Semiparametric estimation for average causal effects using propensity score-based spline

Abstract When estimating the average causal effect in observational studies, researchers have to tackle both self-selection of treatment and outcome modeling. This is difficult because the parametric form of the outcome model is often unknown and there exists a large number of covariates. In this work, we present a semiparametric strategy for estimating the average causal effect by regressing on the propensity score. Furthermore, we show that regression error terms usually depend on the propensity score as well, which could cause heteroscedastic variances, and thus construct a refined estimator to improve the estimation efficiency. Both estimators are shown to be consistent and asymptotically normally distributed, with the latter one having a smaller asymptotic variance. The simulation studies indicate that our methods compare favorably with many competing estimators. Our methods are easy to implement and avoid hazardous impact due to extreme weights as often seen in weighting estimators. They can also be extended to handle subgroup effects with known structure. We apply the proposed methods to data from the Ohio Medicaid Assessment Survey 2012, estimating the effect of having health insurance on self-reported health status for a population with subsidized insurance plan choices under the Affordable Care Act.