Robust Inference with Multi-way Clustering

In this paper we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit and GMM. This variance estimator en- ables cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance es- timator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already o¤er cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random ef- fects model; a Monte Carlo analysis of a placebo law that extends the state-year e¤ects example of Bertrand et al. (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present.