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Gini’s nuclear family

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  • Rolf Aaberge
Abstract
The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve, the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions of income. The scaled conditional mean curve is shown to possess several attractive properties as an alternative interpretation of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the population. The paper also provides asymptotic distribution results for the empirical scaled conditional mean curve and the related family of empirical measures of inequality.
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Suggested Citation

  • Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
    • Handle: RePEc:kap:jecinq:v:5:y:2007:i:3:p:305-322
    DOI: 10.1007/s10888-006-9050-8
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    References listed on IDEAS

    as
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    7. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-851, July.
    8. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    9. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    10. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 183-196.
    11. 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.
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    17. Aaberge, Rolf, 2001. "Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings," Journal of Economic Theory, Elsevier, vol. 101(1), pages 115-132, November.
    18. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
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    22. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
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    25. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    26. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    27. Rolf Aaberge, 2005. "Asymptotic Distribution Theory of Empirical Rank-dependent Measures of Inequality," Discussion Papers 402, Statistics Norway, Research Department.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    the scaled conditional mean curve; measures of inequality; the Gini coefficient; the Bonferroni coefficient; measures of social welfare; principles of transfer sensitivity; estimation; asymptotic distributions; D3; D63;
    All these keywords.

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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