▋Econometrics Journal (2020),
volume 23,pp. 345–362.
First version received: 14 May 2019;
final version accepted: 16 July 2019.
Two-way exclusion restrictions in models with heterogeneous treatment effects
SHENGLONG LIU*, ISMAEL MOURIFI´E† AND YUANYUAN WAN‡
* School of Public Policy and Management, Tsinghua University, 30 Shuangqing Rd, Haidian District, Beijing, China. Email: liushenglong@mail.tsinghua.edu.cn
† Department of Economics, University of Toronto, 150 St. George Street, Toronto ON M5S 3G7,Canada.Email: ismael.mourifie@utoronto.ca
‡ Department of Economics, University of Toronto, 150 St. George Street, Toronto ON M5S 3G7,
Canada. Email: yuanyuan.wan@utoronto.ca
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.
Keywords: Two-way exclusion, nonparametric identification, heterogeneous treatment effect, invalid instrumental variables.
双排除性约束变量在抑制性处理效应模型中的应用
SHENGLONG LIU, ISMAEL MOURIFI´E AND YUANYUAN WAN
在本文中，我们提出了一种新的方法来识别在处理变量内生，且处理效应是异质性的环境下条件平均处理效应的偏导数（CATE_PD）。
在该方法中，我们候选的 "工具变量 "可以与潜在误差项相关，也就是说工具变量可以是弱内生的，处理选择不需要满足严格的单调性假设。这就使得我们的工具变量的选择可以不用像传统的IV估计中那么严格。
CATE-PD估计需要找到两类排除性约束变量，分别是(a) 结果方程排除性约束变量，影响是否接受处理但不包含在结果方程中；(b)处理方程排除性约束变量，影响潜在的结果，但不包括在选择方程中。
我们在理论上证明通过这种方法可以在工具变量不那么“有效”的条件下对CATE_PD进行识别。
我们还提出了渐进正态两步法估计，并运用该方法对中国不同地区教育的异质性回报进行了估计。
研究结果表明：
教育回报在更加贫困或者更加富裕的地方是更高的，在中等发展地区回报率最低。意味着教育发展可以促使低收入地区向中等收入地区收敛，但是无法促使中等收入地区向高收入地区收敛。
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