Synthetic Regressing Control

Area of Science:

• Econometrics
• Causal Inference
• Statistical Modeling

Background:

• The synthetic control method uses optimization to assign weights to control units for matching treated unit outcomes.
• Traditional synthetic control methods can struggle to adequately approximate pre-treatment outcomes, leading to potential bias.

Purpose of the Study:

• To introduce a new method, Synthetic Regressing Control (SRC), to improve the estimation of treatment effects.
• To address the limitations of standard synthetic control methods in approximating pre-treatment data.

Main Methods:

• SRC employs univariate linear regression to align pre-treatment periods between control and treated units.
• A SRC estimator is derived by synthesizing these regressed controls.
• Weights for synthesis are determined using an unbiased risk estimator criterion.

Main Results:

• Theoretically shown to be asymptotically optimal, minimizing the loss compared to infeasible estimators.
• Extensive numerical experiments demonstrate the advantages of the SRC method over existing approaches.

Conclusions:

• SRC offers a simple yet effective enhancement to the synthetic control method.
• The proposed regression-based alignment and synthesis procedure leads to superior estimation of treatment effects.