揭示复杂网络动态系统中难以识别的本质，并提出可验证的条件与估计方法。
Identification and Inference in Nonlinear Dynamic Network Models
- 通过非线性算子建模未知网络中的冲击传播机制
- 当网络谱分布不均时可识别，集中则等价于共同冲击导致无法识别
- 适用于生产网络、传染模型等广泛经济系统，适合做结构推断的研究者
我们研究定义在未知交互网络上的非线性动态系统的可识别性与推断问题。系统演化由一个未观测的依赖矩阵驱动，通过非线性算子实现截面冲击传播。我们证明网络结构并非普遍可识别，其可识别性依赖于足够的谱异质性。特别地，当网络对特征模式的放大作用存在异质性时，会引发不可交换的协方差模式，从而实现识别；而当谱分布集中时，依赖关系在观测上等价于共同冲击或标量异质性，导致不可识别。本文给出了可识别性的充要条件，刻画了观测等价类，并提出具有渐近理论的半参数估计器。此外，我们还开发了基于交互矩阵谱特性的网络依赖检验方法，其功效取决于谱性质。这些结果适用于包括生产网络、传染模型和动态交互系统在内的广泛经济模型。
原文摘要 · Abstract (English)
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.
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