The Joint Measurement of Technical and Allocative Inefficiencies

Abstract

This article estimates technical and allocative inefficiencies and increase in costs therefrom of individual firms using a translog cost system consisting of the cost function and the cost share equations. We call it a nonlinear random-effects system because technical and allocative inefficiencies are random (hence the term random effects) and are separated from the random noise terms appearing in each equation of the system, and because the inefficiency terms appear in the system in a highly nonlinear fashion, which helps in separating them from random errors. We use Bayesian inference procedures based on Markov chain Monte Carlo (MCMC) techniques to estimate the proposed system. Inferences on firm-specific technical inefficiency and both input-specific and firm-specific allocative inefficiencies are developed using MCMC techniques. We apply the new methods to a sample of 500 U.S. commercial banks. We focus on input allocation problem based on the assumption that banks minimize cost. Empirical results show that cost for the top (bottom) 10% of banks is increased by at least 3% (11%) due to technical inefficiency. In contrast, very few banks are found to be efficient in allocating all the inputs. Costs are increased by 13% on average due to input misallocation. Increase in costs due to both technical and allocative inefficiencies for the top (bottom) 10% of the banks is at least 11% (29%). When translated into dollar figures, this result indicates that elimination of technical and allocative inefficiencies would save the top (bottom) 10% of the banks more than $.20 ($3.56) million. We also find that none of the banks in our sample exceeded the efficient scale size, although most of them were operating near their optimum scale (unitary returns to scale).