Synthetic Control as Online Linear Regression

This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize as an instance of Follow-The-Leader (FTL). Standard results in convex optimization then imply that, even when outcomes are chosen by adversary, predictions counterfactual for the treated unit perform almost well oracle weighted average units' outcomes. Synthetic on differenced data performs difference-in-differences, potentially making it attractive choice practice. We argue that this observation further supports use estimators comparative case studies.