Estimation of Zellner-Revankar Production Function Revisited

Zellner and Revankar in their paper “Generalized Production Functions” introduced a production function, which was illustrated by fitting the generalized Cobb-Douglas function to the U.S. data for Transportation Equipment Industry. For estimating the production function, they used a method in which one of the parameters (theta) is repeatedly chosen at the trial basis and other parameters are estimated so as to obtain the global optimum of the likelihood function. We show that this method of Zellner and Revankar (ZR) is caught into a local optimum trap and the estimated parameters reported by ZR are somewhat sub-optimal. Using the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods, we re-estimate the parameters of the ZR production function with data used by ZR and show that our estimates of parameters are better than those of ZR. We also find that the returns to scale do not vary with the size of output in the manner reported by ZR.