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Treatment Effects with Many Covariates and Heteroskedasticity

Author

Listed:
  • Matias D. Cattaneo

    (University of Michigan)

  • Michael Jansson

    (UC Berkeley and CREATES)

  • Whitney K. Newey

    (MIT)

Abstract

The linear regression model is widely used in empirical work in Economics. 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 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: (i) parametric linear models with many covariates, (ii) semiparametric semi-linear models with many technical regressors, and (iii) linear panel models with many fixed effects.

Suggested Citation

  • Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2015. "Treatment Effects with Many Covariates and Heteroskedasticity," CREATES Research Papers 2015-31, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2015-31
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    File URL: https://repec.econ.au.dk/repec/creates/rp/15/rp15_31.pdf
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    References listed on IDEAS

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    1. James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
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    Cited by:

    1. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    2. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.

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    More about this item

    Keywords

    high-dimensional models; linear regression; many regressors; heteroskedasticity; standard errors.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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