Identifying the elasticity of substitution with biased technical change: a structural panel GMM estimator

This paper provides a structural panel GMM (P-GMM) estimator of the elasticity of substitution between capital and labour that does not depend on external instruments, and which can be applied in the presence of biased technical change. We identify the conditions under which P-GMM is a consistent estimator and compare it to a fixed effects estimator. Using a Monte Carlo study, we find that the P-GMM estimator is nearly unbiased provided the number of time periods (T) is not too small. We show analytically how the small-T bias is related to metrics of weak identification. In an application on manufacturing firms in Norway, we estimate the elasticity of substitution to be 1.9 using the P-GMM and 1.0 using the fixed effects estimator. Neglecting simultaneity may thus lead to the conclusion that capital and labour are complements or can be described by Cobb–Douglas technology, when, in fact, they are substitutes.