Robust Inference With Multiway Clustering

TLDR

The variance estimator extends the standard cluster‑robust sandwich estimator for one‑way clustering and relies on similarly weak distributional assumptions. The article proposes a variance estimator for OLS and nonlinear estimators such as logit, probit, and GMM. The estimator enables cluster‑robust inference under nonnested two‑way or multiway clustering and is easily implemented in software such as Stata and SAS. Its performance is illustrated by Monte Carlo studies of a two‑way random‑effects model and a placebo law extending the state‑year effects example, as well as by empirical applications involving two‑way clustering.

Abstract

In this article we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit, and GMM. This variance estimator enables cluster-robust inference when there is two-way or multiway clustering that is nonnested. The variance estimator extends the standard cluster-robust variance estimator 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 offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state–year effects example of Bertrand, Duflo, and Mullainathan (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present.