Causal Forecasting in Panel Data: A Two-Way Synthetic Forecasting Approach

Abstract

Estimating causal effects in panel data is central to policy evaluation, yet existing methods largely address retrospective questions: what would have happened to a target unit under a different intervention during the observed panel? In many applications, however, decision-makers instead face a prospective question: what will happen to a target unit under an intervention it has not yet experienced, beyond the observed horizon? We develop a framework for such causal forecasting problems by combining the counterfactual logic of synthetic controls methods with the extrapolative structure of multivariate time-series forecasting. Building on latent factor models for synthetic controls, we impose a low-rank temporal structure on the treated latent time factors to identify prospective causal forecast estimands. We operationalize this idea through the Two-Way Synthetic Forecasting estimator (TWSF), which learns cross-unit relationships from pre-treatment outcomes and temporal dynamics from the post-treatment trajectories of donors exposed to the intervention of interest. Under suitable conditions, we establish finite-sample error bounds and pointwise consistency, and derive asymptotic normality and feasible pointwise inference for prespecified linear summaries over fixed multi-step horizons. Simulation studies support the theoretical results, and an application to the opening of NFL stadiums during the 2020 season illustrates how TWSF can inform prospective policy evaluation using only information available at the decision date.