A coherent approach to Bayesian Data Envelopment Analysis

Mitropoulos et al. (2015) suggested the use of a Bayesian approach in Data Envelopment Analysis (DEA) which can be used to obtain posterior distributions of efficiency scores. In this paper, we avoid their assumption that alternative data sets are simulated from the predictive distribution obtained from their simple data generating process of a normal distribution for the data. The new approach has two significant advantages. First, the posterior proposed in this paper is coherent or principled in the sense that it is consistent with the DEA formulation. Second, and perhaps surprisingly, it is not necessary to solve linear programming problems for each observation in the sample. Bayesian inference is organized around Markov Chain Monte Carlo techniques that can be implemented quite easily. We conduct extensive Monte Carlo experiments to investigate the finite-sample properties of the new approach. We also provide an application to a large U.S banking data set. The sample is an unbalanced panel of US banks with 2,397 bank–year observations for 285 banks. The main purpose of the analysis is to compare distributions of efficiency scores. Relative to DEA, Bayes DEA provides different efficiency scores and their sample distribution has significantly less probability concentration around unity. The comparison with bootstrap-DEA shows that results from Bayes DEA are in broad agreement.