Identification of average effects under magnitude and sign restrictions on confounding
混杂效应幅度与符号限制下的平均效应识别AI 解读 ↓
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混杂效应幅度与符号限制下的平均效应识别
- 研究问题
- 当解释变量和潜在工具变量均可能受到不可观测混杂影响，且代理变量并不完美时，如何利用混杂效应的幅度和符号限制识别平均效应？
- 方法与思路
- 作者刻画一般结构系统中回归与工具变量估计对象的遗漏变量偏差，再限制混杂对结果和代理变量的平均作用之比或对比关系。
- 材料陈述的贡献
- 摘要称，框架推广经典遗漏变量偏差公式，在基准情形下给出点识别，并以更弱的混杂幅度或符号限制实现部分识别与敏感性分析。
- 阅读关注点
- 应核对各类平均效应的定义、混杂效应对比限制的经济含义，以及代理变量不完美时识别区间、估计和推断的具体构造。
- 阅读边界
- 仅依据所给 Crossref 摘要版本；摘要未完整说明结构条件、限制强度或收入应用结果，允许内生性不意味着无需约束即可识别效应。
原文摘要
This paper studies measuring various average effects of X on Y in general structural systems with unobserved confounders U , a potential instrument Z , and a proxy W for U . We do not require X or Z to be exogenous given the covariates or W to be a perfect one‐to‐one mapping of U . We study the identification of coefficients in linear structures as well as covariate‐conditioned average nonparametric discrete and marginal effects (e.g., average treatment effect on the treated), and local and marginal treatment effects. First, we characterize the bias, due to the omitted variables U , of (nonparametric) regression and instrumental variables estimands, thereby generalizing the classic linear regression omitted variable bias formula. We then study the identification of the average effects of X on Y when U may statistically depend on X and Z . These average effects are point identified if the average direct effect of U on Y is zero, in which case exogeneity holds, or if W is a perfect proxy, in which case the ratio (contrast) of the average direct effect of U on Y to the average effect of U on W is also identified. More generally, restricting how the average direct effect of U on Y compares in magnitude and/or sign to the average effect of U on W can partially identify the average effects of X on Y . These restrictions on confounding are weaker than requiring benchmark assumptions, such as exogeneity or a perfect proxy, and enable a sensitivity analysis. After discussing estimation and inference, we apply this framework to study earnings equations.