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Heteroskedasticity-Robust Inference in Linear Regression Models with Many Covariates

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  • Jochmans, K.

Abstract

We consider inference in linear regression models that is robust to heteroskedasticity and the presence of many control variables. When the number of control variables increases at the same rate as the sample size the usual heteroskedasticity-robust estimators of the covariance matrix are inconsistent. Hence, tests based on these estimators are size distorted even in large samples. An alternative covariance-matrix estimator for such a setting is presented that complements recent work by Cattaneo, Jansson and Newey (2018). We provide high-level conditions for our approach to deliver (asymptotically) size-correct inference as well as more primitive conditions for three special cases. Simulation results and an empirical illustration to inference on the union premium are also provided.

Suggested Citation

  • Jochmans, K., 2020. "Heteroskedasticity-Robust Inference in Linear Regression Models with Many Covariates," Cambridge Working Papers in Economics 2033, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:2033
    Note: kj345
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    Cited by:

    1. Kaspar Wuthrich & Ying Zhu, 2019. "Omitted variable bias of Lasso-based inference methods: A finite sample analysis," Papers 1903.08704, arXiv.org, revised Sep 2021.
    2. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Ng Cheuk Fai, 2022. "Robust Inference in High Dimensional Linear Model with Cluster Dependence," Papers 2212.05554, arXiv.org.
    4. Liang Jiang & Liyao Li & Ke Miao & Yichong Zhang, 2023. "Adjustment with Many Regressors Under Covariate-Adaptive Randomizations," Papers 2304.08184, arXiv.org, revised Nov 2024.
    5. Liu, Lin & Mukherjee, Rajarshi & Robins, James M., 2024. "Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators," Journal of Econometrics, Elsevier, vol. 240(2).
    6. Wei, Waverly & Zhou, Yuqing & Zheng, Zeyu & Wang, Jingshen, 2024. "Inference on the best policies with many covariates," Journal of Econometrics, Elsevier, vol. 239(2).

    More about this item

    Keywords

    heteroskedasticity; inference; many regressors; statistical leverage;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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