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It is common practice in empirical work to employ cluster-robust standarderrors when using the linear regression model to estimate somestructural/causal effect of interest. Researchers also often include a largeset of regressors in their model specification in order to control for observedand unobserved confounders. In this paper we develop inference methods forlinear regression models with many controls and clustering. We show thatinference 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-vanishingfraction of the sample size. We then propose a new clustered standard errorsformula that is robust to the inclusion of many controls and allows to carryout valid inference in a variety of high-dimensional linear regression models,including fixed effects panel data models and the semiparametric partiallylinear model. Monte Carlo evidence supports our theoretical results and showsthat our proposed variance estimator performs well in finite samples. Theproposed method is also illustrated with an empirical application thatre-visits Donohue III and Levitt's (2001) study of the impact of abortion oncrime.

Cluster-Robust Standard Errors for Linear Regression Models with Many Controls