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

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  • Wenjie Wang

    (Graduate School of Economics, Kyoto University)

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:kyo:wpaper:810
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP810.pdf
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    References listed on IDEAS

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    1. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    2. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    3. 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.
    4. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap inference in a linear equation estimated by instrumental variables," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 443-477, November.
    5. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    6. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    7. Anatolyev, Stanislav & Gospodinov, Nikolay, 2011. "Specification Testing In Models With Many Instruments," Econometric Theory, Cambridge University Press, vol. 27(02), pages 427-441, April.
    8. 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.
    9. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
    10. 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.
    11. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
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