Before revision:  In the context of this setup, conclusions from previous results can be generally summarized as follows: (i) imposing instrument monotonicity can misspecify the model; and (ii) when the model is not misspecified, instrument monotonicity does not have any identifying content on the marginal distributions of the potential outcomes. In this paper, I demonstrate that instrument monotonicity can however have identifying content on features of the joint distribution of the potential outcomes when the model is not misspecified.
After revision:  Specifically, I derive necessary and sufficient conditions on the distribution of the data under which the identified set for the distribution of potential outcomes when the model is not misspecified.