This paper introduces a method which permits valid inference given a finite number of heterogeneous, correlated clusters. Many inference methods assume clusters are asymptotically independent or model dependence across clusters as a function of a distance metric. With panel data, these restrictions are unnecessary. This paper relies on a test statistic using the mean of the cluster-specific scores normalized by the variance and simulating the distribution of this statistic. To account for cross-cluster dependence, the relationship between each cluster is estimated, permitting the independent component of each cluster to be isolated. The method is simple to implement, can be employed for linear and nonlinear estimators, places no restrictions on the strength of the correlations across clusters, and does not require prior knowledge of which clusters are correlated or even the existence of independent clusters. In simulations, the procedure rejects at the appropriate rate even in the presence of highly-correlated clusters.
Powell, David, Inference with Correlated Clusters. Santa Monica, CA: RAND Corporation, 2017. https://www.rand.org/pubs/working_papers/WR1137-1.html.
Powell, David, Inference with Correlated Clusters, Santa Monica, Calif.: RAND Corporation, WR-1137-1, 2017. As of November 16, 2021: https://www.rand.org/pubs/working_papers/WR1137-1.html