Heterogeneity and dynamics in network models

We propose an empirical spatial modeling framework that allows for both heterogeneity and dynamics in economic network connections. We establish the model's stationarity and ergodicity properties and show that the model's implied filter is invertible. While highly flexible, the model is straightforward to estimate by maximum likelihood. We apply the model to three datasets for Eurozone sovereign credit risk over the period Dec-2009 to Dec-2022. Accounting for both heterogeneity and time-variation turns out to be empirically important both in-sample and out-of-sample. The new model uncovers intuitive patterns that would go unnoticed in either homogeneous and/or static spatial financial network models.