Two-stage differences in differences

TL;DR

This paper introduces a two-stage estimation method for difference-in-differences analysis that addresses issues with treatment effect heterogeneity and staggered adoption, providing clearer identification of average treatment effects.

Contribution

It extends the difference-in-differences methodology by proposing a simple, robust two-stage framework that improves identification of treatment effects under heterogeneity and staggered adoption.

Findings

Two-stage approach effectively handles treatment heterogeneity.

Method is robust and easy to implement.

Demonstrated through Monte-Carlo simulations and empirical example.

Abstract

A recent literature has shown that when adoption of a treatment is staggered and average treatment effects vary across groups and over time, difference-in-differences regression does not identify an easily interpretable measure of the typical effect of the treatment. In this paper, I extend this literature in two ways. First, I provide some simple underlying intuition for why difference-in-differences regression does not identify a group$\times$period average treatment effect. Second, I propose an alternative two-stage estimation framework, motivated by this intuition. In this framework, group and period effects are identified in a first stage from the sample of untreated observations, and average treatment effects are identified in a second stage by comparing treated and untreated outcomes, after removing these group and period effects. The two-stage approach is robust to treatment-effect heterogeneity under staggered adoption, and can be used to identify a host of different average treatment effect measures. It is also simple, intuitive, and easy to implement. I establish the theoretical properties of the two-stage approach and demonstrate its effectiveness and applicability using Monte-Carlo evidence and an example from the literature.