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The Gini coefficient reveals more

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  • Peter J. Lambert
  • Andre' Decoster

Abstract

We revisit the well-known decomposition of the Gini coefficient into betweengroups, within-groups and overlap terms in the context of two groups in which the incomes in one group may be scaled and that group’s population weight modified. In this more general setting than usual, we focus on the properties of the overlap term, proving inter alia that overlap unambiguously reduces as a result of a within-group progressive transfer, and is increased by scaling up the incomes in the group with the lower mean, reaching a maximum when the two means become the same. In the case of a socially heterogeneous population and equivalized incomes, the effect on the Gini overlap of changing the income unit is determined, along with that of adjusting the equivalence scale deflator in case the income unit is the equivalent adult (such adjustment simultaneously changing the weighting of income units).
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Suggested Citation

  • Peter J. Lambert & Andre' Decoster, 2005. "The Gini coefficient reveals more," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 373-400.
    • Handle: RePEc:mtn:ancoec:si5
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    Cited by:

    1. Schröder, Carsten & Yitzhaki, Shlomo, 2017. "Revisiting the evidence for cardinal treatment of ordinal variables," European Economic Review, Elsevier, vol. 92(C), pages 337-358.
    2. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
    3. Ivica Urban & Peter J. Lambert, 2008. "Redistribution, Horizontal Inequity, and Reranking," Public Finance Review, , vol. 36(5), pages 563-587, September.
    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. Paolo Liberati & Shlomo Yitzhaki, 2012. "GDP and beyond: an implementation of welfare considerations to the distribution of earnings in Italy," Departmental Working Papers of Economics - University 'Roma Tre' 0146, Department of Economics - University Roma Tre.
    6. Paolo Liberati, 2015. "The World Distribution of Income And Its Inequality, 1970–2009," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(2), pages 248-273, June.
    7. Ingvild Almås & Tarjei Havnes & Magne Mogstad, 2011. "Baby booming inequality? Demographic change and earnings inequality in Norway, 1967–2000," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 629-650, December.
    8. Jiandong Chen & Dai Dai & Ming Pu & Wenxuan Hou & Qiaobin Feng, 2010. "The trend of the Gini coefficient of China," Global Development Institute Working Paper Series 10910, GDI, The University of Manchester.
    9. Shlomo Yitzhaki & Edna Schechtman, 2009. "The “melting pot”: A success story?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(2), pages 137-151, June.
    10. Javier Mart n-Rom n & Luis Ayala & Juan Vicente, 2017. "Regional inequality in decentralized countries: a multi-country analysis using LIS," LIS Working papers 697, LIS Cross-National Data Center in Luxembourg.
    11. Allanson, Paul, 2014. "Income stratification and between-group inequality," Economics Letters, Elsevier, vol. 124(2), pages 227-230.
    12. Giovanni M. Giorgi & Stefania Gubbiotti, 2017. "Celebrating the Memory of Corrado Gini: a Personality Out of the Ordinary," International Statistical Review, International Statistical Institute, vol. 85(2), pages 325-339, August.
    13. Ingvild Almås & Magne Mogstad, 2009. "Older or Wealthier? The Impact of Age Adjustments on the Wealth Inequality Ranking of Countries," Discussion Papers 583, Statistics Norway, Research Department.
    14. Francesco Andreoli & Vincenzo Prete & Claudio Zoli, 2023. "The measurement of segregation sensitive spatial income deprivation," Working Papers 03/2023, University of Verona, Department of Economics.
    15. Tetsugen HARUYAMA, 2021. "International Kuznets Curve (?): A Schumpeterian Model of the World Economy," Discussion Papers 2112, Graduate School of Economics, Kobe University.
    16. Chen, Jiandong & Cheng, Shulei & Song, Malin & Wang, Jia, 2016. "Interregional differences of coal carbon dioxide emissions in China," Energy Policy, Elsevier, vol. 96(C), pages 1-13.
    17. Lie Ma & Qiu Xie & Shiying Shi & Xiaosu Ye & Aifeng Zhao, 2017. "Regional Maldistribution of China’s Hospitals Based on Their Structural System," Sustainability, MDPI, vol. 9(6), pages 1-18, June.
    18. Shlomo Yitzhaki, 2015. "Gini’s mean difference offers a response to Leamer’s critique," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 31-43, April.
    19. Ingvild Almås & Magne Mogstad, 2009. "Older or Wealthier? The Impact of Age Adjustments on the Wealth Inequality Ranking of Countries," Discussion Papers 583, Statistics Norway, Research Department.
    20. Timm B nke & Carsten Schr der, 2007. "Inequality and welfare estimates using two alternative weighting schemes," LIS Working papers 463, LIS Cross-National Data Center in Luxembourg.
    21. Christian Otchia, 2014. "Agricultural Modernization, Structural Change and Pro-poor Growth: Policy Options for the Democratic Republic of Congo," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 3(1), pages 1-43, December.
    22. Monti, maria & Santoro, alessandro, 2010. "Stratification and between-group inequality: a new approach to measurement," MPRA Paper 29361, University Library of Munich, Germany.
    23. Shlomo Yitzhaki & Peter Lambert, 2013. "The relationship between the absolute deviation from a quantile and Gini’s mean difference," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 97-104, September.

    More about this item

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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