This paper proposes a simple hierarchical model and a testing strategy to identify intra-cluster correlations, in the form of nested random effects and serially correlated error components. We focus on intra-cluster serial correlation at different nested levels, a topic that has not been studied in the literature before. A Neyman's C(α) framework is used to derive LM-type tests that allow researchers to identify the appropriate level of clustering as well as the type of intra-group correlation. An extensive Monte Carlo exercise shows that the proposed tests perform well in finite samples and under non-Gaussian distributions.Centro de Estudios Distributivos, Laborales y Sociales