Using causal diagrams to assess parallel trends in difference-in-differences studies
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利用因果图评估双重差分研究的平行趋势
- 研究问题
- 在开展双重差分研究前，能否借助因果图判断平行趋势是否合理，并处理该假设依赖结果尺度而图通常不依赖尺度的问题？
- 方法与思路
- 作者在非参数因果图下引入线性忠实性假设，分析处理前结果、未测混杂及前后结果关系对平行趋势的限制。
- 材料陈述的贡献
- 摘要称给出可排除或质疑平行趋势的图形条件，并在特定结构下刻画加法尺度上的充要条件，以医保扩张研究讨论应用。
- 阅读关注点
- 应核对线性忠实性的精确定义、最小充分调整集的作用，以及图形条件与加法尺度关联稳定性如何共同约束平行趋势。
- 阅读边界
- 这是预印本，同行评审及期刊接收未获核实；无法排除平行趋势不等于验证它，摘要也未给出条件的完整形式及证明。
原文摘要
Difference-in-differences (DID) is popular because it can allow for unmeasured confounding when the key assumption of parallel trends holds. However, there exists little guidance on how to decide a priori whether this assumption is reasonable. We attempt to develop such guidance by considering the relationship between a causal diagram and the parallel trends assumption. This is challenging because parallel trends is scale-dependent and causal diagrams are generally scale-independent. We develop conditions under which, given a nonparametric causal diagram, one can reject or fail to reject parallel trends. In particular, we adopt a linear faithfulness assumption, which states that all graphically connected variables are correlated, and which is often reasonable in practice. We show that parallel trends can be rejected if either (i) the treatment is affected by pre-treatment outcomes, or (ii) there exist unmeasured confounders for the effect of treatment on pre-treatment outcomes that are not confounders for the post-treatment outcome, or vice versa (more precisely, the two outcomes possess distinct minimally sufficient sets). We also argue that parallel trends should be strongly questioned if (iii) the pre-treatment outcomes affect the post-treatment outcomes (though the two can be correlated) since there exist reasonable semiparametric models in which such an effect violates parallel trends. When (i-iii) are absent, a necessary and sufficient condition for parallel trends is that the association between the common set of confounders and the potential outcomes is constant on an additive scale, pre- and post-treatment. These conditions are similar to, but more general than, those previously derived in linear structural equations models. We discuss our approach in the context of the effect of Medicaid expansion under the U.S. Affordable Care Act on health insurance coverage rates.