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Confidence Sets Based on Inverting Anderson-Rubin Tests

Author

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  • 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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    References listed on IDEAS

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    1. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(5), pages 707-743, October.
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    4. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    5. Davidson, Russell & MacKinnon, James G., 2010. "Wild Bootstrap Tests for IV Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 128-144.
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    8. Davidson, Russell & MacKinnon, James G., 2008. "Wild Bootstrap Tests for IV Regression," Queen's Economics Department Working Papers 273611, Queen's University - Department of Economics.
    9. Davidson, Russell & MacKinnon, James, 2006. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Queen's Economics Department Working Papers 273460, Queen's University - Department of Economics.
    10. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, November.
    11. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap inference in a linear equation estimated by instrumental variables," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 443-477, November.
    12. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    13. 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.
    14. David C. Wyld, 2010. "ASecond Lifefor organizations?: managing in the new, virtual world," Management Research Review, Emerald Group Publishing Limited, vol. 33(6), pages 529-562, May.
    15. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    16. Davidson, Russell & Flachaire, Emmanuel, 2001. "The Wild Bootstrap, Tamed at Last," Queen's Economics Department Working Papers 273426, Queen's University - Department of Economics.
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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. James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
    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. MacKinnon, James G., 2011. "Thirty Years of Heteroskedasticity-Robust Inference," Queen's Economics Department Working Papers 273816, Queen's University - Department of Economics.
    11. Taner Osman & Tom Kemeny, 2022. "Local job multipliers revisited," Journal of Regional Science, Wiley Blackwell, vol. 62(1), pages 150-170, January.
    12. 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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    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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