A Monte Carlo comparison of estimators for a bivariate probit model with selection

A Monte Carlo experiment is undertaken to examine the small sample properties of three alternative estimators of a bivariate probit model with selection. The three estimators are the censored probit estimator, single-equation probit applied to the selected sub-sample and single-equation probit applied to the full sample. These estimators are compared in terms of properties of coefficient estimates and predicted probabilities. While no estimator dominates in all possible situations a clear recommendation follows from an overall evaluation of the relative performance of the three estimators. Ignoring the selection problem through use of a single-equation probit can often lead to very poor estimator and predictor performance. Both single-equation probit estimators have properties that can vary dramatically over the different design points. The properties of censored probit vary much less than the two single-equation estimators and this robustness characteristic tends to favour its use.