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Inference in Linear Regression Models with Many Covariates and Heteroscedasticity

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

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.

Suggested Citation

  • Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:523:p:1350-1361
    DOI: 10.1080/01621459.2017.1328360
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    1. James H. Stock & Mark W. Watson, 2008. "Heteroskedasticity-Robust Standard Errors for Fixed Effects Panel Data Regression," Econometrica, Econometric Society, vol. 76(1), pages 155-174, January.
    2. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6b.
    3. Pedro Carneiro & James J. Heckman & Edward J. Vytlacil, 2011. "Estimating Marginal Returns to Education," American Economic Review, American Economic Association, vol. 101(6), pages 2754-2781, October.
    4. James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
    5. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    6. Kline, Patrick & Santos, Andres, 2012. "Higher order properties of the wild bootstrap under misspecification," Journal of Econometrics, Elsevier, vol. 171(1), pages 54-70.
    7. Koenker, Roger, 1988. "Asymptotic Theory and Econometric Practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(2), pages 139-147, April.
    8. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    9. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    10. Alberto Abadie & Guido W. Imbens & Fanyin Zheng, 2014. "Inference for Misspecified Models With Fixed Regressors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1601-1614, December.
    11. Shurong Zheng & Dandan Jiang & Zhidong Bai & Xuming He, 2014. "Inference on multiple correlation coefficients with moderately high dimensional data," Biometrika, Biometrika Trust, vol. 101(3), pages 748-754.
    12. Chesher, Andrew, 1989. "Hajek Inequalities, Measures of Leverage and the Size of Heteroskedasticity Robust Wald Tests," Econometrica, Econometric Society, vol. 57(4), pages 971-977, July.
    13. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6a.
    14. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    16. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    17. Joshua Angrist & Jinyong Hahn, 2004. "When to Control for Covariates? Panel Asymptotics for Estimates of Treatment Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 58-72, February.
    18. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    19. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    20. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    21. Ulrich K. Müller, 2013. "Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix," Econometrica, Econometric Society, vol. 81(5), pages 1805-1849, September.
    22. Goncalves, Silvia & White, Halbert, 2005. "Bootstrap Standard Error Estimates for Linear Regression," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 970-979, September.
    23. Donald, S. G. & Newey, W. K., 1994. "Series Estimation of Semilinear Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 30-40, July.
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