Navigating the mismeasurement of intermediary variables in message-based experiments

Abstract Researchers frequently deliver treatments through messages, as in many audit and get-out-the-vote (GOTV) experiments. These message-based experiments often hinge on intermediary variables—actions subjects must take to actually receive the treatment or control embedded in a message. Whether subjects open the message is a crucial intermediary step, which can serve as a condition for estimating downstream treatment effects or as an outcome of interest in its own right. Yet opens are often measured with error, most notably when some openers are misclassified as non-openers in email-based studies. We characterize the resulting bias, derive interpretable bounds on effects for well-defined subgroups, and provide sensitivity analyses for mismeasurement, thereby offering practical guidance for message-based experiments conducted through email and other communication technologies.