[2604.04961] Identification and Inference in Nonlinear Dynamic Network Models

Statistics > Machine Learning arXiv:2604.04961 (stat) [Submitted on 3 Apr 2026] Title:Identification and Inference in Nonlinear Dynamic Network Models Authors:Diego Vallarino View a PDF of the paper titled Identification and Inference in Nonlinear Dynamic Network Models, by Diego Vallarino View PDF HTML (experimental) 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. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG);...