Inferring the incidence of industry inefficiency from DEA estimates

• Published in: European journal of operational research Vol. 224; no. 2; pp. 414 - 424
• Main Authors: Friesner, Daniel, Mittelhammer, Ron, Rosenman, Robert
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.01.2013; Elsevier; Elsevier Sequoia S.A
• Subjects: Applied probability; Applied sciences; Bayesian analysis; Bayesian inference; Data envelopment analysis; Decision making units; Decision theory. Utility theory; Exact sciences and technology; Linear programming; Mathematical programming; Mathematics; Nonparametric inference; Operational research and scientific management; Operational research. Management science; Physicians; Probability and statistics; Sciences and techniques of general use; Statistics; Studies; Applied probability; Bayesian inference; Data envelopment analysis; Bayes estimation; Performance evaluation; Productivity; Statistical analysis; Probabilistic approach; Prior distribution; Decision making; Empirical method; Non parametric method; Non parametric estimation; Inference; Linear programming; Latent variable model; Replacement; Modeling; Latent variable; Sampling; Categorization; Posterior distribution
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2012.08.003

► We use Bayesian methodology to infer the incidence of inefficiency in an industry. ► We place minimal prior information on the nature of the DEA efficiency frontier. ► Our methodology applies to finite populations and sampling without replacement. ► We account for the fact that DEA estimates may misclassify the efficient frontier. ► Three empirical examples support the methodology, especially with low sample sizes. 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.