A Way to Synthetic Triple Difference

Abstract: This paper discusses a practical approach that combines synthetic control with triple difference to address violations of the parallel trends assumption. By transforming triple difference into a DID structure, we can apply synthetic control to a triple-difference framework, enabling more robust estimates when parallel trends are violated across multiple dimensions. The proposed procedure is applied to a real-world dataset to illustrate when and how we should apply this practice, while cautions are presented afterwards. This method contributes to improving causal inference in policy evaluations and offers a valuable tool for researchers dealing with heterogeneous treatment effects across subgroups.