Synthetic Parallel Trends

Popular empirical strategies for policy evaluation in the panel data literature -- including difference-in-differences (DID), synthetic control (SC) methods, and their variants -- rely on key identifying assumptions that can be expressed through a specific choice of weights $\omega$ relating pre-treatment trends to the counterfactual outcome. While each choice of $\omega$ may be defensible in empirical contexts that motivate a particular method, it relies on fundamentally untestable and often fragile assumptions. I develop an identification framework that allows for all weights satisfying a Synthetic Parallel Trends assumption: the treated unit's trend is parallel to a weighted combination of control units' trends for a general class of weights. The framework nests these existing methods as special cases and is by construction robust to violations of their respective assumptions. I construct a valid confidence set for the identified set of the treatment effect, which admits a linear programming representation with estimated coefficients and nuisance parameters that are profiled out. In simulations where the assumptions underlying DID or SC-based methods are violated, the proposed confidence set remains robust and attains nominal coverage, while existing methods suffer severe undercoverage.