Improving precision through design and analysis in experiments with noncompliance

Abstract

Even in the best-designed experiment, noncompliance can complicate analysis. While the intent-to-treat effect remains identified, randomization alone no longer identifies the complier average causal effect (CACE). Instrumental variables approaches, which rely on the exclusion restriction, can suffer from high variance, particularly when the experiment has a low compliance rate. We provide a framework which broadens the set of design and analysis techniques political science researchers can use when addressing noncompliance. Building on the growing literature about the advantages of ex-ante design decisions to improve precision, we show blocking on variables related to both compliance and the outcome can greatly improve all the estimators we propose. Drawing on work in statistics, we introduce the principal ignorability assumption and a class of principal score weighting estimators, which can exhibit large gains in precision in low compliance settings. We then combine principal ignorability and blocking with a simple estimation strategy to derive a more efficient estimation strategy for the CACE. In a re-evaluation of a study on the effect of GOTV on turnout, we find that the principal ignorability approaches result in confidence intervals roughly half the size of traditional instrumental variable approaches.