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The Sample Selection Model from a Method of Moments Perspective

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  • Erik Meijer
  • Tom Wansbeek

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.

Suggested Citation

  • Erik Meijer & Tom Wansbeek, 2007. "The Sample Selection Model from a Method of Moments Perspective," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 25-51.
    • Handle: RePEc:taf:emetrv:v:26:y:2007:i:1:p:25-51
    DOI: 10.1080/07474930600972194
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    References listed on IDEAS

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    1. James J. Heckman, 1977. "Sample Selection Bias As a Specification Error (with an Application to the Estimation of Labor Supply Functions)," NBER Working Papers 0172, National Bureau of Economic Research, Inc.
    2. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
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    Citations

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    Cited by:

    1. Semykina, Anastasia & Wooldridge, Jeffrey M., 2010. "Estimating panel data models in the presence of endogeneity and selection," Journal of Econometrics, Elsevier, vol. 157(2), pages 375-380, August.
    2. Michael Pfaffermayr, 2014. "A GMM-Based Test for Normal Disturbances of the Heckman Sample Selection Model," Econometrics, MDPI, vol. 2(4), pages 1-18, October.
    3. Mora, Jhon James & Muro, Juan, 2014. "Consistent estimation in pseudo panels in the presence of selection bias," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 8, pages 1-25.
    4. Erik Meijer & Arie Kapteyn & Tatiana Andreyeva, 2008. "Health Indexes and Retirement Modeling in International Comparisons," Working Papers 614, RAND Corporation.
    5. Erik Meijer & Edward Oczkowski & Tom Wansbeek, 2021. "How measurement error affects inference in linear regression," Empirical Economics, Springer, vol. 60(1), pages 131-155, January.
    6. Adeline Delavande & Hans-Peter Kohler, 2012. "The Impact of HIV Testing on Subjective Expectations and Risky Behavior in Malawi," Demography, Springer;Population Association of America (PAA), vol. 49(3), pages 1011-1036, August.
    7. Gad Allon & Sarang Deo & Wuqin Lin, 2013. "The Impact of Size and Occupancy of Hospital on the Extent of Ambulance Diversion: Theory and Evidence," Operations Research, INFORMS, vol. 61(3), pages 544-562, June.
    8. Carri W. Chan & Vivek F. Farias & Gabriel J. Escobar, 2017. "The Impact of Delays on Service Times in the Intensive Care Unit," Management Science, INFORMS, vol. 63(7), pages 2049-2072, July.
    9. Hasebe, Takuya & Vijverberg, Wim P., 2012. "A Flexible Sample Selection Model: A GTL-Copula Approach," IZA Discussion Papers 7003, Institute of Labor Economics (IZA).
    10. Erik Meijer & Arie Kapteyn & Tatiana Andreyeva, 2008. "Health Indexes and Retirement Modeling in International Comparisons," Working Papers WR-614, RAND Corporation.

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    Keywords

    GMM; Heckman estimator; Tobit;
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