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Lasso-Type Gmm Estimator

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  • Caner, Mehmet

Abstract

This paper proposes the least absolute shrinkage and selection operator–type (Lasso-type) generalized method of moments (GMM) estimator. This Lasso-type estimator is formed by the GMM objective function with the addition of a penalty term. The exponent of the penalty term in the regular Lasso estimator is equal to one. However, the exponent of the penalty term in the Lasso-type estimator is less than one in the analysis here. The magnitude of the exponent is reduced to avoid the asymptotic bias. This estimator selects the correct model and estimates it simultaneously. In other words, this method estimates the redundant parameters as zero in the large samples and provides the standard GMM limit distribution for the estimates of the nonzero parameters in the model. The asymptotic theory for our estimator is nonstandard. We conduct a simulation study that shows that the Lasso-type GMM correctly selects the true model much more often than the Bayesian information Criterion (BIC) and another model selection procedure based on the GMM objective function.

Suggested Citation

  • Caner, Mehmet, 2009. "Lasso-Type Gmm Estimator," Econometric Theory, Cambridge University Press, vol. 25(1), pages 270-290, February.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:270-290_09
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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. Ning Xu & Jian Hong & Timothy C. G. Fisher, 2016. "Model selection consistency from the perspective of generalization ability and VC theory with an application to Lasso," Papers 1606.00142, arXiv.org.
    3. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    4. 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.
    5. Fan, Jianqing & Liao, Yuan, 2012. "Endogeneity in ultrahigh dimension," MPRA Paper 38698, University Library of Munich, Germany.
    6. Stefano Maria IACUS & Alessandro DE GREGORIO, 2010. "Adaptive LASSO-type estimation for ergodic diffusion processes," Departmental Working Papers 2010-13, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    7. Achim Ahrens & Arnab Bhattacharjee, 2015. "Two-Step Lasso Estimation of the Spatial Weights Matrix," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-28, March.
    8. Zhu, Ying, 2018. "Sparse linear models and l1-regularized 2SLS with high-dimensional endogenous regressors and instruments," Journal of Econometrics, Elsevier, vol. 202(2), pages 196-213.
    9. Inoue, Atsushi & Rossi, Barbara, 2011. "Testing for weak identification in possibly nonlinear models," Journal of Econometrics, Elsevier, vol. 161(2), pages 246-261, April.
    10. 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.
    11. 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.
    12. Caner, Mehmet & Fan, Qingliang, 2015. "Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso," Journal of Econometrics, Elsevier, vol. 187(1), pages 256-274.
    13. Savin Ivan, 2013. "A Comparative Study of the Lasso-type and Heuristic Model Selection Methods," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(4), pages 526-549, August.
    14. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    15. Ning Xu & Jian Hong & Timothy C. G. Fisher, 2016. "Finite-sample and asymptotic analysis of generalization ability with an application to penalized regression," Papers 1609.03344, arXiv.org, revised Sep 2016.
    16. 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.
    17. Eric Gautier & Alexandre Tsybakov, 2011. "High-Dimensional Instrumental Variables Regression and Confidence Sets," Working Papers 2011-13, Center for Research in Economics and Statistics.
    18. Zhu, Ying, 2015. "Sparse Linear Models and l1−Regularized 2SLS with High-Dimensional Endogenous Regressors and Instruments," MPRA Paper 81217, University Library of Munich, Germany.
    19. Martins, Luis F. & Gabriel, Vasco J., 2014. "Linear instrumental variables model averaging estimation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 709-724.
    20. Zhu, Ying, 2013. "Sparse Linear Models and Two-Stage Estimation in High-Dimensional Settings with Possibly Many Endogenous Regressors," MPRA Paper 49846, University Library of Munich, Germany.
    21. Caner, Mehmet & Yıldız, Neşe, 2012. "CUE with many weak instruments and nearly singular design," Journal of Econometrics, Elsevier, vol. 170(2), pages 422-441.
    22. 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.
    23. Ando, Tomohiro & Sueishi, Naoya, 2019. "Regularization parameter selection for penalized empirical likelihood estimator," Economics Letters, Elsevier, vol. 178(C), pages 1-4.

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