IDEAS home Printed from https://ideas.repec.org/p/shr/wpaper/16-01.html
   My bibliography  Save this paper

Improvement of Technical Efficiency of Firm Groups

Author

Listed:
  • Louisa Andriamasy

    (CAEPEM, IAE, Université de Perpignan)

  • Walter Briec

    (CAEPEM, IAE, Université de Perpignan)

  • Stephane Mussard

    (CHROME, Université de Nîmes; LAMETA, Université de Montpellier; GREDI, Universite de Sherbrooke; LISER, Luxembourg)

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 mproves technical efficiency ; the cooperation reduces technical efficiency ; and finally the cooperation between firms yields no variation of technical efficiency. 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 & Stephane Mussard, 2016. "Improvement of Technical Efficiency of Firm Groups," Cahiers de recherche 16-01, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    • Handle: RePEc:shr:wpaper:16-01
    as

    Download full text from publisher

    File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-1601.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Charles Blackorby & R. Russell, 1999. "Aggregation of Efficiency Indices," Journal of Productivity Analysis, Springer, vol. 12(1), pages 5-20, August.
    2. 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.
    3. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.
    4. 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.
    5. Mussard, Stephane & Peypoch, Nicolas, 2006. "On multi-decomposition of the aggregate Malmquist productivity index," Economics Letters, Elsevier, vol. 91(3), pages 436-443, June.
    6. 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.
    7. 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.
    8. Rolf Fare & Shawna Grosskopf & Valentin Zelenyuk, 2008. "Aggregation of Nerlovian profit indicator," Applied Economics Letters, Taylor & Francis Journals, vol. 15(11), pages 845-847.
    9. Li, Sung-Ko, 1995. "Relations between convexity and homogeneity in multioutput technologies," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 311-318.
    10. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    11. 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.
    12. Chambers,Robert G. & Quiggin,John, 2000. "Uncertainty, Production, Choice, and Agency," Cambridge Books, Cambridge University Press, number 9780521785235, January.
    13. 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.
    14. Lozano, S., 2013. "DEA production games," European Journal of Operational Research, Elsevier, vol. 231(2), pages 405-413.
    15. 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.
    16. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Ulrich Kohli, 1983. "Non-joint Technologies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 209-219.
    24. 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.
    25. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Ding & Guo, Peng & Kilgour, D. Marc & Ponnambalam, Kumaraswamy & Hipel, Keith W., 2022. "The evolution of R&D collaboration in inter-organizational project networks: Effects of reference points for competitive preference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    2. Mussard, Stéphane & Pi Alperin, María Noel, 2021. "Accounting for risk factors on health outcomes: The case of Luxembourg," European Journal of Operational Research, Elsevier, vol. 291(3), pages 1180-1197.
    3. Walter Briec & Marc Dubois & Stéphane Mussard, 2021. "Technical efficiency in firm games with constant returns to scale and $$\alpha $$ α -returns to scale," Annals of Operations Research, Springer, vol. 304(1), pages 35-62, September.
    4. Afsharian, Mohsen & Ahn, Heinz & Harms, Sören Guntram, 2021. "A review of DEA approaches applying a common set of weights: The perspective of centralized management," European Journal of Operational Research, Elsevier, vol. 294(1), pages 3-15.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walter Briec & Marc Dubois & Stéphane Mussard, 2021. "Technical efficiency in firm games with constant returns to scale and $$\alpha $$ α -returns to scale," Annals of Operations Research, Springer, vol. 304(1), pages 35-62, September.
    2. 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.
    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. Walter Briec & Marc Dubois & Stéphane Mussard, 2019. "Technical Efficiency in Firm Games with Constant Returns to Scale and α-Returns to Scale," Working Papers hal-02344310, HAL.
    5. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    6. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    7. Mondelaers, Koen & Kuosmanen, Timo & Van Passel, Steven & Buysse, Jeroen & Lauwers, Ludwig H. & Van Huylenbroeck, Guido, 2011. "Sustainable Efficiency Of Firms When New Sustainability Targets Are Introduced," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114633, European Association of Agricultural Economists.
    8. A. Abad & P. Ravelojaona, 2017. "Exponential environmental productivity index and indicators," Journal of Productivity Analysis, Springer, vol. 48(2), pages 147-166, December.
    9. Aparicio, Juan & Ortiz, Lidia & Santín, Daniel, 2021. "Comparing group performance over time through the Luenberger productivity indicator: An application to school ownership in European countries," European Journal of Operational Research, Elsevier, vol. 294(2), pages 651-672.
    10. Walter Briec & Laurent Cavaignac, 2009. "An extension of the multi-output state-contingent production model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(1), pages 43-64, April.
    11. Valentin Zelenyuk, 2023. "Productivity analysis: roots, foundations, trends and perspectives," Journal of Productivity Analysis, Springer, vol. 60(3), pages 229-247, December.
    12. Valentin Zelenyuk, 2018. "Some Mathematical and Historical Clarifications on Aggregation in Efficiency and Productivity Analysis and Connection to Economic Theory," CEPA Working Papers Series WP032018, School of Economics, University of Queensland, Australia.
    13. 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.
    14. 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.
    15. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    16. Juo, Jia-Ching & Fu, Tsu-Tan & Yu, Ming-Miin & Lin, Yu-Hui, 2016. "Non-radial profit performance: An application to Taiwanese banks," Omega, Elsevier, vol. 65(C), pages 111-121.
    17. Briec, Walter & Comes, Christine & Kerstens, Kristiaan, 2006. "Temporal technical and profit efficiency measurement: Definitions, duality and aggregation results," International Journal of Production Economics, Elsevier, vol. 103(1), pages 48-63, September.
    18. Zelenyuk, Valentin, 2013. "A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation," European Journal of Operational Research, Elsevier, vol. 228(3), pages 592-600.
    19. Carlos Pestana Barros & Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Identification of Segments of European Banks with a Latent Class Frontier Model," CESifo Working Paper Series 2110, CESifo.
    20. Hien Thu Pham & Antonio Peyrache, 2015. "Industry Inefficiency Measures: A Unifying Approximation Proposition," CEPA Working Papers Series WP102015, School of Economics, University of Queensland, Australia.

    More about this item

    Keywords

    Aggregation; Cooperative games; Distance functions; Productivity; Technical efficiency;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:shr:wpaper:16-01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Jean-François Rouillard (email available below). General contact details of provider: https://edirc.repec.org/data/deushca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.