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GMM redundancy results for general missing data problems

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  • Prokhorov, Artem
  • Schmidt, Peter

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 151 (2009)
Issue (Month): 1 (July)
Pages: 47-55

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Handle: RePEc:eee:econom:v:151:y:2009:i:1:p:47-55

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Generalized method of moments Inverse probability weighting Missing at random Selectivity;

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References

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  1. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition and stratification," CeMMAP working papers CWP11/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
  3. 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(06), pages 1717-1728, December.
  4. Nevo, Aviv, 2002. "Sample selection and information-theoretic alternatives to GMM," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 149-157, March.
  5. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
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  7. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
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  17. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(02), pages 451-470, April.
  18. Jeffrey M. Wooldridge, 2004. "Inverse probability weighted estimation for general missing data problems," CeMMAP working papers CWP05/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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  22. Atsushi Inoue & Gary Solon, 2005. "Two-Sample Instrumental Variables Estimators," NBER Technical Working Papers 0311, National Bureau of Economic Research, Inc.
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Cited by:
  1. 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.
  2. Yuriy Gorodnichenko & Anna Mikusheva & Serena Ng, 2011. "Estimators for Persistent and Possibly Non-Stationary Data with Classical Properties," NBER Working Papers 17424, National Bureau of Economic Research, Inc.
  3. Mitsukuni Nishida, 2012. "Estimating a Model of Strategic Network Choice: The Convenience-Store Industry in Okinawa," Economics Working Paper Archive 594, The Johns Hopkins University,Department of Economics.
  4. Moser, Christoph & Urban, Dieter M & Weder di Mauro, Beatrice, 2008. "International Competitiveness, Job Creation and Job Destruction - An Establishment Level Study of German Job Flows," CEPR Discussion Papers 6745, C.E.P.R. Discussion Papers.
  5. Ot�vio Bartalotti, 2013. "GMM Efficiency and IPW Estimation for Nonsmooth Functions," Working Papers 1301, Tulane University, Department of Economics.
  6. 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(06), pages 1717-1728, December.

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