Overcoming the Inherent Dependency of DEA Efficiency Scores: A Bootstrap Approach

The efficiency scores generated by DEA (Data Envelopment Analysis) models are clearly dependent on each other in the statistical sense. However, this dependency has been ignored in all published uses of these scores when used to make statistical inferences. For example, regression analysis has been widely applied to the analysis of the variation of the DEA efficiency scores. However, the conventional procedure, which has been generally followed in the literature, is invalid. Because of the presence of the inherent dependence among the DEA efficiency scores, one basic model assumption required by regression analysis, independence within the sample, is violated. This paper provides a Bootstrap method to overcome this dependency problem. The core idea is to substitute the incorrect conventional estimators for the standard errors of the regression coefficient estimates with the Bootstrap estimators for the standard errors of these estimates. The method is illustrated using an empirical example from the U.S. health care system.