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Bootstrap inference in a linear equation estimated by instrumental variables

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  • Russell Davidson
  • James G. MacKinnon

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 weak-instrument 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. Copyright The Author(s). Journal compilation Royal Economic Society 2008

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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 11 (2008)
Issue (Month): 3 (November)
Pages: 443-477

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Handle: RePEc:ect:emjrnl:v:11:y:2008:i:3:p:443-477

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References

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  1. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  2. 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.
  3. 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.
  4. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  5. 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.
  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 & James G. MacKinnon, 2004. "The Power of Bootstrap and Asymptotic Tests," Working Papers 1035, Queen's University, Department of Economics.
  8. Donald W.K. Andrews & Marcelo J. Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," Cowles Foundation Discussion Papers 1476, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
  10. 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.
  11. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages S2-S18, 09.
  12. Hillier, Grant, 2009. "Exact Properties Of The Conditional Likelihood Ratio Test In An Iv Regression Model," Econometric Theory, Cambridge University Press, vol. 25(04), pages 915-957, August.
  13. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
  14. 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.
  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. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  17. 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.
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Citations

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Cited by:
  1. Russell Davidson & James G. MacKinnon, 2008. "Wild Bootstrap Tests for IV Regression," Working Papers 1135, Queen's University, Department of Economics.
  2. Russell Davidson & James G. MacKinnon, 2011. "Confidence Sets Based on Inverting Anderson-Rubin Tests," Working Papers 1257, Queen's University, Department of Economics.
  3. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics.
  4. Simon A. Broda, 2014. "On Distributions of Ratios," Tinbergen Institute Discussion Papers 13-211/VI, Tinbergen Institute.
  5. Simon A. Broda & Raymond Kan, 2013. "On Distributions of Ratios," UvA-Econometrics Working Papers 13-10, Universiteit van Amsterdam, Dept. of Econometrics.
  6. 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.
  7. 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.
  8. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap tests for overidentification in linear regression models," Working Papers 1318, Queen's University, Department of Economics.

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