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Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models

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  • Léopold Simar

    (Institut de Statistique and CORE, Université Catholique de Louvain, Voie du Roman Pays, 20, Louvain-la-Neuve, Belgium)

  • Paul W. Wilson

    (Department of Economics, University of Texas at Austin, Austin, Texas 78712)

Abstract

Efficiency scores of production units are generally measured relative to an estimated production frontier. Nonparametric estimators (DEA, FDH, \cdots ) are based on a finite sample of observed production units. The bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier. The main point in order to validate the bootstrap is to define a reasonable data-generating process in this complex framework and to propose a reasonable estimator of it. This paper provides a general methodology of bootstrapping in nonparametric frontier models. Some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:1:p:49-61
    DOI: 10.1287/mnsc.44.1.49
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    References listed on IDEAS

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    1. Grosskopf, S, 1986. "The Role of the Reference Technology in Measuring Productive Efficiency," Economic Journal, Royal Economic Society, vol. 96(382), pages 499-513, June.
    2. DEPRINS, Dominique & SIMAR, Léopold, 1983. "On Farrell measures of technical efficiency," LIDAM Reprints CORE 589, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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).
    4. 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).
    5. Fare, Rolf & Grosskopf, Shawna & Kokkelenberg, Edward C, 1989. "Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 655-666, August.
    6. 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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