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Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables

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  • Russell Davidson

    ()
    (GREQAM and McGill University)

  • James G. MacKinnon

    ()
    (Queen's University)

Abstract

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that all the test statistics--Student's t, Anderson-Rubin, Kleibergen's K, and likelihood ratio (LR)--can be written as functions of six random quantities. This leads to a number of interesting results about the properties of the tests under weak-instrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and a conditional version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, K and conditional LR have excellent performance under the null, and LR also performs very well. However, power considerations suggest that the conditional LR test, bootstrapped using this new procedure when the sample size is not large, is probably the method of choice.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1024.pdf
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1024.

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Length: 42 pages
Date of creation: Feb 2006
Date of revision:
Handle: RePEc:qed:wpaper:1024

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Keywords: bootstrap test; weak instruments; anderson-rubin test; conditional LR test; wald test; instrumental variables;

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References

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  1. Davidson, R. & Mackinnon, J.G., 1996. "The Size Distorsion of Bootstrap Tests," G.R.E.Q.A.M. 96a15, Universite Aix-Marseille III.
  2. Russell Davidson & James G. MacKinnon, 2008. "Wild Bootstrap Tests for IV Regression," Working Papers 1135, Queen's University, Department of Economics.
  3. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
  4. 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.
  5. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  6. James G. MacKinnon, 2006. "Bootstrap Methods in Econometrics," Working Papers 1028, Queen's University, Department of Economics.
  7. Donald W.K. Andrews & Marcelo Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," NBER Technical Working Papers 0299, National Bureau of Economic Research, Inc.
  8. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  9. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, 05.
  10. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
  11. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.
  12. Grant Hillier, 2006. "Exact properties of the conditional likelihood ratio test in an IV regression model," CeMMAP working papers CWP23/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Marcelo J. Moreira & Jack R. Porter & Gustavo A. Suarez, 2004. "Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak," NBER Technical Working Papers 0302, National Bureau of Economic Research, Inc.
  14. D. S. Poskitt & C. L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Monash Econometrics and Business Statistics Working Papers 4/05, Monash University, Department of Econometrics and Business Statistics.
  15. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  16. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier.
  17. 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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Citations

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Cited by:
  1. Simon A. Broda & Raymond Kan, 2013. "On Distributions of Ratios," UvA-Econometrics Working Papers 13-10, Universiteit van Amsterdam, Dept. of Econometrics.
  2. Russell Davidson & James G. MacKinnon, 2007. "Wild Bootstrap Tests For Iv Regression," Departmental Working Papers 2007-14, McGill University, Department of Economics.
  3. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap tests for overidentification in linear regression models," Working Papers 1318, Queen's University, Department of Economics.
  4. Wenjie Wang, 2012. "Bootstrapping Anderson-Rubin Statistic and J Statistic in Linear IV Models with Many Instruments," KIER Working Papers 810, Kyoto University, Institute of Economic Research.
  5. Simon A. Broda, 2014. "On Distributions of Ratios," Tinbergen Institute Discussion Papers 13-211/VI, Tinbergen Institute.
  6. Russell Davidson & James G. MacKinnon, 2011. "Confidence Sets Based on Inverting Anderson-Rubin Tests," Working Papers 1257, Queen's University, Department of Economics.
  7. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics.
  8. Chau, Tak Wai, 2014. "On the equivalence of indirect inference and bootstrap bias correction for linear IV estimators," Economics Letters, Elsevier, vol. 123(3), pages 333-335.
  9. Noud P.A. van Giersbergen, 2011. "Bootstrapping Subset Test Statistics in IV Regression," UvA-Econometrics Working Papers 11-08, Universiteit van Amsterdam, Dept. of Econometrics.

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