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Bootstrap inference in a linear equation estimated by instrumental variables

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  • Russell Davidson

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579, CIREG - Centre interuniversitaire de recherche en économie quantitative - Université de Montréal, Department of Economics, McGill University - McGill University)

  • James Mackinnon

    ()
    (Department of Economics - Queen's University, Kingston, Ontario)

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 writing all the test statistics—Student's t, Anderson-Rubin, the LM statistic of Kleibergen and Moreira (K), and likelihood ratio (LR)—as functions of six random quantities leads to a number of interesting results about the properties of the tests under weakinstrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and also a new conditional bootstrap 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, both the K and conditional bootstrap LR tests have excellent performance under the null. However, power considerations suggest that the latter is probably the method of choice.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00442713.

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Date of creation: 22 Dec 2009
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Handle: RePEc:hal:wpaper:halshs-00442713

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Keywords: bootstrap; weak instruments; IV estimation;

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References

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  1. Grant Hillier, 2006. "Exact properties of the conditional likelihood ratio test in an IV regression model," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP23/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, The Economic Society of Australia, vol. 82(s1), pages S2-S18, 09.
  3. Davidson, R. & Mackinnon, J.G., 1996. "The Size Distorsion of Bootstrap Tests," G.R.E.Q.A.M., Universite Aix-Marseille III 96a15, Universite Aix-Marseille III.
  4. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, Elsevier, vol. 95(2), pages 375-389, April.
  5. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1365-1388, November.
  6. Peter C.B. Phillips, 1982. "Exact Small Sample Theory in the Simultaneous Equations Model," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 621, Cowles Foundation for Research in Economics, Yale University.
  7. 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, American Statistical Association, vol. 20(4), pages 518-29, October.
  8. D.S. Poskitt & C.L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Department of Economics - Working Papers Series, The University of Melbourne 948, The University of Melbourne.
  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, Econometric Society, vol. 74(3), pages 715-752, 05.
  10. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  11. 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.
  12. Russell Davidson & James G. MacKinnon, 2007. "Wild Bootstrap Tests For Iv Regression," Departmental Working Papers, McGill University, Department of Economics 2007-14, McGill University, Department of Economics.
  13. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, Elsevier, vol. 133(2), pages 421-441, August.
  14. Donald W.K. Andrews & Marcelo J. Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1476, Cowles Foundation for Research in Economics, Yale University.
  15. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  16. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  17. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, Elsevier, vol. 139(1), pages 181-216, July.
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Citations

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Cited by:
  1. Noud P.A. van Giersbergen, 2011. "Bootstrapping Subset Test Statistics in IV Regression," UvA-Econometrics Working Papers, Universiteit van Amsterdam, Dept. of Econometrics 11-08, Universiteit van Amsterdam, Dept. of Econometrics.
  2. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap tests for overidentification in linear regression models," Working Papers, Queen's University, Department of Economics 1318, Queen's University, Department of Economics.
  3. Simon A. Broda, 2014. "On Distributions of Ratios," Tinbergen Institute Discussion Papers 13-211/VI, Tinbergen Institute.
  4. Simon A. Broda & Raymond Kan, 2013. "On Distributions of Ratios," UvA-Econometrics Working Papers, Universiteit van Amsterdam, Dept. of Econometrics 13-10, Universiteit van Amsterdam, Dept. of Econometrics.
  5. 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.
  6. Russell Davidson & James G. MacKinnon, 2008. "Wild Bootstrap Tests for IV Regression," Working Papers, Queen's University, Department of Economics 1135, Queen's University, Department of Economics.
  7. Chau, Tak Wai, 2014. "On the equivalence of indirect inference and bootstrap bias correction for linear IV estimators," Economics Letters, Elsevier, Elsevier, vol. 123(3), pages 333-335.
  8. Russell Davidson & James G. MacKinnon, 2011. "Confidence Sets Based on Inverting Anderson-Rubin Tests," Working Papers, Queen's University, Department of Economics 1257, Queen's University, Department of Economics.
  9. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers, Queen's University, Department of Economics 1127, Queen's University, Department of Economics.

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