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Do efficiency scores depend on input mix? A statistical test and empirical illustration

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Author Info

  • Mette Asmild

    ()
    (Warwick Business School, University of Warwick)

  • Jens Leth Hougaard

    ()
    (Institute of Food and Resource Economics, University of Copenhagen)

  • Dorte Kronborg

    (Department of Finance, Copenhagen Business School)

Abstract

In this paper we examine the possibility of using the standard Kruskal-Wallis rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix. Recently, a general data generating process (DGP) suiting the DEA methodology has been formulated and some asymptotic properties of the DEA estimators have been established. In line with this generally accepted DGP, we formulate a conditional test for the assumption of mix independence. Since the DEA frontier is estimated, many standard assumptions for evaluating the test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, as it is shown here, is applicable when comparing distributions of efficiency scores in two or more groups in models with multiple inputs and one output with constant returns to scale. The approach is illustrated in an empirical case of demolition projects where we reject the assumption of mix independence. This means that it, in this case, is not meaningful to perform a complete ranking of the projects based on their efficiency scores. Thus the example illustrates how common practice can be inappropriate.

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File URL: http://okonomi.foi.dk/workingpapers/MSAPpdf/MSAP2012/MSAP_WP05_2012.pdf
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Bibliographic Info

Paper provided by University of Copenhagen, Department of Food and Resource Economics in its series MSAP Working Paper Series with number 05_2012.

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Length: 18 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:foi:msapwp:05_2012

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Web page: http://www.msap.life.ku.dk/
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Related research

Keywords: Data Envelopment Analysis (DEA); homogeneous efficiencies; small sample properties; Kruskal-Wallis; ranking; demolition projects;

This paper has been announced in the following NEP Reports:

References

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  1. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
  2. Alois Kneip & Léopold Simar & Paul W. Wilson, 2006. "Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models," Bonn Econ Discussion Papers bgse12_2006, University of Bonn, Germany.
  3. Adler, Nicole & Friedman, Lea & Sinuany-Stern, Zilla, 2002. "Review of ranking methods in the data envelopment analysis context," European Journal of Operational Research, Elsevier, vol. 140(2), pages 249-265, July.
  4. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
  5. Simar, Leopold & Zelenyuk, Valentin, 2004. "On testing equality of distributions of technical efficiency scores," MPRA Paper 28003, University Library of Munich, Germany.
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