Jane Berkowitz Carlton and Dennis William Carlton Professor of Microeconomics; Chair, MIT Economics

Prof. Whitney Newey's CV

The linear regression model is widely used in empirical work. Researchers often include many covariates to control for observed and unobserved confounders. Often the number of covariates may be an important fraction of the sample size. We consider corresponding asymptotics where the number of covariates grows as fast as sample size. We show asymptotic normality and give consistent standard errors. With homoscedasticity we find that the usual standard errors with a degrees of freedom correction are correct. We also give new heteroskedasticity consistent standard errors, and show that the usual Eicker-White standard errors are inconsistent. These results add to regression theory where previous asymptotic normality results restricted the number of regressors to grow slower than the sample size.