Generalized Quantile Regression in Stata

Quantile regression techniques are useful in understanding the relationship between explanatory variables and the conditional distribution of the outcome variable, allowing the parameters of interest to vary based on a nonseparable disturbance term. Additional covariates may be necessary (or simply desirable) for identification but including additional variables into a conditional quantile model separates the disturbance term, altering the underlying structural model. To address this problem, Powell (2013) introduces the Generalized Quantile Regression (GQR) estimator, which provides the impact of the treatment variables on the outcome distribution, and allows for conditioning on control variables without altering the interpretation of the estimates. Quantile regression and instrumental variable quantile regression are special cases of GQR, but GQR allows for more flexible estimation of quantile treatment effects. The estimator is easily extended to include instrumental variables and panel data. We introduce a stata command – gqr – that implements a GMM-based GQR estimator. User specified options for the command include the usual panel data options, and also allows the user to control for endogeneity in explanatory variables through the use of instruments. The command allows users a variety of different means for characterizing standard errors of estimated parameters, including both direct methods and Markov-chain-Monte Carlo simulation.