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Income distributions and decomposable divergence measures

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  • Magdalou, Brice
  • Nock, Richard

Abstract

Inequality indices evaluate the divergence between the income distribution and the hypothetical situation where all individuals receive the mean income, and 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 latter can be a reference distribution for the former. In the case where the reference distribution is perfectly egalitarian – and uniquely in this case – we assume that any progressive transfer reduces the divergence, and that the divergence can be additively separated into inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views. We derive the associated relative and absolute subclasses, and we illustrate the applicability of our results. This approach extends the generalized entropy studied in inequality measurement.

Suggested Citation

  • Magdalou, Brice & Nock, Richard, 2011. "Income distributions and decomposable divergence measures," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2440-2454.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:6:p:2440-2454
    DOI: 10.1016/j.jet.2011.06.017
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    Cited by:

    1. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
    2. Nuno Crespo & Sandrina B. Moreira & Nadia Simoes, 2015. "An Integrated Approach for the Measurement of Inequality, Poverty, and Richness," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 62(5), pages 531-555, December.
    3. Frank Cowell & Emmanuel Flachaire & Sanghamitra Bandyopadhyay, 2013. "Reference distributions and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(4), pages 421-437, December.
    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 (IfW), vol. 6, pages 1-32.
    5. X. Ramos & D. Van De Gaer, 2012. "Empirical Approaches to Inequality of Opportunity: Principles, Measures, and Evidence," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 12/792, Ghent University, Faculty of Economics and Business Administration.
    6. Magali Jaoul-Grammare & Brice Magdalou, 2013. "Opportunities in Higher Education: An Application to France," Annals of Economics and Statistics, GENES, issue 111-112, pages 295-325.
    7. Nicholas Rohde, 2016. "J-divergence measurements of economic inequality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(3), pages 847-870, June.
    8. repec:sgh:annals:i:45:y:2017:p:299-314 is not listed on IDEAS

    More about this item

    Keywords

    Inequality measures; Mobility; Responsibility; Heterogeneous households; Generalized entropy; Bregman divergences;

    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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