Bruce E. Hansen
Jackknife Standard Errors for Clustered Regression
December 2023
Abstract:
This paper presents a theoretical case for replacement of conventional
heteroskedasticity-consistent and cluster-robust variance estimators with
jackknife variance estimators, in the context of linear regression with
heteroskedastic and/or cluster-dependent observations. We examine the bias of
variance estimation and the coverage probabilities of confidence intervals.
Concerning bias, we show that conventional variance estimators have full
downward worst-case bias, while our jackknife variance estimator is never
downward biased. Concerning confidence intervals, we show that intervals based
on conventional standard errors have worst-case coverage equalling zero, while
our jackknife-based confidence interval has coverage probability bounded by
the Cauchy distribution. We also extend the Bell-McCaffrey (2002) student $t$
approximation to our jackknife $t$-ratio, resulting in confidence intervals
with improved coverage probabilities. Our theory holds under minimal
assumptions, allowing arbitrary cluster sizes, regressor leverage,
within-cluster correlation, heteroskedasticity, regression with a single
treated cluster, fixed effects, and delete-cluster invertibility failures. Our
theoretical findings are consistent with the extensive simulation literature
investigating heteroskedasticity-consistent and cluster-robust variance estimation.
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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111.
Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.