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The Directional Profit Efficiency Measure: On Why Profit Inefficiency is either Technical or Allocative

Author

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  • Zofío, José Luis

    (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.)

  • Pastor, Jesús

    (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

  • Aparicio, Juan

    (Center of Operations Research, Universidad Miguel Hernández, Elche, Spain)

Abstract

The directional distance function has been introduced in the efficiency literature with the intention of relaxing the fixed orientations represented by its classical input and output counterparts. 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 directional vector that projecting inefficient firms towards profit maximizing benchmarks. Based on that choice of directional vector, we introduce the profit efficiency measure and show that, in this general setting, profit inefficiency can be categorized as either technical -for firms situating in 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, where the profit maximizing benchmark may not be unique, and introduce the necessary optimizing program for profit inefficiency measurement.

Suggested Citation

  • Zofío, José Luis & Pastor, Jesús & Aparicio, Juan, 2010. "The Directional Profit Efficiency Measure: On Why Profit Inefficiency is either Technical or Allocative," Working Papers in Economic Theory 2010/09, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    • Handle: RePEc:uam:wpaper:201009
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    1. Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Southern Economic Journal, John Wiley & Sons, vol. 66(2), pages 294-318, October.
    2. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    3. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    4. Silva Portela, Maria Conceicao A. & Thanassoulis, Emmanuel, 2005. "Profitability of a sample of Portuguese bank branches and its decomposition into technical and allocative components," European Journal of Operational Research, Elsevier, vol. 162(3), pages 850-866, May.
    5. Bogetoft, Peter & Fare, Rolf & Obel, Borge, 2006. "Allocative efficiency of technically inefficient production units," European Journal of Operational Research, Elsevier, vol. 168(2), pages 450-462, January.
    6. 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.
    7. Cooper, W.W. & Pastor, Jesus T. & Aparicio, Juan & Borras, Fernando, 2011. "Decomposing profit inefficiency in DEA through the weighted additive model," European Journal of Operational Research, Elsevier, vol. 212(2), pages 411-416, July.
    8. Asmild, Mette & Paradi, Joseph C. & Reese, David N. & Tam, Fai, 2007. "Measuring overall efficiency and effectiveness using DEA," European Journal of Operational Research, Elsevier, vol. 178(1), pages 305-321, April.
    9. Subhash Ray, 2007. "Shadow profit maximization and a measure of overall inefficiency," Journal of Productivity Analysis, Springer, vol. 27(3), pages 231-236, June.
    10. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-1332, November.
    11. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    12. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264, September.
    13. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    14. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    15. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
    16. Wade D. Cook & Joe Zhu, 2007. "Data Irregularities And Structural Complexities In Dea," Springer Books, in: Joe Zhu & Wade D. Cook (ed.), Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis, chapter 0, pages 1-11, Springer.
    17. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    18. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    19. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
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    More about this item

    Keywords

    Directional Distance Function; Profit Efficiency; Technical Efficiency; Allocative Efficiency; Data Envelopment Analysis.;
    All these keywords.

    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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