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Abstract:
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Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on top shares and top-to-bottom ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this paper strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single underlying inequality measure. Second, it presents a standard form of the underlying inequality measure that satisfies the principle of normalization - ranging from zero to one, with zero representing perfect equality and inequality increasing as the measure goes toward one -- but also finds that, compared to shares and ratios, the standard form is somewhat blunt in depicting changes in inequality. Third, it investigates the measure in mathematically specified probability distributions, showing that it is monotonically related to classical measures, such as the Gini, and thus a good measure.
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