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

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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.

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Bibliographic Info

Paper provided by Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History) in its series Working Papers in Economic Theory with number 2010/09.

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Length: 29 pages
Date of creation: Nov 2010
Date of revision:
Handle: RePEc:uam:wpaper:201009

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Keywords: Directional Distance Function; Profit Efficiency; Technical Efficiency; Allocative Efficiency; Data Envelopment Analysis.;

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  1. Bogetoft, Peter & Fare, Rolf, 1999. "Allocative Efficiency of Technically Inefficient Production Units," Unit of Economics Working papers 24217, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
  2. 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.
  3. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  4. 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.
  5. 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.
  6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  7. 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.
  8. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-32, November.
  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.
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Cited by:
  1. Aparicio, Juan & Pastor, Jesús & Zofío, José Luis, 2013. "How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies," Working Papers in Economic Theory 2013/11, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).

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