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Linearly interpolated FDH efficiency score for nonconvex frontiers

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Author Info

  • Jeong, Seok-Oh
  • Simar, Léopold

Abstract

This paper addresses the problem of estimating the monotone boundary of a nonconvex set in a full nonparametric and multivariate setup. This is particularly useful in the context of productivity analysis where the efficient frontier is the locus of optimal production scenarios. Then efficiency scores are defined by the distance of a firm from this efficient boundary. In this setup, the free disposal hull (FDH) estimator has been extensively used due to its flexibility and because it allows nonconvex attainable production sets. However, the nonsmoothness and discontinuities of the FDH is a drawback for conducting inference in finite samples. In particular, it is shown that the bootstrap of the FDH has poor performances and so is not useful in practice. Our estimator, the LFDH, is a linearized version of the FDH, obtained by linear interpolation of appropriate FDH-efficient vertices. It offers a continuous, smooth version of the FDH. We provide an algorithm for computing the estimator, and we establish its asymptotic properties. We also provide an easy way to approximate its asymptotic sampling distribution. The latter could offer bias-corrected estimator and confidence intervals of the efficiency scores. In a Monte Carlo study, we show that these approximations work well even in moderate sample sizes and that our LFDH estimator outperforms, both in bias and in MSE, the original FDH estimator.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 97 (2006)
Issue (Month): 10 (November)
Pages: 2141-2161

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Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2141-2161

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Related research

Keywords: Nonparametric frontiers Nonconvex monotone boundaries Efficiency Bootstrapping FDH;

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Citations

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Cited by:
  1. Léopold Simar, 2007. "How to improve the performances of DEA/FDH estimators in the presence of noise?," Journal of Productivity Analysis, Springer, vol. 28(3), pages 183-201, December.
  2. Luiza Badin & Cinzia Daraio & Léopold Simar, 2008. "Optimal Bandwidth Selection for Conditional Efficiency Measures: a Data-driven Approach," LEM Papers Series 2008/22, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  3. Halkos, George E. & Tzeremes, Nickolaos G., 2011. "A conditional nonparametric analysis for measuring the efficiency of regional public healthcare delivery: An application to Greek prefectures," Health Policy, Elsevier, vol. 103(1), pages 73-82.
  4. Alois Kneip & Léopold Simar & Paul Wilson, 2011. "A Computationally Efficient, Consistent Bootstrap for Inference with Non-parametric DEA Estimators," Computational Economics, Society for Computational Economics, vol. 38(4), pages 483-515, November.
  5. Daniel Becker, 2008. "Public-Sector Efficiency and Interjurisdictional Competition - an Empirical Investigation," Thuenen-Series of Applied Economic Theory 101, University of Rostock, Institute of Economics, Germany.
  6. Halkos, George & Tzeremes, Nickolaos, 2009. "Exploring the effect of countries’ economic prosperity on their biodiversity performance," MPRA Paper 32102, University Library of Munich, Germany.
  7. George Halkos & Nickolaos Tzeremes, 2010. "The effect of foreign ownership on SMEs performance: An efficiency analysis perspective," Journal of Productivity Analysis, Springer, vol. 34(2), pages 167-180, October.
  8. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.

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