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A remark on the definition of the Färe–Lovell measure for infeasible production vectors: implication for the Luenberger productivity indicator

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  • Stenger, Melle Agathe
  • Stenger, Agathe

Abstract

In a recent paper Mahlberg and Sahoo (2011) introduced a non-radial Luenberger indicator in order to avoid the problem of slacks. They suggest to evaluate the Luenberger indicator by using a directional slacks-based measure. This paper demonstrates, by numerical examples, that directional slacks-based measures do not allow to characterize the technology. Along this line, it follows that a Luenberger indicator based upon a directional slacks-based measure may have some drawback. Mahlberg and Sahoo (2011) mention these problems and suggest to replace non-negative signs of the input-specific inefficiency factors by non-positive signs. In this paper an alternative formulation is proposed. It characterizes both the input (output) sets and the input (output) efficient subset. Its application to the construction of a suitable Färe–Lovell type productivity indicator is suggested.

Suggested Citation

  • Stenger, Melle Agathe & Stenger, Agathe, 2017. "A remark on the definition of the Färe–Lovell measure for infeasible production vectors: implication for the Luenberger productivity indicator," International Journal of Production Economics, Elsevier, vol. 184(C), pages 1-6.
    • Handle: RePEc:eee:proeco:v:184:y:2017:i:c:p:1-6
    DOI: 10.1016/j.ijpe.2016.10.023
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    References listed on IDEAS

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    1. Briec, Walter & Cavaignac, Laurent & Kerstens, Kristiaan, 2011. "Directional measurement of technical efficiency of production: An axiomatic approach," Economic Modelling, Elsevier, vol. 28(3), pages 775-781, May.
    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. Chambers, Robert G. & Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity Growth in APEC Countries," Working Papers 197843, University of Maryland, Department of Agricultural and Resource Economics.
    4. Mahlberg, Bernhard & Sahoo, Biresh K., 2011. "Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application," International Journal of Production Economics, Elsevier, vol. 131(2), pages 721-726, June.
    5. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Debreu–Farrell efficiency measure; Färe–Lovell efficiency measure; Directional efficiency measures; Luenberger indicator; Non-radial Luenberger indicator;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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