Robust synthetic control

Abstract

In this thesis, we present a robust generalization of the synthetic control method. A distinguishing feature of our algorithm is that of de-noising the data matrix via singular value thresholding, which renders our approach robust in multiple facets: it automatically identifies a good subset of donors, functions without extraneous covariates (vital to existing methods), and overcomes missing data (never been addressed in prior works). To our knowledge, we provide the first theoretical finite sample analysis for a broader class of models than previously considered in literature. Additionally, we relate the inference quality of our estimator to the amount of training data available and show our estimator to be asymptotically consistent. In order to move beyond point estimates, we introduce a Bayesian framework that not only provides practitioners the ability to readily develop different estimators under various loss functions, but also equips them with the tools to quantitatively measure the uncertainty of their model/estimates through posterior probabilities. Our empirical results demonstrate that our robust generalization yields a positive impact over the classical synthetic control method, underscoring the value of our key de-noising procedure.