This paper gives a short overview of Monte Carlo studies on the usefulness of Heckman's (1976, 1979) two-step estimator for estimating a selection model. It shows that exploratory work to check for collinearity problems is strongly recommended before deciding on which estimator to apply. In the absence of collinearity problems, the full-information maximum likelihood estimator is preferable to the limited-information two-step method of Heckman, although the latter also gives reasonable results. If, however, collinearity problems prevail, subsample OLS (or the Two-Part Model) is the most robust amongst the simple-to-calculate estimators.
Puhani, Patrick (1997), Foul or Fair? The Heckman Correction for Sample Selection and its Critique - A Short Survey, ZEW Discussion Paper No. 97-07, Mannheim. Download