Conditioning on variables affected by treatment can induce post-treatment bias when estimating causal effects. Although this suggests that researchers should measure potential moderators before administering the treatment in an experiment, doing so may also bias causal effect estimation if the covariate measurement primes respondents to react differently to the treatment. This paper formally analyzes this trade-off between post-treatment and priming biases in three experimental designs that vary when moderators are measured: pre-treatment, post-treatment, or a randomized choice between the two. We derive nonparametric bounds for interactions between the treatment and the moderator in each design and show how to use substantive assumptions to narrow these bounds. These bounds allow researchers to assess the sensitivity of their empirical findings to either source of bias. We then apply these methods to a survey experiment on electoral messaging.

翻译：在估计因果效应时，对处理变量所影响的变量施加条件会产生处理后偏差。尽管这提示研究者应在实验实施处理前测量潜在调节变量，但若协变量测量启动了受访者对处理的差异化反应，也可能导致因果效应估计出现偏差。本文针对三种实验设计（即调节变量分别在处理前、处理后或随机分配两种测量时机进行测量）中处理后偏差与启动偏差的权衡关系展开形式化分析。我们推导了各设计下处理变量与调节变量交互作用的非参数边界，并展示了如何利用实质性假设缩窄这些边界。这些边界使研究者能够评估其实证发现对两类偏差来源的敏感程度。最后，我们将该方法应用于一项关于选举信息传播的问卷实验。