Title: When Should You Adjust Standard Errors for Clustering?,
Abstract: In empirical work in economics it is common to report standard errors that
account for clustering of units. Typically, the motivation given for the
clustering adjustments is that unobserved components in outcomes for units
within clusters are correlated. However, because correlation may occur across
more than one dimension, this motivation makes it difficult to justify why
researchers use clustering in some dimensions, such as geographic, but not
others, such as age cohorts or gender. It also makes it difficult to explain
why one should not cluster with data from a randomized experiment. In this
paper, we argue that clustering is in essence a design problem, either a
sampling design or an experimental design issue. It is a sampling design issue
if sampling follows a two stage process where in the first stage, a subset of
clusters were sampled randomly from a population of clusters, while in the
second stage, units were sampled randomly from the sampled clusters. In this
case the clustering adjustment is justified by the fact that there are clusters
in the population that we do not see in the sample. Clustering is an
experimental design issue if the assignment is correlated within the clusters.
We take the view that this second perspective best fits the typical setting in
economics where clustering adjustments are used. This perspective allows us to
shed new light on three questions: (i) when should one adjust the standard
errors for clustering, (ii) when is the conventional adjustment for clustering
appropriate, and (iii) when does the conventional adjustment of the standard
errors matter.