Can Super-Efficiencies Improve Bias Correction? A Bayesian Data Envelopment Analysis Approach

It has been proven that DEA efficiencies, within the interval (0, 1], are overestimated for finite samples, while asymptotically, this bias reduces to zero. In the extant literature, the statistical inference approaches yielding the best-performing DEA estimates are the smoothed bootstrap and Bayesian DEA methods. All statistical inference techniques apply to DEA models yielding efficiencies between zero and one. This study presents a new Bayesian DEA approach that takes into account efficiencies and super-efficiencies aiming to improve bias correction. We prove that efficiencies and super-efficiencies are interrelated for finite samples. However, bias correction is statistically significant only in the case of efficiencies below one. The new Bayesian super-efficiency DEA approach yields estimates with lower mean absolute error and mean square error than the extant DEA statistical inference techniques referring only to efficiencies with right-censored distributions, where efficiencies are not allowed to exceed unity. Drawing on formal analysis, real-world and simulated data sets, we conclude that the new Bayesian super-efficiency DEA estimates are consistent of DEA parameters.