Progressing from uncertainty to risk for DEA-based decisions

Abstract

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.

Keywords:

• data envelopment analysis
• methodology
• econometrics
• regression
• statistics
• probability

Acknowledgements

The bus schedule reliability project was partially supported by the Chicago Transit Authority under contract to the Urban Transportation Center at the University of Illinois at Chicago. The paratransit project was made possible by the Canadian Urban Transit Association, which provided its data on member paratransit operations.