Instrumented Difference-in-Differences

TL;DR

This paper introduces instrumented difference-in-differences, a novel method combining instrumental variables and difference-in-differences to estimate causal effects amid unmeasured confounding, with robust estimators and extensions for two-sample designs.

Contribution

It develops a new identification framework and estimators for causal inference using exogenous variation in exposure trends, extending to two-sample settings.

Findings

Proposed Wald and semiparametric estimators with proven consistency.

Extended method to two-sample design for delayed effects.

Validated approach with simulations and real data.

Abstract

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.