On the choice between sample selection and two-part models

This paper resolves the vigorous debates between advocates of the sample selection model and the two-part model. Recent Monte Carlo studies by Hay, Leu, and Rohrer (1987) and Manning, Duan, and Rogers (1987) find that the two-part model performs better than the sample selection model even when the latter is the true model. We show that Manning, Duan, and Rogers' negative results regarding the sample selection model are caused by a critical design problem. We demonstrate that their data generating process produces serious collinearity problems that bias against the sample selection model. Once the design problem is rectified. the poor performance of the sample selection model evaporates. Our Monte Carlo results offer a more balanced view on the relative merits of the two models as each model performs well under different conditions. In particular, the sample selection model is susceptible to collinearity problems and a t-test can be used to distinguish between the two models as long as there are no collinearity problems. As an example, we employ Mroz's (1987) labor supply data to illustrate how his tests for selectivity bias might have been affected by collinearity problems.