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Reducing Inequalities among Unequals

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  • Mathieu Faure

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Nicolas Gravel

    (CSH - Centre de sciences humaines de New Delhi - MEAE - Ministère de l'Europe et des Affaires étrangères - CNRS - Centre National de la Recherche Scientifique, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

This article establishes an equivalence between four incomplete rankings of distributions of income among agents who are vertically differentiated with respect to some nonincome characteristic (health, household size, etc.). The first ranking is the possibility of going from one distribution to the other by a finite sequence of income transfers from richer and more highly ranked agents to poorer and less highly ranked ones. The second ranking is the unanimity among utilitarian planners who assume that agents' marginal utility of income is decreasing with respect to both income and the source of vertical differentiation. The third ranking is the Bourguignon (Journal of Econometrics, 42 (1989), 67–80) Ordered Poverty Gap dominance criterion. The fourth ranking is a new dominance criterion based on cumulative lowest incomes.

Suggested Citation

  • Mathieu Faure & Nicolas Gravel, 2021. "Reducing Inequalities among Unequals," Post-Print hal-03002498, HAL.
    • Handle: RePEc:hal:journl:hal-03002498
    DOI: 10.1111/iere.12490
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03002498
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    1. anonymous, 1987. "A new measure of the effective exchange rate," Reserve Bank of New Zealand Bulletin, Reserve Bank of New Zealand, vol. 50, june.
    2. Nicolas Gravel & Patrick Moyes, 2013. "Utilitarianism or welfarism: does it make a difference?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 529-551, February.
    3. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    4. Nicolas Gravel & Abhiroop Mukhopadhyay, 2010. "Is India better off today than 15 years ago? A robust multidimensional answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 173-195, June.
    5. Ebert, Udo, 1997. "Social Welfare When Needs Differ: An Axiomatic Approach," Economica, London School of Economics and Political Science, vol. 64(254), pages 233-244, May.
    6. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    7. Moyes, Patrick, 2012. "Comparisons of heterogeneous distributions and dominance criteria," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1351-1383.
    8. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    9. Bishop, John A & Chakraborti, S & Thistle, Paul D, 1989. "Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves," The Review of Economics and Statistics, MIT Press, vol. 71(4), pages 725-727, November.
    10. Nicolas Gravel & Patrick Moyes & Benoît Tarroux, 2009. "Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods," Economica, London School of Economics and Political Science, vol. 76(303), pages 432-461, July.
    11. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    12. Buhong Zheng, 2007. "Unit-Consistent Poverty Indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 113-142, April.
    13. David Levhari & Jacob Paroush & Bezalel Peleg, 1975. "Efficiency Analysis for Multivariate Distributions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 87-91.
    14. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
    15. James P. Quirk & Rubin Saposnik, 1962. "Admissibility and Measurable Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 140-146.
    16. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    17. André Decoster & Erwin Ooghe, 2006. "A Bounded Index Test To Make Robust Heterogeneous Welfare Comparisons," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 52(3), pages 361-376, September.
    18. 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.
    19. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    20. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    21. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
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    4. Oliver Grothe & Fabian Kächele & Friedrich Schmid, 2022. "A multivariate extension of the Lorenz curve based on copulas and a related multivariate Gini coefficient," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(3), pages 727-748, September.

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