A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning

Pan Zhao () and Yifan Cui ()
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Pan Zhao: PREMEDICAL - Médecine de précision par intégration de données et inférence causale - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - IDESP - Institut Desbrest d'Epidémiologie et de Santé Publique - INSERM - Institut National de la Santé et de la Recherche Médicale - UM - Université de Montpellier
Yifan Cui: Zhejiang University [Hangzhou, China]

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Abstract: Recently, there has been a surge in methodological development for the difference-indifferences (DiD) approach to evaluate causal effects. Standard methods in the literature rely on the parallel trends assumption to identify the average treatment effect on the treated. However, the parallel trends 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 DiD approach for learning the optimal treatment policy. Specifically, we establish identification results using a binary instrumental variable (IV) when the parallel trends assumption fails to hold. Additionally, we construct a Wald estimator, novel inverse probability weighting (IPW) 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 parameters estimation. Furthermore, we extend the instrumented DiD to the panel data setting. We evaluate our methods in extensive simulations and a real data application.

Keywords: unmeasured confounding; individualized treatment rule; instrumental variable; multiple robustness; semiparametric efficiency (search for similar items in EconPapers)
Date: 2023-10-14
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