Difference-in-Differences with Multiple Time Periods

TL;DR

This paper advances Difference-in-Differences methodology by addressing multiple periods, treatment timing variation, and covariate conditioning, providing new identification, estimation, and inference tools for complex causal analysis.

Contribution

It introduces novel identification strategies and estimators for staggered DiD setups with covariate conditioning, along with aggregation schemes and valid bootstrap inference methods.

Findings

Identification of causal effects with multiple periods and covariate conditioning.

Development of estimators with proven asymptotic properties.

Application to minimum wage impact on teen employment.

Abstract

In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create non-parallel outcome dynamics between groups. Our identification results allow one to use outcome regression, inverse probability weighting, or doubly-robust estimands. We also propose different aggregation schemes that can be used to highlight treatment effect heterogeneity across different dimensions as well as to summarize the overall effect of participating in the treatment. We establish the asymptotic properties of the proposed estimators and prove the validity of a computationally convenient bootstrap procedure to conduct asymptotically valid simultaneous (instead of pointwise) inference. Finally, we illustrate the relevance of our proposed tools by analyzing the effect of the minimum wage on teen employment from 2001--2007. Open-source software is available for implementing the proposed methods.