Two-way fixed effects instrumental variable regressions in staggered DID-IV designs

TL;DR

This paper analyzes the properties of two-way fixed effects instrumental variable regressions in staggered DID-IV designs, revealing their decomposition into weighted averages of simpler estimators and discussing conditions for causal interpretation.

Contribution

It provides a decomposition of the TWFEIV estimator in staggered DID-IV settings and discusses conditions for causal interpretation, which was not previously well-understood.

Findings

TWFEIV estimator decomposes into weighted averages of Wald-DID estimators

Causal interpretation requires stable effects of the instrument over time

Empirical application illustrates the decomposition theorem

Abstract

Many studies run two-way fixed effects instrumental variable (TWFEIV) regressions, leveraging variation in the timing of policy adoption across units as an instrument for treatment. This paper studies the properties of the TWFEIV estimator in staggered instrumented difference-in-differences (DID-IV) designs. We show that in settings with the staggered adoption of the instrument across units, the TWFEIV estimator can be decomposed into a weighted average of all possible two-group/two-period Wald-DID estimators. Under staggered DID-IV designs, a causal interpretation of the TWFEIV estimand hinges on the stable effects of the instrument on the treatment and the outcome over time. We illustrate the use of our decomposition theorem for the TWFEIV estimator through an empirical application.