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Robust Inequality Comparisons

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  • Aaberge, Rolf

    ()
    (Statistics Norway)

  • Mogstad, Magne

    ()
    (University of Chicago)

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

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 4769.

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Length: 26 pages
Date of creation: Feb 2010
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Publication status: published in: Journal of Economic Inequality, 2011, 9 (3), 353-371
Handle: RePEc:iza:izadps:dp4769

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Keywords: generalized Gini families of inequality measures; Gini coefficient; rank-dependent measures of inequality; Lorenz dominance; Lorenz curve;

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References

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  1. Almas, Ingvild & Havnes, Tarjei & Mogstad, Magne, 2011. "Baby Booming Inequality? Demographic Change and Earnings Inequality in Norway, 1967-2000," CEPR Discussion Papers 8393, C.E.P.R. Discussion Papers.
  2. 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.
  3. 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.
  4. Almås, Ingvild & Havnes, Tarjei & Mogstad, Magne, 2011. "Baby Booming Inequality? Demographic Change and Inequality in Norway, 1967{2004," Discussion Paper Series in Economics 6/2010, Department of Economics, Norwegian School of Economics.
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  9. Aaberge, Rolf & Langørgen, Audun & Mogstad, Magne & Østensen, Marit, 2008. "The Impact of Local Public Services and Geographical Cost of Living Differences on Poverty Estimates," IZA Discussion Papers 3686, Institute for the Study of Labor (IZA).
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  12. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653.
  13. Rolf Aaberge, 2006. "Asymptotic Distribution Theory of Empirical Rank-dependent measures of Inequity," ICER Working Papers 12-2006, ICER - International Centre for Economic Research.
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  19. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
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  21. 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.
  22. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  23. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July.
  24. 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.
  25. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
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Cited by:
  1. Almas, Ingvild & Havnes, Tarjei & Mogstad, Magne, 2011. "Baby Booming Inequality? Demographic Change and Earnings Inequality in Norway, 1967-2000," CEPR Discussion Papers 8393, C.E.P.R. Discussion Papers.

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