We study identifiability of the parameters in autoregressions defined on a network. Most identification conditions that are available for these models either rely on the network being observed repeatedly, are only sufficient, or require strong distributional assumptions. This paper derives conditions that apply even when the individuals composing the network are observed only once, are necessary and sufficient for identification, and require weak distributional assumptions. We find that the model parameters are generically, in the measure theoretic sense, identified even without repeated observations, and analyze the combinations of the interaction matrix and the regressor matrix causing identification failures. This is done both in the original model and after certain transformations in the sample space, the latter case being relevant, for example, in some fixed effects specifications.
翻译:我们研究了在网络上定义的自动递减参数的可识别性,这些模型现有的大多数识别条件要么依靠反复观测的网络,要么是足够的,要么需要强有力的分布假设,本文提出的条件即使只观察一次网络成员,对于识别来说是必要和充分的,也需要薄弱的分布假设。我们发现,模型参数是通用的,在测量理论意义上,即使没有反复观测,也发现,并分析互动矩阵和递减矩阵的组合导致识别失败,这在最初的模型中以及在样本空间的某些变异之后都是这样做的,例如,在某些固定效果规格中,后一种情况是相关的。