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A test for instrumental variable validity using a correlation restriction

Author

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  • Ratbek Dzhumashev

    (Department of Economics, Monash University)

  • Ainura Tursunalieva

    (Data61, CSIRO)

Abstract

DiTraglia and García-Jimeno (2021) demonstrate that the correlation coefficients between an IV, an endogenous regressor, and the outcome variable must satisfy a specific joint constraint determined by their relationships with the structural error term. We exploit this constraint to develop a novel Correlation Restriction test that becomes feasible when the direction of endogeneity bias is known. Our test quantifies the probability of instrument orthogonality to the structural error across the plausible range of endogeneity magnitudes, providing researchers with a previously unavailable diagnostic tool in the frequentist setting. Through simulations and applications to diverse empirical settings including returns to education, criminal recidivism, and development economics, we establish that our method reliably identifies invalid instruments and characterizes the endogeneity range over which valid instruments maintain their exogeneity. This approach contributes to instrumental variable methods by transforming a key identification assumption from an untestable assertion into an empirically verifiable condition.

Suggested Citation

  • Ratbek Dzhumashev & Ainura Tursunalieva, 2025. "A test for instrumental variable validity using a correlation restriction," Monash Economics Working Papers 2025-06, Monash University, Department of Economics.
    • Handle: RePEc:mos:moswps:2025-06
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    References listed on IDEAS

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    Keywords

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    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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