Finite sample behavior of two step estimators in selection models

The problem of specification errors in sample selection models has received considerable attention both theoretically and empirically. However, very few is known about the finite sample behavior of two step estimators. In this paper we investigate by simulations both bias and finite sample distribution of these estimators when ignoring heteroskedasticity in the sample selection mechanism. It turns out that under conditions traditionally faced by practitioners, the misspecified parametric two step estimator (Heckman, 1979) performs better, in finite sample sizes, than the robust semiparametric one (Ahn and Powell, 1993). Moreover, under very general conditions, we show that the asymptotic bias of the parametric two step estimator is linear in the covariance between the sample selection and the participation equation.