有序结果的差异中的差异：应用于大规模枪击对枪支管制态度的影响
Difference-in-Differences for Ordinal Outcomes: Application to the Effect of Mass Shootings on Attitudes toward Gun Control
摘要：
差异中差异（DID）设计广泛用于观察性研究，以在可获得随时间推移的重复观察时估计治疗的因果效应。然而，几乎所有现有的方法都假设潜在结果呈线性（平行趋势假设），并以累加效应为目标。然而，在社会科学研究中，许多感兴趣的结果都是在有序尺度上测量的。这使得线性假设不合适，因为两个有序潜在结果之间的差异没有很好地定义。在本文中，我提出了一种在DID设计下对有序结果进行因果推断的方法。与现有方法不同，该方法利用潜在变量框架来处理结果的非数值性质，从而能够基于对潜在连续变量分位数的假设来识别和估计因果效应。本文还提出了一种基于等效性的检验，以评估额外的预治疗期时关键识别假设的可行性。所提出的方法被应用到一项研究估计的因果关系影响的大规模枪击事件对公众的支持枪支管制。我发现很少有证据表明，在以前的研究中发现，统一转向亲枪支管制政策，但发现效果集中在左倾受访者谁经历了十多年来第一次射击。
英文摘要：
The difference-in-differences (DID) design is widely used in observational studies to estimate the causal effect of a treatment when repeated observations over time are available. Yet, almost all existing methods assume linearity in the potential outcome (parallel trends assumption) and target the additive effect. In social science research, however, many outcomes of interest are measured on an ordinal scale. This makes the linearity assumption inappropriate because the difference between two ordinal potential outcomes is not well defined. In this paper, I propose a method to draw causal inferences for ordinal outcomes under the DID design. Unlike existing methods, the proposed method utilizes the latent variable framework to handle the non-numeric nature of the outcome, enabling identification and estimation of causal effects based on the assumption on the quantile of the latent continuous variable. The paper also proposes an equivalence-based test to assess the plausibility of the key identification assumption when additional pre-treatment periods are available. The proposed method is applied to a study estimating the causal effect of mass shootings on the public's support for gun control. I find little evidence for a uniform shift toward pro-gun control policies as found in the previous study, but find that the effect is concentrated on left-leaning respondents who experienced the shooting for the first time in more than a decade.
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