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 as closely as possible. The curse of dimensionality, however, means that SCM does not generally achieve exact balance, which can bias the SCM estimate . We propose an extension, Augmented SCM , which uses an outcome model to estimate the bias due to covariate imbalance and then de-biases the original SCM estimate , analogous to bias correction for inexact matching. We motivate this approach by showing that SCM is a (regularized) inverse propensity score weighting estimator, with pre-treatment outcomes as covariates and a ridge penalty on the propensity score coefficients. We give theoretical guarantees for specific cases and propose a new inference procedure. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to canonical SCM examples . We implement the proposed method in the new augsynth R package.
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 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 to extend 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. We bound the bias of this approach under 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.
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The curse of dimensionality, however, means that SCM does not generally achieve exact balance, which can bias the SCM estimate
A critical feature of the original proposal is to use SCM only when the fit on pre-treatment outcomes is excellent
R
an extension, Augmented SCM , which
Augmented SCM to extend SCM to settings where such pre-treatment fit is infeasible. Analogous to bias correction for inexact matching, Augmented SCM
R
covariate imbalance
imperfect pre-treatment fit
R
, analogous to bias correction for inexact matching. We motivate this approach by showing that SCM is a (regularized) inverse propensity score weighting estimator, with
. Our main proposal, which uses ridge regression as the outcome model, directly controls
R
outcomes as covariates and a ridge penalty on the propensity score coefficients. We give theoretical guarantees for specific cases and propose a new inference procedure. We
fit while minimizing extrapolation from the convex hull. We bound the bias of this approach under a linear factor model and show how regularization helps to avoid over-fitting to noise. We
R
canonical SCM examples
estimate the impact of the 2012 Kansas tax cuts on economic growth