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Probabilistic Characterization of Directional Distances and their Robust Versions

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  • Simar, Léopold
  • Vanhems, Anne

Abstract

In productivity analysis, the performance of production units is measured through the distance of the individual decision making units (DMU) to the technology which is defined as the frontier of the production set. Most of the existing methods, Farrell-Debreu and Shephard radial measures (input or output oriented) and hyperbolic distance functions, rely on multiplicative measures of the distance and so require to deal with strictly positive inputs and outputs. This can be critical when the data contain zero or negative values as in financial data bases for the measure of funds performances. Directional distance function is an alternative that can be viewed as an additive measure of efficiency. We show in this paper that using a probabilistic formulation of the production process, the directional distance can be expressed as simple radial or hyperbolic distance up to a simple transformation of the inputs/outputs space. This allows to propose simple methods of estimation but also to transfer easily most of the known properties of the estimators shared by the radial and hyperbolic distances. In addition, the formulation allows to define robust directional distances in the lines of alpha-quantile or order-m partial frontiers. Finally we can also define conditional directional distance functions, conditional to environmental factors. To illustrate the methodology, we show how it can be implemented using a Mutual Funds database.

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Paper provided by Toulouse School of Economics (TSE) in its series TSE Working Papers with number 10-195.

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Date of creation: 30 Sep 2010
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Publication status: Published in Journal of Econometrics, vol.�166, n°2, 2012, p.�342-354.
Handle: RePEc:tse:wpaper:23435

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  1. Sushama Murty & R. Robert Russell & Steven B. Levkoff, 2011. "On modeling pollution-generating technologies," Discussion Papers, Exeter University, Department of Economics 1101, Exeter University, Department of Economics.
  2. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2012. "Regularization of nonparametric frontier estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 168(2), pages 285-299.
  3. 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.
  4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 7(1), pages 77-91, 03.
  5. 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, Elsevier, vol. 145(1-2), pages 209-225, July.
  6. Cinzia Daraio & Leopold Simar, 2003. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," LEM Papers Series 2003/17, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  7. Gregoriou, Greg N. & Sedzro, Komlan & Zhu, Joe, 2005. "Hedge fund performance appraisal using data envelopment analysis," European Journal of Operational Research, Elsevier, Elsevier, vol. 164(2), pages 555-571, July.
  8. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, Springer, vol. 36(1), pages 33-53, August.
  9. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, Elsevier, vol. 126(2), pages 469-492, June.
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  11. Fare, Rolf, et al, 1993. "Derivation of Shadow Prices for Undesirable Outputs: A Distance Function Approach," The Review of Economics and Statistics, MIT Press, vol. 75(2), pages 374-80, May.
  12. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2141-2161, November.
  13. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1663-1697, December.
  14. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, Springer, vol. 20(3), pages 391-424, November.
  15. 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.
  16. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, American Finance Association, vol. 23(2), pages 389-416, 05.
  17. 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.
  18. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, Elsevier, vol. 175(1), pages 516-542, November.
  19. Florens, Jean-Pierre & Simar, Leopold, 2005. "Parametric approximations of nonparametric frontiers," Journal of Econometrics, Elsevier, Elsevier, vol. 124(1), pages 91-116, January.
  20. Morey, Matthew R. & Morey, Richard C., 1999. "Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking," Omega, Elsevier, vol. 27(2), pages 241-258, April.
  21. 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.
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Citations

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Cited by:
  1. George Halkos & George Papageorgiou, 2014. "Spatial environmental efficiency indicators in regional waste generation: A nonparametric approach," DEOS Working Papers 1401, Athens University of Economics and Business.
  2. Halkos, George & Sundström, Aksel & Tzeremes, Nickolaos, 2013. "Environmental performance and quality of governance: A non-parametric analysis of the NUTS 1-regions in France, Germany and the UK," MPRA Paper 48890, University Library of Munich, Germany.
  3. Halkos, George & Tzeremes, Nickolaos, 2012. "Public sector transparency and countries’ environmental performance: A nonparametric analysis," MPRA Paper 39553, University Library of Munich, Germany.
  4. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "Economic growth and environmental efficiency: Evidence from US regions," Economics Letters, Elsevier, vol. 120(1), pages 48-52.
  5. Halkos, George & Tzeremes, Nickolaos, 2013. "An additive two-stage DEA approach creating sustainability efficiency indexes," MPRA Paper 44231, University Library of Munich, Germany.
  6. Bruffaerts, C. & De Rock, B. & Dehon, C., 2013. "The robustness of the hyperbolic efficiency estimator," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 57(1), pages 349-363.
  7. Halkos, George & Tzeremes, Nickolaos, 2013. "Renewable energy consumption and economic efficiency: Evidence from European countries," MPRA Paper 44136, University Library of Munich, Germany.
  8. Cinzia Daraio & Leopold Simar, 2013. "Directional Distances and their Robust versions. Computational and Testing Issues," DIAG Technical Reports 2013-11, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
  9. Halkos, George & Tzeremes, Nickolaos, 2012. "Regional economic growth and environmental efficiency in greenhouse emissions: A conditional directional distance function approach," MPRA Paper 40015, University Library of Munich, Germany.
  10. Cinzia Daraio & Leopold Simar, 2014. "Efficiency and benchmarking with directional distances. A data driven approach," DIAG Technical Reports 2014-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
  11. Halkos, George & Tzeremes, Nickolaos, 2012. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from the UK regions," MPRA Paper 38147, University Library of Munich, Germany.
  12. Wheelock, David C. & Wilson, Paul W., 2013. "The evolution of cost-productivity and efficiency among US credit unions," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 75-88.
  13. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions," European Journal of Operational Research, Elsevier, Elsevier, vol. 227(1), pages 182-189.
  14. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, Elsevier, vol. 220(3), pages 853-864.
  15. Minegishi, Kota, 2013. "Explaining Production Heterogeneity By Contextual Environments: Two-Stage DEA Application to Technical Change Measurement," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C., Agricultural and Applied Economics Association 150289, Agricultural and Applied Economics Association.
  16. Andrea Bonaccorsi & Cinzia Daraio & Leopold Simar, 2014. "Efficiency and economies of scale and scope in European universities. A directional distance approach," DIAG Technical Reports 2014-08, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".

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