Before revision:  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.
After revision:  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 . Our main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment outcomes as covariates and a ridge penalty on the propensity score coefficients.