The Future Strikes Back. Using Future Treatments to Detect and Reduce Hidden Bias

Conventional advice discourages controlling for post-outcome variables in regression analysis. By contrast, we show that controlling for commonly available post-outcome (i.e. future) values of the treatment variable can help detect, reduce, and even remove omitted variable bias (unobserved confounding). The premise is that the same unobserved confounder that affects treatment also affects the future value of the treatment. Future treatments thus proxy for the unmeasured confounder, and researchers can exploit these proxy measures productively. We establish several new results: Regarding a commonly assumed data-generating process involving future treatments, we (1) introduce a simple new approach and show that it strictly reduces bias; (2) elaborate on existing approaches and show that they can increase bias; (3) assess the relative merits of alternative approaches; (4) analyze true state dependence and selection as key challenges. (5) Importantly, we also introduce a new non-parametric test that uses future treatments to detect hidden bias even when future-treatment estimation fails to reduce bias. We illustrate these results empirically with an analysis of the effect of parental income on children’s educational attainment.

传统观点对回归分析中控制结果变量持反对态度。然而，我们通过研究指出，控制治疗变量常见的后续（即未来）值可以帮助发现、减少甚至消除遗漏变量偏差（未观察到的混杂因素）。其核心假设是，影响治疗变量的同一未观察到的混杂因素也会影响治疗变量的未来值。因此，未来的治疗可以被视为未测量混杂因素的代理，研究者可以利用这些代理措施进行有效的分析。本研究取得了以下新的成果：针对涉及未来治疗的常见数据生成过程，我们（1）提出了一种简单的新方法，并证明其严格降低了偏差；（2）对现有方法进行了阐述，并指出它们可能会增加偏差；（3）评估了不同方法的相对优缺点；（4）分析了真实状态依赖性和选择作为关键挑战；（5）更重要的是，我们还引入了一种新的非参数检验方法，该方法利用未来治疗来检测隐藏的偏差，即使未来治疗的估计未能减少偏差。我们通过分析父母收入对子女教育成就的影响，从实证角度展示了这些成果。