摘要翻译：
当估计因果效应时，控制混杂因素是至关重要的，但这些特征可能没有被观察到。一种广泛采用的方法是使用代理变量来代替未观察到的理想控制。然而，这种方法普遍存在测量误差偏差。在本文中，我提出了一种新的识别策略来解决这个问题。我使用代理变量来构造一个随机变量，以治疗变量成为外生变量为条件。其关键思想是，在适当的条件下，未观察到的混杂因子的分布与代理的分布之间存在一一对应关系。为了满足重叠/支持条件，我使用了一个附加变量，称为排除变量，它满足某些排除限制和相关性条件。我还建立了平均结构函数的柔性参数和非参数估计的渐近分布结果。我通过估计天主教教育对大学入学的因果影响来证明我的结果的实证相关性。
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英文标题：
《Treatment Effect Estimation with Noisy Conditioning Variables》
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作者：
Kenichi Nagasawa
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最新提交年份：
2021
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  When estimating causal effects, controlling for confounding factors is crucial, but these characteristics may not be observed. A widely adopted approach is to use proxy variables in place of the unobserved ideal controls. However, this approach generally suffers from measurement error bias. In this paper, I develop a new identification strategy that addresses this issue. I use proxy variables to construct a random variable conditional on which treatment variables become exogenous. The key idea is that, under appropriate conditions, there exists a one-to-one mapping between the distribution of unobserved confounding factors and the distribution of proxies. To satisfy overlap/support conditions, I use an additional variable, termed excluded variable, which satisfies certain exclusion restrictions and relevance conditions. I also establish asymptotic distributional results for flexible parametric and nonparametric estimators of the average structural function. I demonstrate empirical relevance of my results by estimating causal effects of Catholic schooling on college enrollment.
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PDF链接：
https://arxiv.org/pdf/1811.00667