The linear regression model is widely used in empirical work in Economics,Statistics, and many other disciplines. Researchers often include manycovariates in their linear model specification in an attempt to control forconfounders. We give inference methods that allow for many covariates andheteroskedasticity. Our results are obtained using high-dimensionalapproximations, where the number of included covariates are allowed to grow asfast as the sample size. We find that all of the usual versions of Eicker-Whiteheteroskedasticity consistent standard error estimators for linear models areinconsistent under this asymptotics. We then propose a new heteroskedasticityconsistent standard error formula that is fully automatic and robust to both(conditional)\ heteroskedasticity of unknown form and the inclusion of possiblymany covariates. We apply our findings to three settings: parametric linearmodels with many covariates, linear panel models with many fixed effects, andsemiparametric semi-linear models with many technical regressors. Simulationevidence consistent with our theoretical results is also provided. The proposedmethods are also illustrated with an empirical application.
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