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Higher order properties of the wild bootstrap under misspecification

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  • Kline, Patrick
  • Santos, Andres

Abstract

We examine the higher order properties of the wild bootstrap (Wu, 1986) in a linear regression model with stochastic regressors. We find that the ability of the wild bootstrap to provide a higher order refinement is contingent upon whether the errors are mean independent of the regressors or merely uncorrelated with them. In the latter case, the wild bootstrap may fail to match some of the terms in an Edgeworth expansion of the full sample test statistic. Nonetheless, we show that the wild bootstrap still has a lower maximal asymptotic risk as an estimator of the true distribution than a normal approximation, in shrinking neighborhoods of properly specified models. To assess the practical implications of this result we conduct a Monte Carlo study contrasting the performance of the wild bootstrap with a normal approximation and the traditional nonparametric bootstrap.

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  • Kline, Patrick & Santos, Andres, 2012. "Higher order properties of the wild bootstrap under misspecification," Journal of Econometrics, Elsevier, vol. 171(1), pages 54-70.
    • Handle: RePEc:eee:econom:v:171:y:2012:i:1:p:54-70
    DOI: 10.1016/j.jeconom.2012.06.001
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    2. Taisuke Otsu & Yoshiyasu Rai, 2017. "Bootstrap Inference of Matching Estimators for Average Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1720-1732, October.
    3. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    4. Richard, Patrick, 2017. "Robust heteroskedasticity-robust tests," Economics Letters, Elsevier, vol. 159(C), pages 28-32.
    5. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "Coverage Error Optimal Confidence Intervals for Local Polynomial Regression," Papers 1808.01398, arXiv.org, revised Jul 2021.
    6. Kline Patrick & Santos Andres, 2012. "A Score Based Approach to Wild Bootstrap Inference," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 23-41, August.
    7. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    8. Matias D Cattaneo & Michael Jansson & Xinwei Ma, 2019. "Two-Step Estimation and Inference with Possibly Many Included Covariates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1095-1122.
    9. Gonzalo Vazquez-Bare, 2017. "Identification and Estimation of Spillover Effects in Randomized Experiments," Papers 1711.02745, arXiv.org, revised Jan 2022.
    10. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    11. Lavergne, Pascal & Bertail, Patrice, 2020. "Bootstrapping Quasi Likelihood Ratio Tests under Misspecification," TSE Working Papers 20-1102, Toulouse School of Economics (TSE).
    12. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    13. Hershbein Brad J., 2012. "Graduating High School in a Recession: Work, Education, and Home Production," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-32, January.
    14. Spokoiny, Vladimir & Zhilova, Mayya, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers 2014-067, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

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    More about this item

    Keywords

    Wild bootstrap; Misspecification; Edgeworth expansion;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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