Design-Based Analysis in Difference-in-Differences Settings with Staggered Adoption
Causal Question / Estimand
Average treatment effects in panel data with staggered adoption — units adopt an absorbing treatment at different (possibly never) dates. The estimand is a particular weighted average of unit-time causal effects (Causal-Estimand), defined and analyzed from the assignment side rather than via a regression model.
Identification Strategy
A design-based (randomization-inference) perspective: instead of assuming a sampling model and Parallel-Trends, treat the adoption dates as random and derive properties of estimators from the assignment process. Under random assignment of the adoption date, the standard DiD estimator is shown to be unbiased for a specific weighted-average causal effect, and the usual variance estimator is conservative. Characterizes exact finite-sample properties.
Key Assumptions
Random assignment of adoption dates (Randomization over treatment timing), an absorbing/staggered treatment path, No-Anticipation (no effect before adoption), and SUTVA. The design view substitutes randomized timing for the model-based parallel-trends assumption.
Threats to Validity
If adoption dates are not as-good-as-randomly assigned (e.g. units adopt in response to expected outcomes), the design-based unbiasedness fails. The weighted-average estimand may not equal the policy-relevant average if effects are heterogeneous across timing groups (Treatment-Effect-Heterogeneity).
Setting / Data
n/a — econometric methodology for panel data with staggered adoption (firms, states, individuals adopting a policy at different times).
Key Claims
- A design-based foundation for staggered DiD: with randomized adoption timing the standard estimator is unbiased for a clearly defined weighted-average effect.
- The conventional variance estimator is conservative under this design.
- Bridges the sampling-based and randomization-based justifications for DiD, complementing the model-based heterogeneity-robust literature.
Connections
- Companion perspective to: GoodmanBacon2021-DiDVariationInTiming, CallawaySantAnna2021-DiDMultiplePeriods (model-based staggered DiD)
- By the same authors: AtheyImbens2006-NonlinearDiD
- See also: DiD
Citation
Athey, S., & Imbens, G. W. (2022). Design-Based Analysis in Difference-in-Differences Settings with Staggered Adoption. Journal of Econometrics, 226(1), 62–79. https://doi.org/10.1016/j.jeconom.2020.10.012