An alternative Bayesian data envelopment analysis approach for correcting bias of efficiency estimators

Abstract

In this study, we introduce an alternative Bayesian data envelopment analysis (DEA) approach yielding consistent efficiency estimators for convex sets. This approach draws on two distributional assumptions, a uniform likelihood and a beta prior. It is known from the literature that the combination of those two distributions leads to a reasonable estimator of the parameter. The prior of our approach is “non-informative” in a relative sense and does not depend on sample size. The consistency of the estimates is proven by formal statistical analysis, empirical analysis using real-world data, and computational analysis using simulated data. Our findings justify the appropriateness of our distributional assumptions and the validity of the presented bias-correction procedure. Our estimates are strongly correlated with the DEA-smoothed bootstrap estimates while presenting lower mean square error (MSE) and mean absolute error (MAE). Specifically, the correlation coefficients range between 0.898 and 0.952. The MSE of the alternative Bayesian DEA estimates gradually decreases while sample size increases. For samples of 500, 1,000 and 1,500 units, the MSE is as low as 6.4$\times$10⁻⁴, 1.4$\times$10⁻⁴ and 6$\times$10⁻⁵, respectively. Also, an inverse relationship between the sample size and the length of the confidence intervals of the alternative Bayesian DEA estimates is present.

Keywords:

• Data envelopment analysis
• Bayesian methods
• efficiency
• statistical inference
• banking

Disclosure statement

No potential conflict of interest was reported by the authors.