Multi-dimensional Panels in Quantile Regression Models

Abstract

This chapter studies estimation and inference methods for multi-dimensional quantile regression panel data models. First, we discuss the fixed effects (FE) model. This model imposes a relatively restrictive asymptotic condition on the growth of the time series dimension relative to the cross section dimension. Nevertheless, extending the FE to three or more dimensions allows for larger data availability, and might help to relax the stringent condition on the time series. We also present a model for the smoothed FE quantile regression case. Second, we present a random effects (RE) model. This model has the advantage of allowing for small time-series dimension. Then, we present a correlated RE model. In this case, the unobservable individual-specific effects are modeled as a function of observables and a disturbance. Finally, we consider the use of the multi-dimensional setting to model network data.