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Bootstrapping Anderson-Rubin Statistic and J Statistic in Linear IV Models with Many Instruments

  • Wenjie Wang

    (Graduate School of Economics, Kyoto University)

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    A bootstrap method is proposed for the Anderson-Rubin test and the J test for overidentifying restrictions in linear instrumental variable models with many instruments. We show the bootstrap validity of these test statistics when the number of instruments increases at the same rate as the sample size. Moreover, since it has been shown in the literature to be valid when the number of instruments is small, the bootstrap technique is practically robust to the numerosity of the moment conditions. A small-scale Monte Carlo experiment shows that our procedure has outstanding small sample performance compared with some existing asymptotic procedures.

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP810.pdf
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    Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 810.

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    Date of creation: Feb 2012
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    Handle: RePEc:kyo:wpaper:810
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    1. Russell Davidson & James Mackinnon, 2009. "Bootstrap inference in a linear equation estimated by instrumental variables," Working Papers halshs-00442713, HAL.
    2. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    3. Stanislav Anatolyev & Nikolay Gospodinov, 2008. "Specification Testing in Models with Many Instruments," Working Papers w0124, Center for Economic and Financial Research (CEFIR).
    4. Chao, John Chao & Norman R. Swanson, 2003. "Consistent Estimation with a Large Number of Weak Instruments," Cowles Foundation Discussion Papers 1417, Cowles Foundation for Research in Economics, Yale University.
    5. Christian Hansen & Jerry Hausman & Whitney Newey, 2006. "Estimation with many instrumental variables," CeMMAP working papers CWP19/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
    9. Moreira, Marcelo J. & Porter, Jack R. & Suarez, Gustavo A., 2009. "Bootstrap validity for the score test when instruments may be weak," Journal of Econometrics, Elsevier, vol. 149(1), pages 52-64, April.
    10. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    11. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
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