Labor Share Dynamics and Factor Complementarity

Abstract This paper investigates the mechanism behind the cyclical movements in the labor income share. We build a dynamic stochastic general equilibrium model with search and matching frictions to examine the counter-cyclicality and overshooting of the labor income share, following a technology innovation. This model features (i) a time-varying output elasticity of labor, generated from the capital–labor complementarity under a constant-elasticity-of-substitution production function, and (ii) an endogenous markup variation, generated from wage/price rigidity. Through the output elasticity and markup channels, the capital–labor complementarity interacts with wage rigidity, which allows us to produce a satisfactory matching of the amplitude of the labor share overshooting observed in the data. The amplitude of the labor share overshooting is more significant when wages (prices) are more (less) sticky, and when the government’s interest rate rule is more (less) responsive to the deviation in the inflation (output) target.