Identifying the elasticity of substitution between capital and labour. A pooled GMM panel estimator

Simultaneity represents a fundamental problem when estimating the elasticity of substitution between capital and labour. To overcome this problem, a wide variety of external instruments has been applied in the literature. However, the use of instruments may lead to wrong inference if they are either weak, or endogenous to the system being estimated. In this paper, we extend the widely used Feenstra (1994) estimator, which does not depend on external instruments, to make it applicable to the problem of estimating the elasticity of substitution between capital and labour. We propose a pooled GMM (PGMM) estimator, examine its properties in a Monte Carlo study and apply it to a Norwegian sample of manufacturing firms. We identify the conditions under which P-GMM yields unbiased estimates and compare it to a fixed effects estimator which is unbiased when factor prices are exogenous – a typical assumption in the literature. We find that the fixed effects estimator is heavily downward biased in the presence of simultaneity. In contrast, the P-GMM estimator is nearly unbiased provided the number of time periods (T) is not too small (say, more than 10). In our application, with an unbalanced sample and T = 12, we estimate the elasticity of substitution to be 1.8 using P-GMM and 1.0 using a fixed effects estimator. Hence, neglecting simultaneity may lead to the conclusion that capital and labour are complements when, in fact, they are substitutes