Nonparametric bootstrap confidence sets for the quantile ratio

This article proposes a nonparametric bootstrap method for constructing confidence sets for quantile ratios, a key metric in inequality analysis. By bootstrapping the ratio directly, the proposed method circumvents a range of inference challenges associated with quantile ratios, particularly those inherited from kernel density estimation and the delta method, especially in heavy-tailed distributions. Simulation results demonstrate that the bootstrap method achieves near-exact coverage while maintaining power, even for extreme quantiles from heavy-tailed distributions, with sample sizes as small as 50 observations. Although developed in the context of income inequality, the approach is valid across both economic and noneconomic settings under fairly general conditions. An empirical application to world inequality shows that inequality remained stable, with a notable decline following the 2008 financial crisis. This challenges the economic convergence hypothesis and supports the view that major events or shocks drive global inequality dynamics. Notably, the empirical results reveal that the proposed method provides significantly different inference compared to standard approaches, underscoring the practical implications of these findings for empirical research and policy formulation.