Two-way exclusion restrictions in models with heterogeneous treatment effects
提出一种新方法，在存在内生性、处理效应异质性且工具变量可能相关于潜在误差时，识别条件平均处理效应偏导数，并应用于中国教育回报率研究。
Summary In this paper, we propose a novel method to identify the conditional average treatment effect partial derivative (CATE-PD) in an environment in which the treatment is endogenous, the treatment effect is heterogeneous, the candidate 'instrumental variables' can be correlated with latent errors, and the treatment selection does not need to be (weakly) monotone. We show that CATE-PD is point-identified under mild conditions if two-way exclusion restrictions exist: (a) an outcome-exclusive variable, which affects the treatment but is excluded from the potential outcome equation, and (b) a treatment-exclusive variable, which affects the potential outcome but is excluded from the selection equation. We also propose an asymptotically normal two-step estimator and illustrate our method by investigating how the return to education varies across regions at different levels of development in China.