Estimating the Technology of Cognitive and Noncognitive Skill Formation

This paper formulates and estimates a model of the evolution of child cognitive and noncognitive skills as determined by parental investments at different stages of the life cycle. We estimate the elasticity of substitution between contemporaneous investments and inherited stocks of skills to assess the benefits of early investment in children compared to later investment. We develop a nonlinear factor analysis and use it to establish nonparametric identification of the technology of skill formation. A by-product of our approach is a framework for the evaluation of childhood interventions that avoids reliance on arbitrarily scaled test scores. Since any monotonic transformation of a test score is also a valid test score, "value added" analyses of test scores have no clear interpretation. We develop a general nonparametric solution to this problem by anchoring test scores and other outcome measures in adult outcomes with interpretable scales.