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Comments welcome Unequal Opportunities and Human Capital Formation Daniel Mej a and Marc St Pierre1 This Version August 2004 Abstract This paper develops a tractable heterogeneous agents general equilibrium model where individuals have di erent endowments of the factors that complement the schooling process The paper explores the relation between inequality of opportunities inequality of outcomes and e ciency in human capital formation Using numerical solutions we study how the endogenous variables of the model respond to two di erent interventions in the distribution of opportunities a mean preserving spread and a change in the support of the distribution of endowments The results from the simulation of the model suggest that a higher degree of inequality of opportunities is associated with lower average human capital in the population a lower fraction of individuals investing in human capital higher inequality in the distribution of human capital and higher wage inequality In other words the model based on standard assumptions does not predict a trade o between e ciency and equality of opportunity in human capital formation Keywords Human Capital Inequality Equity E ciency Trade o JEL Classification Numbers J24 J31 O15 D33 1 The authors wish to thank Sean Campbell Adriana Camacho Pedro Dal B Oded Galor Herschel Grossman Alaka Holla Peter Howitt Tom Krebs Herakles Polemarchakis Carlos Esteban Posada as well as participants at the Macro Lunch at Brown U and LAMES 2004 in Santiago for helpful comments and suggestions However the remaining errors are the authors responsibility D Mej a Brown University and Banco de la Rep blica Colombia E mail Daniel Mejia brown edu M St Pierre Brown University E mail Marc StPierre brown edu The first author aknowledges financial support from the Tinker Field Research Grant 1 Introduction The importance of human capital accumulation as an engine of economic growth and development has been widely recognized in theoretical and empirical studies 2 Most of the literature that studies the e ects of income inequality on economic growth through its e ects on human capital accumulation has focused on the role of credit constraints The main idea of this line of research is the following relatively poor individuals don t have the means to finance the accumulation of human capital and because they are credit constrained that is there is no way to finance the costs of human capital accumulation using future earnings as the collateral for a loan to pay the tuition fees and living expenses they end up either not investing in human capital or investing very little Furthermore if in addition to credit constraints there are decreasing returns to the accumulation of human capital the final outcome does not maximize the size of the economic pie Consequently there may be space for redistribution of resources from rich to poor individuals which in turn increases the size of the pie This redistribution would reallocate resources towards more profitable investments given that the marginal returns to human capital accumulation are higher for those individuals the relatively poor ones who have less human capital The theoretical idea has been extensively developed in the literature since the work by Galor and Zeira 1993 and Banerjee and Newman 1993 Further developments have been proposed by De Gregorio 1996 and B nabou 1996 2000 3 Empirical evidence has been found in favor of the hypothesis that inequality and credit constraints a ect investment in human capital by Flug et al 1998 De Gregorio 1996 and Mej a 2003 But the accumulation of human capital involves other complementary factors as well This has been extensively documented in a number of recent empirical studies some of which will be reviewed in the next section While some of these complementary factors can be thought of as non purchasable neighborhood e ects shaped by 2 The reader is referred to the seminal contributions of Lucas 1988 on the theoretical side and those of Mankiw Romer and Weil 1992 Benhabib and Spiegel 1994 2003 and Barro 2001 for the empirical evidence supporting the importance of human capital in explaining growth rates across countries 3 See Aghion et al 1999 for a thorough review of this literature 2 local communities family background socioeconomic characteristics genes provision of social connections installation of preferences and aspirations in children others are pre and post natal care parental level of education distance to schools and di erent qualities of books teachers and schools 4 If the previously mentioned factors are important in determining di erences in educational attainment across individuals the distribution of these socio economic characteristics across individuals matters In other words if the distribution of access to the schooling system is important one should encounter di erences in educational attainment across individuals even in economies with universally free public schools This does not rule out the importance of the lack of financial resources to pay for the monetary costs of education 5 As said before di erent studies have shown that they are in fact important However this paper focuses on a complementary explanation namely on the e ects of inequality of endowments of the complementary factors to the schooling system on human capital accumulation decisions made by individuals More precisely the paper explores another explanation for the negative relation between economic inequality and the average amount of human capital based on di erences in the rates of return to time investment in human capital accumulation the latter being determined by each individual s endowment of the complementary factors to the schooling system The model addresses the relationships between inequality of opportunities e ciency in human capital formation and inequality of outcomes in a general equilibrium framework This paper is related to the literature that links economic inequality and human capital accumulation and stresses the negative relation between these two variables see among others Galor and Zeira 1993 and B nabou 1996 2000a 2000b The paper is organized as follows the second section presents the stylized facts that motivate the construction of the model Namely the negative relation between the degree of inequality in the distribution of human capital and the average level of human capital across countries and the positive relation between inequality of opportunities 4 See

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