In this paper, we investigate a treatment effect model in which individuals interact in a social network and they may not comply with the assigned treatments. We introduce a new concept of exposure mapping, which summarizes spillover effects into a fixed dimensional statistic of instrumental variables, and we call this mapping the instrumental exposure mapping (IEM). We investigate identification conditions for the intention-to-treat effect and the average causal effect for compliers, while explicitly considering the possibility of misspecification of IEM. Based on our identification results, we develop nonparametric estimation procedures for the treatment parameters. Their asymptotic properties, including consistency and asymptotic normality, are investigated using an approximate neighborhood interference framework by Leung (2021). For an empirical illustration of our proposed method, we revisit Paluck et al.'s (2016) experimental data on the anti-conflict intervention school program.

翻译：在本文中,我们调查了个人在社会网络中互动的治疗效果模型,他们可能不符合指定的治疗方法。我们引入了接触量绘图的新概念,将外溢效应汇总到工具变量的固定维度统计中,我们称这一绘图为工具性接触量绘图(IEM ) 。我们调查了意图-治疗效应和遵守者平均因果效应的识别条件,同时明确考虑IEM被误判的可能性。我们根据我们的鉴定结果,为治疗参数制定了非参数估计程序。他们缺乏症状的特性,包括一致性和无症状正常性,正在使用Leung (2021年) 的近似邻干扰框架进行调查。为了从经验上说明我们建议的方法,我们重新审视了Paluck等人(Paluck等人)(2016年)关于反冲突干预学校方案的实验数据。