Unconditional Quantile Regression for Exogenous or Endogenous Treatment Variables

This paper introduces an unconditional quantile regression (UQR) estimator that can be used for exogenous or endogenous treatment variables. Traditional quantile estimators provide conditional treatment effects. Typically, we are interested in unconditional quantiles, characterizing the distribution of the outcome variable for different values of the treatment variables. Conditioning on additional covariates, however, may be necessary for identification of these treatment effects. With conditional quantile models, the inclusion of additional covariates changes the interpretation of the estimates. The UQR and IV-UQR estimators allow for one to condition on covariates without altering the interpretation. This estimator is a more general version of traditional quantile estimators.