Journal Article

Inference in Linear Regression Models with Many Covariates and Heteroscedasticity

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

2018

Overview

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.

• Publisher: Taylor & Francis,Taylor & Francis Group,LLC,Taylor & Francis Ltd
• Subject: Economic models / economics / equations / Heteroscedasticity / heteroskedasticity / High-dimensional models / Inference / Linear analysis / linear models / Linear regression / Many regressors / Regression analysis / Regression models / Simulation / Specification / Standard error / Standard error of estimate / Standard errors / Statistical methods / Statistics / Theory and Methods