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A Note on the Convergence of Nonparametric DEA Efficiency Measures

Author

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  • KNEIP, Alois

    (Institut de Statistique and Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

  • PARK, Byeong U.

    (Department of Computer Science and Statistics, Seoul National. University. Seoul, Korea)

  • SIMAR, Léopold

    () (Institut de Statistique and Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

Abstract

Efficiency scores of production units are measured by their distance to an estimated production frontier. Nonparametric DEA estimators are based on a finite sample of observed production units and radial distances are considered. We investigate the consistency and the speed of convergence of these estimated efficiency scores (or of the radial distances) in the very general setup of multi-output and multi-input case. It is shown that the speed of convergence relies on the smoothness of the unknown frontier and on the number of inputs and of outputs. Furthermore, one has to distinguish betwen the output- and the input-oriented case.

Suggested Citation

  • KNEIP, Alois & PARK, Byeong U. & SIMAR, Léopold, 1996. "A Note on the Convergence of Nonparametric DEA Efficiency Measures," CORE Discussion Papers 1996039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1996039
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    File URL: https://uclouvain.be/en/research-institutes/immaq/core/dp-1996.html
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    Citations

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    Cited by:

    1. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
    2. Simar, L. & Wilson, P.W., 1998. "Productivity Growth in Industrialized Countries," Papers 9810, Catholique de Louvain - Institut de statistique.
    3. Kjoeserud,G.G. & Kvamme,O.J. & Kittelsen,S.A.C., 2001. "Errors in survey based quality evaluation variables in efficiency models of primary care physicians," Memorandum 24/2001, Oslo University, Department of Economics.
    4. Ferjani, Ali, 2005. "Does Switzerland Have a Productivity Problem?," Agrarwirtschaft und Agrarsoziologie/ Economie et Sociologie Rurales, Swiss Society for Agricultural Economics and Rural Sociology, issue 1.
    5. Wheelock, David C. & Wilson, Paul W., 2008. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 209-225, July.
    6. Alois Kneip & Léopold Simar & Paul Wilson, 2011. "A Computationally Efficient, Consistent Bootstrap for Inference with Non-parametric DEA Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 483-515, November.
    7. Theodoridis, A.M. & Psychoudakis, A. & Christofi, A., 2006. "Data Envelopment Analysis as a Complement to Marginal Analysis," Agricultural Economics Review, Greek Association of Agricultural Economists, vol. 7(2), August.
    8. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
    9. Hallsteinli, Vidar & Kittelsen, Sverre AC & Magnussen, Jon, 2009. "Scale, efficiency and organization in Norwegian psychiatric outpatient clinics for children," HERO On line Working Paper Series 2001:8, Oslo University, Health Economics Research Programme.
    10. Kittelsen, Sverre A.C. & Magnussen, Jon, 2009. "Testing DEA Models of Efficiency in Norwegian Psychiatric Outpatient Clinics," HERO On line Working Paper Series 1999:4, Oslo University, Health Economics Research Programme.
    11. Kittelsen,S.A.C., 1999. "Monte Carlo simulations of DEA efficiency measures and hypothesis tests," Memorandum 09/1999, Oslo University, Department of Economics.
    12. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1663-1697, December.
    13. David C. Wheelock & Paul W. Wilson, 2003. "Robust nonparametric estimation of efficiency and technical change in U.S. commercial banking," Working Papers 2003-037, Federal Reserve Bank of St. Louis.
    14. David C. Wheelock & Paul W. Wilson, 2000. "Why do Banks Disappear? The Determinants of U.S. Bank Failures and Acquisitions," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 127-138, February.
    15. Léopold Simar & Paul Wilson, 2011. "Two-stage DEA: caveat emptor," Journal of Productivity Analysis, Springer, vol. 36(2), pages 205-218, October.
    16. Laurent Cavaignac, 2009. "Bias of distance functions estimates and Primont and Primont’s homotheticity test," Journal of Productivity Analysis, Springer, vol. 31(2), pages 95-100, April.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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