Jackknife Standard Errors for Clustered Regression

Hansen (2025) makes a theoretical case for replacing the conventional cluster-robust variance estimator (CRVE) and heteroskedasticity-consistent (HC) standard errors with a specific jackknife variance estimator, V5, in linear regression with heteroskedastic and/or cluster-dependent observations.

The paper identifies two fundamental problems with conventional CRVE1 and CRVE2 estimators. First, these estimators can be fully downward biased: Theorem 2 establishes that the infimum of E[v̂1²]/v² and E[v̂2²]/v² over all admissible regressor and covariance matrix configurations equals zero, meaning expected variance can be arbitrarily close to zero relative to the true variance. This pathology arises from extreme regressor leverage — specifically when one cluster dominates the sample — and holds even under homoskedasticity and clusterwise invertibility. Second, Theorem 5 shows that confidence intervals constructed from CRVE1 and CRVE2 standard errors have worst-case coverage probability equal to zero for any finite critical value c, making them unable to achieve any target coverage level uniformly over regression designs.

Bruce E Hansen | Macro Paper Warehouse

Jackknife Standard Errors for Clustered Regression