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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 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," Working Papers 2004, Herman Deleeck Centre for Social Policy, University of Antwerp.
    • Handle: RePEc:hdl:wpaper:2004
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. Giovanna Scarcilli, 2024. "Studying the evolution of cumulative deprivation among European countries with a copula-based approach," Working Papers 667, ECINEQ, Society for the Study of Economic Inequality.
    4. 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.
    5. César García Gómez & Ana Pérez & Mercedes Prieto-Alaiz, 2024. "Changes in the Dependence Structure of AROPE Components: Evidence from the Spanish Region," Hacienda Pública Española / Review of Public Economics, IEF, vol. 248(1), pages 21-51, March.
    6. 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.
    7. 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.

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    More about this item

    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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