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Gini’s Nuclear Family

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Author Info
Rolf Aaberge () (Statistics Norway)

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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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Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 491.

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Date of creation: Dec 2006
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Handle: RePEc:ssb:dispap:491

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Related research
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.;

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Find related papers by JEL classification:
D3 - Microeconomics - - Distribution
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Aaberge, Rolf & Colombino, Ugo & Strøm, Steinar, 2003. "Do More Equal Slices Shrink the Cake? An Empirical Investigation of Tax-Transfer Reform Proposals in Italy," Memorandum 37/2003, Oslo University, Department of Economics. [Downloadable!]
    Other versions:
  2. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August. [Downloadable!] (restricted)
  3. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July. [Downloadable!] (restricted)
  4. Atkinson, A. B. & Bourguignon, F., 1990. "The design of direct taxation and family benefits," Journal of Public Economics, Elsevier, vol. 41(1), pages 3-29, February. [Downloadable!] (restricted)
  5. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June. [Downloadable!] (restricted)
  6. Erik Fjærli and 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. [Downloadable!]
  7. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February. [Downloadable!] (restricted)
  8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
  9. Chotikapanich, D. & Griffiths, W., 2001. "On Calculation of the Extended Gini Coefficient," Department of Economics - Working Papers Series 801, The University of Melbourne. [Downloadable!]
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  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September. [Downloadable!] (restricted)
  11. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April. [Downloadable!] (restricted)
  12. Hey, John D & Lambert, Peter J, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, MIT Press, vol. 95(3), pages 567-73, November.
  13. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August. [Downloadable!] (restricted)
  14. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March. [Downloadable!] (restricted)
  17. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-51, July. [Downloadable!] (restricted)
    Other versions:
  18. Wolfson, Michael C, 1994. "When Inequalities Diverge," American Economic Review, American Economic Association, vol. 84(2), pages 353-58, May.
  19. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653. [Downloadable!] (restricted)
  20. Rolf Aaberge, 2004. "Ranking Intersecting Lorenz Curves," CEIS Research Paper 45, Tor Vergata University, CEIS. [Downloadable!]
    Other versions:
  21. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February. [Downloadable!] (restricted)
  22. Giovanni Maria Giorgi, 2005. "A methodological survey of recent studies for the measurement of inequality of economic welfare carried out by some Italian statisticians," Econometrics 0509007, EconWPA. [Downloadable!]
  23. Rolf Aaberge, 2005. "Asymptotic Distribution Theory of Empirical Rank-dependent Measures of Inequality," Discussion Papers 402, Research Department of Statistics Norway. [Downloadable!]
    Other versions:
  24. 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. [Downloadable!] (restricted)
  25. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September. [Downloadable!] (restricted)
  26. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January. [Downloadable!] (restricted)
    Other versions:
  27. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September. [Downloadable!] (restricted)
  28. Giovanni Maria Giorgi, 2005. "Bibliographic portrait of the Gini concentration ratio," Econometrics 0511004, EconWPA. [Downloadable!]
  29. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June. [Downloadable!] (restricted)
    Other versions:
  30. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Iulie Aslaksen, Tom Wennemo and Rolf Aaberge, 2000. ""Birds of a Feather Flock Together" The Impact of Choice of Spouse on Family Labor Income Inequality," Discussion Papers 276, Research Department of Statistics Norway. [Downloadable!]
  2. Magne Mogstad, 2007. "Measuring Income Inequality under Restricted Interpersonal Comparability," Discussion Papers 498, Research Department of Statistics Norway. [Downloadable!]
  3. Erik Fjærli and 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. [Downloadable!]
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