Clustered Standard Errors

Clustered standard errors are robust standard errors that allow for arbitrary correlation of errors within a cluster (and independence across clusters). In panel data the cluster is typically the unit ($i$) — observations for the same state across years are correlated, so SEs must account for that. Without clustering, classical OLS SEs are typically far too small, t-stats are inflated, and inference over-rejects.

When to use

Cluster SEs at the level at which the treatment varies (or the most plausible level of correlation). PS_4 clusters at the state level — that's where seatbelt laws turn on and where serial correlation in fatalities lives. R: feols(y ~ x | state, cluster = ~state) (fixest) or coeftest(model, vcov = vcovCL(model, cluster = ~state)) (sandwich). Rule of thumb: you need at least ~30–50 clusters for the asymptotic approximation to work; with very few clusters, use wild-cluster bootstrap.