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Measuring cumulative deprivation and affluence based on the diagonal dependence diagram

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  • Koen Decancq

    () (University of Antwerp
    KULeuven
    LSE
    Université catholique to Louvain)

Abstract

In this paper, I introduce the diagonal dependence diagram to chart dependence around the main diagonal of a multivariate distribution. This diagonal dependence diagram is a useful tool to quantify phenomena such as cumulative deprivation and affluence. A society is said to exhibit more cumulative deprivation when more persons occupy bottom positions in all dimensions of well-being. Analogously, there is more cumulative affluence in a society when more persons occupy top positions in all dimensions. The diagonal dependence diagram consists of two curves which are obtained by taking the diagonal section of the underlying copula and survival functions, respectively. I show the elementary multivariate rearrangements underlying dominance in terms of both curves. The area under each curve leads to a natural index of diagonal dependence. Interestingly, the average of both indices equals a multivariate generalization of Spearman’s footrule and is closely related to the cograduation index proposed by Gini.

Suggested Citation

  • Koen Decancq, 2020. "Measuring cumulative deprivation and affluence based on the diagonal dependence diagram," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 103-117, August.
  • Handle: RePEc:spr:metron:v:78:y:2020:i:2:d:10.1007_s40300-020-00173-7
    DOI: 10.1007/s40300-020-00173-7
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    More about this item

    Keywords

    Copula; Cumulative deprivation; Cumulative affluence; Diagonal dependence; Spearman’s footrule; Gini’s cograduation index;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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