Non-Identifiability in Network Autoregressions

TL;DR

This paper establishes necessary and sufficient conditions for the identifiability of parameters in network autoregressions, even with single observations per individual, broadening understanding of when these models can be reliably estimated.

Contribution

It derives the first comprehensive set of conditions that ensure identifiability in network autoregressions with minimal assumptions and single observations.

Findings

Parameters are generically identifiable without repeated observations.

Identification failures are characterized by specific matrix configurations.

Conditions hold for models with transformations like fixed effects.

Abstract

We study identifiability of the parameters in autoregressions defined on a network. Most identification conditions that are available for these models either rely on the network being observed repeatedly, are only sufficient, or require strong distributional assumptions. This paper derives conditions that apply even when the individuals composing the network are observed only once, are necessary and sufficient for identification, and require weak distributional assumptions. We find that the model parameters are generically, in the measure theoretic sense, identified even without repeated observations, and analyze the combinations of the interaction matrix and the regressor matrix causing identification failures. This is done both in the original model and after certain transformations in the sample space, the latter case being relevant, for example, in some fixed effects specifications.