A globally concave, monotone and flexible cost function: derivation and application

Abstract

Empirical analysis of demand often requires that the functional form of the cost function be specified in advance. The form of the function has to be both consistent with economic theory and sufficiently flexible to accommodate the data. Recent research has indicated that flexible forms do not always generate empirically credible elasticity estimates, and often fail to satisfy concavity and/or monotonicity. A priori imposition of both global concavity and monotonicity is generally assured only with functional forms that are not flexible (the CES function, for example). However, such forms produce a poor statistical fit, and may be difficult to estimate and interpret. Here we develop the CES–DCES cost function—which is globally concave and monotone at any possible vector of input prices. We prove that the CES–DCES is a flexible cost function when the number of inputs is two or three. We show how to extend the analysis to acommdodate more than three inputs. Using three data sets we estimate the parameters of the CES–DCES cost function for two and three inputs, and compare its performance to that of the CES–GBC function developed in Tishler and Lipovetsky (The Review of Economics and Statistics 1997; 638–646). Copyright © 2000 John Wiley & Sons, Ltd.