Inference in Linear Regression Models with Many Covariates and Heteroscedasticity

By M. D. Cattaneo, Michael Jansson, Whitney K. Newey. Journal of the American Statistical Association, 2015

143 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fe6100158e9d121755408f8fa6f5357d03ee0c4e

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Citations in the corpus

High-dimensional econometrics and regularized GMM (2018, background): “[39] and [40] consider inference for a low-dimensional set of coefficients in a linear model with number of variables proportional to but smaller than the sample size in a framework allowing for the coefficients on the nuisance variables to be dense.”
Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments (2019, unknown): “For some finite positive constants (4)See Chernozhukov et al. (2018) and references therein.”
Econometric Methods for Program Evaluation (2018, methodology): “Cattaneo et al. (2017d,e) and Cattaneo et al. (2017c) develop program evaluation methods where the distributional approximations do change relative to low-dimensional results, due to the inclusion of many covariates in the estimation.”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, methodology): “ent eect framework, this formula can be used to estimate standard errors of pre-specied interactions of the base treatment and test the hypothesis that all interactions are equal to zero. Weakening Cattaneo et al. (2018)’s conditions, Kline et al. (2018) oer a leave-one-out approach to estimation an”
Leave‐Out Estimation of Variance Components (2018, background): “We study the asymptotic behavior of the proposed leave-out estimator in an environment where the number of regressors may be proportional to the sample size: a framework that has alternately been termed “many covariates” (Cattaneo et al., 2018) or “moderate dimensional” (Lei et al.”
On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls (2019, methodology): “This is consistent with Theorem 1 from Cattaneo et al. (2018), once we consider a change in variables so that we can divide the J control variables into a group of F variables such that their associated estimators give us μ̂OLS, and a remaining group of J − F variables that we are not inherently int”