Data sharpening for improving central limit theorem approximations for data envelopment analysis–type efficiency estimators

Abstract

Asymptotic statistical inference on productivity and production efficiency, using nonparametric envelopment estimators, is now available thanks to the basic central limit theorems (CLTs) developed in Kneip, Simar, and Wilson (2015). They provide asymptotic distributions of averages of Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH) estimators of production efficiency. As shown in their Monte-Carlo experiments, due to the curse of dimensionality, the accuracy of the normal approximation is disappointing when the sample size is not large enough. Simar and Zelenyuk (2020) have suggested a simple way to improve the approximation by using a more appropriate estimator of the variances. In this paper we suggest a novel way to improve the approximation, by smoothing out the spurious values of efficiency estimates when they are in a neighborhood of 1. This results in sharpening the data for observations near the estimated efficient frontier. The method is very easy to implement and does not require more computations than the original method. We compare our approach using Monte-Carlo experiments, both with the basic method and with the improved method suggested in Simar & Zelenyuk (2020) and in both cases we observe significant improvements. We show also that the Simar & Zelenyuk (2020) idea of the variance correction can also be adapted to our sharpening method, bringing additional improvements. We illustrate the method with some real data sets.