Limited Information Estimators and Exogeneity Tests for Simultaneous Probit Models

A two-step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators. Conditions under which these estimators attain the Cramer-Rao lower bound are stated. Simple tests of exogeneity are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator.