Synthetic Control As Online Linear Regression
This provides theoretical justification for using synthetic control in comparative case studies, though it is incremental as it builds on existing online learning results.
The paper connects synthetic control to online learning by framing it as Follow-The-Leader, showing that even with adversarial outcomes, its predictions nearly match an oracle weighted average of control units, with similar performance for differenced data compared to oracle weighted difference-in-differences.
This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize synthetic control as an instance of Follow-The-Leader (FTL). Standard results in online convex optimization then imply that, even when outcomes are chosen by an adversary, synthetic control predictions of counterfactual outcomes for the treated unit perform almost as well as an oracle weighted average of control units' outcomes. Synthetic control on differenced data performs almost as well as oracle weighted difference-in-differences, potentially making it an attractive choice in practice. We argue that this observation further supports the use of synthetic control estimators in comparative case studies.