Model uncertainty and efficiency measurement in stochastic frontier analysis with generalized errors

Abstract

Advanced efficiency measurement methods usually fall within Stochastic Frontier Analysis (SFA), Data Envelopment Analysis (DEA), or their derivatives. Although SFA has some theoretical advantages, it has been criticized for relying on arbitrary and potentially restrictive assumptions about model specification. One strand of the literature suggests the use of nonparametric SF models to cope with the issue. We follow an alternative path and demonstrate that it is possible to deal with specification uncertainty and potentially restrictive assumptions while maintaining the advantages of the parametric approach. First, we develop a flexible stochastic model based on generalized t and generalized beta of second kind distributions, which encompasses virtually all known parametric SFA specifications. Second, we apply Bayesian inference methods, which are less restrictive than those used so far, and propose feasible approximate alternatives based on maximum likelihood. Third, we pool results from alternative specifications using model averaging. Our focus is on the distributional assumptions regarding the compound error in SFA since this aspect has not been addressed so far in a satisfactory way. However, extensions to other elements of specification uncertainty, like the choice of the frontier functional form, are straightforward. Finally, we show simulations results and analyze two well-researched datasets, for which we obtain probabilistic (density) estimates of efficiency scores that take into account the estimation error and model uncertainty in a formally justified manner.