Inferring the incidence of industry inefficiency from DEA estimates

Data envelopment analysis (DEA) is among the most popular empirical tools for measuring cost and productive efficiency within an industry. Because DEA is a linear programming technique, establishing formal statistical properties for outcomes is difficult. We model the incidence of inefficiency within a population of decision making units (DMUs) as a latent variable, with DEA outcomes providing only noisy and generally inaccurate sample-based categorizations of inefficiency. We then use a Bayesian approach to infer an appropriate posterior distribution for the incidence of inefficiency within an industry based on a random sample of DEA outcomes and a prior distribution on that incidence. The approach applies to the empirically relevant case of a finite number of firms, and to sampling DMUs without replacement. It also accounts for potential mismeasurement in the DEA characterization of inefficiency within a coherent Bayesian approach to the problem. Using three different types of specialty physician practices, we provide an empirical illustration demonstrating that this approach provides appropriately adjusted inferences regarding the incidence of inefficiency within an industry.