  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.
