  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).
