A binary IV model for persuasion: profiling persuasion types among compliers

In an empirical study of persuasion, researchers often use a binary instrument to encourage individuals to consume information and take some action. We show that, with a binary Imbens–Angrist instrumental variable model and the monotone treatment response assumption, it is possible to identify the joint distribution of potential outcomes among compliers. This is necessary to identify the percentage of mobilized voters and their statistical characteristic defined by the moments of the joint distribution of treatment and covariates. Specifically, we develop a method that enables researchers to identify the statistical characteristic of persuasion types: always-voters, never-voters, and mobilized voters among compliers. These findings extend Abadie’s kappa theorem. We also provide a sharp test for the two sets of identification assumptions. The test boils down to testing whether there exists a non-negative solution to a possibly underdetermined system of linear equations with known coefficients. We apply these results to a voter mobilization experiment.