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We develop a human capital model with borrowing constraints explicitly derived from government student loan (GSL) programs and private lending under limited commitment. The model helps explain the persistent strong positive correlation between ability and schooling in the United States, as well as the rising importance of family income for college attendance. It also explains the increasing share of undergraduates borrowing the GSL maximum and the rise in student borrowing from private lenders. Our framework offers new insights regarding the interaction of government and private lending, as well as the responsiveness of private credit to economic and policy changes. (JEL D14, H52, I22, I23, J24)

We develop a human capital model with borrowing constraints explicitly derived from government student loan programs and private lending under limited commitment. Two key implications of our analysis are: (i) binding constraints may not depress investment; and (ii) a positive relationship between investment and ability is unlikely to arise in standard exogenous constraint models but arises more generally in our framework. Our model also helps explain a number of important empirical observations in the U.S. higher education sector since the early 1980s: (i) a strong and stable positive correlation between ability and college attendance for all income and wealth backgrounds; (ii) the rising importance of family income as a determinant of college attendance; (iii) the increase in the share of undergraduates borrowing the maximum from government student loan programs; and (iv) the dramatic rise in student borrowing from private lenders. In our framework, all of these are natural responses to the rising costs and returns to college (with stable real government loan limits) observed in recent decades. In contrast, the standard exogenous constraint model cannot simultaneously explain observations (i) and (ii) under standard assumptions about preferences; it is also silent on the rise in private lending. Finally, by incorporating both public and private lending, our framework offers new insights regarding the interaction of government and private student lending as well as the responsiveness of private student credit to economic and policy changes.

This paper presents economic models of child development that capture the essence of recent findings from the empirical literature on skill formation. The goal of this essay is to provide a theoretical framework for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical studies, and for formulating policy. Central to our analysis is the concept that childhood has more than one stage. We formalize the concepts of self-productivity and complementarity of human capital investments and use them to explain the evidence on skill formation. Together, they explain why skill begets skill through a multiplier process. Skill formation is a life cycle process. It starts in the womb and goes on throughout life. Families play a role in this process that is far more important than the role of schools. There are multiple skills and multiple abilities that are important for adult success. Abilities are both inherited and created, and the traditional debate about nature versus nurture is scientifically obsolete. Human capital investment exhibits both self-productivity and complementarity. Skill attainment at one stage of the life cycle raises skill attainment at later stages of the life cycle (self-productivity). Early investment facilitates the productivity of later investment (complementarity). Early investments are not productive if they are not followed up by later investments (another aspect of complementarity). This complementarity explains why there is no equity-efficiency trade-off for early investment. The returns to investing early in the life cycle are high. Remediation of inadequate early investments is difficult and very costly as a consequence of both self-productivity and complementarity.