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Confidence Sets Based on Inverting Anderson-Rubin Tests

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  • Davidson, Russell
  • MacKinnon, James G.

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 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. But, even when they are bounded, their length may be very misleading, and their coverage conditional on quantities that the investigator can observe, no- tably 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

  • Davidson, Russell & MacKinnon, James G., 2011. "Confidence Sets Based on Inverting Anderson-Rubin Tests," Queen's Economics Department Working Papers 273756, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:273756
    DOI: 10.22004/ag.econ.273756
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    Cited by:

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    3. 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.
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    9. MacKinnon, James G., 2011. "Thirty Years of Heteroskedasticity-Robust Inference," Queen's Economics Department Working Papers 273816, Queen's University - Department of Economics.
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    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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