Stata commands to estimate quantile regression with panel and grouped data

In this presentation, we introduce two Stata commands that allow estimating quantile regression with panel and grouped data. The commands implement two-step minimum-distance estimators. We first compute a quantile regression within each unit and then apply GMM to the fitted values from the first stage. The command xtmdqr applies to classical panel data, where we follow the same units over time, while the command mdqr applies to grouped data, where the observations are at the individual level but the treatment varies at the group level. Depending on the variables assumed to be exogenous, this approach provides quantile analogs of the classical least-squares panel-data estimators such as the fixed-effects, random-effects, between, and Hausman–Taylor estimators. For grouped (instrumental) quantile regression, we provide a more precise estimator than the existing estimators. In our companion paper (Melly and Pons, "Minimum distance estimation of quantile panel data models"), we study the theoretical properties of these estimators.