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Fast and Efficient Computation of Directional Distance Estimators

Author

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  • Cinzia Daraio

    (Department of Computer, Control and Management Engineering Antonio Ruberti (DIAG), University of Rome La Sapienza, Rome, Italy)

  • Léopold Simar

    (Institut de Statistique, Biostatistique et de Sciences Actuarielles, Universite´ Catholique de Louvain, Louvain-la-Neuve, Belgium)

  • Paul W. Wilson

    (Department of Economics and School of Computing, Division of Computer Science, Clemson University,Clemson, South Carolina, USA)

Abstract

Directional distances provide useful, flexible measures of technical efficiency of production units relative to the efficient frontier of the attainable set in input-output space. In addition, the additive nature of directional distances permits negative input for outputs quantities. The choice of the direction allows analysis of different strategies for the units attempting to reach the efficient frontier. Simar et al. (2012) and Simar and Vanhems (2012) develop asymptotic properties of full-envelopment, FDH and DEA estimators of directional distances as well as robust order-m and order- a directional distance estimators. Extensions of these estimators to measures conditioned on environmental variables Z are also available (e.g., see Daraio and Simar, 2014). The resulting estimators have been shown to share the properties of their corresponding radial measures. However, to date the algorithms proposed for computing the directional distance estimates suffer from various numerical drawbacks (Daraio and Simar, 2014). In particular, for the order-m versions (conditional and unconditional) only approximations, based on Monte-Carlo methods, have been suggested, involving additional computational burden. In this paper we propose a new fast and efficient method to compute exact values of the directional distance estimates for all the cases (full and partial frontier cases, unconditional or conditional to external factors), that overcome all previous difficulties. This new method is illustrated on simulated and real data sets.Matlab code for computation is provided in an appendix.

Suggested Citation

  • Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Fast and Efficient Computation of Directional Distance Estimators," DIAG Technical Reports 2018-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
  • Handle: RePEc:aeg:report:2018-05
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    Cited by:

    1. Fall, F.S. & Tchakoute Tchuigoua, H. & Vanhems, A. & Simar, L., 2021. "Gender effect on microfinance social efficiency: A robust nonparametric approach," European Journal of Operational Research, Elsevier, vol. 295(2), pages 744-757.
    2. Khezrimotlagh, Dariush & Cook, Wade D. & Zhu, Joe, 2020. "A nonparametric framework to detect outliers in estimating production frontiers," European Journal of Operational Research, Elsevier, vol. 286(1), pages 375-388.
    3. Fusco, Elisa & Vidoli, Francesco & Rogge, Nicky, 2020. "Spatial directional robust Benefit of the Doubt approach in presence of undesirable output: An application to Italian waste sector," Omega, Elsevier, vol. 94(C).
    4. Francisco Javier Sáez-Fernández & Ignacio Jiménez-Hernández & María del Sol Ostos-Rey, 2020. "Seasonality and Efficiency of the Hotel Industry in the Balearic Islands: Implications for Economic and Environmental Sustainability," Sustainability, MDPI, Open Access Journal, vol. 12(9), pages 1-17, April.
    5. Daraio, Cinzia & Simar, Léopold & Wilson, Paul W., 2021. "Quality as a latent heterogeneity factor in the efficiency of universities," Economic Modelling, Elsevier, vol. 99(C).
    6. Thyago C. C. Nepomuceno & Cinzia Daraio & Ana Paula C. S. Costa, 2021. "Multicriteria Ranking for the Efficient and Effective Assessment of Police Departments," Sustainability, MDPI, Open Access Journal, vol. 13(8), pages 1-15, April.
    7. Kounetas, Konstantinos E. & Polemis, Michael L. & Tzeremes, Nickolaos G., 2021. "Measurement of eco-efficiency and convergence: Evidence from a non-parametric frontier analysis," European Journal of Operational Research, Elsevier, vol. 291(1), pages 365-378.
    8. Michael L. Polemis & Thanasis Stengos & Nickolaos G. Tzeremes, 2020. "Modeling the effect of competition on US manufacturing sectors’ efficiency: an order-m frontier analysis," Journal of Productivity Analysis, Springer, vol. 54(1), pages 27-41, August.

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    Keywords

    directional distances ; conditional efficiency ; robust frontiers ; environmental factors ; nonparametric methods;
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