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Axiomatic Foundations of Inefficiency Measurement on Space

Author

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  • R. Robert Russell

    (University of California, Riverside)

  • William Schworm

    (School of Economics, The University of New South Wales)

Abstract

We provide an axiomatic foundation for efficiency measurement in the full space, referred to as “graph efficiency” measurement by Färe, Grosskopf, and Lovell [1985]. We posit four types of axioms: indication, monotonicity, independence of units of measurement, and continuity. We analyze six well-known inefficiency indexes from the operations-research and economics literature and discuss several other related indexes. We present two impossibility results demonstrating that no index can satisfy all of the axioms on a general class of (well-behaved) technologies. Specifically, no inefficiency index can satisfy both indication and continuity (in either quantities or technologies), and no inefficiency index can satisfy both monotonicity and unit independence. We present a full evaluation of the trade-offs involved in selecting among the indexes.

Suggested Citation

  • R. Robert Russell & William Schworm, 2009. "Axiomatic Foundations of Inefficiency Measurement on Space," Discussion Papers 2009-07, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2009-07
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2009-07.pdf
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    References listed on IDEAS

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    1. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    2. Steven Levkoff & R. Russell & William Schworm, 2012. "Boundary problems with the “Russell” graph measure of technical efficiency: a refinement," Journal of Productivity Analysis, Springer, vol. 37(3), pages 239-248, June.
    3. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    4. Salnykov, Mykhaylo & Zelenyuk, Valentin, 2005. "On the Commensurability of Directional Distance Functions," MPRA Paper 7068, University Library of Munich, Germany.
    5. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
    6. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    7. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    8. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
    9. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
    10. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
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    Cited by:

    1. R. Russell & William Schworm, 2009. "Axiomatic foundations of efficiency measurement on data-generated technologies," Journal of Productivity Analysis, Springer, vol. 31(2), pages 77-86, April.
    2. K Kerstens & I Van de Woestyne, 2011. "Negative data in DEA: a simple proportional distance function approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1413-1419, July.
    3. Gómez-Calvet, Roberto & Conesa, David & Gómez-Calvet, Ana Rosa & Tortosa-Ausina, Emili, 2014. "Energy efficiency in the European Union: What can be learned from the joint application of directional distance functions and slacks-based measures?," Applied Energy, Elsevier, vol. 132(C), pages 137-154.
    4. Hirofumi Fukuyama & Hiroya Masaki & Kazuyuki Sekitani & Jianming Shi, 2014. "Distance optimization approach to ratio-form efficiency measures in data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 42(2), pages 175-186, October.
    5. R. Robert Russell & William Schworm, 2018. "Technological inefficiency indexes: a binary taxonomy and a generic theorem," Journal of Productivity Analysis, Springer, vol. 49(1), pages 17-23, February.
    6. Mette Asmild & Tomas Baležentis & Jens Leth Hougaard, 2016. "Multi-directional productivity change: MEA-Malmquist," Journal of Productivity Analysis, Springer, vol. 46(2), pages 109-119, December.
    7. Puggioni, Daniela & Stefanou, Spiro E., 2016. "The Value of Being Socially Responsible. A DEA Approach for Analyzing Efficiency and Recovering Shadow Prices of CSR Activities," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235723, Agricultural and Applied Economics Association.
    8. Aparicio, Juan & Borras, Fernando & Pastor, Jesus T. & Vidal, Fernando, 2015. "Measuring and decomposing firm׳s revenue and cost efficiency: The Russell measures revisited," International Journal of Production Economics, Elsevier, vol. 165(C), pages 19-28.
    9. Wanfang Shen & Guoliang Yang & Zhongbao Zhou & Wenbin Liu, 2019. "DEA models with Russell measures," Annals of Operations Research, Springer, vol. 278(1), pages 337-359, July.
    10. Zhang, Bin & Lu, Danting & He, Yan & Chiu, Yung-ho, 2018. "The efficiencies of resource-saving and environment: A case study based on Chinese cities," Energy, Elsevier, vol. 150(C), pages 493-507.

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    More about this item

    Keywords

    Technical efficiency indexes; technical efficiency axioms;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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