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Linear Inequality Measures and the Redistribution of Income

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  • Duclos, Jean-Yves

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  • Tabi, Martin

Abstract

A class of inequality measures that is a natural companion to the popular Lorenz curve is the class of measures that are linear in incomes. These measures, which include the Gini and S-Gini coefficients, can be interpreted as ethical means of relative deprivation feelings. Their change through the tax and benefit system can be decomposed simply as a sum of progressivity indices for individual taxes and benefits, minus an index of horizontal inequity measured by the extent of reranking in the population. These progressivity and horizontal inequity indices can also be interpreted as ethical means of perceptions of fiscal harshness and ill-performance. We furthermore derive the asymptotic sampling distribution of these classes of indices of redistribution, progressivity, and horizontal inequity, which enables their use with micro-data on a population. We illustrate the theoretical and statistical results through an application on the distribution and redistribution of income in Canada in 1981 and in 1990.

Suggested Citation

  • Duclos, Jean-Yves & Tabi, Martin, 1996. "Linear Inequality Measures and the Redistribution of Income," Cahiers de recherche 9613, Université Laval - Département d'économique.
  • Handle: RePEc:lvl:laeccr:9613
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    File URL: http://www.ecn.ulaval.ca/w3/recherche/cahiers/1996/9613.pdf
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    1. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    2. 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.
    3. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 521-531.
    4. R. A. Musgrave & Tun Thin, 1948. "Income Tax Progression, 1929-48," Journal of Political Economy, University of Chicago Press, vol. 56, pages 498-498.
    5. 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.
    6. Plotnick, Robert, 1981. "A Measure of Horizontal Inequity," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 283-288, May.
    7. Kakwani, Nanok C, 1977. "Measurement of Tax Progressivity: An International Comparison," Economic Journal, Royal Economic Society, vol. 87(345), pages 71-80, March.
    8. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    9. Feldstein, Martin, 1976. "On the theory of tax reform," Journal of Public Economics, Elsevier, vol. 6(1-2), pages 77-104.
    10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    11. 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.
    12. Pfahler, Wilhelm, 1987. "Redistributive Effects of Tax Progressivity: Evaluating a General Class of Aggregate Measures," Public Finance = Finances publiques, , vol. 42(1), pages 1-31.
    13. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    14. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
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    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

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