Model-Assisted Complier Average Treatment Effect Estimates in Randomized Experiments with Noncompliance

Noncompliance is a common problem in randomized experiments in various fields. Under certain assumptions, the complier average treatment effect is identifiable and equal to the ratio of the intention-to-treat effects of the potential outcomes to that of the treatment received. To improve the estimation efficiency, we propose three model-assisted estimators for the complier average treatment effect in randomized experiments with a binary outcome. We study their asymptotic properties, compare their efficiencies with that of the Wald estimator, and propose the Neyman-type conservative variance estimators to facilitate valid inferences. Moreover, we extend our methods and theory to estimate the multiplicative complier average treatment effect. Our analysis is randomization-based, allowing the working models to be misspecified. Finally, we conduct simulation studies to illustrate the advantages of the model-assisted methods and apply these analysis methods in a randomized experiment to evaluate the effect of academic services or incentives on academic performance.

Automated summary

Noncompliance is a common issue in randomized experiments. To improve estimations, three model-assisted estimators are proposed for complier average treatment effect with binary outcome. The asymptotic properties are studied, efficiencies are compared with the Wald estimator, and conservative variance estimators are proposed for valid inferences. Simulation studies demonstrate the advantages of model-assisted methods and the analysis is applied to evaluate the effect of academic services or incentives on academic performance in a randomized experiment.