Robust Estimation of Average Treatment Effects with Observational Studies

Estimating treatment effects has always been one of the hot issues in empirical research. It brings great challenges to estimating treatment effects because heterogeneity exists in the distribution of covariates between treated and controlled groups. Propensity score methods have been widely used to adjust for heterogeneity in observational studies. However, the propensity score is usually unknown and needs to be estimated. In this article, we propose a generalized single-index model to estimate the propensity score and use the propensity score residuals to reduce the estimation bias. The finite-sample performance of the proposed method is evaluated through simulation studies. We use the proposed method to evaluate the policy of "Sunshine Running" and find that the physical test scores of college students participating in the "Sunshine Running" can be improved by 3.72 points.