Limited information estimators and exogeneity tests for simultaneous probit models

Abstract

A two-step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators. Conditions under which each estimator attains the Cramer–Rao lower bound are obtained. Simple tests for exogeneity based on the new two-step estimator 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. Finite sample comparisons between the new and alternative estimators are presented based on some Monte Carlo evidence. The performance of the proposed tests for exogeneity is also assessed.