线性模型中识别信念的提取、验证和修正框架
A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models
摘要：
为了从观测数据中估计因果效应，应用研究者必须强加信念。例如，工具变量排除限制表示工具对感兴趣的结果没有直接影响的信念。然而，关于工具有效性的信念并不是孤立存在的。应用研究人员经常在他们的文章中讨论选择的可能方向和测量误差的可能性，但缺乏将这些信息纳入分析的正式工具。如果不利用所有相关信息，不仅会让钱留在桌面上，而且还可能导致一种矛盾，即人们对手头问题持有相互矛盾的信念。为了解决这些问题，我们首先在一个主力线性模型中描述了与工具无效性、治疗内分泌和非差分测量误差相关的联合限制，展示了这三个维度上的信念如何相互约束，并受到数据的约束。利用这些信息，我们提出了一个贝叶斯框架，以帮助研究人员引出他们的信念，将它们纳入估计，并确保它们的相互一致性。最后，我们通过从实证微观经济学文献中提取的一些例子来说明我们的框架。
英文摘要：
To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of interest. Yet beliefs about instrument validity do not exist in isolation. Applied researchers often discuss the likely direction of selection and the potential for measurement error in their articles but lack formal tools for incorporating this information into their analyses. Failing to use all relevant information not only leaves money on the table; it runs the risk of leading to a contradiction in which one holds mutually incompatible beliefs about the problem at hand. To address these issues, we first characterize the joint restrictions relating instrument invalidity, treatment endogeneity, and non-differential measurement error in a workhorse linear model, showing how beliefs over these three dimensions are mutually constrained by each other and the data. Using this information, we propose a Bayesian framework to help researchers elicit their beliefs, incorporate them into estimation, and ensure their mutual coherence. We conclude by illustrating our framework in a number of examples drawn from the empirical microeconomics literature.
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