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Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso

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  • Caner, Mehmet
  • Fan, Qingliang

Abstract

In this paper, we use the adaptive lasso estimator to choose the relevant instruments and eliminate the irrelevant instruments. The limit theory of Zou (2006) is extended from univariate iid case to heteroskedastic and non Gaussian data. Then we use the selected instruments in generalized empirical likelihood estimators (GEL). In this sense, these are called hybrid GEL. It is also shown that the lasso estimators are not model selection consistent whereas the adaptive lasso can select the correct model with fixed number of instruments. In simulations we show that hybrid GEL estimators have smaller bias and mean squared error than the other estimators in certain cases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:1:p:256-274
    DOI: 10.1016/j.jeconom.2015.01.007
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    References listed on IDEAS

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    Cited by:

    1. Jinyuan Chang & Zhentao Shi & Jia Zhang, 2021. "Culling the herd of moments with penalized empirical likelihood," Papers 2108.03382, arXiv.org, revised May 2022.
    2. Qingliang Fan & Yaqian Wu, 2020. "Endogenous Treatment Effect Estimation with some Invalid and Irrelevant Instruments," Papers 2006.14998, arXiv.org.
    3. Prosper Dovonon & Firmin Doko Tchatoka & Michael Aguessy, 2019. "Relevant moment selection under mixed identification strength," School of Economics and Public Policy Working Papers 2019-04, University of Adelaide, School of Economics and Public Policy.
    4. Gold, David & Lederer, Johannes & Tao, Jing, 2020. "Inference for high-dimensional instrumental variables regression," Journal of Econometrics, Elsevier, vol. 217(1), pages 79-111.
    5. Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates," Papers 2205.00171, arXiv.org, revised Mar 2023.
    6. Tomohiro Ando & Naoya Sueishi, 2019. "On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator," Econometrics, MDPI, vol. 7(1), pages 1-14, March.
    7. Fan, Jianqing & Gong, Wenyan & Zhu, Ziwei, 2019. "Generalized high-dimensional trace regression via nuclear norm regularization," Journal of Econometrics, Elsevier, vol. 212(1), pages 177-202.
    8. 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.

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    More about this item

    Keywords

    Model selection; Near minimax risk bound; Shrinkage estimators;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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