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Title: Cluster-robust standard errors for linear regression models with many controls Authors:  Riccardo D Adamo - University College London (United Kingdom) [presenting]
Abstract: 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. 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 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 us 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.