Nonparametric bounds on treatment effects with imperfect instruments
将Nevo和Rosen(2012)的识别结果扩展到非参数模型，推导了当存在不完美工具变量时平均处理效应的非参数界，并利用单调处理选择和单调工具变量约束来收紧界，最后用青年男性全国纵向调查数据估计教育回报。
Summary This paper extends the identification results in Nevo and Rosen (2012) to nonparametric models. We derive nonparametric bounds on the average treatment effect when an imperfect instrument is available. As in Nevo and Rosen (2012), we assume that the correlation between the imperfect instrument and the unobserved latent variables has the same sign as the correlation between the endogenous variable and the latent variables. We show that the monotone treatment selection and monotone instrumental variable restrictions, introduced by Manski and Pepper (2000; 2009), jointly imply this assumption. Moreover, we show how the monotone treatment response assumption can help tighten the bounds. The identified set can be written in the form of intersection bounds, which is more conducive to inference. We illustrate our methodology using the National Longitudinal Survey of Young Men data to estimate returns to schooling.