Consistency of an Intercept-Shifted Synthetic-Control Estimator under Weighted Parallel Trends

The average treatment effect on the treated (ATT) in a staggered-adoption panel is estimated using an intercept-augmented synthetic-control (SCM) estimator. A weighted parallel trends plus an intercept shift, together with mild regularity on the weight vectors (non-degenerate dispersion) and expanding pre-treatment length, are sufficient for consistency allowing for heavy-tailed shocks. These conditions can be more interpretable than the autoregressive or low-rank factor models with light tails assumed by Ben-Michael, Feller, and Rothstein (2022) and expand the valid DGP pool from the same paper. Practical diagnostics to support the assumptions are discussed and situate these results within the recent literature on SC + DiD hybrids.