A basic feature of many field experiments is that investigators are
only able to randomize clusters of individuals - such as
households, communities, firms, medical practices, schools, or
classrooms - even when the individual is the unit of interest. To
recoup the resulting efficiency loss, some studies pair similar
clusters and randomize treatment within pairs. However, many other
studies avoid pairing, in part because of claims in the literature,
echoed by clinical trials standards organizations, that this
matched-pair, cluster-randomization design has serious problems.
We argue that all such claims are unfounded. We also prove that the
estimator recommended for this design in the literature is unbiased
only in situations when matching is unnecessary; and its standard
error is also invalid. To overcome this problem without modeling
assumptions, we develop a simple design-based estimator with much
improved statistical properties. We also propose a model-based
approach that includes some of the benefits of our design-based
estimator as well as the estimator in the literature. Our methods
also address individual-level noncompliance, which is common in
applications but not allowed for in most existing methods. We show
that from the perspective of bias, efficiency, power, robustness, or
research costs, and in large or small samples, pairing should be
used in cluster-randomized experiments whenever feasible; failing to
do so is equivalent to discarding a considerable fraction of one's
data. We develop these techniques in the context of a randomized
evaluation we are conducting of the Mexican Universal Health
Insurance Program.
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