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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.
Survey weighting allows researchers to account for bias in survey samples, due to unit nonresponse or convenience sampling, using measured demographic covariates. Unfortunately, in practice, it is impossible to know whether the estimated survey weights are sufficient to alleviate concerns about bias due to unobserved confounders or incorrect functional forms used in weighting. In the following paper, we propose two sensitivity analyses for the exclusion of important covariates: (1) a sensitivity analysis for partially observed confounders (i.e., variables measured across the survey sample, but not the target population) and (2) a sensitivity analysis for fully unobserved confounders (i.e., variables not measured in either the survey or the target population). We provide graphical and numerical summaries of the potential bias that arises from such confounders, and introduce a benchmarking approach that allows researchers to quantitatively reason about the sensitivity of their results. We demonstrate our proposed sensitivity analyses using state-level 2020 U.S. Presidential Election polls.
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