  In empirical work it is common to estimate parameters of models and report
associated standard errors that account for "clustering" of units, where
clusters are defined by factors such as geography. Clustering adjustments are
typically motivated by the concern that unobserved components of outcomes for
units within clusters are correlated. However, this motivation does not provide
guidance about questions such as: (i) Why should we adjust standard errors for
clustering in some situations but not others? How can we justify the common
practice of clustering in observational studies but not randomized experiments,
or clustering by state but not by gender? (ii) Why is conventional clustering a
potentially conservative "all-or-nothing" adjustment, and are there alternative
methods that respond to data and are less conservative? (iii) In what settings
does the choice of whether and how to cluster make a difference? We address
these questions using a framework of sampling and design inference. We argue
that clustering can be needed to address sampling issues if sampling follows a
two stage process where in the first stage, a subset of clusters are sampled
from a population of clusters, and in the second stage, units are sampled from
the sampled clusters. Then, clustered standard errors account for the existence
of clusters in the population that we do not see in the sample. Clustering can
be needed to account for design issues if treatment assignment is correlated
with membership in a cluster. We propose new variance estimators to deal with
intermediate settings where conventional cluster standard errors are
unnecessarily conservative and robust standard errors are too small.
