LSM - 35 MAY 1988 Living Standards Measurement Study Working Paper No. 35 The Demand for Medical Care in Developing Countries Quantity Rationing in Rural Cote d'Ivoire Lo LI LSMS Working Papers No. I Living Standards Surveys in Developing Countries No. 2 Poverty and Living Standards in Asia: An Overview of the Main Results and Lessons of Selected Household Surveys No. 3 Measuring Levels of Living in Latin America: An Overview of Main Problems No. 4 Towards More Effective Measurement of Levels of Living, and Review of Work of the United Nations Statistical Office (UNSO) Related to Statistics of Levels of Living No. 5 Conducting Surveys in Developing Countries: Practical Problems and Experience in Brazil, Malaysia, and the Philippines No. 6 Household Survey Experience in Africa No. 7 Measurement of Welfare: Theory and Practical Guidelines No. 8 Employment Data for the Measurement of Living Standards No. 9 Income and Expenditure Surveys in Developing Countries: Sample Design and Execution No. 10 Reflections on the LSMS Group Meeting No. 11 Three Essays on a Sri Lanka Household Survey No. 12 The ECIEL Study of Household Income and Consumption in Urban Latin America: An Analytical History No. 13 Nutrition and Health Status Indicators: Suggestions for Surveys of the Standard of Living in Developing Countries No. 14 Child Schooling and the Measurement of Living Standards No. 15 Measuring Health as a Component of Living Standards No. 16 Procedures for Collecting and Analyzing Mortality Data in LSMS No. 17 The Labor Market and Social Accounting: A Framework of Data Presentation No. 18 Time Use Data and the Living Standards Measurement Study No. 19 The Conceptual Basis of Measures of Household Welfare and Their Implied Survey Data Requirements No. 20 Statistical Experimentation for Household Surveys: Two Case Studies of Hong Kong No. 21 The Collection of Price Data for the Measurement of Living Standards No. 22 Household Expenditure Surveys: Some Methodological Issues No. 23 Collecting Panel Data in Developing Countries: Does it Make Sense? No. 24 Measuring and Analyzing Levels of Living in Developing Countries: An Annotated Questionnaire No. 25 The Demand for Urban Housing in the Ivory Coast No. 26 The Cote d'Ivoire Living Standards Survey: Design and Implementation No. 27 The Role of Employment and Earnings in Analyzing Levels of Living: A General Methodology with Applications to Malaysia and Thailand (List continues on the inside back cover) The Demand for Medical Care in Developing Countries Quantity Rationing in Rural C6te dIvoire The Living Standards Measurement Study The Living Standards Measurement Study (LSMS) was established by the World Bank in 1980 to explore ways of improving the type and quality of household data collected by statistical offices in developing countries. Its goal is to foster increased use of household data as a basis for policy decisionmaking. Specifically, the LSMS is working to develop new methods to monitor progress in raising levels of living, to identify the consequences for households of past and proposed government policies, and to improve communications between survey statisticians, analysts, and policy makers. The LSMS Working Paper series was started to disseminate intermediate products from the LSMS. Publications in the series include critical surveys covering different aspects of the LSMS data collection program and reports on improved methodologies for using Living Standards Survey (LSS) data. More recent publications recommend specific survey, questionnaire and data processing designs, and demonstrate the breadth of policy analysis that can be carried out using LSS data. LSMS Working Paper Number 35 The Demand for Medical Care in Developing Countries Quantity Rationing in Rural C6te d'Ivoire Avi Dor Jacques van der Gaag The World Bank Washington, D.C., U.S.A. Copyright (©) 1988 The International Bank for Reconstruction and Development/THE WORLD BANK 1818 H Street, N.W. Washington, D.C. 20433, U.S.A. All rights reserved Manufactured in the United States of America First printing May 1988 This is a working paper published informally by the World Bank. To present the results of research with the least possible delay, the typescript has not been prepared in accordance with the procedures appropriate to formal printed texts, and the World Bank accepts no responsibility for errors. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author(s) 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. 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The most recent World Bank publications are described in the catalog New Publications, a new edition of which is issued in the spring and fall of each year. The complete backlist of publications is shown in the annual Index of Publications, which contains an alphabetical title list and indexes of subjects, authors, and countries and regions; it is of value principally to libraries and institutional purchasers. The latest edition of each of these is available free of charge from the Publications Sales Unit, Department F, The World Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A., or from Publications, The World Bank, 66, avenue d'1lna, 75116 Paris, France. Jacques van der Gaag was acting chief of the Living Standards Unit of the Development Research Department, the World Bank, when this paper was written. Avi Dor was a long-term consultant for the Living Standards Unit, Library of Congress Cataloging-in-Publication Data Dor, Avi, 1956- The demand for medical care in developing countries : quantity rationing in rural Cote d'Ivoire / Avi Dor, Jacques van der Gaag. p. cm. -- (LSMS working paper, ISSN 0253-4517 ; no. 35) Bibliography: p. ISBN 0-8213-1060-7 1. Rural health services--Ivory Coast--Utilizatlon. 2. Rural health services--Ivory Coast--Finance. 3. Medical care, Cost of- -Ivory Coast. I. Gaag, J. van der. II. Title. III. Series. RA771.I9D67 1988 362.1'0425--dcl9 88-14093 -v - ABSTRACT Several authors have pointed out the implications of financing medical care from general public funds. Among these are Akin (1986), Birdsall (1986), Jimenez (1986) and de Ferranti (1985). The most authoritative treatment of this issue is given in "Financing Health Services in Developing Countries: An Agenda for Reform, (World Bank, 1987). A common theme in the discussion is that user fees can improve efficiency and the prospects for cost recovery, while maintainig current levels of equity. In-order to evaluate this arguement, it is necessary to assess the responsiveness of consumers to changes in the price of medical care. Little evidence from developing countries exists to date. In this paper we attempt to fill the gap by analyzing the demand for health care in the rural Cote d'Ivoire where user fees are zero, but private access costs may be substantial. Using a mixed discrete choice/continuous demand analytical framework, we show that the absence of user fees per se does not guarantee equal access to all consumers. Private costs, represented by travel time, result in non-price rationing similar to the conventional money price mechanism. Our results strongly suggest that if revenues obtained from user fees are used to improve the regional distribution of services, the resulting system may actually improve equity over the long-run. - vi - ACKNOWLEDGENENT The authors benefited from discussions with numerous colleagues from both the Living Standards Unit and other parts fo the World Bank. Special thanks are due to Michael Grossman and Paul Gertler for their comments on earlier drafts. The authors are also indebted to Carmen Martinez for skillfully typing the various drafts. - vii - Table of Contents Page Is Introduction ....... ........... *...I......................... l II. Background Information on Cote d'Ivoire .................. ....... ..7 2.1 The Health Care System....*..*.... ....... ................ 2.2 Health Status as Reflected by the Ivorian Living Standards Survey....*................................. III. Analytical Framework and Data ............. 14 3.1 Analytical Framework... ......................... 14 3.2 Data and Summary Statistics ....... .. ... ..o ..... ....... . . . .16 A. The Ivorian Living Standards Survey .... ................ 16 B. The Rural Sample and Variables ... *.....oo*..........19 IV. Estimation of Demand for Health Care.............................24 4.1 Estimation Results for Adults ............................ 24 A. Entry to the Health Care Market ....................... 24 B. Provider Choice, a Multinomial Logit Model .............28 C. Number of Consultations with Doctors and Nurses ........36 4.2 Demand for Child Health Care .........a.*................. 39 A. Entry to the Health Care Market ......................39 B. Provider Choice Model ...................41 C. Number of Consultations with Doctors and Nurses ........44 V Summary and Conclusion ...... . .... * ....... ..... . ..... .so ...... 48 5.1 Total Utilization Response......................... ...48 5.2 Policy Implications and Conclusion.. ..... ............50 - viii - Appendix A: A Note on Traditional Healers ...........................52 Appendix B: Econometric Specification .............. .... . ..... ...54 Appendix C: Derivation of Elasticities ............................... 59 References ............ ***.............***a*....**.... 63 - ix - List of Tables Table 2.1: Health Indicators for C6te d'Ivoire and Lower Middle Income Countries (Averages) ........ .** ..........-........8. 8 Table 2.2: The Regional Distribution of Welfare in Cote d'Ivoire Consumption Quintiles, Percentages ..... .... ...... 8 Table 2.3: Percentage of Individuals who report An Illness or Injury During the Past Four Weeks; by Location, Age and Sex ....... 11 Table 2.4: Mean Number of Restricted Activity and Sex Days During the Past Four Weeks; by Location, Age and Sex .... ........ 12 Table 2.5: Percentage of Individuals with an Illness or Injury Who Obtained Medical Care (From Doctors, Nurses or Midwives)...13 Table 3.1: Summary Statistics, Rural Adults..*... ..... 22 Table 3.2: Summary Statistics Rural Children with Illness or Injury ... 23 Table 4.1: Determinants of Decision to Seek Medical Care in Case of Illness (Logit) ........................................................... 25 Table 4.2A: Multinomial Logit Model of Provider Choice, Determinants of Choice between Doctor, Nurse, and Home Care Adults in Rural Areas with an Illness or Injury .......... .......... 32 Table 4.2B: Income and Travel Time Elasticities of the Probability of Choosing a Doctor or Nurse..... ........... . ...... ....... ...... . .32 Table 4.3A: Restricted Multinomial - Logit Model, All Adults ........... 35 Table 4.3B: Income and Travel Time Elasticities ........................ 35 Table 4.4A: Demand for Medical Consultations OLS and Two-Step Estimates (Adults) ............................................................... 38 Table 4.4B: Elasticities of Quantity Demand (Adults) ..........* .........38 Table 4.5: Determinants of Decision to Seek Health Care Infants and Children (Logit) ........................................... 42 Table 4.6A: Multinomial Logit Model of Provider Choice (Children) ...... 43 Table 4.6B: Income and Travel Time Elasticities from Provider Choice Model (All Children). .................... 43 -x- Table 4.7A: Demand for Medical Consultations (Children) OLS and Two Stage Procedures ...... . ... ... ....................... . .47 Table 4.7B: Elasticities of Quantity-Demand (Children) ................. 47 Table 5.1: Total Demand Elasticities...*_*........................... 49 Table A.1: Number of Persons with Healer Consultations, Age Group by Place of Consultation ........................o ........ 53 Table A.2: Number of Persons with Healer Contacts Age Group by Sex....53 Figure 1 .. .*............. ,e. ....... .......*18 Introduction Besides the social desirability of improving health, the health status of the population is relevant to the economic development of a country for two reasons: First, as an indicator of economic development, it shows the ability and success or failure of a country to provide for the most basic needs of the people (food, adequate sanitary conditions, shelter). The correlation between such crude indicators as child mortality and life expectancy on the one hand, and per capita income on the other, is very robust and has been extensively documented (e.g. Preston 1975, 1980; WDR, 1984). Secondly, health - as a form of human capital - is an input for the further development of a country. There is ample evidence to suggest that health plays an important role in school enrollment and school performance of children (see for instance, Edwards and Grossman 1979, Bartel and Taubman 1979, Cooper and Rice 1976) and in labor supply and productivity of adults (Berkowitz et al. 1983, Grossman 1975, Grossman and Benham, 1974) and on earnings (Luft, 1976). Furthermore, high infant and child mortality rates are among the most important factors related to high fertility rates, which in turn play a crucial role in development. Life expectancies as low as 38 years at birth may be found in the poorest among developing nations such as Guinea and Somalia. 1! In middle income countries which include Cote d'Ivoire, life expectancies average 55 for males and 58 for females. In comparison most developed countries have attained life expectancies well above 70 years of age. Similar disparities exist in infant mortality rates. The highest infant mortality rate in the 1l 1982 figures. - 2 - world exists in Afghanistan where 205 of every 1,000 live born infants die during the first year of life. In the majority of developing countries exhibit infant mortality rates in excess of 90 infants per 1000, compared with average of 10 in the industrial market economies. In light of the above it is not surprising that improving the population's health features as a major goal on the agendas of many local and national governments in less developed countries (LDCs). Although many other factors are relevant for achieving this goal (adequate food supplies, sanitation, education), providing medical care to those who need it plays a central role in improving health. It is usually quickly recognized that a pure market approach to providing medical goods and services is unlikely to produce satisfactory results. The general arguments for some form of government intervention and regulation are well known. In some cases, health-care is a pure public good (air quality control, general anti-epidemic campaigns), in other cases large externalities exist (inoculations against contagious diseases). And where medical care can be identified as a private good, a market approach may lead to outcomes that are judged to be unacceptable on equity grounds. Add to this: Allegedly widespread consumer ignorance, the need for quality control, the scarcity of private funds for investments in human capital (medical education) and in non-human capital (hospitals), and a heavy government hand in the health-care sector can easily be explained. Indeed, in industrialized countries as well as in LDCs, the health care sector is without exception among the most extensively regulated industries. In LDCs, government intervention in the health-care sector has often lead to a system that provides medical care free-of-charge or for a price that bears little resemblance to the marginal cost of the service or product. General revenues serve as the major source of financing. Revenues from user charges usually contribute less than 10 percent of recurrent expenditures (Ainsworth, 1983, de Ferranti, 1985). Unfortunately, in their quest to provide medical care free-of-charge or at very low cost, governments have sacrificed the availability of care in order to maintain affordability. Public budgets have been proven to be insufficient for providing adequate care to the majority of the population. Though other factors have also played a role, it seems fair to say that the combination of highly subsidized care and insufficient general funds has lead to a general structure of the health care sector that has the following characteristics: (i) Quantity rationing has taken the place of the price mechanism. Where financial resources are insufficient to finance a health-care system that meets the need of the population, effective demand is constrained by the sheer lack of medical facilities, personnel and drugs. (ii) Available supply is unequally distributed, with a strong urban bias. In many LDCs, doctors, nurses and hospital beds are concentrated in the cities, in spite of the fact that the vast majority of the population lives in rural areas. -4- (iii) Modern curative care ("high-technology" hospitals, "western" doctors) has won the battle over scarce resources, leaving little to finance preventive activities and basic care. This is particularly damaging in LDCs where the leading causes of death are infectious and parasitic diseases. Many of these diseases can be prevented or treated adequately with relatively cheap and simple techniques. (iv) With barely enough resources to cover salaries and the most basic drugs, there is no money left for equipment or for maintenance of the existing facilities. Consequently, available resources are used inefficiently (doctors without equipment) and the limited amount of medical care that is provided, is generally of low quality. Growth projections for most of the developing world are not optimistic (WDR 1985, 1986) and many LDCs are coping with IMF-type austerity programs and World Bank-type structural adjustments that usually put severe constraints on the government budget. In recent years, there has been a growing awareness of the need to find new sources of finance in order to expand social services in developing countries and in some cases avert their virtual collapse. Whereas funds for capital investments are often available through international donors the public sector must find new ways to finance operating and maintenance costs, i.e., recurrent costs. Much of the discussion focuses on the usefulness of user fees in the health care sector. (Birdsall 1983, de Ferranti 1985). In most developing countries there appears to be a political consensus in favor - 5 - of free medical care. In C8te d'Ivoire this is manifested in a presidential commitment not to impose fees on medical services. The discussion on how to finance medical care no longer questions the need to search for resources other than general public funds. Rather, the focus is on where and how to introduce so called "user fees", i.e. charges to those who actually use the medical services. 11 The benefits of this option go well beyond revenue raising per se. First of all, if goods and services are priced adequately (i.e. are set equal to their marginal costs), society will allocate it's scarce resources efficiently. For instance, simple measures of preventive medical care are likely to get higher priority under a marginal cost-pricing scheme, because the cost of a unit of preventive care is well below that of a unit of curative care. Furthermore, when prices are zero, there is excess demand for certain goods and services, a situation that can be remedied by the introduction of user charges. The strongest argument in favor of the current policy to provide medical care free-of-charge (or at very low cost), is that it promotes equal access by eliminating financial barriers. However, given the distorted regional distribution of facilities, the policy does not result in an equitable health care delivery system. In fact, the policy tends to be regressive with most beneficiaries living in the higher income urban areas. Nevertheless, the introduction of user fees into a system that is currently providing goods and services free-of-charge raises many questions regarding both the efficiency and the equity of the system. Among them: / For a discussion of other options (.e.g. many variants of risk sharing) see de Ferranti 1985. - 6 - (i) For which goods and services are fees desirable? Should the fee be equal to the marginal cost of the product? Can the marginal cost be measured? Should the fee be high enough to recover all cost, or should certain services be subsidized? (ii) Though money prices are currently zero, the private cost of obtaining medical care can still be substantial. Travel time is often very long and the monetary cost of traveling can be a substantial outlay for poor families. How can user fees be introduced without making the total cost of obtaining medical care prohibitively high? (iii) Many studies show high income elasticities for medical care. Will poor families be able to pay the price, if money fees are to be set high enough to recover a substantial part of the total cost? In this paper we will make a start with answering some of these questions. Our focus will be on current health care utilization patterns in rural Cote d'Ivoire. We will investigate the extent of quantity rationing for medical services provided by doctors and nurses, by estimating own and cross time-price elasticities for these services. We will also look at the corresponding income elasticities. In the next section we will present background information on the health-care system in C6te d'Ivoire. In Section 3 we present the anayltical framework used, as well as descriptive statistics on health status and health care utilization. The data stem from the Ivorian Living Standards Survey. In Section 4 we present the estimation results for adults, infants and children. Section 5 summarizes the main results and draws policy conclusions. II Background Information on C8te d'Ivoire 2.1 The Health Care System In order to provide a general background for the analysis presented in the subsequent sections, we now present some general information on the economy and the health care system in Cote d'Ivoire. Since independence (1960), The C6te d'Ivoire has seen a steady economic growth, from a level of $145 per capita in 1960 up to $1,207 in 1980, I/ the high point of its economic development. During this period crude health indicators improved significantly. The infant mortality rate decreased from 167 in 1960 to 119 in 1982, while life expectancy at birth increased from 39 to 47 years (Table 2.1). Still, these indicators are little better than those prevailing in neighboring West African countries which are much poorer, and they compare unfavorably to those of an "average" lower middle income country. Large differences of health exist within the country. In Abidjan life expectancy was estimated at 56 years in 1979, compared with only 39 years in the rural Savanna regions , and 50 years in the urban Savanna regions. Child mortality rates in rural areas exceed those in Abidjan were twice as high as child mortality prevailing in rural areas. Part of these differences are likely to be related to the unequal distribution of welfare in The Ivory Coast. Based on the value of total household consumption 21 only 3.3 percent of those in the lowest quintile live 11 All dollar equivalents are in current values for the relevant years. 21 Total Household consumption is measured as the sum of cash expenditures on consumption goods, plus the value of home grown produce consumed by the household. -8- in Abidjan, while 45.7 percent of "the poor" live in the Savanna area (Table 2.2). Just 3.9 percent of "the rich" live in the Savanna, while 42.8 percent of them live in Abidjan. 11 This large, urban-rural welfare gap is paralleled by the distribution of health care facilities. TABLE 2.1: Health Indicators for C6te d'Ivoire and Lower Middle Income Countries (averages) Lower Middle C6te d'Ivoire Income 1960 1980 1960 1980 Crude Death Rate 24 17 20 12 Infant Mortality Rate 167 119 114 89 Child Mortality Rate 40 23 28 13 Life Expectancy at Birth 39 47 45 56 SOURCE: The C6te d'Ivoire Country Economic Memorandum, the World Bank, 1986. TABLE 2.2: The Regional Distribution of Welfare in C6te d'lvoire Consumption Quintiles, Percentages. QUINTILES Total 1 2 3 4 5 Abidjan 18.8 3.3 5.2 13.2 29.2 42.8 Other Cities 22.4 7.0 18.1 28.2 27.1 31.8 Rural East 24.7 35.2 35.4 22.5 19.9 10.6 Rural West 15.2 8.8 19.6 21.9 14.9 11.0 Rural Savanna 18.9 45.7 21.8 14.1 9.0 3.9 Total 100.0 1000 100.0 100.0 100.0 100.0 SOURCE: Glewwe (1987) l/ For a more extensive assessment of the distribution of welfare in the Cote d'Ivoire see Glewwe (1987). - 9 - About 40 percent of the population in Cote d'Ivoire lives in urban areas. Abidjan alone accounts for a population of 1.6 million, or about 17 percent of the total of 9.3 million (1983). All major hospital facilities are in the cities. The two university hospitals (about 1300 beds in total) are situated in Abidjan, while the five regional hospitals (general hospitals with a capacity of about 275 beds) are found in the cities of Bouake, Man, Daloa, Abengourou and Korogho. Together these hospital facilities account for 41 percent of all beds. Rural areas are served by small local hospitals, maternity and child care units, dispensaries and mobile health units. The hospital sector employs 70 percent of all doctors, 45 percent of all midwives and over 50 percent of all nurses. About 60 percent of all doctors are based in Abidjan. The overall health manpower situation is unbalanced. In 1983 there were about 600 doctors, 2200 nurses and 1000 midwives, but virtually no skilled auxiliary Workers. C Given the current health manpower training system, the World Bank projects that the number of western doctors will increase from 6.5 per 100,000 population in 1983 to 7.8 in 2000. The number of nurses per capita will increase from about 24.9 to 26.5. Thus, the already low nurse/doctor ratio of 3.8 will further decrease to about 3.4. All health workers are paid by the government. Medical care is, in principle, provided free of charge. For 1984 the government health budget was / There is also an unknown number of traditional healers. Furthermore there are about 7000 "journaliers" working in the health care sector, ranging from gardeners and chauffeurs to laboratory assistants and X-ray machine operators. Most of them are unskilled or received informal training only. - 10 - 32.6 billion CFAF, or 6.8% of the total budget. 1! More than 75 per cent of this budget is for personnel cost, about 8 percent for drugs and the rest for materials, equipment, maintenance and other operating cost. Current manpower projections indicate that the total health budget will soon be insufficient even to cover personnel cost only, unless the budget grows much faster than other parts of the government budget, or unless other financial resources are found. The general quality of the existing facilities leaves much to be desired. A 1979 study showed that of the 309 dispensaries, one third was more than 20 years old, only 19 percent had piped in water and just 21 percent had a working water pump. Pharmaceuticals are in short supply and two thirds of the dispensaries, which are supposed to serve as referral centers, lack any means of transportation. Of the 126 Maternal-Child Health Care units (MCH), 45 percent had no water and 31 percent no electricity. Only 20 percent are able to provide preventive services and general health education, though these tasks are supposed to be part of the workload of all MCHs. The two university hospitals in Abidjan have occupancy rates well in excess of 100 percent, but most of the hospitalized patients are just waiting for the arrival of necessary drugs and other supplies and/or for the repair of equipment. In one university hospital two of the six ORs have not been used during the past three years because basic equipment is broken and funds are lacking for replacement. In light of the above, it is not surprising that there is increasing pressure to search for alternative ways to cover the recurrent costs of the - Recurrent budget only. - 11 - Ivorian health care system. The subsequent analysis aims at providing results that will help to make informed decisions regarding this issue. 2.2 Health Status as Reflected by The Ivorian Living Standards Survey The ILSS which is discussed in detail in Section 3.2 enables us to go beyond the generally available mortality and life expectancy data. It contains information about morbidity, such as the incidence and severity of illness in the population, which is given below by age, sex and geographic location. The weakness of these data is that they are based upon subjective assessments of own states of health. In terms of self reported health status, about 30 percent of the individuals interviewed by the ILSS reported to have suffered from an illness TABLE 2.3: Percentage of Individuals who Report an Illness or Injury during the past four Weeks; by Location, Age and Sex Abidjan Other Cities Villages Ivory Coast Age Male Female Total Male Female Total Male Female Total Male Female Total 0-5 30.73 35.22 33.19 30.26 29.93 30.10 32.08 30.05 31.15 31.48 30.98 31.26 6-15 21.99 20.05 20.98 23.03 20.60 21.84 20.63 19.89 20.28 21.43 20.98 20.27 16-35 26.41 32.93 29.86 27.06 31.57 29.70 23.97 26.81 25.61 25.58 29.40 27.69 36-49 40.80 40.32 40.56 44.80 44.59 44.69 46.08 42.27 43.70 44.60 42.40 43.32 50+ 32.05 42.00 35.94 57.52 51.22 54.24 54,80 55,73 55.26 52.77 53.09 53.32 Total 27.81 30.79 29,36 30.37 30.77 30.57 30.99 31.21 31.11 30.26 31.03 30.67 - 12 - or injury during the four weeks prior to the survey (Table 2.3) 1'. No major sex differentials exist, but there is a distinct age profile. Young children (0-5) show an incidence of illness and injury equal to the overall average, while older children (6-15) show the lowest incidence rate. Adults (16 and over) show a monotonous increase of illness with age. Table 2.4 reflects the anticipated decline in health associated with age: mean restricted activity days increase with age. The mean restricted activity days in rural areas is 7.7 for males and 8.7 for females compared with little over five days in urban areas. Thus, while the incidence of self- reported health problems appears to be higher in the cities, health problems are on average more severe in rural areas. TABLE 2.4: Mean Number of Restricted Activity Days During the Past Four Weeks; by Location, Age and Sex Abidjan Other Cities Villages Ivory Coast Age Male Female Total Male Female Total Male Female Total Male Female Total 0-5 5.57 4.46 4.93 4.73 5.38 5.04 6.11 6.31 6.21 5.74 5.74 5.74 6-15 3.90 4.03 3.97 3.82 3.57 3.71 5.08 4.83 4.96 4.56 4.36 4.46 16-35 3.60 5.52 4.72 3.68 5.63 4.78 7.53 7.32 7.40 5.37 6.40 5.98 36-49 3.88 8.48 6.11 4.47 7.06 5.87 7.50 7.45 6.47 6.07 7.51 6.90 50+ 8.36 10.29 9.24 10.17 7.73 8.97 10.97 12.47 11.71 10.66 11.53 11.09 Total 4.45 5.63 5.09 4.95 5.64 5.31 7.52 7.88 7.71 6.40 6.96 6.69 For the sake of completeness, we present data on individuals who live in Abidjan, Other Cities, and the Villages. Most of our discussion, however, will focus on rural areas, i.e. the Villages. - 13 - Table 2.5 shows the distribution of visits to formal health workers i.e. doctors nurses and midwives. Since obstetric care is included in the table it is no surprise that prime age females usually obtain more medical care than prime age males. In the oldest cohort, where obstetric care is no longer relevant the reverse occurs: elderly females obtain less formal care than elderly males, with the exception of Abidjan. Although the elderly are less healthy than younger adults, they tend to consume less medical care, particularly in rural areas. TABLE 2.5: Percentage of Individuals with an Illness or Injury Who Obtained Medical Care (From Doctors, Nurses or Midwives) Abidjan Other Cities Villages Ivory Coast Age Male Female Total Male Female Total Male Female Total Male Female Total 0-5 68.25 68.97 68.67 69.57 60.25 65.00 46.26 41.91 44.36 54.36 51.44 52.99 6-15 50.68 61.64 56.16 50.45 52.08 51.21 41.94 40.85 41.43 45.60 47.64 46.56 16-35 53.95 62.20 58.72 53.85 57.49 55.89 39.59 47.33 44.27 47.52 53.88 51.26 36-49 60.78 68.00 64.36 62.50 59.09 60.66 45.39 38.89 41.46 52.42 47.29 49.48 50+ 60.00 47.62 54.35 52.31 46.03 49.22 32.30 31.21 31.76 37.53 34.70 36.14 Total 57.45 63.54 60.77 57.05 55.63 56.32 40.59 40.10 40.33 47.30 47.95 47.64 This straight forward presentation of the data clearly illustrates the severity of health problems in The Ivory Coast. Roughly one-third of the population is ill during any given 4-week recall period, and on average, those who are ill loose about one-quarter of their time due to the illness. - 14 - III. Analytical Framework and Data 3.1 Analytical Framework Only a handful of studies of household demand for health care exist to date. The majority of studies has focused on the discrete choice problem of choosing among alternative providers. These include Gertler et al. (1986), Mwabu (1986), Birdsall and Chuhan (1986), Akin et al. (1985 and 1986) and Heller (1982). A conventional analysis of the amount of care demanded, measured by medical expenditures or number of consultations is found in Musgrove (1981) and Heller (1982). Musgrove found that income effects in Latin America are substantially higher than income effects in developed countries. I/ In general, the literature has not been able to show that money prices affect utilization. However, Gertler et al. using a model in which price effects depend on income show that health care demand is highly elastic with respect to prices for low income groups, but that the price effect diminishes as income increases. 1/ Income elasticities in the various Latin American countries tended to concentrate around unity. Income elasticities not exceeding 0.3 are commonly found in the developed countries. This is shown to be the case for the number of health care visits by individuals (van de Ven and Van der Gaag, 1982, Acton, 1975), by the household (Holtman and Olsen, 1978) and for aggregates of the population (Benham and Benham, 1975). Similar results were obtained for health care expenditures by individuals (Phelps, 1975). Income elasticities of demand for pediatric care tend to be considerably higher, as shown by Colle and Grossman (1978). - 15 - As we mentioned earlier, travel time is expected to be a particular powerful rationing devise in poor countries, where the majority of the population inhabit rural areas and health infrastructures are concentrated in the cities. Furthermore, Acton (1975, 1976) has shown that when money prices are low, time becomes the dominant rationing mechanism. Past studies in developing countries have not been able to confirm this, primarily due to data limitations. The main purpose of this paper is to identify the impact of travel time and other economic variables on health care utilization in rural C8te d'Ivoire, where medical services are rendered free of charge. In order to address this issue we define a general health care demand function.: M = M(P, Y, H, Z) with M the demand for medical care P a vector of prices, including time prices Y a measure of income Z a vector of socioeconomic variables H a measure of health capital Throughout this paper we will first look at the determinants of market entry, i.e. we analyze the question of who obtains medical care in case of an illness or injury. M, the demand for medical care, is thus defined as a zero-one dummy variable. We adapted the standard logit model for this part of the analyses. Secondly, we estimate a provider choice model that gives the probabilities of seeking care from a doctor or a nurse, relative to not - 16 - seeking care at all. 11 We use the multinomial logit model for this step of the analyses. Finally, we analyze the number of consultations with each provider using a two step estimation procedure that corrects for the selectivity bias that stems from the fact that a positive number of consultations is only observed from those who have chosen a particular provider. 2/ 3.2 Data and Summary Statistics A. The Ivorian Living Standards Survey The data used in this study are drawn from the Ivorian Living Standard Survey (ILSS). This multi-purpose household survey, which aims at measuring many socioeconomic factors relevant to the living standards of Ivorian households, was started in February 1985. 31 During the first 12 month period, 1588 households will be interviewed, of which 950 were located in rural areas. Approximately 93 percent of these households are farming households. Detailed information on health-care utilization is obtained from all household members who reported an illness or injury during the four weeks prior to the interview. The ILSS also contains extensive information on many socioeconomic aspects relevant to the demand for medical care. 11 The alternative of seeking care from a traditional healer is ignored (see Appendix A). 21 For a more explicit description of the econometric specification see Appendix B. 31 For detailed information on this survey, see Grootaert, 1985. - 17 - The ILSS also contains extensive information on many socioeconomic aspects relevant to the demand for medical care. In this study we use total household consumption ("income") as a measure of the household's economic well-being. Variables such as age, sex and years of schooling are also included as exogenous variables. Health status is indicated by an individual's own assessment of whether or not he suffered from an illness or injury during a 28-day recall period. Recall that Table 2.3 shows the percentage of the population that report an illness during this period. Of the 30 percent reporting an illness, about 57 percent obtained some form of formal or traditional health care. Figure 1 depicts the distribution of care by type of practitioner. While more than half of those who obtained medical care in Abidjan consulted a doctor, in the villages only 17 percent saw a doctor. Still fewer rural dwellers consulted a traditional healer (11 percent), while the majority of rural dwellers consult a nurse (58 percent). Information on medical consumption includes the number of visits to each type of provider, expenditures on consultations (if any) and expenditures on drugs. In addition to household data, the ILSS collects community level information in rural areas. The rural component of the household survey was comprised of 56 sample clusters, which roughly correspond to small villages. However, the community survey was completed in only 52 rural clusters. Relevant to the current study is the data on the availability of various types of health care facilities. Travel time is reported for the nearest available facility of each type (hospital, clinic, maternity center, etc.). When a provider is available in the village, travel time is recorded as zero. HEALTH PRACTITIONER CONSULTED L Doctor Z Healer BY RESIDENCE m Nurse Ea Others Abidjan Other Cities Rural otx x Total ^o~~~~~~0 - 19 - B. The Rural Sample and Variables The rest of this study deals strictly with the rural segment of the population. Summary statistics for adults (everyone over 16 years of age) are shown in Table 3.1; summary statistics for infants (under 6) and toddler (6- 15) are shown in Table 3.2. In three out of the 52 clusters (villages) travel time to sources of health care was not known. Since the analysis presented here draws heavily on travel time information these clusters were deleted from the sample. Of the remaining 49 clusters, only 12 had a nurse, and none had a medical doctor. All of the individuals in the sample belong to one of 665 households interviewed in these clusters. The overwhelming majority of households, i.e. 637, was headed by males. The mean age of heads of households is 48.87 (s.d. = 13.96) and their mean years of schooling is only 1.05 (s.d. = 2.50). Demographic variables such as age, education, sex, and the composition of the household (number of adults and number of children) enter the model in a simple linear fashion. Non-linearities in age were accounted for by dividing the sample into age groups. The education variables are years of schooling in the adult sample and years of father's schooling in the younger age groups. Educational attainment is typically low and there is little variation in schooling. Approximately 83 percent of the adults had no education, with the remainder ranging from 1 to 12 years of schooling. In the combined child sample, about 87 percent had fathers with no education, while less than 2 percent had fathers with more than 10 years of schooling. Since there is even less variation in mother's schooling, this variable was not included in the estimation. Whether a person chooses a doctor or a nurse should also depend on certain preconceptions or cultural biases of the - 20 - decision-maker. Such prejudices will not effect the amount of health care obtained once a provider has been selected. Cultural biases in favor of one type of health provider and against another may be expressed as a function of a person's nationality, ethnic group, religionr or tribal affiliation. Our sample was almost strictly Ivorian, and unfortunately the remaining variables were not available (future LSMS surveys will incorporate such variables). We opted for a regional dummy variable (Savanna) as a proxy for cultural differences. This variable only enters the discrete choice models. An individual's health status is measured by the number of days during the past four weeks that an individual was not restricted in his normal activities. For adults and older children this is obtained by subtracting the number of days someone was restricted by an illness or injury from the 28 day recall period. In the case of infants, for whom this information is not available, we use 28 minus reported sick days. This variable is expected to reduce the probability of seeking medical care. It is important to note that elderly persons typically have more sick time than prime age adults; they can expect a certain number of restricted activity days to be their normal state. This implies that an elderly person would require a relatively large number of restricted activity days in order to motivate an initial visit to a health practitioner. Thus, the anticipated positive effect of restricted activity days on the probability of seeking medical care should decrease with age. Conversely, the positive effect of unrestricted days on the probability of seeking medical care is likely to increase with age (i.e. become less negative). For this reason we include an interaction term between our health measure and age, in the adult discrete choice models. In the case of children, we will assume that the valuation of - 21 - the child's health will depend on the assessment by the parents rather than on the child's own assessment. Therefore we included an interaction of health and the father's education in the "child" discrete choice model. Once a person selects a health care provider, healthiness is likely to affect the number of medical consultations in opposite directions. On the one hand, the healthier the person the fewer the number of consultations needed. On the other hand relatively healthier patients are better equipped to undertake trips to their preferred provider. In order to see which of the two effect prevails, the unrestricted days variable enters the quantity demand regressions in a quadratic fashion. - 22 - TABLE 3.1: Summary Statistics Rural Adults with Illness or Injury SAMPLE Ages 16 - 49 Age 50 + Number of persons with positive sick time 702 492 VAR IABLES Standard Standard Mean Deviation Mean Deviation Endogenous Probability of obtaining formal medical Care .43 .50 .32 .47 Probability of seeing a doctor .10 .31 .08 .27 Probability of seeing a nurse .32 .48 .25 .43 number of doctor consultations 31 1.46 .31 1.88 number of nurse consultations .92 1.98 .95 2.34 Exongenous Travel time to doctor (in hours) .86 .70 .92 .95 Travel time to nurse (in hours) .56 .62 .56 .63 Income; annual household consumption (in millions of CFAF) 1.32 1.21 1.09 .96 Years of age 32.82 10.00 61.56 9.78 Sex (male = 1, female = 0) .37 .48 .51 .50 Years of education 1.46 2.82 .12 .72 Number of adults in the household (age 16+) 5.61 4.93 5.17 3.84 Number of children in the household (age < 16) 5.66 5.71 4.36 4.39 Number of unrestricted activity days (maximum = 28) 20.60 8.56 16.06 11.05 Savanna resident ( 1 answer is yes, = 0 otherwise) 0.29 0.45 0.32 0.46 - 23 - TABLE 3.2: Summary Statistics Rural Children with Illness or Injury SAMPLE Ages 0 - 5 Age 6 - 15 Number of persons with positive 429 380 sick time VARIABLES Standard Standard Mean Deviation Mean Deviation Endogenous Probability of obtaining formal medical Care .46 .50 .43 .50 Probability of seeing a doctor .08 .27 .07 .24 Probability of seeing a nurse .38 .49 .36 .48 number of doctor consultations .19 .95 .17 .79 number of nurse consultations 1.02 1.89 .96 1.81 Exogenous Travel time to doctor (in hours) .74 .64 .79 .81 Travel time to nurse (in hours) .46 .58 .43 .57 Income; annual household consumption 1.40 1.26 1.41 1.20 (in millions of CFAF) Years of age 2.41 1.60 9.52 2.70 Sex (male = 1, female = 0 .52 .50 Years of education of father 1.05 3.12 .79 2.55 Number of adults in the household (age 16+) 5.57 4.96 5.19 4.34 Number of children in the household (age < 16) 6.67 5.50 6.73 5.52 Number of unrestricted activity days (maximum = 28) 21.92 7.52 22.88 6.80 Savanna resident ( 1 if answer is yes = 0 otherwise) 0.21 0.41 0.23 0.42 - -24 - IV. Estimation of Demand for Health Care 4.1 Estimation Results for Adults A. Entry to the Health Care Market In order to quantify the effect of the exogenous variables on the probability of seeking medical care, we estimated a market-entry equation in Logit form for all persons with positive sick time (the dependent dummy variable equals one if the person consulted a medical practitioner). In Table 4.1 we present the estimation results for prime age adults (i.e. for persons between the ages of 16 and 49), for elderly persons, age 50 or above, and finally for the pooled adult sample. The coefficients(the B's) are reported with asymptotic t-values. Throughout this paper, the marginal effects are also reported for all dichotomous regressions. A formal derivation of the slope term is given in Appendix A. In all the regressions in Table 4.1, the age variable has the expected negative effect and it is statistically significant in the elderly and pooled samples. We also ran the pooled regression with quadratic and splined age terms but this did not improve the results. I/ Age splines turned out to be significant in some of the child care regressions. All of the pooled models for children under the age of 16 presented here include an age spline. - 25 - TABLE 4.1: Determinants of Decision to Seek Medical Care in Case of Illness (Logit) Prime Age Adults Elderly All Adults (Age 16 - 49) (Ages 50 + Marginal Marginal Marginal 8 T effect a T effect 8 T effect Constant 2.76 (3.36) 0.676 3.69 (2.99) 0.792 2.59 (5.50) 0.610 Average travel time 0.38 (2.37) -0.090 -0.36 (2.06) -0.076 -0.36 (3.03) -0.081 Income 0.24 (2.86) 0.059 0.13 (0.93) 0.027 0.20 (2.69) 0.048 Age -0.05 (2.60) -0.013 -0.07 (3.61) -0.015 -0.05 (5.79) -0.011 Male 0.00 (0.02) 0.001 0.15 (0.73) 0.032 0.04 (0.29) 0.011 Education -0.01 (0.30) -0.003 -0.03 (0.18) -0.006 -0.02 (0.61) 0.009 Adults -0.08 (2.04) -0.020 -0.01 (0.19) -0.002 -0.06 (2.30) -0.014 Children 0.03 (1.46) 0.008 0.07 (1.79) 0.016 0.04 (2.01) 0.010 Unrestricted days -0.15 (3.33) -0.035 -0.20 (2.03) -0.043 -0.11 (5.36) -0.026 Unrestricted days x Age 0.002 (1.97) 0.0005 0.003 (2.79) 0.001 0.002 (4.00) 0.0004 Savanna -0.15 (0.72) 0.036 0.42 (1.65) -0.090 -0.25 (1.60) -0.058 Log likelihood -444.65 -286.64 -737.76 2 x 70.16 48.81 119.04 Income elasticity 0.183 0.095 0.156 Travel time elasticity -0.149 -0.181 -0.154 The measure of healthiness, i.e. the number of unrestricted activity days has a significantly negative impact on utilization overall. Just as anticipated, this effect is dampened somewhat at old age. The positive sign of the healthiness and age interaction reveals that ceteris paribus, an older person requires relatively fewer healthy days (i.e. more sick days) in order to have the same probability of seeking health care as a younger person. Since home care which is normally provided by adults, is viewed as a substitute for formal medical care, the number of adults in the household is expected to reduce the probability of seeking formal care. Since adults in - 26 - the extended households must also devote a certain portion of their time to child care, the number of children in the household is likely to increase the probability of seeking care. Estimation results confirm our expectations. The household size variables always have the anticipated sign and are usually significant. The remaining demographic variables appear to be less important determinants of market entry. Living in Savanna areas has a negative impact on market entry in all age categories, but is significant at a 10% level only in the elderly category. Sex and education do not have any effect on the decision to seek health care. With the exception of health status, economic variables are the most important determinants of health care utilization. Individuals living in households with a relatively high income, show ceteris paribus a significantly larger probability of seeking care than their poorer counterparts. The income elasticity of the pooled sample, for instance, is 0.17 (at the sample means) comparable to the results usually obtained for industrialized countries, but well below the unit income elasticities obtained by Musgrove (1984). l/ The travel time variable was obtained by averaging travel time to the nearest doctor and travel time to the nearest nurse. Perhaps the most important result is found with respect to this variable. The estimation / Note that Musgrove's estimates refer to health care expenditures while the current analyses deals with the probability of seeking care. - 27 - result implies a time-price elasticity ranging from -0.24 to -0.34 1- at the sample means. Thus we were able to confirm the proposition that in the absence of money prices, other private costs of obtaining medical care play the role of the conventional price mechanism. It should be stated here that, even though actual fees for medical care are zero, total out-of-pocket expenditures are likely to be positive due to transportation costs. Unfortunately, information on the money cost of travel that is associated with the consumption of medical care was not available in the survey. The goodness of fit criterion X , which is given in Table 5.1, is based on the general log likelihood ratio of the form LR = L*(B)/L*(O). L*(B) is the value of the maximized log likelihood using the estimated parameters and L*(0) is the maximized log likelihood function under the null hypothesis that all B's are equal to zero. It can be shown that -2*ln(LR) is approximately distributed as a X (chi-squared), where k degrees of freedom are equal to the number of zero restrictions (Wilks, 1962). 2 Throughout this study, X statistics are sufficiently large to, reject the null hypothesis that the estimated B's are equal to zero. 1/ Comparable estimation procedures are found in Coffey (1983). The time- price elasticity reported there, of entry into the medical care system for low income females in Texas is virtually identical to the above results. - 28 - Finally we tested the validity of pooling across age groups. To do this we used another approximation to the X test, also known as the Wald test. 2 1 x [81 - 82] [V1 + V2] [el - 82] Where 0, is the parameter vector belonging to prime age adults, 82 is the parameter vector from the elderly regression and V1, V2 are the respective variance matrices. The result was 15.4, well below the 95 percent critical level of 19.7. Consequently we cannot reject the null hypothesis that el = 82, hence pooling is appropriate. Before showing how the above results hold up when other models of demand for health care are estimated, concerns about selectivity bias should be mentioned. Although data was available for all persons who completed the interview, the estimating sample excludes all healthy people. To see whether this severely biases the sampled data, the Probit demand equation was estimated conditional upon the probability of being ill or injured. The procedure (due to van der Ven and van der Praag, 1981) yielded small changes in the coefficients and virtually no change in the slopes. Therefore it was concluded that no severe selection bias arose due to the exclusion of health persons. B. Provider Choice, a Multinomial Logit Model In the previous section we analyzed the decision to seek medical care in case of an illness or injury: when ill, an individual either obtained some form of medical care or obtained no care at all. In table 3.3 of the previous - 29 - section we saw that for all rural adults who obtained medical care, the average number of visits to a doctor is .34 and to a nurse 1.14. In this section we first analyze this choice of health-care provider: to visit a doctor or a nurse, relative to not obtaining medical care at all. Then we will turn our attention to the number of consultations with each of these providers. We specify a multinomial logit model of the following form: 2 ln (P./Po L aj. Tjk + y.Z i ° k ~1 Sj jk Y;j with Pj The probability of choosing provider j j = 1 Doctor j = 2 Nurse, and Tjk Travel time to a given provider Z Composite of socioeconomic variables ejk,Yj The corresponding coefficients for choice j PO is the default option, i.e. it is the probability of not seeking care when ill, with coefficients normalized to zero. Thus, ln(P./PO) is the logarithm of the probability of consulting provider j, relative to the probability of not seeking care at all. The composite Z contains the same exogenous variables as in the previous section. The Tk variables denotes travel time, and may be interpreted as choice-related price variables. Note that travel time for the "don't go" option is equal to zero. - 30 - It is easy to see that the log-odds ratio of any two alternatives depends on all choice related variables and on traits of the decision maker which are common to all choices. Thus the multinomial logit does not exhibit the Independence from Irrelevant Alternatives (IIA) property (see McFadden, 1981). The interdependence of all alternatives is reflected in the elasticity of Pj with respect to Xk, where Xk represents any of the exogenous variables. 2 E. =(8. a P x jk jk _1- jk jk k From the above, one may calculate own time-elasticities (j = k), cross time elasticities (j i k), or elasticities with respect to a trait of a decision-maker (replace 8 by y). A derivation of various elasticities is given in Appendix B. Estimation results are given in Table 4.2A. Time prices are represented by the time needed to travel to the nearest doctor and travel time to the nearest nurse. All own time-price effects have the expected negative sign. In the doctor alternative the coefficient is -1.95 with a t-value of 4.03. In the nurse alternative there is a highly significant negative own time-price effect of -0.20. In both alternatives cross time effects are positive and significant at the 0.99 significance level. These results suggest that in Cote d'Ivoire the services of nurses and doctors are substitutes, rather than complements. The income effect in both alternatives is positive and significant. Income and travel time elasticities are given in Table 4.2B. - 31 - The Multinomial Logit Model strongly confirms and augments the results obtained from the simpler bivariate model: own time-price effects are negative, cross time-price effects are generally positive. The magnitude of these effects is substantially greater than those found by Akin et al. in the Philippines (1981, 1986). We finally note that the impact of socioeconomic variables are generally stable across the entry-to-the-market and provider choice models. In particular, the coefficient of age is negative and highly significant. The sex effect (of being a male) is negative an insignificant in the nurse alternative, but positive and significant in the case of doctor visits. This indicates that males are more likely to obtain higher quality health care. These results are not compatible with the notion drawn from the standard utility model framework such as Acton's, that individuals with higher opportunity costs of time (e.g. working-age adult males) demand less medical care. Furthermore, negative age effects were not predicted by either variant of the Grossman (1972) household production model. The results of this study suggest that individuals who are relatively more productive obtain the largest share of medical care in the household. An implicit assumption in the above model is that the probability choice set of an individual includes all prices and is therefore analogous to the conventional demand function. This type of probability choice set is found in Small and Rosen (1981). It differs from the Random Utility Maximization (RUM) framework described in McFadden (1981). - 32 - TABLE 4.2A: Multinomial Logit Model of Provider Choice Determinants of Choice between Doctor, Nurse, and Home Care Adults in Rural Areas with an Illness or Injury Nurse Doctor Alternative Alternative a t a t Constant 2.125 (4.23) 2.135 (3.39) Doctor travel time 0.325 (3.38) -1.953 (4.03) Nurse travel time -0.887 (5.57) 1.028 (2.31) Income 0.234 (2.84) 0.259 (2.86) Age -0.048 (5.46) -0.050 (4.54) Male -0.043 (0.29) 0.439 (1.95) Education -0.042 (1.54) 0.010 (0.21) Adults -0.054 (1.99) -0.080 (1.99) Children 0.039 (1.73) 0.053 (1.49) Unrestricted days -0.106 (4.81) -0.130 (4.46) Unrestricted days x Age 0.002 (3.86) 0.001 (2.52) Savanna 0.093 (0.53) 0.407 (1.31) Log likelihood -967.49 2 x 198.66 TABLE 4.2B: Income and Travel Time Elasticities of the Probability of Choosing a Doctor or Nurse Nurse Doctor Alternative Alternative Income elasticity 0.183 0.214 Travel time elasticities Nurse -0.385 1.082 Doctor 0.310 -1.075 - 33 - The current multinomial model can be made to conform with RUM by imposing zero restrictions on cross price effects. ln(P./P 0) = aiTi+ yj Z J o J J J The log odds ratio will not exhibit IIA in any strict sense, since it will always depend on Z, the person trait(s) common to all alternatives. 2/ As in the unrestricted case income elasticities of each alternative incorporates income effects of all other alternatives. On the other hand alternatives are independent with respect to time prices. The own-time elasticity becomes: P. E.] = 8.T. (1 - P.) J J J J As in the case of binary logit, the cross elasticity of the probability of alternative j with respect to travel time to alternative m is: P. m m mPm / Note that this is computationally identical to a conditional-logit model where socioeconomic variables are interacted with alternative specific dummy variables. 2/ As McFadden (1982 p. 11) states: "... it is not the MNL form per se, but rather the restriction of [the dependent variables] to depend only [our emphasis] on attributes of [alternative] i, that implies the IIA restriction". - 34 - It is immediately obvious that the model does not allow for complementarities. Furthermore, cross elasticities of any number of alternatives with respect to price or time of some other alternative m are always constrained to be equal. - In practice, the restricted version of the multinomial logit model is not expected to yield significant changes in the coefficients of the socioeconomic variables. This is not so in the case of travel time variable where actual and spurious correlations (the correlation between the nurse and doctor travel times was 0.61) may have biased the estimates in the unrestricted model. Results of the restricted version of the multinomial logit model are given in Table 4.3A. As anticipated the coefficients of the various socioeconomic variables remain fairly stable compared with the previous MNL model. There is no significant change in the own-time effect in the nurse alternative. In the doctor alternative, the coefficient of travel time was reduced by nearly one half. New elasticity estimates on the basis of the restricted model are presented in table 4.3B. Although the all own-time and cross-time effect have decreased in absolute values, the basic results of both MNL versions are the same. The t-values tend to be slightly higher in the restricted model. However, the unrestricted model does better in term of goodness-of-fit criteria. Since both models were estimated on the same sample and with the / This does not present a problem in the trinomial case. However, if we were able to add a fourth alternative, say healers, this would imply that the cross-price elasticity of doctor visits with respect to healers and the cross price elasticity of nurse visits with respect to healers are always equal. - 35 - TABLE 4.3A: Restricted Multinomial - Logit Model All Adults Nurse Alternative Doctor Alternative 8 ~~t 8t Constant 2.28 (4.46) 2.180 (3.44) Doctor travel time -1.160 (4.35) Nurse travel time -0.658 (4.89) Income 0.202 (2.48) 0.255 (2.32) Age -0.047 (5.31) -0.032 (4.68) Male -0.061 (0.42) 0.046 (2.07) Education -0.073 (1.54) -0.002 (0.30) Adults -0.053 (1.95) -0.077 (1.79) Children 0.038 (1.71) 0.039 (1.11) Unrestricted days -0.102 (4.67) -0.129 (4.44) Unrestricted days x Age 0.002 (3.69) 0.001 (2.49) Savanna 0.035 (0.20) -0.280 (0.93) Log likelihood -966.73 2 x 180.18 TABLE 4.3B: Income and Travel Time Elasticities Nurse Doctor Alternative Alternative Income elasticity 0.154 0.219 Travel time elasticity Nurse -0.261 0.107 Doctor 0.072 -0.953 - 36 - same set of alternative, their likelihood ratios are directly comparable. We can thus construct a likelihood ratio test for the null hypothesis that cross- time coefficients are zero. 2 - L(82) x -2oln( - ) L(01) S, denotes the coefficients from the unrestricted model, while 82 denotes the coefficients from the restricted model. The test yielded a X value of 1.4, 2 compared with X22 010 = 42.0. Consequently the null hypothesis of zero cross- time effects can not be rejected. C. Number of Consultations with Doctors and Nurses In this section we turn to the actual "quantity" of care demanded, measured by the number of visits to each type of provider. Demand, is estimated conditional on entering the health care market, i.e. for all individuals with positive visits. In order to correct for sample selection bias we used a two step procedure described in Section (3.1). The selection term was generated from the restricted MNL estimates, which were drawn from the pooled adult sample. Consequently the quantity-demand equations were also estimated from the pooled sample. Table 4.4A shows results obtained from both OLS and the two-step procedure. Selection terms in both the nurse alternative and the doctor alternative were not significant (implying that selectivity bias does not arise) and differences between the parameter vectors of the OLS and two step procedures were minor. The coefficients of all the demographic and health variables display the same signs in both the doctor and nurse alternatives. However, these - 37 - variables matter more in the doctor alternative where they are more significant and larger in magnitude. The demographic variables with the greatest impact on doctor consultations are the number of adults and the number of children in the household. There is a negative association between the number of adults and utilization and a positive association between the number of children and utilization. Since the interpretation is the same as in the previous provider choice model, we need not discuss it here. While the education variable had no effect on the decision to chose a doctor, it has a significantly negative effect on the amount of doctor consultations. This result is compatible with the notion that more education makes people more efficient at "home production" of health and therefore it reduces the amount of medical care required (Grossman, 1972). It is also interesting to note that being a male has a significantly positive and large effect on the number of doctor consultations, and a negligible effect on nurse consultations. The provider choice model indicated that males are more likely to obtain health care provided by doctors and less likely to obtain care provided by nurses. If indeed doctors provide higher quality health care then these results imply that households bias their allocation of health care in favor of males. Although the economic variables, i.e. travel time and income fail to attain critical t-values with the exception of the own-time parameter in the nurse alternative, the results do confirm and augment conclusions drawn from the provider choice model. Negative own time effects and positive cross time effects indicate that travel time replaces the conventional price mechanism and that medical care provided by nurses and medical care provided by doctors are indeed substitutes. Since selectivity bias did not arise, income and travel time elasticities reported in Table 4.3B are based on OLS estimates. - 38 - TABLE 4.4A: Demand For Medical Consultations OLS and Two-Step Estimates (ADULTS) Nurse Alternative Doctor Alternative 3 T a T 8 T 8 T Constant 2.275 (5.62) 1.96 (3.75) 2.010 (3.06) 1.402 (1.66) Doctor travel time 0.149 (1.10) 0.143 (1.03) -0,737 (1.01) -0.813 (1.11) Nurse travel time -0.267 (1.67) -0.232 (1.54) 0.550 (0.84) 0.687 (1.04) Income 0.141 (1.66) 0.106 (1.25) 0,150 (0.97) 0.112 (0.71) Age 0.007 (1.17) 0.010 (1.51) 0.002 (0.25) 0.010 (0.86) Male 0.095 (0.68) 0.088 (0.68) 0.501 (1.68) 0.436 (1.70) Education -0.033 (0.83) -0.028 (0.40) -0.092 (1.50) -0.089 (1.99) Adults -0.039 (1.19) -0.031 (0.87) -0.164 (2.36) -0.150 (2.01) Children 0.059 (2.34) 0.052 (1.97) 0.130 (2.44) 0.122 (2.30) Unrestricted days 0.021 (0.66) 0.028 (0.88) 0.083 (1.64) 0.107 (1.95) (Unrestricted days) - -0.002 (1.64) -0.002 (1.61) -0.003 (1.58) -0.003 (1.77) Selection term 1.810 (0.98) 2.918 (1.54) R2 0.102 0.105 .103 0.124 F value 3.600 3.37 1.250 1.400 Sample size 330 a! 109 a/ Excluding observations with more than 7 consultations. TABLE 4.4B: Elasticities of Quantity Demand (Adults, Conditional Upon Market Entry) Nurse Doctor Consultations Consultations Income elasticity 0.075 0.098 Travel-time elasticities Nurse -0.043 0.066 Doctor 0.051 -0.155 - 39 - These estimates apply strictly to the conditional sample of entrants to the health care market and not to the whole population. Section V considers the full market response to economic variables. 4.2 Demand for Child Health Care A. Entry to the Health Care Market Our analysis of health care utilization on behalf of children follows the sequence laid out in the previous section, namely the market-entry decision, a provider choice model and finally the demand for consultations. Initially, the sample of children was divided into two age groups: infants or toddlers under the age of six, and children between ages six an fifteen. The test for pooling previously described indicated that pooling these age groups may not be appropriate in the binary market-entry regressions but is acceptable in the multinomial logit model of provider choice. 1- As in the analysis of adult health care we begin this study by first posing the question, what determines whether an ill or injured child will obtain health care, not distinguishing between the various types of health workers sought. Table 4.5 shows results for all age categories, including the pooled category. The vector of independent variables in the child regressions is similar to the vector independent variables in the adult regressions, but there are several important differences. In order to control for non- / In the binary case the Wald test yielded a statistic of 29.7, in the multinomial case the test statistic was 39.9. - 40 - linearities in the age effect, we introduced an age spline representing the effect of additional years beyond the age of five. This variable turned out to be statistically significant an it improved the overall fit of the model. The age spline shows that infant and toddlers are less likely to obtain medical care as they get older, whereas in later years the overall effect of age is positive. Another change in the use of years of education of the father instead of own-education. The father's education was preferred over the customary mother's education in the light of trial regressions (OLS and Logit) which included either one of these correlated variables. K The coefficients consistently turned out to have the same sign, although father's education usually possessed a higher asymptotic t-value. The healthiness measure of children under the age of six is not unrestricted activity days but rather the number of healthy days during the four-week recall period. As was stated earlier, we assume that the adults decision-makers in the household determine the threshold of sick days which justify entry into the child health care market. Therefore, we interact a proxy for adult tastes, namely the father's education, with the health variable. A number of socioeconomic variables has the same impact as in the adult population. In particular, the number of adults in the household reduces the probability of obtaining medical care, while the number of children increases this probability. Although the relative healthiness does not seem to matter in the case of children between ages six and fifteen, it remains as a significant negative determinant of market entry in the aggregated sample. Similarly, there are no significant differences between the probabilistic market entry elasticities of children and adults. The - 41 - income elasticities of the aggregated adult sample and the aggregated child samples are 0.16 and 0.13. Their respective travel time elasticities are 0.15 and 0.30. It is interesting to note that travel time has the same impact on infants as on prime age adults, perhaps reflecting the fact that parents or certain other adults in the household necessarily devote some of their own time in order to obtain medical care for the child. B. Provider Choice Model As was mentioned above, test statistics allow us to pool the two age groups in the provider choice model. 11 Separate MNL regressions for the two subsamples revealed that education and the education-health interaction were the only variables with different signs across age groups. Therefore, we allow the parameters of these variables to vary by age group in the pooled MNL regression. X Tables 4.8A shows the results of the provider-choice model on behalf of children, which is analogous to the restricted MNL model in Section (4.1). The parameters in the nurse alternative are generally more significant than the parameters in the doctor alternative, probably due to the differences in the sample size, in each alternative. Nevertheless, certain parallels emerge across these alternatives. As in the adult provider choice model, travel time is the major determinant of utilization. On the other hand the income parameter, while positive in both alternatives, does not attain 1/ Another reason for pooling is the small number of observations with positive utilization of doctor services. Only fifty-nine children under the age of sixteen were seen by doctors, compared with 165 infants and 137 older children who were seen by nurses. - 42 - TABLE 4.5: Determinants of Decision to Seek Health Care Infants and Children (LOGIT) Infants Older Children All Children Marginal Marginal Marginal B T Effect B T Effect B T Effect Constant 1,62 (3.77) 0.40 -0.07 (0.61) -0.018 1.18 (3.56) 0.291 Average total time -0.95 (4.13) -0.237 -0.83 (3.44) -0.202 -0.86 (5.31) -0.22 Income 0.21 (2.02) 0.053 0.10 (0.85) 0.025 0.16 (2.06) 0.040 Age -0,20 (3.06) -0.050 0.01 (0.28) (0.003) -0.17 (3.27) -0.043 Age spline (age > 5) 0.22 (2.84) 0.053 Male -0.01 (0.04) -0.002 0.02 (0.15) 0.005 0.08 (0.05) 0.003 Education -0.10 (1.08) -0.025 0.56 (1.49) -0.136 -0.03 (0.34) -0.007 Adults -0.09 (2.36) -0.023 -0.12 (2.32) -0.030 -0.11 (3.42) -0.026 Children 0.06 (1.91) 0.015 0.12 (3.14) 0.030 0.09 (3.65) 0.022 Unrestricted days -0.04 (2.94) -0.011 -0.01 (0.41) -0.002 -0.03 (2.57) -0.007 Unrestricted days x father's education -0.01 (1.52) 0.001 -0.02 (1.58) -0.006 0.00 (0.33) 0.003 Savanna 0.22 (0.79) 0.054 -0.12 (0.42) -0.029 0.06 (0.29) 0.014 Log Likelihood -271.26 -239.22 -515.68 2 x 49.95 40.01 80.79 Income elasticity 0.161 0.086 0.128 Travel time elasticity -0.310 -0.298 -0.299 - 43 - TABLE 4.6A: Multinomial Logit Model of Provider Choice (Children) Nurse Alternative Doctor Alternative B ~t Bt Constant 1.218 (3.17) 0.596 (0.913) Doctor travel time -2.102 (4.02) Nurse travel time -1.243 (6.81) Income 0.154 (1.78) 0.293 (2.13) Age 0.262 (3.96) -0.090 (0.78) Age spline (age > 5) -0.261 (3.16) 0.117 (0.79) Male 0.054 (0.34) -0.325 (1.12) Adults -0.110 (3.32) -0.071 (1.18) Children 0.097 (3.65) 0.016 (0.35) Father's education a/ 0.059 (0.65) -0.292 (1.02) Unrestricted days a/ -0.037 (2.86) 0.042 (2.00) Unrestricted days x Father's education a/ 0.004 (0.94) 0.011 (0.94) Fathers education bI 0.590 (1.53) 1.633 (1.22) Unrestricted days b/ -0.013 (0.98) -0.042 (1.90) Unrestricted days x Father's education b/ -0.249 (1.59) -1.100 (1.06) Savanna 0.435 (2.05) -1.123 (1.79) Log likelihood -637.83 2 x 158.00 a/ Specific to infants less than 6 years of age. b/ Specific to children age 6-15. TABLE 4.6B: Income and Travel Time Elasticities From Provider Choice Model (All Children) Nurse Doctor Income Elasticity 0.121 0.316 Travel Time Elasticities Nurse -0.348 0.208 Doctor 0.005 -1.055 - 44 - critical t-values. A comparison of tables 4.3B and 4.6B shows that trjvel time elasticities in the sample of children are generally higher than travel time elasticities of adults. However, the basic results remain the same: own- time effect are negative and large, the absolute value of own-time elasticities in the doctor alternative exceed unity and cross-time effects are always positive but small. Although income effects are consistently positive in the provider choice models, there are certain differences between the two samples. In the adult sample the elasticities of the nurse and doctor choices were quite similar (0.12 and 0.19 respectively). In the children sample the income elasticity of the nurse choice was very small (0.12) while the income elasticity of the doctor choice was relatively high (0.32). Recall that higher income elasticities in the doctor alternative consistently appeared in the adult models as well. A possible explanation is that although health services are nominally free, there are certain costs of higher quality care (i.e. doctors) which are not observed by the researcher. Consequently, income is a more important determinant of utilization of high quality medical services. C. Number of Consultations with Doctors and Nurses The demand equations for nurse and doctor consultations were estimated with OLS and the two step procedure previously described. Results are given in Table 4.7A. Since the sample size in the doctor alternative is very small, we will not pay much attention to the demand equation in this alternative. The selection term was not significant in either case and the parameter estimates in the two-step method are not significantly different from the OLS estimates. For convenience, the following discussion will refer - 45 - toe the conditional sample of market entrants, namely to the OLS regressions. The demand equation in the nurse alternative suggests that relatively healthier children tend to obtain a greater amount of medical care. The negative sign of the quadratic healthiness term implies that the positive association between healthiness and utilization of nurse services is reversed when children become severely ill. This result confirms previous findings in the case of adults. Given a child's state of health, demand is dominated by economic variables rather than demographic traits. Travel time and income elasticities are given in Table 5.7B. As in all of the previous cases, travel time effects had the expected signs, and income elasticities are low. Note that there are minor differences between elasticities in the doctor alternative and the nurse alternative. Furthermore, a comparison of Tables 4.4B and 4.7B shows that elasticities of demand for adult consultations and elasticities of demand for child consultations are in the same order of magnitude. The little evidence that does exist in the developed world, particularly the United States, reflects substantially higher income elasticities for pediatric health care visits compared with adults visits. Studies by Inman (1976), Colle and Grossman (1978) and Goldman and Grossman (1978) show that income elasticities of pediatric visits conditional upon positive utilization range from 0.16 to 1.32 compared with an income elasticity of 0.07 for pediatric nurse visits in Cote d'Ivoire. One possible explanation of this disparity is that since health care services are provided free-of-charge in rural C6te d'Ivoire, out-of-pocket expenditures there represent a relatively small share of income. Another possibility is that - 46 - given the extended family structure, rural Ivorian households have a greater freedom to select persons with low opportunity costs of time to accompany children. - 47 - TABLE 4.7A: Demand for Medical Consultations (Children) OLS and Two Stage Procedures Nurse Alternative Doctor Alternative B s T 8 T 8 T a T Con'tant 1.556 (3.57) 1.341 (2.19) 3.063 6.34 3.076 (6.32) Doctor travel time 0.325 (2.14) 0.321 (2.19) -0.331 (0.40) -0.492 (0.59) Nurse travel time -0.764 (2.94) -0.678 (2.17) -0.064 (0.09) 0.096 (0.13) Income 0.168 (1.64) 0.150 (1.64) 0.001 (0.01) 0.054 (0.34) Age -0.050 (0.76) -0.027 (0.34) -0.017 (0.16) -0.035 (0.32) Age spline 0.063 (0.65) 0.035 (0.32) 0.134 (0.93) 0.175 (1.18) Male 0.166 (0.86) 0.165 (0.86) 0.003 (0.01) -0.022 (0.08) Education 0.033 (1.05) 0.032 (1.02) 0.021 (0.42) 0.032 (0.61) Adults -0.063 (1.65) -0.048 (1.46) -0.167 (2.16) -0.169 (2.19) Children 0.042 - (1.35) 0.031 (0.79) 0.134 (2.07) 0.125 (1.90) Unrestricted days 0.009 (1.94) 0.094 (2.00) -0.142 (2.05) -0.146 (2.11) (Unrestricted days) 2 -0.003 (2.30) -0.003 (2.38) 0.004 (1.70) 0.004 (1.65) Selection term 0.403 (0.50) -3.66 (1.12) R2 0.054 0.050 0.289 0.309 F Value 2.040 1.898 1.592 1.580 Sample size 295 a 51 a 2/0bservation with 1-7 consultations. TABLE 4.7B: Elasticities of Quantity-Demand (Children, Conditional Upon Market Entry) Nurse Doctor alternative alternative Income elasticity 0.076 0.000 Travel Time Elasticities Nurse -0.120 -0.030 Doctor 0.087 -0.067 - 48 - V. Summary and Conclusion 5.1 Total Utilization Response In this paper we estimated various health care demand models in order to assess the extend of quantity rationing in the health care system in Cate d'Ivoire. Quantity rationing was defined as the effect of travel time to the nearest provider on the decision to seek medical care, on the choice of the health care provider and on the total number of calculations with each provider. We summarize our main results in Table 5.1. Note that total demand, 'j, for services of provider j is given by M. = P. * (N.IN.>O) .J .J J J where P. is the probability of choosing j, and N. is the number of consultations with j, only observed if j is chosen. Thus: aM. aN. ap. J= Pj X + Nj ax pi ax N ax for any exogenous variable X. We evaluate the total demand elasticity .for provider j, Ej as E. = £j + n; - 49 - i.e., the sum of the probability elasticity of demand (e.g.) and the conditional elasticity of demand for consultations. TABLE 5.1: Total Demand Elasticities Nurse Doctor alternative alternative Adults Income elasticity 0.229 0.317 Travel Time Elasticities Nurse -0.304 0.173 Doctor 0.123 -1.108 Children Income elasticity 0.198 0.316 Travel Time Elasticities Nurse -0.468 0.178 Doctor 0.092 -1.122 The results in Table 5.1 clearly show that in the absence of user fees, travel time acts as a rationing mechanism in the health care market. It also seems appropriate to state that access to higher quality care, i.e. doctors, is always completely restricted by long travel times. On the other hand, because medical care is free, income elasticities in the Ivorian health care market are relatively low, much like they are in the developed countries in which the - 50 - market for medical care is generally characterized by a high level of insurance coverage. 5.2 Policy Implications and Conclusion The case against user fees in the health care market stems from the desire to allow everyone who needs it, free access to medical care. However, while money prices may be zero, as they are in rural C8te d'Ivoire, private costs to the patients may still be considerable. As we have shown in this paper, the absence of user fees per se does not guarantee equal access for everyone. In fact, the private costs (here represented by travel time), much like a money price, serve as a rationing mechanism, with those living farther from health care facilities being most restricted. Thus, the case against user fees can not be based on some a priori notion of equity. Furthermore, our results imply that the demand for medical care in rural areas can be significantly increased if the regional distribution of health care providers is improved. Such an improvement could be used to offset the expected negative impact on the demand for medical care that is likely to result from the introduction of user fees. Conversely, if the new revenues obtained from user fees are being used to improve the regional distribution of providers, the resulting system can turn out to be more equitable, rather than less equitable as is usually feared. The outcome, of course, depends on many issues that need further examination. Among them: for which medical services should fees be set; can the fees result in sufficiently high revenues for improving the system; do fees have the same impact on poor and rich households, or should fees be made income dependent? - 51 - Answers to these questions depends on the money price elasticity of demand, the willingness-to-pay for medical care and the cost structure of health care facilities. Research is under way within the World Bank's Living Standards Unit to address these issues in order to help policy makers make the difficult decisions necessary to solve the severe financial problems that are prevalent in the health care delivery systems of many LDCs. - 52 - Appendix A A Note on Traditional Healers There is little evidence about the role of traditional healers in developing countries. In the past it has been suggested that some indigenous forms of medicine may be effective and can be integrated into the health care system (The World Bank, 1980). The Ivorian Living Standards survey contains no data relating practices of faith healers or the types of symptoms treated by them. However, ample data on levels of utilization was collected. The data suggests that although traditional medicine is significant in the rural parts of Co^te d'Ivoire, it is practically non-existent in urban locations. l/ In rural areas 118 persons of all ages consulted a healer compared with only 9 persons in urban locations. Of the fifty villages for which community level data was collected, all but four had a traditional healer on premise. Table 7.1 shows the distribution of visits by age group and place of consultation. The largest proportion of visits occurred in prime age adults. However, after adjusting for population shares it becomes evident that there are no appreciable differences between age groups. Similarly, there are no appreciable differences between sexes (see Table 7.2). A major amenity offered by traditional healers are home visits. Roughly 40 percent of traditional health care episodes took place in the patient's home, while only / Nevertheless, there were too few observations with positive utilization of traditional medicine in the "cleaned" estimating sample to allow for statistical analysis. We could not obtain correct predictors of fees charged by healers, for instance; furthermore, traditional medicine could not be distinguished from other types of home care. Consequently, we incorporated traditional care in the "home care" alternative. - 53 - a negligible number (about 10) of the doctors and nurses in the rural sample made any home visits. Furthermore, healers did not charge for services provided to 67 of the 118 "patients" in the rural sample. The average fee was 218 CFAF (47 cents in 1985 prices). The average number of traditional health care consultations excluding outliers with more than 10 visits, was about 2.7, similar to the average number of consultations with either doctors or nurses, given positive utilization. TABLE A.1: Number of Persons with Healer Consultations Age Group by Place of Consultation a Healer's Person's Home Home Ages 0-5 19 (23) 11 (13) Ages 6-15 8 (11) 11 (14) Ages 16-49 27 (20) 17 (12) Ages 50+ 17 (17) 8 (8) Total 71 (71) 47 (47) a! Figures in parenthesis denote number of persons with healer consultations adjusted for the actual population shares. TABLE A.2: Number of Persons with Healer Contacts Age Group by Sex Male Female Ages 0-5 15 15 Ages 6-15 12 7 Ages 16-49 21 23 Ages 50+ 12 13 - 54 - Appendix B Econometric Specification In the analysis of discrete choice a distinction is made among utility levels associated with each alternative. Furthermore, the random utility maximization (RUM) hypothesis is usually invoked. 1/ In the binary case (easily extended to the case of multiple choices), RUM states that, 2/ Ul = Vi + el U2 = V2 + e2 U1, U2 are utility associated with each choice, V1, V2 are "representative" utility terms and cl,E2 are random, unobservable components of utility which vary across individuals. For convenience, subscripts denoting the individual were suppressed. An individual will chosen the alternative that yields him the most utility. The probability that this individual chooses alternative 2 over alternative 1 is given by P1 = Prob(U2 > Ul) substitution yields 1/ See McFadden 1981. 2/ For an extension of RUM to the trinomial case see Hausman and Wise (1978). - 55 - P1 = Prob(V2 - V1 > -1 62) This probability may be specified as a logit model, V. Z e j j=1 which in turn, is rewritten to reflect differences in representative utilities. The dichotomous market entry decision is written as a binary logit eV2 p2 =- 1 + eV2 where v2 = V2- V1 and the choice among several providers is modeled as a multinomial logit evi P., = a- I 1 + J v. E e-l j=1 j*k where v. = V.- Vk In the third part of our analysis we estimate separate demand equations for the number of doctor contacts and the number of nurse contacts a person had, conditional upon positive utilization of doctor or nurse services. Since our main concern is with price and income effects we opt for - 56 - a simple linear specification adapted, with minor modifications, from Hausman (1981), Ni =a P + bY + c [Z, H] where Ni is demand for consultations with the i'th health care provider. Y is income, Z is a composite of demographic traits and H is an indicator of health needs, al is an alternative specific parameter, b is the income parameter and c is a vector of parameters. Following Action (1975) the theoretically correct price variable is the full price, which is the sum of the money price and the product of the opportunity cost of time (w) multiplied by the time devoted to consumption of medical care (t), that is p + wt = P. Health care in rural C8te d'Ivoire is provided free of charge. In the absence of wage data we will use travel time to the nearest provider as a proxy variable- for the full price of obtaining medical care. A general solution for an indirect utility function yielding the linear demand equation is / An easy way to verify that the above indirect utility function yields a linear demand function is to apply Roys identity N = - av/aP 3V7i3Y - 57 - Vi =ebP (y + P [a1 p + ab + c (Z,H)]) Since V1 > V2 only if e bP V1 > e bP V2 the decision maker effectively chooses an alternative on the basis of a comparison among i a V. = - + Y + aP p + c (Z, H) i. b This function of representative utility is linear in prices, income and i personal traits. Both the constant a and the price effect vary across alternatives. Personal traits may be taken as indicators of the decision- maker's perceived quality of health care, or as "taste" variables that effect the utility derived from consuming services provided by the provider chosen. (For a more detailed discussion see Gertler et al. 1986). Note that in this formulation income is differenced out of the model. However, since income elasticities are of interest to us the income variable was reintroduced in the empirical model. t The advantage of this framework is that it allows us to consistently use the same simple specification for all stages of the analysis while closely conforming with utility maximization. It also enables us to calculate total market response elasticities presented in Section V. Alternatively, we can estimate the market response using a selectivity bias approach developed in Lee (1983) and Trost and Lee (1984). In the first step the following selection term is generated from the multinomial logit model of provider choice: x = *(J(3 X))/F(BsX) I - 58 - where 8 is the parameter vector of the chosen alternative, 4 is the standard normal density function, and F is the cumulative normal distribution. Letting * denote the standard normal distribution function, we also have the transformation J = * F. Detailed proof is given in the above references. Note that there are unique selection terms for the doctor alternative and for the nurse alternative. In the second stage we estimate separate OLS regressions on doctor contacts and nurse contacts, where X is included among the explanatory variables. A high asymptotic t-value on the parameter of X indicates that sample selection is present. Thus the presence of X in the demand regressions corrected for sample selection thereby yielding consistent parameter estimates. Several factors will help us identify the demand equations. First the selection term is highly non-linear. Second, we include a taste parameter in the discrete choice model which affects the decision maker's choice of a health care provider but not the actual amount of health care obtained (Savanna). Finally, the functional form of the "healthiness" assessment variable in the discrete choice model differs for the healthiness measure in The quantity demand equation for reasons given in Section III.2. Results obtained from OLS regressions and the two step procedure7are compared in Section IV. - 59 - Appendix C Derivation of Elasticities Elasticity is defined as the percentage change in variable Y with respect to a percentage change in another variable X. (The individual's subscript is suppressed for convenience) generally: E = y / a x a y x y X 3x X Y In the case of discrete choice variables the above formula is given in probabilistic terms, i.e. Y is replaced by the predicted probability of choosing any given alternative. The marginal effect, aY/ax is derived below. We may then ask, what is the change in the probability of choosing alternative j as x varies? - SA simplified elasticity formula is available for binary logit. Ejk jk ijk This formula also applies to a special variant of the multinomial logit model, where at least some of the explanatory variables are alternative specific. With this specification, the probability of choosing a doctor, for instance, depends only on travel time to a doctor, not on travel time to a 1/ This may be calculated using the means of i. and the predicted probability (Pi) or as an average of all individual elasticities. We used the latter method. - 60 - nurse or healer. (This model is known as conditional logit, or McFadden's multinomial Logit.) PROOF For generality we derive the proof for McFadden's multinomial logit, with J alternatives and at least one alternative specific variable; x; should be thought of as a vector of dependent variables in alternative j, with a corresponding coefficient vector B; We are interested in the marginal effect of the k'th alternative specific variable. a.'x. - e ] / j=o Using the quotient rule: x ~ ~ ~ 8x. 8.e - e i i a z re a P ej xj) xjk 3 Xjk = jk~~~i j a X.k ~ ~ ~ 13X a 8a . X* 2 (e e J ) =(Z e8jx;)(e8ixi) Bjk ~(e8jxj) (e8ii) Bjk (Z e8j j~) x /' Binary logit is a special case of MNL, where P. = e 1 +e8Xj - 61 - Using the definition of P.: a P. 2 a xjk j jk j a jk Hence P. x. Ejk Pj ajk (1- P P Yielding E J = P. . x. (1-P.) 1/ jk j jk jk j In our case, however, each alternative faced the same vector of explanatory variables. (The probability of choosing say, a doctor depended on travel times to each type of practitioner). For convenience we will assume that there is only one dependent variable, xk. Therefore, the marginal probability of selecting the j'th alternative with respect that variable is a p. axk jx k a8jxk OXk (0 xk *(°k +e k (zea )(e ).(e ~ )(e Bo +e a, a. . e 80 (z e8i k)2 / In the presence of an interaction term, between say, variable Xk and variable xk+l, the elasticity formula is simply j jk jk ajk+1 xk+1) (1 - P;) - 62 - Before simplifying invoke the normalization Bo = 0 (see Maddala, p. 42), now the expression above reduces to: a P. J = p. 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LSMS Working Papers (continued) No. 28 Analysis of Household Expenditures No. 29 The Distribution of Welfare in Cote d'Ivoire in 1985 No. 30 Quality, Quantity, and Spatial Variation of Price: Estimating Price Elasticities from Cross-sectional Data No. 31 Financing the Health Sector in Peru No. 32 Informal Sector, Labor Markets, and Returns to Education in Peru No. 33 Wage Determinants in Cote d'Ivoire No. 34 Guidelines for Adapting the LSMS Living Standards Questionnaires to Local Conditions No. 35 The Demand for Medical Care in Developing Countries. Quantity Rationing in Rural Cbte d'Ivoire No. 36 Labor Market Activity in CUte d'Ivoire and Peru No. 37 Health Care Financing and the Demand for Medical Care No. 38 Wage Determinants and School Attainment among Men in Peru No. 39 The Allocation of Goods within the Household: Adults, Children, and Gender No. 40 The Effects of Household and Community Characteristics on the Nutrition of Preschool Children: Evidence from Rural C6te d'Ivoire No. 41 Public-Private Sector Wage Differentials in Peru, 1985-86 No. 42 The Distribution of Welfare in Peru in 1985-86 No. 43 Profits from Self-Employment: A Case Study of CUte d'Ivoire No. 44 Household Surveys and Policy Reform: Cocoa and Coffee in the CUte d'Ivoire No. 45 Measuring the Willingness to Pay for Social Services in Developing Countries No. 46 Nonagricultural Family Enterprises in C6te d'Ivoire: A Descriptive Analysis No. 47 The Poor during Adjustment: A Case Study of the C6te d'lvoire The World Bank to Headquarters European Office Tokyo Office 1818 H Street, N.W. 66, avenue d'Ina Kokusai Building Washington, D.C. 20433, U.S.A. 75116 Paris, France 1-1 Marunouchi 3-chome Telephone: (202) 477-1234 Telephone: (1) 47.23.54.21 Chiyoda-ku, Tokyo 100, Japan X Telex: WUI 64145 WORLDBANK Telex: 842-620628 Telephone: (03) 214-5001 RCA 248423 WORLDBK Telex: 781-26838 Cable Address: INTBAFRAD WASHINGTONDC