Clustered standard errors

Clustered standard errors (or Liang-Zeger standard errors)^[1] are measurements that estimate the standard error of a regression parameter in settings where observations may be subdivided into smaller-sized groups ("clusters") and where the sampling and/or treatment assignment is correlated within each group.^[2][3] Clustered standard errors are widely used in a variety of applied econometric settings, including difference-in-differences^[4] or experiments.^[5]

Analogous to how Huber-White standard errors are consistent in the presence of heteroscedasticity and Newey–West standard errors are consistent in the presence of accurately-modeled autocorrelation, clustered standard errors are consistent in the presence of cluster-based sampling or treatment assignment. Clustered standard errors are often justified by possible correlation in modeling residuals within each cluster; while recent work suggests that this is not the precise justification behind clustering,^[6] it may be pedagogically useful.