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A Meta-learner for Heterogeneous Effects in Difference-in-Differences
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Proposes a doubly robust meta-learner (DR-learner-style, convex loss) for the conditional average treatment effect on the treated under conditional parallel trends in DiD, extended to conditional functionals under covariate shift and IV-DiD with non-compliance.
Problem
Estimating heterogeneous treatment effects on the treated (CATT) in panel data under conditional parallel trends, when conditioning on a subset of covariates X that is smaller than the set W needed for the parallel trends assumption; naive CATE learners are biased in this setting.
Approach
A Neyman-orthogonal, doubly robust moment for the CATT that avoids estimating the treated-group outcome regression, turned into a convex squared loss over the treated units so any ML regressor can be used; extended to conditional linear functionals under covariate shift and to IV-DiD (CLATE).
Key results
- On fully synthetic DiD data with XGBoost nuisances, the DR CATT learner reaches MSE 0.04 ± 0.01 versus 0.09 ± 0.02 for the OR learner (linear/lasso/ridge nuisances).
- On imbalanced synthetic data, XGBoost DR-CATT attains MSE 0.12 ± 0.03 versus 0.21 ± 0.06 for XGBoost OR and 0.15 ± 0.05 for XGBoost CATE DR.
- On semi-synthetic minimum wage data, XGBoost DR-CATT achieves MSE 1.8 ± 0.09 (best) vs 2.07 ± 0.09 for OR and about 2.66-2.73 for CATE learners; calibration shows significant heterogeneity by county population.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the DR learner instead of the OR learner | XGBoost CATT learner · Synthetic DiD | MSE: 0.09 ± 0.02 -> 0.04 ± 0.01 | Helped |
| Use the DR learner instead of the OR learner | Neural Net CATT learner · Synthetic DiD | MSE: 0.12 ± 0.02 -> 0.1 ± 0.02 | Helped |
| Use the DR CATT learner instead of the OR learner | XGBoost CATT learner · Unbalanced synthetic DiD | MSE: 0.21 ± 0.06 -> 0.12 ± 0.03 | Helped |
| Use the DR CATT learner instead of the CATE DR learner | XGBoost learner · Unbalanced synthetic DiD | MSE: 0.15 ± 0.04 -> 0.12 ± 0.03 | Helped |
| Use the DR CATT learner instead of the OR learner | Neural Net CATT learner · Unbalanced synthetic DiD | MSE: 0.21 ± 0.05 -> 0.18 ± 0.05 | Helped |
| Use the DR CATT learner instead of the CATE DR learner | Neural Net learner · Unbalanced synthetic DiD | MSE: 0.21 ± 0.07 -> 0.18 ± 0.05 | Helped |
| Use the DR learner instead of the OR learner | XGBoost CATT learner · Minimum Wage semi-synthetic data | MSE: 2.07 ± 0.09 -> 1.8 ± 0.09 | Helped |
| Use the DR learner instead of the CATE DR learner | XGBoost learner · Minimum Wage semi-synthetic data | MSE: 2.66 ± 0.07 -> 1.8 ± 0.09 | Helped |
| Use the DR learner instead of the OR learner | Linear CATT learner · Minimum Wage semi-synthetic data | MSE: 2.06 ± 0.08 -> 1.83 ± 0.07 | Helped |
Surprising findings
- The DR-CATE learner (which regresses on the treated group's CATE pseudo-outcome) is biased for projections onto a subset of covariates when treated and control covariate distributions differ.
- Random forest nuisances perform markedly worse than linear, lasso, or ridge nuisances for the OR learner in the synthetic experiments (e.g., 0.38 vs 0.12 for neural net OR).
Limitations
- Theoretical guarantees require sample splitting and sufficiently small nuisance-estimation errors; rates depend on overlap constant c.
- Real-data application relies on a calibration-based validation rather than ground-truth CATT, and the minimum wage dataset is low-dimensional so neural networks were not used.
- Parallel trends violations are only examined in appendix simulations; the IV-DiD and lagged-outcome extensions are presented without empirical evaluation.
Experimental setup
Datasets: synthetic DiD data (20 covariates) Minimum Wage dataset (teen employment, 2001-2007)
Benchmarks: synthetic DiD simulations imbalanced synthetic DiD semi-synthetic minimum wage data
Metrics: MSE against true CATT calibration of GATT across quantile bins
Baselines: Outcome regression (OR) learner CATE outcome regression learner CATE DR-learner
Builds on: DR-learner Difference-in-Differences prediction-powered inference Neyman orthogonality
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