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Confidence Sets Based on Inverting Anderson-Rubin Tests

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  • Russell Davidson

    ()
    (McGill University)

  • James G. MacKinnon

    ()
    (Queen's University)

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. But, 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 over-identifying 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.

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File URL: http://www.econ.queensu.ca/working_papers/papers/qed_wp_1257.pdf
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1257.

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Length: 21 pages
Date of creation: Nov 2011
Date of revision:
Handle: RePEc:qed:wpaper:1257

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Keywords: weak instruments; confidence interval; instrumental variables; LIML; Sargan test; F test; overidentifying restrictions;

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  1. Forchini, G. & Hillier, G.H., 1999. "Conditional inference for possibly unidentified structural equations," Discussion Paper Series In Economics And Econometrics 9906, Economics Division, School of Social Sciences, University of Southampton.
  2. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  3. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  4. Russell Davidson & James Mackinnon, 2009. "Bootstrap inference in a linear equation estimated by instrumental variables," Working Papers halshs-00442713, HAL.
  5. Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," STICERD - Distributional Analysis Research Programme Papers 58, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. Russell Davidson & James G. MacKinnon, 2007. "Wild Bootstrap Tests For Iv Regression," Departmental Working Papers 2007-14, McGill University, Department of Economics.
  7. Russell Davidson & Emmanuel Flachaire, 2001. "The wild bootstrap, tamed at last," LSE Research Online Documents on Economics 6560, London School of Economics and Political Science, LSE Library.
  8. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
  9. DUFOUR, Jean-Marie & TAAMOUTI, Mohamed, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Cahiers de recherche 08-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Peter C.B. Phillips, 1982. "Exact Small Sample Theory in the Simultaneous Equations Model," Cowles Foundation Discussion Papers 621, Cowles Foundation for Research in Economics, Yale University.
  11. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  12. 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.
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Cited by:
  1. James G. MacKinnon, 2012. "Thirty Years of Heteroskedasticity-Robust Inference," Working Papers 1268, Queen's University, Department of Economics.

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