Labor income share dynamics with variable elasticity of substitution

The accumulation principle suggests that complementarity between capital and labor forces the labor income share to rise in the presence of capital accumulation. The CES model estimates using data from 20 Japanese industries between 1970 and 2012 explain the same outcome but with substitutable factor inputs. To resolve this puzzle, this paper proposes a variable elasticity of substitution (VES-W) framework that embodies a variable elasticity of substitution and a share parameter as a non-linear function of the Weibull distribution of capital-labor ratio. Empirical findings support the choice of a variable elasticity of substitution. While the estimated structural parameters calibrate the actual output level and the movements in factor income shares reasonably well in both the CES and VES-W models, the VES-W model outcomes support the accumulation principle by achieving the same result but with complementary factor inputs.