A New Approach to Estimating Production Function Parameters: The Elusive Capital--Labor Substitution Elasticity

Parameters of taste and technology are central to a wide variety of economic models and issues. This article proposes a simple method for estimating production function parameters from panel data, with a particular focus on the elasticity of substitution between capital and labor. Elasticity estimates have varied widely, and a consensus estimate remains elusive. Our estimation strategy exploits long-run variation and thus avoids several pitfalls, including difficult-to-specify dynamics, transitory time-series variation, and positively sloped supply schedules, that can bias the estimated elasticity. Our results are based on an extensive panel comprising 1860 firms. Our approach generates a precisely estimated elasticity of 0.40. Although existing estimates range widely, we document a remarkable convergence of results from two related approaches applied to a common dataset. The method developed here may prove useful in estimating other structural parameters from panel datasets.