Quantile Ratio Regression for Panel Data

We develop quantile ratio regression for panel data, to model covariate effects on ratios of upper and lower conditional quantiles. The proposed estimator is based on semi-parametric estimation of conditional quantiles, which are then linked to covariates via a linear model. Dependence within subjects is accommodated by a ridge-type penalty on unit-specific intercepts, which shrinks individual effects while allowing for heterogeneity. We also introduce a computationally efficient one-step empirical Bayes procedure for selecting the penalty parameter. A simulation study under different dependence structures and outcome distributions shows that the ridge-regularized estimator reduces mean squared error and improves out-of-sample prediction relative to unpenalized and naïve alternatives. An application to a four-year panel of about twenty thousand European households illustrates how the method can be used to analyze income inequality through conditional income quantile ratios.