NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Estimating the Technology of Children's Skill Formation

Francesco Agostinelli, Matthew Wiswall

NBER Working Paper No. 22442
Issued in July 2016
NBER Program(s):Children

We develop a new estimator for the process of children's skill formation in which children's skills endogenously develop according to a dynamic latent factor structure. Rather than assuming skills are measured perfectly by a particular measure, we accommodate the variety of skills measures used in practice and allow latent skills to be measured with error using a system of arbitrarily located and scaled measures. For commonly estimated production technologies, which already have a known location and scale, we prove non-parametric identification of the primitive production function parameters. We treat the parameters of the measurement model as "nuisance" parameters and use transformations of moments of the measurement data to eliminate them, analogous to the data transformations used to eliminate fixed effects with panel data. We develop additional, empirically grounded, restrictions on the measurement process that allow identification of more general production technologies, including those exhibiting Hicks neutral total factor productivity (TFP) dynamics and non-constant returns to scale.

We use our identification results to develop a sequential estimation algorithm for the joint dynamic process of investment and skill development, correcting for the biases due to measurement error in skills and investment. Using data for the United States, we estimate the technology of skill formation, the process of parental investments in children, and the adult distribution of completed schooling and earnings, allowing the production technology and investment process to freely vary as the child ages. Our estimates of high TFP and increasing returns to scale at early ages indicate that investments are particularly productive at these ages. We find that the marginal productivity of early investments is substantially higher for children with lower existing skills, suggesting the optimal targeting of interventions to disadvantaged children. Our estimates of the dynamic process of investment and skill development allow us to estimate heterogeneous treatment effects of policy interventions. We show that even a modest transfer of family income to families at ages 5-6 would substantially increase children's skills, completed schooling, and adult earnings, with the effects largest for low income families.

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Document Object Identifier (DOI): 10.3386/w22442

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