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Income Distributions and Decomposable Divergence Measures
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Income Distributions and Decomposable Divergence Measures

Author

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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.

Suggested Citation

  • Brice Magdalou & Richard Nock, 2010. "Income Distributions and Decomposable Divergence Measures," Documents de Travail 2010-01, CEREGMIA, Université des Antilles et de la Guyane.
    • Handle: RePEc:crg:wpaper:dt2010-01
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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. Paul Hufe & Ravi Kanbur & Andreas Peichlifo, 2022. "Measuring Unfair Inequality: Reconciling Equality of Opportunity and Freedom from Poverty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3345-3380.
    3. Magdalou, Brice & Nock, Richard, 2011. "Income distributions and decomposable divergence measures," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2440-2454.
    4. Brice Magdalou, 2018. "Income inequality measurement: a fresh look at two old issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 415-435, October.
    5. Nuno Crespo & Sandrina B. Moreira & Nadia Simoes, 2015. "Integrated Approach for the Measurement of Inequality, Poverty, and Richness," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 62(5), pages 531-555.
    6. 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.
    7. 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 (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-32.
    8. Daniel Gerszon Mahler & Xavier Ramos, 2019. "Equality of Opportunity in Four Measures of Well‐Being," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 65(S1), pages 228-255, November.
    9. 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.
    10. 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.
    11. Ji-Won Park & Chae Un Kim, 2020. "Getting to a feasible income equality," Papers 2011.09119, arXiv.org, revised Mar 2021.
    12. 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.
    13. Ji-Won Park & Chae Un Kim, 2021. "Getting to a feasible income equality," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-16, March.
    14. Ji-Won Park & Jaeup U. Kim & Cheol-Min Ghim & Chae Un Kim, 2021. "The Boltzmann fair division for distributive justice," Papers 2109.11917, arXiv.org, revised Nov 2021.
    15. Domenico Moramarco & Flaviana Palmisano & Vito Peragine, 2020. "Intertemporal inequality of opportunity," Working Papers 554, ECINEQ, Society for the Study of Economic Inequality.
    16. Erwin Ooghe & Erik Schokkaert & Hannes Serruys, 2023. "Fair Earnings Tax Reforms," CESifo Working Paper Series 10242, CESifo.
    17. 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.
    18. Muszyńska Joanna & Wędrowska Ewa, 2018. "Income Inequality of Households in Poland: A Subgroup Decomposition of Generalized Entropy Measures," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 22(4), pages 43-64, December.
    19. Jarosław Oczki & Ewa Wędrowska, 2017. "Changes in Household Income Distributions in EU Countries," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 45, pages 299-314.

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    More about this item

    Keywords

    Inequality measures; progressive transfers; generalized entropy; information theory; Bregman divergences;
    All these keywords.

    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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