Difference-in-Differences with Multiple Time Periods
37 Pages Posted: 24 Mar 2018 Last revised: 25 Nov 2019
Date Written: March 1, 2019
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 propose a simple two-step estimation strategy, 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. We also propose a semiparametric data-driven testing procedure to assess the credibility of the DID design in our context. 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.
Keywords: Difference-in-Differences, Event Study, Multiple Periods, Variation in Treatment Timing, Pre-Testing, Minimum Wage
JEL Classification: C14, C21, C23, J23, J38
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