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Residual bootstrap tests in linear models with many regressors

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  • Richard, Patrick

Abstract

This paper is concerned with bootstrap hypothesis testing in linear regression models with many regressors. I show that bootstrap F, LR and LM tests are asymptotically valid even when the numbers of estimated parameters and tested restrictions are not asymptotically negligible fractions of the sample size. One of the conditions for these results is that the regressors come from an asymptotically balanced design. Depending on the number of restrictions tested and on the errors’ distribution, violation of that condition might render the bootstrap tests asymptotically invalid. In that case, I propose bootstrapping Calhoun’s (2011) G statistic or modified versions of the LR and LM statistics, and show that these procedures remain asymptotically valid.

Suggested Citation

  • Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.
    • Handle: RePEc:eee:econom:v:208:y:2019:i:2:p:367-394
    DOI: 10.1016/j.jeconom.2018.10.002
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    More about this item

    Keywords

    Bootstrap; Linear regressions; Many restrictions; Asymptotic refinements;
    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

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