The Gini coefficient of inequality: a new interpretation

The Gini coefficient is a well-known measure of income inequality. It corresponds to the percentage of area below the 45<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$^\circ $$</EquationSource> </InlineEquation> line that is between the 45<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$^\circ $$</EquationSource> </InlineEquation> line and the Lorenz curve on a graph of cumulative income versus cumulative population. In this paper, new interpretations of the Gini coefficient are provided by disaggregating the Lorenz curve into a hierarchy of curves. These are based on hierarchical redistributions of income, where the population is first divided into “high-income” and “low-income” groups for purposes of the initial reallocation from the former group to the latter. Subsequent rounds further subdivide these groups and additional redistribution is carried out within them to remove remaining inequality. The Gini coefficient may be thought of as the expected percentage of total income that individuals will be involved with through this hierarchical redistribution process. A second, graphical interpretation showing the Gini coefficient as a weighted sum of the scaled Hoover indexes associated with a hierarchy of Lorenz curves is also provided. This latter interpretation allows for analyses that view inequality as an aggregate of inequalities that exist along different segments of the income distribution. Copyright Springer-Verlag Berlin Heidelberg 2013