Policy Analysis using Synthetic Controls in Continuous-Time
This work provides a more flexible and robust method for counterfactual estimation, particularly beneficial for researchers and practitioners working with complex, irregularly-sampled time series data in causal inference.
This paper addresses the limitations of traditional synthetic control methods, which assume time series alignment and linear combinations of control units. It introduces a continuous-time alternative using controlled differential equations to model latent counterfactual paths, applicable to irregularly-aligned multivariate time series.
Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic controls expressed as linear combinations of observed control units. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations. This model is directly applicable to the general setting of irregularly-aligned multivariate time series and may be optimized in rich function spaces -- thereby improving on some limitations of existing approaches.