A Bayesian approach for correcting bias of data envelopment analysis estimators using the super-efficiency frontier

A Bayesian data envelopment analysis (DEA) method incorporating the super-efficiency frontier is developed to correct the bias of efficiencies lying within the zero-to-one interval. It is well-established that DEA efficiencies are overestimated in finite samples. We demonstrate that super-efficiencies are also biased and that super-efficiencies and efficiencies are asymptotically uncorrelated. The proposed bias-correction approach is structured around a uniform likelihood and a beta prior for efficiencies below one, and a uniform likelihood combined with a shifted gamma prior for super-efficiencies exceeding one. Formal and empirical analyses are provided to justify the appropriateness of the adopted distributional assumptions. The new Bayesian DEA method yields consistent and asymptotically unbiased efficiency estimators with lower mean squared error (MSE) and mean absolute error (MAE) values in finite samples and convex sets. Specifically, the MSE of the proposed estimates gradually decreases as the sample size increases, from 6×10−4 for 50 units to 1×10−4 for 300 units. Moreover, the robustness and reliability of the estimates are empirically supported. The findings confirm that efficiencies and super-efficiencies are asymptotically uncorrelated and that the bias correction is statistically significant only for efficiencies below one. The empirical analysis is based on real-world small- and medium-sized samples comprising 50, 100, 200, and 300 banks operating in the European Union, along with 4000 simulated datasets (1000 for each real-world sample). Although the empirical application focuses on the banking industry, the proposed Bayesian DEA approach is broadly applicable to any service-oriented context, including public and manufacturing sectors.