A Note on the Relationship between Top Income Shares and the Gini Coefficient
When a very top group of the income distribution, infinitesimal in numbers, owns a finite share S of total income, the Gini coefficient G can be approximated by G*(1 - S) + S, where G* is the Gini coefficient for the rest of the population. We provide a simple formal proof for this expression, give a general formula of the relationship when the top group is not infinitesimal, and offer two applications as illustrations.
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- Atkinson, A. B. & Piketty, Thomas (ed.), 2007. "Top Incomes Over the Twentieth Century: A Contrast Between Continental European and English-Speaking Countries," OUP Catalogue, Oxford University Press, number 9780199286881.
- Andrew Leigh, 2007.
"How Closely Do Top Income Shares Track Other Measures of Inequality?,"
CEPR Discussion Papers
562, Centre for Economic Policy Research, Research School of Economics, Australian National University.
- Andrew Leigh, 2007. "How Closely Do Top Income Shares Track Other Measures of Inequality?," Economic Journal, Royal Economic Society, vol. 117(524), pages F619-F633, November.
- Dagum, Camilo, 1987. "Measuring the Economic Affluence between Populations of Income Receivers," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 5-12, January.
- Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-31.
- Thomas Piketty & Emmanuel Saez, 2003. "Income Inequality In The United States, 1913-1998," The Quarterly Journal of Economics, MIT Press, vol. 118(1), pages 1-39, February.
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