Indicators and indexes of directional output loss and input allocative inefficiency

Hirofumi Fukuyama and William L. Weber
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Hirofumi Fukuyama: Faculty of Commerce, Fukuoka University, Nanakuma, Jonan-Ku, Fukuoka, Japan, Postal: 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, Postal: Department of Economics and Finance, Harrison College of Business, Southeast Missouri State University, Cape Girardeau, MO, USA

Managerial and Decision Economics, 2008, vol. 29, issue 7, pages 565-574

Abstract: 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.

Date: 2008
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