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The denominator rule for share-weighting aggregation

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  • Färe, Rolf
  • Karagiannis, Giannis

Abstract

In this paper we prove that the denominator rule, namely that weighting shares should be defined in term of the denominator variable of the relevant index, is a necessary and sufficient condition for consistent arithmetic aggregation of any ratio-type performance measures, including efficiency indices. We then illustrate the applicability of the denominator rule in the aggregation of scale efficiency, measures of the effect of input congestion, and of capacity utilization indices.

Suggested Citation

  • Färe, Rolf & Karagiannis, Giannis, 2017. "The denominator rule for share-weighting aggregation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1175-1180.
  • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:1175-1180
    DOI: 10.1016/j.ejor.2017.02.008
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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. Färe, Rolf & Karagiannis, Giannis, 2014. "A postscript on aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 233(3), pages 784-786.
    3. 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.
    4. Pachkova, Elena V., 2009. "Restricted reallocation of resources," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1049-1057, August.
    5. 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.
    6. Kevin Fox, 2012. "Problems with (dis)aggregating productivity, and another productivity paradox," Journal of Productivity Analysis, Springer, vol. 37(3), pages 249-259, June.
    7. Eric Bartelsman & Phoebus Dhrymes, 1998. "Productivity Dynamics: U.S. Manufacturing Plants, 1972–1986," Journal of Productivity Analysis, Springer, vol. 9(1), pages 5-34, January.
    8. 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.
    9. Fare, Rolf & Zelenyuk, Valentin, 2003. "On aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 146(3), pages 615-620, May.
    10. 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.
    11. 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.
    12. Bert Balk, 2003. "The Residual: On Monitoring and Benchmarking Firms, Industries, and Economies with Respect to Productivity," Journal of Productivity Analysis, Springer, vol. 20(1), pages 5-47, July.
    13. Fare, Rolf & Grosskopf, Shawna & Kokkelenberg, Edward C, 1989. "Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 655-666, August.
    14. John McDonald, 1996. "Note: A Problem with the Decomposition of Technical Inefficiency into Scale and Congestion Components," Management Science, INFORMS, vol. 42(3), pages 473-474, March.
    15. Xiyang Lei & Yongjun Li & Qiwei Xie & Liang Liang, 2015. "Measuring Olympics achievements based on a parallel DEA approach," Annals of Operations Research, Springer, vol. 226(1), pages 379-396, March.
    16. K. Kerstens & D. Squires & N. Vestergaard, 2005. "Methodological Reflections on the Short-Run Johansen Industry Model in Relation to Capacity Management," Post-Print hal-00211184, HAL.
    17. Li, Sung-ko & Cheng, Yuk-shing, 2007. "Solving the puzzles of structural efficiency," European Journal of Operational Research, Elsevier, vol. 180(2), pages 713-722, July.
    18. Kristiaan Kerstens & Niels Vestergaard & Dale Squires, 2006. "A short-run Johansen industry model for common-pool resources: planning a fishery's industrial capacity to curb overfishing," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 33(3), pages 361-389, September.
    19. Grosskopf, S, 1986. "The Role of the Reference Technology in Measuring Productive Efficiency," Economic Journal, Royal Economic Society, vol. 96(382), pages 499-513, June.
    20. Dervaux, Benoît & Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1998. "Radial and nonradial static efficiency decompositions: a focus on congestion measurement," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 299-312, June.
    21. Chen, Yao & Cook, Wade D. & Li, Ning & Zhu, Joe, 2009. "Additive efficiency decomposition in two-stage DEA," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1170-1176, August.
    22. Chen, Yao & Du, Juan & David Sherman, H. & Zhu, Joe, 2010. "DEA model with shared resources and efficiency decomposition," European Journal of Operational Research, Elsevier, vol. 207(1), pages 339-349, November.
    23. Fare, Rolf & Zelenyuk, Valentin, 2007. "Extending Fare and Zelenyuk (2003)," European Journal of Operational Research, Elsevier, vol. 179(2), pages 594-595, June.
    24. Rolf Färe & Shawna Grosskopf, 2000. "Research Note. Decomposing Technical Efficiency with Care," Management Science, INFORMS, vol. 46(1), pages 167-168, January.
    25. 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.
    26. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    27. Fox, Kevin J., 1999. "Efficiency at different levels of aggregation: public vs. private sector firms," Economics Letters, Elsevier, vol. 65(2), pages 173-176, November.
    28. Vladimir Nesterenko & Valentin Zelenyuk, 2007. "Measuring potential gains from reallocation of resources," Journal of Productivity Analysis, Springer, vol. 28(1), pages 107-116, October.
    29. Giannis Karagiannis, 2015. "On structural and average technical efficiency," Journal of Productivity Analysis, Springer, vol. 43(3), pages 259-267, June.
    30. 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.
    31. C Kao, 2012. "Efficiency decomposition for parallel production systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(1), pages 64-71, January.
    32. Bjurek, Hans & Kjulin, Urban & Gustafsson, Bjorn, 1992. " Efficiency, Productivity and Determinants of Inefficiency at Public Day Care Centers in Sweden," Scandinavian Journal of Economics, Wiley Blackwell, vol. 94(0), pages 173-187, Supplemen.
    33. Fare, Rolf & Grosskopf, Shawna, 2000. "Outfoxing a paradox," Economics Letters, Elsevier, vol. 69(2), pages 159-163, November.
    34. Cook, Wade D. & Zhu, Joe & Bi, Gongbing & Yang, Feng, 2010. "Network DEA: Additive efficiency decomposition," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1122-1129, December.
    35. Thijs Raa, 2011. "Benchmarking and industry performance," Journal of Productivity Analysis, Springer, vol. 36(3), pages 285-292, December.
    36. P. Byrnes & R. Färe & S. Grosskopf, 1984. "Measuring Productive Efficiency: An Application to Illinois Strip Mines," Management Science, INFORMS, vol. 30(6), pages 671-681, June.
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