  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.
