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Target Shortfall Orderings and Indices

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Author Info
Satya R. Chakravarty
Conchita D'Ambrosio
Pietro Muliere

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Abstract

Given any income distribution, to each income we associate a subgroup containing all persons whose incomes are not higher than this income and a person's target shortfall in a subgroup is the gap between the subgroup highest income and his own income. We then develop an absolute target shortfall ordering, which, under constancy of population size and total income, implies the Lorenz and Cowell-Ebert complaint orderings. Under the same restrictions, one distribution dominates the other by this ordering if and only if the dominated distribution can be obtained from the dominant one by a sequence of rank preserving progressive transfers, where each transfer is shared equally by all persons poorer than the donor of the transfer. The relationship of the ordering with the absolute deprivation and differential orderings, and its consistency with ranking of distributions by absolute target shortfall indices are explored. Well-known inequality indices like the absolute Gini index and the standard deviation are interpreted as absolute target shortfall indices. Finally, the possibility of a relative target shortfall ordering is also discussed.

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File URL: http://www.diw.de/documents/publikationen/73/diw_01.c.40256.de/dp340.pdf
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Paper provided by DIW Berlin, German Institute for Economic Research in its series Discussion Papers of DIW Berlin with number 340.

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Length: 23 p.
Date of creation: 2003
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Handle: RePEc:diw:diwwpp:dp340

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Related research
Keywords: Target shortfall orderings; transfer; indices;

Find related papers by JEL classification:
D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Yitzhaki, Shlomo, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, MIT Press, vol. 93(2), pages 321-24, May. [Downloadable!] (restricted)
  2. Moyes Patrick, 1994. "Inequality Reducing and Inequality Preserving Transformations of Incomes: Symmetric and Individualistic Transformations," Journal of Economic Theory, Elsevier, vol. 63(2), pages 271-298, August. [Downloadable!] (restricted)
  3. Blackorby, Charles & Donaldson, David, 1980. "A Theoretical Treatment of Indices of Absolute Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 107-36, February. [Downloadable!] (restricted)
  4. Chakravarty, S.R. & Mukherjee, D., 1998. "Measures of Deprivation and their Meaning in Terms of Social Satisfaction," DELTA Working Papers 98-17, DELTA (Ecole normale supérieure).
  5. Satya R. Chakravarty & Patrick Moyes, 2003. "Individual welfare, social deprivation and income taxation," Economic Theory, Springer, vol. 21(4), pages 843-869, 06. [Downloadable!] (restricted)
  6. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March. [Downloadable!] (restricted)
  7. Frank A Cowell & Udo Ebert, 2002. "Complaints and Inequality," STICERD - Distributional Analysis Research Programme Papers 61, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  8. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February. [Downloadable!] (restricted)
  9. Weiss, Y. & Fershtman, C., 1997. "Social Status and Economic Performance: A Survey," Papers 19-97, Tel Aviv.
    Other versions:
  10. Hey, John D & Lambert, Peter J, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, MIT Press, vol. 95(3), pages 567-73, November.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," Journal of Economic Inequality, Springer, vol. 5(3), pages 279-303, December. [Downloadable!] (restricted)
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