Matt Wiswall (Arizona State University)

“Estimation of Children’s Skill Formation when Children’s. Skills are Unobserved”

abstract

We develop a new estimator for the process of skill formation where individuals’ skills are unobserved (latent) and measured in data with error. Our model of skill formation has a dynamic factor structure where the latent skills of individuals evolve endogenously over the life-cycle according to a skill formation production technology. In our framework, we treat the parameters of the measurement model as “nuisance” parameters and use transformation of moments of the measurement data to eliminate them, analogous to data transformations used to eliminate fixed effects with panel data. Using this method, we show that we can identify the production technology of skill formation, up to scale, without imposing some of the strong restrictions on the measurement model and the latent distribution of skill factors, as assumed in the prior literature. Our estimator is therefore robust and internally consistent for any scale or location of the skill measures. Our method has several advantages over the existing frameworks. Our method requires only one measure of each latent skill in periods following the initial period and is robust to miss-specification of the parametric distributions of measurement errors and latent factors. We show how to extend our method to estimate richer models of skill formation, including skill production technologies which exhibit non-stationary changes in total factor productivity. In Monte Carlo simulations we show that our method performs well, and that common alternative methods, which impose more restrictive assumptions, can bias the production technology estimates. We apply our method to estimating the skill development of children.