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Input, Output and Graph Technical Efficiency Measures on Non-Convex FDH Models with Various Scaling Laws: An Integrated Approach Based upon Implicit Enumeration Algorithms

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  • Walter Briec

    ()
    (University of Perpignan)

  • Kristiaan Kerstens

    ()
    (CNRS-LEM and IESEG School of Management)

Abstract

In a recent article, Briec, Kerstens and Vanden Eeckaut (2004) develop a series of nonparametric, deterministic non-convex technologies integrating traditional returns to scale assumptions into the non-convex FDH model. They show, among other things, how the traditional technical input efficiency measure can be analytically derived for these technology specifications. In this paper, we develop a similar approach to calculate output and graph measures of technical efficiency and indicate the general advantage of such solution strategy via enumeration. Furthermore, several analytical formulas are established and some algorithms are proposed relating the three measurement orientations to one another.

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Bibliographic Info

Paper provided by IESEG School of Management in its series Working Papers with number 2005-ECO-04.

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Length: 29 pages
Date of creation: Aug 2005
Date of revision:
Publication status: Published in TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, June 2006, 14(1), pp. 135-166
Handle: RePEc:ies:wpaper:e200504

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Keywords: Data Envelopment Analysis; Free Disposal Hull; technical efficiency;

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References

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  1. Herbert E. Scarf, 1984. "Neighborhood Systems for Production Sets with Indivisibilities," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 728, Cowles Foundation for Research in Economics, Yale University.
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  3. KERSTENS, Kristiaan & VANDEN EECKAUT, Philippe, 1997. "Estimating returns to scale using nonparametric deterministic technologies : a new method based on goodness-of-fit," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1997013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  5. François Mairesse & Philippe Vanden Eeckaut, 2002. "Museum Assessment and FDH Technology: Towards a Global Approach," Journal of Cultural Economics, Springer, Springer, vol. 26(4), pages 261-286, November.
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  7. Walter Briec & Kristiaan Kerstens & Philippe Vanden Eeckaut, 2006. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity (Journal of Economics 81(2):155–192)," Journal of Economics, Springer, Springer, vol. 87(3), pages 307-308, 04.
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  17. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, Elsevier, vol. 2(6), pages 429-444, November.
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  19. Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, Elsevier, vol. 168(2), pages 340-344, January.
  20. Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, Springer, vol. 81(2), pages 155-192, 02.
  21. Borger, Bruno De & Ferrier, Gary D. & Kerstens, Kristiaan, 1998. "The choice of a technical efficiency measure on the free disposal hull reference technology: A comparison using US banking data," European Journal of Operational Research, Elsevier, Elsevier, vol. 105(3), pages 427-446, March.
  22. Fare, Rolf & Grosskopf, Shawna & Lovell, C A Knox, 1983. " The Structure of Technical Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, Wiley Blackwell, vol. 85(2), pages 181-90.
  23. Walter Briec & Kristiaan Kerstens & Hervé Leleu & Philippe Eeckaut, 2000. "Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies," Journal of Productivity Analysis, Springer, Springer, vol. 14(3), pages 267-274, November.
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