Identification in a Generalization of Bivariate Probit Models with Endogenous Regressors

This paper provides identification results for a class of models specified by a triangular system of two equations with binary endogenous variables. The joint distribution of the latent error terms is specified through a parametric copula structure, including the normal copula as a special case, while the marginal distributions of the latent error terms are allowed to be arbitrary but known. This class of models includes bivariate probit models as a special case. The paper demonstrates that an exclusion restriction is necessary and sufficient for globally identification of the model parameters with the excluded variable allowed to be binary. Based on this result, identification is achieved in a full model where common exogenous regressors that are present in both equations and excluded instruments are possibly more general than discretely distributed.