Synthetic Control as Online Linear Regression
Econometrica · 2023 · Volume 91 · Issue 2
Abstract
This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize synthetic control as an instance ofFollow-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.
Keywords
Synthetic control, online convex optimization, difference-in-differences, regret
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