Clustered standard errors

Clustered standard errors (or Liang-Zeger standard errors) 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. Clustered standard errors are widely used in a variety of applied econometric settings, including difference-in-differences or experiments.

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, it may be pedagogically useful.