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Partial multidimensional inequality orderings

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  • Duclos, Jean-Yves
  • Sahn, David E.
  • Younger, Stephen D.

Abstract

The paper investigates how comparisons of multivariate inequality can be made robust to varying the intensity of focus on the share of the population that are more relatively deprived. It is in the spirit of Sen (1970)'s partial orderings and follows the dominance approach to making inequality comparisons. By focusing on those below a multidimensional inequality "frontier", we are able to reconcile the literature on multivariate relative poverty and multivariate inequality. Some existing approaches to multivariate inequality actually reduce the distributional analysis to a univariate problem, either by using a utility function first to aggregate an individual's multiple dimensions of well-being, or by applying a univariate inequality analysis to each dimension independently. One of our innovations is that unlike previous approaches, the distribution of relative well-being in one dimension is allowed to affect how other dimensions influence overall inequality. Our methods are also robust to choices of individual "utility" or aggregation functions. We apply our approach to data from India and Mexico to show inter alia how dependence between dimensions of well-being can influence relative poverty and inequality comparisons between two populations.

Suggested Citation

  • Duclos, Jean-Yves & Sahn, David E. & Younger, Stephen D., 2011. "Partial multidimensional inequality orderings," Journal of Public Economics, Elsevier, vol. 95(3-4), pages 225-238, April.
    • Handle: RePEc:eee:pubeco:v:95:y:2011:i:3-4:p:225-238
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    Cited by:

    1. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.
    2. 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.
    3. Maasoumi, Esfandiar & Racine, Jeffrey S., 2016. "A solution to aggregation and an application to multidimensional ‘well-being’ frontiers," Journal of Econometrics, Elsevier, vol. 191(2), pages 374-383.
    4. Stergios Athanassoglou, 2015. "Multidimensional welfare rankings under weight imprecision: a social choice perspective," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 719-744, April.
    5. Mehmet Pinar & Thanasis Stengos & Nikolas Topaloglou, 2022. "Stochastic dominance spanning and augmenting the human development index with institutional quality," Annals of Operations Research, Springer, vol. 315(1), pages 341-369, August.
    6. Sonne-Schmidt, Christoffer & Tarp, Finn & Østerdal, Lars Peter, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series 097, World Institute for Development Economic Research (UNU-WIDER).
    7. M. Azhar Hussain & Mette Møller Jørgensen & Lars Peter Østerdal, 2016. "Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 739-759, November.
    8. Esfandiar Maasoumi & Jeffrey S. Racine, 2013. "Multidimensional Poverty Frontiers: Parametric Aggregators Based on Nonparametric Distributions," Department of Economics Working Papers 2013-07, McMaster University.
    9. Nicholas Rohde & Ross Guest, 2013. "Multidimensional Racial Inequality in the United States," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(2), pages 591-605, November.
    10. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    11. Nicholas Rohde & Ross Guest, 2018. "Multidimensional Inequality Across Three Developed Countries," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(3), pages 576-591, September.
    12. Arndt, Channing & Mahrt, Kristi & Hussain, M. Azhar & Tarp, Finn, 2018. "A human rights-consistent approach to multidimensional welfare measurement applied to sub-Saharan Africa," World Development, Elsevier, vol. 108(C), pages 181-196.
    13. Martyna Kobus, 2014. "Multidimensional polarization for ordinal data," Working Papers 326, ECINEQ, Society for the Study of Economic Inequality.
    14. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series wp-2013-097, World Institute for Development Economic Research (UNU-WIDER).
    15. Thi Kim Thanh Bui & Guido Erreygers, 2020. "Multidimensional Inequality in Vietnam, 2002–2012," Economies, MDPI, vol. 8(2), pages 1-31, April.
    16. Sonne-Schmidt, Christoffer & Tarp, Finn & Peter, Lars, 2011. "Ordinal multidimensional inequality: theory and application to the 2x2 case," MPRA Paper 72838, University Library of Munich, Germany.
    17. Echevin, Damien, 2011. "Vulnerability to asset-poverty in Sub-Saharan Africa," MPRA Paper 35660, University Library of Munich, Germany.
    18. Arndt, Channing & Mahrt, Kristi & Hussain, M. Azhar & Tarp, Finn, 2018. "A human rights-consistent approach to multidimensional welfare measurement applied to sub-Saharan Africa," World Development, Elsevier, vol. 108(C), pages 181-196.
    19. Suman Seth and Maria Emma Santos, 2018. "Multidimensional Inequality and Human Development," OPHI Working Papers ophiwp114_2.pdf, Queen Elizabeth House, University of Oxford.
    20. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.
    21. Athanassoglou, Stergios, 2013. "Multidimensional welfare rankings," MPRA Paper 51642, University Library of Munich, Germany.

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    More about this item

    Keywords

    Inequality Multidimensional comparisons Stochastic dominance;

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

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