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Between-Group Pigou-Dalton Transfers

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  • Mussard, Stéphane

    (CEPS/INSTEAD, GREDI, GEREM)

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.

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Bibliographic Info

Paper provided by IRISS at CEPS/INSTEAD in its series IRISS Working Paper Series with number 2007-02.

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Length: 23 pages
Date of creation: Mar 2007
Date of revision:
Handle: RePEc:irs:iriswp:2007-02

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Keywords: Between-group Gini ; Between-group Transfers ; Entropy ; Pigou-Dalton ; Within-group Transfers;

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References

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  1. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
  2. 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.
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  5. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
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  7. Pyatt, Graham, 1976. "On the Interpretation and Disaggregation of Gini Coefficients," Economic Journal, Royal Economic Society, vol. 86(342), pages 243-55, June.
  8. 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.
  9. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  10. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  11. Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer, vol. 15(1), pages 1-14.
  12. 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.
  13. Chateauneuf, A. & Gajdos, T. & Wilthien, P.-H., 1999. "The Principle of Strong Kiminishing Transfer," Papiers d'Economie Mathématique et Applications 1999-96, Université Panthéon-Sorbonne (Paris 1).
  14. 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 313-29, September.
  15. Gajdos, Thibault, 2004. "Single crossing Lorenz curves and inequality comparisons," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 21-36, January.
  16. 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.
  17. 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.
  18. Gleb A. Koshevoy & Karl Mosler, 2007. "Multivariate Lorenz dominance based on zonoids," AStA Advances in Statistical Analysis, Springer, vol. 91(1), pages 57-76, March.
  19. 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.
  20. 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 107-15, February.
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Citations

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Cited by:
  1. Mussard, Stéphane & Terraza, Michel, 2007. "Décompositions des mesures d’inégalité : le cas des coefficients de Gini et d'entropie," IRISS Working Paper Series 2007-03, IRISS at CEPS/INSTEAD.
  2. Lilla, Marco, 2007. "Income Inequality and Education Premia," IRISS Working Paper Series 2007-11, IRISS at CEPS/INSTEAD.
  3. 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.
  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. 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, revised Jun 2007.
  6. Voicu, Bogdan & Voicu, Malina & Strapcova, Katarina, 2007. "Engendered housework. A cross-european analysis," IRISS Working Paper Series 2007-07, 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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