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An Atkinson-Gini Family of Social Evaluation Functions

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  • Araar, Abdelkrim
  • Duclos, Jean-Yves

Abstract

We propose a class of social evaluation functions and of inequality indices which merge the useful features of the family of Atkinson (1970) and of S-Gini (Donaldson and Weymark (1980, 1983), Yitzhaki (1983) and Kakwani (1980)) indices. These social evaluation functions can be interpreted as average utility corrected for relative deprivation in individual welfare. They can also be understood as averages of altruistic welfare in the population, and have a simple and useful graphical interpretation.

Suggested Citation

  • Araar, Abdelkrim & Duclos, Jean-Yves, 1998. "An Atkinson-Gini Family of Social Evaluation Functions," Cahiers de recherche 9826, Université Laval - Département d'économique.
    • Handle: RePEc:lvl:laeccr:9826
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    6. 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.
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    8. 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.
    9. Jean‐Yves Duclos & Peter J. Lambert, 2000. "A normative and statistical approach to measuring classical horizontal inequity," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 33(1), pages 87-113, February.
    10. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1994. "Generalized Ginis and Cooperative Bargaining Solutions," Econometrica, Econometric Society, vol. 62(5), pages 1161-1178, September.
    11. 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.
    12. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    13. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    14. 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.
    15. Jean-Yves Duclos, 2000. "Gini Indices and the Redistribution of Income," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 7(2), pages 141-162, March.
    16. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    17. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
    18. Plotnick, Robert, 1981. "A Measure of Horizontal Inequity," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 283-288, May.
    19. Shlomo Yitzhaki, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(2), pages 321-324.
    20. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    21. 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.
    22. John D. Hey & Peter J. Lambert, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 567-573.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Abdelkrim Araar, 2008. "Social Classes, Inequality and Redistributive Policies in Canada," Cahiers de recherche 0817, CIRPEE.
    2. 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.
    3. Luis Huesca, 2017. "Income redistribution and inequality in the Mexican tax-benefit system," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, vol. 36(72), October.
    4. Peter J. Lambert & Helen T. Naughton, 2009. "The Equal Absolute Sacrifice Principle Revisited," Journal of Economic Surveys, Wiley Blackwell, vol. 23(2), pages 328-349, April.
    5. 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.
    6. Ivica Urban, 2013. "Implementation Issues in the Duclos–Jalbert–Araar Decomposition of Redistributive Effect," Public Finance Review, , vol. 41(1), pages 121-143, January.
    7. Abdelkrim Araar, 2008. "On the Decomposition of Polarization Indices: Illustrations with Chinese and Nigerian Household Surveys," Cahiers de recherche 0806, CIRPEE.
    8. Abdelkrim Araar, 2006. "On the Decomposition of the Gini Coefficient: an Exact Approach, with an Illustration Using Cameroonian Data," Cahiers de recherche 0602, CIRPEE.
    9. 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).
    10. 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.
    11. Quentin Wodon & Shlomo Yitzhaki, 2002. "Evaluating the Impact of Government Programs on Social Welfare: The Role of Targeting and the Allocation Rules Among Program Beneficiaries," Public Finance Review, , vol. 30(2), pages 102-123, March.

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    More about this item

    Keywords

    Social evaluation functions; Inequality indices; Relative deprivation; Altruism;
    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
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers

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