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Confidence Sets Based on Inverting Anderson-Rubin Tests

Author

Listed:
  • Russell Davidson

    (Department of Mining and Materials Engineering [Montréal] - McGill University = Université McGill [Montréal, Canada], GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • James G. Mackinnon

Abstract

Economists are often interested in the coefficient of a single endogenous explanatory variable in a linear simultaneous-equations model. One way to obtain a confidence set for this coefficient is to invert the Anderson-Rubin (AR) test. The AR confidence sets that result have correct coverage under classical assumptions. However, AR confidence sets also have many undesirable properties. It is well known that they can be unbounded when the instruments are weak, as is true of any test with correct coverage. However, even when they are bounded, their length may be very misleading, and their coverage conditional on quantities that the investigator can observe (notably, the Sargan statistic for overidentifying restrictions) can be far from correct. A similar property manifests itself, for similar reasons, when a confidence set for a single parameter is based on inverting an F-test for two or more parameters.

Suggested Citation

  • Russell Davidson & James G. Mackinnon, 2014. "Confidence Sets Based on Inverting Anderson-Rubin Tests," Post-Print hal-01463107, HAL.
    • Handle: RePEc:hal:journl:hal-01463107
    DOI: 10.1111/ectj.12015
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    Cited by:

    1. Khalaf, Lynda & Lin, Zhenjiang, 2021. "Projection-based inference with particle swarm optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    2. Jeremy Edwards & Sheilagh Ogilvie, 2022. "The Black Death and the origin of the European marriage pattern," Oxford Economic and Social History Working Papers _204, University of Oxford, Department of Economics.
    3. Sheng Wang & Hyunseung Kang, 2022. "Weak‐instrument robust tests in two‐sample summary‐data Mendelian randomization," Biometrics, The International Biometric Society, vol. 78(4), pages 1699-1713, December.
    4. MacKinnon, James G., 2011. "Thirty Years of Heteroskedasticity-Robust Inference," Queen's Economics Department Working Papers 273816, Queen's University - Department of Economics.
    5. Martin Emil Jakobsen & Jonas Peters, 2022. "Distributional robustness of K-class estimators and the PULSE [The colonial origins of comparative development: An empirical investigation]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 404-432.
    6. Nakashima, Kiyotaka & Takahashi, Koji, 2018. "The real effects of bank-driven termination of relationships: Evidence from loan-level matched data," Journal of Financial Stability, Elsevier, vol. 39(C), pages 46-65.
    7. Masakure, Oliver, 2016. "The effect of employee loyalty on wages," Journal of Economic Psychology, Elsevier, vol. 56(C), pages 274-298.
    8. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap Confidence Sets with Weak Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 651-675, August.
    9. Taner Osman & Tom Kemeny, 2022. "Local job multipliers revisited," Journal of Regional Science, Wiley Blackwell, vol. 62(1), pages 150-170, January.
    10. Theodore F. Figinski & Alicia Lloro & Avinash Moorthy, 2022. "Revisiting the Effect of Education on Later Life Health," Finance and Economics Discussion Series 2022-007, Board of Governors of the Federal Reserve System (U.S.).

    More about this item

    Keywords

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    JEL classification:

    • 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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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