Learning the effect of persuasion via difference-in-differences

The persuasion rate is a key parameter for measuring the causal effect of a directional message on influencing the recipient's behavior. Its identification has relied on exogenous treatment or the availability of credible instruments, but the requirements are not always satisfied in observational studies. Therefore, we develop a novel econometric framework for the average persuasion rate on the treated and other related parameters by using the difference-in-differences approach. The average treatment effect on the treated is a standard parameter in difference-in-differences, but we show that it is an overly conservative measure in the context of persuasion. For estimation and inference, we propose regression-based approaches as well as semiparametrically efficient estimators. Beginning with the two-period case, we extend the framework to staggered treatment settings, where we show how to conduct richer analyses like the event-study design. We investigate the British election and the Chinese curriculum reform as empirical examples.