We study a continuous treatment effect model in the presence of treatment spillovers through social networks. We assume that one's outcome is affected not only by his/her own treatment but also by a (weighted) average of his/her neighbors' treatments, both of which are treated as endogenous variables. Using a control function approach with appropriate instrumental variables, we show that the conditional mean potential outcome can be nonparametrically identified. We also consider a more empirically tractable semiparametric model and develop a three-step estimation procedure for this model. As an empirical illustration, we investigate the causal effect of the regional unemployment rate on the crime rate.

翻译：在通过社会网络产生治疗外溢的情况下,我们研究一种持续治疗效应模式,我们假定,一个人的结果不仅受到他/她自己的治疗的影响,而且受到他/她邻居治疗的(加权)平均数的影响,两者都被视为内生变量。我们采用控制功能方法,加上适当的工具变量,表明有条件的潜在潜在潜在潜在结果可以非对等地确定。我们还考虑一种更具有经验性的半对称模式,并为这一模式制定三步估计程序。作为经验说明,我们调查区域失业率对犯罪率的因果关系。