Semiparametric Difference-in-Differences Estimators
Causal Question / Estimand
The average treatment effect on the treated (ATT, Causal-Estimand) when the standard DiD parallel-trends assumption is implausible unconditionally because treated and control groups differ in covariates that drive outcome dynamics.
Identification Strategy
Relaxes unconditional Parallel-Trends to Conditional-Parallel-Trends: parallel paths hold only after conditioning on observed covariates . Identification then proceeds by reweighting — an inverse-propensity-score (IPW) two-step estimator that reweights the control group’s before/after change to match the treated group’s covariate distribution. Also lets the ATT vary with , describing effect heterogeneity across observed characteristics.
Key Assumptions
Conditional-Parallel-Trends (parallel trends given ), Overlap (propensity score bounded away from 0 and 1 so controls exist for every treated covariate profile), and SUTVA.
Threats to Validity
Misspecification or omission of the covariates that govern outcome dynamics (e.g. the Ashenfelter-Dip driven by transitory pre-treatment shocks); propensity scores near the boundary that break Overlap and inflate variance.
Setting / Data
n/a — methodological/econometric. Two-period treated-vs-control panel or repeated cross-section; illustrated with a JTPA training application.
Key Claims
- When covariates create non-parallel raw trends, conditioning restores identification — unconditional DiD is biased but conditional DiD is not.
- A simple propensity-score-weighted two-step estimator recovers the ATT semiparametrically, without a fully specified outcome model.
- The framework characterizes how the treatment effect varies with observed characteristics.
Connections
- Builds on: AshenfelterCard1985-LongitudinalEarnings (the dip motivates conditioning on pre-treatment dynamics)
- Extended by: SantAnnaZhao2020-DoublyRobustDiD (doubly robust combination of propensity-score and outcome-regression DiD)
- See also: CallawaySantAnna2021-DiDMultiplePeriods (uses conditional PT with multiple periods), DiD
Citation
Abadie, A. (2005). Semiparametric Difference-in-Differences Estimators. The Review of Economic Studies, 72(1), 1–19. https://doi.org/10.1111/0034-6527.00321