Asymptotic results under multiway clustering

If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with i.i.d. data, the weak convergence of empirical processes under multiway clustering. This result implies central limit theorems for sample averages but is also key for showing the asymptotic normality of nonlinear estimators such as GMM estimators. We then establish consistency of various asymptotic variance estimators, including that of Cameron et al. (2011) but also a new estimator that is positive by construction. Next, we show the general consistency, for linear and nonlinear estimators, of the pigeonhole bootstrap, a resampling scheme adapted to multiway clustering. Monte Carlo simulations suggest that inference based on our two preferred methods may be accurate even with very few clusters, and significantly improve upon inference based on Cameron et al. (2011).