DP8071 | A Note on the Relationship between Top Income Shares and the Gini Coefficient


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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.