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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. 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.
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    4. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
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    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, 2022. "Wild bootstrap test of overidentification with many instruments and heteroskedasticity," MPRA Paper 115168, University Library of Munich, Germany.
    3. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    4. Max-Sebastian Dov`i & Anders Bredahl Kock & Sophocles Mavroeidis, 2022. "A Ridge-Regularised Jackknifed Anderson-Rubin Test," Papers 2209.03259, arXiv.org, revised Nov 2023.
    5. 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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