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Indicators and indexes of directional output loss and input allocative inefficiency


  • Hirofumi Fukuyama

    (Faculty of Commerce, Fukuoka University, Nanakuma, Jonan-Ku, Fukuoka, Japan)

  • William L. Weber

    (Department of Economics and Finance, Harrison College of Business, Southeast Missouri State University, Cape Girardeau, MO, USA)


We extend Grosskopf et al.'s method and create an output loss indicator using directional output distance functions that allows non-radial efficiency gains in output. We compare our new output loss indicator with an indicator of input allocative inefficiency and derive the necessary and sufficient condition for equivalence between the two indicators. We also present an output loss index and corresponding input allocative inefficiency index and consider how indexes are related. Then we extend our analysis to productivity change and derive the necessary and sufficient condition for an output loss change indicator to be equivalent to an indicator of input allocative inefficiency change. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Hirofumi Fukuyama & William L. Weber, 2008. "Indicators and indexes of directional output loss and input allocative inefficiency," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 29(7), pages 565-574.
  • Handle: RePEc:wly:mgtdec:v:29:y:2008:i:7:p:565-574 DOI: 10.1002/mde.1419

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    References listed on IDEAS

    1. Walter Briec & Kristiaan Kerstens, 2004. "A Luenberger-Hicks-Moorsteen productivity indicator: its relation to the Hicks-Moorsteen productivity index and the Luenberger productivity indicator," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(4), pages 925-939, May.
    2. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    3. Fukuyama, Hirofumi & Guerra, Ramon & Weber, William L., 1999. "Efficiency and ownership: evidence from Japanese credit cooperatives," Journal of Economics and Business, Elsevier, vol. 51(6), pages 473-487.
    4. Fukuyama, Hirofumi & Weber, William L., 2005. "Estimating output gains by means of Luenberger efficiency measures," European Journal of Operational Research, Elsevier, vol. 164(2), pages 535-547, July.
    5. Shawna Grosskopf & Kathy J. Hayes & Lori L. Taylor & William L. Weber, 1999. "Anticipating the Consequences of School Reform: A New Use of DEA," Management Science, INFORMS, vol. 45(4), pages 608-620, April.
    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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    1. repec:pal:jorsoc:v:60:y:2009:i:11:d:10.1057_jors.2009.62 is not listed on IDEAS

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