Decomposing the Quantile Ratio Index with applications to Australian income and wealth data

Abstract: The quantile ratio index introduced by Prendergast and Staudte 2017 is a simple and effective measure of relative inequality for income data that is resistant to outliers. It measures the average relative distance of a randomly chosen income from its symmetric quantile. Another 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 conditional inequality for each set as measured by the quantile ratio index 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.