Comments welcome.U nequal O pportunities and H uman Capital Form ationDaniel Mejía and Marc St-Pierre1This Version: August 2004AbstractThis paper develops a tractable, heterogeneous agents general equilibrium modelwhere individuals have different endowments of the factors that complement theschooling process. The paper explores the relation between inequality of oppor-tunities, inequality of outcomes, and efficiency in human capital formation. Usingnumerical solutions we study ho w the endogenous variables of the model respond totwo different interventions in the distribution of opportunities: a mean-preservingspread and a change in the support of the d istribution of endowments. The re-sults from the simulation of the model suggest that a higher degree of inequalit y ofopportunities is associated with lower average human capital in the population, alower fraction of individuals investing in human capital, higher inequalit y in the dis-tribution of human capital, and higher wage inequality. In other words, the model(based on standard assumptions) does not predict a trade-off between efficiency andequality of opportunity in human capital formation.Keywords: Human Capital, Inequality, Equity-Efficiency Trade-off.JEL Classification Numbers: J24, J31, O15, D33.1The authors wish to thank Sean Campbell, Adriana Camacho, Pedro Dal Bó, Oded Ga-lor, H erschel Grossman, Alaka Holla, Peter Howitt, Tom Krebs, Herakles Polemarchakis, Car-los Esteban Posada, as well as participants at the Macro Lunch at Brown U., and LAMES2004 in Santiago for helpful comments and suggestions. However, the remaining errors arethe authors’ responsibility. D. Mejía: Brown University and Banco de la República, Colom-bia. E-mail: [email protected]. M. St-Pierre: Brown University. E-mail: [email protected]. The first author aknowledges financial support from the Tinker Field Re-searc h Grant.1. I ntroductionThe importance of human capital accumulation as an engine of economic growth anddevelopment has been widely recognized in theoretical and empirical studies.2Most of the literature that studies the effects of income inequality on economicgrowth through its effects on human capital accumulation has focused on the role ofcredit constraints. The main idea of this line of research is the following: relatively poorindividuals don’t have the means to finance the accumulation of human capital, and,because they are credit constrained (that is, there is no wa y to finance the costs of humancapital accumulation using future earnings as the collateral for a loan to pay the tuitionfees and living expenses), they end up either not investing in human capital or investingvery little. Furthermore, if in addition to credit constraints there are decreasing returnsto the accumulation of human capital, the final outcome does not maximize the size ofthe economic pie. Consequently there may be space for redistribution of resources fromrich to poor individuals which, in turn, increases the size of the pie. This redistributionwould reallocate resources towards more profitable investments given that the marginalreturns to human capital accumulation are higher for those individuals (the relativelypoor ones) who have less human capital. The theoretical idea has been extensivelydeveloped in the literature since the work by Galor and Zeira (1993) and Banerjee andNewman (1993). Further developments have been proposed by De Gregorio (1996) andBénabou (1996, 2000).3Empirical evidence has been found in favor of the hypothesisthat inequality and credit constraints affect investment in human capital by Flug et al.(1998), De Gregorio (1996) and Mejía (2003).But the accum u lation of human capital involves other complementary factors aswell. This has been extensively documented in a number of recent empirical studies,some of which will be reviewe d in the next section. While some of these complemen-tary factors can be thought of as non-purchasable (neighborhood effects shaped by2The reader is referred to the seminal contributions of Lucas (1988) on the theoretical side, andthose of Mankiw, Romer and Weil (1992), Benhabib and Spiegel (1994, 2003) and Barro (2001) forthe empirical evidence supporting the importance of human capital in explaining growth rates acrosscountries.3See Aghion et al. (1999) for a thorough review of this literature.2local comm unities, family background, socioeconomic characteristics, genes, provisionof social connections, installation of preferences and aspirations in children), others are(pre and post natal care, parental level of education, distance to sc hools and differen tqualities of books, teachers and schools).4If the previously mentioned factors are importan t in determining differences in ed-ucational attainment across individuals, the distribution of these “socio-economic c har-acteristics” across individuals matters. In other w ords, if the distribution of access tothe sc hooling system is important, one should encounter differences in educational at-tainment across individuals even in economies with universally free public schools. Thisdoes not rule out the importance of the lack of financial resources to pay for the (mone-tary) costs of education.5As said before, different studies have shown that they are, infact, important. However, this paper focuses on a complementary explanation, namely,on the effects of inequality of endowments of the complementary factors to the schoolingsystem on human capital accumulation decisions made by individuals. More precisely,the paper explores another explanation for the negative relation between economi c in-equality and the average amount of human capital based on differences in the rates ofreturn t o time investment in human capital accumulation, the latter being determinedby each individual’s endowment of the complementary factors to the schooling system.The model addresses the relationships between inequality of opportunities, efficiencyin human capital formation, and inequality of outcomes in a general equilibrium frame-work. This paper is related to the literature that links economic inequality and humancapital accumulation and stresses the negative relation between these two variables (see,among others, Galor and Zeira, 1993, and Bénabou, 1996, 200 0a, 2000b).The paper is organized as follows: the second section presents the stylized factsthat motivate the construction of the model. Namely, the negative relation between