Semiparametric single-index estimation for average treatment effects

We propose a semiparametric method to estimate the average treatment effect under the assumption of unconfoundedness given observational data. Our estimation method alleviates misspecification issues of the propensity score function by estimating the single-index link function involved through Hermite polynomials. Our approach is computationally tractable and allows for moderately large dimension covariates. We provide the large sample properties of the estimator and show its validity. Also, the average treatment effect estimator achieves the parametric rate and asymptotic normality. Our extensive Monte Carlo study shows that the proposed estimator is valid in finite samples. Applying our method to maternal smoking and infant health, we find that conventional estimates of smoking’s impact on birth weight may be biased due to propensity score misspecification, and our analysis of job training programs reveals earnings effects that are more precisely estimated than in prior work. These applications demonstrate how addressing model misspecification can substantively affect our understanding of key policy-relevant treatment effects.