A Note on the Importance of Normalizations in Dynamic Latent Factor Models of Skill Formation

Abstract

In this paper we highlight an important property of the translog production function for the identification of treatment effects in a model of latent skill formation. We show that when using a translog specification of the skill technology, properly anchored treatment effect estimates are invariant to any location and scale normalizations of the underlying measures. By contrast, when researchers assume a CES production function and impose standard location and scale normalizations, the resulting treatment effect estimates are biased. Interestingly, the CES technology with standard normalizations yields biased treatment effect estimates even when age-invariant measures of the skills are available. We theoretically prove the normalization invariance of the translog production function and then produce several simulations illustrating the effects of location and scale normalizations for different technologies and types of skills measures.

Keywords: dynamic factor analysis, human capital, children, measurement, policy

JEL Classification: C13, C18, I38, J13, J24