Can variable elasticity of substitution explain changes in labor shares?

In CES production functions, the magnitude of the elasticity of substitution between capital and labor (σ) is crucial to explain the evolution of the labor share. The decline in labor share observed worldwide can be explained by capital accumulation if σ > 1. However, empirical evidence on the value of σ is mixed. To shed light on this issue, we employ a Variable Elasticity of Substitution (VES) production function where σ is an endogenous driver of the labor share. Using macro data for six advanced OECD economies from 1980 to 2020 we provide estimates of σ under imperfect competition. We test the prediction of the model by means of simulations. Mainly, we find that capital deepening, markup and technological change explain a significant part of the observed decline in labor shares. The results suggest complementarity between labor and capital in all the countries except the United States.