This paper investigates the properties of various estimators for probit models where some or all of the explanatory variables may be endogenous. It proposes a two-stage conditional maximum likelihood (2SCML) estimator and compares it with other estimators such as the limited information maximum likelihood (LIML), instrumental variables probit (IVP), and generalized two-stage simultaneous probit (G2SP). The 2SCML estimator is shown to be computationally simpler and more efficient in some cases compared to other estimators. The paper also derives the Cramer-Rao bound for limited information estimators and conditions under which these estimators attain this bound. Additionally, it proposes simple tests for exogeneity and shows that these tests are asymptotically equivalent to classical tests based on the limited information maximum likelihood estimator. The efficiency properties of the 2SCML estimator allow for the construction of optimal tests for exogeneity in probit models.This paper investigates the properties of various estimators for probit models where some or all of the explanatory variables may be endogenous. It proposes a two-stage conditional maximum likelihood (2SCML) estimator and compares it with other estimators such as the limited information maximum likelihood (LIML), instrumental variables probit (IVP), and generalized two-stage simultaneous probit (G2SP). The 2SCML estimator is shown to be computationally simpler and more efficient in some cases compared to other estimators. The paper also derives the Cramer-Rao bound for limited information estimators and conditions under which these estimators attain this bound. Additionally, it proposes simple tests for exogeneity and shows that these tests are asymptotically equivalent to classical tests based on the limited information maximum likelihood estimator. The efficiency properties of the 2SCML estimator allow for the construction of optimal tests for exogeneity in probit models.