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A DEA Estimation of a Lower Bound for Firms' Allocative Efficiency Without Information on Price Data

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  • H. Leleu

    (UMR CNRS 8179 - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

  • W. Briec

Abstract

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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Suggested Citation

  • H. Leleu & W. Briec, 2009. "A DEA Estimation of a Lower Bound for Firms' Allocative Efficiency Without Information on Price Data," Post-Print halshs-00476537, HAL.
    • Handle: RePEc:hal:journl:halshs-00476537
    DOI: 10.1016/j.ijpe.2009.05.002
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    Cited by:

    1. Aparicio, Juan & Pastor, Jesus T. & Ray, Subhash C., 2013. "An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’," European Journal of Operational Research, Elsevier, vol. 226(1), pages 154-162.
    2. Fang, Lei & Li, Hecheng, 2013. "A comment on “solving the puzzles of structural efficiency”," European Journal of Operational Research, Elsevier, vol. 230(2), pages 444-446.
    3. Arnaud Abad & Rabaozafy Louisa Andriamasy & Walter Briec, 2018. "Surplus measures and luenberger Hicks–Moorsteen productivity indicator," Journal of Economics, Springer, vol. 125(3), pages 279-308, November.
    4. Färe, Rolf & Grosskopf, Shawna & Karagiannis, Giannis, 2018. "On technical inefficiency indicators at the industry level," International Journal of Production Economics, Elsevier, vol. 196(C), pages 333-334.
    5. Walheer, Barnabe & Hudik, Marek, 2019. "Reallocation of resources in multidivisional firms: A nonparametric approach," International Journal of Production Economics, Elsevier, vol. 214(C), pages 196-205.
    6. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    7. Francesco Sandulli & José Fernández-Menéndez & Antonio Rodríguez-Duarte & José López-Sánchez, 2012. "The productivity payoff of information technology in multimarket SMEs," Small Business Economics, Springer, vol. 39(1), pages 99-117, July.
    8. Juan Aparicio & Jesus T. Pastor & Subhash Ray, 2012. "An Overall Measure of Technical Inefficiency at the Firm and at the Industrial Level: The 'Lost Return on the Dollar' Revisited," Working papers 2012-02, University of Connecticut, Department of Economics.
    9. Rolf Färe & Giannis Karagiannis, 2022. "Aggregation and decomposition of Farrell efficiencies," Operational Research, Springer, vol. 22(5), pages 5675-5683, November.
    10. Mahlberg, Bernhard & Sahoo, Biresh K., 2011. "Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application," International Journal of Production Economics, Elsevier, vol. 131(2), pages 721-726, June.

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