# Identification and Inference in Nonlinear Dynamic Network Models

arXiv: https://arxiv.org/abs/2604.04961 · HTML: https://mlsanity.com/paper/2604.04961/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 28 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 1 of 1)

- [An Overview on the Estimation of Large Covariance and Precision Matrices](https://mlsanity.com/paper/1504.02995/) (2015)

## Built on by (most cited first, 1 of 1)

- [Sandpile Economics: Theory, Identification, and Evidence](https://mlsanity.com/paper/2604.13890/) (2026)

## Abstract (arXiv)

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.