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Confidence Sets Based On Inverting Anderson-rubin Tests

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Russell Davidson

    (McGill University)

Abstract

Economists are often interested in the coefficient of a single endogenous explanatory variable in a linear simultaneous equations model. One way toobtain a confidence set for this coefficient is to invert the Anderson-Rubin 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. But, even when they are bounded, their length may be very misleading, and their coverage conditional onquantities that the investigator can observe, notably the Sargan statistic for over-identifying restrictions, can be far from correct. Asimilar 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

  • James G. MacKinnon & Russell Davidson, 2011. "Confidence Sets Based On Inverting Anderson-rubin Tests," Working Paper 1257, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1257
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    References listed on IDEAS

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    8. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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    10. Davidson, Russell & MacKinnon, James G., 2008. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Queen's Economics Department Working Papers 273633, Queen's University - Department of Economics.
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    14. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
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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. MacKinnon, James G., 2011. "Thirty Years of Heteroskedasticity-Robust Inference," Queen's Economics Department Working Papers 273816, Queen's University - Department of Economics.
    3. 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.
    4. Masakure, Oliver, 2016. "The effect of employee loyalty on wages," Journal of Economic Psychology, Elsevier, vol. 56(C), pages 274-298.
    5. Davidson, Russell & MacKinnon, James G., 2012. "Bootstrap Confidence Sets with Weak Instruments," Queen's Economics Department Working Papers 274076, Queen's University - Department of Economics.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Taner Osman & Tom Kemeny, 2022. "Local job multipliers revisited," Journal of Regional Science, Wiley Blackwell, vol. 62(1), pages 150-170, January.
    11. 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.).

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    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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