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Consistency of Heckman-type two-step Estimators for the Multivariate Sample-Selection Model

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This analysis shows that multivariate generalizations to the classical Heckman (1976 and 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.

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