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The Social Welfare Implications of the Zenga Index

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  • Francesca Greselin
  • Simone Pellegrino
  • Achille Vernizzi

Abstract

We introduce the social welfare implications of the Zenga index, a recently proposed index of inequality. Our proposal is derived by following the seminal book by Son (2011) and the recent working paper by Kakwani and Son (2019). We compare the Zenga based approach with the classical one, based on the Lorenz curve and the Gini coefficient, as well as the Bonferroni index. We show that the social welfare specification based on the Zenga uniformity curve presents some peculiarities that distinguish it from the other considered indexes. The social welfare specification presented here provides a deeper understanding of how the Zenga index evaluates the inequality in a distribution.

Suggested Citation

  • Francesca Greselin & Simone Pellegrino & Achille Vernizzi, 2020. "The Social Welfare Implications of the Zenga Index," Papers 2006.12623, arXiv.org.
    • Handle: RePEc:arx:papers:2006.12623
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    References listed on IDEAS

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    1. Whitmore, G A, 1970. "Third-Degree Stochastic Dominance," American Economic Review, American Economic Association, vol. 60(3), pages 457-459, June.
    2. Chipman, John S., 1974. "The welfare ranking of Pareto distributions," Journal of Economic Theory, Elsevier, vol. 9(3), pages 275-282, November.
    3. Kats, Amoz, 1972. "On the social welfare function and the parameters of income distribution," Journal of Economic Theory, Elsevier, vol. 5(3), pages 377-382, December.
    4. Sheshinski, Eytan, 1972. "Relation between a social welfare function and the gini index of income inequality," Journal of Economic Theory, Elsevier, vol. 4(1), pages 98-100, February.
    5. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    6. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    7. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    8. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April.
    9. Pasquazzi Leo & Zenga Michele, 2018. "Components of Gini, Bonferroni, and Zenga Inequality Indexes for EU Income Data," Journal of Official Statistics, Sciendo, vol. 34(1), pages 149-180, March.
    10. Newbery, David, 1970. "A theorem on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 264-266, September.
    11. Francesca Greselin & Leo Pasquazzi & Ričardas Zitikis, 2013. "Contrasting the Gini and Zenga indices of economic inequality," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 282-297, February.
    12. Sen, Amartya, 1979. "The Welfare Basis of Real Income Comparisons: A Survey," Journal of Economic Literature, American Economic Association, vol. 17(1), pages 1-45, March.
    13. Willig, Robert D, 1981. "Social Welfare Dominance," American Economic Review, American Economic Association, vol. 71(2), pages 200-204, May.
    14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    15. Sen, Amartya, 1974. "Informational bases of alternative welfare approaches : Aggregation and income distribution," Journal of Public Economics, Elsevier, vol. 3(4), pages 387-403, November.
    16. Blackorby, Charles & Donaldson, David, 1977. "Utility vs equity : Some plausible quasi-orderings," Journal of Public Economics, Elsevier, vol. 7(3), pages 365-381, June.
    17. Paolo Radaelli, 2010. "On the Decomposition by Subgroups of the Gini Index and Zenga's Uniformity and Inequality Indexes," International Statistical Review, International Statistical Institute, vol. 78(1), pages 81-101, April.
    18. Francesca Greselin & Leo Pasquazzi & Ričardas Zitikis, 2010. "Zenga's New Index of Economic Inequality, Its Estimation, and an Analysis of Incomes in Italy," Journal of Probability and Statistics, Hindawi, vol. 2010, pages 1-26, April.
    19. Usher, Dan, 1980. "The Welfare Basis of Real Income Comparisons: A Comment," Journal of Economic Literature, American Economic Association, vol. 18(4), pages 1544-1547, December.
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    Cited by:

    1. Francesca Greselin & Simone Pellegrino & Achille Vernizzi, 2021. "The Zenga Equality Curve: A New Approach to Measuring Tax Redistribution and Progressivity," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(4), pages 950-976, December.

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