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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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    1. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    2. Kateryna Tkach & Chiara Gigliarano, 2018. "Multidimensional poverty measurement: dependence between well-being dimensions using copula function," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 72(3), pages 89-100, July-Sept.
    3. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
    4. Aaberge, Rolf & Peluso, Eugenio & Sigstad, Henrik, 2019. "The dual approach for measuring multidimensional deprivation: Theory and empirical evidence," Journal of Public Economics, Elsevier, vol. 177(C), pages 1-1.
    5. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    6. Anthony B. Atkinson & Christoph Lakner, 2021. "Capital and Labor: The Factor Income Composition of Top Incomes in the United States, 1962-2006," The Review of Economics and Statistics, MIT Press, vol. 103(5), pages 892-904, December.
    7. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2015. "What do normative indices of multidimensional inequality really measure?," Journal of Public Economics, Elsevier, vol. 130(C), pages 94-104.
    8. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 207-251, June.
    9. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    10. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    11. M. Taylor, 2007. "Multivariate measures of concordance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 789-806, December.
    12. Rolf Aaberge & Anthony B. Atkinson & Sebastian Königs, 2018. "From classes to copulas: wages, capital, and top incomes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 16(2), pages 295-320, June.
    13. Koen Decancq & Erik Schokkaert, 2016. "Beyond GDP: Using Equivalent Incomes to Measure Well-Being in Europe," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 126(1), pages 21-55, March.
    14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    15. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    16. Sarabia, José María, 2008. "A general definition of the Leimkuhler curve," Journal of Informetrics, Elsevier, vol. 2(2), pages 156-163.
    17. Alkire, Sabina & Foster, James, 2011. "Counting and multidimensional poverty measurement," Journal of Public Economics, Elsevier, vol. 95(7), pages 476-487.
    18. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    19. Manuel Úbeda-Flores, 2005. "Multivariate versions of Blomqvist’s beta and Spearman’s footrule," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 781-788, December.
    20. Anthony Atkinson, 2011. "On lateral thinking," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 319-328, September.
    21. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
    22. Casey Quinn, 2007. "Using copulas to measure association between ordinal measures of health and income," Health, Econometrics and Data Group (HEDG) Working Papers 07/24, HEDG, c/o Department of Economics, University of York.
    23. Corrado Gini, 2005. "On the measurement of concentration and variability of characters," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-38.
    24. Quinn C, 2009. "Measuring income-related inequalities in health using a parametric dependence function," Health, Econometrics and Data Group (HEDG) Working Papers 09/24, HEDG, c/o Department of Economics, University of York.
    25. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    26. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    27. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 51-65, April.
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    Cited by:

    1. 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.
    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. 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.
    6. 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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