Efficient Estimation of Average Treatment Effects with Mixed Categorical and Continuous Data

In this article, we consider the nonparametric estimation of average treatment effects when there exist mixed categorical and continuous covariates. One distinguishing feature of the approach presented herein is the use of kernel smoothing for both the continuous and the discrete covariates. This approach, together with the cross-validation method. which we use for selecting the smoothing parameters, has the ability to automatically remove irrelevant covariates. We establish the asymptotic distribution of the proposed average treatment effects estimator with data-driven smoothing parameters. Simulation results show that the proposed method is capable of performing much better than the conventional kernel approach whereby one splits the sample into subsamples corresponding to "discrete cells." An empirical application to a controversial study that examines the efficacy of right heart catheterization on medical outcomes reveals that our proposed nonparametric estimator overturns the controversial findings of Connors et al. (1996), suggesting that their findings may be an artifact of an incorrectly specified parametric model.