Inferring the Latent Incidence of Inefficiency from DEA Estimates and Bayesian Priors

Data envelopment analysis (DEA) is among the most popular empirical tools for measuring cost and productive efficiency. Because DEA is a linear programming technique, establishing formal statistical properties for outcomes is difficult. We show that the incidence of inefficiency within a population of Decision Making Units (DMUs) is a latent variable, with DEA outcomes providing only noisy sample-based categorizations of inefficiency. We then use a Bayesian approach to infer an appropriate posterior distribution for the incidence of inefficient DMUs based on a random sample of DEA outcomes and a prior distribution on the incidence of inefficiency. The methodology applies to both finite and infinite populations, and to sampling DMUs with and without replacement, and accounts for the noise in the DEA characterization of inefficiency within a coherent Bayesian approach to the problem. The result is an appropriately up-scaled, noise-adjusted inference regarding the incidence of inefficiency in a population of DMUs.