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An Atkinson-Gini Family of Social Evaluation Functions: Theory and Illustration Using Data from the Luxembourg Income Study

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  • Abdelkrim Araar
  • Jean-Yves Duclos

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. We demonstrate a few of their interesting properties. We also illustrate their application using data from the Luxembourg Income Study.

Suggested Citation

  • Abdelkrim Araar & Jean-Yves Duclos, 2005. "An Atkinson-Gini Family of Social Evaluation Functions: Theory and Illustration Using Data from the Luxembourg Income Study," LIS Working papers 416, LIS Cross-National Data Center in Luxembourg.
    • Handle: RePEc:lis:liswps:416
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    References listed on IDEAS

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    1. Salas, Rafael, 1998. "Horizontal Inequality and Vertical Redistribution in a Social Welfare Framework," Public Finance = Finances publiques, , vol. 53(2), pages 229-242.
    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. King, Mervyn A, 1983. "An Index of Inequality: With Applications to Horizontal Equity and Social Mobility," Econometrica, Econometric Society, vol. 51(1), pages 99-115, January.
    4. 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.
    5. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    6. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Plotnick, Robert, 1981. "A Measure of Horizontal Inequity," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 283-288, May.
    13. 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.
    14. Feldstein, Martin, 1976. "On the theory of tax reform," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 77-104.
    15. 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.
    16. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    17. 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.
    18. 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.
    19. 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.
    20. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
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    2. Abdelkrim Araar, 2007. "Poverty, Inequality and Stochastic Dominance, Theory and Practice: The Case of Burkina Faso," Working Papers PMMA 2007-08, PEP-PMMA.
    3. Peter J. Lambert & Helen T. Naughton, 2006. "The Equal Sacrifice Principle Revisited," University of Oregon Economics Department Working Papers 2006-4, University of Oregon Economics Department, revised 01 Jun 2006.
    4. Peter J. Lambert, 2007. "Positional equity and equal sacrifice: design principles for an EU-wide income tax?," Working Papers 0706, University of Otago, Department of Economics, revised Apr 2007.
    5. Abdelkrim Araar, 2006. "Poverty, Inequality and Stochastic Dominance, Theory and Practice: Illustration with Burkina Faso Surveys," Cahiers de recherche 0634, CIRPEE.

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