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

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  • 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.

Suggested Citation

  • Mette Asmild & Jens Leth Hougaard & Dorte Kronborg, 2012. "Do efficiency scores depend on input mix? A statistical test and empirical illustration," MSAP Working Paper Series 05_2012, University of Copenhagen, Department of Food and Resource Economics.
  • Handle: RePEc:foi:msapwp:05_2012
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    References listed on IDEAS

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    Cited by:

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    2. Min, Hokey & Joo, Seong-Jong, 2016. "A comparative performance analysis of airline strategic alliances using data envelopment analysis," Journal of Air Transport Management, Elsevier, vol. 52(C), pages 99-110.
    3. Natascha Eggers & Torsten Birth & Bernd Sankol & Lukas Kerpen & Antonio Hurtado, 2023. "A Literature Review on Existing Methods and Indicators for Evaluating the Efficiency of Power-to-X Processes," Clean Technol., MDPI, vol. 5(1), pages 1-23, January.
    4. Heesche, Emil & Asmild, Mette, 2022. "Controlling for environmental conditions in regulatory benchmarking," Utilities Policy, Elsevier, vol. 77(C).
    5. Sueyoshi, Toshiyuki & Ryu, Youngbok, 2022. "Performance assessment on technology transition from small businesses to the U.S. Department of Defense," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    6. Mehdi Toloo & Madjid Tavana, 2017. "A novel method for selecting a single efficient unit in data envelopment analysis without explicit inputs/outputs," Annals of Operations Research, Springer, vol. 253(1), pages 657-681, June.
    7. Emil Heesche & Mette Asmild, 2020. "Controlling for environmental conditions in regulatory benchmarking," IFRO Working Paper 2020/03, University of Copenhagen, Department of Food and Resource Economics.
    8. Mehdi Toloo & Mona Barat & Atefeh Masoumzadeh, 2015. "Selective measures in data envelopment analysis," Annals of Operations Research, Springer, vol. 226(1), pages 623-642, March.

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    Keywords

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