Working Paper: NBER ID: w25018
Authors: Andrew Goodman-Bacon
Abstract: The canonical difference-in-differences (DD) model 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 derives an expression for this general DD estimator, and shows that it is a weighted average of all possible two-group/two-period DD estimators in the data. This result provides detailed guidance about how to use regression DD in practice. I define the DD estimand and show how it averages treatment effect heterogeneity and that it is biased when effects change over time. I propose a new balance test derived from a unified definition of common trends. I show how to decompose the difference between two specifications, and I apply it to models that drop untreated units, weight, disaggregate time fixed effects, control for unit-specific time trends, or exploit a third difference.
Keywords: Difference-in-Differences; Treatment Timing; Causal Inference
JEL Codes: C1; C23
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| treatment timing (C41) | average treatment effect on the treated (ATT) (C22) |
| treatment effects vary over time (C22) | DiD estimator bias (C51) |
| timing of treatment (C41) | average treatment effect derived from DiD model (C22) |
| timing of treatment (C41) | decomposed average treatment effect (C22) |
| balance test (C52) | significant differences in covariates (C52) |