Triple Instrumented Difference-in-Differences

TL;DR

This paper introduces a formal framework for triple instrumented difference-in-differences (DID-IV), providing new estimands, assumptions, and methods for analyzing treatment effects with multiple instruments and staggered cases.

Contribution

It formalizes the triple DID-IV design, extends it to staggered instruments, and details practical estimation and inference methods.

Findings

Defines the triple Wald-DID estimand for local average treatment effects

Extends the design to staggered instrument cases

Provides practical estimation and inference procedures

Abstract

In this paper, we formalize a triple instrumented difference-in-differences (DID-IV). In this design, a triple Wald-DID estimand, which divides the difference-in-difference-in-differences (DDD) estimand of the outcome by the DDD estimand of the treatment, captures the local average treatment effect on the treated. The identifying assumptions mainly comprise a monotonicity assumption, and the common acceleration assumptions in the treatment and the outcome. We extend the canonical triple DID-IV design to staggered instrument cases. We also describe the estimation and inference in this design in practice.