Estimating Partially Conditional Quantile Treatment Effects

This paper proposes a new model, termed as the partially conditional quantile treatment effect model, to characterize the heterogeneity of treatment effect conditional on some predetermined variable(s). We show that this partially conditional quantile treatment effect is identified under the assumption of selection on observables, which leads to a semiparametric estimation procedure in two steps: first, parametric estimation of the propensity score function and then, nonparametric estimation of conditional quantile treatment effects. Under some regularity conditions, the consistency and asymptotic normality of the proposed semiparametric estimator are derived. Furthermore, the finite sample performance of the proposed method is illustrated through Monte Carlo experiments. Finally, we apply our methods to estimate the quantile treatment effects of a first-time mother’s smoking during the pregnancy on the baby’s weight as a function of the mother’s age, and our empirical results show substantial heterogeneity across different mother’s ages with a significant negative effect of smoking on infant birth weight across all mother’s ages and quantiles considered.