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  1. Home
  2. Identification And Inference With Invalid Instruments.
  1. Home
  2. Identification And Inference With Invalid Instruments.

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Identification and Inference with Invalid Instruments.

Hyunseung Kang1, Zijian Guo2, Zhonghua Liu3

  • 1Department of Statistics, University of Wisconsin-Madison, Madison, Wisconsin, USA.

Annual Review of Statistics and Its Application
|July 14, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

Instrumental variables (IVs) help study causal effects despite unmeasured confounding. This review explores methods for using IVs even when instruments have potential direct effects or are linked to confounders, offering practical solutions.

Keywords:
Mendelian randomizationheteroskedasticityinstrumental variablesinvalid instruments

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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.