Theory for Identification and Inference with Synthetic Controls: A Proximal Causal Inference Framework

Area of Science:

• Causal Inference
• Econometrics
• Statistical Modeling

Background:

• Synthetic control (SC) methods are widely used for estimating treatment effects in panel data.
• Classical SC relies on a good pretreatment fit, limiting its application when such fits are unattainable.
• Latent confounders can bias treatment effect estimations in traditional SC.

Purpose of the Study:

• To introduce a proximal causal inference framework for synthetic control methods.
• To extend the applicability of SC to settings with poor pretreatment fits and latent confounders.
• To accommodate nonlinear models and understudied outcome types (binary, count) within the SC framework.

Main Methods:

• Repurposing control units not used in SC construction as proxies for latent confounders.
• Formalizing identification and inference for SC and treatment effects using a proximal framework.
• Adapting existing uncertainty quantification methods for classical SC to the proximal approach.

Main Results:

• The proximal framework successfully extends SC applicability to cases with poor pretreatment fits.
• The method accommodates nonlinear models, enabling analysis of binary and count outcomes.
• Demonstrated effectiveness through comprehensive simulation studies and a real-world application.

Conclusions:

• Proximal causal inference offers a robust extension to synthetic control methods.
• The framework enhances the reliability of treatment effect estimation in challenging settings.
• Opens new avenues for SC applications in fields with complex confounding structures.