representative of both traded and nontraded goods. It is the most commonly used index in the calculation of the expenditure-PPP version of the external RER. The CPI is available monthly in most developing countries so that the movements in the RER computed from it can also be tracked on a monthly basis.17 The IMF publishes in International Financial Statistics (IFS) ex- ternal RER indexes based on consumer price indexes for most industrial and developing countries. IFS treats the expenditure-PPP version of the external REER as "the REER" for developing countries, although, as dis- cussed below, it gives primacy to the REER for traded goods computed using unit labor cost in manufacturing for 17 industrial countries for which the required data are available. Two main caveats concerning expenditure-PPP external RER indexes are worth noting. First, CPIs are subject to the influence of price con- trols, subsidies, and indirect taxes; and CPI levels and movements may be affected by these. Hence, in interpreting RERs based on CPIs it is necessary to distinguish between the effects of changes in indirect taxes, subsidies, and price controls and movements in the general price level.8 Second, CPIs for different countries are not based on the same baskets of goods (or even ones that are necessarily fairly comparable), and their weightings often reflect patterns of consumer spending that may differ in the home country from those in its foreign competitors. These differ- ences in expenditure patterns do not pose a conceptual problem from the point of view of relative-PPP theory, which applies to representative domestic and foreign baskets that may differ in composition, but do limit the usefulness of RERs based on CPIs for comparing standards of living. Compared with the CPI, the wholesale price index (WPI) is usually more heavily weighted with traded goods and underweighted with 17. For example, monthly CPIs were available for the period 1980-93 for all of the CFA countries except Benin and Mali. 18. CPIs are also subject to seasonal variations. Although seasonal variations do not pose any particular problems for analysis of annual data, such as those reported in this chapter, they may cause seasonal fluctuations in RER indexes calculated using quarterly or monthly data. The IMF thus adjusts for seasonal variations in computing REERs as explained in Zanello and Desruelle (1997). Although it may be possible for other analysts to adjust home country data for seasonal variations, it may be too time consuming to do so for competing coun- tries unless seasonally adjusted CPI data can be obtained from other sources. 76 EXCHANGE RATE MISALIGNMENT nontraded goods. Thus, the WPI is not an appropriate candidate for calculation of the expenditure-PPP version of the external RER, although the WPI may be used for the traded-goods version of the external RER as noted below. Two plausible alternatives to the CPI for expenditure PPP are the absorption deflator and the overall consumption deflators from the national accounts. However, neither of these is commonly used in the computation of the expenditure-PPP version of the RER. National account data are typically available only annually for low-income de- veloping countries whereas the CPI is usually available monthly. In ad- dition, both the absorption and the total consumption deflators include public consumption, the price of which often is not determined by mar- ket forces. Absorption also includes investment, which makes it a broader measure of the expenditure price level than the CPI but which some analysts prefer to consider as an "intermediate" product for producing final consumption.19 Although for the foregoing reasons the absorption and consumption deflators are not often used, in specific circumstances they may be worth considering. For example, CPIs were not available for Benin and Mali for the period for which the overvaluation of the CFA franc was being analyzed. Since the private consumption deflator from the national ac- counts was the most comparable of the price indexes actually available, it was used as a proxy for the CPI for estimating the expenditure-PPP version of the RER for these two countries. Bilateral RERs can also be readily constructed using absorption and consumption deflators for those competitors for which comparable data are available, but construction of similar multilateral RERs may be more problematic because of prob- lems with timely data availability and comparability for some develop- ing-country competitors. The Mundell-Fleming or Aggregate Production Cost Version of the External RER The second principal external RER concept is based on the standard Mundell-Fleming open economy macroeconomic model used for indus- trial countries. In this model, each country is assumed to produce a single unique aggregate good (that is, its GDP), which it both consumes and exports. This composite good is in imperfect competition with the unique composite goods produced and exported by other countries and faces less than perfectly price-elastic foreign and domestic demand. The price of each country's good is determined by its cost of production. Hence, in the Mundell-Fleming model, the price index in the definition of the 19. See, for example, Jorgenson and Paldam (1986). EXTERNAL REAL EXCHANGE RATES 77 external RER (given in equation 2.2) is an output price index or produc- tion cost index for the economy, which is composed of exports and goods produced and sold domestically by a country, rather than an expendi- ture price index as in the PPP theory, which is composed of imports plus goods produced and sold domestically. The Mundell-Fleming version of the external RER can also be viewed as measuring competitiveness in the aggregate production of all goods, both traded and nontraded.20 In this formulation, the home and foreign GDP (value-added) deflators are clearly the appropriate price indexes to use in computing the exter- nal RER. Thus, in foreign-currency terms, the Mundell-Fleming RER (MFRERC) is computed as shown in equation 2.15: (2.15) MFRER = E Z GDPd PGDPf where PGDPd and PGDPf are, respectively, the domestic and foreign GDP deflators. The Mundell-Fleming model assumes that the home country's GDP and exports are a single composite good whose prices move in parallel. Similarly, the foreign-currency price of imports is assumed to move in parallel with the foreign country's GDP deflator. Hence, the foreign- currency prices of exports and imports are determined as indicated in equations 2.16 and 2.17: (2.16) Efc 'PGDPd = Efc PXdc = 'PXfc 20. Some authors interpret the Mundell-Fleming RER as a way of stating pur- chasing power parity theory in terms of aggregate production costs of all goods, both traded and nontraded. Since the competitiveness of the traded-goods sec- tor depends, among other things, upon cost of inputs produced by the nontraded sector and the opportunity cost of the factors employed in it, these authors view aggregate "cost structure parity" as preferable to the version of the external RER that only takes into account competitiveness in producing traded goods. (See Officer 1982, Chapter 8, for the arguments favoring production cost over expen- diture price parity theories.) This aggregate producer cost parity theory is also sometimes interpreted as producer price parity theory. Perfect competition in domestic and foreign markets would force the domestic price of any commodity (and thus the general price level) to equal its cost of production, including labor, capital, and intermediate inputs. Hence, some authors replace the production cost index by the general producer price level in the formulas defining the Mundell-Fleming RER and arrive at a formulation quite similar to that for ex- penditure PPP. However, the price index used in cost parity theory should, in principle, be a production cost (or price) index whereas that used in expendi- ture-PPP theory is an expenditure or cost of living related index. 78 EXCHANGE RATE MISALIGNMENT (2.17) PGDPf Plfe where Pxac is the home country's export price deflator measured in do- mestic currency, Pxfc is its export price deflator measured in foreign cur- rency, and P is the home country's import price deflator measured in foreign currency. Substituting the right hand sides of equations 2.16 and 2.17 into equation 2.15 yields equation 2.18: P where TOT is the home country's terms of trade. Thus, the Mundell- Fleming formulation makes no distinction between the terms of trade and the RER. Since the export price deflator is assumed to equal the home country's GDP deflator and the import price deflator is assumed to equal the foreign country's GDP deflator, the RER and the terms of trade are the same; and both are endogenous in Mundell-Fleming models. The Mundell-Fleming model is appropriate for many industrial coun- tries because their trade is dominated by differentiated manufactured products, their terms of trade often do not vary substantially, and their CPIs and GDP deflators move largely in parallel. In these circumstances, an external RER computed using GDP deflators provides a good indica- tor of changes in the degree of competitiveness in aggregate production of both traded and nontraded goods and takes into account the interac- tion between these two sectors as discussed in the section below on the comparison of alternative external RER measures.21 It is a broader pro- duction cost measure than the unit labor cost as it includes in principle the cost of all factors of production per unit of value added. While the above assumptions may be reasonable for industrial coun- tries producing diversified manufactured exports, they are less so for small developing countries that rely heavily on exports of a few pri- mary products and whose terms of trade are exogenously determined. In these countries, export prices often move much more sharply than the GDP deflator, and it is often desirable analytically to distinguish between the terms of trade and the RER. Production cost and price in- dexes (such as the GDP deflator) include export prices but exclude the prices of imports of final goods,12 whereas an expenditure price index (such as the CPI) does the opposite, including the prices of imports of 21. See for example Edwards (1990, p. 74), Lipschitz and McDonald (1991), Williamson (1994), and Stein, Allen, and Associates (1995). 22. The prices of imported inputs may be reflected in some production cost indexes. EXTERNAL REAL EXCHANGE RATES 79 final goods and excluding the prices of exports. When the terms of trade (the relative prices of imports and exports) change, the movements in production and expenditure price indexes may differ significantly In these circumstances, the GDP deflator and the Mundell-Fleming RER may be heavily influenced by swings in the volatile prices of commod- ity exports and will tend to diverge from the CPI and the expenditure- PPP RER. Another limitation in using the Mundell-Fleming RER for develop- ing countries is that the GDP deflator is available only on a yearly basis for most developing countries, whereas it is often available quarterly for industrial countries. In addition, the GDP deflator may not always be ideal for international comparisons among developing countries be- cause nonstandardized methods are used for its computation in some low-income countries. The External RER for Traded Goods The external RER for traded goods is defined as the relative cost of pro- ducing traded goods, measured in a common currency, in the home and foreign country. This third version of the external RER uses output price, production cost, or factor cost indexes for traded goods in the home and foreign country in equation 2.2 rather than price or cost indexes for all goods as in the expenditure-PPP and Mundell-Fleming RERs. The ex- ternal RER for traded goods measures competitiveness only among the subsets of goods, produced in the home and foreign countries, that are internationally traded. It, in effect, adjusts the nominal exchange rate to reflect relative prices, costs, or unit costs in the traded-goods sectors at home and abroad. The law of one price and purchasing power parity theory may be applied either broadly to the external RER for all goods or more nar- rowly to the external RER for traded goods. The law of one price holds that, because of competition among sellers and arbitrage in goods mar- kets, the prices of identical goods sold in different countries will be the same after adjustment for transactions costs such as transportation and tariffs. Algebraically, the law of one price may be written for goods i as in equation 2.19: (2.19) l,c = Ed (1+t).pi,ft where t, is a broad measure of transportation, tariffs, and other transac- tions costs. If the prices of individual goods tend to be equalized by the law of one price, so will the prices of baskets of these goods. If the law of one price held for all goods, both traded and nontraded, and transactions 80 EXCHANGE RATE MISALIGNMENT costs were negligible, absolute PPP would also hold for all goods since the price of a standard basket of these would be equalized. If transac- tions costs were non-negligible but constant and the law of one price held for all goods, then relative PPP would hold for all goods since the ratio of the prices of a basket of goods in two competing countries would be constant. However, there is little reason to suppose that international competi- tion will tend to equalize the prices of goods that are not traded. Hence, the law of one price is more logically applied only to traded goods. In this case, if transactions were negligible, absolute PPP would hold for homogeneous traded goods. If transactions costs were non-negligible but constant and the law of one price held for traded goods but not for nontraded goods, relative PPP would hold for traded goods. Hence, for those traded goods to which the law of one price applies, the external RER should be a constant.23 Internationally traded goods are of two basic types: homogeneous, standardized commodities, and more diversified products, usually manufactured. Developing countries typically export combinations of these two types of products, which may range from almost 100 percent standardized commodities to almost 100 percent manufactures depend- ing upon the country. The law of one price is most applicable to homo- geneous commodities and would suggest full price equalization after allowance for transportation, tariffs, and other transactions costs. Di- versified manufactures are, in contrast, usually imperfect substitutes. However, international markets for traded goods are large, with many potential sources of supply, and tend to be highly competitive. Hence, even if manufactured products are not perfect substitutes, the cross-elas- ticities between them are significant; and their prices and costs of pro- duction must be reasonably competitive. Theoretically, how much prices will be equalized by international trade depends critically upon whether traded goods are homogeneous perfect substitutes or differentiated imperfect substitutes. For standard- 23. This relationship should, in theory, hold for both bilateral and multilat- eral RERs. However, the assumptions underlying the theoretical argument that the relative cost of a basket of internationally traded goods should be stable can be questioned on the following grounds: (a) the composition of tradable goods can change with the passage of time; (b) if the weightings of different categories of goods are different in different countries, a change in the relative prices of some tradables can cause the relative prices of different baskets including these to vary; and (c) changes in trade policy or transactions costs can alter the price differentials between countries. See Goldberg and Knetter (1997) and Isard and Faruqee (1998) for a fuller discussion of this point. EXTERNAL REAL EXCHANGE RATES 81 ized commodities, theoretically, complete price equalization should take place; and the empirical evidence is that it does. Although the tendency for the prices of differentiated manufactured goods to be equalized is less strong, a rise in their costs or prices, expressed in foreign currency, still usually leads to a loss of competitiveness and market share. (The empirical evidence on the validity of the law of one price is further dis- cussed in Chapter 3, pages 129 through 131). Hence, the RER for traded goods is often used as an indicator of the competitiveness of industrial countries' external sectors and is often employed as the relative price variable in trade equations for these countries. Since this RER focuses exclusively on the traded-goods sector, it has the important advantage of minimizing the effect of productivity bias resulting from more rapid growth of productivity in the traded-goods sector than in the nontraded- goods sector.24 However, the usefulness of the RER for traded goods for a particular developing country will depend upon the mixture of homogeneous and diversified traded goods that it produces, as will the degree of price equalization to be expected. At the limit, countries that produced only homogeneous commodities would be price takers and face perfectly elas- tic foreign demand. In this case, international demand rather than home country costs would determine prices; and there would be full equal- ization of domestic and foreign prices. If transactions costs are negli- gible (as is the case for gold, for example) the traded-goods version of the external RER must equal one.25 If transaction costs are non-negli- gible but constant, which is the more common case, the external RER for homogeneous goods will also tend to be constant. However, many de- veloping countries produce a mix of homogeneous and differentiated goods so that their overall external RER for traded goods may vary with their competitiveness. While the choice of empirical price indexes for the expenditure-PPP and Mundell-Fleming versions of the external RER is reasonably straight- forward, finding empirical measures of competitiveness in producing traded goods is more problematic because lack of data is a serious con- straint for most developing countries. Four alternative price indexes have been suggested in the economic literature as possible candidates for measuring competitiveness in producing traded goods: unit labor costs for traded goods or manufacturing, the wholesale price index (WPI), 24. See the discussion of the Balassa-Samuelson effect in Chapters 3, 5, and 6 and Wren-Lewis and Driver (1998), Chapter 3. 25. See Rogoff (1996) for data showing that the law of one price holds for gold prices in different countries. 82 EXCHANGE RATE MISALIGNMENT value-added deflators for manufacturing and other sectors producing traded goods, and export unit values.' IFS reports external RER indexes for 17 industrial countries computed using these four price indexes for traded goods. The advantages and drawbacks of using each of these four indexes are reviewed briefly below, and the relationship among profitability, competitiveness, and the different external RERs is dis- cussed in appendix B. Unit Labor Costs in Manufacturing The IMF regards relative unit labor costs in manufacturing, measured in a common currency, as the single most useful measure of competi- tiveness in producing traded goods in industrial countries. Zanello and Desruelle (1997) argue that unit labor costs in manufacturing "capture cost developments in an important sector exposed to international com- petition. They offer a reliable gauge of the relative profitability. And, they bring into focus the largest component of nontraded costs and of value added, thus proxying for significant developments in total vari- able costs." For 17 industrial countries, IFS, in fact, reports the REER computed using unit labor costs in manufacturing most prominently as "the REER," rather than the expenditure-PPP REER computed using CPIs, which is reported for developing countries.27 Because of the difficulty of obtaining data on unit labor cost in most developing countries, the REER computed with unit labor costs is of much less use for them.28 Unit labor cost may be calculated either di- rectly as total labor costs divided by the total value of output or indi- rectly as the average wage rate divided by labor productivity. Unfortu- nately, many developing countries, including C6te d'Ivoire and the ma- jority of low-income countries, lack the data necessary to calculate unit labor costs by either method. The REER computed using unit labor costs has been included in this chapter for use in more advanced developing countries for which the necessary data are available. However, it is not 26. See Mills and Nallari (1992). 27. A set of competitiveness weights (reflecting only trade in manufactured products) that is different from the one used for calculating REERs (which use CPIs) is used for calculating REERs that are based on unit labor costs. In addi- tion, unit labor costs may be highly sensitive to cyclical changes in productivity, caused by labor hoarding. IFS reports both an unadjusted and a "normalized" unit labor cost index that adjusts for cyclical changes in productivity. RERs based on relative unit labor costs are discussed further in this chapter's section on the comparison of alternative external RER measures and in Zanello and Desruelle (1997). 28. Even for some industrial countries, the IMF has to interpolate from quar- terly data to obtain a monthly series on unit labor costs in manufacturing. EXTERNAL REAL EXCHANGE RATES 83 likely to be a practical empirical option for many low-income develop- ing countries with limited data.29 Consequently, some authors have simplified the relative unit labor cost version of the external RER for developing countries by assuming that productivity differentials are constant and restating this version of the RER as the relative nominal wage rate expressed in foreign exchange terms or relative to per capita GDP. Wage data also have important em- pirical advantages: levels as well as changes are meaningful, and wage data can be easily compared with other indicators such as GDP per capita. Relative wage indicators may be used either narrowly for the traded- goods sector or more broadly for the aggregate production of all goods. Although these simplified indicators may be biased when productivity changes at different rates in the countries being compared or labor force participation rates differ significantly (if per capita GDP is used), data are at least available for calculating such relative labor cost indicators for some developing countries. These indicators also provide useful in- formation about competitiveness that is readily comprehensible by non- technical audiences.30 However, even the simplified approach of measuring the external RER as relative labor costs expressed in a common currency could not be used for the CFA countries as adequate time-series data on nominal wages were not available. The best that could be done with the frag- mentary wage data available was, as illustrated in figure 2.10, to ana- lyze the relationship of wages to GNP per capita. This relatively simple presentation does, however, give a striking impression of how inflated relative labor costs in the formal sector were in the CFA countries prior to the January 1994 devaluation. Wholesale Price Indexes WPIs are relatively heavily weighted with traded goods and are, there- fore, generally more representative of traded-goods prices than are other aggregate indexes of traded and nontraded goods. RERs for traded goods, computed with WPIs, are thus often used in import and export equations for industrial countries." Unfortunately, WPIs, like measures of unit labor costs, are not avail- able for many developing countries (including COte d'Ivoire). Hence, 29. See Guerguil and Kaufman (1998) for an example, for Chile, of the type of analysis that can be done when data on unit labor costs are available. 30. See Halpern and Wyplosz (1997) and KrajnyAk and Zettelmeyer (1997) for examples of analyses using wage rates in foreign currencies to measure the RER. 31. See Wren-Lewis and Driver (1998). For an example of the use of WPIs for some developing countries, see Fleissig and Grennes (1994). 84 EXCHANGE RATE MISALIGNMENT Figure 2.10 Annual Labor Compensation in the Largest CFA Economies, 1986-88, as a Multiple of GNP per Capita 14 12- 10- 8- 6- 4- 2- 0- Senegal Cbte d'Ivoire Cameroon Competing United France less developed States countries U Manufacturing O Government Note: "Competing less developed countries" is the average for six adjusting developing countries-Morocco, Ghana, Tunisia, Indonesia, Mauritius, and Malaysia. Source: Computed from World Bank data. the home country's cost of aggregate production is sometimes measured by its CPI or GDP deflator, with the WPI being used to measure the price of traded goods of foreign competitors.32 However, this ratio gives a mixed indicator of competitiveness because the foreign prices of traded goods (as measured by foreign WPIs) are compared with the domestic price or production costs of all goods (as measured by the GDP deflator or CPI). This indicator may be biased by differential changes in produc- tivity in the traded and nontraded sectors as discussed in the following chapter on the two-good internal RER.31 Value-Added Deflators for Manufacturing For the industrial countries, IFS reports external RER indexes based on value-added deflators for the manufacturing sector as a measure of com- petitiveness in producing traded goods. These deflators are calculated as the quotient of the current and constant price estimates of value added 32. See, for example, Stein, Allen, and Associates (1995), Chapter 5. 33. This indicator is sometimes also used as a proxy for the internal RER as noted in Chapter 3. EXTERNAL REAL EXCHANGE RATES 85 in the manufacturing sector, adjusted for changes in indirect taxes. There is, unfortunately, an important conceptual problem with using this in- dicator as a single RER for most developing countries. Although the manufacturing sector may be broadly representative of tradable goods production for industrial countries, it is much less so for developing countries in which many of the actual and potential exports and import substitutes are agricultural products. Nevertheless, relative manufac- turing sector deflators, when available, may still be a useful partial indi- cator of competitiveness trends in manufacturing.' Unfortunately, as is the case with unit labor costs and WPIs, the data required for calculat- ing an index of relative manufacturing sector deflators are not available for many developing countries. The only CFA country for which the value-added deflator for the manufacturing sector was available is C6te d'Ivoire. Even for it, this deflator was only available for the period 1985-93, and the data required for making adjustments for indirect taxes were lacking. Although it is possible to construct bilateral RERs using manufacturing deflators for C6te d'Ivoire's industrial-country trading partners, a representative multilateral RER cannot be constructed because of lack of data on manu- facturing deflators for C6te d'Ivoire's developing-country trading part- ners. This problem is a general one. Lack of data on unit labor costs, WPIs, and manufacturing-sector deflators for many developing coun- tries generally prevents computation of REERs based on these indica- tors even when the required data are available for the home country. Export Unit Values A fourth indicator used to assess competitiveness in traded-goods production in industrial countries is the external RER based on rela- tive export unit values in manufacturing. International Financial Sta- tistics reports this indicator for 17 industrial countries. In this indicator, the unit values serve as proxies for export costs or prices. If the price of the home country's manufactured exports fall relative to its competi- tors', its exports should become more competitive. This RER concept is useful only for countries exporting a group of diversified heterogeneous manufactured products that are in imperfect competition with those of their trading partners.35 Export unit values 34. See Chapter 3 for a discussion of using sectoral value-added deflators for calculating the internal RER. 35. Even for countries exporting differentiated products, the use of export deflators or unit value indexes may bias measures of the external RER since these indexes include only products exportable at the current exchange rate and do not cover those potentially exportable at a more depreciated exchange rate. See Clark and others (1994). 86 EXCHANGE RATE MISALIGNMENT are less useful in cases in which the home country exports significant amounts of homogeneous primary products (such as cocoa, coffee, and cotton in the Cbte d'Ivoire example). In this case, competition in inter- national commodity markets will tend to equalize export prices (and unit values that are proxies for them) expressed in a common currency, and the countries concerned will be price takers facing perfectly elastic foreign demand as discussed earlier. This external RER measure will also be biased if the unit value of a developing country's exports in- creases over time as a result of structural increases in value added in the export sector-for example, through greater processing of primary prod- ucts or diversification into higher-value products. Hence, the external RER based on export unit values is often of less help than in industrial countries in assessing the competitiveness of developing countries in producing traded goods (unless disaggregated data are available for the manufacturing exports separately) and was not computed for Cte d'Ivoire. Comparison of Alternative External RER Measures: Competitiveness and the Terms of Trade The preceding sections have discussed the three basic versions of the external RER: the expenditure-PPP, the Mundell-Fleming or aggregate production cost, and the traded-goods RERs. Although these three RER measures are all used to draw inferences about a country's competitive- ness, fluctuations in the terms of trade can cause them to diverge sig- nificantly. The following two subsections consider first the relationship between competitiveness and the different external RERs and then the effects of fluctuations in the terms of trade on them. Competitiveness and the External RER To more firmly link the different concepts of external competitiveness to internal price incentives, the IMF has done a considerable amount of work on the relationship between the various measures of the external RER and the profitability of production and investment, both in the traded-goods sector and in aggregate domestic production. In this work, an improvement in the competitiveness of an economy is defined as an increase in the relative share of profits in value added and is expected to lead to an expansion of output and investment. To take into account both the cost of inputs produced in the nontraded-goods sector and the opportunity cost of the factors employed by it, this interpretation of com- petitiveness has been applied to aggregate domestic production of both EXTERNAL REAL EXCHANGE RATES 87 traded and nontraded goods as well as to traded goods separately. The IMF's analytical work on the relationship between profitability, com- petitiveness, and the different external RERs is reviewed in appendix B, on which the following discussion is based. To take into account total factor productivity in assessing competi- tiveness in producing traded goods, one formulation of the external RER for traded goods suggests using total unit factor cost (UFC) of produc- ing traded goods, including wages, interest, rents, and profits, adjusted for total productivity and measured in foreign exchange. A simplifica- tion of this approach discussed in the preceding section incorporates the idea of competitiveness, implying an increase in profitability. It uses unit labor costs of producing traded goods, rather than total unit factor costs, measured in foreign exchange terms. The rationale behind using unit labor is that the cost of labor usually represents the largest share in the total cost of production and that the shares of different factors change slowly over time. Labor is usually the least mobile factor of production internationally, whereas capital goods are internationally traded and financial market integration tends to equal- ize long-term real interest rates in liberalized economies. Unit labor costs are in a certain sense the most fundamental measure of a country's pro- ductivity, domestic production costs, and real factor incomes. Relative labor costs can also be directly related both to the internal RER and to other measures of the external RER; and real exchange rates and real wages tend to be closely linked, both theoretically and empirically. Hence, relative unit labor costs are widely used to assess external competitive- ness in producing traded goods, as discussed earlier. Marsh and Tokarick (1994) see three advantages in using unit labor cost for assessing competitiveness in industrial countries. First, data on labor costs are generally available on a comparable basis for these coun- tries. Second, unit labor costs are an important component of overall production costs. And, third, the containment of wage costs is often an important component of policies designed to achieve macroeconomic stability and competitiveness in industrial countries. Because of these advantages, the IMF reports the RER computed using unit labor costs in manufacturing as the primary measure of competitiveness in industrial countries. The main limitation of external RER indexes based on unit labor costs is, of course, that they take into account only one factor of production. As explained in Lipschitz and McDonald (1991) and Marsh and Tokarick (1994), relative unit labor costs accurately measure the relative profit- ability of producing traded goods only under certain conditions: that is, if prices of traded goods are determined by international competition, if the capital stock is fixed, if all countries have the same technology, and 88 EXCHANGE RATE MISALIGNMENT if no imported inputs are used. Under these conditions, increases in rela- tive unit labor costs in the home country will reduce the share of profits in the traded-goods sector and lead to a deterioration in the country's competitiveness and external trade position. If the foregoing conditions are not met, however, movements in relative unit labor costs can some- times give misleading signals about profitability. As the capital-labor ratio differs across countries, this difference may introduce a bias into such indexes.36 Moreover, production activities typically use intermedi- ate inputs, which are not included in factor costs. Imported and domes- tic inputs may be used in differing proportions in the home and foreign countries and may have different shares in total cost. Their prices may also vary significantly across countries. For instance, if petroleum and other forms of energy are important intermediate inputs and their rela- tive prices change significantly, competitiveness may improve or dete- riorate without any corresponding change in unit labor costs. Hence, some economists prefer to use broader measures of competitiveness than relative unit labor costs. The RER measured in terms of the aggregate cost or price level is par- tially a function of unit labor costs in the traded and nontraded sectors but encompasses more information. It takes into account changes in the prices of imported intermediate inputs and developments in the nontraded-goods sector. As noted earlier, external competitiveness in producing traded goods should, ideally, take into account both the cost of inputs produced in the nontraded-goods sector and the opportunity cost of the factors employed by it. Hence, cost competitiveness theory has been applied by some authors to aggregate production of all goods, both traded and nontraded.17 These authors prefer to use the GDP de- flator or the CPI to calculate the external RER as a measure of competi- tiveness in the aggregate production of all goods. For them, the Mundell- Fleming and expenditure-PPP versions of the RER, rather than the exter- nal RER for traded goods, are the preferred measures of competitiveness. Effects of Fluctuations in the Terms of Trade The three principal versions of the external RER are thus all used as measures of a country's external competitiveness. These external RER indexes all contain the nominal exchange rate. Movements in nominal exchange rates tend to be much larger than those in the various mea- sures of relative domestic and foreign prices because floating exchange 36. See Edwards (1990). 37. See, for example, Officer (1982). EXTERNAL REAL EXCHANGE RATES 89 rates are quite flexible and respond quickly to monetary as well as real shocks. Since changes in nominal exchange rates often swamp those in relative prices, the nominal exchange rate and the different measures of the external RER usually show a pronounced tendency to move together statistically, particularly in the short term in industrial countries. Over the longer term, changes in three variables-productivity, tar- iffs, and the terms of trade-can, nevertheless, cause the different mea- sures of the external RER to diverge significantly. Changes in produc- tivity and tariffs, although important in some cases, tend to be less dra- matic than those in the terms of trade. These are most conveniently ana- lyzed using the two- and three-good internal RERs discussed in the next two chapters. However, when a country's terms of trade change signifi- cantly, the effects of such a change tend to be evident even in aggregate external RERs. Hence, this subsection examines the effects of fluctua- tions in the terms of trade on the three principal external RERs in a typi- cal developing country.39 When the external terms of trade change significantly, movements in the CPI (which reflects the cost of imported goods) and in the GDP de- flator (which reflects the cost of exports) may diverge. Typically, when the terms of trade improve, the GDP deflator will rise faster than the CPI. But, when the terms of trade deteriorate, the opposite will happen-the CPI will rise faster than the GDP deflator. Hence, the ex- penditure-PPP and Mundell-Fleming RERs computed using these price indexes will diverge. Figure 2.11 compares the behavior of the GDP deflator, the CPI, the private consumption deflator, and the price deflator for manufacturing for C6te d'Ivoire (the only available indicator of the behavior of the prices of differentiated traded goods as noted in the section on the external RER for traded goods). It shows how in the period 1985-93 the CPI and the private consumption deflator both rose while the GDP deflator fell by 11 percent as a result of the sharp drop in commodity export prices." 38. For a further discussion of the empirical relationship between the nomi- nal and real exchange rates, see the paragraphs on the law of one price in Chap- ter 11, footnote 7 in Chapter 13, and Clark and others (1994). 39. For a further discussion of other factors that can cause the external RER for traded goods and the RER for all goods to diverge, see MacDonald (1997), pages 6-11. 40. Until 1987 the CPI and private consumption deflators tracked each other fairly closely. However, in 1992-93 the CPI series was revised from 1987 on- ward. Since then the two series have increasingly diverged as shown in figure 2.11. 90 EXCHANGE RATE MISALIGNMENT Figure 2.11 Price Deflators and the Terms of Trade for C6te d'Ivoire, 1980-93 (1985=100) 140 CPI 130 Private Consumption 120 Absorbtion Manufacturing Deflator Deflator Deflator 110 --- .......--. 90 -. 8*0 Terms of Trade 80 - . GDP 70 - Deflator 60 I I I 1 1 1 1 1 1980 1982 1984 1986 1988 1990 1992 CPI - - - - Private Consumption Deflator --- Manufacturing Deflator - - - - GDP Deflator --- Terms of Trade -+- Absorption Deflator Note: The manufacturing deflator for C6te d'Ivoire is available only from 1985 onward. Source: Computed from World Bank data. Figure 2.12 shows the effects of the different behavior of the CPI and GDP deflators during 1980-93 on the expenditure-PPP and Mundell- Fleming versions of the REER. It shows that, when C6te d'Ivoire's terms of trade dropped by 35 percent between 1985 and 1993, the expenditure- PPP version of its REER appreciated by 45 percent whereas the Mundell- Fleming REER appreciated by only 10 percent as a result of falling ex- port prices. This figure is a good example of the differences between aggregate expenditure and production cost external RERs that can be caused by changes in the external terms of trade. In addition, the relative prices of traded and nontraded goods will not necessarily behave in the same fashion both at home and abroad. Hence, it is possible for the aggregate and traded-goods production costs RERs to give quite different signals from time to time. As traded goods contain both imports and exports, the net effect of fluctuations in the terms of trade on external RERs measuring competitiveness in produc- ing traded goods is theoretically ambiguous. Rising import and rising exports prices will both tend to appreciate external RERs for traded goods, and declines in both import and export prices will tend to depreciate EXTERNAL REAL EXCHANGE RATES 91 both these RERs. The net effect of a change in the terms of trade will depend upon the relative size of the changes in export and import prices and on the sizes of the export and import competing sectors. Thus, the direction of the net effect cannot be determined a priori. The very limited data on the traded-goods external RER measures that are available for developing countries also make it difficult to make empirical comparisons of the movements in the RERs for traded goods with those in the expenditure-PPP and Mundell-Fleming RERs. Never- theless, in practice, for developing countries exporting primary com- modities, a deterioration in the terms of trade caused by declining com- modity prices will be reflected much less strongly, if at all, in standard IFS measures of the external RER for traded goods computed using the prices of diversified manufactured goods, than in the Mundell-Fleming REER. As figure 2.11 shows, the prices of manufactured goods fell by 2 per- cent in C6te d'Ivoire in the early 1990s, while the private consumption deflator rose by 10 percent. Thus, domestic prices of traded goods may have been falling relative to domestic prices of nontraded goods, Figure 2.12 The REER for C6te d'Ivoire Computed Using CPIs, GDP Deflators, and Domestic CPI-Foreign WPIs, and the Terms of Trade, 1980-95 (1985=100) 180 REER Using CPI/WPIs . 160- 140 ,^REER Using CPIs 120 m 1980 1982 1984 1986 1988 1990 1992 1994 - - REER using Domestic CPIs-Foreign WPIs - - - - REER Using GDP Deflators -w-Terms of Trade -+--REER Using CPIs Note: The REERs have been calcualted using official exchange rates and adjusted IFS coun- try weights. An upward movement represents an appreciation of the REER for C6te d'Ivoire. Source: Computed from World Bank data. 92 EXCHANGE RATE MISALIGNMENT causing the internal RER to appreciate and internal competitiveness to deteriorate as shown in figures 3.1 and 3.2 of Chapter 3 on the two-good internal RER. Similar divergences in the prices of traded and nontraded goods can also occur in foreign countries. Figure 2.13 compares the bi- lateral RERs for C6te d'Ivoire with France and the United States calcu- lated using manufacturing deflators with the same RERs calculated us- ing the CPIs and GDP deflators. It suggests that after 1985 external com- petitiveness in producing manufactured goods compared with both France and the United States was significantly better than the changes in the nominal exchange rates and relative CPIs would indicate.41 Thus, indicators of external competitiveness in traded goods and in aggregate production can sometimes give different pictures, and one needs to ex- ercise some care in interpreting them empirically.42 The significance of RERs for traded goods for a developing country will also depend upon the relative importance of homogeneous com- modities, subject to the law of one price, and differentiated nonstandardized products in its trade. For example, manufactures accounted for only 16 percent of C6te d'Ivoire's exports in 1993, with standardized primary commodities accounting for nearly all of the remainder. Hence, the mac- roeconomic effect of better price performance in manufactures was quite limited. For countries exporting primary products, the external RER for aggregate production is a broader indicator than the RER for traded goods. However, as noted above, when the terms of trade change sig- nificantly aggregate cost-price indicators giving larger weights to im- ports (such as the CPI) may diverge quite significantly from those giv- ing larger weights to exports (such as the GDP deflator). In this case, it is usually more informative to calculate separate RER indexes for imports and exports as discussed in Chapter 4 on the three-good internal RER. Summary and Conclusions This concluding section first summarizes the different measures of the external RER. It then briefly reviews the major factors causing the be- havior of these RER measures in developing countries to differ from that in industrial countries. 41. The bilateral Mundell-Fleming RERs are not reliable indicators in this case as they are distorted by the effects of the falling prices of commodity exports on C6te d'Ivoire's GDP deflator. 42. Neither bilateral RERs for trade in manufactured products with most de- veloping countries nor REERs for manufactured goods can be calculated for C6te d'Ivoire because of lack of comparable data for C6te d'Ivoire's developing-coun- try competitors. EXTERNAL REAL EXCHANGE RATES 93 Figure 2.13 The Bilateral RERs Between C6te d'Ivoire and the United States and France Calculated Using CPIs, GDP Deflators, and Value- Added Deflators for Manufacturing, 1988-93 (1985=100) 180 160 RER with Francesn ~ ilatral ER wth RER Usig thenUactUring DePIos RER with the U.S. Using Manufacturing B Deflators 120- Using CPIs RER with the U.S. Using. IIGDP Deflators 100 1 RER with France Using .o.e C d f.... Manu acturing el ators 80 .- .. . .. . ------ RER with France Using GDP Deflators 60: I:I 1985 1986 1987 1988 1989 1990 1991 1992 1993 - -d Bilateral RER with France Using Manufacturing Deflators --m-Bilateral RER with the U.S. Using Manufacturing Deflators ----Bilateral RER with the U.S. Using GDP Deflators -t-Bilateral RER with France Using GDP Deflators ---- Bilateral RER with France Using CPIs ---r----Bilateral RER with the U.S. Using CPs Note: An upward movement is an appreciation of the RER for C8te d' Ivoire. Source: Computed from World Bank data. Measurement of the External RER: A Summary The four primary versions of the external RER-the expenditure-PPP, Mundell-Fleming or aggregate cost, competitiveness in traded goods, and relative labor cost concepts-are summarized in table 2.4. These alternative RER indexes provide different but related information. Empirically, the use of CPIs in measuring relative expenditure PPP is well established. CPIs are widely available on a fairly current basis for most developing countries and permit the reasonably easy computa- tion of the expenditure-PPP version of the external RER. This is a useful, internationally comparable measure that provides a good indicator of movements in relative price levels between countries and of nominal shocks to exchange rates and price levels. However, it, like all external RERs, can be quite sensitive to assumptions about parallel exchange markets, unrecorded trade, and shifting trade shares as discussed below. Table 2.4 Summary of External RER Measures Price-Cost Index Used in Availability of Developig RER Measure Computation Country Data Comments 1. Purchasing Power Parity a. Expenditure PPP-Relative CPIs Monthly in most countries Most widely used measure in developing countries. b. ICP Exchange Rates-Absolute ICP Price Data Selected years for Data are available only with a long time lag. participating countries These are nominal rather than real exchange rates. 2. Mundell-Fleming Aggregate GDP Deflators Annually, most countries CDP deflators may be heavily influenced Production Cost RER by volatile commodity prices. 3. RERs for Traded Goods to a. Relative Unit Labor Cost in Manufacturing Unit Labor Annually, a few countries Useful partial indicator for manufacturing Manufacturing Costs sector when available. b. Relative Manufacturing Sector Deflators Manufacturing Sector Annually, some countries Useful partial indicator for manufacturing Deflators sector when available. c. Relative Wholesale Prices WPIs Monthly, a few countries Not suitable for most developing countries because of predominance of primary commodities, d. Relative Export Unit Values Export Unit Value Indexes Annually, some countries Not suitable for most developing countries because of predominance of primary commodities. 4. Relative Labor Cost in Production of All Goods a. Relative Wages Average Wage Rates Annually, some countries Useful when available but may be biased by productivity changes. b. Relative Average Unit Labor Cost Average Unit Labor Costs Annually, very few countries Useful when available, but very few countries have necessary data. EXTERNAL REAL EXCHANGE RATES 95 Similarly, GDP deflators are commonly used to measure the Mundell- Fleming or aggregate production cost RER. This measure is widely used in empirical analysis of industrial countries, to which the Mundell-Fleming model of trade in differentiated manufactured products is well suited. This model is, however, much less appropriate for developing countries that export significant quantities of primary commodities and whose terms of trade fluctuate considerably. Volatility in the export prices of primary commodities can cause the Mundell-Fleming RER to diverge significantly from the expenditure-PPP version of the RER and limit the utility of the former to those developing countries that export diversi- fied manufactured products. In addition, although the GDP deflator is usually available quarterly in industrial countries for computing the Mundell-Fleming RER, it is often available only annually in developing countries, making it hard to monitor the Mundell-Fleming RER on a current basis. The traded-goods version of the RER is widely used for the OECD coun- tries. The IMF regularly publishes data on four of these RERs-relative unit labor costs in manufacturing, relative wholesale prices, relative manufacturing sector deflators, and relative export unit values-for 17 industrial countries. The IMF, in fact, treats the external REER for traded goods computed using unit labor costs in manufacturing as "the REER" for 17 industrial countries rather than the REER computed using CPIs, which is used for developing countries. However, the limited availabil- ity of data on unit labor costs, productivity, and wholesale prices makes computation of these four measures of the external RER for traded goods problematic for most low-income developing countries. In addition, the usefulness of relative export unit values and wholesale prices in devel- oping countries is limited by the prevalence of standardized commodi- ties in their exports, for which they are price takers. In those developing countries in which the required data are avail- able, relative unit labor costs and manufacturing sector deflators can be useful partial indicators of competitiveness in producing manufactured goods and differentiated nontraditional exports. Such indexes can be used for making comparisons to industrial countries, although lack of data for competing developing countries will generally prevent the cal- culation of multilateral REERs that include them. However, these RER measures will be representative neither of the incentives facing primary commodity exports nor of the export sector as a whole. The macroeco- nomic significance of these measures will depend upon the relative sizes of a country's manufacturing and commodity-producing sectors. Although, when the required data are available, it is preferable to use unit labor costs to take into account the effects of productivity changes, relative labor costs expressed in foreign exchange can also be 96 EXCHANGE RATE MISALIGNMENT useful indicators for developing countries where unit labor cost data are not available. Labor is usually the least mobile factor of production internationally. Hence, aggregate unit labor costs in the production of all goods are, in a certain sense, the most fundamental measure of a country's productivity, domestic production costs, and real factor in- comes. Relative labor costs can also be directly related both to other measures of the external RER and to the internal RER. Unfortunately, as is the case with the measures of competitiveness in traded goods, the use of relative labor costs in developing countries is often limited by data availability. While ad hoc comparison of labor costs among repre- sentative developing and industrial countries is common and quite use- ful, systematic multilateral comparisons of these are not usually pos- sible. External RERs based on labor costs may also diverge from those based on CPIs because of gains and losses in income caused by move- ments in the terms of trade. The only other empirical index generally available for measuring the traded-goods version of the RER is the mixed one, which uses foreign country WPIs to represent traded-goods prices together with home coun- try GDP deflators or CPIs to represent aggregate domestic production costs. Unfortunately, this indicator is significantly affected by produc- tivity bias as explained in the following chapters on the internal RER. As noted there, it is best used only as a proxy for the RER for imports when more accurate measures are not available. Factors Affecting the Behavior of External RERs in Developing Countries The two most important factors that complicate the interpretation of standard industrial-country RER measures in developing countries are the volatility of commodity export prices and major changes in trade policy. Both of these can cause the expenditure-PPP, Mundell-Fleming, and traded-goods versions of the RER to diverge significantly and limit the representativeness of any single measure of the external RER. The Mundell-Fleming RER is particularly sensitive to the terms of trade be- cause it uses the GDP deflator, which includes volatile commodity ex- port prices. When the terms of trade fluctuate significantly or when pro- ductivity grows at different rates in different sectors at home and abroad, it is often desirable to look at separate RERs for imports and exports, a subject that the following chapters on the internal RERs discuss at length. The expenditure-PPP version of the RER, particularly if computed using import weights, gives a good indication both of the relative gen- eral price level and of the competitive environment faced by import- substituting industries and manufactured exports. Available measures EXTERNAL REAL EXCHANGE RATES 97 of the RER for differentiated traded goods (for example, relative manu- facturing deflators, unit labor costs, or wages) can give additional infor- mation about the manufacturing sector and should be weighted by trade shares that exclude primary commodities. The measurement of relative price incentives for primary commod- ity exports is, however, a different problem. Since the price elasticity of demand for commodity exports is effectively infinite for small produc- ers, the problem in small countries is basically one of the internal incen- tives for producing these commodities-that is, of the internal RER for commodity exports, which the next two chapters treat in detail. In addition to the general problems posed by volatile terms of trade and changes in trade policy, the measurement of the external RER in developing countries can be complicated by parallel markets, unrecorded trade, and quickly shifting trade patterns. Parallel exchange rates can diverge significantly from official exchange rates, causing similar diver- gences in parallel and official RERs. As figure 2.B.3 illustrated, because of parallel markets in competing countries, the parallel REER differed from the official REER for C6te d'Ivoire by 5 percent to 10 percent dur- ing 1980-93, even though C6te d'Ivoire itself had a unified exchange rate. The decisions on which of these REERs is the most representative or whether both the parallel and official REERs should be used may be important for the subsequent analysis. Unrecorded trade can similarly affect the results (by 20 percent in the case of C6te d'Ivoire in 1993 as shown in figure 2.7). Adjustments for unrecorded trade usually tend to increase the weights assigned to countries with parallel exchange mar- kets as unrecorded trade tends to take place through informal market channels at parallel rates. Fixed weight averages become less representative for computing REERs as bilateral RERs and trading patterns change over time, and it is necessary to update country weights periodically. Shifting trade pat- terns can outdate standard base-year country weights fairly quickly and give a misleading impression of current relative prices. As figure 2.5 shows, in 1993 the REER for C6te d'Ivoire was 25 percent more appreci- ated at current year (1993) weights than at base-year (1985) weights. While the new IFS country weights may be useful for intercountry analy- sis, they may be out of date or otherwise unrepresentative for some de- veloping countries. Alternative (reasonable) weighting systems can af- fect the measurement of the REER by as much as 25 percent in some circumstances. Hence, some attention should be devoted to carefully choosing the weights for calculating the REER for a particular develop- ing country; and the sensitivity of the REER index to alternative weight- ing systems should be checked. For calculating REERs, it is desirable to have country weights that reflect reasonably well the structure of trade 98 EXCHANGE RATE MISALIGNMENT in the period being analyzed: that is, fairly recent weights for current and forward-looking policy analysis and representative weights from the past for historical or time-series analysis." When a country experiences significant changes in its terms of trade or trade policy, the different external RER measures may diverge sig- nificantly. Computation of the RERs themselves may also be sensitive to assumptions about parallel markets, unrecorded trade, and trade pat- terns. Hence, to the extent data availability permits, one should calcu- late and interpret the relevant measures together rather than concen- trate exclusively on a single external RER measure. Analyzing the rel- evant measures together helps to give a fuller picture of what may be happening empirically and to avoid potentially misleading signals that might be given by any one measure taken in isolation." Divergent move- ments in different measures can sometimes be consistently interpreted, but the analyst needs to pay some attention both to the theoretical rela- tionship among the various concepts and to data problems involved in their empirical measurement. 43. For example, an appropriate base year or a Fisher average of indexes us- ing beginning- and end-year weights. 44. See Clark and others (1994) for a further discussion of this point. Appendix A International Comparison Programme Exchange Rates Intercountry comparisons of nominal national incomes (or GDPs) mea- sured in different currencies require their conversion into a common numeraire such as the U.S. dollar or the IMF's standard drawing right (SDR). The market (or official) nominal exchange rate is the only readily available exchange rate that can be used for this purpose. However, the use of market exchange rates for making intercountry comparisons of income levels is problematic for two reasons. First, market exchange rates can fluctuate significantly even in the short term and may diverge from their equilibrium levels for temporary or even protracted periods. Second, even equilibrium rates at best reflect only price parity for traded goods. As discussed in Chapter 5 on the determinants of the equilib- rium RER, market-determined rates do not usually reflect parity in the prices of nontraded goods, except perhaps among selected indus- trial countries in the ultra-long term because of the Balassa- Samuelson effect. Hence, conversions using market exchange rates may be distorted by both exchange rate fluctuations and differences in price levels; and relative price levels may bear little relationship to intercountry differ- ences in real incomes. Conceptually, for making intercountry compari- sons it is desirable to have nominal exchange rates based on a standard- ized basket of goods and relative prices that reflect purchasing power parity more accurately than do market rates. This appendix briefly dis- cusses the problem of estimating such "purchasing power parity" ex- change rates and the International Comparison Programme (ICP) that has been undertaken for this purpose. In order to distinguish these nomi- nal exchange rates from the relative-PPP version of the real exchange rate discussed in the text, these rates are referred to here as ICP exchange rates. 99 100 EXCHANGE RATE MISALIGNMENT The Meaning of "Purchasing Power Parity" Intercountry comparisons and aggregations of GDPs are more mean- ingful economically if the nominal conversion factors used reflect a stan- dardized basket of goods and set of relative prices rather than each country's own particular basket of goods and relative prices. The con- version factor would then give each currency's purchasing power rela- tive to the numeraire currency. Converting GDPs measured in terms of current domestic prices and national currencies by such "purchasing power parity" or ICP exchange rates into a common numeraire currency would then yield GDP data valued in the numeraire currency and com- parable across countries. The One Good Case At a disaggregated one-good level, the ICP exchange rate (ICPER) be- tween a given home country j and foreign country k is defined as the ratio of nominal prices for a single specific good i, as shown in equation 2.A.1: (2.A.1) ICPER:;,k = The ICP exchange rate is the number of units of domestic currency per unit of foreign currency required for the purchase of good i. The Economist's "Big Mac Index" is an example of a one good ICP exchange rate. It is simply the ratio of the domestic-currency price of a Big Mac in the home country to its price in the numeraire country.45 The nominal domestic price of a given good in any country, when converted to the currency of the numeraire country by its ICP exchange rate, is equal to its price in the numeraire country and, therefore, is the same in all countries.4 Hence, meaningful real quantity comparisons are possible across countries when ICP exchange rates are used. The expenditures on final output of good i in country j can also be priced in the currency of the numeraire country (in most cases, the United States) by dividing nominal national currency expenditures on good i, P Q,, by its corresponding ICP exchange rate [(P Q)/(P /Ps)]. This procedure is equivalent to valuing the quantity in country J at the numeraire coun- try price (Ps Q,,Q) for good i. The ICP exchange rate is different from the external real exchange rate between countries j and k. The external RER in the one good case is given by equation 2.A.2: 45. See The Econoiist (1995, August 26 and 1996, April 27). 46. For any country j, equation 2.A.1 gives that P / JCPER,k , EXTERNAL REAL EXCHANGE RATES 101 (2.A.2) RERj = E d ' Ec 1 :v ' P I1CPERi,jk and, conversely, as equation 2.A.3 shows, (2.A.3) ICPER,k Edc RERjk The ICP exchange rate is the ratio of two nominal prices in different currencies and is itself a nominal exchange rate. As equation 2.A.3 indicates, the ICP exchange rate will equal the nomi- nal exchange rate only in the special case when the external RER is equal to one, that is, when absolute PPP holds (see page 73). In general, if the external RER is greater than one, then the ICP exchange rate will be lower than the nominal exchange rate in domestic-currency terms. The Multi-Good Case In order to determine the overall purchasing power of home country j's currency relative to that of a foreign country k in the standard multi- good case, a large number of prices for individual items have to be aver- aged in some way to yield a ratio of weighted averages of prices. The overall or aggregate ICP exchange rate for GDP is thus conceptually a function of the sets of domestic and foreign prices (P, Pk) and their re- spective weights (W1, Wk), as expressed in equation 2.A.4: (2.A.4) ICPER,k =f(lPk f IWk) The core problem in constructing multi-good ICP exchange rates for converting aggregate national accounts is to choose the appropriate sets of prices and weights and to determine the precise form of the function f in equation 2.A.4. Note that the resulting ICP rates are absolute PPP exchange rates calculated with a particular standardized basket of goods. The International Comparison Programme The International Comparison Programme, set up by the United Na- tions and the University of Pennsylvania with the support of the World Bank, has generated substantial data on ICP exchange rates and on ICP- based real GDP and its components. The ICP has concentrated on the expenditure side of GDP rather than the production side because more accurate data are available for market prices than for factor cost, and for expenditures than for sectoral output. The exchange rates estimated by the ICP are based on extensive price surveys, which were conducted in 102 EXCHANGE RATE MISALIGNMENT participating countries in phases every three to five years. Six phases have been completed, beginning in 1970. A total of 90 countries have now participated at some point in ICP surveys. During the ICP surveys, data on final product prices (which include taxes and subsidies) and quantities are collected for more than 400 types of goods and services in each of the countries surveyed. These price data are then aggregated into approximately 150 basic categories of goods and services. All of each country's individual final output items are as- signed to one or another of the 150 categories. The averaging procedure used in the ICP involves a specialized method designed to allow for the fact that every item is not priced in every country.47 The averaging procedure most widely employed in the international comparisons is known as the Geary-Khamis method. It is summarized in the following sets of equations, 2.A.5 and 2.A.6: (2.A.5) ICPER, j=1......,n(countries) (2.A.6) ,=y P, q =i=1,......,m(goods), ' =ICPER Y where n = number of countries m = number of categories of goods P = price of good i in country j q, = quantity of good i in country j f1 = international price of good i ICPER, = aggregate ICP exchange rate between country j and the numeraire currency. The Geary-Khamis method yields a vector of international relative prices for the m goods and a vector of aggregate ICP exchange rates for the n countries such that the international price for an individual good is a quantity-weighted average of the relative prices in individual coun- 47. See Summers and Heston (1991). EXTERNAL REAL EXCHANGE RATES 103 tries. With this method, the aggregate ICP exchange rate for a given coun- try j is calculated (in equation 2.A.5) as the ratio of total expenditures on GDP valued at the country j's own prices (P,,) to total expenditures on its GDP valued at international prices (0). Data on domestic expendi- tures on the basic categories of goods for a country are divided by their domestic prices to obtain quantities. These quantities are multiplied by their international prices and aggregated to obtain GDP and its compo- nents in international prices for the country. International prices are calculated simultaneously (in equation 2.A.6) as the quantity-weighted average of domestic prices of the countries being compared, with the domestic prices converted into a common cur- rency using the country's aggregate ICP exchange rate. The price in each country is weighted by that country's share of each of the basic product categories in the total output of the participating countries. The ICP ex- change rates and the international prices are generated simultaneously from the above system of m + n linear equations, using prices and quan- tities in individual countries as inputs. Only m + n - 1 equations of the system described by 2.A.5 and 2.A.6 are independent, and in the calcu- lations the ICP exchange rate for the numeraire country is set equal to one so that international prices are expressed in the numeraire currency. Empirical Uses of ICP Data The ICP data have been used for comparing per capita income levels and aggregating GDP across countries.49 They have also been used in studies of various macroeconomic subjects such as cross-country differ- ences in long-run economic growth and the relationship between prices, income levels, and real quantities."9 In comparing nominal GDPs converted at market exchange rates with ICP-based GDPs, three conclusions are generally reached." The first is that ICP-based GDPs dramatically alter the rankings of the world's largest economies. For example, using market exchange rates in 1992, the five largest economies ranked by GDP were the United States, Japan, Germany, France, and Italy. However, using the 1990 ICP- based GDPs yields the following ranking: the United States, China, Ja- pan, Germany, and India. The second conclusion is that ICP exchange rates for developing countries are generally lower than nominal mar- ket exchange rates with the U.S. dollar (in domestic-currency terms), as one would expect, because of the Balassa-Samuelson effect discussed in the chapter on the two-good internal RER. Figure 7 in Chapter 7, which 48. See, for example, Kravis, Heston, and Summers (1982). 49. See, for example, the World Bank (1993). 50. See Wagner (1995). 104 EXCHANGE RATE MISALIGNMENT compares the aggregate ICP dollar exchange rate for C6te d'Ivoire with the market rate, illustrates this point. Third, the difference between ag- gregate ICP exchange rates for GDP and market exchange rates tends to vary inversely with per capita income. As a result, valuation of GDP in terms of ICP exchange rates yields generally higher income for poorer countries than valuation at nominal exchange rates."' 51. See, for example, Rogoff (1996) for data and regressions documenting these findings. Appendix B The Relationship between Profitability, Competitiveness, and the Different External RERs To more firmly link the different concepts of external competitiveness to internal price incentives, the IMF has done a considerable amount of work on the relationship between measures of the external RER and the profitability of production and investment, both in the traded-goods sector and in aggregate domestic production. In this work, an improve- ment in the competitiveness of an economy is defined as an increase in the relative share of profits in value added and is expected to lead to an expansion of output and investment. To take into account both the cost of inputs produced in the nontraded-goods sector and the opportunity cost of the factors employed by it, this interpretation has been applied to aggregate domestic production of both traded and nontraded goods as well as to traded goods separately. The rest of this appendix discusses the relationship between profit- ability, competitiveness, and the external RERs for both traded goods and aggregate production. The analytical approach employed below fol- lows that used by IMF staff in Lipschitz and McDonald (1991) and in Marsh and Tokarick (1994). The following subsections start by setting out the analytical framework and then discuss profitability first in terms of the cost of producing traded goods and subsequently in terms of ag- gregate production costs. Analytical Framework To provide a common framework for discussing indicators of profitabil- ity (defined as the share of profits in value added), it is useful to start with a basic analytical structure that describes the supply side of the 105 106 EXCHANGE RATE MISALIGNMENT home economy. Consider the case of a small open economy that pro- duces both tradable (T) and nontradable (N) goods. Assume that each category of goods is produced by a two-tier production function, com- bining value added and imported and nontraded intermediate inputs, as shown in equation 2.B.1: (2.B.1) Q, = F,[V,(L,K),I,IM] i= T,N where Q denotes domestic output of good i and V, K,, L,, I,, and I., are, respectively, value added and inputs of capital, labor, nontradable and imported intermediate goods. To simplify the presentation, we will as- sume that the value-added function is based on a constant returns-to- scale Cobb-Douglas technology and that both imported and nontradable intermediate inputs are fixed proportions of domestic output, as shown in equations 2.B.2 through 2.B.4: (2.B.2) V, = A, L K,-a (2.B.3) INi = 9N, Q (2.B.4) I4, = (PA, Q, where A, is a scale technological factor that also measures the total pro- ductivity of labor and capital in sector i, B is the share of labor in value added, and 0, where c is total consumption expenditure measured in terms of traded goods. This specification postulates that transactions costs per unit of consumption are a decreasing function of the stock of money per unit of consumption, but that the productivity of money in reducing transac- tions costs is subject to diminishing returns. The accumulation of net 9. Adding an exogenous currency risk premium to this condition would not affect any of the properties of the model. DETERMINANTS OF THE LRER 269 worth over time is the sum of household saving and net real capital gains or losses. It can be expressed in the form of the budget constraint shown by equation 6.7: (6.7) ti=y+(i*+E)f -t-(11+r)c-r*a where t denotes real (lump-sum) taxes, and x* is the rate of increase in the domestic-currency price of traded goods. The latter, in turn, is the sum of the rate of depreciation of the domestic currency and the exter- nal inflation rate, denoted 7r,: The path of consumption expenditure is determined by the maximi- zation over an infinite horizon of an additively separable utility func- tion in which future felicity (that is, the future flow of utility) is dis- counted at the constant rate of time preference p. Consumption of traded goods, denoted cT, and of nontraded goods cN, are the only direct sources of utility for the household. Thus the representative household will seek to maximize a function of the form: f u(c,,c,)e-'dt To make the analysis more tractable, I will give the felicity function u(c, cN) a specific form. Following Dornbusch (1983), I will assume that the felicity function is of the constant relative risk aversion (CRRA) type in total consumption, while the intratemporal elasticity of substitution be- tween the two types of goods is unity. This means that the felicity func- tion can be written as equation 6.8: (6.8) u(cT,c) - N 1-o The parameter 9 represents the share of traded-goods consumption in total consumption expenditure (see below), while a is the inverse of the intertemporal rate of substitution. The Cobb-Douglas specification for intratemporal substitution between the two types of goods implies that consumption expenditure is allocated in constant shares between the two types of consumption goods as shown in equation 6.9: (6.9) cT-0 c, = (1- 9)ec 270 EXCHANGE RATE MISALIGNMENT where total consumption expenditure c is given by c = CT + c\,/e. Using these in equation 6.8 permits us to express the felicity function in the indirect form in equation 6.10: (6.10) u(c,c,) = v(e, c) = 1C[e C] 1-a where ic is a constant. The term in square brackets is the ratio of the price of traded goods to the "true" consumption price index Po P- (where PT is the domestic-currency price of traded goods, and PN is the domestic-currency price of nontraded goods) times total consump- tion measured in terms of traded goods. Thus this term measures total consumption in units of the consumption bundle, which is the direct source of utility for the household. The household's problem can thus be stated as follows: it chooses paths for consumption expenditure c and money m so as to maximize: (6.11) [Kel0 exp(-pt)dt Jo- 1-C subject to the flow-budget constraint (equation 6.7) and a transversality condition. These constraints can conveniently be written as equation 6.12: a= y - t + ra - im -(1+ - r(m/c))c (6.12) lim a exp(- rdt) > 0 where r is the real interest rate earned by domestic residents on their holdings of foreign bonds, measured in terms of traded goods (r = i - 7t*). This is equivalent to the external nominal interest rate i* faced by domestic residents, minus the foreign-currency rate of inflation in the price of traded goods: r = i - r* = (i* + e) - ( +-e) = i* -r,. The present-value Hamiltonian for this problem can be written as: H = (recf + A)exp(-pt) 1-u where A is the costate variable for the household's financial wealth a, with economic interpretation as the marginal utility of wealth. The so- lution of this problem is characterized by the first-order conditions shown in equations 6.13.a through 6.13.b: DETERMINANTS OF THE LRER 271 (6.13.a) KCYC - A(1 -r(m/c) -T'(m/c))c (6.13.b) -'C'(m / c) (6.13.c) A(p - r) = A as well as the budget constraint and transversality conditions given in equation 6.12. These conditions have intuitive interpretations. Equation 6.13.a describes the necessary condition for the level of consumption to be at its optimal level at each instant, conditional on the marginal utility of wealth. It states that the marginal utility gain from an extra unit of consumption must be equal to its marginal utility cost-that is, the loss arising from forgone saving. The latter is the product of the marginal utility of wealth A and the reduction in saving associated with an extra unit of consumption, given by the quantity (1 + T + '), which includes the transaction costs associated with each extra unit of consumption. Equation 6.13.b is the necessary condition for the allocation of the house- hold portfolio between money and bonds to be at its optimal level, con- ditional on the level of consumption expenditure. It states that the mar- ginal gain from holding an extra unit of money, in the form of re- duced transaction costs, must be equal to its marginal cost, in the form of forgone interest. Finally, equation 6.13.c is necessary for wealth to be allocated optimally over time. It states that since wealth should be drawn down more quickly (through increased consump- tion) when the household is more impatient (that is, when p is large relative to r), the marginal utility of wealth should rise more rapidly under those conditions. These equations can be used to describe the household's demand for money, the path of its consumption expenditure, and its rate of accumu- lation of financial assets at each moment in time. Equation 6.13.b im- plicitly defines a relationship between money and consumption that resembles a standard money-demand equation, shown in equation 6.14: (6.14) m = h(i)c, h' < 0. Thus the demand for money depends in familiar fashion on the interest rate and the level of transactions. To derive an expression for the path of consumption expenditure, differentiate equation 6.13.a with respect to time. Using equations 6.13.b, 6.13.c, and 6.14, we can derive the time path of consumption. It is given by equation 6.15: ( + ihi ] 272 EXCHANGE RATE MISALIGNMENT where y = (1 - a)(1 - 0). This represents a generalization of the familiar Euler equation for the optimal time path of consumption under con- stant relative risk aversion, to incorporate changing relative prices of the two consumption goods as well as the role of the transactions tech- nology. Note that, given the real interest rate measured in terms of traded goods r: a. An expected real depreciation makes consumption cheaper in the future (since it implies a lower relative price of nontraded goods). This increases the consumption-based real interest rate (the op- portunity cost of current consumption), which steepens the con- sumption path (thereby discouraging current consumption), and b. A steepening of the path of the future nominal interest rate (a posi- tive value of i) would tend to increase the transactions costs asso- ciated with future consumption, thus decreasing the consumption- based real interest rate, which tends to tilt the consumption path toward the present, making it flatter. The Consolidated Public Sector The consolidated public sector includes both the government and the central bank. The economy operates with a predetermined exchange rate, administered as a crawling peg in which the domestic currency depreci- ates continuously at the policy-determined rate e. The central bank's functions consist of maintaining the parity (by exchanging domestic and foreign currency for each other on demand in unlimited amounts at the official exchange rate) and providing credit to the government. The lat- ter, in addition to credit from the central bank, receives lump-sum taxes from the private sector and spends by purchasing both traded and nontraded goods, in the amounts g, and g, respectively. Thus the con- solidated period-by-period (flow) budget constraint of the public sector can be expressed as equation 6.16: (6.16) fc = t + rfc + (th + 7r* m) - (g, + g, /e) where fc, which may be positive or negative, is the stock of bonds held by the consolidated public sector. Like the private sector, the govern- ment has to respect an intertemporal budget constraint, given by limfc exp(-*r dt)>O. For concreteness, I shall assume that it does so in a particularly simple way-by levying taxes in an amount sufficient to keep fc - tih = 0. Notice that this does not imply a balanced budget, but rather a reliance on the inflation tax to finance fiscal deficits. DETERMINANTS OF THE LRER 273 Equilibrium Conditions The model is closed with two equilibrium conditions. The first is an arbitrage relationship describing the terms on which the rest of the world will lend to the domestic economy, and the second characterizes equi- librium in the market for nontraded goods. The Supply of Funds Though the home country is a price taker in the world goods market, its financial liabilities are not perfect substitutes for those of the rest of the world, and thus the interest rate at which residents of the country can borrow abroad reflects a risk premium, which is an increasing function of the share of the country's liabilities held in world financial portfolios. This is incorporated in the model in the form of an upward-sloping sup- ply-of-funds schedule relating the external interest rate confronted by the country's residents, i*, to the country's net international indebted- ness, as well as to world financial conditions, measured by the world interest rate iW. The specific formulation expresses i* as the sum of the world interest rate and a risk premium p, which is inversely related to the country's aggregate net creditor position, as expressed by equation 6.17: (6.17) i* = i + p(f), p(0) > 0, p' < 0. The supply-of-funds schedule described by equation 6.17 is depicted as the curve i* in figure 6.1.10 The external interest rate faced by the economy is determined by the height of this schedule above the relevant value of the net external asset position f. Equilibrium in the Market for Nontraded Goods Finally the equilibrium condition in the market for nontraded goods can be expressed as equation 6.18: (6.18) YyeCN +9- = (1-9O)ec + g_ For future reference, it is worth noting that the specification of equilib- rium in the nontraded-goods market (equation 6.18) implies that all 10. For a similar specification, see Bhandari, Haque, and Turnovsky (1990). Agenor (1997) provides more detail on this specification and how it relates to alternative approaches to modeling international capital market imperfections. 274 EXCHANGE RATE MISALIGNMENT Figure 6.1 The Supply-of-Funds Schedule 1 0 production of nontraded goods is available for consumption, either by the households or by the government. This has the consequence that the transactions costs associated with consumption must absorb traded goods only. This assumption is not necessary and is discussed further below. Equation 6.18 can be solved for the value of the real exchange rate that clears the nontraded-goods market, conditional on the values of c and g.. This short-run equilibrium real exchange rate is given by equa- tion 6.19: e = e(c,g,) (6.19) e= (1-O)e/(y' -(1- O)c) <0 e2 =1/(y - (1 -O)c) < 0 The real exchange rate that solves equation 6.19 is a short-run equilib- rium one in the sense that it clears the market for nontraded goods for a given value of private consumption expenditure c. Thus, this real ex- change rate will be sustainable only to the extent that c is itself sustainable. The Long-Run Equilibrium Real Exchange Rate As shown in Montiel (1998), the model of the previous section can be solved to derive the entire dynamic path of the real exchange rate and other endogenous macroeconomic variables in response to a variety of DETERMINANTS OF THE LRER 275 macroeconomic shocks, be they transitory or permanent, occurring in the present, or expected to occur in the future. A key characteristic of the model is that the economy it describes tends to settle into a steady-state equilibrium after a shock in which the stock of net international indebt- edness and the real exchange rate are both unchanging. This section examines the properties of that equilibrium. Since the focus is specifically on the determination of the long-run equilibrium real exchange rate, the solution method chosen in this section is one that focuses specifically on that variable and links up with the traditional literature that views the equilibrium real exchange rate as that value of the real exchange rate that is consistent with the simultaneous attain- ment of internal and external balance. To solve the model, we first reduce it to a smaller number of key relationships. The first step is to consolidate the budget constraints of the household and public sectors. To do so, we differentiate the house- hold balance sheet constraint (equation 6.4) and substitute into the flow- budget constraint (equation 6.12). This permits equation 6.12 to be writ- ten as equation 6.12': (6.12') f, = y-t+rf, -(th+n* m)-(1+r(m/c))c. Adding equations 6.12' and 6.16 together, and using the definitions of y and c as well as the equilibrium condition in the nontraded-goods mar- ket (equation 6.18), we have equation 6.20: (6.20) f = y,(e)+ rf -(8+T(m/c))c- g,. This is the flow-budget constraint for the economy as a whole. Recalling that c, = Oc, and that transactions costs are assumed to be incurred in traded goods, aggregate demand for traded goods is given by (Oc + g,), and aggregate supply is (y,- c). Thus, aggregate excess supply of traded goods, equal to the real trade balance surplus, is (YT - zc) - (Oc - gT) = YT - (T +O)c - gT. Adding the receipt of real interest payments from abroad (recall that f is the country's international net creditor position) yields the inflation-adjusted current account surplus, measured in units of traded goods, which is the right-hand side of equation 6.20. This is equated to the change in the economy's real net creditor position (f). This equation thus determines how the real net creditor position evolves over time. 11. As is common with models of this type, that equilibrium is unique and saddlepoint stable. 276 EXCHANGE RATE MISALIGNMENT Private spending, in turn, evolves over time according to the Euler equation 6.15, reproduced here for convenience: (6.15) c=. r+ye/e- h+-p c. 1 +-tr(h(i)) + ih(i) As is evident from equation 6.15, the evolution of private expenditure over time is itself dependent on the paths of the real exchange rate and domestic nominal interest rates. These are determined respectively by the nontraded-goods market equilibrium condition (equation 6.19, re- produced below for reference) and the arbitrage condition (equation 6.5), reproduced below as equation 6.5': (6.19) e= e(c,g,) (6.5') i= (r + ir, + p(f)) +E- where equation 6.5 has been modified to take into account the foreign Fisher relationship and the supply-of-funds schedule (equation 6.17). To analyze the properties of the long-run equilibrium real exchange rate, begin by imposing the long-run equilibrium conditions c = e = i in the Euler equation 6.15. This implies the steady-state condition equa- tion 6.21: (6.21) p = r" + p(f). Since rw and p are both exogenous, this equation determines the long- run equilibrium value of the net international creditor position for this economy, f*.12 Because the premium p is a decreasing function of the net creditor position f, the equation implies that countries with a high rate of time preference will be driven to have a smaller stock of net external claims in long-run equilibrium than those with lower rates of time preference. Next, to derive the long-run equilibrium value of the domestic nomi- nal interest rate, substitute equation 6.21 in 6.5', yielding equation 6.22: i= (p + Z) + e (6.22) . 12. This value can be positive or negative, without violating the transversality conditions on the private and public sectors. DETERMINANTS OF THE LRER 277 This value of i pins down the long-run values of consumption velocity h and transactions cost per unit of consumption T, as expressed in equa- tions 6.23 and 6.24: (6.23) h*= h(i) = h(p + *) (6.24) * = Tfh(i)] = T[h(p + x*)]. With these results in hand, the conditions that characterize the long- run equilibrium real exchange rate in this model can be described. Us- ing equations 6.22 and 6.24 in 6.21 yields equation 6.25: (6.25) 0 = YT(e)+ pf -(T[h(p +;,r*)] +6)c - g,. This is the long-run external balance condition in the model. It states that for the economy's real external net creditor position to reach an equilibrium value, the inflation-adjusted current account balance must be zero. An alternative and more useful formulation, however, focuses on the conventional (non-inflation-adjusted) current account balance. Adding the inflation adjustment 7rwf* to both sides, we can write equa- tion 6.25 as 6.25': (6.25') ,wf*=y,(e)+(p+rw)f*-(rl h(p+nr +eO+6)c-g,. Condition 6.25' states that in long-run equilibrium the real current ac- count balance, which is equal to real national saving, must be equal to the inflationary erosion of the real value of the country's net claims on the rest of the world.13 The latter represents the sustainable value of the country's capital account balance. A net creditor country (with a posi- tive value of f*) would run a sustainable current account surplus and capital account deficit that would enable it to acquire claims on the rest of the world that are sufficient to offset the inflationary erosion of its existing claims. By contrast, a net debtor country would run a sustain- able current account deficit and capital account surplus, accumulating 13. The model from which equation 6.25 was derived does not feature growth of productive capacity. In a growth context-for example, with constant Harrod- neutral technical change at the rate n-steady-state equilibrium would require constancy of the country's net international creditor position per effective worker, so the left-hand side of equation 6.25 would be modified to (n + 2,)f. In a growth context, a net debtor country would be able to run larger sustainable current account deficits than in the static case. 278 EXCHANGE RATE MISALIGNMENT new debt sufficient to offset the effective amortization of its existing debt through the inflation component of its nominal interest payments. Since YT is increasing in the real exchange rate e, and since an increase in consumption expenditure reduces the trade surplus, the set of combi- nations of e and c that satisfies equation 6.25' is plotted as the positively sloped external balance locus EB in figure 6.2. Internal balance is, of course, given by the nontraded-goods market clearing condition 6.19. As suggested by equation 6.19, the locus traced out by the set of combi- nations of e and c that are consistent with internal balance (IB) has a negative slope in figure 6.2. The long-run equilibrium real exchange rate is that which is simultaneously consistent with external and internal balances in the long run. It is defined by the intersection of the two loci at point A in figure 6.2, and is labeled e*. Long-Run Fundamentals The response of the long-run equilibrium real exchange rate to its fun- damental determinants can be established by examining the effects of permanent changes in the various exogenous variables included in the Figure 6.2 Determination of the Long-Run Equilibrium Real Exchange Rate e EB A e* - - - - - - - - - - - - II Ic C Note: An upward movement is a depreciation of the real exchange rate. DETERMINANTS OF THE LRER 279 model on the location of the long-run equilibrium point A. In this sec- tion, I take up these fundamentals one at a time, identifying individual fundamentals as well as the qualitative nature of their influence on the long-run equilibrium real exchange rate. Fiscal Policy I begin by considering changes in government spending, holding the fiscal deficit constant. As is well known, effects on the long-run equilib- rium real exchange rate depend on the sectoral composition of these changes." Changes in Government Spending on Traded Goods An increase in government spending on traded goods has no effect on the internal balance locus, but it shifts the external balance locus up- ward-to EB' in figure 6.3. The increase in government spending cre- ates an incipient trade deficit, which requires a real depreciation in or- der to maintain external balance. As indicated in figure 6.3, at the new long-run equilibrium B, the equilibrium real exchange rate depreciates, and private consumption of traded goods falls." The reduction in pri- vate consumption of traded goods is smaller than the increase in gov- ernment consumption, however, because the real depreciation induces an increase in the production of traded goods, allowing the accommo- dation of an increase in total spending on traded goods. Changes in Government Spending on Nontraded Goods In contrast to the previous case, the locus affected in this case is the internal balance locus IB. The increased demand for nontraded goods requires an increase in their relative price to maintain equilibrium in the nontraded-goods market, and the IB schedule thus shifts downward, to 14. For earlier work on the effects of the composition of government spend- ing on the long-run equilibrium real exchange rate see Montiel (1986) and Khan and Lizondo (1987). 15. In contrast, Penati (1987) finds that an increase in government spending on traded goods has no effect on the long-run equilibrium real exchange rate. The aspect of model specification that accounts for this difference is that in the present model, a steady-state equilibrium is ensured by an endogenous risk pre- mium, while in Penati's model the same result is achieved by endogenizing the rate of time preference. This feature makes Penati's model block-recursive and permits external balance to be restored after an increase in government spend- ing on traded goods through an increase in the economy's net claims on the rest of the world, with no repercussions for relative prices. 280 EXCHANGE RATE MISALIGNMENT Figure 6.3 Effects of Changes in Government Spending on the Long- Run Equilibrium Real Exchange Rate e EB' EB B A e2 --------------- -- - - C IB' IB Note: An upward movement is a depreciation of the real exchange rate. IB' in figure 6.3. The new equilibrium is at point C. As in the previous case, private consumption expenditure is crowded out in long-run equi- librium, but in this case the equilibrium real exchange rate appreciates. The upshot of this exercise and the previous one is that the long-run equilibrium real exchange rate is a function of the sectoral composition of government spending. A Reduction in the Fiscal Deficit Consider a reduction in the fiscal deficit, in the form of a tax increase. Since taxes are actually endogenous in the model under the assump- tions made in the section on the analytical framework, this shock is equivalent to a reduction in the rate of monetary emission by the central bank, which in turn is equivalent to a reduction in the rate of crawl of the nominal exchange rate. The gain from a lower fiscal deficit in this model comes in the form of a reduction in the distortions associated with the inflation tax. A reduced rate of depreciation lowers the domes- tic interest rate, increases the demand for money, and reduces the trans- actions costs associated with consumption-in other words, T* falls. This has the effect of increasing the supply of real output. Whether the long- run equilibrium real exchange rate will appreciate or depreciate depends DETERMINANTS OF THE LRER 281 on whether transactions costs are borne in the form of traded or nontraded goods.6 This will determine the form that the increase in real output takes. As currently specified, the model assumes that these costs are borne in the form of traded goods. The reduction in r* will thus increase the supply of such goods, shifting the external balance locus downward and resulting in a real appreciation, together with an increase in consumption. On the other hand, if transactions costs are incurred in nontraded goods, the external balance locus would remain fixed, and the internal balance locus would shift to the right. In that case, the equilibrium real exchange rate would depreciate, and consumption would rise." It may be worth noting that the effects of a reduction in the fiscal deficit brought about by changes in spending would simply be a combi- nation of one of the first two shocks described above with the third. The effects would depend on whether the reduction in spending fell on traded or nontraded goods, as well as on the composition of transactions costs. Changes in the Value of International Transfers The other demand-side variable that enters the model is the external real interest rate r,. Before analyzing the effects of changes in external financial conditions, however, it is useful as a point of reference to con- sider the effects on the equilibrium real exchange rate of changes in the level of international transfers received by the domestic economy. These will provide an interesting contrast with the case of interest rate changes. As formulated above, the model does not explicitly consider the role of international transfers. It is straightforward to add them, however. Such transfers would simply represent an addition to household incomes equal to the amount of the transfer. They would appear as an additive term in the household's budget constraint equation 6.7, in the dynamic equa- tion 6.20 forf, and in the long-run equilibrium condition equation 6.25'. "1 Accordingly, the effect of a permanent increase in the receipt of transfer income would be to shift the external balance locus to the right-the 16. This property that the long-run equilibrium real exchange rate is affected by a change in the rate of monetary expansion-that is, the failure of superneutrality-also characterizes the model of Penati (1987). 17. A change in the foreign inflation rate i, affects the model in exactly the same way as a change in the rate of depreciation E, since the two variables enter only in the additive form 7r* = e + tFv in equation 6.25. 18. It makes no difference in this model whether the transfer is received di- rectly by the private sector or whether it goes to the government, since under the fiscal regime assumed above, the latter would transfer the proceeds to the pri- vate sector. 282 EXCHANGE RATE MISALIGNMENT receipt of additional transfer income permits an expansion of consump- tion to be consistent with external balance at an unchanged exchange rate. There are no direct effects on the internal balance locus, so the equi- librium is at B in figure 6.4, with an equilibrium real appreciation and an increase in private absorption. Changes in International Financial Conditions The analysis of transfers is instructive because many observers' intu- ition about the effects of changes in capital inflows on the long-run equi- librium real exchange rate is derived from the corresponding effects of transfers. Capital inflows and transfers have in common the feature that they permit an expansion of absorption relative to income in the short run. However, the two phenomena differ in two important respects. First, the volume of capital inflows is an endogenous variable that can arise from a variety of changes in domestic and external economic conditions. Presumably, the change in the long-run equilibrium real exchange rate associated with a particular capital-inflow episode depends on the source of the shock that triggers the inflow. Second, unlike transfers, capital inflows create repayment obligations in the long run. These also will affect the long-run equilibrium real exchange rate.19 Consider, then, a particular shock that has been associated with the emergence of capital inflows: a reduction in world real interest rates.20 Again, this shock directly affects only the external balance locus. To see in which direction the locus moves, differentiate equation 6.25': de/dr, + <0. Thus, the real exchange rate consistent with external equilibrium moves in a direction opposite to the world interest rate. In this case, when the world real interest rate falls, the external balance locus thus shifts 19. Such obligations will affect the long-run equilibrium real exchange rate under the "stock" approach to the definition of external balance described in the previous chapter, which is the approach adopted here. If the "flow" approach were adopted instead, the effects of capital inflows on the LRER would resemble those of transfers, except that the endogenous nature of capital inflows would cause those effects to depend on the source of the shock triggering the inflows. 20. The view that the capital-inflow episode affecting several large develop- ing countries during the early 1990s was triggered by a reduction in interest rates in the United States, first put forward by Calvo, Leiderman, and Reinhart (1993), is now widely accepted. For a review of this episode, see Fernandez- Arias and Montiel (1996). DETERMINANTS OF THE LRER 283 Figure 6.4 Effects of Changes in Foreign Transfers and World Real Interest Rates on the Long-Run Equilibrium Real Exchange Rate e EB" LB C e2 - -- -- --- - -- - --- EB' A BL I I II C2 C 01 Note: An upward movement is a depreciation of the real exchange rate. upward, to a position similar to EB " in figure 6.4, and the equilibrium real exchange rate, determined at point C, actually depreciates, contrary to what happens in the case of an increase in the level of transfer receipts.1 Why is this the case? Equation 6.25' suggests that the effect of a change in world interest rates on the real exchange rate consistent with external balance depends on the effect of this change on the country's long-run net interest receipts. Thus, like those of a transfer, the effects of a change in external interest rates on the long-run equilibrium real exchange rate depend on their long-run implications for national income. In this model, however, the implications of a reduction in world interest rates for 21. Notice that deldr~, does not depend onf*. Thus, the direction of the shift in the external balance locus, and therefore the result that a change in r, causes the long-run equilibrium value of e to move in the opposite direction, does not de- pend on whether the economy is initially a net external creditor or debtor. This result is also derived, with a different approach to modeling imperfect asset sub- stitutability, by Agenor (1996). However, the dynamics of adjustment to the new equilibrium do indeed depend on the economy's initial international net credi- tor position, as shown in Montiel (1998). 284 EXCHANGE RATE MISALIGNMENT national income are negative in the long run, unlike those of transfers. This is precisely because of the capital inflows induced by the change in world financial conditions. In the new long-run equilibrium, the country's net creditor position with the rest of the world deteriorates, reflecting the effects of net external borrowing (capital inflows) during the transition from one long-run equilibrium to the next.2 The change in the external real interest rate has no other direct effects on the country's long-run current account balance (equation 6.25'). In particular, the in- terest rate that the country actually faces in world capital markets is unchanged from one long-run equilibrium to the next, because changes in the country's net external creditor position drive that interest rate to equality with the domestic rate of time preference. A higher risk pre- mium, associated with a reduced net international creditor position, rec- onciles the constant effective interest rate faced by domestic residents in the long run with the lower world interest rate. Since, unlike in the case of transfers, the borrowing has to be repaid, this is reflected in a reduc- tion in long-run equilibrium national income.2 The Balassa-Samuelson Effect To capture the effects of differential productivity growth in the traded- goods sector, the production function in this sector can be respecified as shown by equation 6.26: (6.26) yT =YT(LT,a); Y- > 0, YT2 >0 where a is a productivity parameter. Since the demand for labor in the traded-goods sector will now be a function of this productivity param- eter, labor market equilibrium becomes equation 6.27: (6.27) LT(w,a)+ L,(w)= L and the equilibrium real wage can be written as equation 6.28: w=w(e,a), with: (6.28) LT2 w2 = _> 0. LTI + LNe This means that output in the traded- and nontraded-goods sectors are given respectively by equations 6.29 and 6.30: 22. The transition is described in Montiel (1998). 23. For a more extensive discussion of this issue, see Agenor (1996). DETERMINANTS OF THE LRER 285 (6.29) YT = yT [LT [w(e, a), a], a] dy,L L4e L YT2>. da LT1 +L've YN = yN[LN[w(e,a)]], with: (6.30) dy,, I,I da = y,L,w2 < 0. Thus, the effect of the productivity shock in the traded-goods sector is to increase the demand for labor in that sector, thereby increasing the equilibrium real wage. In turn, this causes the nontraded-goods sector to release labor, which is absorbed by the traded-goods sector. At a given real exchange rate, the traded-goods sector expands, while the nontraded-goods sector contracts. To examine the effects on the long-run equilibrium real exchange rate, notice that the productivity shock a enters the internal and external bal- ance equations 6.19 and 6.25' only through its effects on yN and y, re- spectively. Since, according to equation 6.30, an increase in a reduces y, it creates excess demand in the nontraded-goods market, requiring a real appreciation to restore internal balance. In figure 6.5, the IB locus shifts downward. At the same time, however, by increasing production of traded goods (see equation 6.29), the shock gives rise to an incipient trade surplus, so a real appreciation is also required for the restoration of external balance. Thus, EB shifts downward as well. Both effects op- erate in the direction of equilibrium real appreciation, as proposed by the Balassa-Samuelson analysis. Thus, differential productivity growth in the traded-goods sector creates an appreciation of the equilibrium real exchange rate." Changes in the Terms of Trade As indicated previously, the model as specified is not suitable for ana- lyzing changes in the terms of trade, since exportable and importable goods are not distinguished from each other in the traded-goods sector. To make the necessary modifications, split up total traded-goods out- put into output of exportables yx and importables yz, both produced under conditions described previously for YT, that is, with a fixed 24. It can be shown that the downward shift in EB exceeds that in IB. The implication is that the favorable productivity shock results in an increase in real private absorption in equilibrium, as one would expect. 286 EXCHANGE RATE MISALIGNMENT Figure 6.5 Effects of Differential Productivity Shocks and Terms-of- Trade Changes on the Long-Run Equilibrium Real Exchange Rate e A e* - - --~-- -- ----- - EB' e B IB I JB' c* C, Note: An upward movement is a depreciation of the real exchange rate. sector-specific factor and mobile labor, with sectoral employment lev- els Lx and LZ. Let 0 denote the terms of trade, defined as the price of exportables in terms of importables, and redefine the real exchange rate e as the relative price of importables in terms of nontraded goods. To keep the demand side of the model simple, assume that the exportable good is not consumed at home. The analysis of the effects of terms-of-trade changes is, as might be expected, quite similar to that of productivity shocks to the traded-goods sector. Labor market equilibrium is now given by equation 6.31: (6.31) Lx(w/) + Lz(w) + L,(we) = L where w is now the real wage in terms of importables. The real wage that clears the labor market becomes: w = w(e, O), with (6.32) L'w /2 w2 = w > 0. L/0 + L' + L',e DETERMINANTS OF THE LRER 287 An improvement in the terms of trade increases the real wage, because this permits labor to be transferred from the importables and nontraded sectors to the expanding exportables sector. Sectoral supplies are now as expressed in equations 6.33, 6.34, and 6.35: dp y = y7[Lw(e, )] (6.34) dy y L W 0 y, = y[L,[w(e,0)e]] (6.35) dyN = yLQw,e <0. The internal balance equilibrium condition remains as before, with the exception that output of nontraded goods is now specified as in equa- tion 6.35. The external balance condition (equation 6.25'), however, has to be modified to take into account that traded-goods production now involves output of both exportables and importables, yielding equa- tion 6.36: (6.36) rwf*= yx(e,)+yz(e,o)+(p+ ,)f*-(z *+O)c -gz As shown above, an improvement in the terms of trade results in a con- traction in output of nontraded goods. The resulting excess demand in the nontraded-goods market causes the internal balance schedule to shift downward. The effects on the external balance schedule depend on whether the real value of total traded-goods output increases or de- creases. This effect is given by: a(0yx +Yz) = yx - Py'IAew,> 0 The value of traded-goods output increases through two channels: a valuation (income) effect arising from the higher relative price of exportables and an output effect arising from the absorption in the ex- portable sector of labor released by the nontraded-goods sector. The implication is that, as in the case of the favorable productivity shock, the external balance locus will shift downward-the incipient improvement 288 EXCHANGE RATE MISALIGNMENT in the trade balance requires a real appreciation to keep the trade bal- ance at its sustainable level. Thus, the effects of a terms-of-trade im- provement can also be represented as in figure 6.5.25,26 Commercial Policy Finally, consider the effects on the long-run real exchange rate of a liber- alization of commercial policy, modeled as a reduction in export subsi- dies. This is the simplest case to model in the present context, because it makes using several of the results derived for the analysis of the effects of terms-of-trade shocks possible. Consider, in particular, an export sub- sidy set at the rate (4 - 1). In this case, the internal terms of trade will be 0, and the previous analysis can be repeated, at least on the supply side of the economy. In particular, an increase in the subsidy would pull la- bor out of the importable and traded-goods sectors into the exportables sector, just as would an equivalent favorable terms-of-trade shock. A direct implication is that effects of subsidy changes on the internal bal- ance schedule IB are the same as those of an equivalent terms-of-trade shock. A subsidy increase causes IB to shift downward by creating an excess demand for nontraded goods, and a subsidy decrease causes it to shift upward. Where matters differ is in regard to the effects of export subsidies on the external balance schedule. Because changes in the internal terms of trade have the same output effects whether brought about by external terms-of-trade changes or by subsidy rate changes, an increase in the subsidy rate would create an expansion in the output of traded goods and cause an incipient trade balance improvement, just as before. Again, the reason is because a subsidy increase draws labor from the nontraded to the exportables sector. However, the income effect is absent in this case. The reason is that, unlike in the case of an external terms-of-trade improvement, the increase in the price of exportables brought about by a subsidy increase has to be financed. In the case of the subsidy, a tax liability is created for the private sector in an amount equal to the sub- sidy rate times the output of exportables-that is, in the amount (4 - 1)yx. When this tax liability is taken into account in equation 6.36, the result is equation 6.37: 25. Just as before, it can be shown that the downward movement in EB exceeds that in IB, so the sustainable level of private absorption increases as a result of this shock. 26. As figure 6.5 suggests, an improvement in the terms of trade is associated with an appreciation of the long-run importables real exchange rate. Whether the long-run exportables real exchange rate, given by eo, depreciates or appreci- ates, however, is ambiguous in the model. DETERMINANTS OF THE LRER 289 (6.37) Irwf* =yx(e,0) +yz(e, )+(p + irw)f]* -(0 - 1)yx(e,) - (z +69)c =yx(e,0)+ yz(e,0)+(p +7,)f *-(r +6)c. The implication is that a given change in the export subsidy rate would cause the external balance schedule to shift in the same direction, but by a smaller amount, than a terms-of-trade change that has an equivalent impact on the internal terms of trade. In the case at hand, the issue concerns the effect on the real exchange rate of liberalization of commercial policy-that is, a reduction in the export subsidy rate. The results just established imply that a shock of this type would shift both the internal and external balance schedules upward, with the implication that commercial liberalization results in a depreciation of the equilibrium real exchange rate. Summary and Conclusions The objective of this chapter has been to analyze the determination of the long-run equilibrium real exchange rate in the context of a simple analytical framework that is flexible enough to accommodate a broad variety of potential influences on the real exchange rate. The long-run equilibrium real exchange rate was defined as the rate consistent with the steady-state value of a country's international net creditor position, given the paths of all relevant policy and exogenous variables. The determinants of the long-run equilibrium real exchange rate iden- tified here consisted of the following: Domestic Supply-Side Factors. The most venerable theory regarding long-run real exchange rate determination is the Balassa-Samuelson ef- fect. This was incorporated in the analysis in the form of an asymmetric productivity shock favoring the traded-goods sector. The equilibrium real exchange rate appreciates, both because excess demand is created in the nontraded-goods sector and because the trade balance tends to improve. Fiscal Policy. Changes in the composition of government spending between traded and nontraded goods affect the long-run equilibrium real exchange rate in different ways. Additional tax-financed spending on nontraded goods creates incipient excess demand in that market, re- quiring a real appreciation to restore equilibrium. By contrast, tax-fi- nanced increases in spending on traded goods put downward pressure on the trade balance, and require a real depreciation to sustain external balance. The effects of a tax-based fiscal adjustment depend on the form in which transactions costs are incurred. 290 EXCHANGE RATE MISALIGNMENT Changes in the International Economic Environment. The aspects of the world economic environment analyzed here consisted of the terms of trade for the domestic economy, the availability of external transfers, the level of world real interest rates, and the world inflation rate. Im- provements in the terms of trade and increases in the flow of transfers received tend to appreciate the equilibrium real exchange rate, the former both by improving the trade balance and creating excess demand for nontraded goods, and the latter through positive effects on the current account. Reductions in world real interest rates and increases in world inflation, by contrast, cause the long-run equilibrium real exchange rate to depreciate. Lower world interest rates cause capital inflows, which reduce the country's net creditor position over time, and the long-run loss of net interest receipts requires a real depreciation to maintain ex- ternal balance. Changes in world inflation affect the equilibrium real exchange rate through effects on transactions costs associated with changes in real money balances. In the case of an increase in world infla- tion, the long-run real exchange rate tended to depreciate in this model, though this conclusion is sensitive to an essentially arbitrary assump- tion about the form in which transactions costs are incurred. Commercial Policy. Finally, trade liberalization, analyzed here in the form of a reduction in export subsidies, is associated with long-run real depreciation. The effect works by channeling resources into the nontraded-goods sectors. The emergence of incipient excess supply in the nontraded-goods market dictates the nature of the adjustment in the real exchange rate. Part III Methodologies for Estimating the Equilibrium RER: Empirical Applications  7 Estimating the Equilibrium RER Empirically: Operational Approaches Theodore 0. Ahlers and Lawrence E. Hinkle* The estimation of long-run equilibrium RERs (LRERs) and measurement of misalignment have traditionally relied on two approaches with strong operational advantages: a relative purchasing power parity-based meth- odology that assumes a stationary LRER and a target resource balance methodology that employs trade equations or elasticities.' In addition, in cases of split or multiple exchange rates, the parallel market rate has sometimes been used as an indicator of misalignment. The two traditional approaches are still widely used in operational applications in both industrial and developing countries, particularly when the data or time required for implementing more complex methodologies are not available. Even when it is feasible to employ the general-equilibrium methodologies discussed in the subsequent chap- ters in Part III of this volume, the traditional operational approaches still provide good starting points for the analysis, and transparent refer- ence points for cross-checking the plausibility, of the results from the more complex methodologies. Most of the input data required to implement * Ms. Ingrid Ivins provided research and computational assistance in the prepa- ration of this chapter. The authors are grateful to Peter Montiel, Fabien Nsengiyumva, and three anonymous readers for very helpful comments on ear- lier drafts. 1. The term resource balance is used in this chapter to refer to the difference between exports of goods and nonfactor services, and imports of goods and nonfactor services. The resource balance equals the current account balance ex- clusive of net interest and other factor service payments. 293 294 EXCHANGE RATE MISALIGNMENT the two operational approaches are needed for the other methodologies in any case. When the RER is stationary in a time-series sense, long-run equilib- rium exchange rates may be estimated on the basis of relative purchas- ing power parity (PPP) by using either a base-year or a trend approach. The base-year approach first establishes a base period in which the ob- served RER is believed to be at its equilibrium level. Misalignment is then measured as the difference between the observed RER and its base- period value, on the implicit PPP assumption that the LRER has remained at its base level. The utility of this PPP-based methodology is limited because of its inability to allow for permanent changes in the LRER that would cause the RER to be nonstationary. The methodology is, how- ever, still useful for analyzing situations where the LRER is believed to have remained unchanged, such as when shocks to the economy have primarily affected nominal variables or when shocks to the "real" fun- damentals have been transitory In both cases, relative PPP would hold during the sample period. Alternatively, the LRER may be estimated as the trend or mean value to which the RER tends to return in the long term under PPP theory; and misalignment is then measured as the de- viation from this trend or mean value. Since all the other methodologies for measuring misalignment, in- cluding the trade-equations approach, are much more time-consuming to implement than the above relative PPP-based approaches, these are often the only feasible methodologies for multicountry studies in which the amount of time that can be devoted to individual country cases is limited. For the same reason, PPP-based graphical analysis is also widely used for making initial diagnoses of individual countries and for identi- fying hypotheses for analysis using more sophisticated techniques. The trade equations-elasticities methodology is the second of the stan- dard operational approaches for estimating the LRER. Although there are a number of variations of this methodology, the key quantitative relationships in each are relatively straightforward and transparent. Each of the variants of this methodology involves the same three basic ana- lytical tasks. First, trade equations or trade elasticities are used to estab- lish a quantitative relationship between the RER, imports, exports, and, hence, the resource balance. Second, a target, norm, or equilibrium re- source balance is determined using independent projections of the sav- ing-investment balance or of sustainable capital flows. And, third, the actual resource balance in the initial year is adjusted for changes in cy- clical, exogenous, and policy variables that affect it in order to estimate the underlying structural balance and provide an appropriate basis for computing the change required in the initial RER. The quantitative rela- tionship between the RER and the resource balance established in the ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 295 first step is then used to calculate the appreciation or depreciation in the initial RER required to move the resource balance from its adjusted level in the initial year to the target level, everything else remaining the same. The estimated long-run equilibrium RER is the one that corresponds to the target or equilibrium resource balance. The trade-equations-elasticities methodology permits taking into ac- count permanent changes in some of the fundamental determinants of the RER. The methodology can directly address the relative price effects of changes in the terms of trade and tariff rates, and cover, at least in a back-of-the-envelope fashion, permanent changes in most of the other fundamental exogenous and policy variables in which one may be in- terested. Like the relative-PPP-based approach, the trade-equations meth- odology can also provide useful inputs for more complex ones. For ex- ample, adjusting the initial resource balance, determining a target re- source balance, and projecting exogenous variables are steps common to many of the approaches used for estimating equilibrium real exchange rates. The analytical techniques for carrying out these steps, which are set out in this chapter, are used both with the trade-equations method- ology and with some of the other methodologies discussed in the subse- quent chapters of Part III of this book. As noted above, a parallel exchange rate has sometimes been used as an additional indicator of distortions in the foreign exchange market and potential misalignment. However, because exchange rate misalign- ment does not necessarily lead to the development of a parallel market and parallel rates are much less common than they were a decade ago, opportunities to apply this approach are limited. Moreover, the approach turns out to be fraught with analytical difficulties. For both reasons, the existence of a parallel foreign exchange market is considered as a spe- cial case in Part IV of this volume. There the chapter by Ghei and Kamin examines the relationship between the parallel and the unified equilib- rium exchange rates and considers the usefulness of the parallel rate as a guide for determining a unified exchange rate. This chapter discusses the two standard operational approaches for estimating the LRER. The structure of the chapter is as follows. The fol- lowing section first sets the PPP-based approach in the context of recent theoretical and empirical work on the determination of equilibrium RERs and then discusses the interpretation and usefulness of PPP-based esti- mates of misalignment. The remainder of the chapter goes on to con- sider alternative ways of carrying out the three basic analytical tasks involved in implementing the trade-equations methodology. Since the trade-equations methodology is more complex than the PPP-based ap- proach, the rest of the chapter is considerably longer than the discussion in the following section on the PPP-based approach. The first section on 296 EXCHANGE RATE MISALIGNMENT the trade-equations approach discusses the use of trade equations and trade elasticities to establish quantitative relationships between the RER and the resource balance. It also presents a specific example of a trade- elasticities methodology employing a three-good framework (with ex- ports, imports, and domestic goods) that is suitable for use in low-in- come countries with minimal data in which changes in the terms of trade and commercial policy are important considerations. Then come two sections on the resource balance. The first of these examines alternative methods of determining a target resource balance using saving-invest- ment balance and sustainable capital flows approaches. The second then considers techniques for adjusting the initial resource balance to reflect changes in cyclical, exogenous, and policy variables affecting it in order to estimate the underlying structural balance. The final section concludes with a brief discussion of the advantages and limitations of the trade- equations methodology. The various analytical techniques are illustrated with empirical examples for C6te d'Ivoire at the time of the devaluation of the CFA francs in 1994. The Relative PPP-Based Approach to RER Misalignment As noted above, the simplest methods of estimating the long-run equi- librium RER are based on relative PPP. Although more sophisticated methodologies that take into account variations in the fundamentals determining the LRER have been developed, the PPP-based approaches are still widely used in both graphical analyses of individual countries and in econometric analyses of large multicountry samples because of the relative ease with which these can be implemented. The use of a relative-PPP-based methodology can be justified in ei- ther of two ways. On the one hand, the analyst may simply adopt ex ante the traditional relative-PPP view on the determination of the long- run equilibrium real exchange rate, which essentially takes the LRER to be a constant. On the other hand, the analyst may view the LRER as being determined by a broad set of fundamentals, which may turn out ex post to be stationary in a time-series sense for the specific country concerned. In the first case, the decision to apply the PPP approach would be made without considering the data. In the second case, the PPP ap- proach would be adapted only after the RER for the country concerned passes a test of stationarity. Whichever justification for using relative PPP is adopted in a specific case, theoretical and empirical work on PPP has suggested that the equi- librium RER may be estimated in two ways-using either a base-year or a long-term trend value. This section gives an updated presentation of ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 297 these two standard techniques for estimating the LRER and then dis- cusses the interpretation of such PPP-based analyses. Base-Year Estimates of the Equilibrium RER When relative PPP is assumed to hold ex ante, measuring the equilib- rium real exchange rate essentially involves removing the effects of nonsytematic transitory shocks. In practice, these are eliminated by iden- tifying a base period in which such shocks are believed, on the basis of independent evidence, to have been negligible-a procedure that en- sures that the actual RER coincided with its equilibrium-PPP value in the base period. Thus the actual RER in the base period represents the estimate of the equilibrium rate, and the nominal exchange rate consis- tent with the LRER from that moment on can be calculated by simply adjusting the nominal exchange rate for the cumulative difference be- tween domestic and foreign inflation. The alternative case is that the LRER is interpreted as subject to change in response to changes in underlying fundamentals but turns out em- pirically to be stationary for a particular country. In this case, the stationarity of the RER forces the analyst to take the position that its fundamental determinants are either individually stationary-that is, their "permanent" values have not changed during the sample period although the fundamentals may have been subject to transitory varia- tions-or that any nonstationary fundamentals must be cointegrated among themselves. In either situation, the LRER can still be measured using a base-year value, although the identification of a suitable base year is more complicated under their interpretation. In this case, the base-year method for estimating the equilibrium RER involves analyz- ing the movements in the fundamental variables determining the LRER to identify a base year in which, on average, these fundamentals, and hence the RER, were at sustainable levels. If the fundamental variables do not change after the base year, or return to their level in that year, then the LRER should also remain at the base-year level. Misalignment is then measured as the difference between the actual RER in the current year and its (unchanged) equilibrium value in the base year.2 Note that the expenditure-PPP version of the external RER (usually computed with CPIs) should be used both in the base-year analysis and in the trend analysis discussed below since this RER concept is the one employed in relative-PPP theory. 2. Appreciations, depreciations, and misalignment may be expressed in ei- ther domestic- or foreign-currency terms. Formulas for converting from one to the other are given in appendix C. 298 EXCHANGE RATE MISALIGNMENT The base-year approach is most useful in cases in which all move- ments after the base year result from either nominal shocks (which tem- porarily cause the actual RER to diverge from its equilibrium level) or from transitory movements in the fundamentals. However, if the fun- damentals change permanently after the base year, so too will the LRERW In this case, the base-year approach will provide little guidance on the RER's new equilibrium value until a new base year has been established. In the base-year approach everything thus depends upon the identifica- tion of a suitable base year. The definition of the long-run equilibrium RER in Part II suggests the criteria for selecting a representative base or equilibrium year. Re- call that this definition requires that the current account deficit can be financed by a "sustainable" level of capital flows and that the market for nontraded (or domestic) goods also be in a sustainable equilibrium for given values of the predetermined, exogenous, and policy variables that influence these objectives. As mentioned above, the procedure for choosing the base year also depends upon whether the rationale under- lying the procedure is a simple ex ante relative-PPP-based one or a more sophisticated one in which the real exchange rate is driven by stationary fundamentals. In the simple PPP case, the "independent evidence" of equilibrium referred to previously is likely to concern the behavior of a particular outcome variable, such as the resource balance. In contrast, from the "stationary fundamentals" perspective, the base year chosen should be a recent year in which the actual exchange rate is believed to have been close to its equilibrium value because all the fun- damentals were close to their sustainable values. As explained in the survey of empirical estimation in Chapter 5, the set of fundamentals to be considered in choosing a base year may include both exogenous and policy variables. In practice, when selecting base years, one usually fo- cuses first on the external balance criteria, typically interpreted as choos- ing a year with a reasonable or normal current account (or resource) deficit for the country concerned. For assessing the sustainability of ex- ogenous variables, the analyst looks for terms of trade that are reason- ably close to their likely long-term trend levels and capital flows that are consistent in amount and terms both with the likely longer-term availability of capital and with the country's debt-servicing capacity. For assessing the sustainability and desirability of policy or objective vari- ables, one looks at growth, investment, employment, and inflation per- formance and compares these to the country's long-run policy targets. 3. In addition, if the law of one price does not hold or only holds loosely, the return to a base-year value could be quite slow even after a purely nominal shock to the exchange rate, as domestic prices may be quite sticky and the actual RER will tend to follow the nominal RER. ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 299 Other things being equal, it is also desirable to select as recent a base year as possible to minimize the changes in the economy's structure taking place between the base year and the current year. Because a year that is appropriate as a base for a particular country may not be appro- priate for another, country-specific rather than standardized base years should be used when measuring misalignment relative to a base year.' The Devarajan-Lewis-Robinson (DLR) constant-elasticities model, the econometric model, and the reduced-form econometric methodology presented in Chapters 8, 9, and 10, respectively, also employ base peri- ods, like those used here, in which the observed RER equals the equilib- rium RER. The criteria for selecting these base periods are essentially the same under these methodologies so that the base period used for the relative-PPP-based analysis may also be used with the more sophisti- cated methodologies. A common problem in determining an appropriate base year is that, because of policy shortcomings and external constraints, years in which exogenous variables are at sustainable levels are not always years in which policy variables were at desirable levels. For example, histori- cally, desirable growth and investment levels have sometimes been at- tained only when the terms of trade have been temporarily inflated or capital flows have been unsustainable. Conversely, sustainable terms of trade and capital flows have often been associated with undesirable growth and investment outcomes. Hence, in determining when the RER was near its long-run equilibrium value and selecting a corresponding base year, one is often forced to make tradeoffs between sustainability and desirability and to take these tradeoffs into account in an ad hoc way in subsequent qualitative analysis. Moreover, in both historical and forward-looking analysis, some care is needed in analyzing the move- ments of the fundamentals to identify shifts in these or breaks in time series that could indicate that a change in the base year is needed. As a result, the choice of a base year may be subjective; and reasonable alter- natives should be considered when they are available. For the C6te d'Ivoire examples shown in the graphs in this section, the RER was nonstationary, as explained in Chapter 10, and 1985 was chosen as the base or equilibrium year for analytical purposes. This was the most recent year before the devaluation year of 1994, in which both the terms of trade and capital flows were at broadly sustainable levels and there was reasonable growth and low inflation. This choice, however, 4. The standard procedure is to select the RER for the base year as its equilib- rium value. However, because of lags in the effects of the RER on the economy, one could also argue that the RER for the preceding year or a three-year moving average centered on the preceding year would be a more accurate estimate of the rate that actually generated the base-year equilibrium. 300 EXCHANGE RATE MISALIGNMENT has elements of both unsustainability and undesirability. The situation in 1985 was unsustainable in that the debt service burden was too heavy for the long term and the terms of trade were more favorable than their historical trend. It was also undesirable in that the investment level was too low to support the desired long-term growth rate and trade policy was too restrictive to promote accelerated export and productivity growth. Hence, even in 1985 the actual RER was probably overvalued relative to the equilibrium RER in normative terms and even somewhat overvalued in positive terms. Furthermore, as a result of the sharp de- cline in the terms of trade in subsequent years, the equilibrium RER probably depreciated in the 1986-93 period rather than remaining con- stant at the 1985 base-year level as assumed in the PPP-based analysis. The effect that choosing different base years can have on PPP-based analysis is illustrated in figure 7.1. In the long debate over the overvalu- ation of the CFA franc, most of those arguing for a devaluation chose 1985 as the best available base year. This choice indicated that on the eve of the devaluation in 1993 Cte d'Ivoire's actual real effective exchange rate (REER) had appreciated by 37 percent relative to the equilibrium base year. In contrast, some of those arguing for maintaining the exist- ing parity chose 1980 as a base year, a choice which showed that C6te d'Ivoire's actual REER in 1993 was close to its base-year level. Note, in addition, that the use of either year as a base assumes that the equilib- rium RER remained constant at the level of that year. If, however, as discussed in the preceding paragraph, the sustainable values of the terms of trade or other fundamentals in fact deteriorated after the base year, the equilibrium RER would depreciate. The use of either base year would thus give an underestimate of the misalignment. Means for Short Base Periods For sustainability of predetermined variables, theoretically it would be desirable to have an equilibrium period, rather than just a single equi- librium year, so that the predetermined variables have time to approach their steady-state values. In addition, in practice all of the fundamentals will not necessarily be at sustainable levels in precisely the same year. One way of dealing with these problems is to use the average value of the RER over a short equilibrium period as a base. However, the utility of this alternative empirically depends very much on the situation in the particular country concerned. In some circumstances, particularly when an appropriate choice of base year is not obvious or when a coun- try has a market-determined exchange rate that fluctuates significantly year to year, a mean for a short time period may be a more representa- tive indicator of the equilibrium value of the RER than a single base- year estimate. In other cases, equilibrium periods may be limited to little ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 301 Figure 7.1 The REER for C6te d'Ivoire, 1970-95 (Base Years 1985= 100 and 1980=100) 140- I 130 120 REER with Base Year 1985 110- 100 . 90 *U .*. 80 REER with Base ---. :Year 1980 70 -- 6 0I I I I I I I I 70 71 72 73 74 75 76 77 78 79 80 81 82 83 S4 85 86 87 88 89 90 91 92 93 94 95 --*--REERwith Base Year 1980 ----REER with Base Year 1985 Note: The REER has been calculated using CPIs, weighted average parallel and official ex- change rates, and adjusted IFS country weights. An upward movement is an appreciation of the REER. Source: Computed from World Bank data. more than a year or two by the volatility of the terms of trade, capital flows, or other fundamentals. In Cte d'lvoire, for example, the longest period in the 1980s that might reasonably have been used as a base was 1985-86. If this two-year period had been used as a base together with a one-year lag in the RER, the results would have been similar to those from using 1985 because the average RER for 1984-85 was almost equal to that in 1985. However, when, as in this case, some exogenous or policy variables diverge in the same direction from sustainable levels for the entire period, the mean value of the RER for the period may not reflect the sustainable values of these variables any better than does the RER for a single year. Long-Period Mean and Trend PPP Estimates of the Equilibrium RER One way of dealing with fluctuations in the fundamentals during the sample period is to estimate their sustainable values on the basis of their sample means or, in the trend-stationary case, as their trend values within the sample. In effect, this procedure amounts to estimating the LRER as the sample mean or the trend value of the RER within the sample, rather than as the particular value of the RER in a specified base year. Hence, 302 EXCHANGE RATE MISALIGNMENT instead of trying to identify a particular year or short span of years in which the RER is believed to be at its equilibrium level, one tries to identify the long-term trend value toward which the actual RER tends. Thus, the LRER could be estimated as being the mean value of the RER over a long period of time or as evolving along a deterministic or sto- chastic trend. Justification for both procedures can be found in the literature. However, as discussed in the survey of empirical research on PPP in Chapter 5, the evidence supporting relative PPP is not that strong; and, hence, some care is needed in using this procedure. For example, ac- cording to Clark and others (1994): "Empirical evidence suggests that PPP-based indicators may be useful to explain long-run movements in exchange rates among industrial countries, but less so to explain move- ments of these exchange rates in the short run, or of exchange rates be- tween industrial and developing countries, either in the long or the short run." Hence, before deciding whether to use a long-period mean or a trend as a base for a particular developing country, time-series data for its RER should be analyzed to determine, if possible, whether its RER has been stationary for the sample period as illustrated for C6te d'Ivoire and Burkina Faso in Chapter 10 on the single-equation methodology. Unfortunately, sometimes the short time period for which RER data are available and the weak power of unit-root tests will make it impossible to determine whether the RER is stationary or nonstationary for the sample period. Both possibilities should then be considered. Means for Long Time Periods. The long-run referred to in the above citation for which relative PPP has been found to hold for a few industrial countries is in fact very long- specifically, periods of 70 to 100 years, over which both nominal and real shocks to the external RER may prove transitory. In addition, ultra- long-term relative PPP has been shown to hold only for a small group of industrial countries with fairly similar income levels. The long-term behavior of RERs between developing and industrial countries at quite different income levels, which is our primary interest here, could be equally different. If a sufficiently long data series is available for a par- ticular developing country, the equilibrium value of the RER in the very long term could be determined as its mean; and RER misalignment could be measured accordingly However, data for 70 to 100 years are only rarely available for developing countries. Data for even 20 to 30 years are hard to come by for many low-income and transition economies. Since PPP theory permits extended periods of misalignment during which the actual RER diverges from its long-term equilibrium value and empirical studies of PPP have found substantial volatility in RERs and ESTIMATING THE EQU[LIBRIUM RER EMPIRICALLY 303 only very slow convergence toward the mean, the significance of a mean for anything other than a very long period is not clear. Despite the weak- ness of the theoretical and empirical support for PPP, it is entirely pos- sible that, as in the Burkina Faso case in Chapter 10, the RER for a par- ticular country will be stationary for a given sample period. In this case, the mean value of the RER for the sample period will be the best esti- mate of its equilibrium value. However, when available time-series data are long enough neither for determining with any accuracy whether the RER for a particular country is stationary or nonstationary nor for com- puting a meaningful long-term mean, a base-year estimate of the equi- librium RER is likely to be preferable. Trend Estimates of the Equilibrium RER As discussed in the chapter on the two-good internal RER and the sur- vey of empirical research, the Balassa-Samuelson effect provides theo- retical justification for observing persistent long-term trends in the equi- librium RER. Countries experiencing significantly higher or lower pro- ductivity growth than their trading partners should show a statistically significant long-term trend appreciation or depreciation in their exter- nal RER. Demand factors (for example, a high-income elasticity of de- mand for services and other nontraded goods) or long-term trends in other fundamentals (for example, a sustained deterioration in the terms of trade) can also generate trends in the RER. In samples for which the RER is nonstationary, such trends are more meaningful measures of the equilibrium RER than the mean; and misalignment should be measured relative to the trend value of the RER rather than relative to its mean. Such time trends can be either deterministic or stochastic. Figure 7.2 shows the time trends in the RER for C6te d'Ivoire and compares these to the mean and 1985 base-year values of the equilibrium RER. Since empirically it is very hard to distinguish between deterministic and sto- chastic time trends with short noisy time-series data, deterministic trends have been used in figure 7.2 for simplicity. Interpretation of PPP-Based Analyses Five points concerning the interpretation of analyses based on relative PPP are worth noting: (a) the alternative of measuring competitiveness only in terms of goods that are internationally traded, (b) the relation- ship between the expenditure-PPP external RER and the internal RER, (c) the effects of structural breaks in the RER series, (d) statistical indica- tors of misalignment from multicountry studies, and (e) measures of misalignment based on data for standardized baskets of goods from the International Comparison Programme (ICP). 304 EXCHANGE RATE MISALIGNMENT Figure 7.2 C6te dIvoire: The REER-Actual Values, Average Values, and Time Trends, 1967-85 and 1986-93 (1985=100) 160 150- 140- 130- 120- 11011---------------- - ---- --------- 100- 90 80 1 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 -*-Actual Values 1967-95 ------ Average Value 1967-85 --- Time Trend 1967-85 -*- Time Trend 1986-93 --- Average Value 1986-93 Note: The time trend value was computed as an OLS regression of the logarithm of the REER and a time trend. The annual growth rate is 0.3 percent in 1967-85 and 1.0 percent in 1986-93. The REER was computed using CPIs, adjusted country weights, and weighted aver- age official and parallel exchange rates. An upward movement of the REER is an appreciation. Source: Computed from World Bank data. Competitiveness in Internationally Traded Goods: An Alternative Approach The base-year and trend approaches for measuring RER misalignment were originally developed for use with the expenditure-PPP version of external RER. However, they can be used equally well with the external RER for traded goods since relative PPP can be applied to traded goods as an interpretation of the law of one price. As discussed in the chapter on the external RER, it can, in fact, be quite reasonably argued that the entire foregoing analysis should be in terms of the external RER for traded goods rather than the expenditure-PPP version using CPJs. Theoretically, somewhat different behavior should be expected in the prices of homogeneous and differentiated traded goods, with the exter- nal RER for homogeneous traded goods obeying relative PPP more closely than the RER for differentiated traded goods. Unfortunately, 5. Although the theoretical basis for expecting relative PPP to hold for inter- nationally traded goods is stronger than for all goods (both traded and nontraded), Isard and Faruquee (1998) note that the hypothesis that the relative price of traded ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 305 data on the relative prices of internationally traded goods are only avail- able for recent years for industrial countries and often not available at all for developing countries. Because of the shortage of data, relatively little empirical research has been done for industrial countries, and even less research for developing countries, on whether relative PPP holds for traded goods. When the required data are available, it is useful to examine the be- havior of the external RERs for both homogeneous and differentiated traded goods. Unfortunately, only limited data are available for the prices of traded goods in C6te d'Ivoire. Since these data have already been presented in figures 2.12 and 2.13 in Chapter 2 on the external RER and the application of the techniques presented above to traded goods is straightforward, the external RER for traded goods is not shown here. Relationship to the Internal RER Because of the Belassa-Samuelson effect and highly income-elastic de- mand for nontraded goods, all countries in which productivity grows faster in the traded-goods sector than in the nontraded-goods sector, the common experience, should experience a sustained trend apprecia- tion in the equilibrium internal RER. This pattern is in fact what has been observed in studies of the internal RER in industrial countries. De Gregorio, Giovannini, and Wolf (1994), for example, find that for 14 in- dustrial countries the internal RER appreciated almost uniformly at an average rate of more than 1 percent per year in the period 1970-85. Fur- thermore, as explained in earlier chapters, it is entirely possible and con- sistent for the external RER for all goods, the external RER for traded goods, and the internal RERs to follow different trends. The typical pat- tern for a country experiencing more rapid productivity growth than its trading partners is a rapidly appreciating internal RER, a more slowly goods should remain constant over time can still be questioned on the following grounds: "(1) the composition of tradable goods across countries can change over time; (2) changes over time in the relative prices of different tradables can contribute to deviations from PPP insofar as the weights of different categories of tradable goods in national price or cost indices differ across countries; and (3) the scope for arbitraging price or cost differentials across countries can be af- fected by the liberalization of trade and foreign exchange restrictions, reduc- tions in transportation costs, or changes in other components of the costs of mar- ket penetration." But they conclude that "these limitations notwithstanding, cal- culations of different measures of international price and cost competitiveness can often be helpful when judging whether exchange rates are reasonably close to medium-run equilibrium levels." 306 EXCHANGE RATE MISALIGNMENT appreciating external RER for all goods, and a constant or depreciating external RER for traded goods. The internal RER is, in addition, gener- ally more useful than the external RER in assessing the magnitude of real shocks. Although relative PPP is not directly applicable to the internal RERs, analytically it is still useful to know how the internal RERs have be- haved both relative to trend and to their values in the last equilibrium (base) year. Figures 7.3 and 7.4 thus look separately at the internal RERs for imports and exports for C8te d'Jvoire. Figure 7.3 indicates that the internal RER for imports behaved in a similar fashion to the expendi- ture-PPP external RER, jumping upward by 20 percent during 1985-86 because of the appreciation of the nominal effective exchange rate (NEER) and then remaining relatively stable until the 1994 devaluation. As fig- ure 7.4 shows, the export sector was more severely affected than the import competing sector. Because of the sustained decline in the prices of its major export commodities (primarily coffee and cocoa) and de- valuations by competing developing-country exporters, C6te d'Ivoire's internal RER for exports appreciated strongly throughout the entire pe- riod, rising by almost 80 percent during 1986-93, four times the appre- ciation in the RER for imports. Structural Breaks Large external shocks and major regime shifts can cause structural breaks in the RER data for developing countries and create significant prob- lems in interpreting these. Such structural breaks can cause nonstationarity in the RER and lead to significant shifts in means, trends, and base years. The data for C6te d'Ivoire provide a good example of the possible effects of structural breaks. The combination of the large drop in C6te d'Ivoire's terms of trade after 1985 and the strong appreciation in its NEER shown in figure 7.5 caused a marked change in the external envi- ronment that the country faced, and its RER was nonstationary as dis- cussed in Chapter 10. Since figure 7.5 shows that the NEER and the terms of trade behaved in significantly different ways in the periods 1967-85 and 1986-93, figures 7.2-7.4 take 1985 as the dividing point between two different time periods and give the means and time trend values separately for the 1967-85 and the 1986-93 periods. During 1967-85, the average value of the expenditure-PPP external RER was 10 percent more appreciated than the 1985 base-year level but showed little trend move- ment over the period. In the 1986-93 period, in contrast, the external RER appreciated strongly and was, on average, nearly 30 percent more appreciated than in the 1985 base year. Figure 7.3 C6te d'Ivoire: The REER and the Internal RER for Imports-Actual Values, Average Values, and Time Trends, 1970-85 and 1986-93 (1985=100) 140 --- ,* -RI . .-*r a.- 130 - - ,II 120 9- 100, '0 ~ I I ' 10 - -- - - - - - --- 90 ' 80 I 70I I I I I I I I I I l i l l I 1 1 1 1 11I 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 -U- Internal RER for Imports: Actual Values 1970-95 0 Internal RER for Imports: Time Trend 1970-85 --- Internal RER for Imports: Time Trend 1986-93 ------ Internal RER for Imports: Average Value 1970-85 - - - Internal RER for Imports: Average Value 1986-93 - - * - - REER Note: The time trend value was computed as an OLS regression of the logarithm of the RER and a time trend. The annual growth rate is 0.4 percent in 1970-85 and -0.5 percent in 1986-93. The REER was computed using CPIs, adjusted country weights, and weighted average official and parallel exchange rates. An upward movement is an appreciation. Source: Computed from World Bank data. Figure 7.4 C6te d1voire: The REER and the Internal RER for Exports-Actual Values, Average Values, and Time Trends, 1970-85 and 1986--93 (1985=100) 200 -- 180 160 14 - e-- -- - - - --.- - 140 120 80 - 60 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 - Internal RER for Exports: Actual Values 1970-95 ------ Internal RER for Exports: Average Value 1970-85 - - - Internal RER for Exports: Average Value 1986-93 ----- Internal RER for Exports: Time Trend 1970-85 ---- Internal RER for Exports: Time Trend 1986-93 - - * - - REER Note: The time trend value was computed as an OLS regression of the logarithm of the RER and a time trend. The annual growth rate is 31 percent in 1970-85 and 7.9 percent in 1986-93. The REER was computed using CPlx, ad3usted country weights, and weighted average official and parallel exchange rates. An upward movement is an appreciation. Source: Computed from World Bank data. ESTIMATING THE EQU1LIBRIUM RER EMPIRICALLY 309 Statistical Indicators of RER Misalignment Because of the availability of CPIs for calculating the expenditure-PPP version of the RER in most developing countries and the relative ease of computing PPP-based measures of misalignment, these measures have been used in numerous multicountry econometric studies. These stud- ies have noted some empirical regularities that are useful in assessing RER misalignment in individual countries. Since selection of appropri- ate base years requires detailed knowledge of individual countries and can be criticized as subjective, most large multicountry studies have measured misalignment of the RER relative to its long-term mean or trend value; and hence their insights apply to misalignment measured in this way. In Chapter 12, for example, in analyzing parallel market exchange rates for a sample of 24 developing countries, Ghei and Kamin use a simple relative PPP-based measure for the equilibrium unified RER-the average of the official real exchange over long periods of time during which a county's exchange markets were unified. Large appreciations of the actual RER relative to its trend value, which are easily detectable in a PPP-based analysis, are often warning signs of serious exchange rate misalignment and potential currency crises. For Figure 7.5 C6te d'Ivoire: The Real Effective Exchange Rate (REER), the NEER, and the Terms of Trade, 1970-95 (1985=100) 180 170- - NEER 160 - 150 140..*. 4 4 130 . 120 -.- 110 - REER 90 80 Teqs 70 ofTrade 60 5 0 l I l l I I I I I I I I I 1 1 I I 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 -a- NEER using Adjusted Country Weights and Weighted Average Official and Parallel Exchange Rates --+-- REER using CPIs, Adjusted Country Weights, and Weighted Average Official and Parallel Exchange Rates -+-- Terms of Trade Note: An upward movement is an appreciation of the REER. Source: Computed from World Bank data. 310 EXCHANGE RATE MISALIGNMENT example, Milesi-Ferretti and Razin (1996, 1998) use the degree of appre- ciation of the RER relative to its 25-year average (median) as a bench- mark for assessing the sustainability of current account deficits and find that even this crude measure of misalignment is a useful predictor of currency crises. Kaminsky, Lizondo, and Reinhart (1997) find that sub- stantial appreciation of the RER above its trend value is a warning sign of a future devaluation and that the 10 percent of RER observations that are the farthest from the trend are accurate leading indicators of a cur- rency crisis within the next 24 months. Similarly, Goldfajn and Valdes (1996, 1997) analyze a large set of RER appreciations for 93 countries from 1960 to 1994 and find that for large real appreciations of 15 percent to 35 percent relative to trend the probability of a subsequent devalua- tion ranged from 68 percent for real appreciations of 15 percent or more to 100 percent for appreciations exceeding 35 percent. Hence, even if there is some uncertainty about the precise level of the equilibrium RER, large appreciations in a short period of time are a warning sign of mis- alignment. Finally, volatility of the real exchange rate, which is readily measurable, implies that the RER spends more time farther away from its equilibrium level. Volatility is, as noted in Chapter 11 on the effect of the RER on trade flows, a deterrent to export growth; and, as Razin and Collins (1997) have observed, volatility has served in effect as a reason- able proxy for misalignment in some multicountry studies. Measures of Misalignment Based on International Comparison Program Data Equilibrium exchange rates can be based on absolute as well as relative PPP. As explained in the chapter on the external RER, measurement of absolute PPP requires the use of standardized baskets of goods. For ex- ample, the "Big Mac Index" is a simple one-good absolute-PPP exchange rate, which The Economist uses as an informal indicator of the equilib- rium nominal exchange rate. It is simply the ratio of the domestic-currency price of a Big Mac in the home country to its price in the numeraire country.' However, data for more comprehensive measures of absolute PPP have been hard to come by. Because relative-PPP-based measures of misalignment have various theoretical shortcomings and estimating equilibrium exchange rates using the more sophisticated methodologies discussed later in this vol- 6. See The Economist (1995, August 26) and (1996, April 27). In a lighter vein, Cumby (1996) analyzes data for 14 countries for the "Big Mac Index" and finds that their exchange rates converge to "Big Mac parity" twice as fast as to relative PPP. ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 311 ume is quite time-consuming, researchers have long sought a method- ology simple enough to use in measuring misalignment for panel data for a large number of countries. Until recently, the lack of price data for representative standardized baskets of goods had inhibited the empiri- cal use of absolute PPP for this purpose. Hence, as the Summers-Heston data for standardized baskets of goods has become available for 90 or so countries from the International Comparison Programme (ICP) described in appendix A to Chapter 2, some researchers have utilized these to de- velop alternative simplified procedures for estimating equilibrium ex- change rates. Aggregate ICP exchange rates have themselves occasionally been used to analyze trade distortions and exchange rate misalignment. Nominal exchange rates for developing countries derived from the ICP data are generally lower (less appreciated) than nominal market exchange rates with the U.S. dollar because of the Balassa-Samuelson effect discussed in Chapters 3, 5, and 6. Figure 7.6, which compares the aggregate ICP dollar exchange rate for GDP for C6te d'lvoire with the official rate, illustrates this point. The magnitude of the differences between aggre- gate ICP exchange rates and nominal exchange rates also tends to vary inversely with per capita income. A predictable tendency in the ICP data for the relative price levels of countries to vary positively with their relative income levels as a result of the Balassa-Samuelson effect has been exploited by a number of re- searchers to derive estimates of the equilibrium RER. Dollar (1992) re- gresses the relative price levels of the standardized baskets of goods from the ICP data on relative per capita GDP. This regression gives him a norm that he considers as the equilibrium relationship between the free trade RER and per capita income. Deviations from this norm give a measure of the combined effects of trade and exchange rate policy on outward orientation. Bosworth, Collins, and Chen (1996) employ a pro- cedure similar to Dollar's to derive a measure of exchange rate mis- alignment that they then use in analyzing the factors affecting growth in an 88-country sample. Razin and Collins (1997) use data on the rela- tive international price of the standardized basket of consumption goods and services in different countries as a measure of the real exchange rate. This measure is then regressed on the fundamental variables deter- mining the RER using panel data, and the fitted values are used as an estimate of the equilibrium RER. 7. See, for example, Rogoff (1996) for data and regression results document- ing these stylized facts. 312 EXCHANGE RATE MISALIGNMENT Figure 7.6 CMte d'Ivoire: The International Comparison Programme and Official Exchange Rates with the U.S. Dollar 0.0095 0.008511-m'. V,M. K- : International Comparison 0.0075-- . Program US$ Exchange Rate 0.0065-- orA 0.0055-- 0.004-- Wit 0.0035- Official US$ 0.0025-. Ex change Rate.. 0.0015- 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 -*--Official US$ Exchange Rate - - a - - International Comparison Program US$ Exchange Rate Note: An upward movement is an appreciation. Source: Computed from World Bank data. Such statistical analyses of ICP exchange rates may give broad indi- cations of misalignment suitable for use in general multicountry studies and provide country-specific information that is useful in particular cases. However, more research is needed on the relationship between these general measures of misalignment and those from the methodolo- gies discussed elsewhere in this volume before basing policy recom- mendations for individual countries on ICP exchange rates. Conclusion: Advantages and Limitations of the Relative-PPP-Based Approach The relative-PPP-based approach set out above has a number of practi- cal advantages in estimating the equilibrium RER in low-income devel- oping countries. Its data requirements are limited. The methodology is both straightforward and transparent. With simple computer spread- sheets it is easy to run extensive sensitivity analyses of the results as- suming different base years or means. A number of multicountry statis- tical analyses of misalignment are also available for comparative pur- poses. These are significant practical advantages for balance-of-payments management in a developing country in which data and professional manpower may both be limited. Relative-PPP-based measures of mis- ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 313 alignment can also be quite useful in high-inflation countries where shocks to the external RER are primarily nominal ones. Thus, for ex- ample, the implementation of real exchange rate targeting has often re- lied on simple relative-PPP-based rules. The PPP-based approach does have some major limitations, however. In developing countries, lack of data on the prices of internationally traded goods usually forces one to use the external RER for all goods (computed with CPIs) rather than the theoretically preferable external RER for traded goods. The PPP-based analysis also relies on relatively simple base-year or mean-trend estimates of the equilibrium RER. If there are structural breaks in the time-series data for the RER or permanent changes in the fundamentals and hence in the equilibrium RER, base- period or mean estimates of misalignment may no longer be relevant, and PPP analysis is of little help in determining the new equilibrium RER. Moreover, real exchange rates can be quite volatile-and conver- gence to the mean, if it occurs at all, is typically quite slow. Hence, the RER may diverge from a PPP-based equilibrium for long periods, and it may be of little practical use for policy purposes. However, all of the other methodologies for measuring misalignment, including the trade-equations approach discussed below, are much more time-consuming to implement than the relative-PPP-based approaches. Thus the relative-PPP-based approaches are often the only feasible meth- odologies for multicountry studies in which the amount of time that can be devoted to individual country cases is limited. For the same rea- son, PPP-based analysis is also widely used for making initial diagnoses of individual countries and for identifying hypotheses for analysis us- ing more sophisticated techniques. A comparison of the movements of the fundamentals with movements of the RER since the last equilib- rium may also be useful for detecting cases of possible misalignment. The PPP-based methodology thus provides a starting point-it may be used alone, when nothing else is available, or as a reference point when more sophisticated methodologies are also used. The Trade-Equations Approach: Establishing the Quantitative Relationship between the RER and the Resource Balance The second of the established operational methodologies for measuring exchange rate misalignment is the trade-equations approach. The 8. See, for example, Calvo, Reinhart, and Vegh (1995). 314 EXCHANGE RATE MISALIGNMENT general rubric "trade-equations approach" is used here to cover a group of similar methodologies, all of which involve three basic ana- lytical tasks: a. Using trade equations or trade elasticities to establish a quantita- tive relationship between the RER, imports, exports, and, hence, the resource balance; b. Independently determining a target, norm, or equilibrium resource balance using projections of the saving-investment balance or sus- tainable capital flows; and c. Estimating the underlying or structural resource balance by ad- justing the actual resource balance in the initial year for cyclical, exogenous, and policy changes that affect it. The quantitative relationship between the RER and the resource bal- ance established in task (a) is then used to calculate the appreciation or depreciation in the initial RER required to move the resource balance from its adjusted level in the initial year to its target level, everything else remaining the same. The estimated long-run equilibrium RER is the one that corresponds to the target or equilibrium resource balance. The following section of this chapter discusses task (a). Tasks (b) and (c) are taken up in the subsequent two sections. Because of the different structures of industrial and low-income de- veloping economies and the greater availability of data in the former, trade is usually modeled in somewhat different fashions for the two groups. In industrial countries, trade equations based on the Mundell- Fleming production structure, the subject of the first part of this section, are usually used. In developing countries, in contrast, a trade-elastici- ties approach based on a three-good production structure, the subject of the last part of this section, is often employed. The Mundell-Fleming Framework-Industrial Countries The general analytical framework used in the trade-equations method- ology in industrial countries usually employs equations 7.1 through 7.3: (7.1) logM =E logRER +r, logYD + f(Z,) (7.2) logX logRER+ qx logY, +g(Zx) (7.3) ARB = AX - AM where M and X are the quantities of imports and exports, YD and Y, are ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 315 domestic and foreign real income, Zm arid Zx are vectors of whatever predetermined or exogenous variables (for example, lagged values of the RER, the terms of trade, commercial policy) are relevant in a particu- lar case, and the resource balance (RB) is expressed in real terms. The two trade equations are usually estimated econometrically to obtain values for eM and Ex, the price elasticities of import and export demand, and for T, and rx, the income elasticities of import and export demand. To solve the above system of three equations, domestic and foreign income are determined exogenously by setting them at full employment or some other desired level. The change in the resource balance is also set exogenously as the difference between the target and the adjusted resource balances, which are determined separately in tasks (b) and (c). One is thus left with three variables-M, X, and RER-to be determined endogenously; and the three equations are solved for these. A number of general points about the application of the trade-equa- tions approach to industrial economies are worth noting. First, the ana- lytical framework used for industrial countries is usually based on the Mundell-Fleming production structure. In this framework, complete spe- cialization of both the domestic and foreign economies in producing one composite good (their own GDPs) makes export supply functions perfectly elastic, while the domestic and foreign goods are taken to be imperfect substitutes in demand. Export and import quantities are thus demand-determined. The RER exerts its effect on the trade balance through the price elasticities of domestic demand for imports and of foreign demand for exports. Second, since industrial-country trade mod- els focus primarily on competitiveness in the domestic and foreign mar- kets for differentiated traded goods, the traded-goods version of the ex- ternal RER (computed using relative wholesale prices or unit labor costs in the traded-goods sector) is commonly used in equations 7.2 and 7.3. Third, the estimated equilibrium exchange rates for large industrial coun- tries like the G-7 that account for large shares of world trade need to be mutually consistent since one country's economy can have important income and relative price effects on the others', a fact that considerably complicates the estimation of equilibrium exchange rates for large in- dustrial economies. Fourth, if the RER is quite volatile and subject to large random fluctuations, these could be reflected either in similar vola- tility in the resource balance or in significant statistical noise in the em- pirical relationship between the RER and the resource balance, either of which could complicate empirical analysis and policy making.' 9. See Knight and Scacciavillani (1998). 316 EXCHANGE RATE MISALIGNMENT Both the International Monetary Fund (IMF) and the Institute for In- ternational Economics (IIE) employ the trade-equations approach for estimating equilibrium exchange rates for the G-7 countries. Major pa- pers by Wren-Lewis and Driver (1998) for the IE and Isard and Faruqee (1998) for the IMF documenting their approaches have been published within the last year. Since both of these papers have already been re- viewed in the survey of empirical research in Chapter 5, they are not discussed further here. The reader is referred, instead, to the previous survey for a review of the papers and to the papers themselves for de- tailed presentations of industrial-country applications of the trade-equa- tions methodology. The Three-Good Framework-Developing Countries The General Analytical Framework An alternative analytical framework is usually adopted for small devel- oping countries whose production structures are less flexible and whose exports are dominated by undifferentiated primary products. For these countries, imports could still reasonably be modeled by equation 7.1, in which the demand for imports depends upon the domestic price and income elasticities of demand. However, equation 7.2 for exports is more problematic in a developing-country context. For a small open develop- ing economy that accounts for a tiny fraction of world trade, it is more appropriate to consider export demand as being infinitely price-elastic and to drop foreign income from the export equation but to allow for a finite elasticity of export supply.0 Then the quantity of exports is deter- mined by the elasticity of export supply. Hence, export supply elasticities are conventionally employed in modeling developing countries rather than export demand elasticities used in equation 7.2. For example, Wren-Lewis and Driver (1998) follow the Mundell- Fleming tradition of modeling trade in industrial countries in terms of differentiated products that are imperfect substitutes. They estimate price elasticities of demand for exports ranging from -0.23 for Canada to -1.36 for Japan, with a median of -0.96. In contrast, the empirical evi- dence on RERs and trade flows in developing countries cited by Ghei and Pritchett in Chapter 11 suggests that the standard assumption of an infinite price elasticity of demand for developing-country exports is rea- sonable. Conversely, Wren-Lewis and Driver assume an infinite price elasticity of export supply for the G-7 countries rather than supply 10. Conceptually, this approach also implies supposing that the home coun- try produces at least one other type of good besides the exportable good and, hence, requires adopting a three-good framework. ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 317 elasticities in the 1.0-2.0 range suggested for developing countries by Ghei and Pritchett. The differences in approach to modeling trade in industrial and de- veloping economies also lead to differences in view about the relevance of the Marshall-Lerner condition. This condition for a real depreciation to improve the resource balance measured in domestic currency terms, starting from a zero balance, requires that the sum of the absolute val- ues of the price elasticities of demand for imports and exports exceed unity.n The Marshall-Lerner condition is satisfied for industrial coun- tries by the average values of the price elasticities of demand for im- ports (-0.9) from Ghei and Pritchett and of the demand for exports (-1.0) from Wren-Lewis and Driver (1998). Although the Marshall-Lemer condition would also be satisfied by the representative values of de- mand elasticities for developing countries, it is not directly applicable to them for two reasons. First, the condition assumes an infinite price elasticity of export supply, whereas the empirical evidence suggests a supply elasticity of 1.0 to 2.0 for developing countries. Second, many developing countries are capital importers and start from a resource deficit rather than from the balanced position assumed in deriving the simplest version of the Marshall-Lerner condition. Because trade models of developing countries focus on domestic re- source allocation incentives, the internal RER rather than the external RER for traded goods is usually the appropriate RER measure for them. The use of the internal RER also has the advantage that the effects of changes in some fundamentals on the equilibrium RER that are difficult to handle in the Mundell-Fleming framework can easily be handled in a three-good framework with importables, exportables, and domestic goods. Because of its assumed production structure, the Mundell- Fleming framework cannot distinguish between the terms of trade and the RER. Thus, it cannot be used to analyze the impact of changes in the terms of trade and commercial policy whereas these can be readily in- corporated in a three-good framework. Finally, for analyzing small economies it is not necessary to deter- mine a set of mutually consistent multicountry RERs as is done in mod- eling the G-7 economies. Rather, a simpler partial-equilibrium approach that ignores the impact of a developing country's RER and trade flows on the rest of the world can be used. Because of the relative ease with which it can be implemented and the availability of estimated elastici- ties from the large amount of empirical work on trade reviewed in 11. The resource balance measured in foreign-currency terms will almost al- ways improve for reasons explained in footnote 40 in Chapter 11 on trade flows and the RER. 318 EXCHANGE RATE MISALIGNMENT Chapter 11, the trade-elasticities approach has been widely used in op- erational applications in developing countries. This chapter and the sub- sequent one on the DLR model give two examples of trade-elasticity methodologies. Both chapters utilize three-good frameworks with ex- ports, imports, and domestic goods and constant-elasticities assump- tions. In this chapter, the relationship between the three goods is in terms of constant price elasticities of the supply of exports and of the demand for imports. The DLR model also assumes constant elasticities-but in this case they are elasticities of transformation in production between exports and domestic goods and of substitution in consumption between imports and domestic goods.12 A Specific Three-Good Methodology The remainder of this section presents a specific trade-elasticities meth- odology that is suitable for use in low-income countries in which only limited data are available. The relationship between the resource bal- ance, trade elasticities, and the internal RER is set in an explicit three- good framework. This formulation allows for different RERs for imports and exports and facilitates the analysis of the relative price effects of changes in the terms of trade and commercial policy.3 Essentially, the approach involves using the definitions of the price elasticities of de- mand for imports and the supply of exports to replace the trade equa- tions 7.1 and 7.2 above for imports and exports." The procedure for cal- culating the equilibrium RER is otherwise the same as that set out above for the trade-equations approach. Appendix A gives the detailed derivation of the basic RER, trade- elasticities, resource balance equation in a three-good framework. As shown there, the RER for imports (RERM) may be expressed as in equation 7.4: (AITT (7.4) ARERM A ITT RERM x- X-e (7.A.1) A(_ Pw PId P, where X is the quantity of exports, PXd is the domestic price of exports, and PDd is the domestic-currency price of domestic goods. Similarly, the price elasticity of import demand, EA, is defined as in equation 7.A.2: AM e- = e <0 (7.A.2) A( PId IP" Pd where M is the quantity of imports and ,, is the domestic price of im- ports. Note that the domestic-currency price of domestic goods, P,,, is used as the numeraire for measuring relative prices in both equations. As in the chapter on the three-good internal RER, domestic goods are defined here as goods that are both produced and consumed in the home country. They are semitradable in the sense that they are substitutes in consumption for imports via the price elasticity of import demand and in production for exports via the price elasticity of export supply. This formulation has the advantages of corresponding directly to the format in which data are actually collected and making it possible to estimate the equilibrium RER empirically using only standard national accounts and balance of payments statistics. The Definition of the Internal RERs In the above three-good framework, the internal RER is the domestic price of exports or imports relative to the price of domestic (nontraded) goods. The internal RERs for exports, RERX, and for imports, RERM, are defined as shown in equation 7.A.3: (7.A.3) RERX = LXd and RERM = Pfd PDd Pld If the home country is a price taker in international trade, its exports and imports are subject to the law of one price. The domestic prices of ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 347 exports, Pd, and imports, Pl,M are then determined by their interna- tional (border) prices and trade taxes as shown in equations 7.A.4 and 7.A.5: (7.A.4) FXd =Pxf ( x - Edc (7.A.5) PMd=Mf ) (1+t)Edc . P,,, and fare the foreign-currency border prices of exports and imports, tx and t2 are the average trade taxes on exports and imports, and Edc is the nominal exchange rate in domestic-currency terms. The definitions of the internal RERs may then be written as in equations 7.A.6 and 7.A.7: Px,f(1-tx)-Ed (7.A.6) RERX = Xd PDd P1Dd P P,(1 + t,)Edc (7.A.7) RERM =Md PMf P1d PDd The trade elasticities may be expressed in terms of the RERs for ex- ports and imports by substituting the definitions of the internal RERs from equations 7.A.3 into equations 7.A1 and 7.A.2 as shown in equa- tions 7.A.8 and 7.A.9: AX (7.A.8) - X RERX AM (7.A.9) em = M RERM The Resource Balance The resource balance and its first difference measured in real terms are given in equation 7.A.10: (7.A.10) RB=X-M and ARB = AX - AM. Expressions for AX and AM in terms of the internal RERs and trade elas- ticities may be derived by rearranging equations 7.A.8 and 7.A.9 to ob- tain equations 7.A.11 and 7.A.12: 348 EXCHANGE RATE MISALIGNMENT (7.A.11) AX = x X ARERX RERX (7.A.12) AM = - M ARERM RERM Subtracting equation 7.A.11 from 7.A.12 yields equation 7.A.13 for the change in the resource balance, ARB: ARERX ARERM (7.A.13) ARB=AX - AM=o AX R - EM- A RERX RERM Solution for the Internal RERs The Relationship between the Internal RERs for Imports and Exports In order to solve equation 7.A.13 for either RERX or RERM, we need an expression for the relationship between them. Dividing the definition of RERX by that for RERM (equation 7.A.3) gives equations 7.A.14 and 7.A.15: PXd RERX P D P (7.A.14) RER_ P =xd -ITT RERM Td Md P" FDd (7.A.15) RERX = RERM - ITT where the internal terms of trade, ITT, are defined as the domestic price of exports relative to the domestic price of imports, that is: PXd/Md. Note, for future reference, that the numeraire, PDd, cancels out in equation 7.A.14 (see page 351). Substituting for Pxd and P, from equations 7.A.4 and 7.A.5 yields equation 7.A.16: Pxd PXf (1 - t)Edc Pxf x(-t (7.A.16) ITT - - . WdPMf M1 + Q Edc PMf M1+ Since all of the variables on the right-hand side of equation 7.A.16 are exogenously determined if the law of one price holds, so are the internal terms of trade, ITT. Hence, RERX can be calculated from RERM and the exogenously determined internal terms of trade using equations 7.A.15 and 7.A.16. ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 349 The Internal RERs By substituting for from equation 7.A.15 in equation 7.A.13 and rear- ranging the terms, equation 7.A.17 for the internal RER for imports can be obtained: ARB XMTT (7.A.17) ARERM IR- TT RERM a,-X-EM*M The above system contains four equations (numbers A.10, A.15, A.16, and A.17) and four endogenous variables (M, X, RERM, and RERX). It also contains the parameters ax and EM; initial values of X, M, and ITT; and the exogenously determined variables ARB and AITT. The determi- nation of the change in the internal terms of trade, AFTT, from equation 7.A.16 is straightforward. Exogenous projected values are used for the external prices of exports and imports, P and P . Average trade taxes on exports, tx, and imports, tm, are policy variables. The other exogenous variable on the right-hand side of equation 7.A.17 is the targeted or required change in the resource balance, ARB. Determination of both the adjustments to the initial resource balance for cyclical, exogenous, and policy changes and determination of the sus- tainable or target resource balance is similar in the trade-equations and the trade-elasticities approaches. This process is considerably more com- plicated than calculating AITT and is discussed separately in the sec- tions of the text on the adjusted and target resource balances. Once the adjusted and target resource balances have determined, as in the trade-equations approach, the trade-elasticity relationships are used to calculate the change in the RER needed to move it from its ac- tual level to its equilibrium level. Thus, the computed values of AITT and ARB are plugged into the right-hand side of equation 7.A.17 to cal- culate the change in the RER for imports necessary to achieve the re- quired change in the resource balance. The RER for exports can then be computed using equation 7.A.15. After the RERs for imports and ex- ports have been calculated, the supply response to the change in the RER (that is, the corresponding changes in the volume of imports and exports) can also be computed using equations 7.A.8 and 7.A.9. Note, however, that equations 7.A.15 and 7.A.17 only permit deter- mining relative prices, not nominal ones. The definitions of the internal RERs, in fact, contain two endogenous variables, the nominal exchange rate, Edc, and the price of domestic goods, PDd, as well as the exogenously set prices of exports or imports.55 In order to determine separate values 55. These two endogenous variables may be compressed into one variable (the price of domestic goods expressed in foreign-currency terms) by multiplying 350 EXCHANGE RATE MISALIGNMENT for these two endogenous variables, either the nominal exchange rate or the domestic-currency price of domestic goods needs to be exogenously determined as a nominal anchor for domestic prices.6 Parameter Estimates Three points concerning the parameters in the relationship between the internal RER, trade elasticities, and the change in the resource balance merit further explanation and possible modification in particular appli- cations. These are (a) the empirical trade-elasticity estimates to be used in equation 7.17; (b) the numeraire used in measuring the elasticities and the RER; and (c) the problem of inelastic export demand. Each of these is discussed in turn below. Trade-Elasticities Estimates The accuracy of the equilibrium RER calculated using the trade-elastici- ties methodology depends upon that of the elasticity estimates used. Econometrically estimating country-specific elasticities can be both a time-consuming and problematic process in developing countries with inadequate data. However, a considerable amount of empirical work has been done on trade elasticities for a wide range of countries and products. Chapter 11 by Ghei and Pritchett on trade flows and elastici- ties summarizes the results of this empirical work and gives a good idea of what are reasonable values to assume for import and export elasticities. The elasticity estimates used in equation 7.A.17 may either be aggre- gate elasticities for imports and exports or a weighted average of the commodity-specific elasticities for major product groups. The defini- tion of trade elasticities (equations 7.A.1 and 7.A.2) and the law of one price (equations 7.A.4 and 7.A.5) used in deriving equation 7.A.17 im- plicitly assume that there is no import compression through exchange them together to arrive at an alternative single measure of the internal RER that is used by some authors. See, for example, the related concept of the equilib- rium GDP deflator used in the DLR model discussed in Chapter 8. 56. For a further discussion of the nominal anchor problem and a methodol- ogy for calculating consistent nominal and relative prices, see Chapter 13 on devaluations and inflation. 57. Nonfactor service receipts and payments should be treated as imports and exports in order to allow for the possibility that they may change in re- sponse to a change in the RER. In some cases, it may also be desirable to treat some factor service flows and private transfers as "imports" and "exports" and allow for a non-zero price elasticity for these. The elasticities of different product groups should be weighted by the ratios of imports or exports of these to GDP to determine the aggregate import and export elasticities. ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 351 controls or nontariff barriers and no smuggling of either exports or im- ports. Hence, the quantities of imports and exports are determined en- tirely by foreign prices, trade taxes, and the market or official exchange rate. If one or more of the foregoing distortions are present, the average tax rate on imports and exports needs to be adjusted to allow for these as discussed below. The Numeraire for the Trade Elasticities and the RER In the formulas for import and export price elasticities (equations 7.A.1 and 7.A.2) relative prices are expressed in terms of the price of domestic goods. Relative prices are, however, more often expressed in terms of the aggregate price level, P,,. Because of the ready availability of data for aggregate price indexes, the common practice when estimating elas- ticities empirically is, in fact, to express import and export prices rela- tive to the aggregate price level rather than to the price of domestic goods. The relationship between the aggregate price level and the prices of imports, exports, and domestic goods are given by equations 7.A.18 and 7.A.19: (7.A.18) PGDP PXI'd- (7.A.19) PGDA d where PGDP is the deflator for GDP, PGDA is the deflator for gross domestic absorption, T is the share of value added in exporting in GDP, and T. is the share of imports of final goods in absorption. If, as often happens, the prices of traded goods vary more than those of domestic goods, elas- ticities with respect to the aggregate price level, which includes traded goods, will be higher than with respect to the price of domestic goods. Fortunately, however, as long as the elasticities for imports and ex- ports and the RER are expressed relative to the same numeraire," equa- tion 7.A.17 can be used for any numeraire as the numeraire cancels out in its derivation as noted above. Hence, standard elasticity estimates expressed relative to the general price level may be used as long as the same numeraire (for example, the deflator for GDP or GDA or the CPI) is used for estimating the elasticities for both imports and exports. How- ever, in this case the RER will also be expressed relative to the general price level rather than to the price of domestic goods. If the equilibrium RER 58. The composition of the numeraire must also not change during the period for which the elasticities are measured empirically. That is, ; and r, must be constant. 352 EXCHANGE RATE MISALIGNMENT expressed relative to the general price level is calculated using equation 7.A.17, then equations 7.A.18 and 7.A.19, which relate the price of do- mestic goods to the general price level, may subsequently be used to calculate the RER expressed relative to the price of domestic goods as discussed in Chapter 13 on devaluations and inflation. The Elasticity of Foreign Exchange Supply The above formulations assume that the home country's imports and exports are small relative to the world markets for these goods and ser- vices and that it is a price taker for both imports and exports. Hence, it faces infinitely elastic import supply and export demand curves. How- ever, if the home country's exports of a particular commodity represent a large share of world exports and foreign demand for them is not highly price elastic, the quantity of the home country's exports will affect the price at which they can be sold. Whenever the absolute value of the price elasticity of demand for a particular country's exports of a given product is less than infinite but greater than unity, the elasticity of for- eign exchange earnings will be less than the elasticity of export supply, although still positive. In this case, the elasticity of the supply of ex- ports, ex, should be replaced in equation 7.A.17 by the elasticity of the supply of foreign exchange, ,, given by equation 7.A.20: (7.A.20) af = 0 a,-ef where ef is the price elasticity of foreign demand for the home country's exports and o6 is the price elasticity of export supply. E, is equal to the price elasticity of demand in the world market for the commodity con- cerned divided by the home country's share of the world market. Consider, for example, the case of exports of cocoa and coffee from the entire CFA zone at the time of the devaluation of the CFA franc in 1994. Together these accounted for 24 percent of total CFA zone exports, and the zone's cocoa exports were a large enough share of the world market (36 percent) that inelastic demand was a reasonable policy concern. Since the price elasticity of world demand for cocoa was estimated at -0.35, an increase in the quantity of cocoa exported by the CFA coun- tries would lower the world price and total revenues from cocoa sales. Using the rule of thumb (from Chapter 11 on trade flows and the RER) that the elasticity of demand for an individual country's exports is the world elasticity divided by the country's market share, the price elastic- ity of demand for cocoa exports from the CFA countries was approxi- mately -1.0 (that is, (-.35)/(-.36)). Using the estimated long-term sup- ply elasticity for the CFA countries' cocoa exports of 1.0 from Ghei and ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 353 Pritchett, the estimated elasticity of foreign exchange earnings from equa- tion 7.A.20 is 0. By contrast, for coffee, the estimated price elasticity of world demand was higher (-0.5 for coffee vs. -0.35 for cocoa); and the CFA zone's mar- ket share was much lower (8 percent for coffee vs. 36 percent for cocoa). Hence, the price elasticity of demand for its coffee exports, although not infinite, was much larger (-6.2 = (-0.5)/(-.08)) than for cocoa. Conse- quently, the elasticity of foreign exchange earnings from equation 7.A.20 was only slightly lower (0.6) than the estimated long-term elasticity of export supply for coffee (0.8). Appendix B Representative Estimates of the Income Elasticity of Demand for Imports Empirically, import demand functions are usually estimated as log lin- ear functions of the relative price of imports and real income. Recent studies (see table 7.B.1) have found that on average, income elasticities of import demand are somewhat higher in industrial countries than in developing countries, another possible reflection of the difference in im- port structure discussed earlier. 5 As with price elasticities, income elas- ticities are lower in the short run than in the long run. As Wren-Lewis and Driver (1998) point out, differences in income elasticities can, other things being equal, lead to changes in equilibrium RERs. They note, for example, that even if the trend growth rates of GDP in the United States and Japan are the same, U.S. imports will grow more rapidly than Japanese imports because the income elasticity of import demand in the United States is 2.0 compared to 1.2 in Japan. More rapid growth of imports will put pressure on the U.S. equilibrium RER to depreciate over time relative to Japan's. Similarly, a low-income elasticity will create pressure on a country's equilibrium RER to appre- ciate over time relative to its trading partners'. However, it is important to bear in mind that, as discussed elsewhere in Parts II and III of this volume, the income elasticity of import demand is only one of many factors determining intertemporal movements in the equilibrium RER. 59. Senhadji (1997) gives individual elasticity estimates for 48 developing countries. 354 ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 355 Table 7.B.1. Estimated Income Elasticity of Import Demand Average Income Number of Study Elasticity Countries Industrial Countries Bayoumi and Faruqee (1998) 1.50 - Wren-Lewis and Driver (1998) 1.82 7 Senhadji (1997) 1.67 19 Reinhart (1995) 2.05 - Developing Countries Senhadji (1997) 1.25 48 Reinhart (1995) 1.22 - Source: Studies cited in table. Appendix C Formulas for Exchange Rate Appreciation, Depreciation, and Misalignment in Domestic- and Foreign-Currency Terms A presentational question involved in measuring exchange rate mis- alignment empirically is whether to express the required appreciation or depreciation in domestic- or foreign-currency terms. Although each of these may be calculated from the other, the two expressions are not equal and may differ substantially in the case of large misalignments. Exchange rates may be expressed in either domestic-currency (Ed) or foreign-currency terms (Ef), where these are the reciprocals of each other, as shown in equation 7.C.1: (7.C.1) Edc Thus, for example, an exchange rate for the CFA franc in domestic- currency terms of CFAF 50 = FF 1.0 is equivalent to an exchange rate in foreign-currency terms of FF 0.02 = CFAF 1.0. Similarly, a depreciation from 50 CFA francs per French franc to 75 CFA francs per French franc (or FF 0.0133= CFAF 1) represents a depreciation of 50 percent in domestic- currency terms and 33 percent in foreign-currency terms. Equations 7.C.2 and 7.C.3 give the formulas for converting a given percentage depreciation (df) or appreciation (af) in foreign-currency terms into the corresponding depreciation (d,) or appreciation expressed in domestic-currency terms: 1 1 (7.C.2) dC =1- and dc 1 1+ddc 1- dfc 356 ESTIMATING THE EQUILIBRIUM RER EMPIRICALLY 357 1 1 (7.C.3) aft = -1 and adc = 1- . 1- adc 1 + aft Note that depreciation and appreciation are expressed relative to the actual exchange rate. Hence, an appreciation (depreciation) of x percent followed by a depreciation (appreciation) of x percent would not return the exchange rate to its original level. An appreciation of Xa percent re- quires a depreciation of Xa /(1+Xa) to return to the original level of the exchange rate. Similarly, a depreciation of Xd would require an offset- ting appreciation of X,/(1-X). For example, an appreciation of 20 percent (a movement of the exchange rate index from 100 to 120 in foreign- currency terms, appreciation of 20/100=20 percent) requires a deprecia- tion of 16.7 percent to return to the original level (movement of the in- dex from 120 back to 100, depreciation of 20/120=16.7 percent). Exchange rate misalignment itself may be expressed relative to the actual or the equilibrium value of the RER. Theoretically, misalignment, MA, is usually expressed as the percentage divergence of the actual rate from its equilibrium value and is calculated as shown in equation 7.C.4: (7.C.4) MA = ( "-1' - 100 ERER , where ARER is the actual RER and ERER is the equilibrium RER. Em- pirically, however, the actual RER is usually known; but the equilib- rium RER, the numeraire in the above formulation, is uncertain. Hence, empirically it is often clearer to use the known actual RER as the numeraire and indicate the estimated depreciation or appreciation re- quired, RD, to bring the actual RER to the equilibrium level as shown in equation 7.C.5:60 (ERE (7.C.5) RD=EE -1 100. ARER) As explained in the chapters in Part I of this book, different RER mea- sures may diverge because of fluctuations in the terms of trade, differ- ential productivity growth in the traded and nontraded sectors, changes in trade taxes, differences in the behavior of the prices of standardized and differentiated products, parallel markets, and unrecorded trade. Furthermore, as the actual value of the RER may vary with the concept employed, so too may its equilibrium value and the resulting estimate 60. See, for example, Clark and MacDonald (1998), p. 30. 358 EXCHANGE RATE MISALIGNMENT of misalignment. Hence, it is important that misalignment be calculated using the same measures for both the equilibrium and the actual RERs. Given the relationship between the internal and external RERs set out in Part I, the equilibrium value of either the internal or the external RER should, in principle, also determine the equilibrium value of the other. However, because of the theoretical and empirical limitations of the vari- ous methodologies, it is desirable to look separately at the behavior of the internal and external RERs, estimate the misalignment in both of them, and then cross-check the results, utilizing the relationships dis- cussed in Part I of this volume. 8 Estimates of Real Exchange Rate Misalignment with a Simple General-Equilibrium Model Shantayanan Devarajan* In addition to the damage they cause the economy, misaligned real ex- change rates (RERs) can be a serious problem for economists. When the RER in a country is overvalued, everyone turns to economists for a quan- titative estimate of the degree of misalignment. The usual response of suggesting a multiyear research project to answer the question often will not do, as urgent policy decisions-such as the magnitude of cur- rency devaluation-hinge on this estimate. Instead, the economist has to make use of available data and other information, often without the aid of a model or other consistency check, to develop quick estimates of the degree of RER misalignment. The situation in the CFA franc zone prior to the January 12, 1994, devaluation illustrates this problem. Most observers agreed that the RER was overvalued, but they disagreed on the extent of the overvaluation. Since data were scarce, robust estimates, let alone formal models, were hard to come by. But the particular nature of the franc zone made the problem even more complicated. Since the CFA franc was convertible, there was no parallel market in foreign exchange, which is often used as * I am grateful to Larry Hinkle for suggesting this chapter and to him, Peter Montiel, and three anonymous readers for helpful comments at various stages. Valuable assistance was provided by Fabien Nsengiyumva and Ingrid Ivins. 359 360 EXCHANGE RATE MISALIGNMENT a guide for estimating RER misalignment.' The fact that 13 countries shared the same currency (across two monetary unions) meant that the degree of misalignment could be (and was) different across the coun- tries of the zone. Finally, the CFA franc had never been devalued before, so the implication of an estimate of extreme misalignment could be quite profound. It could signal the need for a nominal devaluation that would, in turn, call the credibility of the zone's fixed exchange rate regime into question. Theoretically, it would be desirable to estimate the equilibrium ex- change rate using a full macroeconomic model that simultaneously takes into account all of the important interactions of the key variables affect- ing the exchange rate. However, as discussed in the following chapter by Haque and Montiel, constructing and estimating such models is so data- and time-intensive that it is not feasible in many cases in which estimates of the equilibrium exchange rate are needed for policy pur- poses. Fortunately, there are other approaches to estimating RER mis- alignment that do not require a full econometric model. This chapter illustrates one such approach. There is a long tradition of using multisector computable general equilibrium (CGE) models to calculate equilibrium real exchange rates (See Dervis, de Melo, and Robinson (1982), Lewis and Urata (1984)). The model developed in this chapter is a miniature version of these large- scale models. As shown in Devarajan, Lewis, and Robinson (1993), these tiny models can approximate the larger models quite closely for real exchange rate calculations. Consequently, recent efforts have concen- trated on these smaller models-see, for example, Abdelkhalek and Dufour (1997), Sekkat and Varoudakis (1998), and Tokarick (1995). The purpose of this chapter is to show how RER misalignment such as that observed in the CFA zone can be estimated using one such simple general-equilibrium model of an open economy. The model by Devarajan, Lewis, and Robinson (1993) presented here permits a quick calculation of RER misalignment using minimal data. Hence, it is feasible to esti- mate the extent of RER misalignment for a number of countries in a limited amount of time. The model is used here to gauge the extent of misalignment in 12 of the CFA zone countries prior to the January 1994 devaluation. The model captures some of the salient features of such economies, particularly the effects of volatile terms of trade. At the same time, as we will show, the model incorporates the purchasing power parity (PPP) estimate of RER misalignment as a special case. 1. For a cautionary note on this procedure, see Chapter 12 by Ghei and Kamin on the use of the parallel exchange rate as a guide for setting the official rate. A SIMPLE GENERAL EQUILIBRIUM MODEL 361 The following section of this chapter describes the basic model and its relationship to the other methods of calculating RER misalignment. The next section applies the model to 12 of the (then) 13 CFA zone coun- tries to calculate the degree of RER overvaluation just before the de- valuation. For each country, it also shows how RER misalignment evolved over time. Then comes a section that discusses the sensitivity of the calculation to the choice of base-year and model parameters and presents extensions of the model to allow for changes in commercial policy and sustainable capital flows. The final section contains some concluding remarks. The DLR Model The DLR method extends the Salter-Swan model by dividing the economy into three goods:2 exports, imports, and "domestic goods." The latter are goods produced and consumed in the country. Exports are substitutes for domestic goods in production but are assumed not to be consumed domestically. The relationship between exports (E) and do- mestic goods (D) can be expressed as a transformation function, with a constant elasticity of transformation, W. Profit maximization implies that the ratio of E to D is given by equation 8.1: (8.1) E/D=k(PE /pD) where PE and PD are the prices of exports and domestic goods, respec- tively, and k is a constant. Assuming the country's exports are small in relation to world markets and are subject to the law of one price, the domestic price of exports is equal to the border price, PE* multiplied by the nominal exchange rate in domestic-currency terms, s. Imports (M) are (imperfect) substitutes for domestic goods in con- sumption. This relationship is expressed as a constant elasticity of sub- stitution (CES) utility function with elasticity of substitution, a, giving rise to a first-order condition expressed in equation 8.2: (8.2) M / D = k'(PD /PM)0 where Pu is the price of imports. On the assumption again that the law of one price holds, P, is equal to sP, with PF being the border price of 2. This subsection gives a summary description of the DLR model. The model's equations are given in the appendix. Readers interested in applying the DLR model should see Devarajan, Lewis, and Robinson (1993) for a fuller presenta- tion of it. 362 EXCHANGE RATE MISALIGNMENT imports. There are two real exchange rates in the model: the ratio of the price of domestic goods (PD) to either the price of imports (P) or to the price of exports (PE), expressed in domestic-currency terms. Note that the DLR model retains the Salter-Swan notion of the real exchange rate's being a ratio of the internal prices of tradables to nontradables-although here "nontradables" are all domestic goods, which are imperfectly sub- stitutable with traded goods, and traded goods are divided into imports and exports. The advantages of this approach are that P,, P , and P, are readily obtained from national accounts data and that the effects of changes in the terms of trade can be analyzed. The equilibrium real exchange rate in the DLR approach is that rate which is consistent with a specified current account target, given changes in import and export prices-that is, the terms of trade. Equations 8.1 and 8.2 provide two equations for the three unknowns E/D, MID, and PD The current account target provides the third equation, a relation- ship between EID and MID. If, relative to a year in which the current account was in balance, import prices have risen and export prices fallen, for a given nominal exchange rate, PD would most likely have to fall to restore the balance. If the nominal exchange rate were flexible, the re- quired adjustment could also occur through numerous combinations of changes in this rate and in domestic prices. The amount by which PD would have to fall depends not just on the changes in import and export prices but also on the elasticities of trans- formation and substitution. For small changes, the relationship between the required adjustment in PD and the size of the terms-of-trade shocks and elasticities can be derived by log-differentiating equations 8.1 and 8.2. Denoting the log-derivative by a hat (""), we obtain equation 8.3 (equation 16 in DLR): (8.3) PD = [a - fM E( + + To understand the economic intuition behind equation 8.3, it is useful to rewrite it as equation 8.4: (8.4) p, = (a P, + p + ) + (P M + Q). The first term on the right-hand side of equation 8.4 is a weighted aver- age of changes in world prices facing the country, in which the weights are elasticities. This term is similar to the adjustment implied by the 3. See below and Chapter 4 on the three-good internal RER, which explains the calculations of these different RER measures. A SIMPLE GENERAL EQUILIBRIUM MODEL 363 purchasing power parity approach: domestic prices should proportion- ately rise with world prices, in order to keep the real effective exchange rate at its equilibrium level. The second term on the right-hand side of equation 8.4 is the terms-of-trade change divided by a factor represent- ing the "multiplier effect" of world prices on domestic prices. Equation 8.4 says, therefore, that domestic prices have to adjust not just to changes in the overall level of world prices but also to changes in the relative price of exports to imports (the terms of trade). Put another way, the purchasing power parity base-year approach is consistent with the DLR approach when there are no terms-of-trade shocks. There is also some similarity between the DLR method and the trade- elasticities approach, since both use constant elasticity assumptions and aim at a specified current account target. However, note that the elas- ticities in equations 8.1 and 8.2 are constant elasticities of transforma- tion and substitution, whereas the trade-elasticities approach in Chap- ter 7 uses constant elasticities of export supply and import demand. In the DLR model the equilibrium price in the specification of the domes- tic-goods market, PD, and hence the real exchange rate, is that price which clears the nontraded (domestic) goods market. Finally, the basic DLR model can be viewed as a special case of the reduced-form single-equation approach, inasmuch as both calculate the response of the equilibrium real exchange rate to terms-of-trade shocks. The reduced-form approach, though, postulates that the equilibrium RER is also a function of other variables, such as real income, openness, fiscal policy, and a time trend. Furthermore, while the DLR approach esti- mates only the equilibrium real exchange rate, the reduced-form ap- proach also models the adjustment of the actual exchange rate to its equilibrium value. The bare-bones version of the DLR model described above can, how- ever, be extended to take into account several additional fundamental variables. Two such variables-which are particularly relevant for RER misalignment in the CFA countries-are changes in (a) sustainable capital flows and (b) trade policy. The remainder of this section describes how the basic DLR model can be extended to incorporate these. The section on sensitivity analyses and extensions subsequently provides illustra- tive calculations of the impact of these two effects on the estimates of RER misalignment for one country, C6te d'Ivoire. The calculation of the equilibrium real exchange rate in equations 8.3 and 8.4 assumed that there were no changes in the levels of sustainable capital flows; the only changes were the shifts in world import and ex- port prices. Yet in many cases, the source of the RER misalignment is not just a terms-of-trade shock but also a change in the sustainable capi- tal inflow. For example, in the early 1980s many developing countries- 364 EXCHANGE RATE MISALIGNMENT including those that faced no major terms-of-trade shocks-found them- selves with reduced access to financing in world capital markets follow- ing the "debt crisis." To incorporate the impact of a change in the sus- tainable capital flow on the equilibrium real exchange rate, we add a variable, A, which represents the ratio of total imports to total exports. When capital inflows are positive, zero, or negative, A is greater than, equal to, or less than 1, respectively. The effect of a change in A on the equilibrium real exchange rate is given by the following extension of equation 8.4, equation 8.4': (8.4') P,D= (cP,+OP)/(cr+ Q) +P- (+ Q) +A/+a). Thus, a drop in the level of sustainable capital inflows (A declining) will lead to a depreciation of the equilibrium real exchange rate. The magni- tude of this depreciation is a function of the two elasticities, c and Q. To estimate the response of the equilibrium domestic price to a change in the tariff rate, we incorporate the tariff into the definition of the do- mestic price of the import, so that P, = sPZ(1+t), where t is the tariff rate on imports. We make the additional simplifying assumption that tariff revenues are rebated to the consumer in a lump-sum fashion. With this assumption, the change in the equilibrium domestic price for a given change in the tariff rate is expressed by equation 8.5: (8.5) PD=ai/(y+12) where, as shown in equation 8.6: (8.6) i = tt /(1 +t). Note that, as a approaches infinity, the change in the domestic price level approaches the change in the tariff rate. (This result makes sense since in this case imports and domestic goods are almost perfect substi- tutes.) However, for relatively small values of a, the response of the do- mestic price level to tariff changes is also small. The relationship between trade policy and the equilibrium real ex- change rate is a complex one, and occasionally a source of confusion in the literature. By raising the domestic price of importables (part of the tradable sector), an import tariff also causes the internal real exchange rate for imports to depreciate. However, the internal RER for exports may remain constant or appreciate as a result of an induced increase in the price of domestic goods. The explicit distinction among imports, exports, and domestic goods made in the DLR model clarifies the con- fusion. The effect of an import tariff is to raise the price of imports and A SIMPLE GENERAL EQUILIBRIUM MODEL 365 also to raise the price of domestic goods, but not to the same extent as the price of imports (because imports and domestic goods are imperfect substitutes). Thus, the relative price of imports to domestic goods rises, so that the real exchange rate for imports depreciates. In contrast, the relative price of exports to domestic goods falls, so that the real exchange rate for exports appreciates, moving resources away from the export sector. The sign of the net effect of the depreciation of the internal RER for imports and of the appreciation of the internal RER for exports on the weighted average internal RER for all tradable goods and on the external RER is theoretically ambiguous. Empirically, however, the weighted average internal RER for traded goods will usually depreciate like the internal RER for imports because (a) the RER for imports will normally depreciate by much more than the RER for exports will appre- ciate and (b) if the country is a net capital importer like most developing countries, imports are usually larger than exports (see Chapter 4 on the three-good internal RER). As with sustainable capital flows, we provide illustrations of the role of the tariff policy in real exchange rate misalignment for the case of C6te d'Ivoire. Applying the DLR Model to the Pre-1994 CFA Zone We now estimate the extent of RER misalignment in the CFA zone just before the January 1994 devaluation. The model's underlying equations 8.1 and 8.2 are applied to 12 of the 13 member countries of the zone in 1994 for which adequate data were available. Since many of the terms- of-trade shocks these countries faced were large, the linear approxima- tion given by equations 8.3 and 8.4 cannot be used (although these equa- tions will help in interpreting the results). Instead, we solve the full- blown nonlinear model, which consists of equations 8.1 and 8.2 and the set of accounting identities set out in appendix A. The calculation of RER misalignment proceeds in several steps. First, we decide on a base year in which the actual RER was equal to the equi- librium RER so that we can estimate the amount by which domestic prices should have changed in order to preserve equilibrium. Column 2 of table 8.1 lists the base year chosen. In most cases, this choice was based on the last year in which the current account in those countries was thought to be in equilibrium in the sense that it could be financed by sustainable capital flows. For most countries, the base year is in the mid-1980s, the period after which terms of trade began moving sharply against the CFA countries. Since the choice of base year is somewhat arbitrary, we subsequently perform sensitivity tests around the selected year as discussed in the next section on sensitivity analyses and extensions. 366 EXCHANGE RATE MISALIGNMENT Second, we decide on the values of the export transformation and import substitution elasticities to be used (columns 3 and 4, table 8.1). These parameter values are based on informed estimates or, in some cases such as Cameroon, may come from larger models of the country (Devarajan, Lewis, and Robinson (1993)). Again, the following section tests the sensitivity of the results to the assumptions about the param- eters. Recent econometric evidence (Devarajan, Go, and Li, (1998)) sug- gests that these elasticities are less than 1 for most developing countries and are considerably lower for low-income primary-exporting econo- mies. The base case export transformation elasticities were, therefore, assumed to be slightly higher (0.5) for the more diversified middle- and former middle-income economies, such as C6te d'Ivoire, Cameroon, and Senegal, than for the low-income countries (0.3). The elasticity of im- port substitution, in contrast, was assumed to be the same (0.4) in all the countries. We turn now to the data. Table 8.2 presents first the changes in im- port and export prices between the base year and 1993. With a fixed nominal exchange rate in the CFA countries, if there had been no change in domestic prices, the real exchange rate would almost surely have been out of equilibrium in the wake of these terms-of-trade shocks. But, of course, domestic prices did change (column 3 of table 8.2), so the em- pirical question we attempt to answer is whether they changed enough- and in the right direction-to restore equilibrium. Table 8.1 Assumptions Country Base Year Sigma Omega Benin 1986 0.4 0.3 Burkina Faso 1985 0.4 0.3 Cameroon 1984 0.4 0.5 Central African Republic 1981 0.4 0.3 Chad 1984 0.4 0.3 Congo 1984 0.4 0.5 C8te d'Ivoire 1985 0.4 0.5 Gabon 1984 0.4 0.5 Mali 1984 0.4 0.3 Niger 1984 0.4 0.3 Senegal 1977 0.4 0.5 Togo 1984 0.4 0.3 Source: Author's judgment. A SIMPLE GENERAL EQUILIBRIUM MODEL 367 Table 8.2 Changes in Prices between Base Year and 1993 (in percent) Country Base Import Export Terms of Domesticprices Year Prices Prices Trade (GDP Deflator) Benin 1986 25 18 -7 12 Burkina Faso 1985 -14 -13 1 14 Cameroon 1984 -32 -60 -28 15 Central African 1981 97 67 -30 66 Republic Chad 1984 -28 -16 12 -16 Congo 1984 10 -60 -70 -27 C6te d'Ivoire 1985 -3 -32 -29 -11 Gabon 1984 15 -43 -58 -7 Mali 1984 -9 -31 -22 17 Niger 1984 10 -15 -25 -11 Senegal 1977 -3 15 18 56 Togo 1984 -15 -36 -21 20 Source: World Bank data. Table 8.2 shows that 3 of the 12 CFA countries did not suffer a nega- tive terms-of-trade shock between their base year and 1993. Of these, Senegal experienced the largest improvement in its terms of trade. How- ever, as we will show later, this does not necessarily mean that the real exchange rate was undervalued even in that country. The reason is that the observed 56 percent increase in domestic prices in the same period could have been excessive, given the terms-of-trade changes that oc- curred. Similarly, five countries experienced a decline in domestic prices during the period in question. Yet, some of these (such as Gabon) will turn out to be among the most overvalued in 1993 because the decline in their export prices was much sharper. The variations in the terms-of- trade change can be largely attributed to the differences in the composi- tion of the countries' exports.4 Having spelled out the assumptions and presented the basic data, we are now in a position to calculate the degree of RER misalignment in each of the 12 countries. We solve the DLR model using the elasticities in 4. At first glance, it may seem surprising that the import price deflator varied so much across these countries, even though they import roughly the same bas- ket of goods. There are two reasons for this variation. First, the base from which the price change was calculated varied substantially across countries. Second, some countries import petroleum products whereas others export them. 368 EXCHANGE RATE MISALIGNMENT table 8.1 and import- and export-price changes in table 8.2. The model calculates the domestic price level that, for a fixed nominal exchange rate, is consistent with those price changes, given the elasticities and structure of the economy. The economic structure, in turn, is determined by the levels of real GDP, imports, and exports only-hence the claim that the model is economical in its demands on data. We then compare this model-calculated price level with the actual price level in 1993 to determine the extent of RER misalignment in that year. Before discussing the results, two presentational issues must be ad- dressed. First, the essence of the DLR model is the notion that the price of domestic goods adjusts to restore equilibrium in the economy. The calculations assume that the nominal exchange rate is fixed-as it is in the CFA economies. While the adjusting domestic price is precisely de- fined, and can be easily calculated using national accounts data, it is not always reported in standard price statistics. Instead, these statistics usu- ally report the consumer price index (CPI) and the GDP deflator. Since there is a straightforward relationship between the price of domestic goods and the GDP deflator (the latter is a weighted average of the former and the export price deflator) in the national accounts and the DLR model, we will report the results in terms of the GDP deflator in order to make them more readily comparable to available price statistics. That is, we use the model first to calculate the equilibrium domestic price and subsequently compute the equilibrium GDP deflator. We then com- pare the latter to the actual level of the GDP deflator to determine the degree of price level overvaluation. It may seem curious that, while we have stressed the advantage of the DLR model as capturing the two real exchange rates, we use neither in our estimation of price misalignment. We have adopted this proce- dure in order to simplify the presentation and focus it on the model's endogenous price variable-the domestic price level. Recall that the RERs for imports (RERM) and for exports (RERE) are defined as shown in equations 8.7 and 8.8: (8.7) RERM = s P PQ (8.8) RERE - E P 5. See the appendix to Chapter 3 on the two-good internal RER. A SIMPLE GENEFAL EQUILIBRIUM MODEL 369 In the DLR model, P, and P,r are specified exogenously; and (1/s).PD, the price of domestic goods in foreign currency terms, is the model's endogenous price variable. If s is also fixed as in the CFA countries, PD becomes the model's single endogenous price variable and the endog- enous determinant of the RERs for both exports and imports. The equi- librium RERs for imports and exports can, however, be readily com- puted with equations 8.7 and 8.8 using the equilibrium domestic price level and the exogenously determined border prices of imports and exports. A second presentational issue, which all studies of real exchange rates have to confront, is the question of whether the measure should be ex- pressed in domestic- or foreign-currency terms. In the figures in this chapter, the results are presented in foreign-currency terms, so that an upward movement of the RER or domestic price level is an appreciation and a downward one is a depreciation. Since we are comparing price levels, our measure of overvaluation is the degree to which domestic prices will have to fall in order to restore equilibrium. With these clarifications in mind, figure 8.1 presents the degree of overvaluation of the GDP deflator in the CFA countries in 1993. For ex- ample, the domestic price level in Cameroon, the most overvalued coun- try, needed to fall by 78 percent because the equilibrium price level was only 22 percent of the actual price. Several points about these results are worth noting. First, the degree of real overvaluation in 1993 was substantial-an unweighted average of 31 percent for the CFA countries as a group. Second, the variation in RER misalignment across countries was also substantial: the middle- and former middle-income countries, and within that group the oil pro- ducers (Cameroon, Gabon, Congo), were the most overvalued, while some of the low-income countries were only slightly overvalued or, in one case (Chad), undervalued.6 Third, the comparable calculation using the PPP base-year method yields much lower degrees of real overvalu- ation. The reason, as mentioned earlier, is that the PPP base-year ap- proach leaves out the effects of changes in the terms of trade on the country's equilibrium real exchange rate. To the extent that CFA coun- tries suffered adverse terms-of-trade shocks during this period, such an omission will lead to an underestimate of the degree of overvaluation (see equation 8.4).1 6. The large variation in RER misalignment does not necessarily imply that a uniform nominal devaluation was unwarranted, since a nonuniform devalua- tion would have necessitated introducing multiple currencies and, therefore, undermined the zone's two monetary unions. 7. In addition, the PPP base-year approach usually uses the country's overall price level (CPI). Since this index reflects tractable as well as nontradable prices (import prices in the CPI), it is not directly comparable to the price of domestic goods. 370 EXCHANGE RATE MISALIGNMENT Figure 8.1 Overvaluation of the GDP Deflator in the CFA Zone, 1993 > C 70 7j 60 - 50 58 52 5 1 40 5 1 30 20 1022 1020 17 -10- 19 -20 Source: Computed from World Bank data using the DLR model. Figure 8.1 summarizes the extent of price overvaluation on the eve of the devaluation. Was this overvaluation persistent, or had it arisen in the last few years? To answer this question, we examine the evolution of misalignment over time for each of the 12 countries. We do so first by using the DLR model to compute the level of the GDP price deflator required to restore equilibrium for every year after the base year and then by comparing the equilibrium level to the actual levels of those years. Such an exercise helps answer another question: How much of the overvaluation was due to changes in the equilibrium price level, and how much to changes in the actual domestic price level? The results of this exercise for three representative countries are pre- sented in figure 8.2. The picture painted in the previous discussion now comes into sharper view. Cameroon, a major oil producer, suffered a major terms-of-trade shock in 1986 (when the price of oil plummeted) and remained severely overvalued subsequently. Even though the price level in the country rose only slightly, it was still far above the equilib- rium level, which declined sharply. Similarly, in another highly over- valued country, C6te d'Ivoire, the gap between the equilibrium and ac- tual price levels started growing in the mid-1980s and continued to grow until the end of 1993. By contrast, in one of the low-income countries, Niger, the GDP deflator was either in equilibrium or even undervalued for most of the 1980s. Niger's GDP deflator became overvalued only A SIMPLE GENERAL EQUILIBRIUM MODEL 371 Figure 8.2 Equilibrium vs. Actual GDP Deflators Cameroon 8 1.4 ii1.2 - 1- 0.8 Equil 0.6 - ..0.6 Actual 0.4 - 0.2 t U 1 . N cc 31 CD ' 00 00 00 00 00 DO 91 a, C 0a, Cte d'Ivoire 1.2- 0.8 - - Equil Niger ii1.2 0.8 . . -- - - ---Equil S0.- 0.6 ------ Actual 0.4 " 0.2 0 0000cc 00 00 00 a, 0' 0 0 0 0' 0 0'3 ' 0 0 ' 03\ 0 0 Note: An upward movement is an appreciation. Source: Computed from World Bank data using the DLR model. 372 EXCHANGE RATE MISALIGNMENT after 1990, when uranium prices fell. Nevertheless, by the early 1990s, a significant gap between the equilibrium and actual GDP deflator rate had appeared in 10 of the 12 CFA countries, with the gaps becoming ominously large (more than 30 percent) in six countries. Most of the countries were subject to adverse terms-of-trade shocks for their pri- mary export commodities; and the appreciation of the French franc (to which the CFA franc was pegged) relative to the U.S. dollar following the 1985 Plaza Accords exacerbated the decline in their export earning in CFA terms. Sensitivity Analyses and Extensions This section discusses the sensitivity of the estimates of misalignment to the model's assumptions. The two most crucial are the choice of base year and the assumed elasticities of transformation and substitution. The section goes on to give an example of an extension of the basic analy- sis to incorporate changes in sustainable capital flows and commercial policy. Sensitivity to Choice of Base Year As mentioned earlier, the choice of base year for the calculation of RER misalignment is somewhat arbitrary. The analyst has to decide in which year the actual RER equaled the equilibrium RER and the resource bal- ance of the economy reflected a sustainable level of capital flows. Sig- nificantly, that level of capital flows need not be zero: a country may have a current account deficit, or a negative resource balance, and still be in a sustainable equilibrium. Indeed, the resource deficit could be larger in the base year than in a current (disequilibrium) year if the ex- ternal capital inflows have fallen. In this case the smaller current re- source deficit would not be sustainable, although the larger one in the equilibrium base year was sustainable. In short, the choice of a base year does not lend itself to some simple, mechanical formula, such as "the year in which the resource balance was x percent of GDP." Hence, we based our choice of base years on the knowledge of economists fa- miliar with the particular situation of the individual countries. Given that this is a subjective method for determining a potentially crucial com- ponent of the analysis, we examined the sensitivity of the price mis- alignment estimates to the choice of base year. Figure 8.3 reports on simulations with the DLR model using differ- ent candidates for the base year from 1980 to 1990 for three representa- tive countries. For each different base year, both the terms-of-trade shock (with respect to 1993) and the structure of the economy (in the base year) are different. The resulting patterns are quite revealing. For one of the Percent Overvalued in 1993 Percent Overvalued in 1993 Percent Overvalued in 1993 CDCD CD C 0 CD D C D C 1980 1980 1981 1981 1982 1982 1982 1983 1983 1983 O> E æ1984 1984 1984 195 š 4 a1984 1984 M CD fD 1986 1985 1985 1986 1986 1986 1987 1987 1987 1988 1988 1988 C 0 1989 1989 1989 1990 1990 1990 374 EXCHANGE RATE MISALIGNMENT most overvalued former middle-income countries, Cameroon, the de- gree of price misalignment is quite robust to the choice of base year up to 1986-87. This pattern is not surprising. Cameroon faced the largest terms-of-trade shocks in the mid-1980s. Yet, after 1986-87 export and import prices were not that different from the level in 1993. Hence, if one of the years after 1986-87 is chosen as the base year, the degree of misalignment is much lower. Yet no economist familiar with Cameroon would suggest that 1988, for example, was a reasonable base year for it. The country was then in the middle of a major adjustment period be- cause of the oil-price shock. In contrast, for a less overvalued low-in- come country such as Benin, the magnitude, and possibly even the sign, of the price misalignment depends on the choice of base year. Benin could be considered undervalued or overvalued depending on which year in the 1980s was picked as its base year. To be sure for the years after 1982, the degree of misalignment would range only from +10 per- cent to -5 percent so that Benin would still be close to equilibrium in any case. Finally, note that for C6te d'Ivoire-which is often thought to be the leader in the CFA zone-the degree of price overvaluation is quite sensitive to the choice of base year even if the choice is restricted to the first half of the 1980s because of sharp swings in its terms of trade. For instance, if 1982 were to be chosen, the country was hardly out of equi- librium in 1993. But if 1985 were the base year, C6te d'Ivoire was above the CFA average in overvaluation. These results provide a partial expla- nation of why observers of C6te d'Ivoire may have disagreed on whether the country's RER was misaligned: they may have been thinking in terms of different base years. Sensitivity to Elasticities As the DLR model relies on assumed values of two key parameters, it is also important to investigate how robust the results are with respect to assumptions about these parameters. The results of sensitivity tests us- ing values of these elasticities below and above the base case values are reported below. As figure 8.4 indicates, for the most overvalued country, Cameroon, the degree of price overvaluation is not very sensitive to either elastic- ity. The range of price overvaluation between the high elasticity case (both elasticities equal to 2, four to five times the base case levels) and the low elasticity case (0.2 and 0.25, one half the base case levels) is only between 66 percent and 81 percent. This result is not surprising since, as we saw earlier, Cameroon suffered a sharp terms-of-trade decline, which (with a fixed nominal exchange rate and downward price rigidity) would lead to a substantial overvaluation for any reasonable substitution and A SIMPLE GENERAL EQUILIBRIUM MODEL 375 Figure 8.4 Sensitivity of Price Misalignment to Elasticity Assumptions Benin C6te d'Ivoire % overvalued %overw,.1 3 ..50 ,/ 40 - 30 1.5 2 2 1.3 o 10 0.5 omega o e 0 _ 0.4 2 0.4 sigma sigma Cameroon % overvalued rsy omega U.2 0.4 2 sigma Source: Computed from World Bank data using the DLR model. transformation elasticities. This result is repeated for all the highly over- valued oil-producing countries. However, as with the choice of base year, assumptions about the elasticities can affect the sign of the misalign- ment for less overvalued low-income countries such as Benin. Again, though, the range between the high and low cases is not very large- around 20 percentage points. In C6te d'Ivoire's case, the degree of mis- alignment, while somewhat sensitive to the choice of base year, is less sensitive to the elasticities: the range between the high and low cases is around 20 percentage points, with very little variation in the intermedi- ate values. Again, this outcome is driven by the fact that C6te d'Ivoire's overvaluation was the result of the large terms-of-trade shocks it suf- fered in the mid-1980s. These shocks were sufficiently large that they dominated the effect of reasonable variations in the assumed elasticities. 376 EXCHANGE RATE MISALIGNMENT Extensions Finally, as anticipated in the section that introduced the DLR model, we now present some illustrative calculations for C6te d'Ivoire of the RERs for exports and imports, and the two extensions to the DLR model dis- cussed in this chapter-namely, changes in sustainable capital flows and in tariffs. Figure 8.5 shows the evolution of the actual and equilibrium RERs for exports and imports expressed relative to the GDP deflator in Cte d'Ivoire. Note that the two RERs behaved somewhat differently. The actual RER for exports appreciated by about 35 percent, while the equilibrium export rate depreciated by almost 20 percent. For imports, in contrast, the actual RER changed little, whereas the equilibrium rate depreciated by nearly 40 percent. As for the first of the two extensions, estimating sustainable capital flows and determining target current account deficits is a significant analytical problem in its own right, which is discussed further in the preceding chapter on traditional methodologies and operational tech- niques by Ahlers and Hinkle. Recall that the assumption in figure 8.1 that there was no change in the level of sustainable flows yielded a de- gree of overvaluation for Cte d'Ivoire of 36 percent. How does this estimate vary with changes in the level of sustainable capital flows? We can use equation 8.4' to obtain an approximation of the additional over- valuation for a given reduction in the level of sustainable capital flow. Note that since A allows us to adjust for changes in capital flows, the critical factor in choosing a base year is that, taking into account all of the fundamen- tals, the actual RER be as close as possible to the equilibrium RER. The calculation proceeds in the following steps. First, we translate a 1 percent of GDP reduction in the level of capital inflow (or increase in the level of outflow) into a change in the ratio of total imports to total exports. Given the levels of GDP, imports, exports, and the resource bal- ance in Cte d'Ivoire in the base year (1984), this 1 percent of GDP re- duction is equivalent to a 3 percent decrease in . Second, from (8.4'), we determine that a 3 percent reduction in A would require an addi- tional decline in the domestic price of 3.3 percent to restore equilibrium (given elasticities of 0.4 and 0.5). Third, this 3.3 percent decline in the domestic price would lower the overall price level by an additional 2 percentage points (exports are about 40 percent of GDP). The next result is that if Cte d'Ivoire was overvalued by 36 percent when capital flows return to the base-year level, it is overvalued by 39 percent when they are 1 percent of GDP lower than in the base year. In sum, for every 1 percent of GDP decline in the level of sustainable capital inflow from the 1984 level, Cte d'Ivoire's degree of price overvaluation goes up by 3 percentage points. A SIMPLE GENERAL EQUILIBRIUM MODEL 377 Figure 8.5.a C6te d'Ivoire: RER for Exports Export RER (Px/Pe) 1.4 1.2 1.0 11 0.8 ...... Actual 0.6 Equl 0.4 0.2 0' 00 0' 00 00 0' 0Y' 3' a, Figure 8.5.b C6te d'Ivoire: RER for Imports Import RER (Px/Pm) 1.2 ...... S0.8-- ................ ... . ............. .. . . . . A t a .. . . .... . . . .A t u a S0.6- -Equil 2 0.4-- 0.2 0I CC 10 NO 00 CC 0D 0' 0' 0' 00 00 00 0' 0' 0'7\ 0 Note: An upward movement is an appreciation. Source: Computed from World Bank data using the DLR model. 378 EXCHANGE RATE MISALIGNMENT The calculation for a change in tariffs proceeds along similar lines. For example, if the initial effective tariff rate (tariff revenues collected as a share of imports) in C8te d'Ivoire was 20 percent, then a 30 percent reduction in the effective tariff rate (that is, the effective tariff rate being reduced to 14 percent) would have implied a reduction in the equilib- rium domestic price of 2.2 percent (using equation 8.5). However, the domestic price of imports including tariffs would also have fallen by 5 percent, while the domestic price of exports would have remained con- stant. If we go back to the definitions of two real exchange rates-the relative prices of imports to domestic goods and of exports to domestic goods-the former would have appreciated by 2.8 percent, while the latter would have depreciated by 2.2 percent. If one were using a weighted average of the two real exchange rates for the internal RER, the net effect would probably be an appreciation, given the greater change in the import RER and the fact that for most capital importing countries (like C6te d'Jvoire) imports exceed exports. Hence, a reduction in pro- tection is likely to lead to an appreciation of the equilibrium RER but to have asymmetric effects on the RERs for imports and exports, appreci- ating the former but depreciating the latter. Conclusion This chapter has demonstrated the use of a simple general-equilibrium model that captures some salient features of RER misalignment in de- veloping countries (specifically, the change in the equilibrium RER in response to changes in the terms of trade and capital flows) but requires only minimal data for the calculations. The analysis has shown that ne- glecting changes in the equilibrium RER can be seriously misleading in determining the extent of RER overvaluation. Several CFA countries experienced a decline in their domestic price levels over the late 1980s and early 1990s; yet some of these same countries were still the most overvalued as the equilibrium RER declined even further because of adverse terms-of-trade shocks. Two extensions of the basic model-one that allowed for changes in the level of sustainable capital inflows, the other for changes in the tariff regime-were also presented and used to calculate the impact of each of these changes on the degree of RER over- valuation in C6te d'Jvoire. The simplicity of the DLR model permits a range of sensitivity analy- ses of the estimates of misalignment. While the choice of base year is often controversial, we find that our estimates of misalignment do not change significantly for a wide range of base years. Specifically, for the most overvalued countries, any base year in the early- to mid-1980s be- fore the adverse terms-of-trade shock would give more or less the same A SIMPLE GENERAL EQUILIBRIUM MODEL 379 estimate of overvaluation, since the terms of trade of these countries fell sharply in the mid-1980s and have not recovered since. The estimate of domestic price overvaluation for the countries expe- riencing large terms-of-trade shocks is similarly robust to assumptions about the model's elasticities. The terms-of-trade shocks were so severe that for a wide range of elasticities the gap between the equilibrium and actual real exchange rate in 1993 was substantial. In contrast, for the countries where the terms-of-trade shocks were smaller, the estimates are quite sensitive to the elasticities. However, insofar as the economies of these countries are relatively simple, we can attach more confidence to our "base case" levels of the elasticities (which were quite low) and therefore to our initial estimates of RER overvaluation in those countries. Two limitations of the approach in this chapter should be highlighted here. First, being an equilibrium model but not a dynamic one, the model only calculates the gap between the actual and equilibrium real exchange rates. It is silent about the path that the economy should take to achieve equilibrium, or even how long it should take. Second, as a model of relative prices, it is better suited for analyzing countries with fixed ex- change rates, as the domestic price level can be uniquely determined only if the nominal exchange rate is predetermined or exogenously speci- fied. In addition, in countries with fully flexible exchange rates, changes in the nominal exchange rate can affect real variables through the mon- etary sector. These effects are left out of the present model. That said, if the situation calls for the rapid calculation of the equilibrium real ex- change rate in a country subject to terms-of-trade shocks, the general- equilibrium model presented in this chapter can help put the estimate of RER misalignment on a firmer analytical footing. Appendix The DLR Model Equations (8.A.1) X = G(E, D; Qi) (8.A.2) Q = F(M, D; a) (8.A.3) E/D = g(PD, PE; Q) (8.A.4) M/D = f(PD' PM; a) (8.A.5) P = sP* (8.A.6) P1 = sPE* (8.A.7) P,M = PfE (8.A.8) s = 1. Endogenous variables E Exports M Imports D Domestic goods Q Composite goods P Price of domestic goods Domestic price of imports PE Domestic price of exports s Nominal exchange rate Exogenous variables X Aggregate output P* World price of imports P* World price of exports X Ratio of value of imports to value of exports a Elasticity of transformation of supply al Elasticity of substitution in demand 380 9 Long-Run Real Exchange Rate Changes in Developing Countries: Simulations from an Econometric Model Nadeem UI Haque and Peter J. Montiel This chapter describes a methodology for the empirical estimation of the impact on the long-run equilibrium real exchange rate (LRER) of permanent policy changes and external shocks. Because the real exchange rate is one of two key macroeconomic relative prices (the other being the real interest rate), it is endogenous to a wide variety of potential macroeconomic disturbances. A variety of techniques, reviewed else- where in this book, are available for deriving approximate estimates of the reaction of the long-run equilibrium real exchange rate to shocks, using simplified models that focus on the particular aspects of the ad- justment process believed to be most important in specific applications. However, the full general-equilibrium interactions can only be studied in the context of larger models. Consequently an empirical judgment about where the prevailing real exchange rate in a given country stands relative to its sustainable long-run value would ideally be formed by working out the economy's full dynamic adjustment in the context of such a model. Thus, numerical simulation experiments with macroeco- nomic models are-at least in principle-the tool of choice for under- standing both the "real time" and long-run effects of policy measures and external shocks on real exchange rates in developing countries. Such experiments have been conducted for industrial countries by international institutions that maintain large multicountry economic 381 382 EXCHANGE RATE MISALIGNMENT models.' Whether this methodology can in fact be applied more gener- ally in other country circumstances, however, depends on the availabil- ity of a reliable empirical macroeconomic model for the country in ques- tion. Unfortunately, this is rarely available for such countries, and the construction and simulation of custom-made models for the purpose of estimating long-run equilibrium real exchange rates is expensive and time consuming. One approach to this problem is to adapt an existing model, which is broadly applicable to the country in question, to the application at hand. The usefulness of the results from such a procedure, however, would depend on how closely the model chosen for the purpose can replicate the macroeconomic behavior of the country under study In this chapter, we describe how the long-run behavior of the real exchange rate can be explored using a particular empirical developing- country macroeconomic model that may be suitable for many such ap- plications. The model used for this purpose is one developed by Haque, Lahiri, and Montiel (1990). The Haque-Lahiri-Montiel (HLM) model was designed for the purpose of estimating representative developing-coun- try values for the parameters of standard macroeconomic behavioral functions typically used by policymakers in such countries for the quan- titative formulation of fiscal, monetary, and exchange rate policies. This feature makes it a likely candidate for use in the manner just described. Other characteristics of the model make it specifically suitable for the study of real exchange rate dynamics. In particular, while the behav- ioral relationships incorporated in it are of the ad hoc variety typically found in models of this type, the model was specified with careful at- tention to dynamic considerations, and is reasonably comprehensive in its incorporation of dynamic macroeconomic adjustment mechanisms. Among other features, it was estimated and simulated under the as- sumption of rational expectations, and it allows for full adjustment of the capital stock to its long-run equilibrium value. The various adjust- ment mechanisms incorporated in the model can be shown to yield a stable long-run equilibrium, in which the real exchange rate plays an important macroeconomic equilibrating role. Our specific purpose in this chapter is to explore the predictions of the HLM model for the adjustment of this long-run equilibrium real exchange rate to permanent changes in the "fundamentals"-namely, domestic policy shocks and changes in the external environment-as an illustration of how macroeconometric models can be used in a develop- ing-country setting to extract estimates of equilibrium real exchange rates 1. See, for example, Williamson (1994) and Bayoumi and others (1994). SIMULATIONS FROM AN ECONOMETRIC MODEL 383 that reflect full general-equilibrium interactions. As indicated above, the model described here can be used as a template for the specification and estimation of country-specific versions in particular applications in which its general properties match those of the country under study. It can also be used as a source of representative value estimates of key behavioral parameters for simulation purposes, in applications in which country- specific parameter estimation is not feasible. The chapter is organized as follows: The next section presents a brief description of the model and some of its relevant properties. The sec- tion titled "Domestic Policy Shocks" examines the effects of a variety of permanent policy shocks on the long-run equilibrium real exchange rate, while the effects of permanent external shocks are analyzed in the sub- sequent section. A final section summarizes the findings, and an appen- dix describes an application of the methodology to the estimation of the equilibrium real exchange rate for Thailand. A Brief Description of the Model The structure of the HLM model (equations 9.1 through 9.19) is described in table 9.1. A detailed equation-by-equation description is contained in Haque, Lahiri, and Montiel (1990), so the exposition in this section is deliberately brief. We focus on several features of the model that make it particularly suited for the purpose at hand. First, it is designed to be applied to an open economy with a Mundell-Fleming production struc- ture operating under a fixed exchange rate.' Despite the prevalence of the alternative Swan-Salter "dependent-economy" production structure in analytical macroeconomic models for developing countries, data limi- tations described in Part I of this volume have implied that the vast majority of empirical macroeconomic models for developing countries have incorporated the Mundell-Fleming production structure. Thus the HLM model is reasonably representative of the class of models used for quantitative policy formulation and evaluation in such countries. Sec- ond, as mentioned above, the model's individual behavioral equations reflect conventional, widely used specifications. For example, as de- scribed in equations 9.2 and 9.5, respectively, private consumption de- pends on current and lagged values of disposable income and the do- mestic real interest rate, while private investment depends on the real 2. Fixed exchange rate arrangements are common among developing coun- tries, and were even more so during the sample period over which the model was estimated. 3. See Montiel (1993) for a survey of such models. 384 EXCHANGE RATE MISALIGNMENT Table 9.1 Structure of the HLM Model Equation Description Equation Formula Goods market Y = C, + 1, + G, + (Xt - [(e,P,*Z,)/PI]) equilibrium condition (Equation 9.1) Consumption function log C, = o - 0.12 r, + 0.99 log C,_ + 0.34 log Y,d (Equation 9.2) - 0.33 log Y Disposable income yd= + [i*eF,1 PJ - [i,DCP,/ IJ - Tt (Equation 9.3) Household budget Yd = t + 1 t Fp,, Fp,t-1) - (DC,, constraint - DCP,j) }/P (Equation 9.4) Investment function log I, = ko - 0.207 r, + 0.199 log Y - 0.815 log Kt_1 (Equation 9.5) Export demand function log X, = z + 0.054 (etP,*/P,) + 0.106 log Y,* (Equation 9.6) + 0.927 log X,1 Import demand function log (eZ, 1/P) = do - 0.129 log (eP,*/P,) + 0.135 log Y (Equation 9.7) + 0.847 log [(e -Z,,)/(P_)] Production function log Y,= q, + 0.162 log K, + 0.838 log L, (Equation 9.8) Capital stock K, = I, + 0.95 K, accumulation (Equation 9.9) Central bank M,= e,R, + DC, balance sheet (Equation 9.10) Domestic credit identity DC, = DCP, + DCG,t (Equation 9.11) Money market log Mr /P = mo - 0.055i, + 0.203 log Y, equilibrium + 0.796 log (M,l /P-) (Equation 9.12) SIMULATIONS FROM AN ECONOMETRIC MODEL 385 Uncovered parity it = i * + (E,e,+- e)/e, condition (Equation 9.13) Current account identity CA, = p,X, - e,p,*Z + i *e (F,_ +F (Equation 9.14) Balance of e,ARt = CAt - e,(AF' + AF) payments identity (Equation 9.15) Definition of the domestic r, = it - (E,P,, - P) real interest rate (Equation 9.16) Government budget AFc. - ADCG = P,(Tt - G, - (e, P,*/P)GZ,) constraint + i,*e,F GJ-1 -itDC, (Equation 9.17) Expectations formation e,1 = E,(e,, Q ) -- E (Equation 9.18) P = E(P, g) + 1 (Equation 9.19) Note: Definition of Variables Y = Real GDP. C = Real private consumption expenditure. I = Total real investment expenditure. G = Government expenditure on domestic goods. X = Real exports. e = Nominal exchange rate (price of foreign currency in domestic-currency terms). P* = Foreign-currency price of imports. P = Domestic-currency price of domestic goods. Z = Real (private) imports measured in terms of the foreign good. r = Real rate of interest. Yd = Real disposable income. FP = Stock of foreign assets held by the private sector (measured in foreign- currency terms). DC = Stock of domestic bank credit held by the private sector. I = Nominal interest rate. T = Real tax receipts. (table continues on next page) 386 EXCHANGE RATE MISALIGNMENT (Table 9.1 continued) M = Nominal money supply. K = Aggregate capital stock. Y* = Foreign real GDP. R = Stock of foreign exchange reserves. DC = Stock of total domestic credit. DCG = Stock of domestic credit to the public sector. CA = Current account of the balance of payments. FG = Foreign assets held by nonfinancial public sector. L, = Labor force. GZ, = Real government expenditure on foreign goods (measured in foreign- currency terms). E. q = White noise error terms. interest rate, the level of economic activity, and the lagged value of the capital stock. The demand for money is also conventional, depending on the domestic nominal interest rate and the level of real GDP, with partial adjustment allowed for the real money stock (equation 9.12). Third, the behavioral parameters were estimated using a large pooled cross section-time-series sample of countries, a consistent data set, and empirical techniques appropriate for the estimation of rational expecta- tions models with panel data. The objective was to extract "representa- tive" estimates from the data for the parameters involved in these con- ventional specifications. Fourth, the model was designed to test empiri- cally for the degree of effective capital mobility exhibited by the countries in the sample. The degree of capital mobility applicable among devel- oping countries is an issue on which there is little agreement, even for specific countries, and consequently any particular assumption adopted on a priori grounds would essentially be arbitrary. As it happens, the estimation proved unable to reject the hypothesis of perfect capital mo- bility (uncovered interest parity) over the sample period. 4. The parameters were estimated using an error-components three-stage least squares technique for a pooled cross-section time-series sample of 31 develop- ing countries covering various regions of the world and levels of income per capita. Details of the estimation, including diagnostic statistics, are provided in Haque, Lahiri, and Montiel (1990). 5. Consistent with this result, Haque and Montiel (1990, 1991) conducted tests for capital mobility for several developing countries and found a surprisingly high degree of financial openness among developing countries over the 1970s and the 1990s, in panel data tests of the capital mobility hypothesis in isolation as well as for many individual countries in this sample. SIMULATIONS FROM AN ECONOMETRIC MODEL 387 The HLM model assumes flexible prices and thus is characterized by continuous full employment. Unlike other features of the model, such as the production structure and behavioral specifications, this assump- tion is not characteristic of empirical developing-country macroeconomic models. The full-employment assumption is controversial, but the ques- tion of the existence of Keynesian unemployment in developing coun- tries arising from sluggish price adjustment is unsettled and is obvi- ously likely to be country-specific. While short-run nominal wage and price stickiness will make an important difference to the dynamic path that the economy follows from one long-run equilibrium to another, it will not affect the nature of the long-run equilibrium itself. Consequently this issue is not central for the purpose at hand. The assumption that expectations are formed rationally is also more important for the dynamics of adjustment than it is for the nature of the long-run equilibrium. Rational expectations enter the model in two ways. First, expectations of devaluation of the official nominal exchange rate enter the interest-parity condition (equation 9.13 in table 9.1), which determines the domestic nominal exchange rate. Second, the real inter- est rate, which affects both consumption and investment behavior and is given by equation 9.16, is assumed to incorporate a rational forecast of next period's price level. As mentioned previously, the assumption that expectations are formed rationally also played a role in determin- ing the technique used to estimate the model. Steady-State Properties The long-run properties of the policy simulations, which are the subject of this chapter, are better understood if we first examine analytically the steady-state version of the model. The steady-state version of the HLM model is presented in table 9.2. It has been broken into four recursive blocks, according to its solution algorithm. This algorithm works as fol- lows: since in this chapter we work with steady states for which the nominal exchange rate (e) is fixed, we have E, (e,. I Q) = e = e,, where Q, denotes the set of information available at time t and E is the expecta- tions operator. Since the real exchange rate must be constant in the steady state, constancy of the nominal exchange rate implies that the domestic price level must be constant as well, so E, (P1 I Q) = P, = P." With these conditions, equations 9.13 and 9.16 of table 9.1 yield the steady-state values of the domestic nominal (i) and real (r,) interest rates, both of which equal the foreign nominal interest rate i*. These equations appear in block I of table 9.2. The solution for r derived from block I, together 6. For the purpose of the simulations, foreign inflation is set equal to zero. 388 EXCHANGE RATE MISALIGNMENT Table 9.2 Structure of the Steady-State Model Equation Description Equation Formula I. Interest Rate Block (Equation 9.13) i, = i,* (Equation 9.16) r, =i, II. Output-Capital Block (Equation 9.5) log I = ko - 0.207 r + 0.199 log Y + 0.815 log K (Equation 9.8) log Y = q, + 0.162 log K + 0.838 log L (Equation 9.9) 1 = 0.05K III. Monetary Block (Equation 9.10) M = eR + DC (Equation 9.11) DC = DCP + DCc (Equation 9.12) log (M/P) = bc - 0.27 i + log Y IV. Demand Block (Equation 9.1) Y = C + I + G + X - eP*Z/P (Equation 9.2) log C = a, + 12 r + log Y' (Equation 9.3') Y, = Y + ieF*/P - i DCr/P - T (Equation 9.6) log X = t, + 0.74 log (eP*/P) + 1.45 log Y* (Equation 9.7) log Z = d, + 0.84 log (eP*/P) + 0.882 log Y (Equation 9.8) CA = PX - eP* (Z + GZ) + i*e (F, + FG ± R) (Equation 9.9) CA = 0 (Equation 9.17) eP*GZ = P(T - G) + i*e (Fc + R) + iDC, with the steady-state condition for the capital stock K, = Kt-1 in table 9.1 (equation 9.9), permits block II (consisting of the equations 9.5, 9.8, and 9.9) to be solved for real GDP (Y), the capital stock (K), and investment (1). The solutions take the form Y = Y(i*), K = K(i*), and I = 1(i*), with Y', K', I'< 0. The third block contains the monetary equations 9.10, 9.11, and 9.12. The steady-state version of equation 9.12 reflects the condition that Y, = Y1 = Y(i*), with its implication that the money supply (M) is constant- that is, M, = M_ = M. Substituting equations 9.10 and 9.11 into this version of equation 9.12 yields an equation of the form 9.12': (9.12') log[(eR + DCP + DC)/P] = o+ P/i* +02Y(i*) SIMULATIONS FROM AN ECONOMETRIC MODEL 389 where R is the foreign-currency value of international reserves and DCP and DCG denote central bank credit to the private and public sectors, respectively. Since i and Y are determined in blocks I and II respectively, and since e, DC,, and DCG are exogenous, this equation contains only two endogenous variables-R and P. To display the solution of the steady- state model diagrammatically, we can depict the combinations of R and P that satisfy (9.12') as the locus MM in figure 9.1. The slope of this locus is: dR =M/eP>O dP MM Since reserve growth results in an increase in domestic money sup- ply, which, in the absence of other measures, will lead to an increase in the price level, this locus is positively sloped. The remainder of the model is grouped into the fourth block, which we have termed the demand block. Using equations 9.14, 9.15, and 9.17 of table 9.1 in 9.3' we can rewrite private disposable income (Yd) as: eP* Z yd =y+ -(G+X) P where P* is the level of foreign prices, Z is the volume of imports mea- sured in units of the foreign good, G is real government spending on domestic goods, and X denotes real exports. Substituting this in equation Figure 9.1 Steady-State Equilibrium R D M M D P P* 390 EXCHANGE RATE MISALIGNMENT 9.2 and then using equations 9.2, 9.6, 9.7, and 9.9 in equation 9.1, we have equation 9.1': Y(i) )= C{i-, Y(i-)+ (eP* /P)Z(eP/P, Y(i*))} (9.1-)+I1(i) + G+X(eP* /P,Y* ) P* Z e*, Y(i'). P (P Since e, G, i*, and Y* are exogenous, this equation only contains the endogenous variable P. Block IV therefore also generates a locus in (R, P) space, which is given by equation 9.1'. This locus is denoted by DD in figure 9.1. Since R does not appear in equation 9.1', this locus is vertical. The key endogenous variables in the steady-state version of the model are thus the stock of international reserves R and the domestic price level P. The solution of the model is depicted by the intersection of the MM and DD loci at point A in figure 9.1. The model's exogenous variables consist of policy variables-namely, the nominal exchange rate e, the stocks of credit to the private and government sectors, respec- tively (DC and DCG), and government spending on home goods G, as well as external variables consisting of the external interest rate i*, foreign demand Y*, and the foreign price level P*. Once the solution values for R and P are determined as in figure 9.1, the values of the remaining endogenous variables in block IV (C, X, Z, Yd, F, CA, and GZ) can be found. Given the fixed exchange rate and the exogenous value of the international price level, the real exchange rate can then be determined. The stability of the steady-state equilibrium at A was verified in Haque, Lahiri, and Montiel (1990) by calculating the model's character- istic roots. These roots were computed using the parameter estimates in table 9.1 and linearizing around an artificial steady state generated by values of the exogenous variables intended to capture a "representa- tive" developing-country configuration.7 The model has a single root with modulus above unity. Since it also contains a single "jump" vari- able (the domestic price level), it thus exhibits saddlepoint stability (see Blanchard and Kahn 1980). Neutrality to Nominal Shocks Before considering the simulated economy's long-run response to do- mestic policy shocks taken individually, it is useful to verify the model's neutrality by examining the effects of a particular combination of nomi- nal shocks-specifically, an equiproportional exchange rate devaluation and increase in both (private and public) domestic credit stocks. Notice 7. The roots were computed through the subroutine LIMO in TROLL. SIMULATIONS FROM AN ECONOMETRIC MODEL 391 that an x percent increase in e, DC P, and DCG would continue to satisfy equation 9.12' if P also increased by x percent. The same is true of equa- tion 9.1', where DCP and DCG do not appear. Thus, the model is homo- geneous of degree one in e, DCP, and DC'G-since all nominal values change in the same proportion, real variables are unaffected, and the model's neutrality is verified. In terms of figure 9.1, both the A4M and DD loci shift to the right by x percent, increasing the equilibrium price level by this amount, but leaving the equilibrium stock of reserves and all other real variables unchanged. Domestic Policy Shocks With the nature of the steady state described and the model's neutrality established, we now turn to an examination of the long-run effects of policy and external shocks. In this section we examine responses to shocks in the domestic policy variables (the exchange rate, the stock of credit, and government spending on domestic goods), while in the fol- lowing section we turn to the effects of shocks in the external envi- ronment-specifically changes in world interest rates and foreign demand. Devaluation For our first exercise we consider a nominal exchange rate devaluation of 10 percent, taken in isolation-that is, with credit stocks unchanged. The steady-state effects of this shock are depicted analytically in figure 9.2 and the results of the simulation are presented in the second column of table 9.3. Since the stock of domestic credit does not affect equation 9.12', the DD curve shifts horizontally to the right (to D'D', for example), in proportion to the devaluation (that is, by 10 percent), as in the case of the neutral shock. The immediate implication is that the domestic price level must rise by 10 percent, so that the steady-state real exchange rate is unaffected by this nominal shock. Because DC and DCG are unchanged, however, the proportional shift in MM, which can be derived from (9.1'), amounts to: dP e - R/P e - - e = e de P mm (M/P)2 p =(eR/M)e0, dy,/d >0 where f is total net foreign assets, b is the trade balance, z is net foreign grants received by the government, all measured in traded goods, and r is the real yield on foreign assets. The trade balance is the difference between domestic production of traded goods, y,' and the sum of gov- SINGLE-EQUATION ESTIMATION OF THE LRER 409 ernment (g) and private spending on these goods. The equation is stan- dard except for the term 0, which measures the transactions costs asso- ciated with private spending. In Montiel's model of optimizing house- holds, these costs motivate the holding of domestic money, which would otherwise be dominated in rate of return by foreign assets.2 They are assumed to be incurred in the form of traded goods (at the rate 0 per unit of spending) and therefore appear as an outflow in the trade balance. External balance has been defined in various ways in the literature, with earlier approaches tending to focus directly on sustainable net capi- tal flows and more recent work focusing on long-run stock equilibrium. We take the latter approach, following Montiel and others (for example, Khan and Lizondo (1987), Edwards (1989), and Rodriguez 1994). Exter- nal balance therefore holds when the country's net creditor position in world financial markets has reached a steady-state equilibrium. We can solve for the combinations of private spending and the real exchange rate that are consistent with this notion of external balance by hold- ing fat its steady-state level and setting the right-hand side of equation 10.3 to 0. This traces out a second relationship between the real exchange rate and private spending, labeled EB in figure 10.1. Starting at any point on this schedule, a rise in private spending generates a current account deficit at the original real exchange rate. To restore external balance, the real exchange rate must depreciate, switching demand toward nontraded goods and supply toward traded goods; the EB schedule is therefore upward-sloping. We will see below that this stock equilibrium concept of external balance is consistent with a sequence of "flow" restrictions on the trade balance when countries are rationed in the international financial market. A fully specified macroeconomic model must also satisfy fiscal bal- ance in the long run. Since the predetermined rate of crawl of the nomi- nal exchange rate ties down seigniorage revenue as a function of prede- termined money holdings (both measured in traded goods), some fiscal variable must ultimately adjust to guarantee fiscal balance. Government spending is being held fixed, so the adjustment falls to tax revenue. Montiel assumes that any incipient public sector deficit is financed con- tinuously via lump-sum taxes or rebates. Fiscal balance therefore holds at each point in time in this model, with the required adjustments tak- ing place behind the scenes. It is worth noting that if the exchange rate were freely floating rather than managed, the rate of crawl would be- come endogenous and choices regarding lump-sum taxation would help 2. Montiel assumes that transactions costs are a decreasing function of the ratio of money holdings to spending: 0 = 0(m/c), 0'< 0. 410 EXCHANGE RATE MISALIGNMENT tie down the long-run inflation rate; but in other respects the long-run schedules would be unchanged. The equilibrium real exchange rate, e*, is given by the intersection of the lB and EB curves, which occurs at point I in the diagram. Setting the right-hand side of equation 10.3 to zero and combining this with equa- tion 10.2, we obtain equation 10.4: (10.4) - + - where" *" superscripts denote steady-state values of endogenous vari- ables and the signs below the equation are those of the corresponding partial derivatives of e*. The signs of the partial derivatives in equation 10.4 are easily verified, either graphically or algebraically, using equa- tions 10.2 and 10.3. Montiel solves for the steady-state service account r*f* by assuming that the country faces an upward-sloping supply curve of net external funds and that households optimize over an infinite horizon.4 Transac- tions costs per unit,f, are also endogenous; they depend on the ratio of money holdings to private spending and therefore on the nominal in- terest rate, which is the opportunity cost of holding domestic money. Since the nominal interest rate is tied down in the long run by the time preference rate and the domestic inflation rate, the final expression for the equilibrium real exchange rate takes the form e =e (sg,,s7yE (10.5) where r, is the world real interest rate and rT. is the rate of inflation in the domestic price of traded goods. Note that the nominal exchange rate does not appear among the fundamentals in equation 10.5. This is 3. See Agenor and Montiel (1999) for an analysis of the effect of exchange rate regime (managed versus floating) on macroeconomic dynamics in a model simi- lar to the one analyzed here. Note that taxes are assumed to be lump-sum and therefore nondistortionary in our model; otherwise tax rates would enter the long-run balance schedules. 4. The latter feature ties the domestic real interest rate to the time-preference rate in any steady state. Given r*, the value of f* is then determined uniquely by the external supply function. 5. Since 7x, = Yr + t where 7y is the world inflation rate and 7t, is the rate of crawl of the nominal exchange rate, we can think of the latter two variables as among the fundamentals. Note also that we have suppressed the time-preference SINGLE-EQUATION ESTIMATION OF THE LRER 411 because the underlying behavioral relationships are all homogeneous of degree 0 in nominal variables. A nominal devaluation therefore has at most a transitory effect on the real exchange rate. Equation 10.5 emphasizes that the real exchange rate consistent with internal and external balance is a function of a set of exogenous and policy variables. In practical applications, this relationship between e* and its macroeconomic "fundamentals" differentiates the modern ap- proach to equilibrium real exchange rates from the earlier purchasing power parity (PPP) approach. Under PPP, the analyst would identify a reference period of internal and external balance and use the real ex- change rate that prevailed during that period as an estimate of the equi- librium for other periods. Equation 10.5 implies that this is only legiti- mate if the fundamentals did not change between the reference and com- parison periods. This criticism of the PPP approach is now widely accepted.' The analysis underlying equation 10.5 can be readily modified to ac- commodate features that are important in particular applications. For our purposes, important extensions involve rationing of foreign credit, changes in the domestic relative price of traded goods, and short-run rigidities in domestic wages and prices. We discuss these extensions briefly in what follows. Rationing of Foreign Credit Equation 10.6 is derived under the assumption that the country faces an upward-sloping supply curve of external loans. The current account and trade balances are therefore endogenously determined at each moment by the saving and portfolio decisions of households. An extreme ver- sion of this view, more relevant for countries without access to commer- cial international borrowing on the margin, is that the country faces a binding credit ceiling (or equivalently, a floor on its international net rate in writing equation 10.5. Finally, note that while the impact effect of a rise in the world real interest rate depends on whether the country is initially a net debtor or a net creditor, the steady-state domestic real interest rate is constant in this model (see previous footnote) and the long-run effect of a rise in r is inde- pendent of the country's (endogenous) net creditor position. 6. The period of macroeconomic balance used in PPP calculations can be a single year or a group of years; elsewhere in this volume these alternatives are referred to as the "PPP base-year approach" and the "PPP average or trend ap- proach." In the section on the relationship of the PPP approach to the single- equation approach below we discuss further the distinction between these PPP approaches and our econometric approach. 412 EXCHANGE RATE MISALIGNMENT creditor position). Since a binding credit ceiling shuts down the capital account and also determines net interest payments, the trade surplus becomes an exogenous function of aid flows both in the short run and in the long run provided the ceiling remains binding. Credit ceilings thereby generate a natural link between "stock equilibrium" concepts of external balance and "flow" approaches that define external balance as holding when the trade deficit is equal to exogenously given net re- source transfers. With a binding credit ceiling equation 10.4 takes the simpler form (10.6): (10.6) - + ++- In our empirical work below, we treat the trade surplus b = -(rf + z) as one of the fundamentals, consistent with this interpretation. The Terms of Trade, Trade Policy, and Productivity Differentials The domestic relative price of exports and imports is given by equation 10.7: P P +t (10.7) X = , PM1 1 -tx where r is the external terms of trade and r is a parameter summarizing the stance of domestic trade policy. If either r or 7 changes over time, the analysis must be disaggregated to accommodate different real exchange rates for imports and exports-a point well emphasized elsewhere in this volume. The equilibrium real exchange rates for imports and ex- ports can then be written as functions of the set of fundamentals identi- fied above, along with rand n. Since the real exchange rate for tradables is itself a geometrically weighted average of the real exchange rates for imports and exports, it will depend on the same set of fundamentals, and elasticities will depend on the relative weight (a) of imported goods in the tradables price index.' Equation 10.6 then becomes equation 10.8: 7. The domestic real interest rate, in contrast, becomes endogenous. Move- ments in the domestic real interest rate reconcile private spending decisions with the exogenous credit constraint; and the spread between the domestic and for- eign real interest rates captures the shadow price of the credit constraint. 8. Defining real exchange rates for imports and exports as e = EP "/P and ex = EPw/P\ and the price index for traded goods as P,"= (P")a (Px") , the SINGLE-EQUATION ESTIMATION OF THE LRER 413 (10.8) e* e* (gN,IgTb, , , An improvement in the terms of trade increases national income mea- sured in imported goods; this exerts a pure spending effect that raises the demand for all goods and appreciates the real exchange rate. This effect can in principle be overcome by substitution effects on the de- mand and supply sides, leading to an overall real depreciation. A tight- ening of trade policy appreciates the real exchange rate in the long run. As outlined in the subsection on specifying an empirical model be- low, our fundamental task in this chapter will be to estimate the param- eters of equation 10.8. To measure the real exchange rate we will use the ratio of foreign wholesale price indexes to domestic consumer prices (a measure of the "external RER," in the terminology of Chapter 1 of this volume). This has two important implications for the interpretation of equa- tion 10.8. First, as discussed at length in Chapter 1, the external RER tends to move more closely with the internal real exchange rate for imports than with the internal real exchange rate for traded goods, e. While the magnitude of estimated elasticities will reflect this fact, the qualitative predictions indicated in equation 10.8 remain unchanged if the depen- dent variable is the internal real exchange rate for imports. This includes the ambiguity of the terms-of-trade effect, although there is a stronger tendency toward a real appreciation. The external RER has been widely used in empirical applications, and the spending effect has indeed proved dominant in most cases (for example, Edwards (1989), Elbadawi 1994). The second implication of using an external RER measure is that the interpretation of the differential productivity shock 4 must be adjusted accordingly. A tendency for productivity to advance more rapidly in the production of traded goods than in nontraded goods is the basis of the celebrated Harrod-Balassa-Samuelson (HBS) explanation for why nontraded goods are systematically cheaper in poor countries than mar- ket exchange rates would suggest (see Obstfeld and Rogoff 1996). Equa- tion 10.4, of course, focuses on the internal real exchange rate rather than on international comparisons of nontraded goods prices. A rise in 4 depreciates the internal equilibrium real exchange rate by increasing the relative output of traded goods. When using an external real ex- change rate, however, the HBS effect comes into play. To the degree that real exchange rate is e = (em)"(ex)1e. In our empirical work we use the ratio of foreign WPIs to the domestic CPI as our measure of the real exchange rate. As indicated elsewhere in this volume, this "external real exchange rate" tends to be a closer proxy to eM than to the "internal real exchange rate for tradables." 414 EXCHANGE RATE MISALIGNMENT differences between foreign and home productivity are concentrated in traded goods, these differences will show up in nontraded goods prices that are systematically higher in richer countries than purchasing power parity would suggest. This in turn means a more depreciated external real exchange rate for the home country, other things being equal. The sectoral shock ( therefore captures the difference between trading part- ners and the home country in the relative productivity of labor in traded and nontraded goods. In our empirical work we use a ratio of foreign to domestic overall labor productivity as a proxy for 4. Nominal Rigidities and Short-Run Dynamics In Montiel's model, domestic wages and prices are perfectly flexible and internal balance prevails continuously. If we consider the case of a bind- ing credit ceiling, so that the trade balance is exogenous, we conclude that as long as changes in the fundamentals are permanent, the actual real exchange rate never deviates from its long-run equilibrium. This is apparent from the inspection of the internal and external balance sched- ules: with b tied down exogenously, e and c are free to adjust immedi- ately to their new long-run equilibrium values when one of the funda- mentals changes. This is illustrated in figure 10.2, in which we show the adjustment to an increase in the world real interest rate by a net debtor country facing a binding credit ceiling. For a given aid inflow, the rise in r, increases the required trade surplus, shifting EB to the left (to EB') and depreciating the equilibrium real exchange rate. The adjustment from point 1 to point 2 is immediate; with a predetermined path for the nominal exchange rate the adjustment takes place through a fall in do- mestic prices and wages. Given wage-price flexibility, therefore, the bind- ing credit constraint removes the model's only source of internal dy- namics. The only remaining source of a divergence between the actual real exchange rate and its long-run equilibrium is a temporary change in one of the fundamentals. If domestic wages and prices are sticky in the short run, a second important source of internal dynamics comes from disequilibrium in the labor market and the market for nontraded goods. As long as these markets eventually clear, the equilibrium real exchange rate is unaffected by the short-run nominal rigidity. But any shock that alters the equilib- rium real exchange rate will now give rise to an adjustment process during which the actual real exchange rate will deviate from its new equilibrium. In figure 10.2, sticky wages and prices prevent the real ex- change rate from moving to point 2 in the short run, so that output and spending take the burden of the external adjustment. The short-run equi- librium is at point 3, at which unemployment and inventory accumula- tion gradually push nominal wages and the prices of nontraded goods SINGLE-EQUATION ESTIMATION OF THE LRER 415 Figure 10.2 Adjustment to an Increase in rw (under a Binding Credit Constraint) e EB' IEB 2 e 2 3'1I'I *, I I - -I I- IB - I I C C3 C2 CI Note: A rise in r, shifts EB upward to EB'. With flexible wages and prices, adjustment to the new long-run equilibrium at point 2 is immediate. With nominal rigidities, the economy jumps to point 3 and then converges gradually to point 2 along EB'. An upward movement is a depreciation of e. down relative to the prices of traded goods. The real exchange rate de- preciates over time, bringing the economy to point 2 in the long run. The process illustrated in figure 10.2 is often viewed as providing the primary role of nominal devaluation in macroeconomic adjustment: that of speeding an otherwise excessively slow and contractionary adjust- ment to an adverse external shock (Corden 1989). As the foregoing observations suggest, the long-run relationship given by equation 10.8 is consistent with a variety of sources and patterns of short-run dynamics, including not only wage-price stickiness and gradual asset adjustment but also costs of labor mobility and other fric- tions not present above. In the section on specifying an empirical model we incorporate this feature by embedding equation 10.8 in a flexible specification of short-run dynamics. Interpreting Real Exchange Rate Misalignment In this chapter we follow Edwards (1989) and Montiel (1997) in using the term "misalignment" to denote the gap between e and e*. There are 416 EXCHANGE RATE MISALIGNMENT two important differences, however, between this descriptive use of the term and its more normative use in most policy discussions. The first is illustrated by our discussion of nominal rigidities. In the absence of nomi- nal rigidities or other market imperfections, deviations between e and e* are market-clearing responses to temporary movements in the funda- mentals or to permanent movements that alter the long-run equilibrium level of net foreign assets. In such cases the gap between e and e* has no clear normative significance, and in particular there is no presumption in favor of "corrective" policy intervention. The second difference stems from the observation that the real exchange rate may well be misaligned from a normative perspective even when the economy is in a steady- state equilibrium. Dollar (1992), for example, argues that African real exchange rates were systematically overvalued in the 1970s and 1980s, as a result of highly inward-looking trade regimes. In the theory devel- oped here, the equilibrium real exchange rate is conditional on trade policies and other government interventions. Given these policy settings (whether socially optimal or not) misalignment is necessarily a tempo- rary phenomenon, generated by short-run macroeconomic forces that prevent an immediate movement to the long-run equilibrium.9 Specifying an Empirical Model In equation 10.8 we defined the equilibrium real exchange rate as the steady-state real exchange rate conditional on a vector of permanent values for the fundamentals. Given this structure, our task is to con- struct a time series for this unobserved variable (within sample and potentially out of sample), using data on the actual real exchange rate and fundamentals. As a first step we assume that the long-run relation- ship delivered by theory is linear in simple transformations (for example, logs) of the variables. Equation 10.8 therefore becomes equation 10.9: (10.9) In e, = #'F where e* is the equilibrium real exchange rate and F" the vector of per- manent values for the fundamentals. Our task, therefore, is reduced to one of estimating the vector P of long-run "parameters of interest" and choosing a set of permanent values for the fundamentals appropriate to period t. To estimate 0 we need an empirical model that is consistent with equa- tion 10.9 but relates observable variables. We obtain such a model by translating into stochastic terms two straightforward and general fea- 9. For a more extensive discussion, see Chapter 5 by Montiel in Part II. SINGLE-EQUATION ESTIMATION OF THE LRER 417 tures of the theory. The first is that equation 10.9 comes from a steady- state relationship between actual values of the real exchange rate and fundamentals. To capture this relationship we assume that the distur- bance o) in the following equation 10.10 (10.10) In e, = P'F + (>, is a mean-zero, stationary random variable." The second general feature of the theory is that the steady state is dynamically stable." Shocks that cause the exchange rate to diverge from its (possibly new) equilibrium in the short run should produce eventual convergence to the relationship in equation 10.9 in the absence of new shocks (or equivalently, in conditional expectation). A specification that captures this notion while retaining consistency with both equation 10.9 and 10.10 is the general error-correction model expressed in equation 10.11: P p (10.11) Alne,=a(Ine,_ -f'F, + XpAne,+ XYAF+ j=1 ]=0) where Ft = [g, g,, b, f, x, h, t] is the vector of fundamentals and v, is an independent and identically distributed, mean-zero, stationary random variable. Assuming that all variables are either stationary or I(1) (see be- low) in levels, equation 10.11 implies equation 10.10; and for -2 < a < 0 the corresponding long-run equilibrium is stable. Equation 10.11 embodies the central insight of the single-equation approach: that the equilibrium real exchange rate can be identified econometrically as that unobserved function of the fundamentals towards which the actual real exchange rate gravitates over time (Kaminsky (1987), Elbadawi (1994), Elbadawi and Soto (1994, 1995)). Note that in contrast to the long-run relationship, the short-run dynamics are not heavily re- stricted since equation 10.11 is just a re-parameterization of the unre- stricted p'h-order autoregressive distributed lag (ADL) representation of In e, as shown in equation 10.12: P p (10.12) In e,= lu'In e,- + 1y'F,_, +v,, 10. Note that equation 10.9 follows directly from equation 10.10 if In e* and FP are interpreted as long-run conditional expectations of the relevant variables. 11. This does not rule out theoretical models that exhibit instability in certain directions (for example, rational expectations models); the key assumption is that the economy "chooses" a convergent path for given values of the fundamentals. 418 EXCHANGE RATE MISALIGNMENT under the stability restriction II poI < 1 and the assumption that the real exchange rate enters the long-run relationship.12 For different pa- rameter values, the unrestricted error-correction representation (equa- tion 10.11) encompasses a wide variety of commonly used dynamic models (Hendry, Pagan, and Sargan (1984), Ericsson, Campos, and Tran 1991). This flexibility is an advantage, because although the dynamic structure of any particular theoretical model may place restrictions on the parameters in equation 10.11, these restrictions will depend on the nature of nominal and real rigidities, on whether households optimize or use rules of thumb, and on other model-dependent features that have little or no effect on the set of variables that enter the long-run equilib- rium. With unrestricted dynamics, we allow the data maximum scope for determining their actual pattern, while retaining consistency with the long-run specification. Much of our econometric work will take place in versions of equa- tion 10.11. It is straightforward to incorporate variables that in theory do not belong among the long-run fundamentals, but that may affect the short-run dynamics. An example is the nominal exchange rate. De- noting such variables by a vector s, we would capture long-term effects by adding the term 6's inside the parentheses in equation 10.11 (allow- ing a test of the hypothesis 3 = 0) and short-term dynamics by adding YI p,'As_, to the right-hand side. Equation 10.12 would then include the corresponding term X(1). These properties can readily be revealed using standard tests for the presence of a unit root.20 The appropriate unit-root tests are well known; in our applica- tions we use the Dickey-Fuller (DF), augmented Dickey-Fuller (ADF), and Phillips-Perron (PP) tests. Although there are concerns about the low power of these tests against stationary but persistent alternatives, the ADF test appears to perform satisfactorily on this score even when (as in our case) the number of observations is small (Hamilton 1994). We also supplement the unit-root tests with variance ratio tests (Cochrane 1988); these tests exploit the fact that the variances of conditional fore- casts explode for nonstationary series and converge for stationary series as the forecast horizon grows. 20. Hamilton (1994) emphasizes the difficulty of distinguishing truly nonstationary processes from processes that are stationary but persistent. The problem is that the finite-sample autocovariances of any nonstationary series can be reproduced arbitrarily closely by those of a suitably persistent stationary series. The usual tradeoff between consistency and efficiency is therefore present even at this preliminary stage. If we correctly characterize the order of integra- tion, we gain efficiency in estimation and inference by applying the appropriate estimation technique; but a misclassification typically means that these techniques will deliver inconsistent estimates or standard errors. Unfortunately the alterna- tives are non-nested and we see no generally robust way of proceeding in mar- ginal cases. Hamilton (p. 447) suggests comparing estimates obtained under al- ternative classifications; if they differ widely the investigator may sometimes see ancillary statistical or other grounds for preferring one over the other. 428 EXCHANGE RATE MISALIGNMENT Table 10.1 Stationarity Statistics-Levels without and with Time Trend C6te d'Ivoire Burkina Faso DF ADF PP DF ADF PP Levels without Time Trend log(REER) -0.59 -1.26 -1.89 -2.25 -4.25 -2.25 log(TOT) -1.42 -1.54 -1.78 -1.95 -1.82 -1.87 RESGDP -2.11 -2.57 -2.25 -3.84 -2.22 -4.07 log(OPEN1) -1.06 -1.39 -1.42 -4.02 -3.04 -4.30 log(OPEN2) -2.35 -1.99 -2.48 -3.23 -3.02 -3.35 log(OPEN3) -2.52 -2.16 -2.69 -3.63 -2.99 -3.82 log(HBS3) n.a. n.a. n.a. -1.21 -2.05 -1.67 log(ISHARE) -1.01 -0.78 -0.68 n.a. n.a. n.a. Levels with Time Trend log(REER) -1.83 -2.46 -2.09 -4.89 -2.76 -5.35 log(TOT) -1.51 -1.56 -1.69 -2.30 -2.08 -2.34 RESGDP -2.05 -2.50 -2.24 -4.27 -2.69 -4.64 log(OPEN1) -1.02 -1.32 -1.29 -3.84 -2.94 -4.20 log(OPEN2) -2.81 -2.30 -3.02 -3.12 -2.95 -3.31 log(OPEN3) -2.47 -1.99 -2.72 -3.47 -2.91 -3.75 log(HBS3) n.a. n.a. n.a. -3.65 -3.75 -3.68 log(ISHARE) -2.42 -2.19 -2.42 n.a. n.a. n.a. Note: DF, ADF, and PP refer to Dickey-Fuller, augmented Dickey-Fuller, and Phillips-Per- ron stationaritv statistics. The number of observations is 29 for C6te d'Ivoire and 24 for Burkina Faso. The variables are defined in appendix B (ISHARE is not available for Burkina Faso). Source: Computed from data from sources listed in appendix B. Table 10.1 shows the results of unit-root tests for all stochastic vari- ables. C6te d'Ivoire and Burkina Faso represent two extremes. For C6te d'Ivoire, all three tests indicate nonstationarity for all variables. More- over, we can reject the unit-root hypothesis for the first difference of the variables (not reported), so we conclude that these are I(1) variables. For Burkina Faso, all variables appear to be trend-stationary, with the pos- sible exception of the terms of trade, which is bordering on nonstationarity. Figures 10.3 and 10.4 provide some additional informa- tion in the form of variance ratio tests.2" These tests corroborate the unit-root 21. This ratio is defined as (1/k)Var (X,- X,_)/Var (X, - X,_), where X, is the variable of interest and k is the lag length (Cochrane, 1988). SINGLE-EQUATION ESTIMATION OF THE LRER 429 Figure 10.3 Variance Ratio Tests for CMte D'Ivoire log(TOT) RESGDP 1.80 1.80 1.50 150 Z q 1.20 1.20 0.90 0.90 0.90 0.60 0.60 0.30 0.30 0.00 i ii i i I 0.00 I I~ 1 I 1 3 5 7 9 11 13 15 1 3 5 7 9 11213115 loglOPENI) log(REER) 2.10 1.80 0 00 1.50 L 1.20 S0.90 0.90 S0.60 0.60 0.30 0.30 ~~0.00 il 1 1 1 1 1 00 1 3 5 7 9 1113 15 123456 7 8 9 10 11 12 13 14 15 log(REER) 1.80 1.50 Zj 1.20 S0.90 r 0.60 0.30 0.00 I 1 2 3 4 5 6 7 8 9 10 11121314 15 Source: Computed from data from sources listed in appendix B. tests, and for Burkina Faso's terms of trade the variance ratios decline at longer horizons, consistent with a persistent but stationary variable. We therefore proceed under the assumption that the terms of trade are sta- tionary. In principle, of course, the vector [ln e,Fj, sj']' may contain an arbitrary combination of 1(0) and I(1)-or even 1(2)-variables. We focus our exposition, however, on the two cases represented by our examples., 22. Methods have recently been developed that allow consistent estimation and inference in regressions that involve mixtures of integrated processes. See Phillips (1995) and Phillips and Chang (1995). 430 EXCHANGE RATE MISALIGNMENT Figure 10.4 Variance Ratio Tests for Burkina Faso log(TOT) RESGDP 1.80 1.80 150 1.50 1.20 - 120 0.90 0.90 0.30 0.30 0.00 0.00 1 3 5 7 9 11 13 15 1 3 3 7 9 11 13 15 log(OPEN1) log(REER) 1.80 1.80 11.80 II0 1.50 1.2 1.20 0.90 00.90 .0 60 0.30 0.30 0.00 1L iii 0.00 1 3 5 7 9 1 1 3 15 1 3 5 7 9 11 13 15 log(HBS3) 1.80 1.50 S1.20 S0.90 S060 3T 5 7 9 11 13 15 Source: Computed from data from sources listed in appendix B. The 1(1) Case When the variables are all I(1), as for Cte d'Ivoire, stationarity of the residual 1 case is the "struc- tural error correction model" of Boswijk (1995; discussed in Ericsson 1995), which is obtained by premultiplying equation 10.14 by a square matrix and then im- posing a set of restrictions. 432 EXCHANGE RATE MISALIGNMENT Determining the Cointegrating Rank The cointegrating rank is a property of the full system, and a system estimator is required to test for it. Table 10.2 reports the results of Johansen's likelihood ratio tests for the cointegrating rank in COte d'Ivoire. We use a lag length of one for the underlying VAR system; this is very restrictive even for annual data, but longer lag length leaves us with very few degrees of freedom. The null hypothesis for these tests is that the number of cointegrating vectors relating the n nonstationary variables is less than or equal to r (where r < n). Comparing the esti- mated likelihood ratios in column 2 to the asymptotic critical values in column 3, we see (row 1) that the hypothesis of no cointegration (r = 0) can be rejected in favor of at most one cointegrating vector. In row 2, the hypothesis of one