Veranstaltungen des DIW Berlin/
Events of DIW Berlin

4 July 2017

SOEP Brown Bag Seminar Special Brown Bag Seminar: Are Top Shares a Good Measure of Inequality?

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, Atkinson, and Theil measures and the coefficient of variation. Thus, the evidence to date suggests that the family of top shares and top-to-bottom ratios is a genuine inequality measure and a useful all-purpose proxy for other inequality measures. Moreover, this new measure is further distinguished by its ease of calculation and ease of interpretation, making it a widely appealing measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations, and that weakening of correlations – such as between the Gini and Atkinson measures or between the Gini and top shares -- signals differences and shifts in distributional form, themselves signals of income dynamics.

  • Professor Guillermina Jasso, member of the DIW Scientific Advisory Board and former Chair of Sociology at New York University (currently NYU Silver Professor)

  • Time
    12:30 - 13:30
    DIW Berlin (Ferdinand-Friedensburg-Raum) DIW Berlin im Quartier 110 Room 2.2.008 Mohrenstraße 58 10117 Berlin
    at DIW Berlin
    Tel.: +49 30 89789 336
    Tel.: +49 30 89789 272