Estimating Country Heterogeneity in Capital - Labor Substitution Using Panel Data

The aggregate elasticity of substitution between labor and capital is central in understanding the global decline in the labor share and the cross-country heterogeneity in productivities. Available estimates vary substantially because of the different assumptions made about unobserved technologies. In this paper, I develop a flexible framework to estimate the aggregate elasticity of substitution between labor and capital for a panel of countries. In contrast to previous studies, my framework considers country heterogeneity in the elasticity of substitution. The growth rates of labor- and capital- augmenting technologies are also allowed to vary across countries and time while retaining some commonalities across the panel via a dynamic factor model. Estimation is based on posterior distributions in a Bayesian fixed effects framework. I propose a computationally convenient procedure to compute posterior distributions in two steps that combines the Gibbs and the Metropolis-Hasting algorithm. Using the EU KLEMS database, I find evidence of heterogeneity in the elasticity of substitution across countries, with a mean of 0.90 and standard deviation of 0.23. The bias in the technical change is the dominant mechanism in explaining the labor share decline in the majority of countries. However, the increase in the capital-labor ratio (or the decline in the price of investment goods) is also an important mechanism for some countries. Finally, I find a strong correlation between direction of the technical change, the elasticity of substitution and the relative endowment of capital and labor.