When Bias Kills the Variance: Central Limit Theorems for DEA and FDH Efficiency Scores

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. Forthcoming, Econometric Theory ∗Kneip: Institute für Gessellschaftsund Wirtschaftswissennschafen, Statistische Abteilung, Universität Bonn, Bonn, Germany; email: [email protected]. Simar: Institut de Statistique, Biostatistique, et Sciences Actuarielles, Université Catholique de Louvainla-Neuve, Louvain-la-Neuve, Belgium; email: [email protected]. Wilson: Department of Economics and School of Computing, Clemson University, Clemson, South Carolina, USA; email: [email protected]. Research support from the “Interuniversity Attraction Pole”, Phase VII (No. P7/06) of the Belgian Science Policy, from the INRA-GREMAQ, Toulouse, France, from U.S. National Science Foundation (grant no. SMA1243436), and from the Cyber Infrastructure Technology Integration group at Clemson University is gratefully acknowledged. Any remaining errors are solely our responsibility.