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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.

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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series ULB Institutional Repository with number 2013/131706.

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Date of creation: 2013
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Publication status: Forthcoming
Handle: RePEc:ulb:ulbeco:2013/131706

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References

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  1. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 375-400, October.
  2. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, Elsevier, vol. 166(2), pages 342-354.
  3. Laurens Cherchye & Piet Vanden Abeele, 2002. "On Research Efficiency: A Micro-Analysis of Dutch University Research in Economics and Business Management," Public Economics Working Paper Series, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, Working Group Public Economics ces0206, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, Working Group Public Economics.
  4. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, Elsevier, vol. 106(1), pages 1-25, January.
  5. David C. Wheelock & Paul Wilson, 2007. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Working Papers, Federal Reserve Bank of St. Louis 2005-027, Federal Reserve Bank of St. Louis.
  6. Abdelaati Daouia & Irène Gijbels, 2011. "Robustness and inference in nonparametric partial-frontier modeling," Post-Print, HAL peer-00796744, HAL.
  7. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 21(02), pages 358-389, April.
  8. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, Springer, vol. 13(2), pages 93-103, March.
  9. Daouia, Abdelaati & Gijbels, Irène, 2011. "Robustness and inference in nonparametric partial frontier modeling," Journal of Econometrics, Elsevier, Elsevier, vol. 161(2), pages 147-165, April.
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Cited by:
  1. 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, Elsevier, vol. 66(C), pages 292-302.

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