IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v260y2017i3p1175-1180.html
   My bibliography  Save this article

The denominator rule for share-weighting aggregation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717301133
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.02.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 33(3), pages 361-389, September.
    3. Charles Blackorby & R. Russell, 1999. "Aggregation of Efficiency Indices," Journal of Productivity Analysis, Springer, vol. 12(1), pages 5-20, August.
    4. Färe, Rolf & Karagiannis, Giannis, 2014. "A postscript on aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 233(3), pages 784-786.
    5. 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.
    6. Pachkova, Elena V., 2009. "Restricted reallocation of resources," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1049-1057, August.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Kevin Fox, 2012. "Problems with (dis)aggregating productivity, and another productivity paradox," Journal of Productivity Analysis, Springer, vol. 37(3), pages 249-259, June.
    12. 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.
    13. 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.
    14. Fare, Rolf & Zelenyuk, Valentin, 2007. "Extending Fare and Zelenyuk (2003)," European Journal of Operational Research, Elsevier, vol. 179(2), pages 594-595, June.
    15. Rolf Färe & Shawna Grosskopf, 2000. "Research Note. Decomposing Technical Efficiency with Care," Management Science, INFORMS, vol. 46(1), pages 167-168, January.
    16. 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.
    17. 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.
    18. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    19. 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.
    20. Vladimir Nesterenko & Valentin Zelenyuk, 2007. "Measuring potential gains from reallocation of resources," Journal of Productivity Analysis, Springer, vol. 28(1), pages 107-116, October.
    21. Fare, Rolf & Zelenyuk, Valentin, 2003. "On aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 146(3), pages 615-620, May.
    22. 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.
    23. 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.
    24. 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.
    25. Giannis Karagiannis, 2015. "On structural and average technical efficiency," Journal of Productivity Analysis, Springer, vol. 43(3), pages 259-267, June.
    26. 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.
    27. 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.
    28. 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.
    29. 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.
    30. 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.
    31. Fare, Rolf & Grosskopf, Shawna, 2000. "Outfoxing a paradox," Economics Letters, Elsevier, vol. 69(2), pages 159-163, November.
    32. 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.
    33. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    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. J. Van Biesebroeck, 2008. "Aggregating and Decomposing Productivity," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 112-146.
    36. 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.
    37. Thijs Raa, 2011. "Benchmarking and industry performance," Journal of Productivity Analysis, Springer, vol. 36(3), pages 285-292, December.
    38. 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.
    Full references (including those not matched with items on IDEAS)

    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. Giannis Karagiannis, 2015. "On structural and average technical efficiency," Journal of Productivity Analysis, Springer, vol. 43(3), pages 259-267, June.
    2. Ali Homayoni & Reza Fallahnejad & Farhad Hosseinzadeh Lotfi, 2022. "Cross Malmquist Productivity Index in Data Envelopment Analysis," 4OR, Springer, vol. 20(4), pages 567-602, December.
    3. Färe, Rolf & Karagiannis, Giannis, 2014. "A postscript on aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 233(3), pages 784-786.
    4. 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.
    5. Valentin Zelenyuk, 2022. "Aggregation of Efficiency and Productivity: From Firm to Sector and Higher Levels," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 25, pages 1039-1079, Springer.
    6. 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.
    7. Barnabé Walheer, 2019. "Disaggregation for efficiency analysis," Journal of Productivity Analysis, Springer, vol. 51(2), pages 137-151, June.
    8. Walheer, Barnabé, 2019. "Aggregating Farrell efficiencies with private and public inputs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1170-1177.
    9. Antonio Peyrache & Maria C. A. Silva, 2022. "Efficiency and Productivity Analysis from a System Perspective: Historical Overview," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 173-230, Springer.
    10. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    11. Färe, Rolf & Karagiannis, Giannis, 2022. "Aggregating Farrell efficiencies without value data: The case of hospitals," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    12. Valentin Zelenyuk, 2021. "Performance Analysis: Economic Foundations & Trends," CEPA Working Papers Series WP162021, School of Economics, University of Queensland, Australia.
    13. Antonio Peyrache & Maria C. A. Silva, 2023. "Efficiency decomposition for multi-level multi-components production technologies," Journal of Productivity Analysis, Springer, vol. 60(3), pages 273-294, December.
    14. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    15. Cesaroni, Giovanni, 2018. "Industry cost efficiency in data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 37-43.
    16. Chun-kei Tsang & Sung-ko Li, 2020. "Allocation of resources within subgroups of an industry: a case study in the Chinese industrial sector," Journal of Productivity Analysis, Springer, vol. 53(1), pages 125-139, February.
    17. Antonio Peyrache & Maria C. A. Silva, 2019. "The Inefficiency of Production Systems and its decomposition," CEPA Working Papers Series WP052019, School of Economics, University of Queensland, Australia.
    18. 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.
    19. Cesaroni, Giovanni, 2020. "Technically and cost-efficient centralized allocations in data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 70(C).
    20. Valentin Zelenyuk, 2023. "Productivity analysis: roots, foundations, trends and perspectives," Journal of Productivity Analysis, Springer, vol. 60(3), pages 229-247, December.

    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:eee:ejores:v:260:y:2017:i:3:p:1175-1180. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.