Under what circumstances is it a threat to the parallel trends assumption required for Difference in Differences (DiD) studies if treatment decisions are based on past values of the outcome? We explore via simulation studies whether parallel trends holds across a grid of data generating processes generally conducive to parallel trends (random walk, Hidden Markov Model, and constant direct additive confounding), study designs (never treated, not yet treated, or later treated control groups), and outcome responsiveness of treatment (yes or no). We interpret the upshot of our simulation results to be that parallel trends is typically not a credible assumption when treatments are influenced by past outcomes. This is due to a combination of regression to the mean and selection on future treatment values, depending on the control group. Since timing of treatment initiation is frequently influenced by past outcomes when the treatment is targeted at the outcome, perhaps DiD is generally better suited for studying unintended consequences of interventions?

翻译：在何种情况下,如果治疗决定是以过去的结果值为依据,则对差异(DID)研究所需的平行趋势假设构成威胁?我们通过模拟研究探讨平行趋势是否存在于一个数据生成过程网中,这些过程一般有利于平行趋势(随机行走、隐藏的Markov模型和持续的直接添加性混乱)、研究设计(从未治疗过、尚未治疗过或后来治疗过的控制组)和治疗结果反应(是或否)。 我们解释模拟结果的结果是,当治疗受到过去的结果影响时,平行趋势通常不是一个可信的假设。 这是由于根据控制组的情况,逐渐回归到平均值和选择未来治疗值。 由于治疗开始的时间经常受到以往结果的影响,也许Di通常更适合研究干预的意外后果?