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LSM- 127NOV.1996
Living StandardsMeasurement StudyWorking Paper No. 127
Unconditional Demand for Health Carein COte d'Ivoire
Does Selection on Health Status Matter?
William H. Dow
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Unconditional Demand for Health Carein C8te d'Ivoire
The Living Standards Measurement Study
The Living Standards Measurement Study (LSMS) was established by the WorldBank in 1980 to explore ways of improving the type and quality of household datacollected by statistical offices in developing countries. Its goal is to foster increaseduse of household data as a basis for policy decisionmaking. Specifically, the LSMSis working to develop new methods to monitor progress in raising levels of living,to identify the consequences for households of past and proposed governmentpolicies, and to improve communications between survey statisticians, analysts,and policymakers.
The LSMS Working Paper series was started to disseminate intermediate prod-ucts from the LSMS. Publications in the series include critical surveys covering dif-ferent aspects of the LSMS data collection program and reports on improvedmethodologies for using Living Standards Survey (Lss) data. More recent publica-tions recommend specific survey, questionnaire, and data processing designs anddemonstrate the breadth of policy analysis that can be carried out using LSS data.
LSMS Working PaperNumber 127
Unconditional Demand for Health Carein C6te d'Ivoire
Does Selection on Health Status Matter?
William H. Dow
The World BankWashington, D.C.
Copyright C 1996The International Bank for Reconstructionand Development/THE WORLD BANK
1818 H Street, N.W.Washington, D.C. 20433, U.S.A.
All rights reservedManufactured in the United States of AmericaFirst printing November 1996
To present the results of the Living Standards Measurement Study with the least possible delay, thetypescript of this paper has not been prepared in accordance with the procedures appropriate to formalprinted texts, and the World Bank accepts no responsibility for errors. Some sources cited in this paper maybe informal documents that are not readily available.
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 itsBoard of Executive Directors or the countries they represent. The World Bank does not guarantee the accuracy ofthe data included in this publication and accepts no responsibility whatsoever for any consequence of their use.
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The complete backlist of publications from the World Bank is shown in the annual Index of Publications,which contains an alphabetical title list (with full ordering information) and indexes of subjects, authors, andcountries and regions. The latest edition is available free of charge from the Distribution Unit, Office of thePublisher, The World Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A., or from Publications,The World Bank, 66, avenue d'Iena, 75116 Paris, France.
ISSN: 0253-4517
William H. Dow is a postdoctoral fellow and a consultant to the Poverty and Human Resources Division of theWorld Bank's Poverty Research Department.
Library of Congress Cataloging-in-Publication Data
Dow, William H.Unconditional demand for health care in C6te d'Ivoire: does
selection on health status matter? / William H. Dow.p. cm. - (LSMS working paper; no. 127)
Includes bibliographical references.ISBN 0-8213-3757-21. Medical fees-Cote d'Ivoire-Econometric models. 2. Medical
care-Utilization-Cote d'Ivoire-Econometric models. 3. Usercharges-Cote d'Ivoire-Econometric models. I. Title. II. Series.RA410.55.C85D69 1996338.4'33621'096668-dc2O 96-34971
CIP
Contents
Foreword ..... ,viiAbstract . . .. ixAcknowledgments . xi
1. Introduction ......... . 1
2. Economic Interpretation of Conditional and Unconditional Estimates. 3Literature Review. . . . . . . . . . . . . 3A Simple Dynamic Model for Health Inputs. 3Relating the Model to Conditional and Unconditional Demand. 7
3. Conditional Demand and Selection Bias. 9Intuition Behind the Bias of the Conditional Approach. 9Unobserved Correlations in the Nested Multinomial Logit . . 10Unbiased Estimation of Conditional Demand .11
4. Estimating Unconditional Demand .t.*.-.-.-.-.- 13Marginal Demand Estimators (Without Health Infornation) .13Estimating Demand Jointly with Health .15
5. Testing for Selection Bias in Conditional Estimates .18
6. Data and Estimation Procedures .21Cote d'Ivoire Living Standards Survey .21Estimation Procedures ............................... 22Price and Income Specification . ......................... I... 23
7. Short-Run and Long-Run Estimation Results .25Probability of Self-Reporting Sick .253-Choice Unconditional and Conditional Estimates .26Unconditional 4-Choice Nested Multinomial Logits .27MNP Test of Selection Bias in the Conditional Approach .28
8. Discussion and implications .33
Variable Definitions ....... ............. .............. 35
Annex Tables:Al: Time-Price (Own) Elasticities of Demand .36A2: Linear Probability Estimates of Demand Equations .37A3: 3-Choice Non-Nested Multinomial Logits .38
References .39............ 39
v
Foreword
The impact of government investments, regulations, and pricing policies on the use ofhealth care services will depend on how people make health care decisions. Behavioralhealth care demand parameters such as price elasticities have been used in setting user feepolicies at public health care facilities in many developing countries. The existing healthcare demand literature, however, has only considered the immediate demand responses touser fees, without considering how demand behavior may differ given time to adjust to newprices. This paper uses the C6Bte d'Ivoire Living Standards Survey to examine how the long-run effects of user fee policies may differ from the short-run effects that have been used toinform policy thus far. An important finding of this paper is that long-run price elasticitiesof the demand for health care are often smaller than short-run elasticities. This implies thatdebates about the impact of user fees on health care demand need to distinguish betweenlong-term and short-term effects.
Lyn Squire, DirectorPolicy Research Department
vii
Abstract
Health care demand price elasticities are often estimated from samples conditioned toinclude only sick people. This paper shows that not only may such estimates be statisticallybiased, but even when properly estimated they can only be interpreted as short-run priceresponses. In contrast, unconditional estimates take into account the long-run feedback ofprices on health. The paper discusses simple strategies for estimating the long-rununconditional elasticities, which do not depend on controversial exclusion or functional formrestrictions. Using the Cote d'Ivoire Living Standards Survey, a test based on themultinomial probit finds that the usual conditional estimates do not suffer from selection bias.However, short-run conditional estimates differ significantly from long-run unconditionalones for several covariates, with conditional price elasticities being about 25 percent largerthan unconditional ones.
ix
Acknowledgements
This paper is based on Chapter Two of the author's Ph.D. dissertation at YaleUniversity. Discussions with Paul Schultz, Moshe Buchinsky, Mike Boozer, Paul Gertler,Duncan Thomas, Germano Mwabu, Randy Ellis, Harold Alderman, Vassilis Hajivassiliou,and Anne Royalty have been helpful. Thanks are also in order for comments from seminarparticipants at Yale, RAND, Minnesota, Cornell, CIDE (Mexico), and the NortheastUniversities Development Conference. The author is of course responsible for any errors.Permission to use the Ivorian Living Standards Measurement Study (LSMS) data wasgenerously granted by the Institut National de la Statistique, Abidjan, C6te d'Ivoire.Financial support from the Mellon and Rockefeller Foundations is gratefully acknowledged.
xi
1. Introduction
Curative health care is only demanded by people when they are sick. This simpleobservation has led many empirical researchers and policy analysts to ignore "healthy"people when evaluating the determinants of demand for health care and the effects of healthcare policy changes. Individuals, however, can in the long-run adjust health input mixes toaffect the probability of becoming "sick." Thus commonly estimated quantities such as priceelasticities may be biased, or only valid in the short-run, if estimation is conditioned onhealth status. This paper fills a gap in the health care demand literature by analyzing theeconomic and empirical implications of such conditional' estimation.
Economists and policymakers in the past decade have increasingly looked to healthcare demand studies that estimate price elasticities. Proposals to raise public health care userfees in developing countries have been made both by the World Bank (see Akin et al., 1987,for a World Bank policy paper) and a group of African health ministers (see Lancet, 1988,for a description of this "Bamako Initiative"). The potential effects on the poor have raisedcontroversy (for a discussion and review of this literature see Jimenez, 1995), and priceelasticities are a key empirical input to this debate. This paper will not address thecomplexities of interpreting price elasticities,2 but instead focuses on the long-run versusshort-run demand implications of user-fee policies.
Although most health care demand studies only analyze the currently sick, Ellis andMwabu (1991) have shown that the effects of demographic characteristics on who becomessick may be different from the effects on who demands care once sick. Section 2 presents asimple model to formalize the dual effect of user fees on sickness and demand conditional onsickness, and it implies that unconditional estimation better captures the long-run effects ofpolicy reform. The relationship between short-run and long-run elasticities is then discussed.It is shown that the difference between the conditional and unconditional demand elasticitiesis exactly equal to the elasticity of sickness.
Section 3 analyzes the possible selection bias (hypothesized by Schultz and Tansel,1993) in conditioning on health to obtain the usual short-run elasticities. This bias is
"'Unconditional" and "conditional" are used throughout this paper to refer to whether or not the sample hasbeen truncated to exclude healthy people.
2See Dow (1995a) for a discussion of why price elasticities alone mnight not be enough to judge the overallwelfare effects of user fees on the poor. It is argued there that the poor's high price elasticities may reveal that thepoor place a lower value on marginal units of health care than they do on other necessities. That would indicatethat using resources freed up by user fees to finance alternative programs for the poor might be welfare improving.However, more research is still needed as to whether the poor properly value the health care services received.
1
illustrated using discrete choice modeling concepts, and economic explanations of itsexistence are discussed.
In Section 4, unbiased estimation strategies are proposed and evaluated, includingunconditional methods that combine the "sick but zero demand" option with a "not sick"alternative to create a single non-demander's category. By not jointly estimating demandwith health, the correlation between unobserved demand and health need not be explicitlyconsidered, and the resulting unconditional estimates are free of selection bias. In addition,this circumvents the difficult problems raised by using self-reported health status, sinceobjective health indicators are not typically available in multi-purpose household survey data.In Section 5, a formal test of selection bias is derived using the multinomial probit.
Data and estimation procedures are discussed in Section 6. Empirically, Section 7finds that for the Cote d'Ivoire Living Standards Survey the conditional estimates do differfrom the unconditional population effects. Short-run price elasticities are approximately 25percent larger than for the unconditional sample, and the signs and significance of gender,age, and wage variables also differ between the approaches. However, as estimates of theshort-run elasticities, the usual conditional results do not appear to be affected by selectionbias in this sample.
The implications of the findings are discussed in Section 8. For short-run analysis, ifselection bias is also absent in other datasets, then collecting less-expensive choice-basedsamples appears to be a valid option for certain limited purposes. Interpretation may still bedifficult, though, when self-reported health indicators are used to select the sample. Thismust be balanced against the fact that estimated long-run effects may also be difficult tointerpret when changes over time in health care access are unobserved. However,unconditional estimation requires little extra computational effort when data are also collectedfor the healthy. Attention should be paid in the future to whether it is the short-run or long-run effects that one wants to know in a particular application.
2
2. Economic Interpretation of Conditional and Unconditional Estimates
Literature Review
Most empirical studies of the discrete demand for curative medical care conditionestimation on individuals having reported themselves sick, especially in studies of lowincome populations. Recent examples include Akin et al. (1985), Gertler and van der Gaag(1990), Lavy and Quigley (1993), Mwabu, Ainsworth, and Nyamete (1993), and Lavy,Palumbo, and Stern (1995). Akin et al. justify this by arguing that healthy people will notdemand curative care. It is argued here, however, that this is only true in the short-run.The possibility of selectivity bias was mentioned by Dor and van der Gaag (1993), whoreport testing to see if selection on sickness was a severe problem. To do this they used aHeckman-type selectivity correction; Section 3, however, discusses why this will notnecessarily be the preferred test.
Not all health care demand studies condition in this way. In studies of the UnitedStates, for example, Manning et al. (1987) retain healthy people in the analysis, although adifferent type of selection issue arises in their study. In general, however, consideration ofthe role of healthy people in curative care demand has received little attention.
Ellis and Mwabu (1991) provide a notable exception to this literature, as they focusattention on the effects of demographic covariates on the probability of falling ill,3 as well ason demand behavior once ill. However, they do not go on to calculate the net combined("unconditional") effects. Furthermore, they do not discuss or allow for in their estimationany possible correlation between unobservables in the health demand and the health caredemand equations. As Schultz and Tansel (1993) point out in a footnote, if theunobservables in these two equations are correlated, then the conditional estimates will bebiased.
A Simple Dynamic Model for Health Inputs
This section provides a simple behavioral model of health care demand decisions. Itemphasizes the idea that people choose their expected health level, and in the process, futurehealth outcomes are affected by current health care prices. Furthermore, dynamic feedbacksthrough health status imply potential differences between short-run and long-run health caredemand responses to price changes.
Since Grossman's (1972) contribution, numerous models have been formulated toemphasize different aspects of the health production process. These have been reviewed inthe developing country context by Akin (1985), Behnnan and Deolalikar (1988), and Straussand Thomas (1995). The distinctive feature of this model is the focus on the trade-offs
3Strauss et al. (1993) also provide a detailed analysis of how reported illness differs across age and gender.
3
between curative and preventive inputs, in addition to the usual trade-offs between health andother consumption. This highlights different pathways through which health care prices mayeffect health care consumption. The main implication for empirically estimating inputdemands is that health itself is endogenous, and the level of healthiness in the population willchange when health care prices change. This in turn implies different temporalinterpretations of different estimation strategies, as discussed in Section 2.
In the model, individuals at the beginning of period t choose consumption Ct andhealth Ht (through curative I" and preventive I Pre health inputs) to maximize the discounted(by p) sum of expected current and future utilities. Maximization is subject to each period'sbudget constraint, which depends on income Y, and prices ptCur and p Pre (the price of otherconsumption may be normalized to one):
max E, p'E[U(Ct^,)]V
s.t. t= + + 1 Pretpre
Maximization is also constrained by the production technology for health at time t.The time subscript on health denotes the health status at the end of each period. At thebeginning of each period health is altered by a stochastic shock X, before health inputs arechosen. The affect of past health on current health is also altered by depreciation 6 of thehealth stock (H increases with good health):
Ht = 8H, 1 +pI c+ p2Je7+XA
In this system, health at period T may depend on all previous shocks and inputs.This can be seen by assuming Ho = 1 l 0cur + k0 and solving forward:
HT = 6T p1 It+ ST-1 8T-t-1p 2 it4 r+ ST 8Ttt
Prices in all past periods may thus also affect health at T, through the input demandequations. To explicitly analyze the price effects, specify simple linear input demandequations:
lCtypCt + Y2tP; 3 y(N-1 +At)
cur+ epre
,Pr, = yPt+ YP2Pt + YP3(68Ht-+Xt)
Then substitute them into the health production function, yielding
Ht = aoHt_l + + ax prPe +a X
where C1 (1= 17 1C+B 2 71P), etc.
4
The effect of a permanent change at time T in pcr can now be written as:
dHr_dH = al
dp T
By period T+s this differs from the initial effect in period T, since there is a cumulativeeffect of the new HT affecting HT+I (which then affects IT,,", etc.):
dHT+SY,v 4a
dp '
Next, see how this price change affects the demand equations. In the first period there is animmediate impact effect through the budget constraint:
clur = Y
dp '
This is expected to be negative. However, again there is a dynamic feedback effect byperiod T+ 1, through health:
cur = Yi + byo(lYl +
dp T
This effect can be decomposed into several components. The first term is the impact effecty,' as seen in period T. The second is the feedback through Ht, from T's price changeaffecting both curative and preventive inputs in time T, and thus changing the health status atthe beginning of the period when I,+, is chosen. The total effect, taking into account thefeedback, is analogous to dynamic multipliers in macroeconomic models.
Whether the dynamic feedback amplifies or dampens the impact (short-run) effect isambiguous. Of the dynamic term in parentheses, the first part ( 3 1-y1C) is positive, sincecurative care decreased last period, meaning health is worse now; thus more curative care isdemanded (assuming curative care is a normal good). The second effect cannot be signed,however, because it depends on the cross-price substitution effect of curative price onpreventive care.
For example, people might spend more resources on preventing illness when curativecosts are higher. Even if period T's ill health is not as well cured, new illnesses could thenbe prevented so much so as to improve health. In that case, curative care demand woulddecrease even more over time than it had in the first period, in response to the price change.However, if the increased preventive care is not sufficient to offset the effect of decreased
5
curative care in the previous period, implying worse health at the beginning of period T+ 1,then the long-run elasticity will be smaller than the short-run elasticity.
One case where the long-run elasticity may be more likely to be smaller than theshort-run is if preventive prices increase along with curative prices. This may occur whenthe "price" referred to is actually travel time to a clinic which provides both types of care.Then preventive care is not as attractive a substitute for curative care, making it more likelythat health will worsen over time and thus drive demand levels back towards their originallevels.
The relationship between the long-run and short-run elasticities is further complicatedby the fact that it may change as the price change becomes more distant in the past. This isseen by the effect on demand in period T+s of a permanent price change in period T:
dIT=s + 8yo -1 t
For many goods, demand is thought to be more elastic in the long-run, as people arebetter able to substitute to alternative goods such as preventive care. In the present modelthe effect of the preventive feedback may be stronger in the long-run, due to substitution, butit cannot be determined a priori whether on net the long-run health care demand elasticitywill be larger than in the short-run.
It is important to consider more generally in what scenarios the long-run price effectsare likely to differ substantially from the short-run. One factor is whether the healthdimension being conditioned on is of a durable nature. Childhood diarrhea, for example,may persist over time if high prices cause it to have gone untreated in the past.Furthermore, it has been shown to worsen the health effects of other childhood diseases indeveloping countries, thus magnifying health feedbacks on demand. A second factor iswhether health input prices are a large portion of the budget, which would cause past inputsto have wealth effects through the budget constraint, thus affecting current health. This ispostulated to occur, for example, when families sell their goats to finance health care, butthen children are deprived of nutrition and become sicker. Substitution effects may also playa role: If substitute inputs are readily available at similar prices, then while price responsesmay be large, the response of health status to price may be small, and thus little differencewill be apparent between the long-run and short-run. As mentioned earlier, however, whenpreventive prices are highly correlated with curative prices, then substitution is less likely,meaning that there may be larger health feedbacks.
6
To summarize the implications of the model for examining these issues, write thelong-run demand effect of a curative care price change more generally:
dITc7, dIc',+s dIT"+, dHT+s-,= +
dpeur dpcu5 dHT+31l dpcur
It is seen here to equal the sum of the short-run negative demand effect (holding healthconstant) plus the a priori unsignable feedback through health.
Relating the Model to Conditional and Unconditional Demand
To understand the implications of the previous model for interpreting conditional andunconditional discrete choice demand, consider the following simple econometric equations.Let St be a sickness indicator variable equal to 1 when an individual reports his health tohave fallen below a threshold in the current period, such that he is "sick":
St = 1 if report sickSt = 0 otherwise
Similarly, let M, be a medical care indicator equal to 1 if curative care was demanded in thecurrent period:
M, = 1 if ItC r>OMt = 0 otherwise
Let X represent a vector of observables assumed exogenous,' p represent the price ofcurative medical care, and vs and UM represent unobserved residuals. Then
(1) St = S(p,X) + us(2) Mt = M(p,X) + vM(3) [MtI(St=l)] = MS(p,X) + UMIS
Assume for this section that Cov(vS,UM) =0, or else a non-zero correlation has been taken intoaccount in the conditional estimates, methods for which are described in Section 3.
Clearly, the population probability of seeking medical care E[MJ differs from theconditional expectation E[M, I S= 1]. To see this, re-write E[MJ as:
4Exogeneity will be difficult to determine for variables such as income. Health is another variable which isoften included as an exogenous covariate. While health indicators may vastly improve predictive power formedical care demand, the model in Section 2.2 should caution against including them due to potentialendogeneity.
7
(4) E[MJ = E[MtlSt=l]*E[S,=l] + E[M,IS,=O]*E[St=O]= E[M,IS,=1]*E[S,=1]
The last equality relies on the fact that if M is defined as curative care, then E[M, I S1=0I =0.This also shows that the effects of the covariates on conditional medical care demand willdiffer from those on the unconditional. By substituting the second line of (4) into theelasticity formula for prices, the effects can be separated into distinct components:
(5) dE[Mj] p _dEMjSt= 1] p_ dE[S p
dp E[Mj] dp E[MjSt=l] dp E[S,3This indicates that the unconditional elasticity of curative care demand equals the sum of theconditional elasticity of curative care demand plus the elasticity of health with respect to thecovariate, or EM = EMIs + ES.
This allows easy interpretation of the different estimates. The model in the previoussection highlights the fact that current health is affected by past inputs, which in turn will beaffected by covariates such as prices. Equation (1) can thus be interpreted as a reduced formhealth demand equation. By taking into account this feedback effect through the probabilityof sickness, the unconditional estimates from equation (2) can then be interpreted asmeasuring long-run effects of changes in covariates. In contrast, the conditional estimatesfrom (3) give only the short-run impacts, before healthiness has been affected by pricechanges.
8
3. Conditional Demand and Selection Bias
The analysis thus far has assumed that the short-run and long-run responses were bothcorrectly estimated. As alluded to above, however, direct estimates from the conditionalsample may suffer from selection bias if health is correlated with the error term of the healthcare demand equation. This section first discusses intuitively why such a correlation mayarise. It then reviews the assumptions about unobserved correlations that are implicit in thenested multinomial logit which is typically used. Next, it outlines methods for using discretechoice models for unbiased estimates of conditional and unconditional demand. Finally, testsfor selection bias in conditional estimates are discussed, including the use of the multinomialprobit for a nested testing strategy.
A key idea relied on in the econometric modeling below is that in addition to theusual discrete alternatives when sick, the state of "not sick" can be considered as anotherdiscrete choice. This interpretation arises from the model in Section 2.2, where peoplechoose their probability of sickness in a given period by adjusting prior inputs. Becausepeople optimize dynamically, this sickness probability is chosen jointly with expectedcurative care demand levels when sickness does occur. Thus it is analytically reasonable todefine joint health and health care demand error distributions on the entire population. Thisavoids the difficulties of sequential selection rules discussed by Lee and Maddala (1985), andsimplifies unconditional estimation, as shown below.
Intuition Behind the Bias of the Conditional Approach
One reason for concern over conditional estimates is that health indicators used tocondition the sample are often self-reported. Sindelar and Thomas (1991) find that such self-reported morbidity may only be tenuously related to objective measures. In the Cote d'Ivoiresample used in Section 7, the probability of reporting a sickness actually increases withincome. It is speculated that this phenomenon is largely a result of lower income personstolerating higher levels of discomfort before declaring themselves "sick." Anecdotalaccounts depict chronically ill poor people in developing countries who often suffer frommalaria while attempting to continue with their work. If this is perceived as normal, thenthey may not report malaria as an illness. Wealthier people, on the other hand, may be ableto purchase drugs to treat the malaria and would then classify themselves as sick, given thesame objective illness level.
If such reporting biases were solely correlated with an observable such as income,then that by itself would not lead to biased estimates of short-run price effects. However,more generally the problem is one of unobserved attitudes towards both illness and care-seeking behavior. This hypothesis is supported by Wolfe and Behrman (1984), who find that"women's childhood backgrounds affect both their adult health and health-care utilization."Such attitudes may be rooted in one's personality and be unlikely to change as incomechanges. If so, then income marginal effects estimated from conditional cross-sections willbe biased.
9
Furthermore, it may be that those who tend to under-report illness also tend to avoidmodem health care even when sick. Or a person with an unobservably poor healthendowment may become accustomed to the medical care system and be more likely todemand care when sick. Conversely, those who tend to avoid health care (due to unobservedpreferences) may be more likely to be sick currently as a result of neglecting to get care inthe past.
There are numerous potential reasons to suspect correlation between the health andhealth care demand residuals.5 Unfortunately, because several effects may work in oppositedirections, no clear prediction can be made for the net sign of the correlation.
Unobserved Correlations in the Nested Multinomial Logit
The treatment of correlation between sickness and demand unobservables in nestedmultinomial logit models is reviewed here, based on established results in the literature (seee.g., McFadden, 1984). For this analysis, assume that three mutually exclusive choices areavailable, which we may refer to as well w, self care6 s, and curative modem medical carem. Let V represent the observed portion of the utility index, The unobserved portion ofutility contains a random term E for each alternative. The options when sick may havecorrelated unobserved elements Esm, and the non-demanders may have unobservables c'scommon to their sub-groups, or "nests."
Uwe1i(Sick=O,Med=O) = Vw + Ew + Ews
Use,ISick=1,Med=O) = Vs + Es + Ews + esm
Um,d(Sick=1,Med=1) = Vm + Em + Esm
Assume first that the true specification of these probabilities is multinomial logit(MNL), and thus Independence of Irrelevant Alternatives (IIA) holds. Then McFadden(1981) shows that when the joint probability distribution f(Sick,Med) =f(Med I Sick)f(Sick) isdecomposed into its marginal and conditional probabilities, each of these two componentprobabilities in turn has an MNL form. This is convenient, allowing each to be separatelyestimated. This will also hold if the true model is a nested MNL (NMNL), allowing forcorrelations between choices within each of these separate components (E,,=0, Esm *0). Thus
5Correlation may also arise if the data on morbidity and care demand are contemporaneous. Often peopleare asked how many days they were sick in a recall period, and then if they sought care in that same recallperiod. However, this should not induce an unobserved correlation between care demand and the probability ofreporting any sickness. Nevertheless, the fact that the length of illness should be shorter if care was demandedis strong evidence that sickness intensity should not be used as an exogenous variable, as has been done in manypast studies.
6'he term self care is often used for this category, although it is somewhat of a misnomer. Actually, in allcases individuals are likely to provide some care at home. When no formal care is demanded, this is merelylikely to be more time-consuming (for a given illness level). It is more appropriately thought of as a residualcategory for those who are sick.
10
for example, if the choices for sick people all have common unobserved elements, then it isstill possible to estimate f(Med I Sick) as a distinct NMNL.
These probabilities can be expressed as follows. Let j = 1,. . ,J index a branch of achoice model, for example the alternatives available when Sick= 1. Let k= 1,. .,K index thesub-choices of that branch, for example to seek curative care or not. Define an "inclusivevalue" (or "dissimilarity") parameter that summarizes the observed information of aparticular branch:
Dj=1ngk'X eXP(V%k)
Choice probabilities can then be written as Pjk = PkljPj, where:
- exp(V%k)
M exp(D,)
(6)
exp[V +(l -o1)D1]
E=l eXP[V"+(l-(F")Dj]
The parameter aj on the inclusive value is the correlation between the unobservables of thechoices within a sub-group and can be estimated up to a scale normalization.
Unfortunately, decomposing Pik into two parts, each of which has the logit form, isonly valid when there is correlation between unobservables within branches. If instead thereis correlation between unobservables in different branches, then the resulting conditionalprobability f(Med I Sick) will no longer have an NMNL form. This would arise, forexample, if there is correlation between the alternatives in which care is not demanded (, isnon-zero). Thus when demand is estimated as an NMNL conditional on sickness, theimplicit assumption is that E,, is zero. Ignoring this correlation between sickness anddemand is analogous to estimating OLS on continuous data with sample selection, instead ofusing a selection model.
Unbiased Estimation of Conditional Demand
One estimation option to avoid selection bias when e., is non-zero is a two-stepmethod similar to that proposed in Heckman (1976). Dor and van der Gaag (1993) reporthaving found no selection bias in conditional health care demand estimation, using a discretechoice version (due to Van de Ven and Van Praag, 1981a) of this procedure. However, theydo not report how identification was achieved. Relying on functional form has been foundunreliable in many applications (e.g., Manning, Duan, and Rogers, 1987), and in mostdatasets there are no obvious identifying variables that affect health but not health caredemand.
11
An alternative is to instead estimate an unconditional model, without constrainingEs= 0. If desired, conditional elasticities can then be calculated either directly from themodel, or indirectly by subtracting the health elasticity from the unconditional elasticities, asshown in Equation (5) of Section 2.3. It is important to recognize that Heckman-typecorrections are unnecessary in this application, because the data are typically not censored.As pointed out earlier, the healthy people who are selected out of the sample for conditionalestimates are known to have zero curative care demand by definition.
12
4. Estimating Unconditional Demand
Several options are discussed here for unbiased estimation of unconditional demand,ranging from Ordinary Least Squares (OLS) to the Multinomial Probit (MNP). These fallinto two categories, based on whether they estimate health status jointly with health caredemand, or only estimnate the marginal (in the statistical sense) probability of health caredemand. With all of them, however, instead of only using a sample of sick people as in theusual conditional estimates, the non-sick are also included in the regressions.
As argued earlier, the dynamic model in Section 2 implies that the health care demanddecision can be modeled for the entire unconditional population. This implies that the choiceset can be redefined to consist of hospital h, clinic c, and none n, where now no distinctionis made between whether non-demanders consider themselves as sick or not. This marginalprocedure still yields consistent estimates of unconditional health care demand, assuming thatthe error distributions are appropriately specified (as discussed below). It may be lessefficient than the joint estimation, but the marginal procedure may be preferred when self-reported health indicators are suspect or when identification of the au, covariance isproblematic.
In discussing the following unconditional estimation strategies, it is useful to sub-divide the medical care choice, since often elasticities are desired for particular care types.In accord with the Cote d'Ivoire data used in Section 7, medical care options considered hereare hospital h and clinic c, in addition to the non-care options of self s and well w.
Marginal Demand Estimators (without Health Information)
Listed below are four variants of unconditional demand estimators that circumvent theissue of possible correlation between health and demand residuals, which is done by ignoringthe health status data and simply treating health care demand in the population like thedemand for any other discrete good. Just as many transportation mode choice models ignorethe complexity of jointly considering employment status, the amount of health care demandedcan be analyzed without reference to health status.
A. Binary Regression
The simplest unconditional demand estimates are obtained from binary techniques, forexample regressing hospital choice against all other choices (clinic and none), as depicted inFigure 1. The estimator could be the binary logit, or even the Linear Probability Model(LPM). However, assuming that the non-hospital choice aggregation has a type I extremevalue distributed error may contradict the implicit assumption that the non-clinic choiceaggregation also has this distribution. Coherently estimating both the hospital and clinicdemands in this way requires IIA to hold across the underlying options and thus may bebiased when Ehc,O.
13
Choice Trees Covariance Structures
hosp h c n
none + clin a 2
clin ° ac
none + hosp 0 0 a2
Figure 1: Binary Models
hosp -aCclin O a2
none 0 0 a2
Figure 2: 3-Choice MNL
hosp [at72
< clin aoc a2
none O 0 a2Figure S: 3-Choice NMNL
hosp ah
clin ahc ac
none Uhn acn a:2
Figure 4: 3-Choice MNP, free covariance structure
14
B. 3-Choice Multinomial Logit
Three-choice MNL's can be estimated between hospital, clinic, and no care n, as inFigure 2. This assumes that (Eh,EC en) are jointly distributed type I extreme value, instead ofspecifying the distribution over (eh,eC,eW,ES). Notice that this specification does not precludecorrelation from non-zero eW. and thus is unaffected by any possible selection bias.
C. 3-Choice Nested Multinomial Logit
A reasonable generalization of the MNL in 4.1 .B would be to allow correlationbetween the unobserved components of hospital and clinic utilities in an NMNL, as in Figure3.
D. 3-Choice Multinomial Probit
Finally, a general pattern of unobserved correlations could be allowed for byestimating a 3-choice multinomial probit (MNP) for hospital, clinic, and no care, as inFigure 4. This would allow for the possibility that no care unobservables are correlated withhospital and/or clinic unobservables. While this estimator is not biased by the correlationswhich could bias conditional regressions, it does present a practical barrier in that MNP's arestill very costly to estimate (estimates in this paper took 6-12 hours of workstation timeeach).
Furthermore, as with continuous selection correction techniques such as Heckman'stwo-step method, identification of the unobserved correlations does rely on certainassumptions. Keane (1992) argues that even though in theory the joint normality assumptionformally identifies the model, in practice estimates may be fragile in the absence of exclusionrestrictions. For robustness, he recommends dropping one variable from each utility indexV, and notes that such exclusion restrictions arise naturally when choice-specific attributessuch as prices are available. These cross-price restrictions may not always be valid,however, when a dynamic model implies that past and future prices for goods not chosentoday may still affect today's utility. Such exclusions would instead be more justifiable inshort-run estimates conditional on health. Fortunately, Keane showed that unidentifiedmultinomial probit models were characterized by larger standard errors than the same modelsestimated with covariance restrictions, which provides an informal identification test.
Estimating Demand Jointly with Health
The next set of estimators adds a layer of complexity to the 3-choice unconditionalmodels by splitting the "none" choice into a "self" and a "well" choice. The addition of"well" as a choice essentially implies that health demand is now being estimated jointly withhealth care demand and requires that ew, now be considered explicitly. This expansion of themodel may make inferences more precise in some cases, but it is not necessary for obtainingconsistent estimates of unconditional demand, as has been shown in Section 4.1.Furthermore, the computationally burdensome 4-choice multinomial probit may be necessary
15
in some cases. However, even this may not always be sufficient to identify a flexiblecovariance structure without additional assumptions, which could jeopardize the consistencyof these joint unconditional estimates.
A. 4-Choice Multinomial Logit
A direct extension of the usual conditional 3-choice MNL's is to add a separate"iwell" alternative, assuming now that the population chooses between hospital, clinic, self,and well, as in Figure 5. While this provides unconditional (long-run) demand estimates,they may be biased by the same unobserved correlations that may bias conditional estimates.
B. 4-Choice TMANl, with unobserved correlations among the sick
An extension of 4.2.A is to allow the self, hospital, and clinic options to make up anest separate from the well option, as in Figure 6. This makes the reasonable assumption ofsome common unobserved utility element to all of these sick categories. This could befurther refined with a separate nest within the sick category, separating self from hospital andclinic. However, this still does not allow non-zero er,,.
C. 4-Choice NMNL, nesting non-demanders
To allow ews to differ from zero, a different nesting structure could be assumed whichnests demanders separately from non-demanders, as in Figure 7. This remedies the selectionbias problem, but as discussed in Section 3.2, this nesting pattern cannot simultaneouslyallow 4.2.B's general correlations among the sick options.
D. 4-Choice Multinomial Probit
The most general estimator for this problem is the 4-choice multinomial probitdepicted in Figure 8. Although an order of magnitude more computationally burdensomethan the 3-choice MNP, it does allow for a general pattern of correlation between unobservedutility elements.
16
hosp o 2 U8U
clin 0 u2 conditional
self 0 0 a 2 MNL
well o 0 0 a2
Figure 5: 4-Choice MNL
hosp aT2
clin a7,h, o 2
self u1h. a.h. a2
well 0 0 0 a 2
Figure 6: 4-Choice NMNL, sick nest
hosp [CT2
clin OCh o 2
self 0 0 a2
well L 0 a,0,, a2
Figure 7: 4-Choice NMNL, non-demanders' nest
hosp a ]hclin ahc ac
self ah. ac, a jwell L ah,C aTa a,, a 2
Figure 8: 4-Choice MNP, free covariance structure
17
5. Testing for Selection Bias in Conditional Estimates
It is useful to test for when it is inappropriate statistically to condition the sample onsickness. As Duan et al. (1983,1984) show, it is always possible to obtain consistentestimates of a conditional mean without explicitly modeling the correlations between theequation of interest and a "selection" equation. The question here, however, is when theconditional probability will have a logit specification, given that the population probabilitydoes. In other words, when can the marginal and conditional components of the populationprobability be estimated separately within the logit framework? If it is simply assumed thatthe conditional probabilities are logistic, their relationship to the population effects will bevery difficult to interpret, unless it is known that the transition probability of falling sick isalso logistic.
A first test for the relationship of the conditional and unconditional effects can beobtained by estimating the bivariate model E(S=1). This will reveal any selection effectsbased on observables. Next, the elasticity of health can be added to the conditional elasticitywith respect to the variables of interest, and a rough test for consistency will be whether thatequals the unconditional elasticity (obtained from a method that does not assume e,ws =0, suchas 4.1. C). If the two methods of recovering the unconditional elasticity are approximatelyequal, then this application of Equation 5 may be a sufficient test for "rough and ready"policy purposes.
A second rough test can be carried out when Model 4.2.B indicates U,hc==O. Asdiscussed above, Model 4.2.C can then be estimated, and this will allow a t-test orLikelihood Ratio or other classical tests of whether r,,.=. This is the test of whether thecoefficient on the inclusive value for the "no medical care" option equals one. This is not anexact nested test, though, since it could yield different results when oshc is simultaneouslyallowed to differ from zero.
Finally, exact nested tests can be derived from the multinomial probit (MNP) model.To clearly understand this test, assume again that the choices are restricted to well w, self s,and medical care m. The probability that w is chosen is:
P(w) = P(e-eW < V,m-V, w EM-e< Vw,Vm)
McFadden (1973) has shown that the logit models can be derived from stochastic utilitymaximization, assuming the J unobservables are distributed iid type I extreme-value. TheMNP, however, assumes that the ej are distributed multivariate normal. Thus the differences
18
e,-eW,em-ew will also have a normal distribution, with a J-1 dimensional covariance matrix(superscripted by P for Probit):
Iw2 w2 +02 2o }Because the scale of the latent utility is ambiguous, a normalization must be made in Q,which only leaves two free elements to be estimated. This implies that identification of uawwould require several restrictions on the other parameters of D. However, this does notinterfere with an omnibus test against the null of the NMNL-type covariance restrictions.This is seen more clearly by writing the 0 L analogous to that assumed by the logit, whichallows only one free parameter (assumed here to be uor). Notice that the logit also implicitlyrestricts the variances of the unobservables to be equivalent. The combination of theserestrictions results in the two diagonal terms of 9wL being constrained to equivalence:
2a2
{a =2+G 2a}QL a osm 2
It can be seen here that if either of the logit assumptions of equal variances, or of rwm=O, isincorrect, then a nested test of 0" against a restricted version of the MNP with covariance 0 L
will reveal this. By next comparing the D's for the probability that (m) is chosen, it is seenthat uas not equal to zero would also result in a classical test rejecting the logit covariancestructure. This occurs through the nesting restriction here that two times the off-diagonalequals the lower diagonal term:
a a+O -2awm { w m m2Ows
la -aw -as +o a 2+5 2_asm
m ( Wmsm Ws 2s m{2~a 2 a~am
Because 0" only has one more free parameter than 0 L, the overall NMNL type structure isrejected if only just one of these restrictions is rejected:
2 2 20 w 0s 0 M 0= =O " awm=
0
19
Without further identifying assumptions, however, it will not be known which restriction wasviolated. For testing purposes, it is irrelevant which of these restrictions is relaxed; they willall yield identical results. A Likelihood Ratio test of the MNP under these two nestedalternative covariance structures then serves as an omnibus discrete choice selection bias test.
To summarize this discussion, the simplest (though non-nested) test of u,as=0 isthrough an NMNL such as Model 4.2.C, in the fortuitous case where Model 4.2.B revealsushc=O. A second test estimates Model 4.1.C and uses Equation 5 in Section 2.to compare itto unconditional estimates. If the elasticities are "sieilar enough" for the application athand, then selection bias is not a practical problem. When a more precise test is needed,however, the MNP may be used.
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6. Data and Estimation Procedures
This section discusses the data and estimation algorithms used in the empirical sectionthat follows. In addition, a solution is proposed for a problem that has been raised in theliterature regarding the empirical specification of price and income variables.
C6te d'Lvoire Living Standards Survey
The data used are the 1985 round of the Living Standards Measurement Study(LSMS) survey collected by the World Bank and the Ivorian government (see Ainsworth andMunoz 1986, for a more detailed description of the data). This same dataset has beenpreviously used by others for health care demand estimation; see for example Dor, Gertler,and van der Gaag (1987), Gertler and van der Gaag (1990), and Dor and van der Gaag(1993). Means for the conditional and unconditional samples are reported in Table 1.
The most commonly demanded health care options in the data can be divided intohospitals and clinics. The analysis will be confined to the choice of the first provider visitedin the reference period. In 1985, monetary fees for curative services were virtually zero, butthere is considerable variation in the distance and time to travel to the facilities; thus time-price elasticities will be estimated below. One implication of this is that preventive andcurative care (time) prices are highly correlated, implying that it is possible that the long-runelasticities could be either smaller or larger than the short-run responses.'
The health indicator typically used to identify the "sick" sample is whether individualsreport themselves to have been sick in the past four weeks. As mentioned earlier, this ispositively correlated with income in this sample, which may partly be due to reporting bias.This may make the long-run elasticities easier to interpret, and thus preferable a priori. Thisis supported by the fact that distances to clinics have not dramatically changed in the recentpast for rural areas. The estimation is confined to an adult (age > 15) rural sample in orderto minimize confounding factors, while highlighting the issue of the conditional versusunconditional differences.
The regressor set includes individual gender, age, and education, and uses householdconsumption per adult as a proxy for income. Also included are community-level wages,hospital travel-time and clinic travel-time (to the nearest facility). The community-levelcharacter of the data is intended to reduce the possible endogeneity problems from self-reported data. There is still a danger that endogenous migration (Rosenzweig and Wolpin,1988) or program placement (Rosenzweig and Wolpin, 1986) will introduce correlationbetween health care prices and the demand residual, but this possibility will be ignored forthe present purposes.
7The high correlation between curative and preventive prices also implies that cross-elasticities betweenthese cannot be obtained from these data. This is unfortunate, because many user fee proposals in Africa focuson raising curative fees only.
21
Table 1: Descriptive Statistics, Unconditional and Conditional Samples
Unconditional Conditional on Sick = I
Standard StandardMean Deviation Mean Deviation
Probability Sick .34 .47 1 0(= 1 if self reported sickin last 4 weeks)
Probability visit Hospital .048 .22 .144 .35(last 4 weeks)
Probability visit Clinic .078 .27 .231 .42(last 4 weeks)
Travel Time: Hospital (hours)a .95 1.00 .93 .88
Travel Time: Clinic (hours)a .54 .61 .56 .62
Income (annual, 1985 CFA)b 2.47 2.13 2.62 2.19
Wage (daily, 1985 CFA)cd .51 .19 .53 .20
Male .43 .50 .42 .49
Education (years) 1.14 2.62 .87 2.23
Aged 37 16.9 44 17
Sample size 4042 1359
a. To closest facility reported by community elders.b. Permanent income is proxied by total household consumption, normalized by number of adults in
household. Divided by 10,000 for estimation.c. Community reported agricultural wage, by gender.d. Divided by 100 for estimation.
The data come from the 57 rural communities surveyed in 1985, and the communityreported variables are correlated as expected. The hospital and clinic travel times have acorrelation of 0.47; the wage correlations with these are -0.20 and -0.27, respectively.
Estimation Procedures
The models estimated below begin with the simplest linear probability models andgradually relax assumptions. The more complex non-linear models include binomial logits,
22
multinomial logits (MNL's), nested multinomial logits (NMNL's), and simulated multinomialprobits (MNP's).
The logits were estimated using the "hlogit" routine by Axel Borsch-Supan.Davidson-Fletcher-Powell (dfp) was the principal non-linear search algorithm employed, witha covariance correction through recalculating the exact hessian. The multinomial probitswere estimated using the "ssmlmnp" smoothly simulated maximum-likelihood routine byBorsch-Supan and Vassilis Hajivassiliou; see Hajivassiliou and Ruud (1994) for details onsimulation methods.
Because the coefficients do not directly give the marginal effects, Appendix Table Alpresents price elasticities for each of the models estimated. Although classical LikelihoodRatio tests indicate whether the logit models are statistically different from each other, this ofcourse depends on sample size, and the probit cannot be compared using the classical nestedtests. The elasticity table will also aid in determining whether the estimates differ much forpolicymakers.
Elasticities were obtained from the calculus derivations of the marginal effects bytaking the average of the elasticities evaluated at each observation. Simulations throughsample enumeration (Train, 1985) generally yielded very similar results.
The four potential discrete choices are denoted as hospital h, clinic c, self s, and wellw. The conditional MNL's allow choice between h, c, and s. The unconditionals allowchoices between h, c, s and w, although Table 3 also gives estimates with s and w aggregatedinto a none n category.
For identification, each observable covariate is interacted in the likelihood functionwith an alternative specific dummy. Because a constant could be added to the coefficient foreach choice on a specific variable without changing the probabilities in the likelihoodfunction, the coefficient vector for one alternative is normalized to zero in the estimation.For ease of interpretation, this reference category is "well" in the 3-choice unconditionalestimnates, and "self" in the other cases.
Price and Income Specification
Each of the regressors is specified through interactions with alternative-specificdummies for the hospital and clinic choices. Following Gertler, Locay, and Sanderson(1987), the functional form for these observables arises from assuming that individualsmaximize utility by choosing health provider j such that conditional utility Uj> = Uk for all kin the set of health providers J. The additively separable utility function U1 for each chosen jis defined over the expected health outcome Hj after treatment j, and consumption C, afterpaying treatment price pj (given the budget constraint). Choices are constrained by the healthproduction technology for each provider type j, which is approximated by an intercept Q9,and allowed to vary based on socioeconomic characteristics X such as age, education, andgender:
23
choose j to max Ui = ,Cj + a2Hjsubject to Cj = Y - pjand Hj = Qj + Qjx og + ,ljX
This leads to the specification of observables Vj in the indirect utility function:
Vj-= U2I3 0j + oelY - alPj + 2gljX
Gertler et al. (1987) and Gertler and van der Gaag (1990) argue that the model also logicallyimplies that al must be constrained to equality across choices j, and that estimating equationswhich do not impose this theoretical restriction are misspecified.
However, Dow (1995b) shows that with a more general utility function, suchrestrictions are not necessary. For example, the utility function may also include aninteraction term a 3Cj*Qjc between consumption and some dimension Qjc of the healthimprovement from health care j. This relaxes the strict separability of health andconsumption in the utility function and captures the idea that the rich and poor may placedifferent values on improvements in their health status. Similar arguments can be made forrelaxing other such restrictions, implying that previous estimates have not necessarily beenmisspecified. This paper estimates unrestricted (though linear) specifications of price andincome variables in order to ease generalizability of results to most other studies, which havetypically used this specification.
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7. Short-Run and Long-Run Estimation Results
The previous sections have outlined many theoretical differences between estimationstrategies; this section empirically explores the magnitude of these differences. First, theeffects of covariates on the probability of sickness are examined, as a simple way todeternine how covariates will affect health care demand in the short versus long-run.Sections 7.2 and 7.3 estimate conditional and unconditional demand models with a variety ofcovariance assumptions, and Section 7.4 presents results of selection bias tests. To helpcompare the different models, Appendix Table Al presents the price elasticities from eachone.
Probability of Self-Reporting Sick
The first step in empirically evaluating the effects of conditioning is to examine thelogit results in Table 2 for the probability that sickness is reported in the past 28 days. Thefarther away clinics are, the higher the probability is of reporting sick, while the effect forhospitals is negative, although tiny and statistically not different from zero. Income andwages are both positively correlated with the probability of reporting sick. This couldperhaps be due to higher risk activities by the wealthier, or it might represent differences inthe level of discomfort that defines sickness for people in different circumstances. Finally,females and the more highly educated also report more sickness. The hospital and clinicprice elasticities of health from Table 2 are -0.02 and -0.08, respectively.8 These lowelasticities suggest that empirically, for this dataset, the difference between long-run andshort-run price elasticities is not large.' The significant effects for other covariates,however, are seen below to lead to different inferences depending on whether conditional orunconditional estimation is used. Simply by virtue of the significant coefficients on theseobservables, it can be seen that the conditional estimates are not equal to the unconditionalpopulation effects.
8A rough test of the effects of multicollinearity when both prices are included as regressors was performedby dropping each in turn. The results were virtually identical.
9Virtually the same information is revealed by simple Linear Probability (OLS) estimates. They yield healthelasticities of -0.015 with respect to hospital prices, and -0.071 for clinics--versus the logit estimates of -0.015 and -0.079.
25
3-Choice Unconditional and Conditional Estimates
Table 3 compares the 3-choice'0 unconditional models--choosing between none,hospital, and clinic (model I.C)--to the conditional models between self, hospital, and clinic.Correlation is allowed between hospital and clinic unobservables in these nested MNL's."Conditional price (travel time) elasticities are estimated to be -0.11 for hospitals, and -0.49for clinics, though the t-statistics on the hospital price parameters are insignificant in most ofthe models estimated. Adding these to the health elasticities from the earlier logit of theprobability of sickness P(S =1) gives the simplest estimate of the population elasticities:
Eh =-0.11 + (-0.02)= -0.13Ec =-0.49 + (0.08) = -0.41
These can be compared to the estimated unconditional elasticities from column 1 which usedthe entire sample:
Eh = -0. 15E, = -0.37
These two methods of recovering the population elasticities yield remarkably similar results.As discussed in Section 5, this gives indirect evidence that in this sample conditioning onsickness yields "not too inconsistent" estimates of the short-run effects. However, theconditional clinic elasticity is more than 25 percent higher than the unconditional elasticity.Depending on the application, this difference may or may not be meaningful.'2
'"To check robustness, Linear Probability (OLS) estimates are reported in Appendix Table A2, with eachalternative estimated separately as in Model 4.1 .A. Columns 2 and 4 give the conditional estimates (i.e., omittinghealthy people; thus the non-hospital choice aggregates only self and clinic) with price elasticities of Eh = -0.10and E = -0.36. The unconditional elasticities from columns 1 and 3 were also OLS's, but used the entire sample(thus the non-hospital category includes well, in addition to self and din): Eh = -0.10 and Ec = -0.26. Thoughslightly smaller in magnitude, the patterns are quite similar to the results from the more complex non-linear models.
"Results from non-nested versions of all of the following models are reported in Appendix Table A3.Significance of nesting parameters and likelihood ratio tests reject these MNL's in some cases, but in generalparameter estimates and inferences are unaffected by nesting patterns.
'2Standard errors for these elasticities are complex to derive. For the easier to estimate Linear Probability andnon-nested MNL models reported in the Appendix, bootstrapped standard errors for the elasticities are presentedin Appendix Table 1. Fifty replications at the original sample sizes were used. It can be seen that the t-ratios onthe estimated price coefficients closely approximate the t-ratios from these standard errors. While they may differin some cases by as much as 15 percent, in no case do they yield qualitatively different conclusions, and thedirection of this difference appears random.
26
Table 2: Binary Logit ofProbability of Reporting Sick In addition to the differences in price
elasticities, there are also other potentiallyTime Hosp -.02 important differences between the conditional
(O.55)a and unconditional approaches in the effects ofindividual socioeconomic characteristics. For
Time Clin .23 example, while wages positively effect reported(3.37) sickness, they negatively impact conditional
Income .11 hospital demand, possibly since they represent(5.26) the opportunity cost of travel time. In the
unconditional estimates, however, the wageWage (4.22) effects cancel, with point estimates being
(4.22* insignificant but positive on net. One potentialMale -.27 inference is then that investing in labor
(3.55) productivity may lower utilization (and henceobjective health outcomes) in the short-run, but
Education .04 in the long-run that effect will be fully offset by(2.23) the positive effects of higher earnings.
Age 4.20Age (18.160) Another difference is that older persons
demand more care unconditionally, while in theIntercept -3.01 samples truncated to contain only the sick, age
(18.29) appears negatively correlated with demand.
InL -2334 Furthermore, while females in thenl at zero -2771 unconditional sample are more likely to demand
clinic services than self-care, in the conditionalElasticities of Prob(Sick= 1) with respect to: sample the only statistical effect is that males
Time Hosp: Eh = -.015 are more likely to demand hospitals. SuchTime Clin:E= .079 differences may be important, for example,Income: Ey = .18 when assessing which groups benefit from
El..ticitie fro Linear ProbabilityModel(nothealth care subsidies, as conditional estimatesElasticities from Linear Probability Model (not ma giv miladn infrecsreported here) of Prob(Sick= 1), evaluated at sample may give misleadig inerences.means:
Eh = -.014 Unconditional 4-Choice Nested MultinomialE,= .071 LogitsE, = .09
a. Absolute values of t-statistics in parentheses. Next, the self-reported health status isexplicitly considered in a 4-choice
unconditional model, which includes the well w alternative jointly with the self, hospital, andclinic choices. First, Table 4 column 1 reports estimates assuming zero correlation betweenerror terms, as in Model 4.2.A. Results are very similar to the 3-choice unconditional modelreported above, with hospital and clinic elasticities of -0.05 and -0.35.
In column 2, a version of Model 4.2.B is estimated, allowing for non-zero covarianceU,hc. Both the Likelihood Ratio (LR) test and the t-test on the inclusive value for 0
shc in the
27
Table 3: 3-Choice Nested Multinomial Logits nested logit clearly reject the MNL.However, the clinic elasticity is essentially
NMNL NMNAISick=I unchanged at -0.37, and the hospitalTimne Hosp__h -.10 -.15 elasticity of -0.14 remains insignificantly
(1.67) (1.07) different from zero.Ttme Clinmc -.46 -1.11
(2.86) (4.72) Although the significant ashc in this
Income h .10 .12 last regression indicates that Model 4.2.C(4.90) (3.31) may be inappropriate, it is nevertheless
Income_c .07 .05 interesting to estimate the model as part of(3.34) (1.50) a non-nested testing strategy. This will help
Wage_h -. 01 -.91 show whether a general pattern exists, or(0.29) (1.76) whether Model 4.2.C in turn indicates that
Wage_c .04 -.31 au,, is non-zero. Column 3 of Table 4(1.38) (0.80) reports this regression, which estimates ahc
Male_h -.06 .35 and ow, simultaneously, and it can be seen(0.43) (1.69) that the LR test again rejects the MNL
Male_c -.25 -.09 against this specification. Furthermore, the(2.19) (0.56) coefficient on the inclusive value for the
Education h -.02 .0001 "no medical care" sub-branch is(0.77) (0.00) significantly larger than 1, indicating that
Education c -.00 -.05 this particular model is not consistent with(0.13) (1.25) utility maximization (McFadden, 1981).
Age_h 1.60 -2.22 This provides ambiguous evidence(4.43) (3.60) concerning the statistical bias of
Atge_c 0(6.34) -(28378) conditioning. However, the fact that theelasticities again do not change much (now -
Intercepth -3.28 -.54 0.36 and +0.02) indicates that any(12.46) (1.11) statistical selection bias may be unimportant
Intercept_c -3.04 .15 economically. This is corroborated by the(14.28) (0.43) fact that the 4-choice clinic elasticity is
Inclusive value .50 1.18 virtually identical to the 3-choice(h,c nest) (-2.49) (0.50) unconditional elasticity, since while the 4-
log-Likelihood -1811 -1185 choice model may be affected by selection
Elasticities bias, the 3-choice model cannot be.Uncondl Condl
Hosp -.15 -. 11 MNP Test of Selection Bias in theClin -.37 -.49 Conditional ApproachNotes: NMNL's allow correlation between hospital and clinicunobservables; MNL's reported in Appendix Table A3. The informal selection tests abovea. The alternatives in the (3-choice) unconditional model are .d.ihospital, clinic, and self. b. _h and _c suffixes indicate that the provided evidence that conditionig oncoefficient measures the effect of the variable on the hospital sickness did not appear to inappropriatelyand clinic options, respectively, through interactions with restrict short-run estimates. In Section 7.2,alternative-specific dummies. c. t-test for null hypothesis that the unconditional price elasticity wascoefficient equals one. roughly equal to the sum of the conditional
28
price elasticity plus the elasticity of sickness. In Section 7.3, elasticities appeared robust tonon-nested comparisons of covariance assumptions. Finally, the more formal test usingsimulated multinomial probits is reported in Table 5.
Four-choice models were estimated between well, self, hospital, and clinic. InColumn 1, the MNP was estimated with no free covariance parameters, which is similar tothe non-nested MNL; this model has been termed the Independent Probit (IMNP) byHausman and Wise (1978). In Column 2, the "covariance" MNP was estimated with fivefree covariance parameters, which is the most that can be identified given that four choicesare estimated. The latter nests the IMNP, providing for an omnibus nested test for selectionbias.
29
Table 4: 4-Choice Unconditional (Nested) Multinomial Logits
MNL NMNL NMNLb
Time Hosp_hc -.06 .02 -.10(0.66) (0.31) (1.57)
Time Clin_c -.68 -.44 -.48(5.16) (3.10) (2.86)
Income_h .12 .09 .13(4.62) (3.78) (3.64)
Income_c .07 .05 .10(2.60) (2.56) (2.73)
Income_s .02 .04 .12(0.85) (2.14) (1.20)
Wage_h .04 .14 .86(0.10) (0.37) (1.93)
Wage_c .63 .76 1.18(1.93) (2.77) (2.93)
Wage_s .71 .71 2.64(3.27) (3.72) (2.73)
Male h .01 -.01 -.39(0.04) (0.09) (2.14)
Male c -.40 -.39 -.60(3.04) (3.60) (3.53)
Male_s -.26 -.27 -1.26(2.94) (3.44) (2.87)
Education_h .03 .03 .06(0.99) (1.12) (1.97)
Education_c .01 .01 .04(0.36) (0.60) (1.53)
Education s .03 .03 .10(1.56) (1.87) (1.20)
Age_h 2.76 3.28 7.80(5.82) (7.69) (6.28)
Age_c 3.66 4.10 8.33(9.62) (12.55) (6.69)
Age_s 4.63 4.37 20.48(9.62) (18.01) (5.09)
Intercept_h -3.96 -3.57 -4.60(12.10) (12.51) (12.12)
Intercept_c -3.57 -3.30 -4.41(13.71) (15.67) (12.37)
Intercept_s -3.29 -2.94 -14.57(19.87) (18.01) (2.95)
30
Table 4 (continued)
MNL NMIWN NMNLb
Inclusive value 0.38(shc nest) (-5.07)
Inclusive value .53(hc nest) (-2. 14)d
Inclusive value 4.62(sw nest) (3.57)d
log-Likelihood -3571 -3566 -3560
Elasticities (Uncondl):Hospital own-price -.05 -.14 +.02
Clinic own-price -.35 -.37 -.36
a. This model nests the hospital, clinic, and self alternatives in a separate branch from the well category.b. This model nests hospital and clinic together, and then self and well in a separate nest.c. The _h, _c, and _w suffixes indicate that the coefficient measures the effect of the variable on the hospital,clinic, and well options, respectively, through interactions with alternative-specific dummies.d. t-test for null hypothesis that coefficient equals one.
The hospital and clinic prices were only allowed to enter their own utility indices,providing additional identification restrictions of the covariance parameters. As mentioned inSection 4, Keane (1992) shows that "fragilely" identified models are characterized by largestandard errors when the covariance terms are freely estimated. The fact that the standarderrors are very similar across the restricted and unrestricted regressions in Table 5 isevidence that the model is appropriately identified.
From these two regressions, selection bias does not appear to be a problem in thisdataset. The t-tests indicate that the estimated covariance parameters are all individuallyinsignificant. Furthermore, the Likelihood Ratio test reveals them to be jointly insignificant:the chi-squared value of 4.71 is less than even the 75 percent critical value of 6.63 with fivedegrees of freedom. Finally, the elasticity estimates between the models are quite similar,varying only from -0.07 to -0.11 (both insignificantly different from zero) for hospitals, andfrom -.25 to -0.27 for clinics.
31
Table 5: 4-Choicea Multinonilal Probits
IMNP (MNL-type MNP (unrestricted IMNP (MNL-type MNP (unrestrictedcovariances)b covariances)c covariances)b covariances)c
Time Hosp_h -.04 -.04 Intercept_h -2.92 -2.14(0.89) (1.24) (16.32) (3.88)
Time Clin_c -.39 -.22 Intercept_c -2.72 -1.87(4.49) (4.08) (16.09) (15.73)
Intercept_s -2.66 -2.67Income_h .08 .06 (21.36) (21.22)
(4.98) (2.91)Income c .05 .04 sd_h 1.00 .55
(2.84) (3.02) (0.44)dIncome_s .02 .01
(1.01) (0.95) sd_c 1.00 olO( 0. 98 )d
Wage_h .10 .14(0.42) (0.64) corr_h,c 0.00 -.85
Wage_c .46 .36 (0.08)(2.03) (2.59)
Wage_s .56 .58 corr_h,s 0.00 -.52(3.26) (3.48) (.51)
Male_h -.03 -.06 corr_c,s 0.00 .18(.35) (0.69) (0.46)
Male_c -.27 -.18(3.13) (3.19) log-Likelihood -3570 -3565
Male_s -.20 -.21(2.98) (3.10)
Education_h .02 .02 Elasticities (Uncondl):(1.26) (1.24) Hospital own-price -.07 -.11
Education_c .01 .01(0.59) (0.97) Clinic own-price -.25 -.27
Education_s .03 .03(1.92) (1.84)
Age_h 2.18 1.76(7.80) (4.79)
Age_c 2.76 2.28- (11.77) (13.32)
Age_s 3.72 3.68(18.07) (18.42)
a. The four choices in these MNP models are well, self, hospital, clinic.b. This model mimics the covariance structure of the MNL, restricting all covariances between unobservables tozero.c. This model nests the NMNL-type covariance structure, by allowing an unrestricted pattern of covariancesbetween unobservables.d. t-test for null hypothesis that coefficient equals one.
32
8. Discussion and Implications
Evidence in the previous section suggests that in C6te d'Ivoire, health care demandestimates conditioned on health status do not suffer from statistical selection bias. If this iscorroborated in other data, it would indicate that conditional estimation may not be a badstrategy for capturing short-run demand effects. Separate estimates of the probability ofsickness (such as those in Ellis and Mwabu, 1991) could then be used to recover consistentestimates of unconditional effects, as discussed in Section 2.3. Absence of selection bias alsoimplies that less expensive data collection efforts may be acceptable in some cases for short-run analysis. For example, among randomly sampled individuals, questionnaires would onlyneed to be administered to those who were sick during a reference period. This could beuseful for planners who need to allocate and price health care inputs (including personnel,supplies, medications, etc.) in the short-run, but who do not have resources for morecomprehensive data collection efforts.
However, the C6te d'Ivoire evidence also suggests that price elasticity magnitudes, aswell as the signs and significance of gender, age, and wage covariates, may not be the samein unconditional samples as in such choice-based samples. For example, the price elasticitiesare about 25 percent larger in conditional samples than in unconditional ones. Depending onthe application, this difference could be important economically, as user fee debates typicallyinvolve price changes of several hundred percent. The finding in the C6te d'Ivoire data thatlong-run unconditional elasticities are smaller than short-run elasticities may be due to thefact that travel distances to clinics affect both curative and preventive health inputs, leadingto a cumulative worsening of health for those living farther from clinics. More evidence onthe relative magnitudes of conditional and unconditional elasticities in other data would beuseful.
This is especially true since differences between long-run and short-run estimates mayalso arise due to data problems. As discussed earlier, short-run estimates may be biasedfrom the subjectivity of self-reported health indicators used to condition the sample. Thelong-run estimates, however, also suffer from potential problems. First, health status is apowerful determinant of curative care demand, and if health information is not used, thealready noisy estimation becomes even less precise. Second, the price effect on health maybe spurious due to correlations with other unobserved inputs. Third, the "long-run"interpretation becomes clouded when input access prices are not constant during the pastlong-run period which affects current health. For adults, the prices of vaccinations as a childare virtually always unobserved by the researcher. For children, however, this has becomeless of a problem as better data is collected. Also, in rural areas (such as the C6te d'Ivoiresample used in this paper), distances to clinics may be reasonably constant over a decade ortwo, and inputs before that may not have much effect on current health status.
All of these problems make the demand estimates difficult to interpret. Howimportant these problems are, and whether the conditional or unconditional estimates aremore precise, will depend on the application. As discussed in Section 2.3, at least a general
33
idea of the sensitivity of estimates to these problems can be obtained by estimating theelasticity of sickness, which is equal to the difference between the unconditional andconditional elasticities. Furthermore, more precise analysis of the effects of conditioning wasshown to be feasible by comparisons with unconditional effects, which can be easilyobtained, for example, by estimating the choice between hospitals, clinics, and neither. Thelatter category simply combines those who report themselves as sick but not seriously enoughto visit a provider, with those whose unobserved health was good enough by their standardsto label themselves as not sick.
It appears that focusing attention on the effects of health care for the healthy inaddition to the sick may have important payoffs. The effects of truncating healthy peoplefrom samples is not merely a statistical issue. Whether or not conditional techniques areconsistent in other datasets, it is important that health care demand studies pay more attentionto the fact that the conditional estimates can only be interpreted as short-run effects.Unconditional estimates require little extra computational burden and may possibly yieldsignificantly different policy implications for forward-looking planners.
34
Variable Definitions
E[.] = expected valuet = time indexj,k = choice indexesU = utility functionV = observable portion of utilityHt = Health status at time t (before period t's inputs)I = health Input, where:
IPre = health Input, preventiveIcur health Input, curative
C = Consumption of non-health goodsp = priceY = incomep = discount factorxt = health innovation at start of period t6 = depreciation of health stockS = Sickness indicatorM = Medical care utilization indicatorX = observables in a particular modelEMIS = Elasticity of medical care conditional on sicknesse, u = unobserved residuals01jk = covariance between unobservables in choices j,kDj = inclusive value variable for nested multinomial logitsP = Probabilityh,c = hospital, clinics,w = self care, welln = no formal care (neither hospital nor clinic)Oj = health care quality for provider type j
35
Table Al: Time-Price (Own) Elasticities of Demand(leftmost column gives Table # and column of regression results)Bootstrapped standard errors (50 replications) are in parentheses for OLS and MNL models.
Elasticitiesa
Hospital Clinic
Regression Conditional Unconditional Conditional Unconditional
A2.1 OLS Prob(Hosp) -.10 (.07) --
A2.2 OLS Prob(Hosp I Sick= 1) -.10 (.08) --
A2.3 OLS Prob(Clin) -- -.26 (.06)
A2.4 OLS Prob(ClinISick=1) -- -.36 (.05)
A3.1 MNLnhc -.05 (.07) -.35 (.08)
A3.2 MNL shc -. 15 (.08) -.49 (.08)(conditional on Sick)
3.1 NMNL nhc (nest a,) -.15 -.37
3.2 NMNL shc (nest ahC) -. 11 -.49(conditional on Sick)
4.1 MNL wshc -.05 (.07) -.35 (.08)
4.2 NMNL wshc (nest oShC) -.14 -.37
4.3 NMNL wshc (nest oWSh¢) +.02 -.36
5.1 MNP wshc -.07 -o25(MNL type covariances)
5.2 MNP wshc -.11 -.27(unrestricted covariances)
a. Elasticities reported are averages of those evaluated at each individual observation, except for the OLS Linear ProbabilityModels which are evaluated at the means.
36
Table A2: Linear Probability Estimates of Demand Equations
P(hosp) P(hosp Sick= 1) P(clin) P(clin I Sick = 1)
Time Hosp -.005 -.02 .002 .01(1.36)a (1.33) (0.51) (0.98)
Time Clin .02 .03 -.04 -.15(2.44) (1.37) (4.85) (6.72)
Income .008 .01 .004 .004(4.65) (3.36) (2.15) (0.81)
Wage -.004 -.09 .03 -.02(0.19) (1.71) (1.48) (0.40)
Male .005 .04 -.02 -.02(0.66) (1.90) (2.58) (0.95)
Education .001 .002 -.00 -.01(0.74) (0.39) (0.04) (1.15)
Age .05 -.20 .16 -. 16(2.56) (3.30) (6.03) (2.23)
Intercept .005 .22 .02 .39(0.34) (4.99) (1.02) (7.29)
Elasticities: Uncondl Condl Uncondl Condl
Hospital own-price -.10 -.10
Clinic own-price -.26 -.36
a. t-statistics have not been corrected for heteroscedasticity.
37
Table A3: 3-Choicea Non-Nested Multinomial Logits(nested versions are reported in Table 3)
MNL MNL I Sick = 1
Time Hosp hb -.06 -.18(0.68) (1.67)
Time Clin_c -.68 -1.01(5.17) (6.95)
Income_h .12 .11(4.62) (3.45)
Income_c .06 .05(2.54) (1.69)
Wage_h -.02 -.82(0.40) (1.84)
Wage_c .04 -.32(1.28) (0.87)
Male h .07 .30(0.48) (1.75)
Male c -.33 -.07(2.54) (0.45)
Education_h .02 1.002(0.67) (0.05)
Education c -.00 -.04(0.07) (1.24)
Age_h 1.35 -2.12(3.00) (3.93)
Age_c 2.15 -1.40(6.08) (3.14)
Intercept_h -3.64 -.41(11.43) (1.10)
Intercept_c -3.21 .19(12.8) (0.61)
log-Likelihood -1813 -1185
Elasticities: Uncondl Condi
Hospital own-price -.05 -.15
Clinic own-price - .35 -.49
a. The altematives in the (3-choice) unconditional model are hospital,clinic, and none (the aggregation of well and self); in the conditionalmodels they are hospital, clinic, and self.b. _h and _c suffixes indicate that the coefficient measures the effect ofthe variable on the hospital and clinic options, respectively, throughinteractions with altemative-specific durmnies.
38
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44
LSMS Working Papers
No. 1 Chander, Grootaert, and Pyatt ,Living Standards Surveys in Developing Countries
No. 2 Visaria, Poverty and Living Standards in Asia: An Overview of the Main Results and Lessons of SelctedHousehold Surveys
No. 3 United Nations Statistical Office, Measuring Levels of Living in Latin America: An Overview of MainProblems
No. 4 Scott, de Andre, and Chander, Towards More Effective Measurement of Levels of Living, and Review ofWork of the United Nations Statistical Office (UNSO) Related to Statistics of Levels of Living
No. 5 Scott, de Andre, and Chander, Conducting Surveys in Developing Countries: Pracdcal Problems andExperience in Brazil, Malaysia, and the Philippines
No. 6 Booker, de Andre, and Chander, Household Survey Experience in Afrtica
No. 7 Deaton, Measurement of Welfare: Theory and Practical Guidelines
No. 8 Mehran, Employment Data for the Measurement of Living Standards
No. 9 Wahab, Income and Expenditure Surveys in Developing Countries: Sample Design and Execution
No. 10 Saunders and Grootaert, Reflections on the LSMS Group Meeting
No. 11 Deaton, Three Essays on a Sri Lanka Household Survey
No. 12 Musgrove, The ECIEL Study of Household Income and Consumption in Urban Latin America: AnAnalytical History
No. 13 Martorell, Nutrition and Health Status Indicators: Suggestions for Surveys of the Standard of Living inDeveloping Countries
No. 14 Birdsall, Child Schooling and the Measurement of Living Standards
No. 15 Ho, Measuring Health as a Component of Living Standards
No. 16 Sullivan, Cochrane, and Kalsbeek, Procedures for Collecting and Analyzing Mortality Data in LSMS
No. 17 Grootaert, The Labor Market and Social Accounting: A Framework of Data Presentation
No. 18 Acharya, Time Use Data and the Living Standards Measurement Study
No. 19 Grootaert, The Conceptual Basis of Measures of Household Welfare and Their Implied Survey DataRequirements
No. 20 Grootaert, Cheung, Fung, and Tam, Statistical Experimentation for Household Surveys: Two CasesStudies of Hong Kong
No. 21 Wood and Knight, The Collection of Price Data for the Measurement of Living Standards
No. 22 Grootaert and Cheung, Household Expenditure Surveys: Some Methodological Issues
No. 23 Ashenfelter, Deaton, and Solon, Collecting Panel Data in Developing Countries: Does it Make Sense?
No. 24 Grootaert, Measuring and Analyzing Levels of Living in Developing Countries: An AnnotatedQuestionnaire
No. 25 Grootaert and Dubois, The Demand for Urban Housing in the Ivory Coast
No. 26 Ainsworth and Muntoz, The CBte d'Ivoire Living Standards Survey: Design and Implementation
No. 27 Grootaert, The Role of Enployment and Earnings in Analyzing Levels of Living: A General Metiodologywith Applications to Malaysia and Thailand
No. 28 Deaton and Case, Analysis of Household Expenditures
No. 29 Glewwe, The Distribution of Welfare in CBte d'Ivoire in 1985
No. 30 Deaton, Quality, Quantity, and Spatial Variation of Price: Estimating Price Elasticities from Cross-sectional Data
No. 31 Suarez-Berenguela, Financing the Health Sector in Peru
No. 32 Suarez-Berenguela, Informal Sector, Labor Markets, and Returns to Education in Peru
No. 33 van der Gaag and Vijverberg, Wage Determinants in CBte d'Ivoire
No. 34 Ainsworth and van der Gaag, Guidelines for Adapting the LSMS Living Standards Questionnaires to LocalConditions
No. 35 Dor and van der Gaag, The Demand for Medical Care in Developing Countries: Quantity Rationing in
Rural C6te dI'voire
No. 36 Newman, Labor Market Activity in Cote d 'lvoire and Peru
No. 37 Gertler, Locay, Sanderson, Dor, and van der Gaag, Health Care Financing and the Demand for MedicalCare
No. 38 Stelcner, Arriagada, and Moock, Wage Determinants and School Attainment among Men in Peru
No. 39 Deaton, The Allocation of Goods within the Household. Adults, Children, and Gender
No. 40 Strauss, The Effects of Household and Community Characteristics on the Nutrition of Preschool Children:Evidence from rural C6te dI'voire
No. 41 Stelcner, van der Gaag, and Vijverberg, Public-Private Sector Wage Differentials in Peru, 1985-86
No. 42 Glewwe, The Distribution of Welfare in Peru 1985-86
No. 43 Vijverberg, Profits from Self-Employment: A Case Study of C6te d 'Ivoire
No. 44 Deaton and Benjamin, The Living Standards Survey and Price Policy Reform: A Study of Cocoa andCoffee Production in Cote dI'voire
No. 45 Gertler and van der Gaag, Measuring the Willingness to Pay for Social Services in Developing Counties
No. 46 Vijverberg, Nonagricultural Family Enterprises in Cote d'Ivoire: A Descriptive Analysis
No. 47 Glewwe and de Tray, The Poor during Adjustment: A Case Study of Cote dI'voire
No. 48 Glewwe and van der Gaag, Confronting Poverty in Developing Countries: Definitions, Information, andPolicies
No. 49 Scott and Amenuvegbe, Sample Design for the Living Standards Surveys in Ghana and Mauritania/Plansde sondage pour les enquetes sur le niveau de vie au Ghana et en Mauritanie
No. 50 Laraki, Food Subsidies: a Case Study of Price Reform in Morocco (also in French, 50F)
No. 51 Strauss and Mehra, Child Anthropometry in Cote d'Ivoire: Estimates from Two Surveys, 1985 and 1986
No. 52 van der Gaag, Stelcner, and Vijverberg, Public-Private Sector Wage Comparisons and Moonlighting inDeveloping Countries: Evidence from C6te d 'Ivoire and Peru
No. 53 Ainsworth, Socioeconomic Determinants of Fertility in C6te d'lvoire
No. 54 Gertler and Glewwe, The Willingness to Pay for Education in Developing Countries: Evidence from RuralPeru
No. 55 Levy and Newman, Rigidite des salaires: Donnees microeconomiques et macroeconomiques surI'ajustement du marche du travail dans le secteur moderne (in French only)
No. .56 Glewwe and de Tray, The Poor in Latin America during Adjustment: A Case Study of Peru
No. 57 Alderman and Gertler, The Substitutability of Public and Private Health Care of the Treatment ofChildren in Pakistan
No. 58 Rosenhouse, Identifying the Poor: Is 'Headship" a Useful Concept?
No- 59 Vijverberg, Labor Market Performance as a Determinant of Migration
No. 60 Jimenez and Cox, The Relative Effectiveness of Private and Public Schools: Evidence from TwoDeveloping Countries
No. 61 Kakwani, Large Sample Distribution of Several Inequality Measures: With Application to C6te d'lvoire
No. 62 Kakwani, Testing for Significance of Poverty Differences: With Application to C6te d 'Ivoire
No. 63 Kakwani, Poverty and Economic Growth: With Application to Cote dI'voire
No. 64 Moock, Musgrove, and Stelcner, Education and Earnings in Peru's Informal Nonfarm Family Enterprises
No. 65 Alderman and Kozel, Fornal and Informal Sector Wage Determination in Urban Low-IncomeNeighborhoods in Pakistan
No. 66 Vijverberg and van der Gaag, Testing for Labor Market Duality: The Private Wage Sector in Coted 'Ivoire
No. 67 King, Does Education Pay in the Labor Market? The Labor Force Participation, Occupation,Occupation, and Earnings of Peruvian Women
No. 68 Kozel, The composiiion and Distribution of Income in Cote d'Ivoire
No. 69 Deaton, Price Elasticities from Survey Data: Extensions and Indonesian Results
No. 70 Glewwe, Efficient Allocation of Transfers to the Poor: The Problem of Unobserved Household Income
No. 71 Glewwe, Investigating the Determinants of Household Welfare in Cote d'lvoire
No. 72 Pitt and Rosenzweig, The Selectivity of Fertility and the Determinants of Human Capital Investments:Parametric and Semiparametric Estimates
No. 73 Jacoby, Shadow Wages and Peasant Family Labor Supply: An Econometric Application to the PeruvianSierra
No. 74 Behrman, The Action of Human Resources and Poverty on One Another: What We Have Yet to Learn
No. 75 Glewwe and Twum-Baah, The Distribution of Welfare in Ghana, 1987-88
No. 76 Glewwe, Schooling, Skills, and the Returns to Government Investment in Education: An ExplorationUsing Data from Ghana
No. 77 Newman, Jorgensen, and Pradhan, Workers' Benefits from Bolivia's Emergency Social Fund
No. 78 Vijverberg, Dual Selection Criteria with Multiple Alternatives: Migration, Work Status, and Wages
No. 79 Thomas, Gender Differences in Household Resource Allocations
No. 80 Grosh, The Household Survey as a Tool for Policy Change: Lessons from the Jamaican Survey of LivingConditions
No. 81 Deaton and Paxson, Patterns of Aging in Thailand and Cote d'Ivoire
No. 82 Ravallion, Does Undernutrition Respond to Incomes and Prices? Dominance Tests for Indonesia
No. 83 Ravallion and Datt, Growth and Redistribution Components of Changes in Poverty Measure: ADecomposition with Applications to Brazil and India in the 1980s
No. 84 Vijverberg, Measuring Income from Family Enterprises with Household Surveys
No. 85 Deaton and Grimard, Demand Analysis and Tax Reform in Pakistan
No. 86 Glewwe and Hall, Poverty and Inequality during Unorthodox Adjustment: The Case of Peru, 1985-90
No. 87 Newman and Gertler, Family Productivity, Labor Supply, and Welfare in a Low-Income Country
No. 88 Ravallion, Poverty Comparisons: A Guide to Concepts and Methods
No. 89 Thomas, Lavy, and Strauss, Public Policy and Anthropometric Outcomes in Cote d'Ivoire
No. 90 Ainsworth and others, Measuring the Impact of Fatal Adult Illness in Sub-Saharan Africa: An AnnotatedHousehold Questionnaire
No. 91 Glewwe and Jacoby, Estimating the Determinants of Cognitive Achievement in Low-Income Countries:The Case of Ghana
No. 92 Ainsworth, Economic Aspects of Child Fostering in Cote d'Ivoire
No. 93 Lavy, Investment in Human Capital: Schooling Supply Constraints in Rural Ghana
No. 94 Lavy and Quigley, Willingness to Pay for the Quality and Intensity of Medical Care: Low-IncomeHousehold in Ghana
No. 95 Schultz and Tansel, Measurement of Returns to Adult Health: Morbidity Effects on Wage Rates in Coted'lvoire and Ghana
No. 96 Louat, Grosh, and van der Gaag, Welfare Implications of Female Headship in Jamaican Household
No. 97 Colombe and Demery, Household Size in Cote d'Ivoire: Sampling Bias in the CILSS
No. 98 Glewwe and Jacoby, Delayed Primary School Enrollment and Childhood Malnutrition in Ghana: AnEconomic Analysis
No. 99 Baker and Grosh, Poverty Reduction through Geographic Targeting: How Well Does It Work?
No. 100 Datt and Ravallion, Income Gains for the Poor from Public Works Employment: Evidence from TwoIndian Villages
No. 101 Kostermans, Assessing the Quality of Anthropometric Data: Background and Illustrated Guidelines forSurvey Manager
No. 102 van de Walle, Ravallion, and Gautam, How Does the Social Safety Net Work?: The Incidence of CashBenefits in Hungary, 1987-89
No. 103 Benefo and Schultz, Determinants of Fertility and Child Mortality in C6te d'Ivoire and Ghana
No. 104 Behrman and Lavy, Children's Health and Achievement in School
No. 105 Lavy and Germain, Quality and Cost in Health Care C7hoice in Developing Countries
No. 106 Lavy, Strauss, Thomas, and De Vreyer, The Impact of the Quality of Health Care on Children's Nutritionand survival in Ghana
No. 107 Hanushek and Lavy, School Quality, Achievement Bias, and Dropout Behavior in Egypt
No. 108 Feyistan and Ainsworth, Contraceptive Use and the Quality, Price, and Availability of Family Planning
No. 109 Thomas and Maluccio, Contraceptive Choice, Fertility, and Public Policy in Zimbabwe
No. 110 Ainsworth, Beegle, and Nyamete, The Impact of Female Schooling on Fertility and Contraceptive Use: AStudy of Fourteen Sub-Saharan Countries
No. 111 Oliver, Contraceptive Use in Ghana: The Role of Service Availability, Quality, and Price
No. 112 Montgomery, Kouame, and Oliver, The Tradeoff between Number of Children and Child Schooling:Evidence from Cote d 'Ivoire and Ghana
No. 113 Pradhan, Sector Participation Decisions in Labor Supply Models
No. 114 Beegle, The Quality and Availability of Family Planning Services and Contraceptive Use in Tanzania
No. 115 Lavy, Spratt, and Leboucher, Changing Patterns of Illiteracy in Morocco: Assessment Methods Compared
No. 116 Lavy, Palumbo, and Stern, Health Car in Jamaica: Quality, Outcomes, and Labor Supply
No. 117 Glewwe and Hall, Who Is Most Vulnerable to Macroeconomic Shocks? Hypotheses Tests Using PanelData from Peru
No. 118 Grosh and Baker, Proxy Means Tests for Targeting Social Programs: Simulations and Speculation
No. 119 Pitt, Women's Schooling, the Selectivity of Fertility, and Child Mortality in Sub-Saharan Africa
No. 120 Grosh and Glewwe, A Guide to Living Standards Measurement Study Surveys and their Data Sets
No. 121 van de Walle, Infrastructure and Poverty in Viet Nam
No. 122 Ravallion, Poverty Comparisons: A Guide to Concepts and Methods
No. 123 Ii, The Demand for Medical Care: Evidence from Urban Areas in Bolivia
No. 124 Hentschel and Lanjouw, Constructing and Indicator of consumption for the Analysis of Poverty: Principlesand Illustrations with Reference to Ecuador
No. 125 Leibrrandt, Woolard, Woolard, The contribution of Income Components to Income Inequality in SouthAfrica: A Decomposable Gini Analysis
No. 126 Grosh, Mufioz, A Manual for Planning and Implementing the Living Standards Measurement Study Survey
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