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Axiomatic Foundations of Inefficiency Measurement on Space

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Author Info

  • 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.

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File URL: http://research.economics.unsw.edu.au/RePEc/papers/2009-07.pdf
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Bibliographic Info

Paper provided by School of Economics, The University of New South Wales in its series Discussion Papers with number 2009-07.

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Length: 27 pages
Date of creation: Apr 2009
Date of revision:
Handle: RePEc:swe:wpaper:2009-07

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Keywords: Technical efficiency indexes; technical efficiency axioms;

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References

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  1. 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.
  2. 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.
  3. Salnykov, Mykhaylo & Zelenyuk, Valentin, 2005. "On the Commensurability of Directional Distance Functions," MPRA Paper 7068, University Library of Munich, Germany.
  4. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
  5. Robert Russell, R., 1985. "Measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 35(1), pages 109-126, February.
  6. 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. Robert Russell & William Schworm, 2007. "Axiomatic Foundations of Efficiency Measurement on Data-Generated Technologies," Discussion Papers 2007-35, School of Economics, The University of New South Wales.

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