The Elasticity of Elasticity of Substitution Estimates: Is Anything Robust?

Abstract

We use a CES production function with no restrictions on technical bias to derive relationships between the growth in relative factor shares and (i) the capital to labor ratio and (ii) the ratio of marginal products. These relationships constitute a parsimonious specification used to identify the elasticity of substitution between labor and capital (σ). We estimate σ using (a) quarterly and annual data sets, (b) level and growth rate specifications, and (c) OLS as well 2SLS and GMM estimators utilizing (d) instruments that are tested for both relevance and exogeneity. Estimation in each of the above cases is carried out (e) both imposing and not imposing cross-equation restrictions. The most robust result is that estimation with imposed cross-equation restrictions and "demand-shifter" instrumentation yields σ estimates that are, in most cases, very close to unity.

Keywords: Elasticity of Substitution, Factor Shares, Labor's Share, Biased Technical Change

JEL Classification: E60, E22, E23, H25, O47