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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

  • Walter Briec

    ()

    (University of Perpignan)

  • Kristiaan Kerstens

    ()

    (CNRS-LEM and IESEG School of Management)

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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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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  1. H. Leleu, 2006. "A linear programming framework for free disposal hull technologies and cost functions: primal and dual models," Post-Print hal-00204497, HAL.
  2. W. Briec & K. Kerstens & P. Vanden Eeckaut, 2006. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Post-Print hal-00211174, HAL.
  3. 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, vol. 87(3), pages 307-308, 04.
  4. François Mairesse & Philippe Vanden Eeckaut, 2002. "Museum assessment and FDH technology: Towards a global approach," ULB Institutional Repository 2013/166509, ULB -- Universite Libre de Bruxelles.
  5. Sylvain Bouhnik & Boaz Golany & Ury Passy & Steven Hackman & Dimitra Vlatsa, 2001. "Lower Bound Restrictions on Intensities in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 16(3), pages 241-261, November.
  6. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
  7. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
  8. Alam, Ila M Semenick & Sickles, Robin C, 2000. "Time Series Analysis of Deregulatory Dynamics and Technical Efficiency: The Case of the U.S. Airline Industry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 203-18, February.
  9. 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, vol. 14(3), pages 267-274, November.
  10. Simar, L. & Wilson, P.W., 1999. "Statistical Inference in Nonparametric Frontier Models: the State of the Art," Papers 9904, Catholique de Louvain - Institut de statistique.
  11. DE BORGER, Bruno & FERRIER, G.D. & KERSTENS, K., 1995. "The choice of a technical efficiency measure on the Free Disposal Hull reference technology: A comparison using US banking data," SESO Working Papers 1995001, University of Antwerp, Faculty of Applied Economics.
  12. Tone, Kaoru & Sahoo, Biresh K., 2003. "Scale, indivisibilities and production function in data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 84(2), pages 165-192, May.
  13. Thore, Sten, 1996. "Economies of Scale in the US Computer Industry: An Empirical Investigation Using Data Envelopment Analysis," Journal of Evolutionary Economics, Springer, vol. 6(2), pages 199-216, May.
  14. Scarf, Herbert E, 1986. "Neighborhood Systems for Production Sets with Indivisibilities," Econometrica, Econometric Society, vol. 54(3), pages 507-32, May.
  15. Destefanis, Sergio, 2002. "The Verdoorn Law: Some Evidence from Non-parametric Frontier Analysis," MPRA Paper 60954, University Library of Munich, Germany.
  16. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.
  17. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
  18. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
  19. Bauer, Paul W. & Hancock, Diana, 1993. "The efficiency of the Federal Reserve in providing check processing services," Journal of Banking & Finance, Elsevier, vol. 17(2-3), pages 287-311, April.
  20. Fare, Rolf & Li, Sung Ko, 1998. "Inner and outer approximations of technology: a data envelopment analysis approach," European Journal of Operational Research, Elsevier, vol. 105(3), pages 622-625, March.
  21. repec:cor:louvrp:-571 is not listed on IDEAS
  22. 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 1997013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  23. Drake, Leigh & Simper, R., 2003. "The measurement of English and Welsh police force efficiency: A comparison of distance function models," European Journal of Operational Research, Elsevier, vol. 147(1), pages 165-186, May.
  24. 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.
  25. Fare, Rolf & Grosskopf, Shawna & Lovell, C A Knox, 1983. " The Structure of Technical Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 85(2), pages 181-90.
  26. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part II: The Case of Two Activities," Econometrica, Econometric Society, vol. 49(2), pages 395-423, March.
  27. 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.
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