Testing Identifying Assumptions in Bivariate Probit Models

This paper focuses on the bivariate probit model's identifyingassumptions: joint normality of errors, instrument exogeneity, and relevance conditions. First, we develop novel sharp testable equalities that can detect all possible observable violations of the assumptions. Second, we propose an easy-to-implement testing procedure for the model's validity based on feasible testable implications using existing inference methods for intersection bounds. The test achieves correct empirical size for moderately sized samples and performs well in detecting violations of the conditions in Monte Carlo simulations. Finally, we provide researchers with a road map on what to do when the bivariate probit model is rejected, including novel bounds for the average treatment effect that relax the normality assumption. Empirical examples illustrate the methodology's implementation.