Synthetic Difference in Differences
@article{Arkhangelsky2018SyntheticDI, title={Synthetic Difference in Differences}, author={D. Arkhangelsky and Susan Athey and David A. Hirshberg and Guido Imbens and Stefan Wager}, journal={NBER Working Paper Series}, year={2018} }
We present a new perspective on the Synthetic Control (SC) method as a weighted least squares regression estimator with time fixed effects and unit weights. This perspective suggests a generalization with two way (both unit and time) fixed effects, and both unit and time weights, which can be interpreted as a unit and time weighted version of the standard Difference In Differences (DID) estimator. We find that this new Synthetic Difference In Differences (SDID) estimator has attractive…
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References
SHOWING 1-10 OF 91 REFERENCES
Balancing, Regression, Difference-in-Differences and Synthetic Control Methods: A Synthesis
- Mathematics, Economics
- 2016
In a seminal paper Abadie et al (2010) develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single treated unit and a number of control units, with…
Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models
- EconomicsPolitical Analysis
- 2017
Difference-in-differences (DID) is commonly used for causal inference in time-series cross-sectional data. It requires the assumption that the average outcomes of treated and control units would have…
The Augmented Synthetic Control Method
- Economics
- 2018
The main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment fit while minimizing extrapolation from the convex hull and bound the bias of this approach under a linear factor model and shows how regularization helps to avoid over-fitting to noise.
Synthetic Controls and Weighted Event Studies with Staggered Adoption
- Economics
- 2019
This paper proposes "partially pooled" SCM weights that instead minimize both average and state-specific imbalance, and combines traditional fixed effects methods to obtain an augmented estimator that improves over both SCM weighting and fixed effects estimation alone.
Inference on average treatment effects in aggregate panel data settings
- Economics, Mathematics
- 2019
A K-fold cross-fitting procedure to remove the bias induced by regularization is proposed and demonstrates an excellent performance in simulation experiments, and is taken to a data application, where it is re-evaluate the economic consequences of terrorism.
Robust Synthetic Control
- Computer ScienceJ. Mach. Learn. Res.
- 2018
The condition under which the fundamental assumption in synthetic control-like approaches holds holds is established, i.e. when the linear relationship between the treatment unit and the donor pool prevails in both the pre- and post-intervention periods.
Revisiting Event Study Designs
- Mathematics, Economics
- 2017
A broad empirical literature uses "event study" research designs for treatment effect estimation, a setting in which all units in the panel receive treatment but at random times. We make four novel…
Combining Matching and Synthetic Control to Trade Off Biases from Extrapolation and Interpolation
- Economics
- 2020
The synthetic control method is widely used in comparative case studies to adjust for differences in pre-treatment characteristics. A major attraction of the method is that it limits extrapolation…
Difference-in-Differences with Multiple Time Periods
- MathematicsJournal of Econometrics
- 2020
This article considers identification and estimation of treatment effect parameters using DID with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the "parallel trends assumption" holds potentially only after conditioning on observed covariates.
Synthetic Control Method: Inference, Sensitivity Analysis and Confidence Sets
- MathematicsJournal of Causal Inference
- 2018
Abstract We extend the inference procedure for the synthetic control method in two ways. First, we propose parametric weights for the p-value that includes the equal weights benchmark of Abadie et…