Testing the validity of instrumental variables in just-identified linear non-Gaussian models

Area of Science:

• Econometrics
• Causal Inference
• Statistical Modeling

Background:

• Instrumental variable (IV) estimation is vital for causal inference in observational data.
• Key assumptions include instrument relevance and exclusion restriction.
• The exclusion restriction is untestable in just-identified models, posing a challenge for validity.

Purpose of the Study:

• To introduce properties of non-Gaussian IV models for testing hidden confounding.
• To develop a two-step approach for testing IV validity in just-identified models.
• To address the challenge of validating IVs when the exclusion restriction is empirically untestable.

Main Methods:

• Utilized properties of non-Gaussian instrumental variable models.
• Developed and evaluated a two-step diagnostic procedure for IV validity.
• Employed Monte-Carlo simulations to assess the performance of the proposed approach.
• Illustrated the method with an empirical example from psychological research.

Main Results:

• Non-Gaussian IV models offer a way to test for hidden confounding between instruments and outcomes.
• The proposed two-step approach enables testing IV validity against hidden confounding in just-identified models.
• Detecting direct IV-outcome paths (exclusion restriction violations) is limited to over-identified models.

Conclusions:

• The study provides valuable insights for developing diagnostic procedures for instrumental variable models.
• While progress has been made, universally validating just-identified IV models remains a complex task.
• Recommendations for best practices and future research in IV validation are discussed.