J-divergence measurements of economic inequality

Abstract

The paper uses a symmetric entropy statistic to study income inequality. The index quantifies the information content of a two-way message that transforms the empirical income distribution into an egalitarian reference distribution, and then back to the original. This allows the measure to be interpreted as an average of n income-to-mean divergences such that the inequality estimate can be broken down into contributions across population subgroups. Various properties of the index are analysed and an application comparing the USA, Germany and Britain is provided. We focus on the sensitivity of inequality to the tails of the income distribution and show that the extreme right-hand tail accounts for a large and generally increasing proportion of total inequality. This result holds even if incomes are measured at the household level, averaged over a 5-year period and taken after government taxes and transfers.