Elasticity of substitution between capital and labor: A meta-analysis

A key parameter in many fields of economics is the elasticity of substitution between capital and labor, yet estimates vary widely. In what is to our knowledge one of the largest meta-analyses conducted in economics so far, we collect 3,186 estimates of the elasticity from the constant elasticity of substitution production functions previously reported in the literature and trace the differences in results to differences in the context in which researchers obtain their estimates. We detect selective reporting in favor of large positive estimates. To correct for the resulting publication bias, we use three novel techniques introduced recently and independently by Furukawa (2019); Andrews and Kasy (2019); and Ioannidis, Doucouliagos, and Stanley (2017). Our results suggest that publication bias inflates the mean reported elasticity almost twofold, from 0.4 to 0.8. That is a strong evidence against the nearly exclusive use of the Cobb-Douglas production function. Next, we collect 60 variables that reflect the data and methods used by researchers to estimate the elasticity. To address the resulting model uncertainty, we use both Bayesian and Mallows frequentist model averaging. We find that several characteristics of data and methodology are systematically associated with the reported elasticities. The elasticities are smaller when industry-level data instead of country-level data are used, and time-series estimates are smaller than cross-section and panel estimates. Estimates from normalized specifications and system estimation approaches are smaller than those from the single equation approach. Linear approximation of the production function biases elasticity towards the higher value. Finally, elasticities derived from the first-order condition for capital are on average about half the elasticities derived from the first-order condition for labor.