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）效果的实验旨在评估各类动员活动对选民投票率的因果效应。然而，此类研究常存在显著的不遵从性。常规方法是使用工具变量（IV）分析来估计遵从者的影响，此处指实际被研究者接触到的群体。不幸的是，当研究中遵从者比例较小时，常用的IV估计量可能不稳定。我们探索利用预测遵从者状态（及潜在结果）的变量对数据进行后分层（例如，在每一层内对IV估计值进行加权平均）以缓解这一问题。我们从偏差、方差及标准误估计改进角度论证了后分层的优势，并给出了有限样本渐近方差公式。我们还比较了不同IV方法的性能，并讨论了基于设计的后分层方法相较于将预测遵从性的协变量纳入两阶段最小二乘估计量的优势。最终研究发现，预测遵从性的协变量可提高精度，但前提是愿意通过降低权重或剔除遵从者稀少的层来权衡偏差与方差。相比之下，两阶段最小二乘等标准方法无法利用此类信息。我们在两个GOTV应用案例中检验了本方法的优势。