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

Author(s):	Facundo Alvaredo
Publication Date:	October 2010
Date Revised:	February 2011
Keyword(s):	Gini coefficient, Pareto distribution, top income shares
JEL(s):	D31, H2
Programme Areas:	Public Economics
Link to this Page:	cepr.org/active/publications/discussion_papers/dp.php?dpno=8071

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.