Technical, allocative and overall efficiency: Estimation and inference

Abstract

Nonparametric data envelopment analysis and free-disposal hull estimators are frequently used to estimate cost, revenue and profit efficiency as well as the corresponding allocative efficiencies. Papers in the literature often report sample means of such estimates along with sample standard deviations, inviting readers to make inference about means of these efficiencies using classical methods based on the standard Lindeberg–Feller central limit theorem (CLT). A number of papers explicitly make inference using the classical methods. However, the statistical properties of these estimators are (until now) unknown. This paper establishes rates of convergence and existence of limiting distributions for the various estimators. These properties are needed in order to make inference about individual producers using subsampling methods. In addition, properties of the first two moments of the estimators are derived, and these results are subsequently used to establish new CLTs for the estimators, providing formal justification for inference-making. The results reveal that the classical CLTs and methods do not provide valid inference when FDH estimators are used, and provide valid inference when DEA estimators only in a few restrictive, special cases.