Difference-in-Differences with multiple time periods

By Brantly Callaway, Pedro H. C. Sant’Anna. Journal of Econometrics, 2018

6,124 citations recorded by the source corpus.

Difference-in-Differences (DID) is one of the most important and popular designs for evaluating causal effects of policy changes. In its standard format, there are two time periods and two groups: in the first period no one is treated, and in the second period a "treatment group" becomes treated, whereas a "control group" remains untreated. However, many em- pirical applications of the DID design have more than two periods and variation in treatment timing. In this article, we consider identification and estimation of treatment effect parameters using 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 prop- erties of the proposed estimators, and prove the validity of a computationally convenient bootstrap procedure. Furthermore we propose a semiparametric data-driven testing procedure to assess the credibility of the DID design in our context. Finally, we analyze the effect of the minimum wage on teen employment from 2001-2007. By using our proposed methods we confront the challenges related to variation in the timing of the state-level minimum wage policy changes. Open-source software is available for implementing the proposed methods.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c7ca83353b0269fc7d04fa06a28c7f323217758e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Statistics and Probability

Citations in the corpus

Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey (2021, methodology): “More generally, to estimate c’s effect at period c + `, Callaway and Sant’Anna (2020) propose to compare its c − 1 to c + ` outcome evolution to that of the never treated groups. Callaway and Sant’Anna (2020) also propose estimators of more aggregated treatment effects, such as the average effect of”
The Effects of Social Movements: Evidence from #MeToo (2020, positive): “A recent literature has shown that the two-way fixed effects estimator is not an unbiased estimator of the ATT when the intervention is staggered and treatment effects are heterogeneous or dynamic (Callaway and Sant’Anna, 2020; De Chaisemartin and d’Haultfoeuille, 2020). Therefore, in Column (1) of ”
Assessing the Effectiveness of Energy Efficiency Measures in the Residential Sector Gas Consumption Through Dynamic Treatment Effects: Evidence from England and Wales (2022, background): “…these quasi-experimental design as they assume that the treatment effect is constant, between groups and overtime (de Chaisemartin and D ’ Haultfoeuill, 2020; de Chaisemartin and d ’ Haultfoeuille, 2021; Callaway and Sant ’ Anna, 2021; Sun and Abraham, 2021; Roth et al., 2022; Goodman-Bacon, 2021).”
Efficient Estimation for Staggered Rollout Designs (2021, methodology): “Although Although we again ﬁnd no statistically signiﬁcant effects on complaints and borderline signiﬁcant effects on force, the standard errors from using our methodology are between 1.4 and 8.4 times smaller than those from the Callaway and Sant ’ Anna (2021) estimator used in Wood et al. (2020).”
Difference-in-Differences Estimators of Intertemporal Treatment Effects (2020, positive): “First, when the treatment is binary and the design is staggered, Callaway and Sant’Anna (2020) have proposed DID estimators of the instantaneous and dynamic treatment effects that use the not-yet-treated groups as controls. de Chaisemartin and D’Haultfœuille (2020a) have also proposed to use the not”
Generative AI at Work (2023, positive): “…produce these same patterns and magnitudes for the log of RPH. Appendix Table A.1 finds similar results using alternative difference-in-difference estimators in- troduced in Callaway and Sant’Anna (2021), Borusyak et al. (2022), de Chaisemartin and D’Haultfœuille (2020), and Sun and Abraham (2021).”
Synthetic controls with imperfect pretreatment fit (2016, background): “…estimate the effect of the treatment for unit 1 at a specific date t, this circumvents the problem of aggregating heterogeneous effects, as considered by de Chaisemartin and D’Haultfauille (2020), Callaway and Sant’Anna (2018), Athey and Imbens (2018), and Goodman-Bacon (2018) in the DID setting.”
Difference-in-Differences with a Continuous Treatment (2021, positive): “…and Callaway and Sant’Anna (2021), when AT T es loc ( e ) is the target parameter, one can binarize the treatment (i.e., classify units as being treated if they experience any positive amount of the treatment) and simply rely on the event-study procedures proposed by Callaway and Sant’Anna (2021).”
Synthetic Difference In Differences (2018, neutral): “Raw data rarely exhibit parallel time trends for treated and control units, and researchers use different techniques, such as adjusting for covariates or selecting appropriate time periods to address this problem ( e.g., Abadie 2005, Callaway and Sant’anna 2020 .”
Generative artificial intelligence, human creativity, and art (2024, methodology): “Using an event study difference-in-differences approach (8), we first estimate the causal impact of adopting generative AI on creative productivity, artwork value measured as favorites per view, and artifact novelty with respect to Content and Visual features.”