On the identifying content of instrument monotonicity

SUMMARY: The existing literature has established that the instrument monotonicity assumption of Imbens and Angrist (1994) has no identifying content on the average treatment effect and more generally on the marginal distributions of potential outcomes in the sense that additionally imposing this assumption does not affect the identified set for the parameters of interest under instrument exogeneity whenever these assumptions are consistent with the data. This paper demonstrates that the identifying content of instrument monotonicity presents itself in features of the joint distribution of potential outcomes. In the context of a model with a binary outcome, a binary treatment, and an exogenous binary instrument, I derive identified sets for the distribution of potential outcomes with and without instrument monotonicity. Comparing the two identified sets, I provide necessary and sufficient conditions on the distribution of the data under which the former identified set can be a strict subset of the latter. I empirically illustrate the results by revisiting the study of Angrist and Evans (1998).