Consistency of Heckman-type two-step estimators for the multivariate sample-selection model

This analysis shows that multivariate generalizations to the classical Heckman (1976 Heckman, JJ. 1976. The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. Annals of Economics and Social Measurement, 5: 475–92.  Google Scholar], 1979) two-step estimator that account for cross-equation correlation and use the inverse Mills ratio as correction term are consistent only if certain restrictions apply to the true error-covariance structure. An alternative class of generalizations to the classical Heckman two-step approach is derived that condition on the entire selection pattern rather than selection in particular equations and, therefore, use modified correction terms. It is shown that this class of estimators is consistent. In addition, Monte-Carlo results illustrate that these estimators display a smaller mean square prediction error.