32.8 Inference in SCM

Unlike traditional methods, SCM does not rely on standard statistical inference due to:

  1. Undefined sampling mechanism (e.g., only one treated unit).
  2. SCM is deterministic, making p-values difficult to interpret.

32.8.1 Permutation (Placebo) Inference

To perform inference:

  1. Iteratively reassign the treatment to units in the donor pool.
  2. Estimate placebo treatment effects for each synthetic control.
  3. Compare the actual treatment effect to the placebo distribution.

The treatment effect is considered statistically significant if it is extreme relative to the placebo distribution.

32.8.2 One-Sided Inference

  • Recommended due to the limited number of treated cases.
  • The permutation test is more robust than standard p-values.

For benchmark distributions (e.g., uniform permutation distributions), see (Firpo and Possebom 2018).

References

Firpo, Sergio, and Vitor Possebom. 2018. “Synthetic Control Method: Inference, Sensitivity Analysis and Confidence Sets.” Journal of Causal Inference 6 (2): 20160026.