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The Sample Selection Model from a Method of Moments Perspective

Authors: Erik Meijer a; Tom Wansbeek a
Affiliation:   a Faculty of Economics, University of Groningen, Groningen, The Netherlands
DOI: 10.1080/07474930600972194
Publication Frequency: 6 issues per year
Published in: journal Econometric Reviews, Volume 26, Issue 1 January 2007 , pages 25 - 51
Formats available: HTML (English) : PDF (English)
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Abstract

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.
Keywords: GMM; Heckman estimator; Tobit
JEL Classification: C34; C13
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