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Aggregation of Efficiency and Productivity: From Firm to Sector and Higher Levels

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Abstract

Here we consider various cases where researchers are interested in measuring aggregate efficiency or productivity levels or their changes for a group of decision making units. These could be entire industry composed of individual firms, banks, hospitals, or a region composed of sub-regions or countries, or particular sub-groups of these units within a group, e.g., sub-groups of public vs. private or regulated vs. non-regulated firms, banks or hospitals within the same industry, etc. Such analysis requires solutions to the aggregation problem some theoretically justified approaches that can connect individual measures to aggregate measures. Various solutions are offered in the literature and our goal is to try to coherently summarize at least some of them in this chapter. This material should be interesting not only for theorists but also (and perhaps more so) for applied researchers, as it provides exact formulas and intuitive explanations for various measures of group efficiency, group scale elasticity and group productivity indexes and refers to original papers for more details.

Suggested Citation

  • Valentin Zelenyuk, 2019. "Aggregation of Efficiency and Productivity: From Firm to Sector and Higher Levels," CEPA Working Papers Series WP062019, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:136
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    File URL: https://economics.uq.edu.au/files/14339/WP062019.pdf
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    References listed on IDEAS

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    1. Mayer, Andreas & Zelenyuk, Valentin, 2014. "Aggregation of Malmquist productivity indexes allowing for reallocation of resources," European Journal of Operational Research, Elsevier, vol. 238(3), pages 774-785.
    2. repec:eee:ecolet:v:179:y:2019:i:c:p:72-74 is not listed on IDEAS
    3. Rolf Fare & Shawna Grosskopf & Valentin Zelenyuk, 2004. "Aggregation bias and its bounds in measuring technical efficiency," Applied Economics Letters, Taylor & Francis Journals, vol. 11(10), pages 657-660.
    4. Rolf Fare & Valentin Zelenyuk, 2005. "On Farrell's Decomposition and Aggregation," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 4(2), pages 167-171, August.
    5. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    6. Valentin Zelenyuk, 2013. "A Note on Equivalences in Measuring Returns to Scale," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 12(1), pages 85-89, June.
    7. Zelenyuk, Valentin, 2006. "Aggregation of Malmquist productivity indexes," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1076-1086, October.
    8. 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.
    9. Charles Blackorby & R. Russell, 1999. "Aggregation of Efficiency Indices," Journal of Productivity Analysis, Springer, vol. 12(1), pages 5-20, August.
    10. 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.
    11. Pachkova, Elena V., 2009. "Restricted reallocation of resources," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1049-1057, August.
    12. repec:eee:ejores:v:267:y:2018:i:1:p:349-367 is not listed on IDEAS
    13. 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.
    14. Fare, Rolf & Zelenyuk, Valentin, 2004. "Aggregation of Scale Elasticities Across Firms," MPRA Paper 28055, University Library of Munich, Germany, revised 11 Jan 2010.
    15. Mussard, Stephane & Peypoch, Nicolas, 2006. "On multi-decomposition of the aggregate Malmquist productivity index," Economics Letters, Elsevier, vol. 91(3), pages 436-443, June.
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    17. Fare, Rolf & Zelenyuk, Valentin, 2007. "Extending Fare and Zelenyuk (2003)," European Journal of Operational Research, Elsevier, vol. 179(2), pages 594-595, June.
    18. Loren Tauer, 2001. "Input aggregation and computed technical efficiency," Applied Economics Letters, Taylor & Francis Journals, vol. 8(5), pages 295-297.
    19. Gary Ferrier & Hervé Leleu & Vivian Valdmanis, 2009. "Hospital capacity in large urban areas: is there enough in times of need?," Journal of Productivity Analysis, Springer, vol. 32(2), pages 103-117, October.
    20. Färe, Rolf & Zelenyuk, Valentin, 2019. "On Luenberger input, output and productivity indicators," Economics Letters, Elsevier, vol. 179(C), pages 72-74.
    21. Rolf Fare & Shawna Grosskopf & Valentin Zelenyuk, 2008. "Aggregation of Nerlovian profit indicator," Applied Economics Letters, Taylor & Francis Journals, vol. 15(11), pages 845-847.
    22. 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.
    23. A. Mugera & A. Ojede, 2014. "Technical Efficiency In African Agriculture: Is It Catching Up Or Lagging Behind?," Journal of International Development, John Wiley & Sons, Ltd., vol. 26(6), pages 779-795, August.
    24. 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.
    25. Rolf Fare & Valentin Zelenyuk, 2002. "Input aggregation and technical efficiency," Applied Economics Letters, Taylor & Francis Journals, vol. 9(10), pages 635-636.
    26. 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.
    27. 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.
    28. Thijs Raa, 2011. "Benchmarking and industry performance," Journal of Productivity Analysis, Springer, vol. 36(3), pages 285-292, December.
    29. John C. Panzar & Robert D. Willig, 1977. "Free Entry and the Sustainability of Natural Monopoly," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 1-22, Spring.
    30. Vladimir Nesterenko & Valentin Zelenyuk, 2007. "Measuring potential gains from reallocation of resources," Journal of Productivity Analysis, Springer, vol. 28(1), pages 107-116, October.
    31. Daniel J. Henderson & Valentin Zelenyuk, 2007. "Testing for (Efficiency) Catching-up," Southern Economic Journal, Southern Economic Association, vol. 73(4), pages 1003-1019, April.
    32. Fare, Rolf & Zelenyuk, Valentin, 2003. "On aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 146(3), pages 615-620, May.
    33. Färe, Rolf & Karagiannis, Giannis, 2017. "The denominator rule for share-weighting aggregation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1175-1180.
    34. Kuosmanen, Timo & Kortelainen, Mika & Sipiläinen, Timo & Cherchye, Laurens, 2010. "Firm and industry level profit efficiency analysis using absolute and uniform shadow prices," European Journal of Operational Research, Elsevier, vol. 202(2), pages 584-594, April.
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    More about this item

    Keywords

    Efficiency; Productivity; Aggregation; Industry Efficiency; Duality.;

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance

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