Instrumented difference-in-differences

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.

Automated summary

This article introduces a causal inference method based on observational studies, which estimates treatment effects by leveraging exogenous randomness in the exposure trend. A new method called instrumented difference-in-differences is proposed, along with corresponding estimators, and their properties are analyzed. The method is also extended to a two-sample design.