The Essential Role of Pair Matching in Cluster-Randomized Experiments, with Application to the Mexican Universal Health Insurance Evaluation

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; 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.

💡 Research Summary

The paper addresses a fundamental problem in many field experiments: researchers often can only randomize clusters (e.g., schools, villages, clinics) even though the unit of interest is the individual. Randomizing at the cluster level reduces statistical efficiency because intra‑cluster correlation inflates variance. A common remedy is to pair similar clusters and randomize treatment within each pair, thereby regaining much of the lost precision. Despite this intuitive appeal, a substantial portion of the literature and several clinical‑trial guidelines claim that matched‑pair cluster randomization is problematic—citing analytical complexity, biased estimators, and invalid standard errors.

The authors first demonstrate that these criticisms are unfounded. They show that the estimator most frequently recommended for matched‑pair designs—essentially the average of within‑pair differences weighted by cluster size—is unbiased only when matching is unnecessary (i.e., when all clusters are exchangeable). In any realistic setting where matching is used to reduce heterogeneity, that estimator is biased and its variance estimator is inconsistent, leading to confidence intervals that are too narrow.

To resolve this, the authors develop a design‑based estimator that directly averages the raw difference between the treated and control cluster means within each pair:

\