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

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.