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An Atkinson-Gini family of social evaluation functions

Author

Listed:
  • Jean-Yves Duclos

    () (CIRPEE and Departement d'economique, Universite Laval, Canada)

  • Abdelkrim Araar

    () (CIRPEE and PEP, Universite Laval, Canada)

Abstract

We investigate the properties of a family of social evaluation functions and inequality indices which merge the features of the family of Atkinson (1970) and S-Gini (Donaldson and Weymark (1980, 1983), Yitzhaki (1983) and Kakwani (1980)) indices. Income inequality aversion is captured by decreasing marginal utilities, and aversion to rank inequality is captured by rank-dependent ethical weights, thus providing an ethically-flexible dual basis for the assessment of inequality and equity. These social evaluation functions can be interpreted as average utility corrected for the illfare of relative deprivation. They can alternatively be understood as averages of altruistic well-being in a population. They moreover have a simple graphical interpretation.

Suggested Citation

  • Jean-Yves Duclos & Abdelkrim Araar, 2003. "An Atkinson-Gini family of social evaluation functions," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-16.
  • Handle: RePEc:ebl:ecbull:eb-03c60001
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    References listed on IDEAS

    as
    1. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    2. Duclos, Jean-Yves, 1998. "Social evaluation functions, economic isolation and the Suits index of progressivity," Journal of Public Economics, Elsevier, vol. 69(1), pages 103-121, July.
    3. 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.
    4. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1994. "Generalized Ginis and Cooperative Bargaining Solutions," Econometrica, Econometric Society, vol. 62(5), pages 1161-1178, September.
    5. Berrebi, Z. M. & Silber, Jacques, 1981. "Weighting income ranks and levels : A Multiple-Parameter Generalization For Absolute and Relative Inequality Indices," Economics Letters, Elsevier, vol. 7(4), pages 391-397.
    6. Feldstein, Martin, 1976. "On the theory of tax reform," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 77-104.
    7. Weymark John A., 1995. "An Alternative Proof of Ben Porath and Gilboa's Generalized Gini Characterization Theorem," Journal of Economic Theory, Elsevier, vol. 66(2), pages 573-580, August.
    8. Shlomo Yitzhaki, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, Oxford University Press, vol. 93(2), pages 321-324.
    9. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    10. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    11. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    12. 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.
    13. Jean-Yves Duclos & Peter J. Lambert, 2000. "A normative and statistical approach to measuring classical horizontal inequity," Canadian Journal of Economics, Canadian Economics Association, vol. 33(1), pages 87-113, February.
    14. Porath Elchanan Ben & Gilboa Itzhak, 1994. "Linear Measures, the Gini Index, and The Income-Equality Trade-off," Journal of Economic Theory, Elsevier, vol. 64(2), pages 443-467, December.
    15. Aronson, J Richard & Johnson, Paul & Lambert, Peter J, 1994. "Redistributive Effects and Unequal Income Tax Treatment," Economic Journal, Royal Economic Society, vol. 104(423), pages 262-270, March.
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    17. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
    18. John D. Hey & Peter J. Lambert, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, Oxford University Press, vol. 95(3), pages 567-573.
    19. Plotnick, Robert, 1981. "A Measure of Horizontal Inequity," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 283-288, May.
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    Citations

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    Cited by:

    1. Michael Savage, 2016. "Poorest Made Poorer? Decomposing income losses at the bottom of the income distribution during the Great Recession," Papers WP528, Economic and Social Research Institute (ESRI).
    2. repec:col:000093:015846 is not listed on IDEAS
    3. Makdissi, Paul & Yazbeck, Myra, 2016. "Avoiding blindness to health status in health achievement and health inequality measurement," Social Science & Medicine, Elsevier, vol. 171(C), pages 39-47.
    4. Heinz Welsch & Udo Ebert, 2004. "The Social Evaluation of Income Distribution: An Assessment Based on Happiness Surveys," LIS Working papers 381, LIS Cross-National Data Center in Luxembourg.
    5. Ivica Urban, 2013. "Implementation Issues in the Duclos–Jalbert–Araar Decomposition of Redistributive Effect," Public Finance Review, , vol. 41(1), pages 121-143, January.
    6. Udo Ebert & Heinz Welsch, 2009. "How Do Europeans Evaluate Income Distributions? An Assessment Based On Happiness Surveys," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(3), pages 803-819, September.

    More about this item

    Keywords

    altruism.;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D3 - Microeconomics - - Distribution

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