Lack of identification in semiparametric instrumental variable models with binary outcomes

Area of Science:

• Statistics
• Epidemiology
• Econometrics

Background:

• Parameter identification is crucial for unique estimation in statistical models.
• Instrumental variable analysis is used for estimating causal effects with binary outcomes.
• Generalized method of moments and structural mean models rely on estimating equations.

Purpose of the Study:

• To demonstrate non-identification issues in instrumental variable analysis.
• To investigate the impact of weak instruments on parameter identification.
• To examine the relationship between instrument strength, sample size, and unique solution proportion.

Main Methods:

• Simulation studies were conducted to assess parameter identification.
• The proportion of unique solutions for estimating equations was analyzed.
• The influence of instrument strength (ρ(2)) and sample size was investigated.

Main Results:

• Lack of parameter identification can occur, especially with weak instruments (ρ(2) ≤ 0.01).
• Estimating equations may yield no or multiple solutions, irrespective of sample size.
• Poor identification was prevalent even for instruments explaining 10% of exposure variance in large datasets.

Conclusions:

• Weak instruments pose a significant risk to the identification of causal parameters in statistical models.
• Standard estimation procedures may produce misleading results when identification is poor.
• Careful assessment of instrument strength is essential for valid causal inference.