Efficient Covariate Balancing for the Local Average Treatment Effect

This paper develops an empirical balancing approach for the estimation of treatment effects under two-sided noncompliance using a binary conditionally independent instrumental variable. The method weighs both treatment and outcome information with inverse probabilities to produce exact finite sample balance across instrument level groups. It is free of functional form assumptions on the outcome or the treatment selection step. By tailoring the loss function for the instrument propensity scores, the resulting treatment effect estimates exhibit both low bias and a reduced variance in finite samples compared to conventional inverse probability weighting methods. The estimator is automatically weight normalized and has similar bias properties compared to conventional two-stage least squares estimation under constant causal effects for the compliers. We provide conditions for asymptotic normality and semiparametric efficiency and demonstrate how to utilize additional information about the treatment selection step for bias reduction in finite samples. The method can be easily combined with regularization or other statistical learning approaches to deal with a high-dimensional number of observed confounding variables. Monte Carlo simulations suggest that the theoretical advantages translate well to finite samples. The method is illustrated in an empirical example.