Decomposing the Quantile Ratio Index with Applications to Australian Income and Wealth Data

Luke Anthony Prendergast, Robert G Staudte

Abstract

The quantile ratio index is a simple and effective measure of relative inequality for income data that is resistant to outliers. A useful property of this index is investigated here: given a partition of the income distribution into a union of sets of symmetric quantiles, one can find the inequality for each set and readily combine them in a weighted average to obtain the index for the entire population. When applied to data for various years, one can track how these contributions to inequality vary over time, as illustrated here for Australian Bureau of Statistics income and wealth data.

Keywords

confidence intervals, Gini index, inequality measures, quantile density, robust statistics

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