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The Gini coefficient reveals more


  • Peter J. Lambert
  • Andre' Decoster


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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    1. Davydov, Youri & Zitikis, Ricardas, 2002. "Convergence of generalized Lorenz curves based on stationary ergodic random sequences with deterministic noise," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 329-340, October.
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    3. Giovanni Maria Giorgi, 2005. "A fresh look at the topical interest of the Gini concentration ratio," Econometrics 0511005, EconWPA.
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    Cited by:

    1. Ivica Urban & Peter J. Lambert, 2008. "Redistribution, Horizontal Inequity, and Reranking: How to Measure Them Properly," Public Finance Review, , vol. 36(5), pages 563-587, September.
    2. Schröder, Carsten & Yitzhaki, Shlomo, 2017. "Revisiting the evidence for cardinal treatment of ordinal variables," European Economic Review, Elsevier, vol. 92(C), pages 337-358.
    3. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, 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. Bönke, Timm & Schröder, Carsten, 2007. "Equivalence scales reconsidered: an empirical investigation," Economics Working Papers 2007-31, Christian-Albrechts-University of Kiel, Department of Economics.
    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," Brooks World Poverty Institute Working Paper Series 10910, BWPI, 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 Martín-Román & 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. repec:bla:istatr:v:85:y:2017:i:2:p:325-339 is not listed on IDEAS
    13. Almås, Ingvild & Mogstad, Magne, 2010. "Older or Wealthier? The Impact of Age Adjustment on Cross-Sectional Inequality Measures," Discussion Paper Series in Economics 9/2010, Norwegian School of Economics, Department of Economics.
    14. 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.
    15. repec:gam:jsusta:v:9:y:2017:i:6:p:1046-:d:101639 is not listed on IDEAS
    16. 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.
    17. Magne Mogstad & Ingvild Almås, 2009. "Older or Wealthier? The Impact of Age Adjustments on the Wealth Inequality Ranking of Countries," LWS Working papers 9, LIS Cross-National Data Center in Luxembourg.
    18. Timm Bönke & Carsten Schröder, 2007. "Inequality and welfare estimates using two alternative weighting schemes," LIS Working papers 463, LIS Cross-National Data Center in Luxembourg.
    19. Monti, maria & Santoro, alessandro, 2010. "Stratification and between-group inequality: a new approach to measurement," MPRA Paper 29361, University Library of Munich, Germany.

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    JEL classification:

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


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