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Between-Group Pigou Dalton Transfers

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  • Stéphane Mussard

    (GREDI, Université de Sherbrooke and GEREM, Université de Perpignan)

Abstract

This paper introduces the concept of Pigou-Dalton transfers between populations of income receivers. Gini's mean difference and Dagum's Gini index between populations are axiomatically derived in order to gauge the impact of within- and between-group Pigou-Dalton transfers on Dagum's measure. We show its sensitiveness for any given transfer in the sense that inequality-reducing transfers are captured when transfers occur from higher-income donors to lower-income recipients, which belong to two distinct populations. Accordingly, we point out the implications of between-group transfers on: the ordering of multivariate majorization, the multivariate stochastic dominance in the sense of multivariate Lorenz ordering and zonotope inclusions, the Gini decomposition, and on the use of the generalized entropy index.

Suggested Citation

  • Stéphane Mussard, 2007. "Between-Group Pigou Dalton Transfers," Cahiers de recherche 07-06, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    • Handle: RePEc:shr:wpaper:07-06
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    File URL: http://gredi.recherche.usherbrooke.ca/wpapers/GREDI-0706.pdf
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    References listed on IDEAS

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    1. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    2. Yitzhaki, Shlomo & Lerman, Robert I, 1991. "Income Stratification and Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
    3. Gajdos, Thibault, 2004. "Single crossing Lorenz curves and inequality comparisons," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 21-36, January.
    4. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    5. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2004. "Polarization: Concepts, Measurement, Estimation," Econometrica, Econometric Society, vol. 72(6), pages 1737-1772, November.
    6. Chateauneuf, Alain & Gajdos, Thibault & Wilthien, Pierre-Henry, 2002. "The Principle of Strong Diminishing Transfer," Journal of Economic Theory, Elsevier, vol. 103(2), pages 311-333, April.
    7. Rolf Aaberge & Steinar Bjerve & Kjell Doksum, 2005. "Decomposition of rank-dependent measures of inequality by subgroups," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 493-503.
    8. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-255, June.
    9. Fields, Gary S. & Ok, Efe A., 1996. "The Meaning and Measurement of Income Mobility," Journal of Economic Theory, Elsevier, vol. 71(2), pages 349-377, November.
    10. Chakravarty, Satya Ranjan & Dutta, Bhaskar, 1987. "A note on measures of distance between imcome distributions," Journal of Economic Theory, Elsevier, vol. 41(1), pages 185-188, February.
    11. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
    12. Fleurbaey, Marc & Michel, Philippe, 2001. "Transfer principles and inequality aversion, with an application to optimal growth," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 1-11, July.
    13. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    14. Gleb A. Koshevoy & Karl Mosler, 2007. "Multivariate Lorenz dominance based on zonoids," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(1), pages 57-76, March.
    15. Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 1-14.
    16. Bossert, Walter & D'Ambrosio, Conchita, 2006. "Reference groups and individual deprivation," Economics Letters, Elsevier, vol. 90(3), pages 421-426, March.
    17. Marc Fleurbaey, 2006. "To Envy or to be Envied? Refinements of No-Envy fot the Compensation Problem," IDEP Working Papers 0603, Institut d'economie publique (IDEP), Marseille, France, revised Jul 2006.
    18. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
    19. Dagum, Camilo, 1987. "Measuring the Economic Affluence between Populations of Income Receivers," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 5-12, January.
    20. Shlomo Yitzhaki & Robert I. Lerman, 1991. "Income Stratification And Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
    21. Ebert, Udo, 1984. "Measures of distance between income distributions," Journal of Economic Theory, Elsevier, vol. 32(2), pages 266-274, April.
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    Cited by:

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    2. STRAPCOVA Katarina & VOICU Bogdan & VOICU Malina, 2007. "Engendered housework. A cross-european analysis," IRISS Working Paper Series 2007-07, IRISS at CEPS/INSTEAD.
    3. LILLA Marco, 2007. "Income Inequality and Education Premia," IRISS Working Paper Series 2007-11, IRISS at CEPS/INSTEAD.
    4. MARTIN Ludivine, 2007. "The impact of technological changes on incentives and motivations to work hard," IRISS Working Paper Series 2007-15, IRISS at CEPS/INSTEAD.
    5. Pascaline Vincent & Frédéric Chantreuil & Benoït Tarroux, 2012. "Appraising the breakdown of unequal individuals in large French cities," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201220, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    6. KANKARASH Milosh & MOORS Guy, 2007. "Heterogeneity in solidarity attitudes in Europe. Insights from a multiple-group latent-class factor approach," IRISS Working Paper Series 2007-06, IRISS at CEPS/INSTEAD.
    7. VALENTOVA Marie, 2007. "Attitudes to Family Policy Arrangements in Relation to Attitudes to Family and division of Labour between Genders," IRISS Working Paper Series 2007-05, IRISS at CEPS/INSTEAD.

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    More about this item

    Keywords

    Between-group Gini; Between-group Transfers; Entropy; Pigou-Dalton; Within-group Transfers.;
    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

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