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

2026-06-16

AI Summary

This study addresses the problem of prospective causal forecasting in panel data—specifically, predicting counterfactual outcomes for a target unit over future periods during which an intervention has not yet been implemented. To this end, the authors propose the Two-Way Synthetic Forecasting (TWSF) estimator, which uniquely integrates synthetic control methods with multivariate time series extrapolation. The approach leverages a low-rank latent factor model to capture both cross-sectional dependencies and temporal dynamics, combining unit-specific regressors, time factor modeling, and orthogonalization-based bias correction. Theoretical analysis establishes pointwise consistency, asymptotic normality, and finite-sample error bounds for multi-step-ahead predictions. Extensive simulations confirm the estimator’s empirical performance, and a real-world application demonstrates its utility in evaluating the causal impact of 2020 NFL stadium reopenings on public health outcomes.

Abstract

Estimating causal effects in panel data is a central problem in policy evaluation. Existing methods largely address retrospective questions of the form: what would have happened to a target unit under a different intervention during the observed panel? In many applications, however, decision-makers face prospective questions: what will happen to a target unit under an intervention it has not yet experienced, beyond the observed panel? This article develops a framework for answering such causal forecasting questions by integrating the retrospective counterfactual logic of synthetic-controls-based approaches with the extrapolative structure of multivariate time-series forecasting. Building on the latent factor models that justify unit-side regressions in synthetic controls, we impose low-rank temporal structure on the latent time factors to identify prospective causal forecast estimands. We operationalize this strategy through the Two-Way Synthetic Forecasting estimator, or TWSF, which learns cross-unit relationships from pre-treatment outcomes and combines them with a time-series model learned from treated donor trajectories under the intervention of interest. Under suitable conditions, we establish finite-sample forecasting error bounds that imply pointwise consistency and introduce an orthogonalized correction that yields asymptotic normality and thus enables pointwise inference. We extend the framework to fixed multi-step forecasting horizons through both direct and recursive procedures, each of which inherits analogous pointwise guarantees. We corroborate the theory with simulation studies and illustrate the practical utility of TWSF by studying the public-health impact of opening NFL stadiums during the 2020 season.

Problem

• causal forecasting
• panel data
• prospective causal inference
• synthetic controls
• time-series forecasting

Innovation

• causal forecasting
• panel data
• synthetic controls
• low-rank factor models
• time-series extrapolation