Testing identifying assumptions in bivariate probit models

This paper considers the bivariate probit model's identifying assumptions: linear index specification, joint normality of errors, instrument exogeneity, and relevance. First, we develop sharp testable equalities that detect all possible observable violations assumptions. Second, propose an easy-to-implement testing procedure for validity using existing inference methods intersection bounds. The test achieves correct empirical size performs well in detecting conditions simulations. Finally, provide a road map on what to do when model is rejected, including novel bounds average treatment effect relax assumption.