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On bootstrap validity for specification testing with many weak instruments

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  • Kaffo, Maximilien
  • Wang, Wenjie

Abstract

This paper studies the asymptotic validity of bootstrapping the J test of over-identifying restrictions and the Anderson–Rubin (AR) test under many/many weak instrument sequences. We show that the (residual-based) bootstrap consistently estimates the limiting distributions of interest under these asymptotic frameworks. Interestingly, such bootstrap validity holds even if the bootstrap cannot mimic well certain important properties in the model. In addition, the studied bootstrap procedures are easy to implement in practice because they do not require an a priori choice between the conventional asymptotics and the many/many weak instrument asymptotics. Monte Carlo simulation shows that the bootstrap techniques provide a more reliable method to approximate the null distribution of the J and AR test statistics under many/many weak instruments.

Suggested Citation

  • Kaffo, Maximilien & Wang, Wenjie, 2017. "On bootstrap validity for specification testing with many weak instruments," Economics Letters, Elsevier, vol. 157(C), pages 107-111.
    • Handle: RePEc:eee:ecolet:v:157:y:2017:i:c:p:107-111
    DOI: 10.1016/j.econlet.2017.06.004
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    References listed on IDEAS

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    1. Anatolyev, Stanislav & Gospodinov, Nikolay, 2011. "Specification Testing In Models With Many Instruments," Econometric Theory, Cambridge University Press, vol. 27(2), pages 427-441, April.
    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. 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.
    4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    5. 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.
    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. 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.
    8. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    9. Anatolyev, Stanislav & Yaskov, Pavel, 2017. "Asymptotics Of Diagonal Elements Of Projection Matrices Under Many Instruments/Regressors," Econometric Theory, Cambridge University Press, vol. 33(3), pages 717-738, June.
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    Cited by:

    1. Wang, Wenjie, 2021. "Bootstrap Inference for Partially Linear Model with Many Regressors," MPRA Paper 106391, University Library of Munich, Germany.
    2. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    3. Wang, Wenjie, 2022. "Wild bootstrap test of overidentification with many instruments and heteroskedasticity," MPRA Paper 115168, University Library of Munich, Germany.
    4. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    5. Wenjie Wang & Yichong Zhang, 2024. "Gradient Wild Bootstrap for Instrumental Variable Quantile Regressions with Weak and Few Clusters," Papers 2408.10686, arXiv.org.
    6. Max-Sebastian Dovì & Anders Bredahl Kock & Sophocles Mavroeidis, 2024. "A Ridge-Regularized Jackknifed Anderson-Rubin Test," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1083-1094, July.
    7. Wang, Wenjie, 2020. "On Bootstrap Validity for the Test of Overidentifying Restrictions with Many Instruments and Heteroskedasticity," MPRA Paper 104858, University Library of Munich, Germany.

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    More about this item

    Keywords

    Bootstrap; J test; Anderson–Rubin test; Many instruments; Weak instruments;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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