Extending the use of super-efficiency under undesirable outputs: An application to energy efficiency in the European Union

Data Envelopment Analysis (DEA) models have been intensively used for measuring efficiency in a variety of contexts. More recently, the inclusion of undesirable outputs has extended their use to analyze relevant fields such as environmental efficiency. In this context, Slacks-Based Measure (SBM) models offer a remarkable alternative, largely due to their ability to deal with undesirable outputs. Additionally, super-efficiency evaluation in DEA is a useful complementary analysis for ranking the performance of efficient DMUs. Although the literature has already considered a pioneering proposal for dealing with super-efficiency in SBM models, which may be referred to as Super-SBM, we extend this approach to the presence of undesirable outputs. We illustrate this contribution in three scenarios where super-efficiency SBM models with undesirable outputs may be of interest: (i) the analysis of productivity change; (ii) the provision of a full ranking of efficiency (also including efficient units); and (iii) the detection of influential units. Finally, we present and discuss an empirical application dealing with environmental efficiency in electricity and derived heat generation in the European Union.