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A general rank-dependent approach for distributional comparisons

Author

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  • Flaviana Palmisano

    (Sapienza University of Rome)

  • Ida Petrillo

    (University of Bari)

Abstract

This paper provides a normative framework for distributional comparisons within a rank-dependent and bidimensional setting where individuals' well-being is characterized by a monetary and a non-monetary dimension (income and needs for instance) and when the focus is on inequality at the bottom as well as at the top of distribution in both dimensions. To this end, we develop third order inverse stochastic dominance conditions for classes of social welfare functions satisfying: i) Threshold Dependent Positional Transfer Sensitivity with respect to the monetary dimension (TDPT); ii) TDPT combined with downside inequality aversion with respect to the non-monetary dimension; iii) TDPT combined with upside inequality aversion with respect to the non-monetary dimension. Our results emerge along with the existing one, formulated by Zoli (2000) supporting downside inequality aversion both with respect to income and needs and Aaberge (2009) supporting upside inequality aversion with respect to income.

Suggested Citation

  • Flaviana Palmisano & Ida Petrillo, 2021. "A general rank-dependent approach for distributional comparisons," Working Papers 567, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2021-567
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    File URL: http://www.ecineq.org/milano/WP/ECINEQ2021-567.pdf
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    References listed on IDEAS

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    1. P. Brunori & F. Palmisano & V. Peragine, 2014. "Income taxation and equity: new dominance criteria and an application to Romania," SERIES 0050, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Dec 2014.
    2. Flaviana Palmisano, 2018. "Evaluating Patterns of Income Growth when Status Matters: A Robust Approach," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(1), pages 147-169, March.
    3. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    4. Roy van der Weide & Branko Milanovic, 2018. "Inequality is Bad for Growth of the Poor (but Not for That of the Rich)," The World Bank Economic Review, World Bank, vol. 32(3), pages 507-530.
    5. Flaviana Palmisano & Vito Peragine, 2015. "The Distributional Incidence of Growth: A Social Welfare Approach," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 440-464, September.
    6. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    7. Ebert, Udo, 2000. "Sequential Generalized Lorenz Dominance and Transfer Principles," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 113-122, April.
    8. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    9. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    10. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 183-196.
    11. Rolf Aaberge & Tarjei Havnes & Magne Mogstad, 2013. "A theory for ranking distribution functions," Discussion Papers 763, Statistics Norway, Research Department.
    12. Lambert, Peter J & Ramos, Xavier, 2002. "Welfare Comparisons: Sequential Procedures for Heterogeneous Populations," Economica, London School of Economics and Political Science, vol. 69(276), pages 549-562, November.
    13. Glaeser, Edward & Scheinkman, Jose & Shleifer, Andrei, 2003. "The injustice of inequality," Journal of Monetary Economics, Elsevier, vol. 50(1), pages 199-222, January.
    14. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    15. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    16. Anthony Atkinson & Thomas Piketty, 2010. "Top Incomes : A Global Perspective," PSE-Ecole d'économie de Paris (Postprint) halshs-00754875, HAL.
    17. Stephen P. Jenkins & Peter J. Lambert, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 39(4), pages 337-356, December.
    18. Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
    19. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
    20. Easterly, William, 2001. "The Middle Class Consensus and Economic Development," Journal of Economic Growth, Springer, vol. 6(4), pages 317-335, December.
    21. Anthony B. Atkinson & François Bourguignon, 1987. "Income Distribution and Differences in Needs," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 12, pages 350-370, Palgrave Macmillan.
    22. Anthony Atkinson & Thomas Piketty, 2007. "Top incomes over the twentieth century: A contrast between continental european and english-speaking countries," Post-Print halshs-00754859, HAL.
    23. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    24. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
    25. Atkinson, A. B. & Piketty, Thomas (ed.), 2010. "Top Incomes: A Global Perspective," OUP Catalogue, Oxford University Press, number 9780199286898.
    26. Maria C. Lo Bue & Flaviana Palmisano, 2020. "The Individual Poverty Incidence of Growth," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1295-1321, December.
    27. Jenkins, Stephen P & Lambert, Peter J, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 39(4), pages 337-356, December.
    28. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    29. Peragine, Vitorocco, 2002. "Opportunity egalitarianism and income inequality," Mathematical Social Sciences, Elsevier, vol. 44(1), pages 45-64, September.
    30. Christine Chambaz & Eric Maurin, 1998. "Atkinson And Bourguignon'S Dominance Criteria: Extended And Applied To The Measurement Of Poverty In France," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 44(4), pages 497-513, December.
    31. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    32. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    33. Atkinson, A. B. & Piketty, Thomas (ed.), 2007. "Top Incomes Over the Twentieth Century: A Contrast Between Continental European and English-Speaking Countries," OUP Catalogue, Oxford University Press, number 9780199286881.
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    Cited by:

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    More about this item

    Keywords

    sequential stochastic dominance; social welfare; inequality;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • 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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