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

  • Alois Kneip
  • Léopold Simar
  • Paul W. Wilson

    ()

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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File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse12_2006.pdf
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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
Date of revision:
Handle: RePEc:bon:bonedp:bgse12_2006
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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  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.
  2. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
  3. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
  4. Gijbels, Irène & Mammen, Enno & Park, Byeong U. & Simar, Léopold, 1998. "On estimation of monotone and concave frontier functions," SFB 373 Discussion Papers 1998,9, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," CORE Discussion Papers 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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