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The directional profit efficiency measure: on why profit inefficiency is either technical or allocative


  • Jose Zofio


  • Jesus Pastor


  • Juan Aparicio



The directional distance function encompasses Shephard’s input and output distance functions and also allows nonradial projections of the assessed firm onto the frontier of the technology in a preassigned direction. However, the criteria underlying the choice of its associated directional vector are numerous. When market prices are observed and firms have a profit maximizing behavior, it seems natural to choose as the directional vector that projecting inefficient firms towards profit maximizing benchmarks. Based on that choice of directional vector, we introduce the directional profit efficiency measure and show that, in this general setting, profit inefficiency can be categorized as either technical, for firms situated within the interior of the technology, or allocative, for firms lying on the frontier. We implement and illustrate the analytical model by way of Data Envelopment Analysis techniques, and introduce the necessary optimization programs for profit inefficiency measurement. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Jose Zofio & Jesus Pastor & Juan Aparicio, 2013. "The directional profit efficiency measure: on why profit inefficiency is either technical or allocative," Journal of Productivity Analysis, Springer, vol. 40(3), pages 257-266, December.
  • Handle: RePEc:kap:jproda:v:40:y:2013:i:3:p:257-266
    DOI: 10.1007/s11123-012-0292-0

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    References listed on IDEAS

    1. J L Ruiz & I Sirvent, 2011. "A DEA approach to derive individual lower and upper bounds for the technical and allocative components of the overall profit efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 1907-1916, November.
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    Cited by:

    1. repec:kap:jproda:v:48:y:2017:i:2:d:10.1007_s11123-017-0512-8 is not listed on IDEAS
    2. Pastor, Jesus T. & Zofio, Jose L., 2017. "Can Farrell's allocative efficiency be generalized by the directional distance function approach?Author-Name: Aparicio, Juan," European Journal of Operational Research, Elsevier, vol. 257(1), pages 345-351.
    3. 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.
    4. Álvarez, Inmaculada & Barbero, Javier & Zofío, Jose Luis, 2016. "A Data Envelopment Analysis Toolbox for MATLAB," Working Papers in Economic Theory 2016/03, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    5. repec:eee:jomega:v:72:y:2017:i:c:p:1-14 is not listed on IDEAS
    6. repec:eee:ejores:v:262:y:2017:i:2:p:792-801 is not listed on IDEAS
    7. repec:spr:empeco:v:54:y:2018:i:1:d:10.1007_s00181-017-1233-6 is not listed on IDEAS
    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. Mircea Epure, 2016. "Benchmarking for routines and organizational knowledge: a managerial accounting approach with performance feedback," Journal of Productivity Analysis, Springer, vol. 46(1), pages 87-107, August.
    10. Lee, Chia-Yen, 2014. "Meta-data envelopment analysis: Finding a direction towards marginal profit maximization," European Journal of Operational Research, Elsevier, vol. 237(1), pages 207-216.
    11. 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.
    12. repec:eee:ejores:v:266:y:2018:i:3:p:1013-1024 is not listed on IDEAS
    13. repec:eee:ejores:v:262:y:2017:i:1:p:361-369 is not listed on IDEAS
    14. Pedro Macedo & Elvira Silva, 2017. "Sensitivity of directional technical inefficiency measures to the choice of the direction vector: a simulation study," Economics Bulletin, AccessEcon, vol. 37(1), pages 52-62.
    15. Lee, Chia-Yen, 2016. "Nash-profit efficiency: A measure of changes in market structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 659-663.
    16. 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.

    More about this item


    Directional distance function; Profit efficiency; Technical efficiency; Allocative efficiency; C61; D21; D24;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity


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