The Augmented Synthetic Control Method
By Eli Ben-Michael, Avi Feller, Jesse M. Rothstein. Journal of the American Statistical Association, 2018
479 citations recorded by the source corpus.
Abstract The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The “synthetic control” is a weighted average of control units that balances the treated unit’s pretreatment outcomes and other covariates as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pretreatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pretreatment fit is infeasible. Analogous to bias correction for inexact matching, augmented SCM uses an outcome model to estimate the bias due to imperfect pretreatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pretreatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data-generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package.
Subfields: Economics and Econometrics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/97da0ad450e2ef3b304d23737b72a2462ee4a88c
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Citations in the corpus
- Synthetic Difference In Differences (2018, unknown): “Methodologically, our work draws most directly from the literature on SC meth-ods, including Abadie and Gardeazabal ( 2003 ) ; Abadie, Diamond, and Hainmueller ( 2010, 2015 ; Abadie and L’Hour ( 2016 ) ; Doudchenko and Imbens ( 2016 ) ; and Ben-Michael, Feller, and Rothstein ( 2018 ) .”
- Synthetic controls with imperfect pretreatment fit (2016, background): “Ben-Michael et al. (2018) derive finite-sample bounds on the bias of the SC estimator, and show that the bounds they derive do not converge to zero when J is fixed and T0 ! 1.”