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Measuring cumulative deprivation and affluence based on the diagonal dependence diagram

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  • Koen Decancq

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 re-arrangements 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," Working Papers of Department of Economics, Leuven 652198, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    • Handle: RePEc:ete:ceswps:652198
    Note: paper number DPS20.02
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    Cited by:

    1. Koen Decancq & Annemie Nys, 2021. "Growing Up In A Poor Household In Belgium: A Rank-Based Multidimensional Perspective On Child Well-Being," Working Papers 2104, Herman Deleeck Centre for Social Policy, University of Antwerp.
    2. Koen Decancq, 2023. "Cumulative deprivation: identification and aggregation," Chapters, in: Udaya R. Wagle (ed.), Research Handbook on Poverty and Inequality, chapter 4, pages 52-67, Edward Elgar Publishing.
    3. Luis Ayala & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The impact of different data sources on the level and structure of income inequality," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(3), pages 583-611, September.
    4. César Garcia-Gomez & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The evolution of poverty in the EU-28: a further look based on multivariate tail dependence," Working Papers 605, ECINEQ, Society for the Study of Economic Inequality.
    5. Koen Decancq, 2020. "Bad news does not come alone: Cumulative deprivation in Belgium," Working Papers 2007, Herman Deleeck Centre for Social Policy, University of Antwerp.

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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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