In estimating the effects of a treatment/policy with a network, an unit is subject to two types of treatment: one is the direct treatment on the unit itself, and the other is the indirect treatment (i.e., network/spillover influence) through the treated units among the friends/neighbors of the unit. In the literature, linear models are widely used where either the number of the treated neighbors or the proportion of them among the neighbors represents the intensity of the indirect treatment. In this paper, we obtain a nonparametric network-based "causal reduced form (CRF)" that allows any outcome variable (binary, count, continuous, ...) and any effect heterogeneity. Then we assess those popular linear models through the lens of the CRF. This reveals what kind of restrictive assumptions are embedded in those models, and how the restrictions can result in biases. With the CRF, we conduct almost model-free estimation and inference for network effects.

翻译：在估计具有网络结构的处理/政策效应时，个体受到两种处理类型的影响：一是施加于个体自身的直接处理，二是通过个体朋友/邻居中受处理单元产生的间接处理（即网络/溢出效应）。现有文献广泛采用线性模型，其中通常使用受处理邻居的数量或其占邻居总数的比例来表示间接处理的强度。本文提出了一种基于网络的非参数"因果简化形式"，该形式允许任意结果变量（二元、计数、连续等）与任意效应异质性存在。随后通过该因果简化形式的视角评估了常用的线性模型，揭示了这些模型所隐含的限制性假设，以及这些限制如何导致估计偏差。基于因果简化形式，我们实现了近乎无模型约束的网络效应估计与统计推断。