Capital skill substitutability and the labor income share: Identification using the Morishima elasticity of substitution

The relationship between a declining labor income share and a falling relative price of capital requires capital and labor to be gross substitutes at the aggregate level (i.e., σ-Agg>1). We argue that this restriction can be relaxed if we distinguish labor by skills and identify differential capital-labor substitutability across skill groups. Using the Morishima elasticity of substitution in a three-factor nested-CES production function, we analytically estimate the elasticity of substitution parameters between capital and skilled labor (ρ) and between capital and unskilled labor (σ). We then derive the necessary conditions for a decline in the labor income share based on ρ and σ, which does not require σ-Agg to be greater than unity.