Child Skill Production

The paper presented in this Research Seminar studies the multidimensional nature of investments in children within a dynamic framework. In particular, the authors examine the roles of parental time investments, purchased home goods/services inputs, and market-based child care services. The paper presented in this Research Seminar first documents strong increases in total investment expenditures by maternal education; yet, expenditure shares, which skew heavily towards parental time, very little with parental schooling. Second, the authors develop an intergenerational lifecycle model with multiple child investment inputs to study these patterns and the impacts of policies that alter the prices of different inputs. They analytically characterize investment behavior, focusing on the substitutability of different investment inputs and the way parental skills affect the productivity of family-based inputs. Third, the authors develop an estimation strategy that exploits infratemporal optimality conditions based on relative demand to estimate substitutability between inputs, the relative productivity of different inputs, and the role played by parental education. This approach requires no assumptions about the dynamics of skill investment, preferences, or credit markets. They also account for mis-measured inputs and wages, as well as unobserved heterogeneity in parenting skills. The paper presented in this Research Seminar further shows how noisy measures of child achievement (measured several years apart) can also be incorporated in a GMM approach to additionally identify the dynamics of skill accumulation. Fourth, the authors use data from the Child Development Supplement of the Panel Study of Income Dynamics to estimate the skill production technology for children ages 12 and younger. Their estimates suggest complementarity between parental time and home goods/services inputs as well as between these family-based inputs and market-based child care, with elasticities of substitution ranging from 0.2 to 0.5. The authors find no systematic effects of parental education on the relative productivity of parental time and other home inputs. Finally, they use counterfactual simulations to explore the extent and sources of variation in investments across families, as well as investment responses to changes in input prices. The authors find that variation in prices explains 48% of the overall variance in investment expenditures, and differences in wages explain more than half of the investment expenditure gap between college and non-college educated parents. They further show that accounting for the degree of input complementarity implied by our estimates has important implications for the responses of individual inputs to any price change and for the responses in total investments and skill accumulation to large (but not small) price changes.