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A Note on α -Gini Measures

Author

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  • Stéphane Mussard

    (CHROME - Détection, évaluation, gestion des risques CHROniques et éMErgents (CHROME) - Université de Nîmes - UNIMES - Nîmes Université)

  • Pauline Mornet

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

This note provides a characterization of α-Gini inequality measures. These measures generalize the standard Gini index by including one sensitivity parameter α, which captures different value judgments. The α-Gini measures are shown to be weakly decomposable and unit-consistent. Weak decomposition provides within-group and between-group inequalities. Unit consistency keeps unchanged the ranking of two income distributions when the income units vary. It is shown that the α-Gini measures are relevant with either "leftist" or"rightist" views. JEL Codes: D63, D31, C43

Suggested Citation

  • Stéphane Mussard & Pauline Mornet, 2018. "A Note on α -Gini Measures," Post-Print hal-02132104, HAL.
    • Handle: RePEc:hal:journl:hal-02132104
    DOI: 10.1111/roiw.12373
    Note: View the original document on HAL open archive server: https://hal.science/hal-02132104v1
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    References listed on IDEAS

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    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    3. Chameni Nembua, Célestin, 2008. "Measuring and explaining economic inequality: An extension of the Gini coefficient," MPRA Paper 31242, University Library of Munich, Germany, revised 2010.
    4. Mornet, Pauline & Zoli, Claudio & Mussard, Stéphane & Sadefo-Kamdem, Jules & Seyte, Françoise & Terraza, Michel, 2013. "The (α, β)-multi-level α-Gini decomposition with an illustration to income inequality in France in 2005," Economic Modelling, Elsevier, vol. 35(C), pages 944-963.
    5. Célestin Chameni Nembua, 2006. "Linking Gini to Entropy : Measuring Inequality by an interpersonal class of indices," Economics Bulletin, AccessEcon, vol. 4(5), pages 1-9.
    6. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    7. Mornet, Pauline, 2016. "On the axiomatization of the weakly decomposable inequality indices," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 71-78.
    8. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    9. Gajdos, Thibault, 2002. "Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities," Journal of Economic Theory, Elsevier, vol. 106(1), pages 190-200, September.
    10. Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
    11. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
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    Cited by:

    1. Christian Ahlin & Hyeok Jeong, 2021. "A conditional Gini: measure, estimation, and application," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(2), pages 363-384, June.

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    More about this item

    Keywords

    α-Gini measures; Unit-consistency; Weak decomposition;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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