  This paper studies inference in cluster randomized trials where treatment
status is determined according to a "matched pairs" design. Here, by a cluster
randomized experiment, we mean one in which treatment is assigned at the level
of the cluster; by a "matched pairs" design, we mean that a sample of clusters
is paired according to baseline, cluster-level covariates and, within each
pair, one cluster is selected at random for treatment. We study the
large-sample behavior of a weighted difference-in-means estimator and derive
two distinct sets of results depending on if the matching procedure does or
does not match on cluster size. We then propose a single variance estimator
which is consistent in either regime. Combining these results establishes the
asymptotic exactness of tests based on these estimators. Next, we consider the
properties of two common testing procedures based on t-tests constructed from
linear regressions, and argue that both are generally conservative in our
framework. We additionally study the behavior of a randomization test which
permutes the treatment status for clusters within pairs, and establish its
finite-sample and asymptotic validity for testing specific null hypotheses.
Finally, we propose a covariate-adjusted estimator which adjusts for additional
baseline covariates not used for treatment assignment, and establish conditions
under which such an estimator leads to strict improvements in precision. A
simulation study confirms the practical relevance of our theoretical results.
