Quantile ratio regression

We introduce quantile ratio regression. Our proposed model assumes that the ratio of two arbitrary quantiles of a continuous response distribution is a function of a linear predictor. Thanks to basic quantile properties, estimation can be carried out on the scale of either the response or the link function. The advantage of using the latter becomes tangible when implementing fast optimizers for linear regression in the presence of large datasets. We show the theoretical properties of the estimator and derive an efficient method to obtain standard errors. The good performance and merit of our methods are illustrated by means of a simulation study and a real data analysis; where we investigate income inequality in the European Union (EU) using data from a sample of about two million households. We find a significant association between inequality, as measured by quantile ratios, and certain macroeconomic indicators; and we identify countries with outlying income inequality relative to the rest of the EU. An R implementation of the proposed methods is freely available.