Isoelastic Elasticity of Substitution Production Functions

Abstract

We generalize the normalized Constant Elasticity of Substitution (CES) production function by allowing the elasticity of substitution to vary isoelastically with (i) relative factor shares, (ii) marginal rates of substitution, (iii) capital-labor ratios, or (iv) capital-output ratios. Ensuing four variants of Isoelastic Elasticity of Substitution (IEES) production functions have a range of intuitively desirable properties and yield empirically testable predictions for the functional relationship between relative factor shares and (raw or technology-adjusted) capital-labor ratios. As an empirical application, the parameters of IEES functions are estimated in a three-equation supply-side system with factor-augmenting technical change, based on data on aggregate production in the post-war US economy. Our estimates consistently imply that the elasticity of substitution between capital and labor has remained relatively stable, at about 0.8-0.9, from 1948 to the 1980s, followed by a period of secular decline.

Keywords: production function, factor share, elasticity of substitution, marginal rate of substitution, normalization

JEL Classification: E23, E25, O33, O47