Instrumented Difference-in-Differences with Heterogeneous Treatment Effects

TL;DR

This paper develops an instrumented difference-in-differences (DID-IV) framework to identify local average treatment effects with heterogeneous effects, extending to multiple periods and providing robust estimation methods, demonstrated through schooling returns in the UK.

Contribution

It formalizes the DID-IV identification strategy, extends it to multiple periods with staggered adoption, and proposes a robust estimation method for heterogeneous treatment effects.

Findings

The conventional two-way fixed effects IV regression yields a negative estimate of schooling returns.

The proposed method indicates a substantial positive gain from schooling.

Application demonstrates the importance of robust methods in policy evaluation.

Abstract

Many studies exploit variation in the timing of policy adoption across units as an instrument for treatment. This paper formalizes the underlying identification strategy as an instrumented difference-in-differences (DID-IV). In this design, a Wald-DID estimand, which scales the DID estimand of the outcome by the DID estimand of the treatment, captures the local average treatment effect on the treated (LATET). We extend the canonical DID-IV design to multiple period settings with the staggered adoption of the instrument across units. Moreover, we propose a credible estimation method in this design that is robust to treatment effect heterogeneity. We illustrate the empirical relevance of our findings, estimating returns to schooling in the United Kingdom. In this application, the two-way fixed effects instrumental variable regression, the conventional approach to implement DID-IV designs, yields a negative estimate. By contrast, our estimation method indicates a substantial gain from schooling.