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The robustness of the hyperbolic efficiency estimator

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  • Christopher Bruffaerts
  • Bram De Rock
  • Catherine Dehon

Abstract

The robustness properties of a specific type of orientation in the context of efficiency measurement using partial frontiers are investigated. This so called unconditional hyperbolic quantile estimator of efficiency has been recently studied and can be seen as an extension of the input/output methodology of partial frontiers that was introduced previously. The influence function as well as the breakdown point of this fully non-parametric and unconditional estimator are derived for a complete multivariate setup (multiple inputs and outputs). Like for the input and output quantile estimators, the hyperbolic quantile estimator is B-robust but unlike the two former types of estimator its breakdown point does not depend on the actual input or output level of the production unit. Some examples are given to assess the relevance of this type of estimator and to show the differences with the input and output quantile estimators of efficiency from both a robustness and a statistical efficiency point of view. Finally, a real life example is used to illustrate how the hyperbolic efficiency estimator might be used in a robust context. © 2012 Elsevier B.V. All rights reserved.

Suggested Citation

  • Christopher Bruffaerts & Bram De Rock & Catherine Dehon, 2013. "The robustness of the hyperbolic efficiency estimator," ULB Institutional Repository 2013/131706, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:ulb:ulbeco:2013/131706
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    References listed on IDEAS

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    1. Cherchye, L. & Abeele, P. Vanden, 2005. "On research efficiency: A micro-analysis of Dutch university research in Economics and Business Management," Research Policy, Elsevier, vol. 34(4), pages 495-516, May.
    2. repec:hal:journl:peer-00796744 is not listed on IDEAS
    3. 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.
    4. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    5. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(02), pages 358-389, April.
    6. Daouia, Abdelaati & Gijbels, Irène, 2011. "Robustness and inference in nonparametric partial frontier modeling," Journal of Econometrics, Elsevier, vol. 161(2), pages 147-165, April.
    7. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
    8. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
    9. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
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    Cited by:

    1. Christopher Bruffaerts & Bram De Rock & Catherine Dehon, 2014. "Outlier Detection in Nonparametric Frontier Models," Working Papers ECARES ECARES 2014-12, ULB -- Universite Libre de Bruxelles.
    2. Song, Junmo & Oh, Dong-hyun & Kang, Jiwon, 2017. "Robust estimation in stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 243-267.
    3. Xia, X.H. & Chen, Y.B. & Li, J.S. & Tasawar, H. & Alsaedi, A. & Chen, G.Q., 2014. "Energy regulation in China: Objective selection, potential assessment and responsibility sharing by partial frontier analysis," Energy Policy, Elsevier, vol. 66(C), pages 292-302.
    4. Ghulam, Yaseen & Jaffry, Shabbar, 2015. "Efficiency and productivity of the cement industry: Pakistani experience of deregulation and privatisation," Omega, Elsevier, vol. 54(C), pages 101-115.
    5. Christopher Bruffaerts & Bram De Rock & Catherine Dehon, 2013. "The Research Efficiency of US Universities: a Nonparametric Frontier Modelling Approach," Working Papers ECARES ECARES 2013-31, ULB -- Universite Libre de Bruxelles.

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