This paper investigates the importance of family borrowing constraints in determining human capital investments in children at early and late ages. While a number of papers have recently examined the effects of credit constraints on college-going behavior (see Carniero and Heckman (2002) for a summary of the empirical literature, and Caucutt and Kumar (2003) for a calibrated theoretical approach), very little attention has been paid to the role of borrowing constraints when children are younger. Yet, it seems possible that constraints at early ages play a more important role in determining investment decisions for a number of reasons. First, most empirical studies indicate that early investments in children produce high long-term payoffs (see Karoly et al. (1998) or Blau and Currie (2005) and references therein).
Not only are children able to learn quickly when they are young, but early learning begets later learning as emphasized by Cunha (2004), Cunha and Heckman (2004), and Cunha, et al (2005). Second, empirical studies suggest that family income has a greater impact on child outcomes at earlier ages (e.g. Duncan and Brooks-Gunn (1997), Levy and Duncan (1999)). Third, parents age with their children. And, as both children and parents age, parental resources tend to increase with the accumulation of human capital and the associated rise in earnings. Fourth, despite generous government student loan programs for college-age students and their families in the U.S. and other developed countries, governments have not traditionally offered loans to parents with young children to help finance earlier human capital investments.
While the direct costs of public elementary and secondary education are fully subsidized, a good education through high school is not free. In many U.S. communities, parents must choose between sending their child to poor public schools and paying for their child to attend better private schools.
Alternatively, parents may choose between high-cost communities with good public schools and low-cost neighborhoods with poor ones. Other investments in young children can also be costly. Preschool programs in the U.S. can cost as much as attendance at a top university. While the government does not fully neglect poor preschool-age children, the quality of publicly provided pre-school programs (e.g. Head Start) is far below what it could be (Zigler 1994, Blau and Currie, 2005). Expenditures on computers and books also add up. Finally, parental time is an important, yet costly, input that poor parents may be unable to afford.
We provide a number of empirical tests for family credit constraints when children are teenagers or younger. We distinguish between intergenerational borrowing constraints, which would prevent parents from borrowing against their children’s future earnings, and intragenerational borrowing constraints, which would prevent individuals from borrowing against their own future income.
Intuitively, testing for the former amounts to estimating whether the present value of parental lifetime income affects child success, while testing for the latter amounts to estimating whether the timing of family income matters. We focus on the latter, estimating the effects of family income at different ages of the child on the math and reading achievement of those children at ages 5-14. We interpret evidence that the timing of income matters as evidence that intragenerational borrowing constraints distort investment decisions. In particular, we would expect early income to matter more if families with young children are constrained from borrowing against their future earnings, thereby causing them to pass on highly productive investment options.
We provide three tests for intragenerational constraints using data from Children of the National Longitudinal Survey of Youth (NLSY). First, we estimate the effects of past income on math and reading scores on the Peabody Individual Achievement Tests (PIAT), to see whether income earned when a child is younger has larger effects on test scores (at any given age) than does income earned at later ages. Empirically, we find statistically different (though quantitatively small) effects of income earned at different ages.
Second, we test whether past family income has a greater effect on test scores than does future family income. Even when we limit our sample to individuals with smooth earnings trajectories (a proxy for the level of uncertainty), we find that past income matters more than future income. Finally, we test whether the slope of a family’s income profile affects child test scores after conditioning on the present value of income discounted over many years. Again, our results are consistent with borrowing constraints in that the slope is negatively related to test scores. Taken altogether, these results suggest that borrowing constraints inhibit early childhood investments within some families and that early deficiencies are not fully compensated for with later investment once income levels have risen. In short, early borrowing constraints have long-term consequences for children.
The rest of this paper develops a theory of the family that incorporates the dynamic nature of investment in children, as well as the dynamic nature of borrowing constraints faced by parents and college-age youth. Our theory recognizes that later investments build on earlier investments, that early childhood investments are made by young parents at the beginning of their careers, and that opportunities for borrowing may differ substantially over the life-cycle of an individual.
We assume that people live through six stages in their lives: childhood, young adulthood, young parenthood, old parenthood, post-parenthood, and retirement. Young parents make early investments in their children and provide them with consumption. These parents also make their own consumption choices and borrow or save to intertemporally allocate resources. Constraints on their borrowing may limit consumption and investments in young children.
Once children become young adults, they make investments in themselves (e.g. college), using their own earnings, transfers from their (now older) parents, and student loans to cover their own costs and consumption. Again, choices may be constrained by imperfect credit markets. Older parents must decide how much to transfer to their college-age children and how much to borrow or save for their own current and future consumption. Once a child leaves the home to establish his own family, parents continue to work, save, and consume until retirement. This cycle repeats itself, as young adults grow into parenthood.
The human capital production process, which translates a child’s ability and early and late human capital investments into final skill levels, is of central importance. We assume that each child has a learning ability that is correlated with his parent’s ability. Total human capital acquired at the end of the two investment periods is increasing in learning ability and the investments made in each period. Ability and investments are assumed to be complements so that an extra unit of investment for a child with higher ability results in a greater increase in human capital.
We make no assumptions about the complementarity or substitutability of investments across periods; although, Cunha, et al (2005) argue that empirical evidence on the returns to early and late investments is most consistent with complementarity. An important contribution of this research will be the use of different empirical strategies and calibration of our model to gain a better understanding of the interaction of investments over time (i.e. the extent of complementarity) and the role borrowing constraints at different ages.
This is a novel and complex problem for several reasons. First, we include an early and late childhood investment period along with potential borrowing constraints at each of these stages. This extends previous work by Becker and Tomes (1976), Keane and Wolpin (2001), Aiyagari, Greenwood, and Seshadri (2002), and Caucutt and Kumar (2003), who consider a single investment period. Second, we allow for intergenerational linkages by assuming Barro-Becker preferences. This breaks from the standard micro literature on human capital production, which typically neglects the family altogether or assumes parental transfers are exogenous (e.g. Ben-Porath, 1967, Cameron and Heckman 1998, Keane and Wolpin, 2001). And, third, we assume that parents can pass financial assets and human capital on to their children.
This breaks from the work by Caucutt and Kumar (2003) and Restuccia and Urrutia (2004), which assumes that parents can only transfer human capital to their children and skews family decisions towards investment in human capital rather than financial assets. In their models, parents with low ability children who would benefit little from investments in human capital cannot transfer their children assets instead. Further, both Caucutt and Kumar (2003) and Restuccia and Urrutia (2004) assume that young adults are either successful or unsuccessful in college, and that young adults with low ability are unlikely to be successful. It is, therefore, difficult for parents of low ability children to transfer anything at all to their children.
