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On Mr. Farrell's Decomposition and Aggregation

Author

Listed:
  • Fare, Rolf
  • Zelenyuk, Valentin

Abstract

In this paper we show that in order to aggregate individual efficiency scores into a group (e.g., industry) efficiency score, in such a way that the multiplicative structure of further decompositions is preserved with equal weights across components, the weighted geometric mean is required. We also show how the weights can be chosen using a variation of a theorem by Koopmans (1957). In the end, our paper provides a mathematically consistent and economic-theory justified way of aggregation of Farrell-type efficiency scores.

Suggested Citation

  • Fare, Rolf & Zelenyuk, Valentin, 2002. "On Mr. Farrell's Decomposition and Aggregation," MPRA Paper 28005, University Library of Munich, Germany, revised 23 May 2005.
  • Handle: RePEc:pra:mprapa:28005
    as

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    File URL: https://mpra.ub.uni-muenchen.de/28005/1/MPRA_paper_28005.pdf
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    References listed on IDEAS

    as
    1. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    2. Fare, Rolf & Zelenyuk, Valentin, 2003. "On aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 146(3), pages 615-620, May.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. repec:eee:jomega:v:75:y:2018:i:c:p:1-12 is not listed on IDEAS
    2. 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.

    More about this item

    Keywords

    Farrell efficiency; Index Aggregation;

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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