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Inference in Linear Regression Models with Many Covariates and Heteroskedasticity

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

arXiv 9 Jul 2015 · Mathematics — Statistics Theory · 50 citations (OpenAlex)

arXiv:1507.02493 · PDF · DOI · OpenAlex · Extracted main text

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 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 find 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 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 also provided. The proposed methods are also illustrated with an empirical application.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Stock and Watson (2008) Heteroskedasticity-Robust Standard Errors for Fixed Effects Panel Data Regression1.00053100%
2MacKinnon (2012) Thirty Years of Heteroskedasticity-Robust Inference0.92844100%
3Mammen (1993) Bootstrap and Wild Bootstrap for High Dimensional Linear Models0.87452100%
4Verdier (2017) Estimation and Inference for Linear Models with Two-Way Fixed Effects and Sparsely Matched Data0.81142100%
5Belloni, Chernozhukov, and Hansen (2014) Inference on Treatment Effects after Selection among High-Dimensional Controls0.64422100%
6Cattaneo, Jansson, and Newey (2017) Alternative Asymptotics and the Partially Linear Model with Many Regressors self0.64422100%
7Long and Ervin (2000) Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model0.64422100%
8Bera, Suprayitno, and Premaratne (2002) On Some Heteroskedasticity-robust Estimators of Variance-Covariance Matrix of the Least-squares Estimators0.51121100%
9El Karoui, Bean, Bickel, Lim, and Yu (2013) On Robust Regression with High-Dimensional Predictors0.51121100%
10Huber (1973) Robust Regression: Asymptotics, Conjectures, and Monte Carlo0.51121100%

Showing the top 10 of 41 scored citations.

Cited by, within the corpus

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1Variance Estimation for Saturated Fixed-Effect Specifications0.81142
2Two-Step Estimation and Inference with Possibly Many Included Covariates0.64422
3Deep Learning for Individual Heterogeneity0.51122
4Identification and Estimation of Spillover Effects in Randomized Experiments0.40511
5High-Dimensional Econometrics and Regularized GMM0.40511
6On Rank Estimators in Increasing Dimensions0.40511
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