Identification and Inference in Nonlinear Dynamic Network Models

TL;DR

This paper investigates the conditions under which nonlinear dynamic network models can be identified and inferred, emphasizing the importance of spectral heterogeneity for successful identification.

Contribution

It provides necessary and sufficient conditions for identification, characterizes observational equivalence, and proposes a semiparametric estimator with asymptotic properties.

Findings

Network structure is not generically identified without spectral heterogeneity.

Identification depends on the network inducing non-exchangeable covariance patterns.

Spectral properties of the interaction matrix influence the power of tests for network dependence.

Abstract

We study identification and inference in nonlinear dynamic systems defined on unknown interaction networks. The system evolves through an unobserved dependence matrix governing cross-sectional shock propagation via a nonlinear operator. We show that the network structure is not generically identified, and that identification requires sufficient spectral heterogeneity. In particular, identification arises when the network induces non-exchangeable covariance patterns through heterogeneous amplification of eigenmodes. When the spectrum is concentrated, dependence becomes observationally equivalent to common shocks or scalar heterogeneity, leading to non-identification. We provide necessary and sufficient conditions for identification, characterize observational equivalence classes, and propose a semiparametric estimator with asymptotic theory. We also develop tests for network dependence whose power depends on spectral properties of the interaction matrix. The results apply to a broad class of economic models, including production networks, contagion models, and dynamic interaction systems.