Unmeasured confounding is a key threat to reliable causal inference based on observational studies. Motivated from two powerful natural experiment devices, the instrumental variables and difference-in-differences, we propose a new method called instrumented difference-in-differences that explicitly leverages exogenous randomness in an exposure trend to estimate the average and conditional average treatment effect in the presence of unmeasured confounding. We develop the identification assumptions using the potential outcomes framework. We propose a Wald estimator and a class of multiply robust and efficient semiparametric estimators, with provable consistency and asymptotic normality. In addition, we extend the instrumented difference-in-differences to a two-sample design to facilitate investigations of delayed treatment effect and provide a measure of weak identification. We demonstrate our results in simulated and real datasets.

翻译：根据观察研究,我们从两个强大的自然实验装置 -- -- 工具变量和差异 -- -- 出发,提出了一种名为 " 工具差异 " 的新方法,在暴露趋势中明确利用外源随机性,以估计在未计量差异情况下的平均和有条件平均治疗效果。我们利用潜在结果框架来制定识别假设。我们提议一个Wald 估量器和一组多功能、强健、高效的半参数估量器,具有可变一致性和无药可治的正常性。此外,我们将仪器差异扩大到两个样本设计,以便于调查延迟治疗效应并提供薄弱的识别度。我们在模拟和真实数据集中展示我们的结果。