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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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    References listed on IDEAS

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    6. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
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    Cited by:

    1. Koen Decancq & María Ana Lugo, 2009. "Measuring inequality of well-being with a correlation-sensitive multidimensional Gini index," Working Papers 124, ECINEQ, Society for the Study of Economic Inequality.
    2. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    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. repec:bla:revinw:v:63:y:2017:i:4:p:706-730 is not listed on IDEAS
    5. Tony Addison & Yukka Pirttilä & Finn Tarp & 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, pages 706-730.
    6. 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.
    7. Elizabeth Lwanga Nanziri, 2017. "Financial Inclusion and Welfare in Post-Apartheid South Africa," Research Papers RP_323, African Economic Research Consortium.

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