🤖 AI Summary
This study addresses the challenge of structural unidentifiability and inference difficulty in nonlinear dynamic systems operating on unknown interaction networks. The authors propose an identification framework based on an implicit dependence matrix, establishing necessary and sufficient conditions for network identifiability by revealing its reliance on the spectral heterogeneity of the interaction matrix. The framework characterizes observational equivalence classes and overcomes the limitation of conventional approaches that erroneously conflate network dependencies with common shocks. Methodologically, it integrates semiparametric estimation, spectral analysis, and asymptotic theory to construct estimators with desirable asymptotic properties and develops a test for network dependence whose power is governed by spectral characteristics. The proposed framework demonstrates broad applicability across economic systems, including production networks and contagion models.
📝 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.