Estimating a Continuous Treatment Model with Spillovers: A Control Function Approach
研究了社会网络中连续处理效应存在溢出效应时的识别与估计问题，利用控制函数和工具变量非参数识别条件均值潜在结果，并开发了三步估计程序，以区域失业率对犯罪率的因果效应为例进行实证。
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.