Matching estimators of causal effects in clustered observational studies

Abstract Marine conservation preserves fish biodiversity, protects marine and coastal ecosystems, and supports climate resilience and adaptation. Despite the importance of establishing marine protected areas (MPAs), research on the effectiveness of MPAs with different conservation policies is limited due to the lack of quantitative MPA information. In this article, by leveraging a global MPA database, we investigate the causal impact of MPA policies on fish biodiversity. To address challenges posed by this clustered and confounded observational study, we construct a bias-corrected matching estimator of the average treatment effect assuming treatment is assigned at the cluster level and a cluster-weighted bootstrap method for variance estimation. We establish the theoretical guarantees of the matching estimator and its variance estimator. Under our proposed matching framework, we recommend matching on both cluster-level and unit-level covariates to achieve efficiency. The simulation study results demonstrate that our matching strategy minimizes the bias and achieves the nominal confidence interval coverage. Applying our proposed matching method to compare different MPA policies reveals that the no-take policy is more effective than the multi-use policy in preserving fish biodiversity.