Treatment Effects in Staggered Adoption Designs with Non-Parallel Trends

TL;DR

This paper develops a method for estimating causal effects in staggered adoption studies with non-parallel trends, leveraging treatment timing variation without needing large time panels or extra restrictions.

Contribution

It introduces a novel approach that uses treatment timing variation to identify causal effects under non-parallel trends, applicable to interactive fixed effects models.

Findings

Method recovers a wide class of causal effects.

Does not require many time periods or exclusion restrictions.

Applicable to various non-parallel trend settings.

Abstract

This paper considers identifying and estimating causal effect parameters in a staggered treatment adoption setting -- that is, where a researcher has access to panel data and treatment timing varies across units. We consider the case where untreated potential outcomes may follow non-parallel trends over time across groups. This implies that the identifying assumptions of leading approaches such as difference-in-differences do not hold. We mainly focus on the case where untreated potential outcomes are generated by an interactive fixed effects model and show that variation in treatment timing provides additional moment conditions that can be used to recover a large class of target causal effect parameters. Our approach exploits the variation in treatment timing without requiring either (i) a large number of time periods or (ii) requiring any extra exclusion restrictions. This is in contrast to essentially all of the literature on interactive fixed effects models which requires at least one of these extra conditions. Rather, our approach directly applies in settings where there is variation in treatment timing. Although our main focus is on a model with interactive fixed effects, our idea of using variation in treatment timing to recover causal effect parameters is quite general and could be adapted to other settings with non-parallel trends across groups such as dynamic panel data models.