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Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models

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Author Info
Alois Kneip
Léopold Simar
Paul W. Wilson ()

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Abstract

Non-parametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proven consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns-to-scale. This result is then used to prove that two different bootstrap procedures (one based on sub-sampling, the other based on smoothing) provide consistent inference. The smooth bootstrap requires smoothing the irregularly-bounded density of inputs and outputs as well as smoothing of the DEA frontier estimate. Both bootstrap procedures allow for dependence of the inefficiency process on output levels and the mix of inputs in the case of input-oriented measures, or on inputs levels and the mix of outputs in the case of output-oriented measures.

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Publisher Info
Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse12_2006.

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Length: 37
Date of creation: Apr 2006
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Handle: RePEc:bon:bonedp:bgse12_2006

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 9221
Web page: http://www.bgse.uni-bonn.de/index.php?id=494

For technical questions regarding this item, or to correct its listing, contact: (Daniel Park).

Related research
Keywords: bootstrap; frontier; efficiency; data envelopment analysis; DEA;

Other versions of this item:

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Kneip, A & Park, B-U & Simar, L, 1996. "A Note on the Convergence of Nonparametric DEA Efficiency Measures," Papers 9603, Catholique de Louvain - Institut de statistique.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. David C. Wheelock & Paul Wilson, 2007. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Working Papers 2005-027, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  2. Randall Campbell & Kevin Rogers & Jon Rezek, 2008. "Efficient frontier estimation: a maximum entropy approach," Journal of Productivity Analysis, Springer, vol. 30(3), pages 213-221, December. [Downloadable!] (restricted)
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This page was last updated on 2009-11-17.


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