Income Distribution and the Public-Private Mix in Health Care Provision: The Latin American Case

Transcription

1 InterAmerican Deveoment Bank Banco Interamericano de Desarroo Office of the Chief Economist Working aer #391 November 1998 Income Distribtion and the PbicPrivate Mix in Heath Care Provision: The Latin American Case By Danie Maceira November 1998 Boston University. This aer was deveoed dring my stay as a constant at the InterAmerican Deveoment Bank, Office of the Chief Economist. I eseciay areciate the comments and sggestions of Bi Savedoff, as we as those from articiants in the OCE worksho on heath care in Latin America. I aso thanks Deborah Davis for her editoria he.

2 Abstract Recent iteratre on LatinAmerican contries shows that rivate exenses as a share of the tota exenditres in heath tend to be higher the ower the eve of economic deveoment of the nation. This aer exains this fact by considering a discrete choice mode of rodct differentiation, where consmer choice is based on a riceaity tradeoff. Physicians are invoved in a dajob hoding strctre, working as agents in the officia sector whie they maximize rofits in a fragmented rivate sector. The mode which characterizes a significant nmber of systems within LatinAmerica, shows the inkages between consmer choice and hysician behavior, and the interaction between bic and rivate systems in the face of externa macroeconomic shocks and investments in heath. The aer concdes that the ack of incentives in the bic sector generates a decine in heath coverage. It not ony redces the aity of bic services bt aso generates negative siovers in the rest of the system, rovoking a oss of aity in the entire heath care sector. In addition, the mode simates how changes in income distribtion affect the seection of aity and rices in the rivate sector, determining individas= choices among different roviders InterAmerican Deveoment Bank 1300 New York Avene, N.W. Washington, D.C The views and interretations in this docment are those of the athors and shod not be attribted to the InterAmerican Deveoment Bank, or to any individa acting on its behaf. The Office of the Chief Economist (OCE aso bishes the Latin American Economic Poicies Newsetter, as we as working aer series and books, on diverse economic isses. Visit or Home Page at: htt:// To obtain a comete ist of OCE bications, and to read or downoad them, ease visit or Web Site at: htt://

3 Introdction Recent iteratre on Latin American contries shows that rivate exenses as a share of tota heath exenditres tend to be higher the ower a nation=s eve of economic deveoment. This aer exains this fact by considering a discrete choice mode of rodct differentiation, where consmer choice is based on a riceaity tradeoff. Physicians are invoved in a da job hoding strctre, working as agents in the officia sector nder a fixed wage strctre whie they maximize rofits in a fragmented rivate sector. The mode which characterizes a significant nmber of systems in Latin America and many other deveoing contries shows: (1 the inkages between consmer choice and hysician behavior, and ( the interaction between bic and rivate systems in the face of externa macroeconomic shocks and investments in heath. The aer concdes that the ack of incentives in the bic sector generates a decine in heath coverage. It not ony redces the aity of bic services bt aso generates negative siovers in the rest of the system, rovoking a oss of aity in the entire heath care sector. In addition, the mode simates how changes in income distribtion affect the seection of aity and rices in the rivate sector, determining individas= choices among different roviders. Heath care systems in Latin American and Caribbean contries exhibit many strctres with different abiities or inabiities to exand heath care coverage, increase heath care otts, imrove heath otcomes, 1 and enhance aity and efficiency. Recent efforts have soght to nderstand not ony the characteristics of these systems, in terms of comarative bic and rivate exenditres and otcomes within the region, bt aso the way they are organized, the reationshi and coordination among roviders, and consmers= abiity to find aroriate coverage. 3 This work is attemt to ay indstria organization theory to the anaysis of heath care markets. Indstria organization theory is imortant in this context becase it hes exain the behavior of consmers and hysicians within the revaiing incentives strctre in most Latin American and Caribbean contries. In the foowing ages a sime mode is introdced. It contains the main featres of a significant nmber of heath care systems in Latin American and Caribbean contries. These systems are characterized by a bic sector ayment strctre that ses fixed wages, and where hysicians work as agents in the officia sector at the same time that they act in the rivate sector as rofit maximizers. The rivate market is deey fragmented, and insrance mechanisms are oor or nonexistent. This strctre faciitates hysicians= abiity to discriminate among consmers based on abiity to ay. The mode shows the inkages between 1 Heath care otts are defined as those indicators that refect the erformance of the heath care system in terms of services rovided, sch as immnization, rofessiona birth attendance, and coverage. Heath otcomes are the effects of these services s a broad range of factors in addition to the effectiveness of the heath care strctre itsef. Otcome measres incde infant mortaity, ife exectancy, mortaity rate for chidren nder five. Govindaraj, Mrray and Chearaj (1995 and Sarez, Henderson, Barias and Vieira ( See InterAmerican Deveoment Bank (1996 and Maceira (1996, for comarisons across contries. 3

4 consmers choice and hysicians= behavior, and the interaction between bic and rivate systems in the face of externa shocks factors as macroeconomic erformance and fctations in heath care investments. Sections one and two rovide a brief discssion of the backgrond iteratre and show the main differences among heath care systems across the region. They aso introdce the framework within which the resent mode is aied and describe those cases where the roosed strctre hods. In section three, the mode is deveoed. In this mode, the oation of a contry chooses between bic and rivate rovision, or no rovision at a (home sotion. The choice is based on a riceaity tradeoff. Physicians decide the characteristics of the services they rovide in the rivate shere of the market. They are abe to set rices by discriminating among consmers according to their income, simified in the mode as Ahigh@ and Aow@ income tyes. The hysicians aso choose the aity of bic services, as a fnction of a bic rice and the resence of externa shocks sch as bdget constraints, infation, etc. The rose of this aer is to define the threshod between bic and rivate coverage by soving the mode backwards. First, consmers= choices are anayzed to find the margina atients who are indifferent to the tye of services (nonforma care vs. bic heath care and bicrivate heath care. Given those references, the hysicians maximize their rofits in the rivate sector by setting rices and aity. Finay, the hysicians decide how mch effort to rovide in the bic sector, given the bic ayment strctre and exogenos constraints. The anaysis is cometed by finding the critica vaes for the two extremes of the distribtion: the eve of income of the margina consmer between nonforma heath coverage and bic coverage (Y 0, and the rice aid by consmers in the rivate Ahigh income@ sector ( h. The forth section of the aer simates the findings of the mode by considering both a niform and a ognorma distribtion of oation in terms of income. The niform distribtion shows the effects of a mixed bicrivate heath care system in terms of rice and aity eves. The ognorma distribtion mirrors the same rests nder more reaistic income distribtions. Then, simations show how hysicians= behavior defines oation choice among different roviders, as we as the imortance that incentives in one area of the market have on the others. 4

5 The ast section contrasts the rests obtained in the mode with the concsions fond in the comarative iteratre on the Latin American and Caribbean heath care market. The mode hes to exain why atients refer bic inatient and rivate otatient care nder crrent conditions and why rivate heath care exenditres have been increasing as a share of tota heath exenditres, eseciay in reativey ess deveoed contries in the region. 1. Backgrond Discssion Latin American and Caribbean contries vary a great dea in terms of heath care indicators, as we as in heath exenditres er caita. Both tyes of variabes are highy correated to the GDP er caita of each nation. 4 At the same time, even thogh there are severa simiarities in the strctre of incentives on the sy side, strong differences in the organization of heath care rovision are fond among contries. According to the Inter American Deveoment Bank (1996, and sing data from Sarez et a. (1995 and Govindaraj et a. (1995, severa observed emirica facts have to be taken into accont in order to nderstand the strctre of these markets 5 : The rivate heath sector in Latin American and Caribbean (LAC contries is imortant in the rovision of heath care. The strctre of incentives in the bic heath sector is weak (e.g., workers are not aid according to their efforts, hosita directors are not free to fi vacant osts. In genera, hysicians work in bic and rivate faciities at the same time. In 17 ot of 6 contries, direct otofocket ayment is the main mechanism for contracting rivate services. In amost a contries, the share of oation seeking inatient services in the bic sector is mch higher than in the rivate sector. The roortions are reversed for otatient care. In oorer contries, where bic exenditres in heath are ow and there are oorer heath otcomes, the rivate heath care sector has higher shares of GDP than the bic shere. By 1990, for different bocks of contries cod be identified in terms of organization: The Contract Intensive Bock (Argentina, Chie, Urgay is characterized by high rates of heath care coverage, where the bic sector acts as rovider of ast resort. The rivate sector is organized mainy nder heath insrance strctres. This bock invests a high ercentage of GDP in heath, and sends reativey more than the rest of the region in terms of internationa doars er caita. Heath otts and otcomes are aso above regiona standards. 4 Word Bank (1993; Mrray, Govindaraj, and Msgrove ( Tabe 1.1. smmarizes the main eements of LAC=s heath care systems. 5

6 Pbic Sbcontractor Strctre: Brazi is the ony contry in the region where bicy 6

7 financed services are rovided mainy by rivate sbcontracted siers. A significant share of its oation is withot heath care coverage, and its heath care otts and exenditres are above the region=s standards. Heath insrance is deveoing raidy in the rivate sector. The Pbic Integrated Bock (The Bahamas, Barbados, Trinidad and Tobago, Jamaica, Costa Rica has high eves of both heath exenditres and otts. The bic sector dominates the market, whie the rivate sector is atomistic and covers a reativey sma share of the oation. The Segmented Bock (the rest of the contries: In this gro, the bic sector and the socia secrity system (SSS seek to rovide services for a broad segment of the oation. However, the effective coverage is ow, and rivate siers are increasing their share of the market. In genera, there is no coordination between bic and SSS faciities with the excetion in Mexico and Panama athogh both systems are financed by bic fnds. With the excetion of Venezea, Sriname, and the Dominican Rebic where an increasing share of the oation is covered by heath insrance contracted by firms the rivate sector is highy atomistic. The mode introdced in the next section assmes the existence of a rivate feeforservice atomistic market, where hysicians are abe to discriminate among consmers based on abiity to ay. The bic sector and the socia secrity system are considered to be nified for the rose of simification. The strctre of the mode is reevant to a vast gro of contries in the region, incding Haiti, Gatemaa, Hondras, E Savador, Beize, Nicaraga, Per, Boivia, Paragay, Ecador, and Gyana, a of them beonging to the Segmented Bock; and Costa Rica, The Bahamas, Barbados, and Trinidad and Tobago, from the Pbic Integrated Bock. The ack of a defined reationshi in the mode between the bic sector and the socia secrity system redces its ower to exain the cases of Mexico and Panama, athogh the genera concsions can be aied to these two nations. Introdcing a heath insrance base for the rivate sector and minor additiona modifications wod be necessary to extend the mode to the cases of Argentina, Brazi, Chie, Coombia, and Urgay. The heath care systems of Venezea, Sriname, Dominican Rebic, and Jamaica are combinations of the resent mode and one that wod consider heath insrance in the rivate sector. Athogh it mirrors the main featres of many of LAC=s heath care systems, the mode does not cover severa toics. First, the mode does not distingish between reventive and crative medica assistance and the resting imact on costeffectiveness. Second, it considers acta incentive strctres, bt not changes in incentive mechanisms. It is known that differences in who rovides and finances heath services, and in the way that ayment strctres are imemented affect the aity and costs of rovision. Whie the focs on the aer is not the strctre of the contracts, this wod be fertie grond for ftre research. 7

8 . Literatre Review In a market where aity is homogeneos among a its rodcts, consmer choice is based on rice: a consmers wi by the cheaest service offered. As soon as a higher aity rodct is introdced into the market, consmers= choices wi differ based on their references for aity and their abiity to ay. As a conseence, each rodcer wi choose for his/her rodction the combination of rice and aity that aows him/her to acheve the highest rofits. The indstria organization iteratre incdes severa anaysis of this isse, reated mainy to discrete choice modes of rodct differentiation (e.g., Gabszewicz and Thisse 1979, Shaked and Stton 198, Choi and Shin 199, Beath and Katsoacos The mode in this aer is based on that iteratre. I introdce a mode with vertica rodct differentiation, 6 where consmer choice is the rest of a tradeoff between rice and aity: according to their eve of income, atients decide the rice they wi ay and the aity of service they wi seek given that rice. In their artice, Shaked and Stton (198 reresent the oation as niformy distribted aong a inear city sch that the cstomer with the owest income is ocated at one extreme, and the one with the highest income is fond at the other end. The athors deart from a scenario where each firm, after choosing whether or not to enter the indstry, offers a good with different aity. The ranking of reative aities is known by the oation. As in other inear city modes, the sotion is focsed on the ocation aong the income distribtion of the margina consmer, who is indifferent between each air of different rodcts. The margina consmer (as defined in the indstria organization iteratre stands at the threshod between the gro that demands a certain combination of riceaity for the good, from a second gro that ays a higher rice in order to have access to better aity. Shaked and Stton (198 focs their anaysis on the otima nmber of cometitors that are abe to srvive nder these conditions. Using the same framework, Choi and Shin (199 anayze the case where the decision abot aity is taken seentiay among two firms, sch that the second firm observes the choice made by the first before deciding. In a third ste, both firms define their rices. The case introdced here has the articarity that siers (in this case, hysicians choose rice and aity in the rivate sector, given a rice and a aity defined in the bic sector, where they aso articiate as agents. In addition, I comare the otts of the 6 Vertica rodct differentiation is defined in the foowing way: AGiven two distinct rodcts, if they were sod at the same rice, then a consmers cod choose the same one (the highest aity rodct@ (Shacked and Stton The observed heterogeneity among rodcts differentiates this kind of market from ones in which horizonta rodct differentiation revais, where choices are triggered by differences in rices. 8

9 robem (bicrivate heath care coverages by introdcing different income distribtions. The iteratre on heath economics acknowedges the existence of da job hoding by hysicians. This henomenon is resent not ony in deveoing contries bt aso in deveoed nations. There are basicay two reasons why hysicians work in the bic (or rivate sector as emoyees and at the same time have their own ractice. The first is the assrance of a basic wage (generay fixed at the first job at the same time they obtain additiona income throgh comementary efforts in their rivate ractice. This argment is sorted by research abot the shae of the hysicians= sy crve (Eastagh 199, McGire and Pay 1991, among others. The second reason for da job hoding is the ositive siovers obtained by sch ractice. By working in a hosita, hysicians have the oortnity to Ahnt@ atients who can ask for additiona rivate care, de to retation or sefreferras. In addition, hosita networks faciitate cross referras among doctors. Chawa (1996 anayzes da job hoding by introdcing a mode of time aocation among ractices. That stdy focses on the generation of siovers across jobs and sbseent time aocation, which are tested for the Indian case. Finay, Gazer and McGire (1993 stdy secific isses reated to da jobs in heath care markets. The artice introdces the case where the insrer (ossiby the government ays a fee for each rocedre, and aows the doctor to charge a sementary fee, a ractice known as baance biing. Given this strctre, hysicians are abe to discriminate among atients based on rice and aity. The athors concde that when rice discrimination is ermitted, and nder certain conditions for fee determination, aity is set at a higher eve for a atients, and not ony for the ones who ay the sementary rice. This finding is extremey imortant for oicy design. As wi be shown in this aer, simiar effects can be fond in the Latin American context, athogh these are imited given the different stye of bicrivate ayment mechanisms. In Latin America, siovers in aity are fond ony by changes in bic aity, which are indeendent of the fee oicy. However, simations for different income arameters aow s to recognize the effects of changes in rices and aity according to aternative income distribtions. 3. An Exanatory Mode 3.1. Strctre The Government, throgh its heath athority, defines the ayment strctre in the bic sector as a fixed wage for a hysicians, indeendent of the nmber of services rovided. No reward is given de to imrovements in rodctivity and there is no reation with otts. Given that strctre, and considering externa shocks sch as changes in genera 9

10 rices and bic bdgetary constraints hysicians set the aity of bic services throgh their effort eve (. Once the aity in the bic sector is defined, hysicians, as rivate rofit maximizers, decide the rice and aity they wi charge in the rivate sector. Finay, consmers choose whether they wi ask for heath care or not. If they do, they wi seect according to their references between bic and rivate rovision. The mode is soved backwards. First, consmers= choices are anayzed, and three consmers are identified. They are the ones who are indifferent in choosing among different tyes of services. Once these margina consmers are fond, heath care markets can be artitioned among roviders. Then hysicians decide the rice and the aity they wi offer in the rivate sector, given the bic aity, which is defined by the bic sector ayment strctre and externa factors. 3.. Assmtions The mode ses the foowing assmtions for simicity: A1 Each consmer bys, at most, one nit of heath care. It res ot the ossibiityof overconsmtion beyond the first nit. The rests can be extended to reax this assmtion withot sbstantivey atering the concsions (see Aendix 1.a.. A Heath care services are effective with certainty. A3 Physicians discriminate between two gros of atients, charging high rices to one gro and ow rices to another. It is known that hysicians in atomistic markets are abe to discriminate rices according to atients= characteristics. For simicity, it is assmed that there are jst two gros of atients distingished by their income eve. There is an income threshod, Y h, which searates the two gros of consmers. As hysicians maximize their rofits in the rivate sector, rice discrimination is the strategy they foow, given that they know income eve Y h. A4 Physicians maximize rofits in the rivate sector by sitting monooy rofits, sch that i = m /n, where n is the nmber of hysicians (see Aendix 1.b Consmer Choice Consmers= references are defined according to the tiity fnction U (Y, k = k (Y k (1 where k : is the aity of services in sector k, and is ositivey associated with effort; k : is the rice of services in sector k; Y : is the consmer=s income eve; 10

11 and k = bic sector rovision; rivate sector, owrice rovision; h rivate sector, highrice rovision; 0 no consmtion. Consmers are indifferent between goods k and k1 if which rests in U (Y, k = U (Y, k1 k (Y k = k1 (Y k1 Interest is focsed on three secific consmers. They are the ones who are indifferent between the consmtion of heath care from different sorces. The first margina consmer is indifferent between consming bic heath services, with rice (exogenos to the mode and aity, and not consming at a in heath care faciities, with associated aity 0 and rice 0. This consmer wi have an income eve of Y 0. The choices are reresented by: 0 (Y 0 = (Y ( The second margina consmer is the one whose references are: (Y = (Y (3 The consmer with income Y wi be indifferent between consming heath care in the owrice rivate sector, with aity and aying, or receiving ower aity care,, associated with a ower rice,, in the bic sector. Finay, there is a third consmer who is indifferent between the Ahigh income@ rivate sector and the bic sector. His/her references are reresented by: (Y h = (Y (4 11

12 Note that in eation 4, the first term has becase the rivate consmers of both tyes wi receive the same aity of care athogh the ower income consmer wi ay ess than the high income consmer. That is why there is no ossibiity of a consmer choosing between ow and highriced rivate care; hysicians are the ones who discriminate among atients. 7 Figre 1 shows the distribtion of these indifference oints. Consmers are ordered on the horizonta axis according to income eve, and the resting tiities are shown on the vertica axis. The intersections between U (Y, and U (Y, 0, and U (Y, L and U (Y, H, resectivey, show the indifferent consmers defined by (, (3, and (4, named Y 0, Y L, and Y H, aong the income axis. Figre shows the distribtion of consmers between roviders given a ognorma density fnction f (Y and considering the margina consmers aready fond. The distribtion indicates the existence of a higher concentration of consmers in ow and medim ranges of income, as we as a smaer oation with high income eves. Peoe ocated between 0 and Y 0 wi receive no rofessiona rovision, whie consmers between Y 0 and infinity do demand heath care services, distribted between bic heath care from Y 0 to Y, rivate ow rice heath care from Y and Y h, and rivate highrice heath care from Y h on. Section 4 wi show the rests of simating the mode, not ony nder a niform distribtion, which arises from the eations resented in this section, bt aso nder a ognorma distribtion. In that case, severa means and standard deviations are considered, reresenting different income distribtions. A higher mean is associated with a higher GDP er caita, whie greater standard deviations reresent ess eitabe societies. Before trning to the simation, however, it is sef to anayze the strctre of the mode so as to better nderstand how behavior in the different segments affects otcomes Physicians Behavior and the Private Sector. Strategy in the Private Lowrice Sector. Sections 3.4 and 3.5 wi stdy consmer choice between bic and rivate ow heath care, based on hysicians= behavior. That is, the behavior of the hysicians in terms of aity and rice wi determine the margina consmer (in terms of income. The oint at which this choice is made is the focs of this aer. Section and 3.6. exain the choices avaiabe to consmers at the extremes of the income distribtion (ot of the heath care system and rivate high income. Physicians ay a dobe roe in the rovision of heath care in LAC contries. They care ans. 7 Comare with some other systems where consmers sef seect by choosing cheaer or more exensive heath 1

13 sy services for a fixed ayment in the bic sector and they rovide services in the 13

14 rivate sector of the market, not ony in their own cinics and offices, bt aso in bic faciities. Accordingy, the aity in bic and rivate faciities, as we as the rices charged in the rivate sector, are inked to each other. Given consmers= choices, hysicians in the rivate owrice sector seect the rice and aity they wi offer in this range of the market. Physicians wi maximize a rofit fnction = ( (Y h Y (5 where the nit cost of rodcing a aity is normaized to one. For simicity, a niform income distribtion is assmed, bt this assmtion is reaxed in the foowing section. Y h is assmed to be fixed, and refects the known threshod between high and owincome consmers. On the other hand, Y deends on rice and aity decisions in the bic and rivate owrice sectors. Given (3, Y wi be: ( Y = (6 ( where and : are chosen by hysicians in this stage, : is chosen by hysicians in the bic sector, and : is exogenos. Reacing (6 into (5 and taking first order conditions, the hysicians= strategy in eiibrim for the rivate ow income sector [ (, (, ] is given by (,, = 1 Y h + (7 and ( ( (,, = + Y h (8 Eation (7 shows the otima rice 14

15 in the rivate ow sector, evaated at the otima rivate and bic aity. This rice is an average of two factors. The first is the rodct of the er bond cstomer=s income (Y h mtiied by the increment of aity in the rivate ow sector. This rodct can be seen as the amont of aity added to the system by the rivate sector. The second factor is the difference between the dissatisfaction with bic rovision (seen as the reation /, vaed in terms of the bic rice, and the cost of receiving rivate aity. This factor can be seen as the oortnity for a mark that consmers wi accet. This rice eation is simiar to the ones fond in the iteratre on market strctres in genera. Price is a fnction of the margina cost (of higher aity and of the mark (defined by the consmer=s wiingness to ay for higher aity. Eation (8 aso has a straightforward interretation. The aity rovided by rivate heath care is ea to the bic aity at the otima eve s an additiona factor, which is ositive. This formation ensres the existence of a rivate sector. In addition, this factor is a fnction of three eements: the reference effort eve (, the monetary earnings er nit of aity sied (, and the maximm eve of the mark ( when, in the margin, =. These three factors are weighted by the avaiabe income after heath care exenditres of the richest atient, which is in the denominator of eation (8. To some extent, the denominator is a measre of demand. Two exanations can be sggested. The first is that the effort of hysicians in the rivate sector is inversey reated to the nits of heath care to be rovided. This exanation foows the argment of a tradeoff between income and effort sorted by the iteratre. An aternative view is that higher market ower aows hysicians to redce their costs (aity. As the mode considers a rivate sector behaving monooisticay, the inverse reationshi between aity and a measre of demand is a signa of market ower. Given the characteristics of eations (7 and (8, it is not ossibe to obtain definite anaytica sotions by sbstitting one into the other. 8 However, by tota differentiation, it is feasibe to define how and react to changes in. Rests show 9 that changes in bic aity affect rivate aity ositivey and rivate rices negativey. Simations in Section 8 Second order conditions to ensre the resence of oca maxima were erformed and are incded in Aendix. These conditions reire known secific reations between endogenos and exogenos variabes that can be fond by simating the mode. Section 4 shows the rests of simations by sing both niform and ognorma distribtions. The rests were reaced in the second order condition, confirming that the Hessian is negative definite. 9 See Aendix 3. 15

16 4 show that this condition hods in a cases. Eations (7 and (8 introdce the sotion of the mode as a rest of the interaction between consmers and hysicians in the rivate sector, sbject to the aity decision in the bic shere. The riceaity tradeoff between bic and rivate owrice sectors wi define the income eve of the consmer who wi be indifferent between the two tyes of services Pbic Sector The ast ste considers the choice of effort that hysicians make in the bic sector in order to maximize their rofits. This decision incororates the sotion reached in the rior stes. In a ossibe cases, given the ayment strctre in the bic sector, the sotion for is trivia: =0. This can be seen by ooking at the sotion to maximizing the foowing rofit fnction: = w (Y [,,, ] Y 0 (9 where w is the fixed wage aid by the heath athority, indeendent of the eve of aity and the nmber of atients in the bic sector. However, there are severa restrictions on doctors decisions in the bic shere of the market. They are associated mainy with two factors: (1 soidarity or mora effects in rovision sch that hysicians rovide a certain minimm aity of service, which can be introdced by a ower bond, m; and ( a contro/monitoring constraint, x, which can be defined as a fnction of exogenos variabes sch as bdgetary redctions, infation, etc. Externa shocks cod redce the effectiveness of monitoring hysicians and hence rest in ower aity services. A ossibe fnction for this reationshi is: = m, if x > x f [ g( x], if x < x (10 where g(x = e x, and = sg(x, with s a constant rate of controing effectiveness. As it was mentioned before, the signs M /M and M /M are tied to the vae of the arameters. 16

17 Poation Located at the Extremes of the Distribtion Even when the Y (bicrivate threshod constittes the main isse nder anaysis, two other additiona asects have to be considered. They are: (1 the threshod between the oation sied by the bic sector those withot coverage (Y 0 ; and ( the rice defined in the rivate high income sector Poation Otside the System Y 0 is obtained from eation (: 0 (Y 0 = (Y and assming 0 to be cose to zero, (11 where the variation of Y 0 in terms of is given by: (1 = Y 0 0 ( ( = Y < ( = Y 0 0

18 The higher the aity in the bic sector the ower the threshod between those otside of the system and bic rovision, ths increasing the share of oation that receives heath care in the forma sector Private Sector Highrice On the other extreme of the distribtion, and according to eation (4, the rice decision is the foowing: (Y h h = (Y h which, in terms of h is: h = Y h + i (13 where the first term on the right side refects the income effect weighted by differences in aity, whie the second term shows the sbstittion effect in terms of the ratio of service aity between bic and rivate services. By sbstitting (7 and (8 in (13, the sotion for h can be exressed as a fnction of. 4. Simations and Rests The anaytica rests obtained in section 3 and in Aendixes and 3 show that nder certain conditions, imrovements in bic aity ositivey affect rivate aity and negativey affect rivate rices. According to the mode, hysicians in the bic sector define the eve of aity in bic faciities based on atristic behavior and the abiity of the bic financier to monitor their efforts, which are negativey associated with externa factors sch as bdgetary constraints. Pbic aity=s direct and indirect effects on rivate aity and rivate rices act in oosite directions (see Aendix 3, sch that the net effect deends on the magnitde of the variabes. This section is devoted to showing how these effects interact, by simating the conditions introdced in the mode. The mode, as noted before, considers the consmers niformy distribted aong the income adder. This assmtion makes it easier to nderstand the reationshi between deendent and exogenos variabes, net of distribtiona effects. However, the incsion of different scenarios in terms of income distribtion may he nderstand the imact of eity on the rovision of heath care services. 18

19 Therefore, the simations were erformed for two different scenarios, which beong to aternative demand fnctions. Each of them refers to two main income distribtions. The first beongs to the case introdced in section 3, the niform distribtion, sch that the hysicians= rofit fnction to be maximized takes the form: = ( c (Y h Y (5 where (Y h Y is the demand of a oation that has niformy distribted income. The second fnction reaces the niform demand fnction to aow different densities for each eve of income. In order to reicate the distribtion introdced in Figre, a ognorma form was sed for simation roses: π = ( c f (,, Y Y h µ, σ (14 where s is ositivey reated to the eve of ineity in the distribtion of income and µ is a measre of average income er caita. In both cases, ( Y = (6 ( 4.1. Uniform Distribtion The simations erformed for the mode nder the niform income distribtion show that increasing aity in bic sector services has ositive siovers on rivate sector aity, confirming that direct effects more than offset indirect effects throgh rivate rices. The need to differentiate rodcts between the bic and rivate sectors, and the amost zero rice that atients ay for bic services, sh the aity in rivate faciities when bic erformance imroves. This trend was fond for different eves of bic rices (Chart 4.1. right. However, rivate aity seems to imrove by rogressivey smaer increments as 19

20 bic aity imroves. The effects on rivate rices de to changes in bic aity (Chart 4.1. eft are not homogeneos, deending on the eves of. Even when in a cases there is a negative correation between the two variabes when direct effects offset indirect ones, if the aity in the bic sector is ow, the change in rivate rice is negative and stronger than at higher eves of bic aity. A ossibe exanation for that difference in rice reaction is that at ow eves of bic erformance atients erceive oor enogh bic aity to refer aying higher rices to get reativey better aity. Therefore, at ow eves of bic erformance, aity differences revai over rice differences from the atients oint of view. As ong as the aity in bic rovision becomes better, the rofitabiity in the rivate sector fas. At the same time, bic rices (assmed here to be transortation costs or ow fees in bic faciities affect the reationshi between bic aity and rivate rice in the exected way: given identica changes in bic aity, the ower the sooner is the fa in rivate rices. Considering the riceaity tradeoff between bic and rivate faciities, the ower the rice in bic faciities, the higher the atients= accetance of ower aity in bic services in regard to shing the rivate market to be more cometitive with the bic sector. The strctre of constraints in the bic sector, the obtained rests show that higher eves of bic deficit and bdget cts in heath care rovoke ooser contro over bic otts, thereby redcing the aity of bic rovision. This in trn redces the incentive to raise aity in the rivate sector, becase hysicians wi receive rivate atients with minimm additiona effort. As a rest, the socia heath stats fas as a whoe. Likewise, the more hysicians identify with socia needs the more the erformance of the entire heath care sector imroves, not ony in the bic segment bt aso in the rivate one. This inkage exains the tradeoff between socia references and rofit goas in the hysicians fnction. The atristic motive, refected by the ower bond m in bic aity, raises the aity of the rivate sector, redcing doctors rivate rofit (Tabe 4.1. and Chart 4.. right. The income of the margina consmer ocated between the bic sector and the rivate owrice sector, Y, is defined as the rest of rices and aities in both, the bic and rivate systems (eation 6. Chart 4.. (eft shows that Y moves the income adder as soon as aity in the bic sector imroves, which means higher demand for heath care in bic faciities. This movement in the bicrivate threshod sggests that the infence of on consmers= choice of aity among systems revais over the rice redction in the rivate owrice sector. However, the margina change in the threshod is not roortiona to the rise in bic aity. Sch change is sensitive to the eve of rices in bic rovision. At ower eves of bic aity, the resonse is higher when bic rices are higher. On the other hand, the margina variation in Y de to changes in bic rices diminishes in reative terms when bic faciities offer higher aity. To sm, even when the choice of 0

21 rovision seems to be driven by aity, the magnitde of the change in the bicrivate threshod is determined by a rice effect. Tabe 4.1. shows the transition as ercentage of the rivate owrice sector=s coverage, and for different eves of Y h. At the imit, if is high enogh, rice and aity in the rivate owrice sector tend sowy to converge, eaving zero rofits to the rivate rovision in this segment of the market. Therefore, no incentives wod be offered to sy rivate services,y wod match Y h, and the bic sector wod sy the entire range of oation between Y 0 and Y h. This ictre might reresent the case of the Pbic Integrated Bock of contries described in section 1. There, bic rovision covers a arge ercentage of the oation, eaving rivate rovision to a sma gro of highincome consmers. Charts 4.1. and 4.. Fie: nisoc.wk4 Location: P X148 Position: vertica 1

22 Tabe 4.1. Fie: nisoc.wk4 Location: P149...X1460 Position: Vertica

23 4..Lognorma Distribtion The ognorma distribtion anaysis is introdced in order to ook in deth at the reationshi between income distribtion and the bicrivate mix in heath care rovision. The choice of the ognorma distribtion is based on its simiarities to the aocation of income among a contry=s oation: it sggests a significanty ower share of eoe with higher eves of income, at the same time that the majority of the oation is concentrated in ow and middeow income segments. As is shown in this section, the contry income eve, as we as its distribtion affect in how changes in bic aity and rices infence rivate heath care. Therefore, not ony the distribtion of consmers among systems bt aso the eve of rivate rofits are sbject to distribtiona characteristics, ths affecting the imact of any bicaity enhancement. As in the case of the niform distribtion, the simations were erformed for a set of bic rices and aities and for different eves of Y h. In addition, three different means and standard deviations were taken into accont. The mean is seen as the GDP er caita of the contry, sch that higher µ mirrors (on average a richer nation. The standard deviation reresents the degree of ineaity in income distribtion, where s grows with ineaity. 10 The simations comrised a gro of nine different Asocieties@ in terms of income distribtion, each one for every eve of Y h, and a set of sixtyfive combinations of rices and aities in the bic sector. Iterative exercises were erformed to find the maximm sotion for each combination, given that the endogenos variabes and are resent in Y, one of the extremes of the integra (eation 14. A seection of the rests is resented in Charts and in tabes 4. and 4.3. Chart 4.3. (eft shows rivate rice and aity reactions to bic aity for for income distribtions. The reactions are defined at a high eve of Y h, which is the er bond of the demand in the owrice market. Obviosy, higher means are associated with higher rice eves. However, changes in rivate rice, as a conseence of increments in bic aity, are associated with the standard deviation: societies with more eitabe distribtions observe ower rices in the rivate sector as a resonse to increments of bic aity,whie in the high sigma cases the rices go in resonse to the same bic aity behavior. In other words, and based on (A.1 in Aendix 3, when a society is more eitabe the aity effect on rices (indirect effect is stronger that the re rice effect. When societies are ess eitabe, the segmentation in heath care rovision among systems is stronger, aowing hysicians to charge more for their services in the rivate sector. 10 Given the characteristics of the ognorma distribtion, no anaytica rests can be fond for and withot nmerica exerimentation. 3

24 In terms of rivate aity reactions to bic imrovements in rovision (Chart 4.3. right, simations sggest that direct effects aways offset indirect effects throgh rices as was observed in the niform distribtion case. Therefore, rises in bic aity enhance rivate aity for any income distribtion. In a cases, the imact diminishes in magnitde when bic aity goes (decreasing siovers. However, simations show that richer societies (higher µ are more resonsive to changes in bic aity than are oor ones, and that the degree of ineity redces sch imact across systems. Rests are not the same when we anayze the same reactions for a ower Y h (Chart A ower eve of Y h reresents a smaer demand in the owrice market for any µ and s. It reresents a measre of market size, as was defined in eation (8. The simations show that in this case, the net rest of direct and indirect effects on rices varies according to the eve of income ineaity. Price is reativey ess resonsive to bic aity and in genera foows the oosite direction, as it was seen in the case with oation distribted niformy. 11 In addition, even when richer societies are sti charged with higher rices, standard deviations are inked with two different henomena: at ow income eves, the rice behavior reicates the one discssed before. However, at reative higher µ more egaitarian societies are charged higher than ess eitabe ones. A ossibe exanation is that the smaer size of the market shes hysicians to rice rivate services higher in more eitabe cases, where it is more robabe to catre atients. At ow eves of Y h (Chart 4.4., right, the rivate aity reaction to bic aity is the one exected (ositive, and the aity ga among services is smaer than in the high Y h case. However, the rivate aity resonse is reativey stronger in this case, which shows that when markets are smaer, siers have more incentives to differentiate their rodcts from the ones rovided in the bic system. This resonse was observed in section 3, when otimm rivate aity conditions were anayzed (eation 8. Chart 4.5. (eft shows how the observed rivate resonses to bic behavior affect the otcomes of the heath care system. In a cases, the threshod between bic and rivate coverage rises with bic aity. In ine with the reactions discssed before, in more eitabe societies, where rivate rices decrease with bic aity, the threshod=s reaction is sma, and it is stronger when the reaction of rivate rices is the oosite. The concsion is that even when there is a tradeoff between costs and erformance of heath care services, the aity affects more consmers= references than rices, which matches the rests observed nder the niform distribtion. At smaer market sizes smaer Y h the bicrivate threshod shows a ositive trend in reaction to bic aity (Chart 4.5., eft, athogh the costaity tradeoff is ambigos at ow eves of bic aity. 11 Private rice reactions to bic aity aear to be more insensitive in this case than in the rior ones. Even when this is tre reative to a higher Y h case, these rests are robaby infenced by the iterativey method sed to sove the mode. 4

25 Charts 4.3 / 4.4. Fie: LGNT.wk4 Location: AA1...AK70 Position: Vertica 5

26 Charts 4.5 / 4.6. Fie: LGNT.wk4 Location: AA71...AK140 Position: Vertica 6

27 Tabe 4..(a, (b and (c. Fie: LGNT11.wk4 Location: B1...AE37 Position: Horizonta 7

28 Tabe 4.3. Fie: LGNT11.wk4 Location: AH1...AR47 Position: Vertica 8

29 Finay, reativey oorer societies are associated with ower eves of hysicians= rofits (Chart 4.5., right, which decrease with increments in bic aity. This dro is even more drastic at smaer market sizes (Chart 4.6., right, resembing the niform distribtion exame. Here an interesting isse arises: in contries with ower demand, the ctoff in rofits is given by the disersion in income distribtion rather than by the mean, sch that more eitabe societies give more rofits to hysicians, who choose the riceaity combination to sy according to the average income. This exanation cometes the anaysis of rivate rice reactions to bic aity introdced in Chart 4.3. A more detaied ook at the effects of income distribtion on heath care otts is introdced in tabes 4..(a, (b, and (c, and Tabe 4.3. These tabes smmarize the main otcomes of the mode for different combinations of income distribtion, demand size, and bic aity and rices. The first two tabes amify the information aready shown, confirming the anaysis introdced before within a wider range of vaes for the arameters, whie Tabe 4.3. disays a range of gas in rice and aity among services for a set of income distribtions and market sizes. As anayzed throghot the aer, different rice and aity resonses in the rivate sector refect different tradeoffs that siers take into accont to maximize their articiation in the rivate owrice system. Therefore, the rivate sector market share is the rest of the interaction of bic incentives, hysicians= resonses, and consmers= choices nder different eves and distribtions of nationa income. Tabe 4..(c shows the rivate ow rice share of the market by income distribtion when bic aity changes, and for different eves of bic rices. The tabe reinforces the hyothesis in the first section of this aer: ower aity in the bic sector rovokes a shift of consmers toward rivate faciities. In addition, oor and smasized societies tend to deveo a higher rivate share in the coverage of heath care services, whie rich and bigger ones show the oosite trend. Finay, the degree of income ineaity negativey affects the deveoment of the rivate owrice sector. 5.Concsions The aer shows the otcome of decisions taken by consmers and hysicians nder the conditions revaiing in a significant nmber of Latin American and Caribbean contries. It demonstrates how fixed ayment res in the bic sector and hysicians dobe jobs affect the erformance of heath services in these contries, as we as the distribtion of atients among different tyes of roviders. Based on a sime riceaity tradeoff in heath care services, doctors maximize their rofits in every area in which they act, conditioned by externa shocks and the income distribtion of the oation, and sbject to their wiingness to behave atristicay toward the oation s needs. The aer aso sorts two of the main observations resented in the iteratre: first, contries with greater bdget constraints in the heath sector generate ower aity otts 9

30 in the bic sector, eaving increasing roortions of the oation withot coverage in the eft side of the income distribtion and, by defat, creating an atomistic and broadened rivate sector that covers many consmers needs. Second, the mode shows why consmers refer otatient sy in the rivate sector rather than in the bic faciities, whie the reverse is identified for inatient care: Given that inatient care is more exensive than otatient attention, it is easier for consmers to trade better aity for higher rice in the inatient case. This effect is frther amified by rice discrimination in rivate sector rovision. It has aso been shown that high aity in the bic sector not ony increases heath care coverage and imroves rovision in bic faciities, bt aso rodces ositive siovers for consmers of rivate services, in terms of aity and rices in the owrice range of rovision. In sm, imrovements in bic aity raise the entire socia heath stats. An additiona argment that foows from the mode is that in designing doctors contracts in the bic sector in order to imrove erformance, one mst not ony ook into the strctre of bic sector comensation, bt aso consider the inkages between the two tyes of roviders, as we as enforcement mechanisms that take into accont the severa markets where hysicians erform. 30

31 Aendix 1.a. Anaysis of Assmtion 1 According to Assmtion 1, each erson consmes at most one nit of heath care. However, the same strctre can be sed if instead of ony one, N nits of heath care are received and aid er consmer in the rivate sector. Let s assme that exante the margina consmer between the bic sector and the rivate ow market remains the same: ( Y = ( Y bt, exost, each atient receives (is indced to consme N nits of heath care. Then, hysicians maximize: = ( N (Y h Y, where Y = ( ( The resting aity and rice which means the signa to consmers remain the π i = N π n m same. Therefore, atients wi not change their behavior, and hysicians rofits wi be: where n is the nmber of doctors in the market and m is the monooy rofit. The remaining estion is whether atients, nder these sy characteristics, earn from exerience. The answer is yes. If rice and aity do not change in the bic sector, atients, as soon as they nderstand that they were oversied by a rivate doctor, wi switch their doctor next time, athogh sti within the rivate sector. However, and according to Dranove (1988, it is Nash eiibrim for every hysician to reicate the same condct, sch that the consmers wi face the same sitation whoever their rovider is. 31

32 Aendix 1.b. Anaysis of Assmtion 4 π i = N π n m According to Assmtion 4, i= 1...n, nmber of hysicians, which means that the monooy rofit is distribted among the nmber of siers. One reason to sort the assmtion is to consider that there is a erfect satia distribtion of atients and doctors, and each hysician obtains his/her share of the monooy rofits. A more genera argment is that it is Nash eiibrim for hysicians to act as monooists. The strctre of the mode shows that hysicians in the rivate owrice sector offer > ; otherwise there wod be no rivate market eoe wod not ay more to receive the same rodct. At the same time they set > ; otherwise there wod be no incentive to rovide rivate services. These two res define the existence of a rivate market, where = +.e with e being the mark in the rivate sector in terms of aity of the service. Then, = ( 1 + e = ( 1 +? /? where? = 0 if erfect cometition, = 1 if monooy, and? is the rice easticity of demand. The estion is why hysicians do not act Aa a Bertrand@, redcing e sch that it is Nash eiibrim to charge cometitive rices. They know that the market is not erfect in terms of satia differentiation, bt aso de to reasons sch as trst, wiingness to kee a famiy doctor, etc. These eements generate a articar tye of rodct differentiation. Becase of them, hysicians know that these differences aow them to charge rices higher than margina cost where the ony stabe imit is the monooy rice, etting doctors charge according to their atients easticity of demand. 3