Synthetic Control As Online Linear Regression

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. We argue that this observation further supports the use of synthetic control estimators in comparative case studies.

Causality in Econometrics: Choice vs Chance

“…Here the use of supervised learning methods such as deep neural nets and random forests have proven helpful in improving methods for estimating average treatment effects (e.g., Chernozhukov et al (2017)), and for estimating heterogeneous treatment effects and treatment policies (e.g., , Athey and Wager (2021)). In addition, generative adversarial networks and reinforcement learning methods are making inroads into econometrics (see Athey, Imbens, Metzger, and Munro (2021) and Chen (2022)). These methods are likely to be of increasing importance in methodological and empirical work in economics.…”