Identification of Treatment Effects under Limited Exogenous Variation
有限外生变异下处理效应的识别AI 解读 ↓
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有限外生变异下处理效应的识别
- 研究问题
- 存在多维异质性与内生性、且外生变异有限时，能否放宽非参数识别所需的支持条件，仍识别平均处理效应？
- 方法与思路
- 作者将结果的条件期望写成变系数形式，让已知处理函数或控制变量函数与未知系数组合，并分析条件二阶矩矩阵。
- 材料陈述的贡献
- 摘要称给出平均处理效应识别的必要与充分条件，说明不同变系数设定下离散工具变量的识别能力，并连接半参数与非参数框架。
- 阅读关注点
- 应核对控制变量的有效性、已知函数的选择和条件非奇异性，并区分两类变系数设定对离散工具支持点的要求。
- 阅读边界
- 所给版本为 arXiv 预印本，不能据此认定已同行评审或被期刊接收；摘要未列完整条件，识别结论依赖具体模型设定。
原文摘要
Multidimensional heterogeneity and endogeneity are important features of a wide class of econometric models. With control variables to correct for endogeneity, nonparametric identification of treatment effects requires strong support conditions. To alleviate this requirement, we consider varying coefficients specifications for the conditional expectation function of the outcome given a treatment and control variables. This function is expressed as a linear combination of either known functions of the treatment, with unknown coefficients varying with the controls, or known functions of the controls, with unknown coefficients varying with the treatment. We use this modeling approach to give necessary and sufficient conditions for identification of average treatment effects. A sufficient condition for identification is conditional nonsingularity, that the second moment matrix of the known functions given the variable in the varying coefficients is nonsingular with probability one. For known treatment functions with sufficient variation, we find that triangular models with discrete instrument cannot identify average treatment effects when the number of support points for the instrument is less than the number of coefficients. For known functions of the controls, we find that average treatment effects can be identified in general nonseparable triangular models with binary or discrete instruments. We extend our analysis to flexible models of increasing dimension and relate conditional nonsingularity to the full support condition of Imbens and Newey (2009), thereby embedding semi- and non-parametric identification into a common framework.