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High-dimensional linear models with many endogenous variables

Author

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  • Belloni, Alexandre
  • Hansen, Christian
  • Newey, Whitney

Abstract

High-dimensional linear models with endogenous variables play an increasingly important role in the recent econometric literature. In this work, we allow for models with many endogenous variables and make use of many instrumental variables to achieve identification. Because of the high-dimensionality in the structural equation, constructing honest confidence regions with asymptotically correct coverage is non-trivial. Our main contribution is to propose estimators and confidence regions that achieve this goal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:228:y:2022:i:1:p:4-26
    DOI: 10.1016/j.jeconom.2021.06.011
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    References listed on IDEAS

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    1. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1577-1606, December.
    2. Eric Gautier & Alexandre Tsybakov, 2011. "High-Dimensional Instrumental Variables Regression and Confidence Sets," Working Papers 2011-13, Center for Research in Economics and Statistics.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments," American Economic Review, American Economic Association, vol. 105(5), pages 486-490, May.
    5. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "High-Dimensional Methods and Inference on Structural and Treatment Effects," Journal of Economic Perspectives, American Economic Association, vol. 28(2), pages 29-50, Spring.
    6. Ruben Dezeure & Peter Bühlmann & Cun-Hui Zhang, 2017. "High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 685-719, December.
    7. Ng Serena & Bai Jushan, 2009. "Selecting Instrumental Variables in a Data Rich Environment," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-34, April.
    8. Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2016. "Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3632-3651.
    9. 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.
    10. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2010. "LASSO Methods for Gaussian Instrumental Variables Models," Papers 1012.1297, arXiv.org, revised Feb 2011.
    11. Gold, David & Lederer, Johannes & Tao, Jing, 2020. "Inference for high-dimensional instrumental variables regression," Journal of Econometrics, Elsevier, vol. 217(1), pages 79-111.
    12. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 649-688, August.
    13. Eric Gautier & Alexandre Tsybakov, 2013. "Pivotal estimation in high-dimensional regression via linear programming," Papers 1303.7092, arXiv.org, revised Apr 2013.
    14. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    15. Mehmet Caner & Xu Han & Yoonseok Lee, 2018. "Adaptive Elastic Net GMM Estimation With Many Invalid Moment Conditions: Simultaneous Model and Moment Selection," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 24-46, January.
    16. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey, 2017. "Double/Debiased/Neyman Machine Learning of Treatment Effects," American Economic Review, American Economic Association, vol. 107(5), pages 261-265, May.
    17. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
    18. Hyunseung Kang & Anru Zhang & T. Tony Cai & Dylan S. Small, 2016. "Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 132-144, March.
    19. Han Hong, 2007. "A Statistical Inquiry into the Plausibility of Recursive Utility," Journal of Financial Econometrics, Oxford University Press, vol. 5(4), pages 523-559, Fall.
    20. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
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    Cited by:

    1. Eric Gautier & Christiern Rose, 2022. "Fast, Robust Inference for Linear Instrumental Variables Models using Self-Normalized Moments," Papers 2211.02249, arXiv.org, revised Nov 2022.

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    More about this item

    Keywords

    Honest confidence regions; Instrumental variables; High dimensional models;
    All these keywords.

    JEL classification:

    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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