Improving finite sample approximation by central limit theorems for estimates from Data Envelopment Analysis

We propose an improvement of the finite sample approximation of the central limit theorems (CLTs) that were recently derived for statistics involving production efficiency scores estimated via Data Envelopment Analysis (DEA) or Free Disposal Hull (FDH) approaches. The improvement is very easy to implement since it involves a simple correction of the variance estimator with an estimate of the bias of the already employed statistics without any additional computational burden and reserves the original asymptotic results such as consistency and asymptotic normality. The proposed approach persistently showed improvement in all the scenarios that we tried in various Monte-Carlo experiments, especially for relatively small samples or relatively large dimensions (measured by total number of inputs and outputs) of the underlying production model. This approach therefore is expected to produce more accurate estimates of confidence intervals of aggregates of individual efficiency scores in empirical research using DEA or FDH approaches and so must be valuable for practitioners. We also illustrate this method using a popular real data set to confirm that the difference in the estimated confidence intervals can be substantial. A step-by-step implementation algorithm of the proposed approach is included in the Appendix.