Instruments can be used to identify causal effects in the presence of unobserved confounding, under the famous relevance and exogeneity (unconfoundedness and exclusion) assumptions. As exogeneity is difficult to justify and to some degree untestable, it often invites criticism in applications. Hoping to alleviate this problem, we propose a novel identification approach, which relaxes traditional IV exogeneity to exogeneity conditional on some unobserved common confounders. We assume there exist some relevant proxies for the unobserved common confounders. Unlike typical proxies, our proxies can have a direct effect on the endogenous regressor and the outcome. We provide point identification results with a linearly separable outcome model in the disturbance, and alternatively with strict monotonicity in the first stage. General doubly robust and Neyman orthogonal moments are derived consecutively to enable the straightforward root-n estimation of low-dimensional parameters despite the high-dimensionality of nuisances, themselves non-uniquely defined by Fredholm integral equations. Using this novel method with NLS97 data, we separate ability bias from general selection bias in the economic returns to education problem.

翻译：工具变量可在存在未观测混杂因素的情况下，通过著名的相关性与外生性（无混淆性与排他性）假设来识别因果效应。由于外生性难以论证且在一定程度上不可检验，这在应用研究中常引发质疑。为缓解这一问题，我们提出了一种新的识别方法，将传统工具变量的外生性条件放宽为在部分未观测共同混淆变量下的条件外生性。我们假设存在与未观测共同混淆变量相关的代理变量。与传统代理变量不同，我们的代理变量可直接作用于内生回归变量与结果变量。在扰动项线性可分的结局模型设定下，或通过第一阶段严格单调性假设，我们给出了点识别结果。进一步推导了广义双稳健估计量与内曼正交矩，使得即使存在由弗雷德霍姆积分方程非唯一确定的高维 nuisance 参数，也能实现低维参数的根号 n 一致估计。利用美国国家纵向调查97数据，我们运用该方法在教育的经济回报问题中分离了能力偏差与一般性选择偏差。