This paper introduces a new framework for quantile estimation. Quantile regression techniques have proven to be extremely valuable in understanding the relationship between explanatory variables and the conditional distribution of the outcome variable. Quantile regression allows the effect of the explanatory variables to vary based on a nonseparable disturbance term, frequently interpreted as "unobserved proneness" for the outcome, and provides conditional quantile treatment effects. Researchers are typically interested in the impact of the treatment variables on the unconditional distribution of the outcome. Additional covariates may be necessary (or simply desirable) for identification but adding these variables alters the interpretation of the resulting estimates as some of the "unobserved proneness" becomes observed and the disturbance term is separated. The Generalized Quantile Regression (GQR) estimator provides unconditional quantile treatment effects - the impact of the treatment variables on the unconditional distribution of the outcome variables. The control variables are conditioned on for identification or variance reduction but without altering the interpretation of the estimates. This property parallels mean regression. An IV version (IV-GQR) is also introduced. The estimator is extremely straightforward to implement using standard statistical software. Quantile Regression and Instrumental Variables Quantile Regression are special cases of the introduced estimation technique, but the proposed technique provides additional flexibility in the estimation of quantile treatment effects.
Powell, David, A New Framework for Estimation of Quantile Treatment Effects: Nonseparable Disturbance in the Presence of Covariates. Santa Monica, CA: RAND Corporation, 2013. https://www.rand.org/pubs/working_papers/WR824-1.html.
Powell, David, A New Framework for Estimation of Quantile Treatment Effects: Nonseparable Disturbance in the Presence of Covariates, RAND Corporation, WR-824-1, 2013. As of February 15, 2024: https://www.rand.org/pubs/working_papers/WR824-1.html