Are Synthetic Control Weights Balancing Score?

TL;DR

This paper explores conditions under which Synthetic Control weights function as balancing scores, effectively mimicking randomized control trials by balancing covariates when certain criteria are met.

Contribution

It establishes theoretical conditions where Synthetic Control weights serve as balancing scores, linking them to randomized trial emulation.

Findings

SC weights can be balancing scores under specific conditions

Exact identification of treatment effects is crucial

Boundedness of weights ensures emulation of randomized trials

Abstract

In this short note, I outline conditions under which conditioning on Synthetic Control (SC) weights emulates a randomized control trial where the treatment status is independent of potential outcomes. Specifically, I demonstrate that if there exist SC weights such that (i) the treatment effects are exactly identified and (ii) these weights are uniformly and cumulatively bounded, then SC weights are balancing scores.