标题： 偏差-方差权衡在平行趋势被违反时匹配先验的双重差分法 显示英文标题

标题： Bias-Variance Tradeoff of Matching Prior to Difference-in-Differences When Parallel Trends is Violated

摘要： 准实验因果推断方法在实证运营管理（OM）中变得至关重要，用于指导管理决策。 其中，实证研究者利用差异中的差异（DiD）估计量，该估计量依赖于平行趋势假设。 为了提高其合理性，研究人员通常在应用DiD之前匹配处理组和对照组，其直觉是，如果没有处理，匹配组更可能相似发展。 然而，现有分析这一做法的研究仅关注偏差。 我们通过分析完整的偏差-方差权衡来补充并填补一个重要空白。 在具有未观察到的时间变化混杂因素的线性结构模型下，我们表明方差结果与已建立的偏差见解相反：由于样本量权衡，在DiD之前对观察到的协变量进行匹配并不总是优于经典的（未匹配）DiD；此外，在事前结果上进行额外匹配总是有益的，因为一旦进行匹配，这种权衡就不存在了。 因此，我们提倡均方误差（MSE）作为最终指标，并提供具有理论保证的实践友好指南，说明何时（以及在哪些变量上）应进行匹配。 我们将这些见解应用于一项关于知识共享平台引入货币激励如何影响其总体参与度的最新研究，并表明作者在DiD之前的匹配选择是合理且关键的。 特别是，我们提供了新的管理见解，即在进行全面偏差校正后，他们的匹配估计效果仍然统计显著，这表明所选择的匹配-DiD方法足够稳健，可以解决对平行趋势假设违反的管理担忧。 显示英文摘要

摘要： Quasi-experimental causal inference methods have become central in empirical operations management (OM) for guiding managerial decisions. Among these, empiricists utilize the Difference-in-Differences (DiD) estimator, which relies on the parallel trends assumption. To improve its plausibility, researchers often match treated and control units before applying DiD, with the intuition that matched groups are more likely to evolve similarly absent treatment. Existing work that analyze this practice, however, has focused solely on bias. We complement and fill an important gap by analyzing the full bias-variance tradeoff. Under a linear structural model with unobserved time-varying confounders, we show that variance results contrast with established bias insights: matching on observed covariates prior to DiD is not always recommended over the classic (unmatched) DiD due to a sample size tradeoff; furthermore, matching additionally on pre-treatment outcomes is always beneficial as such tradeoff no longer exists once matching is performed. We therefore advocate mean squared error (MSE) as a final metric and give practitioner-friendly guidelines with theoretical guarantees on when (and on what variables) they should match on. We apply these insights to a recent study on how the introduction of monetary incentives by a knowledge-sharing platform affects its general engagement and show that the authors' matching choice prior to DiD was both warranted and critical. In particular, we provide new managerial insights that after a full bias correction, their estimated effect with matching still remains statistically significant, demonstrating that the chosen matching-DiD approach is sufficiently robust to address managerial concerns over violations of parallel trends.