A skeptical note on the role of constant elasticity of substitution in labor income share dynamics

The constancy of the elasticity of factor substitution (σ) makes its role as a driver of the labor income share exogenous. The constant elasticity of substitution (CES) (Arrow et al., 1961) production function has predominantly been used to support this causal relationship. This paper argues that (i) capital-labor ratio determines the value of σ, and (ii) both capital-labor ratio and σ vary over time. I use a variable elasticity of substitution (VES) production framework that allows both labor income share and σ to change over time. Statistically significant empirical support is provided using the Japanese industrial productivity (JIP) data. This suggests that the CES model may not be an ideal choice to examine the factor income share dynamics.