The sample selection model from a method of moments perspective

It is shown how the usnal two-step estimator for the standard sample selection model can be seen as a method of moments estimator Standard GMM theory can be brought to bear on this model, greatly simpliftying the derivation of the asymptotic properties of this model. Using this setup, the asymptotic variance is derived in detail and a consistent estimalot of it is obtained that is guaranteed to be positive definite, in contrast with the estimator given in the literature. It is demonstrated how the MM approach easily accommodate's variations on the estimator like the two-step IV estimalor that handles endogenons regressors, and a two-step GLS estimator. Futhermore, it is shown that from the MM formulation, it is straightfoward to derive various specification tests, in particular tests for selection bias, equivalence with the censored regression model, normality, homoskedasticity, and exogeneity.