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Estimation of Sparse Structural Parameters with Many Endogenous Variables

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  • Zhentao Shi

Abstract

We apply the generalized method of moments--least absolute shinkage and selection operator (GMM-Lasso) (Caner, 2009) to a linear structural model with many endogenous regressors. If the true parameter is sufficiently sparse, we can establish a new oracle inequality, which implies that GMM-Lasso performs almost as well as if we knew a priori the identities of the relevant variables. Sparsity, meaning that most of the true coefficients are too small to matter, naturally arises in econometric applications where the model can be derived from economic theory. In addition, we propose to use a modified version of AIC or BIC to select the tuning parameter in practical implementation. Simulations provide supportive evidence concerning the finite sample properties of the GMM-Lasso.

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  • Zhentao Shi, 2016. "Estimation of Sparse Structural Parameters with Many Endogenous Variables," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1582-1608, December.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:8-10:p:1582-1608
    DOI: 10.1080/07474938.2015.1092805
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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
    3. Phillips, P. C. B., 1984. "The exact distribution of exogenous variable coefficient estimators," Journal of Econometrics, Elsevier, vol. 26(3), pages 387-398, December.
    4. Ackerberg, Daniel & Lanier Benkard, C. & Berry, Steven & Pakes, Ariel, 2007. "Econometric Tools for Analyzing Market Outcomes," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 63, Elsevier.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    7. Eric Gautier & Alexandre Tsybakov, 2013. "Pivotal estimation in high-dimensional regression via linear programming," Working Papers hal-00805556, HAL.
    8. Mehmet Caner & Hao Helen Zhang, 2014. "Adaptive Elastic Net for Generalized Methods of Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 30-47, January.
    9. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    10. 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.
    11. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    12. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
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    Cited by:

    1. 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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    3. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    4. Zhan Gao & Ji Hyung Lee & Ziwei Mei & Zhentao Shi, 2024. "Econometric Inference for High Dimensional Predictive Regressions," Papers 2409.10030, arXiv.org, revised Nov 2024.

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