Difference-in-differences with variation in treatment timing

By Andrew Goodman-Bacon. Journal of Econometrics, 2018

6,271 citations recorded by the source corpus.

Abstract 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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0610a9dfc1fc1cfc1223c6550dfa029ad9b67f3c

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Citations in the corpus

Two-stage differences in differences (2022, positive): “…regression specification does not identify a readily interpretable measure of the typical effect of the treatment (see Borusyak and Jaravel, 2017; Athey and Imbens, 2018; Goodman-Bacon, 2018; de Chaisemartin and D’Haultfœuille, 2020; Imai and Kim, 2020; Sun and Abraham, 2020).”
Pre-Event Trends in the Panel Event-Study Design (2019, background): “A recent literature explores properties (and failures) of the two-way fixed effects estimator under heterogeneous causal effects (Abraham and Sun 2018; Athey and Imbens 2018; de Chaisemartin and D’Haultfoeuille 2018; Goodman-Bacon 2018).”
Contamination Bias in Linear Regressions (2021, neutral): “Furthermore, like in the previous case with 35This example is a special case of the example discussed in Figure 2 of Goodman-Bacon (2021). static treatment, the own-treatment weights in the first term are potentially negative.”
What’s trending in difference-in-differences? A synthesis of the recent econometrics literature (2022, positive): “Gardner (2021) shows that this approach estimates a convex weighted average of the ATT ( g , t ) under parallel trends and no anticipation, although the weights are determined by the number of treated units and variance of treatment within each stacked event, rather than by economic considerations.”
The Effects of Police Violence on Inner-City Students* (2020, background): “…about the possibility of negative weights in two-period DD estimators when treatment timing is staggered and there exists heterogeneity in treatment effects within-unit over time or between groups of units treated at different times (Goodman-Bacon 2018; de Chaisemartin and d’Haultfoeuille 2020).”
Generative AI at Work (2023, positive): “…assumptions about the homogeneity of treatment effects, and may be biased when treatment effects vary over time or by adoption cohort (Cengiz et al., 2019; de Chaisemartin and D’Haultfœuille, 2020; Sun and Abraham, 2021; Goodman-Bacon, 2021; Callaway and Sant’Anna, 2021; Borusyak et al., 2022).”
Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey (2021, methodology): “In the data of Stevenson and Wolfers (2006) used by Goodman-Bacon (2021) in his empirical application, if one restricts the sample to states that are not always treated and to the ﬁrst ten years of the panel, all the weights in (2.2) are positive, but the sum of the weights in (2.4) on DIDs…”
Can Technology Solve the Principal-Agent Problem? Evidence from China’s War on Air Pollution (2020, neutral): “More discussions can be found in de Chaisemartin and D’HaultfŒuille (2018, 2019); Goodman-Bacon (2018); Imai and Kim (2018). significant post-automation discontinuity of 3.0 ppb or 6.0% in NO2 concentrations and a statistically insignificant effect on reported SO2 concentrations.”
Selection into Identification in Fixed Effects Models, with Application to Head Start (2019, neutral): “See, for example, Goodman-Bacon(2018);BorusyakandJaravel(2017);CallawayandSant ’ Anna(2018);andChaisemartinand D ’ Haultfoeille (2019).”
Assessing the Effectiveness of Energy Efficiency Measures in the Residential Sector Gas Consumption Through Dynamic Treatment Effects: Evidence from England and Wales (2022, methodology): “With a staggered DiD approach we avoid the bias generated with an estimator that represents the weighted average of all possible two-group and two-period DiD in case the effect changes overtime (Goodman-Bacon, 2021).”
Early Evidence on Social Distancing in Response to COVID-19 in the United States (2020, background): “…indicating that estimates of equation (3) may be biased if there are time-varying treatment effects and that difference-in-differences estimates would, likewise, be biased (Goodman-Bacon, 2018; Callaway and Sant’Anna, 2019; Abraham and Sun, 2018; de Chaisemartin and D’Haultfœuille, forthcoming).”
Panel experiments and dynamic causal effects: A finite population perspective (2020, neutral): “Boryusak and Jaravel (2017), Athey and Imbens (2018), and Goodman-Bacon (2018) also provided a decomposition of the two-way fixed effects estimand in staggered designs.”