Child skill production: Accounting for parental and market-based time and goods investments

Families make several conceptually different types of investments in their children, including parental time, purchased home goods/services inputs, and market-based child care services. This paper develops an intergenerational lifecycle model with multiple child investment inputs, focusing on two key issues both theoretically and empirically. First, we study the role of parental human capital in child development through input prices (i.e., wages) and income, productivity differences, and preferences for children’s skills. Second, we examine the impacts of different tax/subsidy policies on the composition of investments, effective investment levels, and child skill accumulation. Both of these issues depend heavily on the substitutability across different inputs. We develop an estimation strategy that exploits intratemporal optimality conditions based on relative input demand to estimate this substitutability, as well as 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. It accounts for mismeasured inputs and wages, as well as unobserved heterogeneity in parenting skills. We further show how noisy measures of child achievement (measured several years apart) can be incorporated to additionally identify the dynamics of skill accumulation.

Using data from the Child Development Supplement of the PSID, we estimate the skill production technology for children ages 12 and younger. Our estimates suggest moderate 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. We find no systematic effects of parental education on the relative productivity of parental time and other home inputs: more educated parents invest more in all investment inputs, because they have higher incomes and stronger preference for their children’s skills. Counterfactual simulations show that accounting for the degree of input complementarity implied by our estimates has important implications for the input responses to price changes and for the skill growth impacts of large (but not small) price changes.