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Simultaneous Confidence Intervals for High-dimensional Linear Models with Many Endogenous Variables

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  • Alexandre Belloni
  • Christian Hansen
  • Whitney Newey

Abstract

High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve identification. Because of the high-dimensionality in the second stage, constructing honest confidence regions with asymptotically correct coverage is non-trivial. Our main contribution is to propose estimators and confidence regions that would achieve that. The approach relies on moment conditions that have an additional orthogonal property with respect to nuisance parameters. Moreover, estimation of high-dimension nuisance parameters is carried out via new pivotal procedures. In order to achieve simultaneously valid confidence regions we use a multiplier bootstrap procedure to compute critical values and establish its validity.

Suggested Citation

  • Alexandre Belloni & Christian Hansen & Whitney Newey, 2017. "Simultaneous Confidence Intervals for High-dimensional Linear Models with Many Endogenous Variables," Papers 1712.08102, arXiv.org, revised Aug 2019.
    • Handle: RePEc:arx:papers:1712.08102
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    Cited by:

    1. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2020. "Ill-posed estimation in high-dimensional models with instrumental variables," Journal of Econometrics, Elsevier, vol. 219(1), pages 171-200.
    3. Caner, Mehmet, 2023. "Generalized linear models with structured sparsity estimators," Journal of Econometrics, Elsevier, vol. 236(2).
    4. Baris Ata & Alexandre Belloni & Ozan Candogan, 2018. "Latent Agents in Networks: Estimation and Targeting," Papers 1808.04878, arXiv.org, revised Jan 2022.
    5. Victor Chernozhukov & Chen Huang & Weining Wang, 2021. "Uniform Inference on High-dimensional Spatial Panel Networks," Papers 2105.07424, arXiv.org, revised Sep 2023.

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