Before revision:  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 .
After revision:  We motivate this approach by showing that SCM is a (regularized) inverse propensity score weighting estimator, with 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 canonical SCM examples .