Synthetic estimation for the complier average causal effect

TL;DR

This paper introduces a synthetic estimator for the complier average causal effect that optimally combines multiple estimators to improve efficiency and robustness in studies with noncompliance.

Contribution

The paper presents a novel synthetic estimator that minimizes mean squared error by combining all available estimators, including biased ones, for CACE estimation.

Findings

The synthetic estimator outperforms individual estimators in simulations.

It maintains low bias while reducing variance.

Robust to inclusion of high-bias estimators.

Abstract

We propose an improved estimator of the complier average causal effect (CACE). Researchers typically choose a presumably-unbiased estimator for the CACE in studies with noncompliance, when many other lower-variance estimators may be available. We propose a synthetic estimator that combines information across all available estimators, leveraging the efficiency in lower-variance estimators while maintaining low bias. Our approach minimizes an estimate of the mean squared error of all convex combinations of the candidate estimators. We derive the asymptotic distribution of the synthetic estimator and demonstrate its good performance in simulation, displaying a robustness to inclusion of even high-bias estimators.