The Augmented Synthetic Control Method
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 pre-treatment outcomes and other covariates as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pre-treatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pre-treatment fit is infeasible. Analogous to bias correction for inexact matching, Augmented SCM uses an outcome model to estimate the bias due to imperfect pre-treatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment 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.
We thank Alberto Abadie, Josh Angrist, Matias Cattaneo, Alex D’Amour, Peng Ding, Erin Hartman, Chad Hazlett, Steve Howard, Guido Imbens, Brian Jacob, Pat Kline, Caleb Miles, Luke Miratrix, Sam Pimentel, Fredrik Sävje, Jas Sekhon, Jake Soloff, Panos Toulis, Stefan Wager, Kaspar Wutrich, Yiqing Xu, Alan Zaslavsky, and Xiang Zhou for thoughtful comments and discussion, as well as seminar participants at Stanford, UC Berkeley, UNC, the 2018 Atlantic Causal Inference Conference, COMPIE 2018, and the 2018 Polmeth Conference. We also thank editors and referees for constructive feedback. The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305D200010. The opinions expressed are those of the authors and do not represent views of the Institute, the U.S. Department of Education, or the National Bureau of Economic Research.
Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2021. "The Augmented Synthetic Control Method," Journal of the American Statistical Association, vol 116(536), pages 1789-1803.