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Directional distances and their robust versions: Computational and testing issues

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  • Daraio, Cinzia
  • Simar, Léopold

Abstract

Directional distance functions provide very flexible tools for investigating the performance of Decision Making Units (DMUs). Their flexibility relies on their ability to handle undesirable outputs and to account for non-discretionary inputs and/or outputs by fixing zero values in some elements of the directional vector. Simar and Vanhems (2012) and Simar, Vanhems, and Wilson (2012) indicate how the statistical properties of Farrell–Debreu type of radial efficiency measures can be transferred to directional distances. Moreover, robust versions of these distances are also available, for conditional and unconditional measures. Bădin, Daraio, and Simar (2012) have shown how conditional radial distances are useful to investigate the effect of environmental factors on the production process. In this paper we develop the operational aspects for computing conditional and unconditional directional distances and their robust versions, in particular when some of the elements of the directional vector are fixed at zero. After that, we show how the approach of Bădin et al. (2012) can be adapted in a directional distance framework, including bandwidth selection and two-stage regression of conditional efficiency scores. Finally, we suggest a procedure, based on bootstrap techniques, for testing the significance of environmental factors on directional efficiency scores. The procedure is illustrated through simulated and real data.

Suggested Citation

  • Daraio, Cinzia & Simar, Léopold, 2014. "Directional distances and their robust versions: Computational and testing issues," European Journal of Operational Research, Elsevier, vol. 237(1), pages 358-369.
  • Handle: RePEc:eee:ejores:v:237:y:2014:i:1:p:358-369
    DOI: 10.1016/j.ejor.2014.01.064
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    1. Simar, Léopold & Wilson, Paul W., 2013. "Estimation and Inference in Nonparametric Frontier Models: Recent Developments and Perspectives," Foundations and Trends(R) in Econometrics, now publishers, vol. 5(3–4), pages 183-337, June.
    2. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
    3. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, September.
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    5. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
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