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. Crown Copyright (C) 2008 Published by Elsevier B.V. on behalf of IMACS. All rights reserved.
probit selection choice modelling finite sample properties