WHEN BIAS KILLS THE VARIANCE: CENTRAL LIMIT THEOREMS FOR DEA AND FDH EFFICIENCY SCORES

Aloïs Kneip · Léopold Simar · Paul W. Wilson

112 citations0/0 files storedEconometric Theory

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Efficiency Analysis Using DEA Sports Analytics and Performance Advanced Statistical Methods and Models

Abstract

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that standard central limit theorems do not apply in the case of means of DEA or FDH efficiency scores due to the bias of the individual scores, which is of larger order than either the variance or covariances among individual scores. The main difficulty comes from the fact that such statistics depend on efficiency estimators evaluated at random points. Here, new central limit theorems are developed for means of DEA and FDH scores, and their efficacy for inference about mean efficiency levels is examined via Monte Carlo experiments.

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References

1978Measuring the efficiency of decision making units 1984Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis 1957The Measurement of Productive Efficiency 2005Estimation and inference in two-stage, semi-parametric models of production processes 2015Theory of Cost and Production Functions 1985The Measurement of Efficiency of Production 1996Benefit and Distance Functions 1972Efficiency Estimation of Production Functions

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