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Robust inequality comparisons

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  • Rolf Aaberge

    ()

  • Magne Mogstad

    ()

Abstract

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations Aaberge (2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves which was proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families and thus the least restrictive social preferences required to reach unambiguous ranking of a set of Lorenz curves. From the weight-functions of these inequality measures we obtain intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967-2005.

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Bibliographic Info

Article provided by Springer in its journal The Journal of Economic Inequality.

Volume (Year): 9 (2011)
Issue (Month): 3 (September)
Pages: 353-371

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Handle: RePEc:kap:jecinq:v:9:y:2011:i:3:p:353-371

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Web page: http://springerlink.metapress.com/link.asp?id=111137

Related research

Keywords: The Lorenz curve; Lorenz dominance; Rank-dependent measures of inequality; The Gini coefficient; Generalized Gini families of inequality measures; D31; D63;

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References

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  1. Rolf Aaberge, 2007. "Gini’s nuclear family," Journal of Economic Inequality, Springer, vol. 5(3), pages 305-322, December.
  2. Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-86, September.
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  5. Rolf Aaberge, 2006. "Asymptotic Distribution Theory of Empirical Rank-dependent measures of Inequity," ICER Working Papers 12-2006, ICER - International Centre for Economic Research.
  6. 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 617-28, October.
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  10. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196.
  11. Ingvild Almås & Tarjei Havnes & Magne Mogstad, 2010. "Baby Booming Inequality? Demographic Change and Earnings Inequality in Norway, 1967-2000," CESifo Working Paper Series 3200, CESifo Group Munich.
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  19. Erik Fjærli & Rolf Aaberge, 2000. "Tax Reforms, Dividend Policy and Trends in Income Inequality Empirical Evidence based on Norwegian Data," Discussion Papers 284, Research Department of Statistics Norway.
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  23. Peter Gottschalk & Timothy M. Smeeding, 1997. "Cross-National Comparisons of Earnings and Income Inequality," Journal of Economic Literature, American Economic Association, vol. 35(2), pages 633-687, June.
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  26. Schechtman, Edna & Shelef, Amit & Yitzhaki, Shlomo & Zitikis, Ričardas, 2008. "Testing Hypotheses About Absolute Concentration Curves And Marginal Conditional Stochastic Dominance," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1044-1062, August.
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Cited by:
  1. Ingvild Almås & Tarjei Havnes & Magne Mogstad, 2010. "Baby Booming Inequality? Demographic Change and Earnings Inequality in Norway, 1967-2000," CESifo Working Paper Series 3200, CESifo Group Munich.

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