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Individual Diversity and the Gini Decomposition

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  • Lidia Ceriani
  • Paolo Verme

Abstract

The paper defines the Gini index as the sum of individual contributions where individual contributions are interpreted as the degree of diversity of each individual from all other members of society. Among various possible forms of individual contributions to the Gini found in the literature, we show that only one form satisfies a set of desirable properties. This form can be used for decomposing the Gini into population subgroups. An empirical illustration shows the use of this approach. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • Lidia Ceriani & Paolo Verme, 2015. "Individual Diversity and the Gini Decomposition," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 121(3), pages 637-646, April.
    • Handle: RePEc:spr:soinre:v:121:y:2015:i:3:p:637-646
    DOI: 10.1007/s11205-014-0656-0
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    1. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    2. Lidia Ceriani & Paolo Verme, 2012. "The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(3), pages 421-443, September.
    3. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    4. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-685, November.
    5. Frank Cowell & Udo Ebert, 2004. "Complaints and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 71-89, August.
    6. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
    7. Shlomo Yitzhaki, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(2), pages 321-324.
    8. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    9. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
    10. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June.
    11. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
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    Cited by:

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    3. Luciano Rossoni & Rodrigo Assunção Rosa, 2024. "Reducing the Matthew Effect on Journal Citations through an Inclusive Indexing Logic: The Brazilian Spell (Scientific Periodicals Electronic Library) Experience," Publications, MDPI, vol. 12(1), pages 1-24, February.
    4. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    5. Neves Costa, Rita & Pérez-Duarte, Sébastien, 2019. "Not all inequality measures were created equal - The measurement of wealth inequality, its decompositions, and an application to European household wealth," Statistics Paper Series 31, European Central Bank.
    6. Iñaki Permanyer & Nicolai Suppa, 2022. "Racing ahead or lagging behind? Territorial cohesion in human development around the globe," Regional Studies, Taylor & Francis Journals, vol. 56(12), pages 2086-2101, December.
    7. Anson Au, 2023. "Reassessing the econometric measurement of inequality and poverty: toward a cost-of-living approach," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-10, December.
    8. José Manuel Gavilan-Ruiz & África Ruiz-Gándara & Francisco Javier Ortega-Irizo & Luis Gonzalez-Abril, 2024. "Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index," Stats, MDPI, vol. 7(4), pages 1-12, November.

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    More about this item

    Keywords

    Gini; Inequality; Decomposition; Income distribution; Welfare measurement;
    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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