Bias-Variance Tradeoff of Matching Prior to Difference-in-Differences When Parallel Trends is Violated
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平行趋势违反时双重差分前匹配的偏差—方差权衡
- 研究问题
- 当平行趋势受到未观测时变混杂影响时，双重差分前匹配协变量或处理前结果，会如何改变估计的偏差、方差与均方误差？
- 方法与思路
- 作者在线性结构模型下推广既有偏差分析，同时推导方差和均方误差性质，形成匹配变量选择建议，并重新分析平台激励的应用。
- 材料陈述的贡献
- 摘要称协变量匹配存在样本量权衡，未必优于未匹配估计；在其模型与已匹配的比较下，进一步匹配处理前结果被称为总是有益。
- 阅读关注点
- 应核对线性模型和混杂过程限制、匹配实施及样本量变化，以及追加结果匹配的比较基准和均方误差改善所需条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要中的总是有益具有模型和比较范围，不能据此推荐所有双重差分研究预先匹配。
原文摘要
Quasi-experimental causal inference methods have become central in empirical operations management 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 analyzes this practice, however, has focused solely on bias. In this work, we not only generalize earlier bias results under weaker assumptions but also analyze properties of variance and mean squared error (MSE), a practically relevant metric for decision making. 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 MSE as an additional metric if applied researchers weigh bias and variance equally and further give practitioner-friendly guidelines with theoretical guarantees on when and on what variables they should match. As an illustration, we apply these guidelines to re-examine a recent empirical study that matches prior to DiD to study how the introduction of monetary incentives by a knowledge-sharing platform affects general engagement on the platform. Our results show that the authors' decision was both warranted and critical to produce a credible causal estimate.