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Efficiency and benchmarking with directional distances. A data driven approach

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  • Cinzia Daraio

    ()
    (Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza")

  • Leopold Simar

    ()
    (Institute of Statistics, Biostatistics et Actuarial Sciences, Universite' Catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

In efficiency analysis the assessment of the performance of Decision Making Units (DMUs) relays on the selection of the direction along which the distance from the efficient frontier is measured. Directional Distance Functions (DDFs) represent a flexible way to gauge the inefficiency of DMUs. Permitting the selection of a direction towards the efficient frontier is often useful in empirical applications. As a matter of fact, many papers in the literature have proposed specific DDFs suitable for different contexts of application. Nevertheless, the selection of a direction implies the choice of an efficiency target which is imposed to all the analyzed DMUs. Moreover, there exist many situations in which there is no a priori economic or managerial rationale to impose a subjective efficiency target. In this paper we propose a data-driven approach to find out an ÒobjectiveÓ direction along which to gauge the inefficiency of each DMU. Our approach permits to take into account for the heterogeneity of DMUs and their diverse contexts that may influence their input and/or output mixes. Our method is also a data driven technique for benchmarking each DMU. We describe how to implement our framework and illustrate its usefulness with simulated and real datasets.

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File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/report/2014-07.pdf
File Function: First version, 2014
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Bibliographic Info

Paper provided by Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza" in its series DIAG Technical Reports with number 2014-07.

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Date of creation: 2014
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Handle: RePEc:aeg:report:2014-07

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Keywords: DEA; benchmarking; directional distance functions; nonparametric estimation; heterogeneity; performance; productivity; organizational studies;

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References

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  1. 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.
  2. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, Elsevier, vol. 70(2), pages 407-419, August.
  3. Korhonen, Pekka & Tainio, Risto & Wallenius, Jyrki, 2001. "Value efficiency analysis of academic research," European Journal of Operational Research, Elsevier, Elsevier, vol. 130(1), pages 121-132, April.
  4. R. Färe & S. Grosskopf & G. Whittaker, 2013. "Directional output distance functions: endogenous directions based on exogenous normalization constraints," Journal of Productivity Analysis, Springer, Springer, vol. 40(3), pages 267-269, December.
  5. Simar, Léopold & Vanhems, Anne, 2010. "Probabilistic Characterization of Directional Distances and their Robust Versions," TSE Working Papers, Toulouse School of Economics (TSE) 10-195, Toulouse School of Economics (TSE).
  6. A. Charnes & W. W. Cooper & E. Rhodes, 1981. "Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through," Management Science, INFORMS, INFORMS, vol. 27(6), pages 668-697, June.
  7. K Kerstens & A Mounir & I Van de Woestyne, 2012. "Benchmarking mean-variance portfolios using a shortage function: the choice of direction vector affects rankings!," Journal of the Operational Research Society, Palgrave Macmillan, vol. 63(9), pages 1199-1212, September.
  8. Emrouznejad, Ali & Parker, Barnett R. & Tavares, Gabriel, 2008. "Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA," Socio-Economic Planning Sciences, Elsevier, Elsevier, vol. 42(3), pages 151-157, September.
  9. Jose Zofio & Jesus Pastor & Juan Aparicio, 2013. "The directional profit efficiency measure: on why profit inefficiency is either technical or allocative," Journal of Productivity Analysis, Springer, Springer, vol. 40(3), pages 257-266, December.
  10. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521355643.
  11. Dyson, Robert G., 2004. "Strategic development and SWOT analysis at the University of Warwick," European Journal of Operational Research, Elsevier, Elsevier, vol. 152(3), pages 631-640, February.
  12. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
  13. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2013. "Non-parametric Regression for Circular Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 238-255, 06.
  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. Jeffrey Racine, 2008. "Nonparametric econometrics: a primer (in Russian)," Quantile, Quantile, Quantile, issue 4, pages 7-56, March.
  16. Antonio Peyrache & Cinzia Daraio, 2012. "Empirical tools to assess the sensitivity of directional distance functions to direction selection," Applied Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 44(8), pages 933-943, March.
  17. Wilson, Paul W, 1993. "Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 11(3), pages 319-23, July.
  18. 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.
  19. Racine, Jeffrey S., 2008. "Nonparametric Econometrics: A Primer," Foundations and Trends(R) in Econometrics, now publishers, now publishers, vol. 3(1), pages 1-88, March.
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