Effects of the Brazilian University Policy of Targeting the Poor

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1 Effects of te Brazilian University Policy of Targeting te Poor Eduardo de Carvalo Andrade Resumo Este trabalo analisa, teoricamente, os efeitos do Programa Universidade para Todos (ProUni), introduzido pelo governo federal do Brasil no ano de 2005, sobre a qualidade da força de trabalo formada nas universidades privadas. Esse programa concede isenção fiscal para as universidades privadas que, em contrapartida, fornecem bolsas de estudo para alunos provenientes de famílias de baixa renda. A análise sugere que a qualidade da força de trabalo pode aumentar ou diminuir dependendo de duas variáveis-cave: o formato da curva de oferta do setor universitário e o nível de preparação para cursar a universidade dos bolsistas vis-à-vis aos não-bolsistas. Palavras-cave ProUni, universidade privada, ação afirmativa, eficiência Abstract Tis paper analyzes teoretically te effects on te quality of te labor force of te introduction of te program called ProUni (Programa Universidade para Todos), adopted by te Brazilian government in Tis program consists of giving tax exemptions to private universities tat provide scolarsips to students coming from low income families. Te analysis suggests tat te quality of te labor force can eiter increase or decrease depending on two crucial variables: te sape of te university sector's supply curve and te level of preparation to face university studies of te students wo are targeted by te program vis-à-vis te non-targeted ones. Key Words ProUni, private university, affirmative action, efficiency JEL Classification H0, H41, I22, I28 I ave benefited from comments and discussions wit Paulo Barelli and Ernesto Sepúlveda and participants in seminar at te SBE Meeting in Natal in 2005 and te international conference on Te Quality of Education in Latin America and te Caribbean in Mexico City in 2007.Obviouly, all remaining errors are my sole responsability. Ibmec, São Paulo. Endereço para contato: Rua Quatá, 300 4º andar. CEP: São Paulo SP tel: eduardo.andrade@isp.edu.br. Recebido em março de Aceito para publicação em fevereiro de Est. econ., São Paulo, v. 37, n. 3, p , JULHO-SETEMBRO 2007

2 664 Effects of te Brazilian University Policy of Targeting te Poor INTRODUCTION In 2005, te Brazilian government introduced a program called ProUni (Programa Universidade para Todos) to finance university tuition to low income families students. Te program as two main caracteristics. First, private universities receive tax exemptions if tey provide one full scolarsip for eac 10,7 students regularly registered. 2, Participation in te program is voluntary. However, if private universities adere to te program, te agreement lasts for ten years and it can be renewed. Second, te eligible students to receive te new scolarsips are tose wo studied all tree years in public ig scools. Moreover, teir families must ave a montly income no greater tan one and a alf and tree minimum wages, respectively, to receive full and partial (50% or 25%) scolarsips. 5 As in Brazil te best elementary and ig scools are in general private, tese students tend to be, on average, relatively less prepared to face university studies. Te students selected are tose among te eligible ones wo obtain te igest scores in te national exam called ENEM and are, as a last pre-requisite, selected by te private universities. Out of 1652 private universities in te Brazilian educational system, 1135 adered to te program, wic corresponds to almost 70% of te total. As a result of tis ig participation, 112,000 slots wit scolarsips were directed to students coming from low income families. Tis number corresponds to close to 7% of all slots available to new students in all private universities in Brazil in 2003 wose selection were made troug exam. 7, Te objective of tis paper is to analyze teoretically te effects of tis government s program on te quality of te labor force. Te focus on te quality of te labor force is a very important one for two main reasons. On te one and, it affects te economic growt rate and te economy s productivity. Hanusek and Kimko (2000) run a cross-country growt regression using data from 1960 to Tey found For details, see ttp:// 2 Universities tat adered to te program in 2005 ad to provide only one full scolarsip for eac 9 regularly registered students. To simplify, te term university also includes colleges and oter institutions tat provide tertiary education. Wit respect to te exemptions, tey include reduction in corporate income tax and oter contributions. Students wo studied in private ig scool wit scolarsips are also eligible to take part in te program. 5 Te minimum wage in Brazil in 2005 is equal to R$ 300 reais (or approximately US$ 126, using te excange rate of July 8t, 2005). Families wo can afford do send teir cildren to private scools, even toug tey ave te option of public education free of carge. Te difference between te two types of scool s quality is significant. 7 Only 9% of all slots in all private universities in 2003 are filled wit students selected troug oter forms rater tan exam. See MEC (2003) for furter details about te iger education in Brazil.

3 Eduardo de Carvalo Andrade 665 tat an increase of one standard deviation of labor force quality, measured by te grades obtained by students on matematic and science tests, may enance te real per capita growt rate by approximately 1.4% per year. Bisop (1989) suggests tat a drop in te american students performance in te exam known as SAT, from 1967 to 1980, coincides wit te decline in te american economy s productiviy. On te oter and, te quality of te labor force also affects te individuals. For example, Murpy and Peltzman (2004) suggest tat a drop in one standard deviation of te students performance in tests of proficiency leads to a reduction of 3% teir average wage. Tis empirical evidence indicates te centrality of te nation s uman capital and, in particular, its quality. 9 Wit tis aim to explore te effects of ProUni on te quality of te labor force, I develop a two-period model wit two main features. First, te university sector is modelled explicitly, assuming tat tere is a continuum of private universities autorized by te government to function and tey are price-takers. Second, tere are two types of families. In families of te first type, parents ave ig level of uman capital and can eiter send a cild to university or not. If tey do, tere is a probability tat a cild wo is sent to university becomes an individual wit a ig level of uman capital, wic depends positively on is or er level of preparation. In families of te second type, parents ave low level of uman capital and are credit constrained: tey do not ave enoug resources to pay te university tuition. Te government s program s target is clearly te latter type of families and its introduction can alter te allocation of uman resources in te spots available in private universities, wic affects te quality of te labor force. Te analysis in tis paper suggests te following. As a result of te introduction of te program, te quality of te labor force can eiter increase or decrease depending on two crucial variables: te university sector s supply curve and te level of preparation to face university studies of te students wo are te target of te program visà-vis te non-target ones. Independently of te former, if te level of preparation of te beneficiaries of te program are greater, te quality of te labor force necessarily rises. Te explanation is te following. By providing scolarsips to credit constrained families, te program s first effect is to increase te fraction of individuals wo obtain te university degree. As a consequence, te skill premium reduces. Additionally, depending on te university sector s supply curve, te university tuition may increase. Combining tese two effects, it makes not profitable for some families wit ig level of uman capital to continue paying for a private education and obtain a lower immediate utility. Hence, tey witdraw teir cildren from university. As tey are 9 Tis empirical evidence considers te effects on te quality of te labor in te pre-college period, as tere are exams tat allow an international comparison. However, one sould also expect a significant impact (possibly lower) of te quality of college education, te focus of tis investigation, on te same variables.

4 666 Effects of te Brazilian University Policy of Targeting te Poor replaced by better students (te scolarsips recipients), te quality of te labor force necessarily rises. Terefore, te program can increase efficiency and, at te same time, te income mobility. However, te most likely scenario is one in wic te level of preparation of te beneficiaries of te program is lower, as tey come from public scools. Under tis case, as more inelastic te university sector s supply curve, te greater is te increase in te university tuition, as a consequence of te iger demand in te university sector caused by te program. Tere is also a reduction in te skill premium, wic is not very significant as te level of preparation of te scolarsip s recipients are relatively low. Combining tese two effects, a relatively large number of families wit ig level of uman capital witdraw teir cildren from university, wo are now replaced by students wit worse levels of preparation. As a consequence, te quality of te labor force is lower. Tus, te program increase te income mobility at te expense of less eficiency. Tere is a clear trade-off. In contrast, as more elastic te supply curve, te quality of te labor force increases after te introduction of te program and no trade-off between efficiency and equity exists. It occurs because te university tuition does not cange significantly. As te skill premium also does not cange significantly, tere are relatively few families wit ig level of uman capital witdrawing teir cildren from university. Combining tis effect wit a relatively greater number of scolarsip s recipients entering te university, te final outcome is an increase in te fraction of individuals attending university and in te quality of te labor force. Tis result takes place despite te fact tat te beneficiaries of te program are relatively less prepared to face university studies. One can say tat tat te quantity effect dominates. Tus, ow te university sector responds to te increase in demand is crucial to understand te impact of te program. Te overall level of idle capacity in te Brazilian private university sector is around 20%. 10 However, tis percentage is possibly not omogenous across different courses, wic suggests tat te effects of te program may also vary across courses. Moreover, government s legislation tat restricts te opening eiter of new universities or new slots in universities may play an important role in te program s outcome, wic I discuss in te final section of tis paper. To my knowledge, tis is te first paper tat analyzes te recently implemented ProUni. It adapts a teoretical framework developed by Caucutt and Kumar (2003), wic analyzes te effects of increasing iger education subsidies in te US on inequality, welfare, and efficiency. Andrade (2004) uses a different version of tis 10 Te idle capacity number in te iger sector sould be looked at wit caution. Te Ministry of Education is responsible for autorizing new places in most of te universities. As tis process may take a long time, many universities demand new slots even if tey do not plan to use tem immediately.

5 Eduardo de Carvalo Andrade 667 paper in wic te goal was to investigate teoretically te impact on efficiency of te introduction of quotas into te Brazilian public universities entrance system. Te rest of tis paper is organized as follows. Te next section presents te structure of te model. Section 2 sows te competitive equilibrium witout te government s program. In section 3, te effects of te introduction of te program on te quality of te labor force are analyzed. Te last section concludes, wit special empasis on te discussion about te level of idle capacity in te university sector in Brazil now and in te near future, as tis variable is key to understand te effect of te program. 1. MODEL It is a two-period model. Tere are two types of families, wic differ by te parent s level of uman capital. At time t = 0, parent as eiter a ig or a low level of uman capital. Eac parent works, receives wages, decides weter to send is cild to university, consumes, and dies. At time t = 1, is cild becomes a worker wit ig or low level of uman capital, depending on te educational decision of is parent, receives a wage, and consumes. 11 Te measure of eac generation (and te number of workers in eac period) is constant and is normalized to one. Let n,t and n l,t be te fraction of individuals, respectively, wit ig and low levels of uman capital at time t. Note tat n,0 = n and,0 n = n are exogenously given, and n = 1,0 + n.,0 l,0 l,0 As I do not model te scooling decision, it is assumed tat all cildren ave a scool degree and are able to attend university. However, tey differ in teir level of preparation to perform well at university and become an individual wit a ig level of uman capital. A cild wit level of preparation a wo attends university becomes an individual wit ig or low level of uman capital, respectively, wit probability π(a) and (1 - π(a)). Tis feature of te model limits te eterogeneity to two levels of uman capital, and terefore to two income levels, wic simplifies te analysis. If a cild does not attend university, e as te lower level of uman capital wit probability one. I assume tat te distribution function for te level of preparation is different across types and identical witin families of te same type, and all level of preparation draws are independent of eac oter. Let F(.) be te distribution function for te ig income families level of preparation on te support [a,1], and f(.) be te corresponding density function. Let G(.) be te distribution function for te low income families l 11 As it is going to become clear in te next section, te low type individual ends up not sending teir cild to university as e is credit constrained.

6 668 Effects of te Brazilian University Policy of Targeting te Poor level of preparation on te support [0, a l ], and g(.) be te corresponding density function. Note tat 0 < a l, < a 1. Assumption 1: a [0,1], 0 π(a) 1, π (a) > 0, π (a) < 0, a, and π( a ) = 0. Tis feature of te model is motivated by te following. Te level of preparation of an individual to attend university and acquire a ig level of uman capital is determined in great part by two factors. Te first is te individual s innate or cognitive ability, wic is independent of te social environment were te individual grows up. Tere is no reason to assume tat te distribution of tis innate ability differ between groups of individuals wo differ by family income status. 12 Te second factor is related to expenditures in education received by te individual before entering university. Tis second factor is greatly affected by te income of te individual s family. For example, ig-income families are capable of paying for extra courses and better quality scools. 13 Tis is particularly true in Brazil as ig income families are able to afford private scools, wic are in general better tan public scools. Combining tese two factors, it is set a l < 1 and 0 < a. Te parent wose cild as level of preparation a as two options: sending te cild to attend university or college (option c) or letting te cild remain solely wit a scool degree (option s). Hence, te family s problem can be written in te following way: { c, s} ( i,0 + i ) + β p (,1 ) + ( p ) ( l,1) max{ u w P T ( a) ( a) u w 1 ( a) u w ( i,0 ) + β ( l,1) u w u w }, i =, l were β (0 < β < 1) is te discount factor, w i,t is te wage of individual wit i level of uman capital at time t, P is te university tuition, T i (a) is government s transfer to family i wit cild s level of preparation equal to a and te utility function as te usual properties. 14 Te first term indicates te university option. At t = 0, te family consumes its wage net of te tuition expenditures and sends its cild to university. At t = 1, te cild wo becomes a worker eiter wit ig or low level of uman capital earns is wage. Te second term is te option of not sending te cild to university at all: te cild becomes a worker wit low level of uman capital. 15,16 (1) 12 See Heckman (1995). 13 See discussion in Becker (1993). 14 Below in tis section, I explain wic families receive transfers. 15 To simplify te analysis, te tuition P is te only cost of iger education. Tis paper ignores te opportunity cost of foregone earnings, an important component of te cost of education, and assume tat te cild wo do not attend university can not work at time t = It is wort mentioning tat parents income is not necessarily equal to teir consumption as part of its income may be directed to invest in teir cildren s uman capital. However, cildren s consumption is equal to teir income at t = 1.

7 Eduardo de Carvalo Andrade 669 Two comments are wort noting before proceeding to describe production in tis economy. First, te only type of bequest allowed in tis model is troug investments in education. Oter types of bequests are not empirically relevant for most families, even in te most developed countries. 17 Second, tere is no capital market to finance education. Tis assumption is commonly used and widely accepted. 18 In general, tere are two types of uncertainties associated wit investments in uman capital. On te one and, it is not clear if te student is capable of finising is studies. Tis type of uncertainty is someow modelled ere troug te probability p. On te oter and, after graduating, tere is a moral azard problem. Te individual may not work properly or be a lazy person. As a consequence, e may not earn enoug money to repay is debts. Altoug tis possibility is not modelled ere, it is implicitly incorportated by assuming te lack of a market to finance investiments in education. As in Andrade (2004), tere is a single non-storable good in te economy produced by firms operating in a competitive market. Te inputs in te production process are te two types of labor, individuals wit ig and low levels of uman capital. Terefore, tere is no pysical capital in tis economy. Te constant returns to scale production function is as follows: ( ) ( )( ) 1 d d d,,,, Y = A θ N + γ N + 1 θ N + en t t l t l t t were A > 0, 0 < θ,e,d,γ < 1, γ < e. N,t and N l,t are, respectively, te number of individuals wit ig and low levels of uman capital employed in te production process at time t. Note tat te possible values for te variables N l,t and N,t are in te interval [0, 1], as te number of workers in eac period is constant and is normalized to one. Hence, total output can be expressed as a function of te fraction of individuals wit a ig level of uman capital in eac period. Bot types of individuals provide two distinct productive services, wic one may tink of as mental effort ( brains ) and pysical effort ( brawn ). 19 Te first and second terms witin te square brackets can be tougt of, respectively, as brain and brawn, wit te parameter θ indicating te importance of te mental effort. Tus, mental and pysical efforts are combined into an aggregate by a CES tecnology wit 1 an elasticity of substitution,, tat exceeds unity. Te parameter e is te relative 1 d efficiency of te individuals wit ig level of uman capital in supplying pysical effort. Wereas te parameter γ is te relative efficiency of te individuals wit low 17 See Stokey (1998) for an extensive discussion of tis topic. 18 See Becker (1991) for an extensive discussion of tis topic and Caucutt and Kumar (2003). 19 Tis type of production function is used in Stokey (1996), Caucutt and Kumar (2003) and Andrade (2004).

8 670 Effects of te Brazilian University Policy of Targeting te Poor level of uman capital in providing te mental effort. Bot parameters (e and γ) are important in determining te wage differential between te individuals wit ig and low level of uman capital, as assumption 2 below indicates. Tere are two important ideas beind tis production function. First, as γ is assumed to be close to zero, te individuals wit ig level of uman capital are te main providers of brain. Second, as e < 1, te individuals wit a ig level of uman capital can perform (almost) all te tasks tat te oter type of labor can, and more. Te following assumption simplifies te analysis and guarantees tat te wages paid to te individuals wit a ig level of uman capital are always greater tan te ones for te individuals wit a low level of uman capital, for all possible values for N,t and N l,t. 1 1 d 1 θ Assumption 2: e >. ( 1 γ) θ 20 I now turn to te market for iger education. It is assumed tat tere is no free-entry and tere is a continuum of universities wit measure U. Te maximum number of students tat eac university can ave is equal to Q max (tat is, te maximum capacity). University i s profit (PR i ) is given by: PRi = P Qi CiQ i (1 t) were t is te corporate income tax, C i is university i s marginal cost, Q i is te number of students enrolled in university i and P is te market price. Universities ave different marginal costs and its range is given by te interval min max C, C. Recall tat tere is a continuum of universities wit measure U. Te universities are labeled according wit its marginal cost: from te one wit te lowest marginal cost labeled i = 0 to te one wit te igest marginal cost labeled i = U. Tese features of te model try to capture te main caracteristics of te Brazilian education sector. Tis market is strongly regulated by te government. Tere is no free-entry as te government determines te number of of universities tat can operate in eac field of knowledge. Moreover, it specifies te number of slots tat te university can ave, tat is, te maximum number of students tat can be enrolled in eac university. 20 Tis assumption indicates tat ɛ (te coefficient of te individual wit a ig level of uman capital in te production of brawn ) is large enoug to guarantee tat w,t > w l,t.

9 Eduardo de Carvalo Andrade 671 Te government s budget constraint as to be balanced. Te revenue comes from te corporate income taxes on te universities imposed at t = 0. Government makes transfer denoted by T. Terefore: i P Qi CiQ i tdi = T Te last feature of te model is te following. I make te simplifying assumption tat ig income families wose cildren ave te igest level of preparation (tat is, a = 1) receive all transfers from te government and all profits as tey are assumed to own all universities. Te motivation being tis assumption is te following. Note tat tese families are te ricest wit te brigtest cildren. As next section sows, it certainly pays off for tese families to finance teir cildren s tertiary education. Te extra cas troug transfers and profits does not affect teir decision to invest in teir cildren s education. Tey would make tis decision anyway if teir income was only teir salaries. Te only effect of tis extra cas is to increase teir consumption in te first period. As section 3 sows, te government s university policy of targeting te poor affects te amount of transfers and profits. If tey were canneled to families wit lower income or wit cildren wit lower level of preparation, te amount of transfers and profits could distort and affect teir decisions to send or not teir cildren to university. In order to avoid tis possibility, I make tis simplifying assumption. 2. COMPETITIVE EQUILIBRIUM Tis section discusses te equilibrium of te model. First, it is important to recall tat te focus of tis paper is to analyze te effect of te government program of targeting poor families wose cildren are not enrolled in university. Hence, te type of equilibrium of interest is te one in wic all low income families opt not to send teir cildren to university. It can appen for two reasons. Eiter because tey do not ave enoug income to pay te tuition (tat is, w l,0 < P ) and can not borrow wit tis objective as tere is no capital markets to finance education.; or because te potential increase in future utility if te cild becomes an individual wit ig level of uman capital does not compensate te reduction in current utility related to te payment of tuition P. To simplify, I make te following assumption: Assumption 3: w l,0 < C min and w,0 > C max.

10 672 Effects of te Brazilian University Policy of Targeting te Poor In words, it indicates tat low income families do not ave income to pay te university tuition. Teir income is lower tan te lowest possible university tuition, as te minimum possible marginal cost to provide te university service is C min. Hig income families do ave enoug income to pay tuition. It is wort caracterizing te beavior of parents wit ig level of uman capital wit respect to te decision to send teir cild to university. Proposition 1: Given te equilibrium wages and university tuition, tere exists an unique a [a,1], suc tat a parent wit ig level of uman capital sends is cild to university if a a, and does not oterwise. 21 Tis proposition indicates tat tere is tresold level of ability beavior. Parents wit ig level of uman capital send teir cildren to university only if teir cildren s level of preparation is greater tan te tresold values a. If a cild as a level of preparation lower tan tis tresold value, it is not profitable to pay for private education and obtain a lower immediate utility. Tis is te case because te expected future gain in utility, as a result of te expenditure P in education today, is very small, as te probability of tis cild becoming an individual wit a ig level of uman capital is very low. Before proceeding to define te competitive equilibrium in tis economy, it is wort discussing te equilibrium in te university sector, wic is caracterized by a competitive market. From te beavior of parents wit ig level of uman capital, tere is a certain number of students wo attend university, say, D. Tere are two possible types of equilibrium. In te first one, tere is no idle capacity in te university sector. Formally, D = UQ, tat is, te number of students enrolled in universities are equal to te number of slots available, te ones autorized by te government to operate. Hence, all universities are operating at full capacity and te equilibrium price is equal to P = C max, as te least efficient universities (wit te igest marginal cost given by C max ) equate te marginal cost to price. In suc environment, wen te demand increases, it leads to a greater equilibrium price witout any increase in te number of students enrolled in universities. In te second possible equilibrium, tere is idle capacity in te university sector as D < UQ. It means tat te least efficient universities ave te autorization to operate but tere is no demand to fill teir slots. Te equilibrium price is suc tat C min P < C max, as te least efficient universities wit students equate teir marginal cost (wic is in te interval [C min,c max )) to te equilibrium price. Under tis circumstance, an increase in demand may lead to greater price and necessarily increases te number of university students. 21 See in te appendix te proof of all propositions in tis paper.

11 Eduardo de Carvalo Andrade 673 In sort, it is straigtforward to conclude tat, in equilibrium, tere is a tresold C suc tat universities wit marginal cost: (i) greater tan C do not ave students; (ii) lower tan C operate at full capacity; (iii) equal to C ave students but do not necessarily operate at full capacity. I now turn to te definition and te proof of existence and uniqueness of te equilibrium. Definition 1: Given n i,0, a competitive equilibrium is caracterized by n i,1, w i,0, w i,1, P and a ( a,1 ) suc tat ( i =, l) : (i) given wages, firms maximize profits; (ii) given P, universities maximize profits; (iii) te labor market clears, tat is, N, t = n, t and N l, t = nl, t ( t = 0,1); (iv) given wages and P, a solves te university decision problem of family wit ig level of uman capital in (1); (v(v) te government budget constraint is balanced; and (vi) te law of motion for te variable n, wic is given by: 1 n,1 = n,0 p (a)f(a)da (2) a In order to understand te above law of motion, it is important to recall te following points. First, cildren from low income families do not attend university. Second, te number of individuals wit ig level of uman capital at t = 0 is equal to n,0 and eac one as a cild. Tird, teir cildren wo attend te university are only tose wose level of preparation is in te te interval a,1. Finally, only a fraction of tose students becomes an individual wit ig level of uman capital at time t = 1, wic is determined by te probability function π. Terefore, at t = 1, te number of individuals wit ig level of uman capital is a fraction given by 1 π(a)f (a)da of a n. te current ones (,0) Proposition 2: Tere exists a competitive equilibrium and it is unique. 22 Tis unique equilibrium as te following caracteristics. First, tere are cildren coming from ig income families wo attend university. Second, te skill premium and te fraction of individuals wit a ig level of uman capital at t = 1 are positive. Finally, a tresold marginal cost suc tat universities wit iger costs do not ave students and te ones wit lower costs operate at full capacity. 22 If one takes into consideration te opportunity cost of foregone earnings as an additional cost of iger education, te equilibrium would still be caracterized by tresold ability. However, it would be greater as it would be an additional cost of attending university.

12 674 Effects of te Brazilian University Policy of Targeting te Poor 3. TARGETING THE POOR In tis section, I analyze te effect of ProUni in te quality of te labor force. In te model, tis quality is measured by te fraction of individuals wit ig level of uman capital in period 1, te variable n,1. Te goal is to ceck ow n,1 is affected, wen one considers te possible canges in te equilibrium price in te university sector as a result of a greater demand caused by te introduction of te government program. As mentioned in te introduction, ProUni s objective is to find a way to finance te private university tuition for students coming from low income families. Te program as two important caracteristics. First, only students wose families ave an income level below a certain tresold are eligible to take part in te program. Tose students take an exam and te ones wit te igest scores obtain te scolarsip. Second, it gives tax exemption to universities tat give a certain minimum of full or partial scolarsips to students enrolled in teir program. Te way tat tese two caracteristics are incorporated into te model is te following. Wit respect to te first caracteristic, families wose parents ave te low level of uman capital and an income of w l,0 are te ones eligible to take part in te program. In oter words, it is assumed tat w l,0 is lower tan te income tresold level establised in te program. Moreover, te students wit te rigt to receive te scolarsip are selected using a ranking of te individual s level of preparation, wic is assumed to be public information. Tey are te S individuals wit te igest level of preparation among te ones coming from low income families, were S is te total number of scolarsips. Implicitly, it is assumed tat tese individuals are te ones wo obtain te igest scores in te exam tat selects te students to receive te scolarsips. Formally, te S indiviuals are te following: S = g( a) da, al a l were a l is te lowest level of preparation of tose individuals coming from low income families wo receive te scolarsip. Wit respect to te second caracteristic of te program, I assume tat te minimum number of full or partial scolarsips an university as to offer to obtain te tax exemption and take part in te program is equal to αq max, were α < 1. Wen operating at full capacity, university i s profit if it decides to take part in te program is equal to:

13 Eduardo de Carvalo Andrade 675 max max PR = i P (1 a) Q CiQ (1 t) + F were F is te tax exemption, P is te new equilibrium price wen te program is implemented. Obviously, tis university decides to join te program only if it leads to a greater profit. Formally, tis is te case wen: ( ) F P Q max 1 t a (3) tat is, wen total exemption is greater tan te amount te university gives up in terms of net revenues by providing scolarsips. It is obvious tat if an university operating at full capacity is better off taking part in te program, ten all universities join te program. To simplify te analysis, I assume tat inequality (3) olds. 23 Wit tis assumption, total number of scolarsips (S) is equal to αq max U. It is important to note tat tis simplifying assumption does not play any role in te results below. As it is going to be clear, one of te crucial aspects to evaluate ow te program affects te quality of te labor force is troug its impact on te university tuition (P ), wic depends on te supply curve of te educational sector and not on wat types of universities take part in te program. 24 Before proceeding wit te analysis, it is wort making on comment about te way te production in te education sector is modelled ere. Obviously, te fixed cost is an important aspect of te production in tis sector. However, tose universities wo can take part in ProUni are tose wo are already operating and ave teir full capacity determined by te government. Terefore, teir decisions to join or not te program are made at te margin. Tis point explains te focus on te marginal cost in te analysis. 25 I now turn to te effects of te program in n,1, first considering te case wen te supply curve in te university sector is perfectly inelastic. Proposition 3: After te introduction of te program, if te university sector s supply curve is perfectly inelastic and te level of preparation of targeted students vis-à-vis te non-targeted ones is greater (lower), te quality of te labor force increases (decreases). 23 As pointed out in te introduction, about 70% of all private universities adered to te program. Terefore, tis assumption is not really far from reality. 24 In order to guarantee tat te government as enoug resources to finance te program suc tat te condition (3) olds, adjustments can be made in te corporate income tax (t) or in te number of scolarsips troug a. 25 In propositions and below, te university sector s supply curve can be, respectively, perfectly elastic and upward sloping. Terefore, implicitly it is assumed tat new universities can enter into te market or old universities can increase teir full capacity as a consequence of te initial impact of ProUni.

14 676 Effects of te Brazilian University Policy of Targeting te Poor Te intuition beind tis result is te following. Wen te program is introduced, tere is an increase in demand in te university sector. As te supply curve is perfectly inelastic, it leads only to an increase in te university tuition, witout any cange in te total number of students enrolled in university. Tis new equilibrium price is suc tat it is not in te interest of αq max U students wit te lowest level of preparation coming from ig income families wo were attending university witout te program to continue doing so. Teir families decide to witdraw teir cildren from university as it is not profitable to pay te iger tuition for an university education and obtain a lower immediate utility. In oter words, wit te new equilibrium price, te costs are now greater tan te benefits of enrolling in te university. Tese studentes are ten replaced by te α aq max U recipients of te scolarsips, te students coming from low income families wo are eligible to take part in te government s program. Wen a < a l, te level of preparation of tese new students are greater tan te ones of te old students. Tey were not previously enrolled in university because tey were credit constrainted (w 0,1 < P < P). Tus, te government s program is capable of increasing te quality of te students enrolled in universities, leading to a greater quality in te labor force in te future (greater n,1 ). As a second order effect, tis increase in n,1 reduces te expected skill premium in te future and ig income families are less inclined to send teir cildren to university. Wen tis effect is taken into consideration, te new equilibrium price of university service and te new fraction of individuals wit ig level of uman capital at time t = 1 are lower tan oterwise. However, tey are still greater tan te ones witout te government program. In tis case (wen a < a l ), it is important to mention tat tere is no trade-off in terms of efficiency and income mobility. Te government s intervention not only increases te efficiency of te educational system (by increasing n,1 ), but it allows individuals coming from low income families to obtain a ig level of uman capital. Moreover, te skill premium is lower. Te reverse result occurs wen a > al as te new students ave lower level of preparation. In tis case, te overall quality of te labor force (n,1 ) decreases after te introduction of te program. Under tis scenario, te government would spend resources troug tax exemptions and reduce te efficiency of te educational system. Tere is now a clear trade-off between efficiency and income mobility: more income mobility is only possible at te cost of less efficiency. Proposition 4: After te introduction of te program, if te university sector s supply curve is perfectly elastic, te quality of te labor force increases. Te above result is a straigtforward one and it is considered for te sake of completeness. Te explanation is te following. Wen te supply curve is perfectly elas-

15 Eduardo de Carvalo Andrade 677 tic, tere is enoug idle capacity in te university sector and te introduction of te government s program does not cause any cange in te university tuition. Hence, in te first moment, te old students families do not ave any incentive to cange teir decisions to send teir cildren to university. As a result, tere are new αq max U university students and tey receive scolarsips. Recall tat tese students are te ones coming from low income families wo do not ave enoug income to pay for te tuition. Terefore, te quality in te labor force in te future (measured by n,1) is necessarily greater. Note tat tis result does not depend on te level of te preparation of te new student vis-à-vis te oter students as tere is no replacement of students wen tere is idle capacity in te system. As a second order effect, tis increase in n,1 reduces te expected skill premium in te future and ig income families are less inclined to send teir cildren to university. Wen tis effect is taken into consideration, te new fraction of individuals wit ig level of uman capital at time t = 1 are lower tan oterwise. But it is still greater tan tis same fraction witout te program. In te case of perfectly elastic supply curve, te effect of te program is unequivocal: more efficiency and income mobility, wit a lower skill premium. Proposition 5: After te introduction of te program, if te university sector s supply curve is upward sloping and te level of preparation of targeted students vis-à-vis te non-targeted ones is greater (lower), te effect on te quality of te labor force is positive (uncertain). Te above propostion presents te intermediary case wen te supply curve is neiter perfectly inelastic nor perfectly elastic, but it is positively inclined. Te results are tus a combination of te previous ones. Recall tat, in tis case, wen demand increases due to te program s implementation, price and quantity rise. As seen above, wen a < a l, tere is an increase in n,1 even wen te increase in demand affects solely te equilibrium price (te perfectly inelastic case). Wen tis effect is distributed in price and quantity, it is straigtforward to conclude tat n,1 necessarily rises too. Wen a > a l, it is uncertain wat is te effect of te introduction of te program on n,1. From te previous results, we learned two facts: first, in te perfectly inelastic case, only price increases (no quantity cange) and n,1 reduces; second, in te perfectly elastic case, only quantity increases (no price cange) and n,1 rises. In te upward sloping case, price and quantity increase. Tus, as more inelastic te supply curve, greater is te increase in price vis-à-vis te quantity, and it is more likely to occur a decrease in n,1. In oter words, te price effect dominates. Wereas, te more elastic te supply curve, te reverse occurs and te quantity effect overrules.

16 678 Effects of te Brazilian University Policy of Targeting te Poor CONCLUSION In 2005, te Brazilian government launced ProUni, a program to finance university tuition to credit constrained families. Private universities provide scolarsips to te target group defined by te government and receive tax exemptions in return. As te analysis above sows, te effect of tis program on te quality of te labor force is ambigous. Te result depends on two key variables: te university sector s supply curve and te level of preparation to face university studies of te students wo are targeted by te program vis-à-vis te non-targeted ones. Wen te program is introduced, tere is an increase in demand in te university sector. Depending on te supply curve, tree possibilities can occur. First, university tuition rises and total number of university students does not cange, wen te supply curve is perfectly inelastic. Second, price does not cange and quantity increases, wen te supply curve is perfectly elastic. Finally, price and quantity increase, wen te supply curve as an upward slope. Non-target families are penalized wen te university tuition rises. Some of tem may decide to witdraw teir cildren from university. If teir levels of preparation are lower tan te ones of te cildren from te target families wo received te scolarsips, ten te program is capable of increasing te quality of te labor force by eliminating te credit constraint of better qualified students. However, it is more likely tat te level of preparation of te individuals from te target group be lower. In tis case, te more inelastic te supply curve, greater is te increase in tuition after te program s introduction and more individuals from te non-target group do not go to university. As tey are replaced by individuals from te target group wo are less prepared students, te quality of te labor force drops. Te current situation in te university sector, wit an idle capacity in general around 20%, may suggest tat university tuition may not increase significantly after te program. However, it is possible tat te level of capacity utilization may vary from course to course and, as a result, te effects of te program on te quality of te labor force may also vary across tem. It would be interesting to ceck empirically if tere are important canges, in te future, in te quality of tose professionals graduating from courses operating close to full capacity today vis-à-vis te oters. Moreover, one could argue tat tuition could decrease witout te program exactly because te idle capacity and benefit at te margin individuals better qualified to pursue university studies tan individuals from te target group.

17 Eduardo de Carvalo Andrade 679 As pointed out in te introduction, 70% of all private universities joined te program and tey ave to stay in te program for at least ten years. It is true tat te model in tis paper is a static two-period model. Neverteless, it is possible to use it to make some speculations about te effects of te program in te near future. Even if tere is today, in general, idle capacity in te university sector, one could argue tat tis reality may cange in te future. On te demand side, tere as been an important increase in te number of students graduating from ig scool tat is expected to continue. On te supply side, it is expected to ave some important limitations. On te one and, te government as important budget limitations and is not likely to be able to expand te number of slots available in te public universities. On te oter and, te current government as maintained a very strict policy regarding te autorization for new universities to start operating and old ones to augment teir operating size. Two examples illustrate tis policy. In 2004, te Ministry of Education suspended for 180 days any autorization to create new courses. In 2005, in te project to reform te university sector, te same Ministry of Education suggested te transfer from te government to professional associations of te legal rigt to autorize te openings of new courses in some areas, suc as in medicine. Tese associations tend to limit severely te number of new professionals (and slots in universities) in order to guarantee to teir members a certain degree of monopoly. 26 Combining te demand and supply sides, te no idle capacity case, in wic te quality of te labor force declines as a result of te government s program, may occur in te future. It is important to make one final comment. Te analysis in tis paper focus solely on te impact of te program on te quality of te labor force. It concludes tat it is not unlikely tat its impact is negative. If a more complete analysis is implemented it is possible tat one can find tat its additional impacts can be even more negative. In particular, if one takes into consideration te costs and te benefits of te alternative uses of te funds employed to finance te program. Terefore, a more complete analysis sould be implemented in future researc and its overall effect on economic welfare considered. REFERENCES Andrade, E. Quotas in Brazilian public universities: good or bad idea? Revista Brasileira de Economia, v. 58, n. 4, p , Becker, G. A treatise on te family. Harvard University Press, enlarged edition, For a good discussion on tis topic, see Friedman (2002).

18 680 Effects of te Brazilian University Policy of Targeting te Poor. Human capital: a teoretical and empirical analysis, wit special reference to education. Te University of Cicago Press, Bisop, J. Acievement, test score, and relative wage. In: Workers and teir wages. Wasington, DC: Te AEI Press, Caucutt, E.; Kumar, K. Higer education subsidies and eterogeneity: a dynamic analysis. Journal of Economic Dynamic & Control, 27, p , Friedman, M. Capitalism and freedom. Te University of Cicago Press, Hanusek, E.; Kimko, D. Scooling, labor-force quality, and te growt of nations. Te American Economic Review, December Heckman, J. Lessons from te bell curve. Journal of Political Economy, v. 103, n. 5, p , MEC. Censo da Educação Superior. Disponível em: ttp:// censosuperior/, 2003 Murpy, K.; Peltzman, S. Scool performance and te yout labor market. Journal of Labor Economics, v. 22, n. 2, Stokey, N. Free trade, factor returns, and factor accumulation. Journal of Economic Growt, v. 1, n. 4, p , Sirtsleeves to sirtsleeves: te economics of social mobility. In: Frontiers of researc in economic teory: Te Nancy L. Scwartz Memorial Lectures, , p Cambridge University Press, APPENDIX Proposition 1: Given te equilibrium wages and university tuition, tere exists an unique a ( a,1], suc tat a parent wit ig level of uman capital sends is cild to university if a a, and does not oterwise. Proof: Given te equilibrium wages and university tuition and using assumption 3, te utility of te family wit ig level of uman capital wit and witout sending is cild to university are, respectively, equal to: (,0 ) + β p (,1 ) + ( p ) ( l,1) LHS( a) = u w P ( a) u w 1 ( a) u w and (,0) + β (,1) RHS u w u w = l

19 Eduardo de Carvalo Andrade 681 Note tat RHS does not depend on a. Using te facts tat π(a ) = 0 from assumption 1 and u > 0, one obtains tat for any possible value for w l,1 te following: LHS( a ) < RHS Using te fact tat πˊ(a) > 0 from assumption 1, LHS(a) is strictly increasing in a. Hence, te LHS and te RHS eiter intersect at a unique a > a, or do not intersect at all, in wic case a = 1 > a. Proposition 2: Tere exists a competitive equilibrium and it is unique. Proof. Proof. Te equilibrium is caracterized by seven unknowns ( w, t, w l, t, n,1, a, P ; t = 1,2 ) and seven equations (te four first-order conditions of te firm s problem (two in eac period), te equilibrium condition in te university sector, te law of motion for te variable n, t and te tresold ability for individuals wit ig level of uman capital). Given n i,0, te te two first-order conditions of te firm s problem at t = 0 determine w i,0 ( i =, l ). Ten, we are left wit a system wit five equations and five unknows. From proposition ( 1 ), given te equilibrium wages and university tuition, tere exists an unique a a,1] 2, one obtains an uni- que ( 0,1),1 (,1 + n l,1 n. As 1. From te law of motion ( ) n =, ten tere is an unique n ( 0,1) l,1. As in equili- brium N = i,1 ni,1 (for i =, l ), ten wages are uniquely determined using te firm s 1 first-order conditions. Total number of students is equal to f(a)da. Terefore, at te margin, te university wit te igest marginal cost tat as student is given 1 X max by i = X in te following equation: f ( a) da = Q idi a. From te first-order 0 condition of tis university s problem (university i = X ), P is determined, as it equates price to its marginal cost. Universities wit a marginal cost greater tan P do not operate as tey maximize profits witout aving students. Te proof is analogous to te case in wic a = 1. Proposition 3: After te introduction of te program, if te university sector s supply curve is perfectly inelastic and te level of preparation of targeted students vis-à-vis te non-targeted ones is greater (lower), te quality of te labor force increases (decreases). Proof. Te following condition must old in te competitive equilibrium wit and witout te government s program: a

20 682 Effects of te Brazilian University Policy of Targeting te Poor ( ) ( ),1,1 (,0 ) (,0 ) βp( a ) u w u wl = u w u w P In te competitive equilibrium witout te program, te above equality olds wit te combination a, w,1, w l,1, and P. Wen te program is introduced, tere are S new university students and, ceteris paribus, P and n,1 increases and te wage premium reduces, wic leads to an increase in te RHS and a decrease in te LHS in te above equation. Hence, a cannot be part of te competitive equilibrium anymore. To restore te equality in te above equation, a as to increase (wic affects P, n,1 and te skill premium, reducing te RHS and increasing te LHS ) suc tat S old students leave te university and te number of students enrolled in university does not cange as te university sector s supply curve is perfectly inelastic. Let a be te new equilibrium tresold. After te program s introduction, te new n in equilibrium (call it n ) is equal to:,1,1,0,1 1 al n = n p ( a) f ( a) da + S p( a) g( a) da a a l If te level of preparation of targeted students vis-à-vis te non-targeted ones is greater ( a < ) ten n n. If it is lower ( a > a l ), ten n n. a l >,1,1 <,1,1 Proposition 4: After te introduction of te program, if te university sector s supply curve is perfectly elastic, te quality of te labor force increases. Proof. Te following condition must old in te competitive equilibrium wit and witout te government s program: ( ) ( ),1,1 (,0 ) (,0 ) βp( a ) u w u wl = u w u w P In te competitive equilibrium witout te program, te above equality olds wit te combination a, w,1, w l,1, and P. Wen te program is introduced, tere are S new university students and P does not cange as te university sector s supply curve is perfectly elastic. Ceteris paribus, n,1 increases and te wage premium reduces, wic leads to a decrease in te LHS and an increase in te RHS in te above equation. Hence, a cannot be part of te competitive equilibrium anymore. To restore te equality in te above equation, a as to increase (wic affects n,1 and te skill premium, increasing te LHS and decreasing te RHS ). Let a and n be, respectively, te new equilibrium tresold and te new fraction of individuals wit ig level of uman capital. As a > a, ten te new skill premium must be lower, indicating tat n > (tat is, te quality of te labor force increases). n