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Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator

Author

Listed:
  • Walter Briec

    () (University of Perpignan, LAMPS)

  • Kristiaan Kerstens

    (CNRS-LEM (UMR 8179), IESEG School of Management)

Abstract

The purpose of this contribution is to highlight an underexplored property of the directional distance function, a recently introduced generalization of the Shephard distance function. It diagnoses in detail the economic conditions under which infeasibilities may occur for the case of directional distance functions and explores whether there exist any solutions that remedy the problem in an economically meaningful way. This discussion is linked to determinateness as a property in index theory and illustrated by analyzing the Luenberger total factor productivity indicator, based upon directional distance functions. This indicator turns out to be impossible to compute under certain weak conditions. A fortiori, the same problems can also occur for less general productivity indicators and indexes.

Suggested Citation

  • Walter Briec & Kristiaan Kerstens, 2008. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Working Papers 2008-ECO-11, IESEG School of Management.
  • Handle: RePEc:ies:wpaper:e200811
    as

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    References listed on IDEAS

    as
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    5. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
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    Citations

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    Cited by:

    1. Kristiaan Kerstens & Ignace Van de Woestyne, 2009. "Negative Data in DEA: A Simple Proportional Distance Function Approach," Working Papers 2009-ECO-03, IESEG School of Management.
    2. Epure, Mircea & Kerstens, Kristiaan & Prior, Diego, 2011. "Technology-based total factor productivity and benchmarking: New proposals and an application," Omega, Elsevier, vol. 39(6), pages 608-619, December.
    3. Färe, Rolf & Grosskopf, Shawna & Lundgren, Tommy & Marklund, Per-Olov & Zhou, Wenchao, 2012. "Productivity: Should We Include Bads?," CERE Working Papers 2012:13, CERE - the Center for Environmental and Resource Economics.
    4. Briec, Walter & Kerstens, Kristiaan, 2010. "Portfolio selection in multidimensional general and partial moment space," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 636-656, April.
    5. Briec, Walter & Kerstens, Kristiaan, 2009. "The Luenberger productivity indicator: An economic specification leading to infeasibilities," Economic Modelling, Elsevier, vol. 26(3), pages 597-600, May.
    6. Mondelaers, Koen & Kuosmanen, Timo & Van Passel, Steven & Buysse, Jeroen & Lauwers, Ludwig H. & Van Huylenbroeck, Guido, 2011. "Sustainable Efficiency Of Firms When New Sustainability Targets Are Introduced," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114633, European Association of Agricultural Economists.
    7. Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.

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