Many economic applications have found quantile models useful when the explanatory variables may have varying impacts throughout the distribution of the outcome variable. Traditional quantile estimators provide conditional quantile 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. This paper discusses identification of unconditional quantile treatment effects when it is necessary or simply desirable to condition on covariates. It discusses identification for both exogenous and endogenous treatment variables, which can be discrete or continuous, without functional form assumptions.
Powell, David, Unconditional Quantile Treatment Effects in the Presence of Covariates. Santa Monica, CA: RAND Corporation, 2010. https://www.rand.org/pubs/working_papers/WR816.html.
Powell, David, Unconditional Quantile Treatment Effects in the Presence of Covariates, RAND Corporation, WR-816, 2010. As of November 29, 2022: https://www.rand.org/pubs/working_papers/WR816.html