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合成控制作为在线线性回归

Synthetic Control as Online Linear Regression
Econometrica · 2023 · Jiafeng Chen

中文摘要

本文指出了合成控制与在线学习之间的一个简单联系。具体而言,我们将合成控制识别为跟随领导者(Follow-The-Leader,FTL)的一个实例。在线凸优化的标准结果由此意味着:即使结果由对手选择,合成控制对处理单元反事实结果的预测,也与控制单元结果的预言机加权平均表现几乎一样好。基于差分数据的合成控制的表现几乎与预言机加权双重差分一样好,这可能使其在实践中成为一个有吸引力的选择。我们认为,这一观察进一步支持了在比较案例研究中使用合成控制估计量。

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.
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