Identification and Inference with Invalid Instruments

Area of Science:

• Epidemiology
• Biostatistics
• Econometrics

Background:

• Instrumental variables (IVs) are crucial for causal inference with unmeasured confounding.
• Valid instruments must be associated with exposure, affect the outcome only through exposure, and be independent of confounders.
• Real-world application often challenges these strict validity conditions.

Purpose of the Study:

• To review methods for causal inference using potentially invalid instrumental variables.
• To explore identification and inference strategies when instruments violate standard assumptions.
• To provide an empirical comparison of different methods for handling invalid instruments.

Main Methods:

• Review of existing literature on instrumental variable methods under assumption violations.
• Analysis of identification and inference in linear, nonlinear, and heteroskedastic models with invalid instruments.
• Empirical reanalysis of body mass index and systolic blood pressure using UK Biobank data.

Main Results:

• The study reviews various statistical techniques to address violations of instrumental variable assumptions.
• Different models (linear, nonlinear, heteroskedastic) are examined for their suitability with invalid instruments.
• An empirical comparison demonstrates the practical application and performance of reviewed methods.

Conclusions:

• Using instrumental variables with potential violations of standard assumptions is feasible with appropriate methods.
• The choice of method depends on the specific nature of the instrument's invalidity and the statistical model.
• Empirical validation provides insights into the practical utility of these advanced causal inference techniques.