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Sparse linear models and l1-regularized 2SLS with high-dimensional endogenous regressors and instruments

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  • Zhu, Ying

Abstract

We explore the validity of the 2-stage least squares estimator with l1-regularization in both stages, for linear triangular models where the numbers of endogenous regressors in the main equation and instruments in the first-stage equations can exceed the sample size, and the regression coefficients are sufficiently sparse. For this l1-regularized 2-stage least squares estimator, we first establish finite-sample performance bounds and then provide a simple practical method (with asymptotic guarantees) for choosing the regularization parameter. We also sketch an inference strategy built upon this practical method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:202:y:2018:i:2:p:196-213
    DOI: 10.1016/j.jeconom.2017.10.002
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    References listed on IDEAS

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    1. Eric Gautier & Alexandre Tsybakov, 2011. "High-Dimensional Instrumental Variables Regression and Confidence Sets," Working Papers 2011-13, Center for Research in Economics and Statistics.
    2. Alexandre Belloni & Victor Chernozhukov, 2011. "High Dimensional Sparse Econometric Models: An Introduction," Papers 1106.5242, arXiv.org, revised Sep 2011.
    3. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    4. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference for high-dimensional sparse econometric models," CeMMAP working papers CWP41/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    Cited by:

    1. Sida Peng, 2019. "Heterogeneous Endogenous Effects in Networks," Papers 1908.00663, arXiv.org.
    2. Gold, David & Lederer, Johannes & Tao, Jing, 2020. "Inference for high-dimensional instrumental variables regression," Journal of Econometrics, Elsevier, vol. 217(1), pages 79-111.
    3. Hao Zeng & Wei Zhong & Xingbai Xu, 2024. "Transfer Learning for Spatial Autoregressive Models with Application to U.S. Presidential Election Prediction," Papers 2405.15600, arXiv.org, revised Sep 2024.
    4. Nandana Sengupta & Fallaw Sowell, 2020. "On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples," Econometrics, MDPI, vol. 8(4), pages 1-25, October.

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    More about this item

    Keywords

    High-dimensional statistics; Lasso; Sparse linear models; Endogeneity; Two-stage least squares;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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