When do linear regressions estimate causal effects in quasi-experiments? This paper provides a generic diagnostic that assesses whether a given linear regression specification on a given dataset admits a design-based interpretation. To do so, we define a notion of potential weights, which encode counterfactual decisions a given regression makes to unobserved potential outcomes. If the specification does admit such an interpretation, this diagnostic can find a vector of unit-level treatment assignment probabilities -- which we call an implicit design -- under which the regression estimates a causal effect. This diagnostic also finds the implicit causal effect estimand. Knowing the implicit design and estimand adds transparency, leads to further sanity checks, and opens the door to design-based statistical inference. When applied to regression specifications studied in the causal inference literature, our framework recovers and extends existing theoretical results. When applied to widely-used specifications not covered by existing causal inference literature, our framework generates new theoretical insights.

翻译：准实验中，线性回归何时能估计因果效应？本文提出一种通用诊断方法，用于评估给定数据集上的特定线性回归设定是否允许基于设计的解释。为此，我们定义了潜在权重的概念，其编码了给定回归对未观测潜在结果做出的反事实决策。若该设定确实允许此类解释，本诊断方法可找到一组单元水平处理分配概率向量——我们称之为隐含设计——在此设计下回归可估计因果效应。该诊断方法还能确定隐含的因果效应估计量。了解隐含设计与估计量可增强透明度，支持进一步的合理性检验，并为基于设计的统计推断开辟道路。将本框架应用于因果推断文献中研究的回归设定时，我们恢复并扩展了现有理论结果。将其应用于现有因果推断文献未涵盖的常用设定时，本框架产生了新的理论见解。