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Statistical Inference in Nonparametric Frontier Models: The State of the Art

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  • Léopold Simar
  • Paul Wilson

Abstract

Efficiency scores of firms are measured by their distance to an estimated production frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-type estimators). Many have claimed that FDH and DEA techniques are non-statistical, as opposed to econometric approaches where particular parametric expressions are posited to model the frontier. We can now define a statistical model allowing determination of the statistical properties of the nonparametric estimators in the multi-output and multi-input case. New results provide the asymptotic sampling distribution of the FDH estimator in a multivariate setting and of the DEA estimator in the bivariate case. Sampling distributions may also be approximated by bootstrap distributions in very general situations. Consequently, statistical inference based on DEA/FDH-type estimators is now possible. These techniques allow correction for the bias of the efficiency estimators and estimation of confidence intervals for the efficiency measures. This paper summarizes the results which are now available, and provides a brief guide to the existing literature. Emphasizing the role of hypotheses and inference, we show how the results can be used or adapted for practical purposes. Copyright Kluwer Academic Publishers 2000

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  • Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
    • Handle: RePEc:kap:jproda:v:13:y:2000:i:1:p:49-78
    DOI: 10.1023/A:1007864806704
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    References listed on IDEAS

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    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. 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. Wheelock, David C & Wilson, Paul W, 1995. "Explaining Bank Failures: Deposit Insurance, Regulation, and Efficiency," The Review of Economics and Statistics, MIT Press, vol. 77(4), pages 689-700, November.
    4. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    5. 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.
    6. Gary Ferrier & Joseph Hirschberg, 1997. "Bootstrapping Confidence Intervals for Linear Programming Efficiency Scores: With an Illustration Using Italian Banking Data," Journal of Productivity Analysis, Springer, vol. 8(1), pages 19-33, March.
    7. SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," LIDAM Discussion Papers CORE 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June.
    9. KNEIP, Alois & SIMAR, Léopold, 1995. "A General Framework for Frontier Estimation with Panel Data," LIDAM Discussion Papers CORE 1995060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
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    More about this item

    Keywords

    DEA; FDH; Nonparametric estimation; Efficiency; Frontier models; Bootstrapping;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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