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

Author Info

Listed author(s):
  • Jose Zofio

    ()

  • Jesus Pastor

    ()

  • Juan Aparicio

    ()

Abstract

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

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File URL: http://hdl.handle.net/10.1007/s11123-012-0292-0
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Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 40 (2013)
Issue (Month): 3 (December)
Pages: 257-266

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Handle: RePEc:kap:jproda:v:40:y:2013:i:3:p:257-266
DOI: 10.1007/s11123-012-0292-0
Contact details of provider: Web page: http://www.springer.com

Order Information: Web: http://www.springer.com/economics/microeconomics/journal/11123/PS2

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

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Find related papers by 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

References listed on IDEAS
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  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.
  2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  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. Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Southern Economic Journal, Southern Economic Association, vol. 66(2), pages 294-318, October.
  12. 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.
  13. 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.
  14. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
  15. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
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Cited by:

  1. 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.
  2. 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.
  3. 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).
  4. repec:eee:ejores:v:262:y:2017:i:2:p:792-801 is not listed on IDEAS
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. repec:eee:ejores:v:262:y:2017:i:1:p:361-369 is not listed on IDEAS
  10. 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.
  11. 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.
  12. Aparicio, Juan & Zofío, José L., 2017. "Revisiting the Decomposition of Cost Efficiency for Non-homothetic Technologies: A Directional Distance Function Approach," Efficiency Series Papers 2017/01, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).

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