Journal of the Operational Research Society (2010) 61, 1548--1555  2010 Operational Research Society Ltd. All rights reserved. 0160-5682/10 www.palgrave-journals.com/jors/ Progressing from uncertainty to risk for DEA-based decisions DT Barnum 1 ∗ , JM Gleason 2 , B Hemily 3 , J Lin 4 and P Wang 5 1 University of Illinois at Chicago (MC 243), Chicago, USA; 2 Creighton University, Omaha, USA; 3 Transit Consultants, Toronto, Canada; 4 University of Illinois at Chicago, Chicago, USA; and 5 East Asia Transport and Energy Division, World Bank, Washington DC, USA We demonstrate a methodology for estimating, with a specified probability, the interval within which the true DEA efficiency of an individual Decision Making Unit occurs. With this procedure, decisions based on DEA scores are made under conditions of risk, as opposed to the current practice in which decisions are made under uncertainty. The method applies statistical Panel Data Analysis (PDA), which provides proven and powerful methodologies for diagnostic testing of residuals and estimation of confidence intervals. Using PDA, we demonstrate, with a sample of real-world data, that DEA score residuals sometimes are independent and Normally distributed, and estimate confidence intervals based on these validated assumptions. Then, using another sample of real-world data in which violations of these assumptions do occur, we demonstrate well- known PDA Generalized Least Squares statistical models that account for the violations in the estimation of confidence intervals. Journal of the Operational Research Society (2010) 61, 1548 – 1555. doi:10.1057/jors.2009.120 Published online 28 October 2009 Keywords: data envelopment analysis; methodology; econometrics; regression; statistics; probability Introduction It is well known that the DEA scores of a Decision Making Unit (DMU) are stochastic, composed of the DMU’s true effi- ciency and an error component (Banker and Natarajan, 2004). Over a decade ago, Seiford (1996, pp 106–107) observed that stochastic DEA ‘appears on almost everyone’s list of future research areas for DEA and presents a formidable challenge’. He argued that stochastic DEA was the ‘most critical and diffi- cult future issue in DEA’, agreeing with Lovell et al (1994) that statisticians and others would remain sceptical of manage- rial and policy implications of DEA until there was a valid methodology for estimating true efficiencies from stochastic DEA scores. Indeed, developing statistical methodologies to deal with the ubiquitous presence of errors (often called ‘noise’) has become a significant focus of DEA research. It has been shown that stochastic DEA scores possess statis- tical characteristics that permit many types of hypoth- esis tests (Grosskopf, 1996; Banker and Natarajan, 2004), and the errors in DEA scores have been addressed with methodologies such as chance-constrained programming ∗ Correspondence: DT Barnum, Department of Information & Decision Sciences, Department of Managerial Studies, and Great Cities Institute, University of Illinois at Chicago (MC 243), 601 South Morgan Street, Chicago, IL 60607-7123, USA. E-mail: dbarnum@uic.edu (Cooper et al, 2002; Chen, 2002), bootstrapping (Simar and Wilson, 2000, 2007), window analysis (Cooper et al, 2004b), use of means (Ruggiero, 2004), and sensitivity-robustness- stability analysis (Cooper et al, 2004a; Nerali´ c and Wendell, 2004; Cherchye et al, 2008). In spite of this significant progress, none of the preceding methodologies can estimate, with a specified probability, the interval within which the true efficiency of an individual DMU occurs. Even conventional bootstrapping, which yields ‘confidence intervals’ for DEA scores, does not consider the stochastic variations of individual DMUs. It treats the inputs and outputs of each DMU as fixed (Simar and Wilson, 2000, p 67). So, bootstrapped confidence interval estimates incor- porate only frontier noise and ignore noise in the scores of a target DMU. Thus, bootstrapped confidence intervals are biased by an unknown amount, and, because of heteroskedas- ticity in DMU variances, the mean unknown bias varies across DMUs by an unknown amount. As a result, if decision makers use any of the aforemen- tioned methodologies for addressing noise in the data, they still do not know whether a DMU of interest is efficient (or inefficient) with a specific degree of statistical significance. Further, it is not possible to determine if apparent efficiency uptrends or downtrends over time are statistically significant at a given probability, or whether an ongoing process evalu- ated by DEA scores is in or out of control with a prespecified level of confidence.