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Statistical inference for DEA estimators of directional distances

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  • Simar, Léopold
  • Vanhems, Anne
  • Wilson, Paul W.

Abstract

In productivity and efficiency analysis, the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set. The most familiar non-parametric methods use Farrell–Debreu, Shephard, or hyperbolic radial measures. These approaches require that inputs and outputs be non-negative, which can be problematic when using financial data. Recently, Chambers et al. (1998) have introduced directional distance functions which can be viewed as additive (rather than multiplicative) measures efficiency. Directional distance functions are not restricted to non-negative input and output quantities; in addition, the traditional input and output-oriented measures are nested as special cases of directional distance functions. Consequently, directional distances provide greater flexibility. However, until now, only free disposal hull (FDH) estimators of directional distances (and their conditional and robust extensions) have known statistical properties (Simar and Vanhems, 2012). This paper develops the statistical properties of directional d estimators, which are especially useful when the production set is assumed convex. We first establish that the directional Data Envelopment Analysis (DEA) estimators share the known properties of the traditional radial DEA estimators. We then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance, estimation of confidence intervals, and bias correction. The methods are illustrated in some empirical examples.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:220:y:2012:i:3:p:853-864
    DOI: 10.1016/j.ejor.2012.02.030
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    References listed on IDEAS

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    1. repec:kap:jproda:v:48:y:2017:i:2:d:10.1007_s11123-017-0512-8 is not listed on IDEAS
    2. 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.
    3. George E. Halkos & Roman Matousek & Nickolaos G. Tzeremes, 2016. "Pre-evaluating technical efficiency gains from possible mergers and acquisitions: evidence from Japanese regional banks," Review of Quantitative Finance and Accounting, Springer, vol. 46(1), pages 47-77, January.
    4. Minegishi, Kota, 2014. "Integrating Efficiency Concepts in Technology Approximation: A Weighted DEA Approach," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170277, Agricultural and Applied Economics Association.
    5. Ke Wang & Yujiao Xian & Chia-Yen Lee & Yi-Ming Wei & Zhimin Huang, 2017. "On selecting directions for directional distance functions in a non-parametric framework: A review," CEEP-BIT Working Papers 99, Center for Energy and Environmental Policy Research (CEEP), Beijing Institute of Technology.
    6. Kapelko, M. & Horta, I.M. & Camanho, A.S. & Oude Lansink, A., 2015. "Measurement of input-specific productivity growth with an application to the construction industry in Spain and Portugal," International Journal of Production Economics, Elsevier, vol. 166(C), pages 64-71.
    7. Minegishi, Kota, 2013. "Explaining Production Heterogeneity By Contextual Environments: Two-Stage DEA Application to Technical Change Measurement," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150289, Agricultural and Applied Economics Association.
    8. Aparicio, Juan & Pastor, Jesus T. & Zofio, Jose L., 2015. "How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies," European Journal of Operational Research, Elsevier, vol. 240(3), pages 882-891.
    9. Hampf, Benjamin & Rødseth, Kenneth Løvold, 2015. "Carbon dioxide emission standards for U.S. power plants: An efficiency analysis perspective," Energy Economics, Elsevier, vol. 50(C), pages 140-153.
    10. Cinzia Daraio & Léopold Simar, 2016. "Efficiency and benchmarking with directional distances: a data-driven approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(7), pages 928-944, July.
    11. Hampf, Benjamin & Krüger, Jens J., 2013. "Optimal Directions for Directional Distance Functions: An Exploration of Potential Reductions of Greenhouse Gases," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79699, Verein für Socialpolitik / German Economic Association.
    12. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    13. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    14. Duan, Na & Guo, Jun-Peng & Xie, Bai-Chen, 2016. "Is there a difference between the energy and CO2 emission performance for China’s thermal power industry? A bootstrapped directional distance function approach," Applied Energy, Elsevier, vol. 162(C), pages 1552-1563.
    15. repec:eee:eneeco:v:66:y:2017:i:c:p:279-289 is not listed on IDEAS
    16. Falavigna, Greta & Ippoliti, Roberto & Manello, Alessandro & Ramello, Giovanni B., 2015. "Judicial productivity, delay and efficiency: A Directional Distance Function (DDF) approach," European Journal of Operational Research, Elsevier, vol. 240(2), pages 592-601.
    17. repec:spr:empeco:v:54:y:2018:i:1:d:10.1007_s00181-017-1232-7 is not listed on IDEAS
    18. Thanassoulis, Emmanuel & Silva Portela, Maria & Graveney, Mike, 2016. "Identifying the scope for savings at inpatient episode level: An illustration applying DEA to chronic obstructive pulmonary disease," European Journal of Operational Research, Elsevier, vol. 255(2), pages 570-582.
    19. Sahoo, Biresh K. & Singh, Ramadhar & Mishra, Bineet & Sankaran, Krithiga, 2017. "Research productivity in management schools of India during 1968-2015: A directional benefit-of-doubt model analysis," Omega, Elsevier, vol. 66(PA), pages 118-139.
    20. Hampf, Benjamin & Rødseth, Kenneth Løvold, 2014. "Carbon dioxide emission standards for US power plants: An efficiency analysis perspective," Darmstadt Discussion Papers in Economics 219, Darmstadt University of Technology, Department of Law and Economics.
    21. Juan Aparicio & José L. Zofío, 2017. "Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 133-146, December.
    22. Manh D. Pham & Valentin Zelenyuk, 2018. "Slack-based directional distance function in the presence of bad outputs: theory and application to Vietnamese banking," Empirical Economics, Springer, vol. 54(1), pages 153-187, February.

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