A note on the identification in two equations probit model with dummy endogenous regressor

This paper deals with the question whether exclusion restrictions on the exogenous regressors are necessary to identify two equation probit models with endogenous dummy regressor. Contradictory opinions have been exposed in the literature on the necessity of an exclusion restriction. Wilde (2000) argued that an exclusion restriction is not necessary, and proposed a simple criterion for identification in this model. We contradict his result, and show how the inherent incompleteness of the model leads to failure of (point) identication. We provide an exact identification proof when an exclusion restriction is available.