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# If results differ substantially, investigate heterogeneity
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### Borusyak-Jaravel-Spiess Imputation Estimator
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The Borusyak et al. (2024) imputation estimator is the **efficient** estimator for staggered DiD under parallel trends, producing ~50% shorter confidence intervals than Callaway-Sant'Anna and 2-3.5x shorter than Sun-Abraham under homogeneous treatment effects.
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```python
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from diff_diff import ImputationDiD, imputation_did
Triple Difference (DDD) is used when treatment requires satisfying two criteria: belonging to a treated **group** AND being in an eligible **partition**. The `TripleDifference` class implements the methodology from Ortiz-Villavicencio & Sant'Anna (2025), which correctly handles covariate adjustment (unlike naive implementations).
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|`print_summary(alpha)`| Print summary to stdout |
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|`to_dataframe(level)`| Convert to DataFrame ('event_study' or 'cohort') |
-**Conservative variance**: Theorem 3 clustered variance estimator with auxiliary model
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-**Pre-trend test**: Independent of treatment effect estimation (Proposition 9)
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-**Efficiency gains**: ~50% shorter CIs than Callaway-Sant'Anna under homogeneous effects
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-**Callaway, B., & Sant'Anna, P. H. C. (2021).** "Difference-in-Differences with Multiple Time Periods." *Journal of Econometrics*, 225(2), 200-230. [https://doi.org/10.1016/j.jeconom.2020.12.001](https://doi.org/10.1016/j.jeconom.2020.12.001)
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-**Sant'Anna, P. H. C., & Zhao, J. (2020).** "Doubly Robust Difference-in-Differences Estimators." *Journal of Econometrics*, 219(1), 101-122. [https://doi.org/10.1016/j.jeconom.2020.06.003](https://doi.org/10.1016/j.jeconom.2020.06.003)
More efficient than Callaway-Sant'Anna when treatment effects are homogeneous across groups/time. Uses imputation rather than aggregation.
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- Imputes untreated potential outcomes using pre-treatment data
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- More efficient under homogeneous effects assumption
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- Can handle unbalanced panels more naturally
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**Reference**: Borusyak, Jaravel, and Spiess (2024). *Review of Economic Studies*.
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Implemented as `ImputationDiD` — see `diff_diff/imputation.py`. Includes conservative variance (Theorem 3), event study and group aggregation, pre-trend test (Equation 9), multiplier bootstrap, and Proposition 5 handling for no never-treated units.
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