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

Published online by Cambridge University Press:  08 September 2014

Alois Kneip ,
Léopold Simar  and
Paul W. Wilson
Alois Kneip*
Affiliation:
Universität Bonn
Léopold Simar
Affiliation:
Université Catholique de Louvain-la-Neuve
Paul W. Wilson
Affiliation:
Clemson University
*
*Address correspondence to Alois Kneip, Institute für Gessellschafts- und Wirtschaftswissennschafen, Statistische Abteilung, Universität Bonn, Bonn, Germany; e-mail: akneip@uni-bonn.de or to Léopold Simar, Institut de Statistique, Biostatistique, et Sciences Actuarielles, Université Catholique de Louvain-la-Neuve, Louvain-la-Neuve, Belgium; e-mail: leopold.simar@uclouvain.be or to Paul W. Wilson, Department of Economics and School of Computing, Clemson University, Clemson, South Carolina, USA; e-mail: pww@clemson.edu.
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 2: Haavelmo Memorial Issue: Part Two , April 2015 , pp. 394 - 422
Copyright
Copyright © Cambridge University Press 2014 

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