Benefits and costs of matching prior to a Difference in Differences analysis when parallel trends does not hold
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平行趋势不成立时，双重差分分析前匹配的收益与成本
- 研究问题
- 当平行趋势不成立时，双重差分前匹配基线协变量或处理前结果，分别如何影响偏差，何时匹配收益可能超过成本？
- 方法与思路
- 作者在允许时不变混杂因素具有时变结果效应的线性结构模型中刻画匹配偏差，并用校长更替研究展示启发式判断规则。
- 材料陈述的贡献
- 摘要称，匹配基线协变量通常减少偏差；匹配处理前结果既能部分平衡潜在混杂，也会通过均值回归引入额外偏差。
- 阅读关注点
- 应核对线性结构模型的具体限制、结果可靠性的定义，以及匹配减少混杂与引入均值回归偏差的分解和适用条件。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未经核实；摘要未说明完整模型条件，应用中可信度提升也不能替代识别论证。
原文摘要
The Difference in Difference (DiD) estimator is a popular estimator built on the "parallel trends" assumption, which is an assertion that the treatment group, absent treatment, would change "similarly" to the control group over time. To bolster such a claim, one might generate a comparison group, via matching, that is similar to the treated group with respect to pre-treatment outcomes and/or pre-treatment covariates. Unfortunately, as has been previously pointed out, this intuitively appealing approach also has a cost in terms of bias. To assess the trade-offs of matching in our application, we first characterize the bias of matching prior to a DiD analysis under a linear structural model that allows for time-invariant observed and unobserved confounders with time-varying effects on the outcome. Given our framework, we verify that matching on baseline covariates generally reduces bias. We further show how additionally matching on pre-treatment outcomes has both cost and benefit. First, matching on pre-treatment outcomes partially balances unobserved confounders, which mitigates some bias. This reduction is proportional to the outcome's reliability, a measure of how coupled the outcomes are with the latent covariates. Offsetting these gains, matching also injects bias into the final estimate by undermining the second difference in the DiD via a regression-to-the-mean effect. Consequently, we provide heuristic guidelines for determining to what degree the bias reduction of matching is likely to outweigh the bias cost. We illustrate our guidelines by reanalyzing a principal turnover study that used matching prior to a DiD analysis and find that matching on both the pre-treatment outcomes and observed covariates makes the estimated treatment effect more credible.