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

TL;DR

This paper introduces a semiparametric instrumented difference-in-differences method for policy learning that addresses unmeasured confounding and relaxes the parallel trends assumption, providing robust estimators with theoretical guarantees.

Contribution

It develops a novel instrumented DiD framework with identification, estimation, and inference methods that work under violations of parallel trends, extending to panel data and incorporating machine learning.

Findings

The proposed estimators are consistent and asymptotically normal.

Simulation studies demonstrate the effectiveness of the methods.

Application to real data shows practical utility.

Abstract

Recently, there has been a surge in methodological development for the difference-in-differences (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.