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Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection

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  • Liao, Zhipeng

Abstract

This paper proposes a generalized method of moments (GMM) shrinkage method to efficiently estimate the unknown parameters θo identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties; i.e., it consistently selects the correct moment conditions in the second set and at the same time, its estimator is as efficient as the GMM estimator based on all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify θo. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981, Journal of Political Economy 89(6), 1059–1085) and Altonji (1986, Journal of Political Economy 94(3), 176–215). Our empirical findings support the validity of the instrumental variables used in both papers and confirm that wage is an endogenous variable in the labor supply equation.

Suggested Citation

  • Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(5), pages 857-904, October.
  • Handle: RePEc:cup:etheor:v:29:y:2013:i:05:p:857-904_00
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    Cited by:

    1. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    2. Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, Open Access Journal, vol. 1(2), pages 1-23, September.
    3. Prosper Donovon & Alastair R. Hall, 2015. "GMM and Indirect Inference: An appraisal of their connections and new results on their properties under second order identification," The School of Economics Discussion Paper Series 1505, Economics, The University of Manchester.
    4. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    5. Yoonseok Lee & Mehmet Caner & Xu Han, 2015. "Adaptive Elastic Net GMM Estimation with Many Invalid Moment Conditions: Simultaneous Model and Moment Selection," Center for Policy Research Working Papers 177, Center for Policy Research, Maxwell School, Syracuse University.
    6. Cheng, Xu & Liao, Zhipeng, 2015. "Select the valid and relevant moments: An information-based LASSO for GMM with many moments," Journal of Econometrics, Elsevier, vol. 186(2), pages 443-464.
    7. Francis J. DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 14-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Dec 2014.
    8. Francis DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 15-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 10 Aug 2015.
    9. Timothy B. Armstrong & Michal Kolesár, 2018. "Sensitivity Analysis using Approximate Moment Condition Models," Cowles Foundation Discussion Papers 2158R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2019.
    10. repec:eee:econom:v:206:y:2018:i:2:p:554-573 is not listed on IDEAS
    11. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    12. Fan, Jianqing & Liao, Yuan, 2012. "Endogeneity in ultrahigh dimension," MPRA Paper 38698, University Library of Munich, Germany.
    13. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
    14. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    15. Blasques, Francisco & Duplinskiy, Artem, 2018. "Penalized indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 34-54.
    16. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    17. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    18. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    19. repec:bla:ecorec:v:91:y:2015:i:s1:p:1-24 is not listed on IDEAS
    20. Federico A. Bugni & Mehmet Caner & Anders Bredahl Kock & Soumendra Lahiri, 2016. "Inference in partially identified models with many moment inequalities using Lasso," CREATES Research Papers 2016-12, Department of Economics and Business Economics, Aarhus University.
    21. Timothy B. Armstrong & Michal Kolesár, 2018. "Sensitivity Analysis using Approximate Moment Condition Models," Cowles Foundation Discussion Papers 2158, Cowles Foundation for Research in Economics, Yale University.
    22. Timothy B. Armstrong & Michal Koles'ar, 2018. "Sensitivity Analysis using Approximate Moment Condition Models," Papers 1808.07387, arXiv.org, revised Feb 2019.
    23. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.

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