Synthetic Control As Online Linear Regression

TL;DR

This paper reveals that synthetic control methods are equivalent to online linear regression techniques, providing theoretical guarantees for their performance even under adversarial outcome scenarios.

Contribution

It establishes a connection between synthetic control and online learning, demonstrating their equivalence to Follow-The-Leader algorithms with theoretical performance bounds.

Findings

Synthetic control performs nearly as well as an oracle weighted average.

On differenced data, synthetic control matches oracle weighted difference-in-differences.

The approach offers theoretical support for synthetic control in case studies.

Abstract

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.