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A multidimensional Gini index

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  • Banerjee, Asis Kumar

Abstract

This paper considers the problem of construction of a multidimensional Gini index (MGI) of relative inequality satisfying normatively acceptable conditions. One of the conditions considered is that of Correlation Increasing Majorization (CIM) which has been studied in the existing literature. A new condition called Weighting of Attributes under Unidirectional Comonotonicity (WAUC) is introduced. It requires that, in the case where the allocation of all attributes are comonotonic and attribute i is more unequally distributed than attribute j, a reduction of inequality of i is socially more beneficial than that of inequality of j. An MGI is constructed by taking each individual's well-being to be a weighted average of the attribute levels and applying the univariate Gini formula to the resulting vector of individual well-beings. The weights, same for all individuals, are determined by the attribute levels of all the individuals. It is shown that the suggested MGI satisfies both CIM and WAUC. The existing literature does not seem to contain any other MGI satisfying these two conditions simultaneously.

Suggested Citation

  • Banerjee, Asis Kumar, 2010. "A multidimensional Gini index," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 87-93, September.
    • Handle: RePEc:eee:matsoc:v:60:y:2010:i:2:p:87-93
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    Cited by:

    1. Philipp Poppitz, 2019. "Multidimensional Inequality and Divergence: The Eurozone Crisis in Retrospect," Working Papers V-420-19, University of Oldenburg, Department of Economics, revised Feb 2019.
    2. Asis Kumar Banerjee, 2019. "Economic Properties of Statistical Indices: The Case of a Multidimensional Gini Index," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(1), pages 41-56, March.
    3. Asis Kumar Banerjee, 2012. "Multidimensional Gini Indices, Weak Pigou-Dalton Bundle Dominance and Comonotonizing Majorization," Working Papers 275, ECINEQ, Society for the Study of Economic Inequality.
    4. Charpentier, Arthur & Mussard, Stéphane & Ouraga, Téa, 2021. "Principal component analysis: A generalized Gini approach," European Journal of Operational Research, Elsevier, vol. 294(1), pages 236-249.
    5. Martin Wittenberg & Murray Leibbrandt, 2017. "Measuring Inequality by Asset Indices: A General Approach with Application to South Africa," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(4), pages 706-730, December.
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    7. Maria Ana Lugo & Koen Decancq, 2009. "Measuring Inequality of Well-Being with a Correlation-Sensitive Multidimensional Gini Index," Economics Series Working Papers 459, University of Oxford, Department of Economics.
    8. Asis Banerjee, 2014. "A multidimensional Lorenz dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 171-191, January.
    9. Tanti Novianti & Dian Verawati Panjaitan, 2022. "Income Inequality in Indonesia: Before and during the Covid-19 Pandemic," International Journal of Economics and Financial Issues, Econjournals, vol. 12(3), pages 29-37, May.
    10. Shifa, Muna & Leibbrandt, Murray, 2021. "Spatial Inequality in Sub-Saharan Africa," EconStor Preprints 244591, ZBW - Leibniz Information Centre for Economics.
    11. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    12. Ida D’Attoma & Mariagiulia Matteucci, 2024. "Multidimensional poverty: an analysis of definitions, measurement tools, applications and their evolution over time through a systematic review of the literature up to 2019," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(4), pages 3171-3213, August.
    13. Hodler, Roland & Srisuma, Sorawoot & Vesperoni, Alberto & Zurlinden, Noémie, 2020. "Measuring ethnic stratification and its effect on trust in Africa," Journal of Development Economics, Elsevier, vol. 146(C).
    14. Yanqin Fan & Marc Henry & Brendan Pass & Jorge A. Rivero, 2022. "Lorenz map, inequality ordering and curves based on multidimensional rearrangements," Papers 2203.09000, arXiv.org, revised Apr 2024.
    15. Daniel Felix Ahelegbey & Paolo Giudici, 2024. "Multidimensional Inequality Metrics for Sustainable Business Development," Mathematics, MDPI, vol. 12(22), pages 1-22, November.
    16. Thi Kim Thanh Bui & Guido Erreygers, 2020. "Multidimensional Inequality in Vietnam, 2002–2012," Economies, MDPI, vol. 8(2), pages 1-31, April.
    17. Ulysse Lawogni, 2019. "Measures of Inequality In Vectors Distributions," Working Papers hal-02377802, HAL.

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