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A DEA estimation of a lower bound for firms' allocative efficiency without information on price data

  • Leleu, Hervé
  • Briec, Walter

In this paper, we estimate a lower bound for the sum of firms' allocative efficiencies in the absence of information on prices. For this purpose, we only estimate technical efficiency at both the firm and the industry level using a directional distance function and choosing a relevant direction. Our result relies on the decomposition of overall inefficiency into technical and allocative inefficiency at both the firm and the industry level. The convexity of a technology induces a transfer from both total technical inefficiency and part of allocative inefficiency at the firm level to technical inefficiency solely at the industry level. The remaining firms' allocative inefficiency could be counted at the industry level. Hence, the difference between technical inefficiencies at both levels can be interpreted as a lower bound for the sum of allocative inefficiency in the industry. We show how to implement this bound in a DEA framework.

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Article provided by Elsevier in its journal International Journal of Production Economics.

Volume (Year): 121 (2009)
Issue (Month): 1 (September)
Pages: 203-211

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Handle: RePEc:eee:proeco:v:121:y:2009:i:1:p:203-211
Contact details of provider: Web page: http://www.elsevier.com/locate/ijpe

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  1. Subhash C. Ray & Lei Chen & Kankana Mukherjee, 2008. "Input Price Variation Across Locations and a Generalized Measure of Cost Efficiency," Working papers 2008-11, University of Connecticut, Department of Economics.
  2. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
  3. Cherchye, Laurens & Kuosmanen, Timo & Post, Thierry, 2002. "Non-parametric production analysis in non-competitive environments," International Journal of Production Economics, Elsevier, vol. 80(3), pages 279-294, December.
  4. Rodriguez-Alvarez, Ana & Fernandez-Blanco, Victor & Lovell, C. A. Knox, 2004. "Allocative inefficiency and its cost:: The case of Spanish public hospitals," International Journal of Production Economics, Elsevier, vol. 92(2), pages 99-111, November.
  5. Briec, W. & Lemaire, B., 1999. "Technical efficiency and distance to a reverse convex set," European Journal of Operational Research, Elsevier, vol. 114(1), pages 178-187, April.
  6. Walter Briec & Benoit Dervaux & Hervé Leleu, 2003. "Aggregation of Directional Distance Functions and Industrial Efficiency," Journal of Economics, Springer, vol. 79(3), pages 237-261, 07.
  7. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
  8. Walter Briec & Christine Comes & Kristiaan Kerstens, 2005. "Temporal Technical and Profit Efficiency Measurement: Definitions, Duality and Aggregation Results," Working Papers 2005-ECO-01, IESEG School of Management.
  9. Ylvinger, Svante, 2000. "Industry performance and structural efficiency measures: Solutions to problems in firm models," European Journal of Operational Research, Elsevier, vol. 121(1), pages 164-174, February.
  10. Halme, Merja & Joro, Tarja & Koivu, Matti, 2002. "Dealing with interval scale data in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 137(1), pages 22-27, February.
  11. Fare, Rolf & Grosskopf, Shawna & Li, Sung-Ko, 1992. " Linear Programming Models for Firm and Industry Performance," Scandinavian Journal of Economics, Wiley Blackwell, vol. 94(4), pages 599-608.
  12. W. Briec & C. Comes & K. Kerstens, 2006. "Temporal technical and profit efficiency measurement: Definitions, duality and aggregation results," Post-Print hal-00211164, HAL.
  13. Rodriguez-Alvarez, Ana & Tovar, Beatriz & Trujillo, Lourdes, 2007. "Firm and time varying technical and allocative efficiency: An application to port cargo handling firms," International Journal of Production Economics, Elsevier, vol. 109(1-2), pages 149-161, September.
  14. 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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