Synthetic Control with Foundation Models: Nonlinear Gains and Context-Axis Sensitivity

Synthetic control (SC) predicts a target’s untreated path using comparable unaffected units as donors. We show that classical SC with convex weights admits a restricted single-query attention form, motivating frozen foundation models (FMs) as in-context predictors. We formalize the finite-context tradeoff: nonlinear approximation gains must exceed the recovery error. We also identify context-axis sensitivity: transposing the same panel can change a checkpoint’s predictions. Our two-way centering procedure reduces the mean absolute log-MSE gap between orientations by 61–85%. Our simulations show tabular FMs recover nonlinear structure better than tuned CatBoost and kernel ridge when sufficient context exists. In a real-panel study spanning 673 prediction tasks from 12 datasets, we find that centered FMs are competitive when pre-treatment history is long relative to donor-pool size, while synthetic difference-in-differences (SDID) performs best when it is short. In a semi-synthetic experiment using real U.S. traffic-fatality data, we show that tabular FMs with a suitable context-axis interface can reduce the time to reach 80% test power for a 0.7-standard-deviation effect from 12 to 9 months versus the best baseline SDID, a 25% reduction.