Quantile regression with panel data

We propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data. Specifically, we extend the correlated random coeffi-cients representation of linear quantile regression (e.g., Koenker, 2005; Section 2.6). We show that panel data allows the econometrician to (i) introduce dependence between the regressors and the random coefficients and (ii) weaken the assumption of comonotonic-ity across them (i.e., to enrich the structure of allowable dependence between different coefficients). We adopt a “fixed effects ” approach, leaving any dependence between the regressors and the random coefficients unmodelled. We motivate different notions of quantile partial effects in our model and study their identification. For the case of discretely-valued covariates we present analog estimators and charac-terize their large sample properties. When the number of time periods (T) exceeds the number of random coefficients (P), identification is regular, and our estimates are N- consistent. When T = P, our identification results make special use of the subpopu-lation of stayers- units whose regressor values change little over time- in a way whic