Identification of dynamic latent factor models of skill formation with translog production

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 vary with the chosen normalizations. Access to age-invariant measures does not solve this problem since arbitrary scale and location restrictions are still imposed in the initial period. We theoretically prove the normalization invariance of the translog production function and then complete several empirical exercises illustrating the effects of location and scale normalizations for different technologies and types of skills measures.