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-step maximum likelihood procedure for estimating simultaneous probit models and compares it to alternative limited information estimators. The paper also proposes simple tests of exogeneity and shows that they are asymptotically equivalent to each other and have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator. The paper discusses several estimators, including LIML, IVP, and G2SP, and introduces a new estimator, two-stage conditional maximum likelihood (2SCML), which has several advantages over the Heckman and Amemiya estimators. 2SCML is easier to compute than G2SP and in some cases more efficient. It also incorporates a simple test for the exogeneity of the explanatory variables. The paper provides a unifying perspective on the various estimators by placing the estimation problem in a likelihood framework. It derives the Cramer-Rao bound for limited information estimators and discusses the conditions under which the estimators attain this bound. The paper also discusses the efficiency properties of the 2SCML estimator and shows that it enables the construction of analogs of the Wald, likelihood ratio, and score tests based on the conditional likelihood function. The paper concludes that the 2SCML estimator has the same asymptotic properties as the classical LIML tests under the null hypothesis of exogeneity and local alternatives. The paper also discusses the assumptions made in the model and the model's special case, which is Heckman's (1978) hybrid model without structural shift.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-step maximum likelihood procedure for estimating simultaneous probit models and compares it to alternative limited information estimators. The paper also proposes simple tests of exogeneity and shows that they are asymptotically equivalent to each other and have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator. The paper discusses several estimators, including LIML, IVP, and G2SP, and introduces a new estimator, two-stage conditional maximum likelihood (2SCML), which has several advantages over the Heckman and Amemiya estimators. 2SCML is easier to compute than G2SP and in some cases more efficient. It also incorporates a simple test for the exogeneity of the explanatory variables. The paper provides a unifying perspective on the various estimators by placing the estimation problem in a likelihood framework. It derives the Cramer-Rao bound for limited information estimators and discusses the conditions under which the estimators attain this bound. The paper also discusses the efficiency properties of the 2SCML estimator and shows that it enables the construction of analogs of the Wald, likelihood ratio, and score tests based on the conditional likelihood function. The paper concludes that the 2SCML estimator has the same asymptotic properties as the classical LIML tests under the null hypothesis of exogeneity and local alternatives. The paper also discusses the assumptions made in the model and the model's special case, which is Heckman's (1978) hybrid model without structural shift.