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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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Bibliographic Info

Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 13 (2000)
Issue (Month): 1 (January)
Pages: 49-78

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Handle: RePEc:kap:jproda:v:13:y:2000:i:1:p:49-78

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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: DEA; FDH; Nonparametric estimation; Efficiency; Frontier models; Bootstrapping;

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  1. Simar, L. & Wilson, P.W., 1998. "A General Methodology for Bootstrapping in Nonparametric Frontier Models," Papers 9811, Catholique de Louvain - Institut de statistique.
  2. 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.
  3. 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.
  4. Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
  5. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
  6. SIMAR, Léopold & WILSON, Paul, 1996. "Estimating and bootstrapping malmquist indices," CORE Discussion Papers 1996060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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