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Difference-in-Differences with Multiple Time Periods

Brantly Callaway, Pedro H. C. Sant'Anna

arXiv 23 Mar 2018 · Econometrics · publishedJournal of Econometrics (2020) · 1,413 citations (OpenAlex)

arXiv:1803.09015 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

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appendix boundary found by appendix_titled_section at “Appendix A: Proofs of Main Results\label{App.A}” · 75% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Sun \ Abraham (2020) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects1.000133100%
2de Chaisemartin \ D'Haultfuille (2020) Two-way fixed effects estimators with heterogeneous treatment effects1.000114100%
3Athey \ Imbens (2018) Design-based analysis in difference-in-differences settings with staggered adoption1.00083100%
4Goodman-Bacon (2019) Difference-in-differences with variation in treatment timing1.00063100%
5Heckman, Ichimura \ Todd (1997) Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme0.9619389%
6Abadie (2005) Semiparametric difference-in-difference estimators0.92810480%
7Borusyak \ Jaravel (2017) Revisiting event study designs0.92843100%
8Sant’Anna \ Zhao (2020) Doubly robust difference-in-differences estimators0.91613577%
9Heckman, Ichimura, Smith \ Todd (1998) Characterizing selection bias using experimental data0.87472100%
10Dube, Lester \ Reich (2010) Minimum wage effects across state borders: Estimates using contiguous counties0.87462100%

Showing the top 10 of 79 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey1.000363
2What's Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature1.000214
3Machine Learning for Staggered Difference-in-Differences and Dynamic Treatment Effect Heterogeneity1.000195
4Difference-in-Differences Designs: A Practitioner's Guide1.000193
5Instrumented Difference-in-Differences with Heterogeneous Treatment Effects1.000174
6Improved Inference for CSDID Using the Cluster Jackknife1.000178
7Good Controls Gone Bad: Difference-in-Differences with Covariates1.000157
8When Can We Use Two-Way Fixed-Effects (TWFE): A Comparison of TWFE and Novel Dynamic Difference-in-Differences Estimators1.000145
9Difference-in-Differences when Parallel Trends Holds Conditional on Covariates1.000145
10Refining the Notion of No Anticipation in Difference-in-Differences Studies1.000143