IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v151y2009i1p47-55.html
   My bibliography  Save this article

GMM redundancy results for general missing data problems

Author

Listed:
  • 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.

Suggested Citation

  • Prokhorov, Artem & Schmidt, Peter, 2009. "GMM redundancy results for general missing data problems," Journal of Econometrics, Elsevier, vol. 151(1), pages 47-55, July.
  • Handle: RePEc:eee:econom:v:151:y:2009:i:1:p:47-55
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(09)00070-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Imbens, Guido W, 1992. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Econometrica, Econometric Society, vol. 60(5), pages 1187-1214, September.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Zellner, Arnold, 1970. "Estimation of Regression Relationships Containing Unobservable Independent Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 441-454, October.
    4. Crepon, Bruno & Kramarz, Francis & Trognon, Alain, 1997. "Parameters of interest, nuisance parameters and orthogonality conditions An application to autoregressive error component models," Journal of Econometrics, Elsevier, vol. 82(1), pages 135-156.
    5. Judith K. Hellerstein & Guido W. Imbens, 1999. "Imposing Moment Restrictions From Auxiliary Data By Weighting," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 1-14, February.
    6. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    7. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
    8. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    9. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-235, April.
    10. Esmeralda Ramalho & Joaquim Ramalho, 2006. "Bias-Corrected Moment-Based Estimators for Parametric Models Under Endogenous Stratified Sampling," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 475-496.
    11. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    12. Joshua D. Angrist & Alan B. Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
    13. Nevo, Aviv, 2002. "Sample selection and information-theoretic alternatives to GMM," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 149-157, March.
    14. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    15. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition, and stratification," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 117-139, August.
    16. 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.
    17. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    18. Nevo, Aviv, 2003. "Using Weights to Adjust for Sample Selection When Auxiliary Information Is Available," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 43-52, January.
    19. Goldberger, Arthur S, 1972. "Maximum-Likelihood Estimation of Regressions Containing Unobservable Independent Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 1-15, February.
    20. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(2), pages 451-470, April.
    21. Atsushi Inoue & Gary Solon, 2010. "Two-Sample Instrumental Variables Estimators," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 557-561, August.
    22. Wooldridge, Jeffrey M., 2007. "Inverse probability weighted estimation for general missing data problems," Journal of Econometrics, Elsevier, vol. 141(2), pages 1281-1301, December.
    23. Hahn, Jinyong, 1997. "Efficient estimation of panel data models with sequential moment restrictions," Journal of Econometrics, Elsevier, vol. 79(1), pages 1-21, July.
    24. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-1988, November.
    25. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 261-294.
    26. Masayuki Henmi & Shinto Eguchi, 2004. "A paradox concerning nuisance parameters and projected estimating functions," Biometrika, Biometrika Trust, vol. 91(4), pages 929-941, December.
    27. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
    28. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
    29. Qian, Hailong & Schmidt, Peter, 1999. "Improved instrumental variables and generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 91(1), pages 145-169, July.
    30. Chamberlain, Gary, 1992. "Sequential Moment Restrictions in Panel Data: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 20-26, January.
    31. Angrist, Joshua D, 1995. "Introduction to the JBES Symposium on Program and Policy Evaluation," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 133-136, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Chris Muris, 2020. "Efficient GMM Estimation with Incomplete Data," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 518-530, July.
    6. 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.
    7. 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.
    8. Hirukawa, Masayuki & Prokhorov, Artem, 2018. "Consistent estimation of linear regression models using matched data," Journal of Econometrics, Elsevier, vol. 203(2), pages 344-358.
    9. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    10. Otávio Bartalotti, 2013. "GMM Efficiency and IPW Estimation for Nonsmooth Functions," Working Papers 1301, Tulane University, Department of Economics.
    11. 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.
    12. Akanksha Negi, 2020. "Doubly weighted M-estimation for nonrandom assignment and missing outcomes," Papers 2011.11485, arXiv.org.
    13. 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.
    14. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    15. 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.
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 1053-1079.
    2. 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.
    3. Kyungchul Song, 2009. "Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling," PIER Working Paper Archive 09-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    5. Joachim Inkmann, 2010. "Estimating Firm Size Elasticities of Product and Process R&D," Economica, London School of Economics and Political Science, vol. 77(306), pages 384-402, April.
    6. Buchinsky, Moshe & Li, Fanghua & Liao, Zhipeng, 2022. "Estimation and inference of semiparametric models using data from several sources," Journal of Econometrics, Elsevier, vol. 226(1), pages 80-103.
    7. Nevo, Aviv, 2003. "Using Weights to Adjust for Sample Selection When Auxiliary Information Is Available," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 43-52, January.
    8. 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.
    9. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    10. Wooldridge, Jeffrey M., 2007. "Inverse probability weighted estimation for general missing data problems," Journal of Econometrics, Elsevier, vol. 141(2), pages 1281-1301, December.
    11. Ramalho Esmeralda A., 2010. "Covariate Measurement Error: Bias Reduction under Response-Based Sampling," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-34, September.
    12. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    13. Sasaki, Yuya & Ura, Takuya, 2023. "Estimation and inference for policy relevant treatment effects," Journal of Econometrics, Elsevier, vol. 234(2), pages 394-450.
    14. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 343-364.
    15. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Dec 2017.
    16. Denis Heng Yan Leung & Ken Yamada & Biao Zhang, 2015. "Enriching Surveys with Supplementary Data and its Application to Studying Wage Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 155-179, March.
    17. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    18. Esmeralda Ramalho, 2004. "Covariate Measurement Error in Endogenous Stratified Samples," Economics Working Papers 2_2004, University of Évora, Department of Economics (Portugal).
    19. Joachim Inkmann, 2000. "Finite Sample Properties of One-Step, Two-Step and Bootstrap Empirical Likelihood Approaches to Efficient GMM Estimation," Econometric Society World Congress 2000 Contributed Papers 0332, Econometric Society.
    20. Esmerelda A. Ramalho & Richard Smith, 2003. "Discrete choice non-response," CeMMAP working papers 07/03, Institute for Fiscal Studies.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:151:y:2009:i:1:p:47-55. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.