  This paper examines a commonly used measure of persuasion whose precise
interpretation has been obscure in the literature. By using the potential
outcome framework, we define the causal persuasion rate by a proper conditional
probability of taking the action of interest with a persuasive message
conditional on not taking the action without the message. We then formally
study identification under empirically relevant data scenarios and show that
the commonly adopted measure generally does not estimate, but often overstates,
the causal rate of persuasion. We discuss several new parameters of interest
and provide practical methods for causal inference.
