Capital Skill Substitutability and the Labor Income Share: Identification Using the Morishima Elasticity of Substitution

Abstract

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., 𝜎𝐴𝑔𝑔 > 1). I 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, I analytically estimate the elasticity of substitution parameters between capital and skilled labor ( 𝜌 ) and between capital and unskilled labor (𝜎). I then derive the necessary conditions for a decline in the labor income share based on 𝜌 and 𝜎, which does not require 𝜎𝐴𝑔𝑔 to be greater than unity.