Estimating the Technology of Cognitive and Noncognitive Skill Formation

TLDR

Skills are shaped by parental environments and investments across childhood stages. The study formulates and estimates multistage production functions for children’s cognitive and noncognitive skills and establishes nonparametric identification of a general class of production technologies using nonlinear factor models with endogenous inputs. The authors formulate and estimate multistage production functions, estimate the elasticity of substitution between period investments and skill stocks to evaluate early versus later investment benefits, and use the estimated technology to determine optimal intervention targeting based on parental and personal endowments. The approach yields a framework for evaluating interventions without relying on scaled test scores, shows that substitutability of cognitive skills decreases in later life stages while remaining constant for noncognitive skills, implying that policies targeting the disadvantaged should invest more in early childhood than later stages.

Abstract

This paper formulates and estimates multistage production functions for children's cognitive and noncognitive skills. Skills are determined by parental environments and investments at different stages of childhood. We estimate the elasticity of substitution between investments in one period and stocks of skills in that period to assess the benefits of early investment in children compared to later remediation. We establish nonparametric identification of a general class of production technologies based on nonlinear factor models with endogenous inputs. A by-product of our approach is a framework for evaluating childhood and schooling interventions that does not rely on arbitrarily scaled test scores as outputs and recognizes the differential effects of the same bundle of skills in different tasks. Using the estimated technology, we determine optimal targeting of interventions to children with different parental and personal birth endowments. Substitutability decreases in later stages of the life cycle in the production of cognitive skills. It is roughly constant across stages of the life cycle in the production of noncognitive skills. This finding has important implications for the design of policies that target the disadvantaged. For most configurations of disadvantage it is optimal to invest relatively more in the early stages of childhood than in later stages.