Non-Identifiability in Network Autoregressions

We study identification in autoregressions defined on a general network. Most identification conditions that are available for these models either rely on repeated observations, are only sufficient, or require strong distributional assumptions. We derive conditions that apply even if only one observation of a network is available, are necessary and sufficient for identification, and require weak distributional assumptions. We find that the models are generically identified even without repeated observations, and analyze the combinations of the interaction matrix and the regressor matrix for which identification fails. This is done both in the original model and after certain transformations in the sample space, the latter case being important for some fixed effects specifications.