A semiparametric instrumented difference-in-differences approach to policy learning

SummaryRecently, there has been a surge in methodological development for the difference-in-differences approach to evaluate causal effects. Standard methods in the literature rely on the parallel-trend assumption to identify the average treatment effect on the treated. However, the parallel-trend assumption may be violated in the presence of unmeasured confounding, and the average treatment effect on the treated may not be useful in learning a treatment assignment policy for the entire population. In this article, we propose a general instrumented difference-in-differences approach for learning the optimal treatment policy. Specifically, we establish identification results using a binary instrumental variable when the parallel-trend assumption fails to hold. Additionally, we construct a Wald estimator, novel inverse probability weighting estimators and a class of semiparametric efficient and multiply robust estimators, with theoretical guarantees on consistency and asymptotic normality, even when relying on flexible machine learning algorithms for nuisance parameter estimation. Furthermore, we extend the instrumented difference in differences to the panel data setting. We evaluate our methods in extensive simulations and in an analysis of the Australian Longitudinal Survey.