Model-assisted complier average treatment effect estimates in randomized experiments with non-compliance and a binary outcome

TL;DR

This paper introduces three model-assisted estimators for the complier average treatment effect in randomized experiments with non-compliance and binary outcomes, improving efficiency and allowing valid inference.

Contribution

It develops new estimators that enhance efficiency and extend to multiplicative effects, with asymptotic properties and variance estimators under misspecified models.

Findings

The proposed estimators outperform the Wald estimator in simulations.

They provide valid inference even with model misspecification.

Application to real data demonstrates practical advantages.

Abstract

In randomized experiments, the actual treatments received by some experimental units may differ from their treatment assignments. This non-compliance issue often occurs in clinical trials, social experiments, and the applications of randomized experiments in many other fields. Under certain assumptions, the average treatment effect for the compliers is identifiable and equal to the ratio of the intention-to-treat effects of the potential outcomes to that of the potential 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.