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On the Commensurability of Directional Distance Functions

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  • Salnykov, Mykhaylo
  • Zelenyuk, Valentin

Abstract

Shephard’s distance functions are widely used instruments for characterizing technology and for estimating efficiency in contemporary economic theory and practice. Recently, they have been generalized by the Luenberger shortage function, or Chambers-Chung-Färe directional distance function. In this study, we explore a very important property of an economic measure known as commensurability or independence of units of measurement up to scalar transformation. Our study discovers both negative and positive results for this property in the context of the directional distance function, which in turn helps us narrow down the most critical issue for this function in practice—the choice of direction of measurement.

Suggested Citation

  • Salnykov, Mykhaylo & Zelenyuk, Valentin, 2005. "On the Commensurability of Directional Distance Functions," MPRA Paper 7068, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:7068
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    File URL: https://mpra.ub.uni-muenchen.de/7068/1/MPRA_paper_7068.pdf
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    References listed on IDEAS

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    1. Luenberger David G., 1994. "Optimality and the Theory of Value," Journal of Economic Theory, Elsevier, vol. 63(2), pages 147-169, August.
    2. 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.
    3. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
    4. Bol, Georg, 1986. "On technical efficiency measures: A remark," Journal of Economic Theory, Elsevier, vol. 38(2), pages 380-385, April.
    5. Rolf Färe & Shawna Grosskopf, 2000. "Theory and Application of Directional Distance Functions," Journal of Productivity Analysis, Springer, vol. 13(2), pages 93-103, March.
    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. Laurens Cherchye & Timo Kuosmanen & Hervé Leleu, 2010. "Technical and Economic Efficiency Measures Under Short Run Profit Maximizing Behavior," Recherches économiques de Louvain, De Boeck Université, vol. 76(2), pages 163-173.
    2. 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.
    3. Cherchye, Laurens & Van Puyenbroeck, Tom, 2009. "Semi-radial technical efficiency measurement," European Journal of Operational Research, Elsevier, vol. 193(2), pages 616-625, March.

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    More about this item

    Keywords

    Directional distance functions; commensurability; efficiency;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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