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Inference in Linear Regression Models with Many Covariates and Heteroscedasticity

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  • Matias D. Cattaneo
  • Michael Jansson
  • Whitney K. Newey

Abstract

The linear regression model is widely used in empirical work in economics, statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroscedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates is allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker–White heteroscedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroscedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroscedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is provided, and the proposed methods are also illustrated with an empirical application. Supplementary materials for this article are available online.

Suggested Citation

  • Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
  • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:523:p:1350-1361
    DOI: 10.1080/01621459.2017.1328360
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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. Zhuan Pei & Jörn-Steffen Pischke & Hannes Schwandt, 2019. "Poorly Measured Confounders are More Useful on the Left than on the Right," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 205-216, April.
    3. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
    4. Riccardo D'Adamo, 2018. "Cluster-Robust Standard Errors for Linear Regression Models with Many Controls," Papers 1806.07314, arXiv.org, revised Apr 2019.
    5. Yanqin Fan & Fang Han & Wei Li & Xiao-Hua Zhou, 2019. "On rank estimators in increasing dimensions," Papers 1908.05255, arXiv.org.
    6. Patrick Kline & Raffaele Saggio & Mikkel S{o}lvsten, 2018. "Leave-out estimation of variance components," Papers 1806.01494, arXiv.org, revised Aug 2019.
    7. Jochmans, K., 2019. "Heteroskedasticity-Robust Inference in Linear Regression Models," Cambridge Working Papers in Economics 1957, Faculty of Economics, University of Cambridge.
    8. repec:eee:econom:v:208:y:2019:i:2:p:367-394 is not listed on IDEAS

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