Estimating a Quantile-Based Income Inequality Indicator on Complex Sampling Data

Several statistical indicators exist for the measurement of economic inequality. They are mostly based on distribution moments or depend on few percentiles at the tails of the distribution, selected a priori. This work analyzes a recently proposed quantile-based income inequality indicator, the Quantile Ratio Index, which solely depends on quantiles and considers the whole distribution. A complete finite population estimation framework for this indicator is here proposed, that works for data collected with complex sampling design. In order to obtain a reliable measure, special attention is dedicated to the task of estimating quantiles, particularly when accounting for sampling weights. Simulations based on Italian EU-SILC 2017 data demonstrates that the proposed direct estimator has large accuracy, precision and robustness to outlying observations, if based on an appropriate choice of quantile estimator.