Imperfect Synthetic Controls

Area of Science:

• Econometrics
• Causal Inference
• Public Health

Background:

• The standard synthetic control method (SCM) assumes a perfect synthetic control, which is often unrealistic due to transitory shocks.
• These shocks can introduce bias, as they may not average out and can affect expected outcomes.

Purpose of the Study:

• To develop an improved synthetic control estimator that accommodates transitory shocks.
• To provide a method for valid treatment effect inference even with limited control units.
• To evaluate the impact of repealing Wisconsin's handgun purchase waiting period on suicide rates.

Main Methods:

• Estimating synthetic controls for all units, not just the treated one.
• Developing moment conditions robust to transitory shocks.
• Introducing a weighting metric to exclude units lacking appropriate synthetic controls.
• Utilizing multiple treatment effect estimates for valid inference.

Main Results:

• The proposed estimator generates synthetic controls for all units, allowing for independent treatment effect identification.
• Moment conditions are developed to ensure validity in the presence of transitory shocks.
• A weighting metric is introduced to improve the selection of control units.
• The method allows for valid inference even with a small number of control units.

Conclusions:

• The novel synthetic control estimator offers a more robust approach to causal inference in the presence of transitory shocks.
• The method provides a reliable way to estimate treatment effects and conduct valid statistical inference.
• The study applies this estimator to a real-world policy evaluation concerning firearm access and suicide rates.