Investments in Children When Markets Are Incomplete ∗

This paper proposes a model of investments in the cognitive skills of children that is based on three features: that it takes time to build a child’s stock of cognitive skills; that parental resources evolve stochastically over time; and that parents face constraints that limit their ability to transfer resources across states of nature, across time, and across generations. These constraints distort the equilibrium allocation of investments throughout a child’s life and, in turn, produce sub-optimal stocks of cognitive skills. In order to verify the quantitative importance of these distortions, I estimate the model’s key parameters and I compute its steady-state equilibrium. I show that the empiricallygrounded steadystate explains a variety of facts about cognitive skills, education, and child development. For example, it correctly predicts selection into college by quartiles of family income and terciles of skills measured at adolescent years. Moreover, it is consistent with gaps in cognitive skills that are present at early ages. Finally, it reproduces the pattern of selection into college based on cognitive skills. I use the model to evaluate the impact of different remediation policies on the stationary distribution of cognitive skills and welfare. I analyze the effects of a 50% tuition subsidy, a targeted early investment subsidy, and a targeted early and late investment subsidy that is contingent on parental resources. I show that the policy that subsidizes early and late childhood investments dominates the other policies in welfare, since it is the one that generates the highest equivalent variation across all deciles of permanent income. This also generates a stationary distribution of cognitive skills that first-order stochastically dominates the ones generated by the baseline economy and the other remediation policies.