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Aggregation of Scale Efficiency

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  • Valentin Zelenyuk

    (CEPA - School of Economics, The University of Queensland)

Abstract

In this article we extend the aggregation theory in efficiency and productivity analysis by deriving solutions to the problem of aggregation of individual scale efficiency measures, primal and dual, into aggregate primal and dual scale efficiency measures of a group. The new aggregation result is coherent with aggregation framework and solutions for the other related efficiency measures that already exist in the literature.

Suggested Citation

  • Valentin Zelenyuk, 2012. "Aggregation of Scale Efficiency," CEPA Working Papers Series WP042012, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:80
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    File URL: http://www.uq.edu.au/economics/cepa/docs/WP/WP042012.pdf
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    References listed on IDEAS

    as
    1. Hanoch, Giora, 1975. "The Elasticity of Scale and the Shape of Average Costs," American Economic Review, American Economic Association, vol. 65(3), pages 492-497, June.
    2. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
    3. 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.
    4. Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
    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. Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
    7. Fare, Rolf & Grosskopf, Shawna, 1985. " Nonparametric Cost Approach to Scale Efficiency," Scandinavian Journal of Economics, Wiley Blackwell, vol. 87(4), pages 594-604.
    8. Valentin Zelenyuk, 2013. "A Note on Equivalences in Measuring Returns to Scale," International Journal of Business and Economics, College of Business and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 12(1), pages 85-89, June.
    9. Zelenyuk, Valentin, 2006. "Aggregation of Malmquist productivity indexes," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1076-1086, October.
    10. Kuosmanen, Timo & Cherchye, Laurens & Sipilainen, Timo, 2006. "The law of one price in data envelopment analysis: Restricting weight flexibility across firms," European Journal of Operational Research, Elsevier, vol. 170(3), pages 735-757, May.
    11. 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.
    12. Charles Blackorby & R. Russell, 1999. "Aggregation of Efficiency Indices," Journal of Productivity Analysis, Springer, vol. 12(1), pages 5-20, August.
    13. Léopold Simar & Valentin Zelenyuk, 2007. "Statistical inference for aggregates of Farrell-type efficiencies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1367-1394.
    14. Forsund, Finn R & Hjalmarsson, Lennart, 1979. "Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Economic Journal, Royal Economic Society, vol. 89(354), pages 294-315, June.
    15. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, vol. 42(1), pages 15-24, August.
    16. Valentin Zelenyuk, 2011. "Scale Efficiency: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP092011, School of Economics, University of Queensland, Australia.
    17. 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.
    18. Zelenyuk, Valentin, 2011. "Aggregation of economic growth rates and of its sources," European Journal of Operational Research, Elsevier, vol. 212(1), pages 190-198, July.
    19. Valentin Zelenyuk, 2011. "A Scale Elasticity Measure for Directional Distance Function and its Dual," CEPA Working Papers Series WP062011, School of Economics, University of Queensland, Australia.
    20. Petros Hadjicostas & Andreas Soteriou, 2010. "Erratum to: Different orders of one-sided scale elasticities in multi-output production," Journal of Productivity Analysis, Springer, vol. 34(2), pages 181-181, October.
    21. Vladimir Nesterenko & Valentin Zelenyuk, 2007. "Measuring potential gains from reallocation of resources," Journal of Productivity Analysis, Springer, vol. 28(1), pages 107-116, October.
    22. Valentin Zelenyuk, 2011. "A Note on Equivalences in Measuring Returns to Scale in Multi-output-multi-input Technologies," CEPA Working Papers Series WP052011, School of Economics, University of Queensland, Australia.
    23. 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.
    24. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    25. 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.
    26. Golany, Boaz & Yu, Gang, 1997. "Estimating returns to scale in DEA," European Journal of Operational Research, Elsevier, vol. 103(1), pages 28-37, November.
    27. John C. Panzar & Robert D. Willig, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, Oxford University Press, vol. 91(3), pages 481-493.
    28. Petros Hadjicostas & Andreas Soteriou, 2010. "Different orders of one-sided scale elasticities in multi-output production," Journal of Productivity Analysis, Springer, vol. 33(2), pages 147-167, April.
    29. Banker, R. D. & Bardhan, I. & Cooper, W. W., 1996. "A note on returns to scale in DEA," European Journal of Operational Research, Elsevier, vol. 88(3), pages 583-585, February.
    30. Fare, Rolf & Zelenyuk, Valentin, 2007. "Extending Fare and Zelenyuk (2003)," European Journal of Operational Research, Elsevier, vol. 179(2), pages 594-595, June.
    31. Hadjicostas, Petros & Soteriou, Andreas C., 2006. "One-sided elasticities and technical efficiency in multi-output production: A theoretical framework," European Journal of Operational Research, Elsevier, vol. 168(2), pages 425-449, January.
    32. Podinovski, Victor V. & Førsund, Finn R. & Krivonozhko, Vladimir E., 2009. "A simple derivation of scale elasticity in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 197(1), pages 149-153, August.
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    1. repec:eee:phsmap:v:486:y:2017:i:c:p:595-609 is not listed on IDEAS
    2. Fare, Rolf & Zelenyuk, Valentin, 2002. "On Mr. Farrell's Decomposition and Aggregation," MPRA Paper 28005, University Library of Munich, Germany, revised 23 May 2005.
    3. Zelenyuk, Valentin, 2006. "Aggregation of Malmquist productivity indexes," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1076-1086, October.
    4. Andreas Mayer & Valentin Zelenyuk, 2018. "Aggregation of Individual Efficiency Measures and Productivity Indices," CEPA Working Papers Series WP012018, School of Economics, University of Queensland, Australia.
    5. Léopold Simar & Valentin Zelenyuk, 2016. "Asymptotic Theory for Aggregate Efficiency," CEPA Working Papers Series WP042016, School of Economics, University of Queensland, Australia.
    6. Andreas Mayer & Valentin Zelenyuk, 2014. "An Aggregation Paradigm for Hicks-Moorsteen Productivity Indexes," CEPA Working Papers Series WP012014, School of Economics, University of Queensland, Australia.
    7. Färe, Rolf & Karagiannis, Giannis, 2017. "The denominator rule for share-weighting aggregation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1175-1180.
    8. Fare, Rolf & Zelenyuk, Valentin, 2004. "Aggregation of Scale Elasticities Across Firms," MPRA Paper 28055, University Library of Munich, Germany, revised 11 Jan 2010.

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