ABSTRACT
This chapter attempts to provide a progress report on the current state of quantile regression (QR) methods for panel data. Roger Koenker introduced a general approach to the estimation of QR models for longitudinal data where individual effects are treated as pure location shift parameters common to all quantiles and may be subject to shrinkage toward a common value. The properties of the QR method are well established for cross-sectional models; see the landmark monograph by Koenker for references and discussion. A conceptually simple way of applying the QR method to panel data is to model the conditional quantile of the response variable given the regressors and individual effect as the addition of the individual effect and a linear function of the regressors, and then apply fixed effects estimation by treating the individual effects as parameters to be estimated. The chapter describes a few extensions of QR methods for longitudinal data to models with endogeneity, semiparametric QR models for longitudinal data.
