The Sample Selection Model from a Method of Moments Perspective
展示标准样本选择模型的两步估计量可视为矩估计量，利用GMM理论简化渐近性质推导，给出保证正定的方差一致估计量，并轻松扩展至工具变量和GLS估计，以及多种设定检验。
It is shown how the usual 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 simplifying the derivation of the asymptotic properties of this model. Using this setup, the asymptotic variance is derived in detail and a consistent estimator 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 accommodates variations on the estimator, like the two-step IV estimator that handles endogenous regressors, and a two-step GLS estimator. Furthermore, it is shown that from the MM formulation, it is straightforward to derive various specification tests, in particular tests for selection bias, equivalence with the censored regression model, normality, homoskedasticity, and exogeneity.