Experiments studying get-out-the-vote (GOTV) efforts estimate the causal effect of various mobilization efforts on voter turnout. However, there is often substantial noncompliance in these studies. A usual approach is to use an instrumental variable (IV) analysis to estimate impacts for compliers, here being those actually contacted by the investigators. Unfortunately, popular IV estimators can be unstable in studies with a small fraction of compliers. We explore post-stratifying the data (e.g., taking a weighted average of IV estimates within each stratum) using variables that predict complier status (and, potentially, the outcome) to mitigate this. We present the benefits of post-stratification in terms of bias, variance, and improved standard error estimates, and provide a finite-sample asymptotic variance formula. We also compare the performance of different IV approaches and discuss the advantages of our design-based post-stratification approach over incorporating compliance-predictive covariates into the two-stage least squares estimator. In the end, we show that covariates predictive of compliance can increase precision, but only if one is willing to make a bias-variance trade-off by down-weighting or dropping strata with few compliers. By contrast, standard approaches such as two-stage least squares fail to use such information. We finally examine the benefits of our approach in two GOTV applications.

翻译：研究动员投票（GOTV）效果的实验旨在估计各类动员措施对选民投票率的因果效应。然而，此类研究常存在严重的非依从性问题。通常采用工具变量（IV）分析来估计依从者（即实际被调查者联系到的群体）的效应。遗憾的是，在依从者比例较低的研究中，常用的工具变量估计量可能不稳定。本文探讨通过使用能预测依从状态（及潜在结果）的变量对数据进行后分层处理（例如在各层内取工具变量估计量的加权平均）以缓解该问题。我们从偏差、方差及改进标准误估计的角度阐述后分层的优势，并提供有限样本渐近方差公式。同时比较不同工具变量方法的性能，并讨论基于设计的后分层方法相较于将依从预测协变量纳入两阶段最小二乘估计器的优势。最后证明：仅当研究者愿意通过降权或剔除依从者稀少的层级来权衡偏差与方差时，预测依从性的协变量才能提升估计精度。相比之下，两阶段最小二乘法等标准方法无法有效利用此类信息。最终通过两个GOTV应用案例验证本方法的优势。