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，借助经典的相关性与外生性（无混淆性与排他性）假设识别因果效应。由于外生性难以论证且在一定程度上不可检验，其在应用分析中常引发质疑。为缓解此问题，我们提出一种新颖的识别方法，将传统工具变量外生性放松为在部分未观测共同混杂因素条件下的条件外生性。我们假设存在与这些未观测共同混杂因素相关的若干代理变量。与典型代理变量不同，我们的代理变量可对内生回归变量与结果变量产生直接影响。我们分别在线性可分离扰动项的结果模型以及第一阶段严格单调性条件下，提供了点识别结果。继而推导出广义双重稳健性与奈曼正交矩，使低维参数能够在高维 nuisance 参数（其本身由弗雷德霍姆积分方程非唯一确定）存在下实现直接根号 n 一致性估计。应用此新方法于 NLS97 数据，我们在教育经济回报问题中分离了能力偏差与一般性选择偏差。