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Gini’s nuclear family

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  • Rolf Aaberge

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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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File URL: http://hdl.handle.net/10.1007/s10888-006-9050-8
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Bibliographic Info

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

Volume (Year): 5 (2007)
Issue (Month): 3 (December)
Pages: 305-322

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Handle: RePEc:kap:jecinq:v:5:y:2007:i:3:p:305-322

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

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; D3; D63;

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References

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  1. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Social Choice: A Mean Voter Theorem," Discussion Papers 1989_31, Columbia University, Department of Economics.
  2. 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.
  3. DONALDSON, David & WEYMARK, John A., . "Ethically flexible Gini indices for income distributions in the continuum," CORE Discussion Papers RP -520, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  5. 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.
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  7. 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.
  8. Rolf Aaberge, 2006. "Asymptotic Distribution Theory of Empirical Rank-dependent measures of Inequity," ICER Working Papers 12-2006, ICER - International Centre for Economic Research.
  9. Rolf Aaberge, 2000. "Ranking Intersecting Lorenz Curves," Discussion Papers 271, Research Department of Statistics Norway.
  10. Esteban, Joan & Ray, Debraj, 1994. "On the Measurement of Polarization," Econometrica, Econometric Society, vol. 62(4), pages 819-51, July.
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  13. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
  14. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September.
  15. An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
  16. 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.
  17. WEYMARK, John A., . "Generalized Gini inequality indices," CORE Discussion Papers RP -453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. Chotikapanich, Duangkamon & Griffiths, William, 2001. "On Calculation of the Extended Gini Coefficient," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 47(4), pages 541-47, December.
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  24. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  25. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653.
  26. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
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