Difference-in-Differences with Multiple Time Periods

45 Pages Posted: 24 Mar 2018 Last revised: 18 Aug 2020

See all articles by Brantly Callaway

Brantly Callaway

University of Mississippi - Department of Economics

Pedro H. C. Sant'Anna

Vanderbilt University - College of Arts and Science - Department of Economics

Date Written: March 1, 2019

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.

Keywords: Difference-in-Differences, Event Study, Multiple Periods, Variation in Treatment Timing, Pre-Testing, Minimum Wage

JEL Classification: C14, C21, C23, J23, J38

Suggested Citation

Callaway, Brantly and Sant'Anna, Pedro H. C., Difference-in-Differences with Multiple Time Periods (March 1, 2019). Available at SSRN: https://ssrn.com/abstract=3148250 or http://dx.doi.org/10.2139/ssrn.3148250

Brantly Callaway

University of Mississippi - Department of Economics ( email )

371 Holman Hall
University, MS 38677
United States

Pedro H. C. Sant'Anna (Contact Author)

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

HOME PAGE: http://https://sites.google.com/site/pedrohcsantanna/

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