Are Synthetic Control Weights Balancing Score?
This work addresses methodological rigor in causal inference for researchers, but it is incremental as it builds on existing SC theory.
The paper tackles the problem of ensuring that Synthetic Control (SC) weights emulate randomized control trials by establishing conditions under which SC weights act as balancing scores, specifically when treatment effects are exactly identified and weights are uniformly and cumulatively bounded.
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.