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Income Distributions and Decomposable Divergence Measures

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  • Brice Magdalou

    ()
    (CEREGMIA, Université des Antilles et de la Guyane)

  • Richard Nock

    ()
    (CEREGMIA, Université des Antilles et de la Guyane)

Abstract

Inequality indices (i) evaluate the divergence between the income distribution and the hypothetical situation where all individuals have the mean income and (ii) are unambiguously reduced by a Pigou-Dalton progressive transfer. This paper proposes a new approach to evaluate the divergence between any two income distributions, where the second one can be a reference distribution for the first. In the case where the reference distribution is perfectly egalitarian, and uniquely in this case, we assume (i) that any progressive transfer reduces the divergence and (ii) that the divergence can be additively separated between inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views, and we derive the associated relative (resp. absolute) subclasses, which express constant relative (resp. absolute) inequality aversion. This approach extends the generalized entropy studied in inequality measurement.

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File URL: http://www2.univ-ag.fr/RePEc/DT/DT2010-01_Magdalou_Nock.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by CEREGMIA, Université des Antilles et de la Guyane in its series Documents de Travail with number 2010-01.

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Length: 21 pages
Date of creation: Apr 2010
Date of revision:
Handle: RePEc:crg:wpaper:dt2010-01

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Keywords: Inequality measures; progressive transfers; generalized entropy; information theory; Bregman divergences;

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References

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Citations

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Cited by:
  1. Magali Jaoul-Grammare & Brice Magdalou, 2013. "Opportunities in Higher Education: An Application in France," Working Papers 13-05, LAMETA, Universtiy of Montpellier, revised Mar 2013.
  2. Xavier Ramos & Dirk Van de gaer, 2012. "Empirical approaches to inequality of opportunity: Principles, measures, and evidence," Working Papers 259, ECINEQ, Society for the Study of Economic Inequality.
  3. Nuno Crespo & Sandrina B. Moreira & Nádia Simões, 2012. "An Integrated Approach for the Measurement of Inequality, Poverty and Richness," Working Papers Series 2 12-03, ISCTE-IUL, Business Research Unit (BRU-IUL).
  4. Yalonetzky, Gaston, 2012. "Measuring group disadvantage with inter-distributional inequality indices: A critical review and some amendments to existing indices," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 6(9), pages 1-32.
  5. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
  6. Frank Cowell & Emmanuel Flachaire & Sanghamitra Bandyopadhyay, 2013. "Reference distributions and inequality measurement," Journal of Economic Inequality, Springer, vol. 11(4), pages 421-437, December.

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