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On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity

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  • Wang, Wenjie
  • Doko Tchatoka, Firmin

Abstract

We focus on the linear instrumental variable model with two endogenous regressors under conditional homoskedasticity, and study the subset Anderson and Rubin (1949, AR) test when the nuisance structural parameter, the unrestricted slope coefficient of endogenous regressor, may be weakly identified. Weak identification leads to nonstandard null limiting distributions, and alternative to the usual chi-squared critical value is needed. We first investigate the bootstrap validity for the subset AR test based on various plug-in estimators, and show that the bootstrap provides asymptotic refinement when the nuisance structural parameter is strongly identified, but is inconsistent when it is weakly identified. This is in contrast to the result of bootstrap validity in Moreira et al. (2009). Then, we propose a Bonferroni-based size-correction method that yields correct asymptotic size for all the test statistics considered. The power performance of size-corrected tests can be further improved by applying the mapping between structural and endogenous parameters in the model. Monte Carlo experiments confirm the bootstrap inconsistency and demonstrate that all the subset tests based on our correction technique control the size.

Suggested Citation

  • Wang, Wenjie & Doko Tchatoka, Firmin, 2018. "On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity," Journal of Econometrics, Elsevier, vol. 207(1), pages 188-211.
  • Handle: RePEc:eee:econom:v:207:y:2018:i:1:p:188-211
    DOI: 10.1016/j.jeconom.2018.07.003
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    Cited by:

    1. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Size-corrected Bootstrap Test after Pretesting for Exogeneity with Heteroskedastic or Clustered Data," MPRA Paper 110899, University Library of Munich, Germany.
    2. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Apr 2022.
    3. Prosper Dovonon & Firmin Doko Tchatoka & Michael Aguessy, 2019. "Relevant moment selection under mixed identification strength," School of Economics Working Papers 2019-04, University of Adelaide, School of Economics.
    4. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Uniform Inference after Pretesting for Exogeneity with Heteroskedastic Data," MPRA Paper 106408, University Library of Munich, Germany.
    5. Doko Tchatoka, Firmin & Wang, Wenjie, 2020. "Uniform Inference after Pretesting for Exogeneity," MPRA Paper 99243, University Library of Munich, Germany.
    6. Wang, Wenjie, 2020. "On the inconsistency of nonparametric bootstraps for the subvector Anderson–Rubin test," Economics Letters, Elsevier, vol. 191(C).
    7. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    8. 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

    Subvector inference; Linear IV model; Anderson–Rubin test; Plug-in estimator; Weak identification; Bootstrap inconsistency; Edgeworth expansion; Asymptotic size; Bonferroni-based size-correction;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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