A METHODOLOGICAL REVIEW OF DEMAND ANALYSIS: AN EXAMPLE OF HEALTH CARE SERVICES

Transcription

1 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue A METHODOLOGICAL REVIEW OF DEMAND ANALYSIS: AN EXAMPLE OF HEALTH CARE SERVICES Shva Raj Adhkar, PhD* Abstract Demand descrbes the quantty of goods or servces per unt of tme that an ndvdual purchases and consumes gven the set of the prces and ncome of the consumer. The demand models based on contnuous choce or dscrete choce are popular n the economc lteratures. Dscrete choce depcts where and what knds of health servces to consume whle the contnuous choce portrays how much of health servces to consume. Specfcaton of the behavoural model and estmaton of the parameters of the model that are nterrelated tasks n dscrete choce model are challengng for the researchers. Health sector data have specal features lke dscrete nature of the data, problems of censorng, nteger counts or tme duraton and several factors complcate attempts to obtan unbased estmates of the mpact of varables that nfluence demand for health care. The health care data provde wder applcatons of econometrcs models. These models have some advantages n presentng and analyzng the choce behavour; however, they have some lmtatons as well. Subsequently, the researchers are contnuously nterested to fnd and to apply approprate models to descrbe the choce behavour of the decson makers. Key words: demand for health care servces, contnuous choce, dscrete choce, behavoural model and econometrc model INTRODUCTION In economc analyss, consumer behavor s expressed as a utlty maxmzaton problem subject to a gven budget constrant. The demand functons are derved by solvng the optmzaton problem. Demand descrbes the quantty of goods or servces per unt of tme that an ndvdual purchases and consumes gven the set of the prces and ncome of the consumer. The demand models based on contnuous choce or dscrete choce are popular n the economc lteratures. Contnuous choce model s based on neoclasscal theory of consumer behavor whle the relatvely new dscrete choce model s derved from the random utlty theory. In the neoclasscal theory, the utlty s the functon of quanttes of commodty consumed, but n the dscrete choce model, the utlty s expressed as a functon of attrbutes of the commodtes. The neoclasscal theory assumes determnstc behavor and deals wth contnuous (.e., nfntely dvsble) products. Calculus s used to derve many of the key results. Lancaster (1966) proposed that t s the attrbutes of the goods that determne the utlty. Utlty, therefore, can be expressed as a functon of the attrbutes of the commodtes. Ths theory explored the deas of random utlty theory or dscrete choce theory. The ndvdual choce behavor s ntrnscally probablstc. Dscrete choce theory deals * Mr. Adhkar s Assocate Professor of Economcs, Patan Multple Campus, Trbhuvan Unversty Shva Raj Adhkar 119

2 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue A Methodologcal Revew of... wth a choce among a set of fnte, mutually exclusve alternatves and so dfferent technques need to be used. However, the underlyng hypotheses of random utlty reman ntact. In health economcs, both models are equally mportant although dscrete choce models are often used because of the nature and avalablty of health data. Dscrete choce depcts where and what knds of health servces to consume whle the contnuous choce portrays how much of health servces to consume. DERIVATION OF DEMAND FOR HEALTH CARE In the econometrc modelng of demand functon, the dependent varable usually reflects utlzaton of health care servces. Observed utlzaton level reflects the pont of ntersecton of demand and supply functons (market equlbrum) and the utlzaton of health care servces reflects satsfed demand or observed demand. Sometmes, t s hard to clearly dstngush between these two functons from the observed data. In ths stuaton, the explct and mplct assumptons facltate to estmate the demand functon. For example, we use the term, n economcs, other thngs beng equal that lmts the shftng factors, or supply factors, then t s possble to estmate demand functons. Smlarly, the assumpton of ratonal behavour of the consumer reduces or gnores the possblty of suppler-nduced demand n medcal servce. Utlzaton of health care servces has become a topc of wdespread nterest among the health economsts. The determnants of demand for health care are mportant for a number of reasons. For example, quantfcaton of these factors s necessary to assess medcal care needs of the communty and potental mpact of utlzaton on health. Demand analyss can also ndcate to the polcy makers the role of consumer awareness and knowledge can play n mprovng the utlzaton of hghly cost-effectve health nterventons or health servces. The economc models that are most relevant and commonly used n health care demand are the human captal theory and the orthodox utlty theory. The frst approach used for the analyss of health care demand s the nter-temporal model of utlty functon where utlty depends upon the flow of healthy days from the stock of health and consumpton of other commodtes. The second approach s smlar to orthodox utlty theory that consders health as a choce commodty (Jack, 1999). Inter-temporal Utlty Model Grossman (2000; 1972) has developed nter-temporal utlty model, whch s based on the household producton framework. The model, for the frst tme ntroduced the concept that consumers do not demand medcal care per se, but t s a derved demand generated through the demand for health. Indvdual demands health for two purposes: consumpton and nvestment purposes. Indvdual can maxmze hs utlty by generatng good health and better health enhances utlty or happness. Health s 120

3 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue Shva Raj Adhkar desred as an nvestment good snce good health enhances earnng capacty. Health, thus, s both a consumpton and nvestment good. Accordng to ths model, the stock of health captal deprecates over tme and the consumer can produce gross nvestments by usng medcal care and ther own tme as nputs. It s assumed that the effcency of the producton process depends on ndvduals stocks of other forms of human captal, especally educaton. The rate of deprecaton of the health stock rses wth age. Ths mples that the stock of health falls wth age. The optmal gross nvestment n health s postve untl the last perod of lfe. The margnal product of the stock of health dmnshes as the stock ncreases. Grossman s demand model has revolutonzed the economc analyss of health (Lebowtz, 2004). Ths model has opened up the possblty of further research n the areas of health economcs, for example, allocatng tme between ncome and lesure, allocatng remanng lesure tme on health and non health actvtes, allocatng earned ncome to health and non health resources, producng health captal for use n future years. The model, however, s not free from crtcsms. The questons rased by the researchers are on unrealstc assumptons of the theory. The assumptons that are often crtczed are the assumpton of perfect nformaton, determnstc nature of the model, and the endogenety of length of lfe, among others. Some researchers have rased serous ssues on methodologes that are used n estmaton of Grossman demand model. For example, Ehrlch and Chuma (1990) have clamed that f health nvestment functons assume constant returns to scale technology, whch s used by Grossman, creates bang-bang problem wth respect to optmal nvestment and health mantenance choces. Smlarly, Wagstaff (1993) has argued that the emprcal formulaton used by Grossman s napproprate because t fals to take nto account the nherently dynamc character of the health nvestment process. Grossman has used a very dfferent theoretcal paradgm to descrbe the determnants of health outcomes (Grossman, 2000). The emprcal analyss of demand for health s also complcated because of the fact that theoretcal models often nvolve nherently latent (unobservable) varables, whch are often proxed by ndcator varables. Many researchers have used the multple ndcators multple causes (MIMIC) model, whch can be estmated as lnear structural relatonshps (LISREL). The researchers face problems of measurement of health related ssues, partcularly health status of the people among others. The Grossman model of demand for health, thus, has contnued to be refned, modfed from both the theoretcal and emprcal prospectve. Grossman (2000) has provded a comprehensve revew of ths model n the theoretcal and emprcal ground and suggested further research areas of nterest. Grossman model s more consstency wth longtudnal data. In developng countres, data needed for the estmaton of ths model are not usually avalable and as a result, Grossman s models are usually appled n the developed country context. 121

4 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue A Methodologcal Revew of... Orthodox Utlty Model The second approach, the statc concept of demand analyss, however, s derved from Grossman s model and focuses on the estmaton of the effects of prce and ncome on utlzaton of medcal servces and health care expendture. Ths approach supports the condtonal utlty functon that depends on health outcome and consumpton of goods and servces other than health care, subject to health producton functon and budget constrant. Many dfferent model specfcatons have been used n the lterature for the estmaton of demand for health care. The model specfcatons are based on: a) prce s nteracted wth ncome and b) tme prces are entered nto the utlty functon rather than the budget constrant (Levn et al., 1998) that leads to two groups of results on demand for health care. Former group of studes have shown that prce elastctes are relatvely nelastc as n the case of the studes conducted n Malaysa (Heller, 1982) and the Phlppnes (Akn et al., 1986; Schwartz et al., 1988). The later group of research studes suggest that changes n prce affect quantty of health care demanded as shown by the studes conducted n Pakstan (Alderman and Gertler, 1989); Cote d'ivore (Dor and van der Gaag, 1987); (Gertler and van der Gaag, 1990); and Kenya (Mwabu, 1986). The later concept of demand for health care that explores the effects of access prces of health care s popular n developng countres because the polces of developng countres concentrate on how to mprove the access to health care servces to the populaton. MODELING OF DEMAND FOR HEALTH CARE Contnuous Choce Model Contnuous choce model can analyze the ntensty of consumpton and can predct the quanttes of health care servces consumed. Health care expendture s a measure of ntensty of consumpton of the servces. The analyss of determnants of health expendture can be used to derve the optmal amount of health expendture for a socety (Matteo, 2003) and can dentfy the factors affectng the health care expendture. The health care expendture model can be appled to both mcro and macro-level data; however, ths revew focuses on the studes based on mcro-level data. The studes on determnants of health expendture are lmted n developng countres due to the fact that requred data are not avalable and modelng of the health care demand s not straght forward (Rous and Hotchkss, 2003). Two major problems arse when attempts to analyze demand by usng health care expendture data: health expendture data are hghly skewed volatng the assumpton of normal dstrbuton of the dependent varable and have presence of a large number of zero expendtures makng t mpossble to apply the ordnary least squared (OLS) methods (Chaze, 2005). The lteratures on health care expendture have demonstrated that most of the studes used parametrc technques to estmate the elastctes of ncome and prces (Matteo, 122

5 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue Shva Raj Adhkar 2003). The parametrc technque assumes a functonal form, normal dstrbuton and lnear relatonshps; however, true shape of the functonal form s unknown and t s hghly senstve to the choce of the functonal form. The OLS method s hghly senstve to outler values of expendtures. Sometmes the researchers have appled weghted least squares or generalzed lnear model, to get rd of these problems but ths does not able to solve all problems that arses from nature of health expendture data. The log lnear specfcatons are used to mnmze these problems n estmatons of demand functons, as well. Agan, the researchers use log for dependent varable (log lnear) to avod the normalty problems however, ths technque cannot ruled out but reduces the problems (Wooldrdge, 1992).The log lnear form, applyng natural log of both dependent and ndependent, facltates the estmaton of elastctes. However, from theoretcal prospectve, both lnear and log lnear specfcatons are nconsstent wth budget constrant (Hunt-McCool, et al 1994; Deaton and Muellbauer, 1980). In ths case, sum of all prce and ncome elastctes are equal to one. We can t get the nformaton from the estmated elastctes on luxurous goods or necessty goods or nferor goods. Under such crcumstances, relatvely advanced methods, such as non-parametrc and maxmum lkelhood technques are used to solve these problems. Non-parametrc technque s qute flexble that reduce the dstrbuton assumptons. The technques assume that there are non-lnear relatonshps between health care expendtures and other economc varables, such as ncome. Ths technque s also called dstrbuton free method that s useful to deal wth both nadequaces of functonal form and data wth respect to outlers. These methods are consstence wth budget constrant and consumer behavour as well. Deaton and Muellbauer (1980) have developed an deal demand system that s derved from dual of utlty maxmzaton. They derved the expendture functon, whch s nverted of the ndrect utlty functon. The dependent varable of ths demand functon s log of share of partcular expendture on goods or medcal servces to total expendture. Hunt-McCool, et al. (1994) has estmated demand for npatent servces and outpatent servces usng ths concept. There are also estmators known as sem-parametrc, whch make some dstrbutonal assumptons, but fewer than the parametrc estmators. Quntle regresson, semparametrc based method, assumes a parametrc specfcaton for the qth quntle of the condtonal dstrbuton (Jones, 2000). Heteroskedatcty problem can be dealt wth by estmatng quantle regressons (Deaton, 1997). If the quntle regresson lnes are not parallel, ths nforms heteroskedatcty. The quntle regresson estmator s popular now because t provdes more effcent estmaton than the least square models do (Yu et al., 2003). Quntle regresson explores the nformaton about the dstrbuton of the dependent varable rather than the condtonal mean. As we know that there are two alternatve methods n econometrcs to analyze the data n dependent varable (y) and gven x (ndependent varables): condtonal expectaton or mean, E(y/x) or condtonal medan, M(y/x). Condtonal mean s conventonally popular than condtonal medan 123

6 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue A Methodologcal Revew of... (Wooldrdge, 1992). Mannng et al. (1995) has appled quantle regresson to estmate the demand for alcohol. Non-lnearty can arse many ways. For examples, nature of the data, truncated and censored, causes nonlnear. Maxmum lkelhood estmators has been contnued to use as an alternatve method for non-lnear estmator (Cameron and Trved, 2005). The generalzed flexble Box-Cox transformaton model, whch s based on maxmum lkelhood estmates, uses nonlnear transformatons of the dependent and the explanatory varables of an OLS regresson model. The Box-Cox devce s also approprate for a model wth no apror functonal form has been utlzed wdely n econometrc modelng. The researchers have clamed that the Box-Cox transformaton method s approprate for hedonc relatonshps as well. Hedonc expendture relatonshp approaches are also appled n health care expendture modelng, such as (Goldman and Grossman, 1978; Levy and Qugley, 1993). The Box-Cox technque has been used n strctly postve contnuous value order to acheve normalty. The method does not use the nonlnear transformaton of dummy varables. It has some features that can solve the problems of robust estmaton as well as hedonc prcng. Ths devce, however, has some lmtatons, for example, ths yelds transformaton bas (Kanamor and Takeuch, 2006). There are several approaches of modelng lmted dependent varable lke the two-part model, the Tobt model, the sample selecton model, hurdle models and fnte mxtures models. Two-part model comprses bnary logt/probt model and OLS model. Bnary logt/probt models have been appled for understandng whether ndvduals make any health care expendtures and OLS has been used only on the sub-sample wth non-zero expendtures (log of expendture). However, there s possblty of sample selecton bas f there are many zeros (Chaze, 2005). The Tobn model assumes that the ndvduals choose the levels of health expendture to maxmze ther welfare. Zero expendture represents a corner soluton where preferences for health care are so low that the ndvdual s better-off spendng nothng on health care. Dscrete Choce Model Dscrete choce models are typcally used to obtan estmates of prce elastctes of demand for health care. The left-hand sde dependent varable s often measured as the ncdence of use of varous knds of health facltes (for example, self care, prvate faclty, publc faclty, tradtonal healer), though some studes utlzes contnuous varable as ntensty of consumpton of health servce to measure demand for health care. As mentoned above, the dscrete choce theory s derved from the random utlty model (RUM) that expresses the ratonal utlty theory of the consumer and a lack of nformaton regardng the characterstcs of ndvdual or alternatves on the part of 124

7 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue Shva Raj Adhkar the researchers (Tran, 2003). The researcher only observes that part of the utlty that makes up from the alternatves. The alternatves are mutually exclusve, fnte and exhaustve n the dscrete choce model. The ndrect utlty functon s decomposed nto two functons: one depends on observable factors and the other captures the effect of unobserved characterstcs. Ths can be represented by the followng equaton, note that Smlar equaton can be used n the neoclasscal model however there s dfferent n meanng ofε. In neoclasscal theory, ε represents measurement error, msspecfcaton, left out varables etc. but not the utlty (Varan, 1992). U = V + ε Where, = alternatves, V s a systemc component of utlty and ε s a stochastc component of utlty. A decson maker faces a choce among alternatves. U s the true but unobservable (latent) utlty for alternatve, V s the observable systematc component of utlty, and ε s the factor unobservable to the researcher. There are some aspects of utlty that the researcher does not or cannot observe, therefore, representatve utlty s not equal to true utlty, U V. ε captures the factors that affect utlty but are not ncluded n V. Assumng that the ndvdual can choose between two alternatves, and j, then the probablty that alternatve s chosen s gven by π = prob( U > U j ) = prob( V + ε > V j + ε j ) = prob( V -V j > ε j -ε ), j For all, From ths, t can be seen that the hgher dfference n the probablty for choosng an alternatve, the larger the dfference n observed utlty. Hence, observed choce s determned by the dfference n utlty not the level of utlty per se. Due to ths reason, n the process of estmaton of demand for health care, one alternatve should be normalzed. Most of the studes have used self-care as a base category whose prces are almost zero n most cases. Specfcaton of the behavoural model and estmaton of the parameters of the model that are nterrelated tasks n dscrete choce model are challengng for the researchers. The dscrete choce models that are based on probablty of events are relatvely less nformatve to the researchers. Researchers are facng the problems how to take full advantages of nformaton avalable from estmated results and to present the reader 125

8 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue A Methodologcal Revew of... frendly manner. For ths purpose, the researchers need to know at least the capabltes and lmtatons of the choce models. Logt (bnary as well as multnomal) and nested logt are derved under the assumptons that the error terms are ndependent and dentcally dstrbuted (d) and extreme value dstrbuted. The probt model (bnary as well as multnomal), on the other hand, s derved under the assumpton that the unobservable part of utlty s normally dstrbuted (Tran, 2003). The multnomal logt (MNL) model has a specal property as t assumes ndependence of rrelevant alternatves (IIA). The IIA assumpton s dentcal to the assumpton of ndependent and dentcally dstrbuted (d) random components of each alternatve. There are three propertes of IIA vz: a) probabltes range from zero to one b) sum to one over alternatves and c) S- shaped functon of representatve utlty. Unobserved factors uncorrelated over alternatves and same varance for all alternatves, known as IIA. Ths mples that the rato of the probabltes of choosng one alternatve over another s unaffected by the presence or absence of any addtonal alternatves n the choce set. Consder the rato of the choce probabltes for two alternatves j and k. The rato of these two probabltes does not depend on any alternatves other than j and k. Snce the rato s ndependent from alternatves other than j and k, t s sad to be ndependent from rreverent alternatves. The cross elastcty s the same for all alternatve due to IIA assumptons. MNL, therefore, s not useful to estmate cross elastcty among the alternatves. The nested logt (NL) model s a generalzaton of the MNL model that allows for a partcular pattern of correlaton n unobserved utlty (that s dfferences n cross-elastctes of substtuton across alternatves). An NL model s approprate when the set of alternatves faced by a decson maker can be parttoned nto subsets, called nests. Theoretcally, the multnomal probt model does not mpose IIA and s attractve; however, t has some practcal lmtatons. The practcal complexty not only makes t dffcult to obtan the partal effects on the response probabltes, but also makes maxmum lkelhood nfeasble for more than about fve alternatves (Wooldrdge, 2002). Ordered logt model uses categorcal varable where respondents are asked to report a partcular category and where there s a natural orderng such as excellent health, good health, far or poor health. It seems reasonable to assume that excellent health s better than good, whch s better than far, whch s better than poor, for everyone n the populaton. An econometrc model that can be used to deal wth ordered categorcal varables s the ordered probt model. Mxed logt s based on the assumpton that the unobserved porton of utlty conssts of a part that follows any dstrbuton specfed by the researcher plus a part that s d extreme value. Wth probt and mxed logt, the ntegral does not have a closed form and s evaluated numercally through smulaton. All studes have demonstrated that prces of health servces do affect the demand for health care; however, the sze of the mpacts may dffer wth model specfcatons and the nature of data. 126

9 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue Shva Raj Adhkar Health sector data have specal features lke dscrete nature of the data, problems of censorng, nteger counts or tme duraton and several factors complcate attempts to obtan unbased estmates of the mpact of varables that nfluence demand for health care. The health care data provde wder applcatons of econometrcs models that are bnary logt/probt, multnomal logt/probt, nested logt, ordered logt, mxed logt, Tobt, negatve bnomal, fnte mxture, among o thers. These models have some advantages n presentng and analyzng the choce behavour; however, they have some lmtatons as well. Subsequently, the researchers are contnuously nterested to fnd and to apply approprate models to descrbe the choce behavour of the decson makers. Scott et al. (1996) conducted a research to explore the assocatons between outcome varables and the consumer's characterstcs usng three set of bnary choce: decson to follow up; to prescrbe; and to perform or to order a dagnostc test utlzng natonal health survey data 1989/90 of Australa. Yp et al. (1998) estmated the utlzaton of health care usng multnomal logt model to estmate the factors that nfluenced consumers choce of medcal provder n the three tred health care system n rural chna. Gertler and van der Gaag (1990) and Mwabu et al. (1993), a few of them, have nvestgated mpact of user fee n choce of health care servces usng nested logt and multnomal logt models. Cameron et al. (1988) have developed a count data model to analyze the choces of nsurance plans and health care provders usng household survey data of Australa. Dow (1995) has compared the specfcaton of the models: parsmonous non-lnear, lnear and flexble usng Cote d Ivore health care data and found that results are senstve to choces of model specfcaton and flexble model was consdered more approprate to get robust estmaton of health care demand. Smlarly, Bolduc et al. (1996) has estmated demand for health care usng three dfferent models: multnomal logt, ndependent multnomal probt and multnomal probt usng data from rural vllages of Afrca. They have found smlar result as suggested by Dow (1995) about the mpact of model specfcaton on results and questoned prevous results of usng multnomal logt specfcatons. Kenkel (1990) has appled ordered logt model n categorcal measures of health related nformaton of US natonal health ntervew survey to estmate the effect of socoeconomc varables to health nformaton and demand for health care. Recently, Borah (2006) has appled a very sophstcated and more powerful model, mxed logt model, on health care data collected n Inda. For the emprcal analyss of demand for health care, self-reported llness and frst consultaton wth health care provders are used as the prmary varables, although questons have been rased about the relablty and valdty of these varables. Selfreported llness may produce based results as the percepton of llness may be dfferent for poor and non-poor ndvduals and percepton about a dsease affects the choce of health care servces and provders (Akn et al., 1998). Akn et al. (1998) have ncely 127

10 Economc Journal of Development Issues Vol. 13 & 14 No. 1-2 (2011) Combned Issue A Methodologcal Revew of... descrbed the possble bas n the estmaton of health care demand and suggested solvng ths problem by controllng for bas n sample selecton. They used symptoms of the dseases n order to determne ll respondents. Another potental problem n the estmaton of demand s that the consumers may consult more than one provder for treatment for the same epsode (Gertler et al., 2000); therefore, analyss based on the frst vst to health care provder does not capture the complex decson-makng behavour of the people. The demand analyss wth multlevel approach could be extremely useful n ths stuaton (Jack, 1999). CONCLUSIONS Demand analyss of health care s determned by approaches of demand, the nature of data, econometrc models. The longtudnal data requres nter-temporal utlty model. Orthodox utlty model therefore s more popular then nter- temporal utlty model n developng countres. Contnuous choce model can analyze the ntensty of consumpton; however, dscrete choce s used to explan the lkelhood of usng dfferent knds of servces and whether or not to consume certan types of care. The dscrete choce cannot descrbe the ntensty of consumpton of the servces and can predct the quanttes of health care servces consumed. Due to dscrete nature of the data, dscrete choce models are more popular than contnuous choce model. Indeed, the exstng lteratures on dscrete choce model deal wth frst consultaton of health care provders, however; n realty, the consumers may make several vsts to fnd the standard health care. The demand analyss based on frst consultaton of health care provders does not capture path of decson makng process and underestmates the total cost of health care and ts consequences. It needs to develop the mult-stage demand model that can capture the sequental demand for health care. The revews reach to the conclusons that the debates on theores as well as emprcal estmatons of demand for health care are contnung, consequently, the varous arguments encourage the researchers to experment and develop new, more-approprate approaches for the estmaton of health care demand. 128 References Akn, J. S. Gulkey, D. K. Hutchnson, P. L. & Mcntosh, M. T. (1998). Prce Elastctes of Demand for Curatve Health Care Wth Control for Sample Selectvty on Endogenous Illness: An Analyss for Sr Lanka. Health Econ. 7: Akn, J. Grffn, C. Gulkey, D. & Popkn, B. (1986). The demand for prmary health care servces n the Bcol Regon of the Phlppnes. Economc Development and Cultural Change, 34(4): Alderman, H. & Gertler, P. (1989). Substtutablty of publc and prvate health care for the treatment of chldren n Pakstan. Lvng Standards Measurement Study Workng Paper 57, Washngton: The World Bank, Bolduc, D. Lacrox, G. Muller, C. (1996). The choce of medcal provders n rural Benn: a comparson of dscrete choce models. Journal of Health Economcs,15:

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