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Adaptive Elastic Net GMM Estimation with Many Invalid Moment Conditions: Simultaneous Model and Moment Selection

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Abstract
This paper develops the adaptive elastic net GMM estimator in large dimensional models with many possibly invalid moment conditions, where both the number of structural parameters and the number of moment conditions may increase with the sample size. The basic idea is to conduct the standard GMM estimation combined with two penalty terms: the quadratic regularization and the adaptively weighted lasso shrinkage. The new estimation procedure consistently selects both the nonzero structural parameters and the valid moment conditions. At the same time, it uses information only from the valid moment conditions to estimate the selected structural parameters and thus achieves the standard GMM efficiency bound as if we know the valid moment conditions ex ante. It is shown that the quadratic regularization is important to obtain the efficient estimator. We also study the tuning parameter choice, with which we show that selection consistency still holds without assuming Gaussianity. We apply the new estimation procedure to dynamic panel data models, where both the time and cross section dimensions are large. The new estimator is robust to possible serial correlations in the regression error terms.

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  • 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.
    • Handle: RePEc:max:cprwps:177
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    File URL: https://surface.syr.edu/cpr/209/
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    2. Caner, Mehmet & Fan, Qingliang & Grennes, Thomas, 2021. "Partners in debt: An endogenous non-linear analysis of the effects of public and private debt on growth," International Review of Economics & Finance, Elsevier, vol. 76(C), pages 694-711.
    3. Gyuhyeong Goh & Jisang Yu, 2022. "Causal inference with some invalid instrumental variables: A quasi‐Bayesian approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(6), pages 1432-1451, December.
    4. Marco Battaglini & Forrest W. Crawford & Eleonora Patacchini & Sida Peng, 2020. "A Graphical Lasso Approach to Estimating Network Connections: The Case of U.S. Lawmakers," NBER Working Papers 27557, National Bureau of Economic Research, Inc.
    5. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    6. Nicolas Apfel, 2019. "Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation," Papers 1907.00222, arXiv.org, revised Jul 2022.
    7. Jinyuan Chang & Zhentao Shi & Jia Zhang, 2021. "Culling the herd of moments with penalized empirical likelihood," Papers 2108.03382, arXiv.org, revised May 2022.
    8. Qingliang Fan & Yaqian Wu, 2020. "Endogenous Treatment Effect Estimation with some Invalid and Irrelevant Instruments," Papers 2006.14998, arXiv.org.
    9. Tae-Hwy Lee & Tao Wang, 2023. "Estimation and Testing of Forecast Rationality with Many Moments," Papers 2309.09481, arXiv.org.
    10. Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.
    11. Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates," Papers 2205.00171, arXiv.org, revised May 2024.
    12. Yoonseok Lee & Yu Zhou, 2015. "Averaged Instrumental Variables Estimators," Center for Policy Research Working Papers 180, Center for Policy Research, Maxwell School, Syracuse University.
    13. 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.
    14. Mehmet Caner & Xu Han, 2021. "An upper bound for functions of estimators in high dimensions," Econometric Reviews, Taylor & Francis Journals, vol. 40(1), pages 1-13, January.
    15. Chiang, Harold D. & Rodrigue, Joel & Sasaki, Yuya, 2023. "Post-Selection Inference In Three-Dimensional Panel Data," Econometric Theory, Cambridge University Press, vol. 39(3), pages 623-658, June.
    16. Belloni, Alexandre & Hansen, Christian & Newey, Whitney, 2022. "High-dimensional linear models with many endogenous variables," Journal of Econometrics, Elsevier, vol. 228(1), pages 4-26.
    17. Mehmet Caner, 2021. "A Starting Note: A Historical Perspective in Lasso," International Econometric Review (IER), Econometric Research Association, vol. 13(1), pages 1-3, March.

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    More about this item

    Keywords

    Adaptive Elastic Net; GMM; many invalid moments; large dimensional models; efficiency bound; turning parameter choice; dynamic panel;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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