Simple Formulas for Standard Errors that Cluster by Both Firm and Time

by Samuel B. Thompson of the Arrowstreet Capital L.P.

May 12, 2009

Abstract: When estimating finance panel regressions, it is common practice to adjust standard errors for correlation either across firms or across time. These procedures are valid only if the residuals are correlated either across time or across firms, but not across both. This note shows that it is very easy to calculate standard errors that are robust to simultaneous correlation along two dimensions, such as firms and time. The covariance estimator is equal to the estimator that clusters by firm, plus the the estimator that clusters by time, minus the usual heteroskedasticity-robust OLS covariance matrix. Any statistical package with a clustering command can be used to easily calculate these standard errors.

JEL Classification: C23, G12, G32.

Keywords: Cluster standard errors, Panel data, Finance panel data

Published in: Journal of Financial Economics, Vol. 99, No. 1, (January 2011), pp. 1-10.

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