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Higher Order Properties of the Wild Bootstrap Under Misspecification


  • Patrick M. Kline
  • Andres Santos


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. 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, potentially leading to only a partial refinement (Liu and Singh, 1987). To assess the practical implications of this result, we conduct a Monte Carlo study contrasting the performance of the wild bootstrap with the traditional nonparametric bootstrap.

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  • Patrick M. Kline & Andres Santos, 2011. "Higher Order Properties of the Wild Bootstrap Under Misspecification," NBER Working Papers 16793, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:16793
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    Cited by:

    1. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2015. "Inference in Linear Regression Models with Many Covariates and Heteroskedasticity," Papers 1507.02493,, revised Jan 2017.
    2. Vladimir Spokoiny & Mayya Zhilova, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers SFB649DP2014-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. 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.
    4. repec:eee:ecolet:v:159:y:2017:i:c:p:28-32 is not listed on IDEAS
    5. Taisuke Otsu & Yoshiyasu Rai, 2015. "Bootstrap inference of matching estimators for average treatment effects," STICERD - Econometrics Paper Series /2015/580, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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    JEL classification:

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

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