We introduce 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 is the quantile share ratio, a measure of primary interest in the study of income inequality. Our specification is completely distribution-free. We introduce 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 about three million households.