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
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Stock and Watson (2008) Heteroskedasticity-Robust Standard Errors for Fixed Effects Panel Data Regression | 1.000 | 5 | 3 | 100% |
| 2 | MacKinnon (2012) Thirty Years of Heteroskedasticity-Robust Inference | 0.928 | 4 | 4 | 100% |
| 3 | Mammen (1993) Bootstrap and Wild Bootstrap for High Dimensional Linear Models | 0.874 | 5 | 2 | 100% |
| 4 | Verdier (2017) Estimation and Inference for Linear Models with Two-Way Fixed Effects and Sparsely Matched Data | 0.811 | 4 | 2 | 100% |
| 5 | Belloni, Chernozhukov, and Hansen (2014) Inference on Treatment Effects after Selection among High-Dimensional Controls | 0.644 | 2 | 2 | 100% |
| 6 | Cattaneo, Jansson, and Newey (2017) Alternative Asymptotics and the Partially Linear Model with Many Regressors self | 0.644 | 2 | 2 | 100% |
| 7 | Long and Ervin (2000) Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model | 0.644 | 2 | 2 | 100% |
| 8 | Bera, Suprayitno, and Premaratne (2002) On Some Heteroskedasticity-robust Estimators of Variance-Covariance Matrix of the Least-squares Estimators | 0.511 | 2 | 1 | 100% |
| 9 | El Karoui, Bean, Bickel, Lim, and Yu (2013) On Robust Regression with High-Dimensional Predictors | 0.511 | 2 | 1 | 100% |
| 10 | Huber (1973) Robust Regression: Asymptotics, Conjectures, and Monte Carlo | 0.511 | 2 | 1 | 100% |
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