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Conditioning on variables affected by treatment can induce post-treatmentbias when estimating causal effects. Although this suggests that researchersshould measure potential moderators before administering the treatment in anexperiment, doing so may also bias causal effect estimation if the covariatemeasurement primes respondents to react differently to the treatment. Thispaper formally analyzes this trade-off between post-treatment and primingbiases in three experimental designs that vary when moderators are measured:pre-treatment, post-treatment, or a randomized choice between the two. Wederive nonparametric bounds for interactions between the treatment and themoderator in each design and show how to use substantive assumptions to narrowthese bounds. These bounds allow researchers to assess the sensitivity of theirempirical findings to either source of bias. We extend the basic framework intwo ways. First, we apply the framework to the case of post-treatment attentionchecks and bound how much inattentive respondents can attenuate estimatedtreatment effects. Second, we develop a parametric Bayesian approach toincorporate pre-treatment covariates in the analysis to sharpen our inferencesand quantify estimation uncertainty. We apply these methods to a surveyexperiment on electoral messaging. We conclude with practical recommendationsfor scholars designing experiments.

Priming bias versus post-treatment bias in experimental designs