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Inference in linear regression models with many covariates and heteroskedasticity

Author

Listed:
  • Matias Cattaneo

    (Institute for Fiscal Studies and University of Michigan)

  • Michael Jansson

    (Institute for Fiscal Studies and Berkeley)

  • Whitney K. Newey

    (Institute for Fiscal Studies and MIT)

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 speci?cation in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates are allowed to grow as fast as the sample size. We fi?nd that all of the usual versions of Eicker-White heteroskedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our fi?ndings 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 also provided. The proposed methods are also illustrated with an empirical application.

Suggested Citation

  • Matias Cattaneo & Michael Jansson & Whitney K. Newey, 2017. "Inference in linear regression models with many covariates and heteroskedasticity," CeMMAP working papers CWP03/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:03/17
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    Keywords

    high-dimensional models; linear regression; many regressors; heteroskedastic- ity; standard errors.;
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