Difference-in-differences with variation in treatment timing

The canonical difference-in-differences (DD) estimator contains two time periods, ”pre” and ”post”, and two groups, ”treatment” and ”control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper shows that the two-way fixed ef...

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Bibliographic Details
Published in:Journal of econometrics Vol. 225; no. 2; pp. 254 - 277
Main Author: Goodman-Bacon, Andrew
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.12.2021
Elsevier Sequoia S.A
Subjects:
Asymptotic methods
Difference-in-differences
econometrics
Estimating techniques
Quantitative analysis
Statistical analysis
temporal variation
Time periods
Treatment effect heterogeneity
Two-way fixed effects
Variation in treatment timing
Difference-in-differences
Two-way fixed effects
Treatment effect heterogeneity
Variation in treatment timing
ISSN:0304-4076, 1872-6895
Online Access:Get full text
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Summary:The canonical difference-in-differences (DD) estimator contains two time periods, ”pre” and ”post”, and two groups, ”treatment” and ”control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper shows that the two-way fixed effects estimator equals a weighted average of all possible two-group/two-period DD estimators in the data. A causal interpretation of two-way fixed effects DD estimates requires both a parallel trends assumption and treatment effects that are constant over time. I show how to decompose the difference between two specifications, and provide a new analysis of models that include time-varying controls.
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ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2021.03.014