<p>We introduce a distribution-free approach to quantile share ratio regression. Our proposal involves the specification of a generalised linear model for the ratio of tail areas above and below two pre-specified quantiles. The latter ratio is the quantile share ratio, a measure of primary interest in the study of income inequality. We derive inference through an efficient two-step approach for parameter estimation that entails estimation of the conditional cumulative distribution function at the first step. A scalable strategy is discussed for large sample sizes. We are motivated by the study of income inequality in the European Union. Using data from a sample of approximately 2.8 million households across twenty-three countries and fifteen years (2007-2021) we make formal claims on the significance of adjusted and unadjusted differences among countries, and time trends. Interestingly enough, we find independent negative associations of economic inequality with gender equality and control of corruption.</p>