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GMM Redundancy Results for General Missing Data Problems

Author

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  • Artem Prokhorov

    (Concordia University)

  • Peter Schmidt

    (Michigan State University)

Abstract

We consider questions of efficiency and redundancy in the GMM estimation problem in which we have two sets of moment conditions, where two sets of parameters enter into one set of moment conditions, while only one set of parameters enters into the other. We then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest, and the second set of moment conditions is for the selection process. We use these results to explain the counterintuitive result in the literature that, under an ignorability assumption that justifies GMM with weighted moment conditions, weighting using estimated probabilities of selection is better than weighting using the true probabilities. We also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid, and we show that when weighting is not needed for consistency, it is also not useful for efficiency.

Suggested Citation

  • Artem Prokhorov & Peter Schmidt, 2008. "GMM Redundancy Results for General Missing Data Problems," Working Papers 08003, Concordia University, Department of Economics.
  • Handle: RePEc:crd:wpaper:08003
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    Cited by:

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    2. Moser, Christoph & Urban, Dieter & di Mauro, Beatrice Weder, 2010. "International competitiveness, job creation and job destruction--An establishment-level study of German job flows," Journal of International Economics, Elsevier, vol. 80(2), pages 302-317, March.
    3. Hirukawa, Masayuki & Prokhorov, Artem, 2018. "Consistent estimation of linear regression models using matched data," Journal of Econometrics, Elsevier, vol. 203(2), pages 344-358.
    4. Gorodnichenko, Yuriy & Mikusheva, Anna & Ng, Serena, 2012. "Estimators For Persistent And Possibly Nonstationary Data With Classical Properties," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1003-1036, October.
    5. Stanislav Anatolyev & Renat Khabibullin & Artem Prokhorov, 2012. "Reconstructing high dimensional dynamic distributions from distributions of lower dimension," Working Papers 12003, Concordia University, Department of Economics.
    6. Han, Chirok & Kim, Beomsoo, 2011. "A GMM interpretation of the paradox in the inverse probability weighting estimation of the average treatment effect on the treated," Economics Letters, Elsevier, vol. 110(2), pages 163-165, February.
    7. Kyoo il Kim, 2019. "Efficiency of Average Treatment Effect Estimation When the True Propensity Is Parametric," Econometrics, MDPI, vol. 7(2), pages 1-13, May.
    8. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    9. Mitsukuni Nishida, 2015. "Estimating a Model of Strategic Network Choice: The Convenience-Store Industry in Okinawa," Marketing Science, INFORMS, vol. 34(1), pages 20-38, January.
    10. Hao, Bowen & Prokhorov, Artem & Qian, Hailong, 2018. "Moment redundancy test with application to efficiency-improving copulas," Economics Letters, Elsevier, vol. 171(C), pages 29-33.
    11. Hristache, Marian & Patilea, Valentin, 2021. "Equivalent models for observables under the assumption of missing at random," Econometrics and Statistics, Elsevier, vol. 20(C), pages 153-165.
    12. Hitomi, Kohtaro & Nishiyama, Yoshihiko & Okui, Ryo, 2008. "A Puzzling Phenomenon In Semiparametric Estimation Problems With Infinite-Dimensional Nuisance Parameters," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1717-1728, December.
    13. Masayuki Hirukawa & Di Liu & Irina Murtazashvili & Artem Prokhorov, 2023. "DS-HECK: double-lasso estimation of Heckman selection model," Empirical Economics, Springer, vol. 64(6), pages 3167-3195, June.
    14. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    15. Chris Muris, 2020. "Efficient GMM Estimation with Incomplete Data," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 518-530, July.
    16. Akanksha Negi, 2020. "Doubly weighted M-estimation for nonrandom assignment and missing outcomes," Papers 2011.11485, arXiv.org.

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