A consistent moment equations for binary probit models with endogenous variables using instrumental variables

A methodology is developed for obtaining consistent moment estimators of the parameters in probit models that include both exogenous and endogenous variables. The approach is based on the use of instrumental variables in the formulation of moment conditions in order to solve a system of equations from which the consistent estimators are derived. The moment conditions also enable the correlations between the endogenous variables and the error terms to be estimated. Comparisons with uncorrected maximum likelihood and Heckman's classic two-stage method using simulated data demonstrate that the proposed method generates consistent estimators with relatively smaller mean square errors. We also apply our method to a real data case, confirming the good estimation properties of our new approach.