  We propose a bootstrap procedure for data that may exhibit clustering in two
or more dimensions. We use insights from the theory of generalized U-statistics
to analyze the large-sample properties of statistics that are sample averages
from the observations pooled across clusters. The asymptotic distribution of
these statistics may be non-standard if there is no clustering in means. We
show that the proposed bootstrap procedure is (a) point-wise consistent for any
fixed data-generating process (DGP), (b) uniformly consistent if we exclude the
case of clustering without clustering in means, and (c) provides refinements
for any DGP such that the limiting distribution is Gaussian.
