The linear regression model is widely used in empirical economics to estimate the structural/ treatment effect of some variable on an outcome of interest. Researchers  often include a large set of regressors in  order to control for observed and unobserved confounders. In this paper , we develop inference methods for linear regression models with many controls and clustering. We show that inference based on the usual cluster-robust standard errors by White (1984 ) is invalid in general when the number of controls is a non-vanishing fraction of the sample size. We then propose a new clustered standard errors formula that is robust to the inclusion of many controls and allows to carry out valid inference in a variety of high-dimensional linear regression models, including multi-way fixed effects panel data models and the semiparametric partially linear model. Monte Carlo evidence supports our theoretical results and shows that our proposed variance estimator performs well in finite samples.
It is common practice in empirical work to employ cluster-robust standard errors when using the linear regression model to estimate some structural/ causal effect of interest. Researchers also often include a large set of regressors in their model specification in order to control for observed and unobserved confounders. In this paper we develop inference methods for linear regression models with many controls and clustering. We show that inference based on the usual cluster-robust standard errors by Liang and Zeger (1986 ) is invalid in general when the number of controls is a non-vanishing fraction of the sample size. We then propose a new clustered standard errors formula that is robust to the inclusion of many controls and allows to carry out valid inference in a variety of high-dimensional linear regression models, including fixed effects panel data models and the semiparametric partially linear model. Monte Carlo evidence supports our theoretical results and shows that our proposed variance estimator performs well in finite samples.
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The linear regression model is widely used in empirical economics to estimate the
It is common practice in empirical work to employ cluster-robust standard errors when using the linear regression model to estimate some
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treatment effect of some variable on an outcome of
causal effect of
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also
A
their model specification in
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,
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White (1984
Liang and Zeger (1986
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multi-way