Uniformly Semiparametric Efficient Estimation of Treatment Effects With a Continuous Treatment

This article studies identification, estimation, and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption. We show identification of the parameters of interest, the dose-response functions, under the assumption that selection to treatment is based on observables. We propose a semiparametric two-step estimator, and consider estimation of the dose-response functions through moment restriction models with generalized residual functions that are possibly nonsmooth. This general formulation includes average and quantile treatment effects as special cases. The asymptotic properties of the estimator are derived, namely, uniform consistency, weak convergence, and semiparametric efficiency. We also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice. Monte Carlo simulations show that the proposed methods have good finite sample properties. Finally, we apply the proposed methods to estimate the unconditional average and quantile effects of mothers' weight gain and age on birthweight. Supplementary materials for this article are available online.