Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption

By Susan Athey, Guido W. Imbens. 2018

783 citations recorded by the source corpus.

In this paper we study estimation of and inference for average treatment effects in a setting with panel data. We focus on the setting where units, e.g., individuals, firms, or states, adopt the policy or treatment of interest at a particular point in time, and then remain exposed to this treatment at all times afterwards. We take a design perspective where we investigate the properties of estimators and procedures given assumptions on the assignment process. We show that under random assignment of the adoption date the standard Difference-In-Differences estimator is is an unbiased estimator of a particular weighted average causal effect. We characterize the proeperties of this estimand, and show that the standard variance estimator is conservative.

How researchers see this paper

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

Citations in the corpus

Learning When-to-Treat Policies (2019, background): “We can 3See also Athey and Imbens (2018) for a closely related discussion of potential outcomes in the context of staggered adoption.”
Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference (2019, unknown): “(14)See (Athey et al., 2018; Athey and Imbens, 2018) (15)t and s can be the same.”
Pre-Event Trends in the Panel Event-Study Design (2019, unknown): “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).”
Revisiting event study designs: robust and efficient estimation (2021, methodology): “For the overall ATT, the imputation estimator is also a matrix-completion estimator without a factor model or regularization in the class considered by Athey et al. (2021). Compared with these studies, we derive the imputation estimator as the most efficient one for a class of problems and a general”
Two-stage differences in differences (2022, unknown): “…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).”
Difference-in-Differences Estimators of Intertemporal Treatment Effects (2020, unknown): “To do so, a commonly-used method, first proposed by Autor (2003), is to regress the outcome on group fixed effects, time fixed effects, the value of the treatment in group g and period t, and lags of the treatment in group g.”
How Much Should We Trust Staggered Difference-In-Differences Estimates? (2021, background): “…treatment effect on the treated (ATT)—even under random assignment of treatment (e.g., Sun and Abraham, 2020; Borusyak and Jaravel, 2017; Callaway and Sant’Anna, 2020; Goodman-Bacon, 2019; Imai and Kim, 2020; Strezhnev, 2018; Athey and Imbens, 2018; de Chaisemartin and D’Haultfœuille, 2020).”
Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey (2021, background): “This excludes papers that have assumed randomized treatment timing (see, e.g., Athey and Imbens, 2022; Roth and Sant’Anna, 2021) or sequential treatment randomization (see, e.g., Bojinov et al., 2021), rather than parallel trends.”
On the Use of Two-Way Fixed Effects Regression Models for Causal Inference with Panel Data (2020, background): “In addition, a number of scholars have recently considered causal interpretations of the standard 2FE estimator (see, e.g., Borusyak and Jaravel 2017; Abraham and Sun 2018; Athey and Imbens 2018; Chaisemartin and D’Haultfœuille 2018; Goodman-Bacon 2018).”
Synthetic Difference In Differences (2018, unknown): “Another important special case is that of staggered adoption ( e.g.,Athey and Imbens 2021 with multiple dates at which the treatment is started.”
Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects (2018, unknown): “More recently, Borusyak and Jaravel ( 2017 ) , Abraham and Sun ( 2018 ) , Athey and Imbens ( 2018 ) , Callaway and Sant’Anna ( 2018 ) , and Goodman-Bacon ( 2018 ) study the special case of staggered adoption designs, where the treatment of a group is weakly increasing over time.”
Contamination Bias in Linear Regressions (2021, unknown): “In their Comment 2, Athey and Imbens (2022) say that “the sum of the weights [used in Theorem 1(iv)] is one, although some of the weights may be negative.””
Panel experiments and dynamic causal effects: A finite population perspective (2020, background): “Similarly, Athey and Imbens (2018), Athey et al. (2018) and Arkhangelsky and Imbens (2019) also introduce a potential outcome model for panel data, but assume away carryover effects.”
A Practical Guide to Counterfactual Estimators for Causal Inference with Time-Series Cross-Sectional Data (2020, methodology): “Below is an illustration adapted from Athey et al. (2018), in which hard compute (left) selects two factors: Hard Impute (“best subset”/IFEct) Soft Impute  σ1 0 0 · · · 0 0 σ2 0 · · · 0 0 0 0 .”