We show that temporal, spatial, and dyadic dependencies among observations complicate the estimation of covariance structures in panel databases. Ignoring these dependencies results in covariance estimates that are often too small and inferences that may be more confident about empirical patterns than is justified by the data. In this article, we detail the development of a nonparametric approach, window subseries empirical variance estimators (WSEV), that can more fully capture the impact of these dependencies on the covariance structure. We illustrate this approach in a simulation as well as with a statistical model of international conflict similar to many applications in the international relations literature.
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