Identification and Inference in Nonlinear Dynamic Network Models
For econometricians and economists studying network effects in dynamic systems, this paper provides rigorous identification conditions and inference methods for nonlinear network models.
The paper studies identification and inference in nonlinear dynamic systems with unknown interaction networks, showing that network structure is not generically identified and requires sufficient spectral heterogeneity. It provides necessary and sufficient conditions for identification, proposes a semiparametric estimator with asymptotic theory, and develops tests for network dependence.
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.