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Improvement of technical efficiency of firm groups

Author

Listed:
  • Louisa Andriamasy

    (CAEPEM - Centre d'Analyse de l'Efficience et de la Performance en Economie et Management - UPVD - Université de Perpignan Via Domitia)

  • Walter Briec

    (CAEPEM - Centre d'Analyse de l'Efficience et de la Performance en Economie et Management - UPVD - Université de Perpignan Via Domitia)

  • Stéphane Mussard

    (CHROME - Détection, évaluation, gestion des risques CHROniques et éMErgents (CHROME) / Université de Nîmes - UNIMES - Université de Nîmes)

Abstract

Cooperation between firms can never improve the technical efficiency of any coalition of firms. This standard result of the productivity measurement literature is based on the directional distance function computed on firm groups. Directional distance functions are usually defined on the standard sum of input/output vectors. In this paper, the aggregation of input/output vectors is generalized thanks to an isomorphism in order to capture three results: the cooperation improves technical efficiency ; the cooperation reduces technical efficiency ; and finally the cooperation between firms yields no variation of technical efficiency, i.e. , the distance function is quasi linear. The improvement of technical efficiency is shown to be compatible with semilattice technologies. In this case, the firms merge according to their inputs only because constraints are imposed on outputs, and conversely, they may merge according to the outputs they can produce because some limitations are imposed on the use of inputs.

Suggested Citation

  • Louisa Andriamasy & Walter Briec & Stéphane Mussard, 2016. "Improvement of technical efficiency of firm groups," Working Papers hal-01784209, HAL.
    • Handle: RePEc:hal:wpaper:hal-01784209
    Note: View the original document on HAL open archive server: https://hal.science/hal-01784209
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    References listed on IDEAS

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    1. Charles Blackorby & R. Russell, 1999. "Aggregation of Efficiency Indices," Journal of Productivity Analysis, Springer, vol. 12(1), pages 5-20, August.
    2. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    3. Peyrache, Antonio, 2013. "Industry structural inefficiency and potential gains from mergers and break-ups: A comprehensive approach," European Journal of Operational Research, Elsevier, vol. 230(2), pages 422-430.
    4. 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.
    5. Rolf Fare & Shawna Grosskopf & Valentin Zelenyuk, 2008. "Aggregation of Nerlovian profit indicator," Applied Economics Letters, Taylor & Francis Journals, vol. 15(11), pages 845-847.
    6. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    7. 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, July.
    8. Chambers,Robert G. & Quiggin,John, 2000. "Uncertainty, Production, Choice, and Agency," Cambridge Books, Cambridge University Press, number 9780521785235.
    9. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    10. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-685, November.
    11. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    12. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    13. Louisa Andriamasy & Walter Briec & Stephane Mussard, 2016. "On Some Relations between Several Generalized Convex DEA Models," Cahiers de recherche 16-02, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    14. Briec, Walter & Liang, Qi Bin, 2011. "On some semilattice structures for production technologies," European Journal of Operational Research, Elsevier, vol. 215(3), pages 740-749, December.
    15. Walter Briec & K. Kerstens, 2009. "Infeasibilities and directional distance functions: with application to the determinateness of the luenberger productivity indicator," Post-Print hal-00372560, HAL.
    16. Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 629-641.
    17. Kohli, Ulrich R, 1981. "Nonjointness and Factor Intensity in U.S. Production," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 3-18, February.
    18. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    19. Briec, Walter & Mussard, Stéphane, 2014. "Efficient firm groups: Allocative efficiency in cooperative games," European Journal of Operational Research, Elsevier, vol. 239(1), pages 286-296.
    20. Mussard, Stephane & Peypoch, Nicolas, 2006. "On multi-decomposition of the aggregate Malmquist productivity index," Economics Letters, Elsevier, vol. 91(3), pages 436-443, June.
    21. Li, Sung-Ko, 1995. "Relations between convexity and homogeneity in multioutput technologies," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 311-318.
    22. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    23. Lozano, S., 2013. "DEA production games," European Journal of Operational Research, Elsevier, vol. 231(2), pages 405-413.
    24. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
    25. Ulrich Kohli, 1983. "Non-joint Technologies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 209-219.
    26. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    27. Post, Thierry, 2001. "Transconcave data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 132(2), pages 374-389, July.
    28. Luenberger, David G., 1995. "Externalities and benefits," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 159-177.
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    Cited by:

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    More about this item

    Keywords

    Technical efficiency; Productivity; Aggregation; Cooperative games; Distance functions;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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