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Uniform Inference after Pretesting for Exogeneity with Heteroskedastic Data

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  • Doko Tchatoka, Firmin
  • Wang, Wenjie

Abstract

Pretesting for exogeneity has become a routine in many empirical applications involving instrumental variables (IVs) to decide whether the ordinary least squares (OLS) or the two-stage least squares (2SLS) method is appropriate. Guggenberger (2010) shows that the second-stage t-test – based on the outcome of a Durbin-Wu-Hausman type pretest for exogeneity in the first-stage – has extreme size distortion with asymptotic size equal to 1 when the standard asymptotic critical values are used. In this paper, we first show that the standard wild bootstrap procedures (with either independent or dependent draws of disturbances) are not viable solutions to such extreme size-distortion problem. Then, we propose a novel hybrid bootstrap approach, which combines the residual-based bootstrap along with an adjusted Bonferroni size-correction method. We establish uniform validity of this hybrid bootstrap under conditional heteroskedasticity in the sense that it yields a two-stage test with correct asymptotic size. Monte Carlo simulations confirm our theoretical findings. In particular, our proposed hybrid method achieves remarkable power gains over the 2SLS-based t-test, especially when IVs are not very strong.

Suggested Citation

  • Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Uniform Inference after Pretesting for Exogeneity with Heteroskedastic Data," MPRA Paper 106408, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:106408
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    More about this item

    Keywords

    DWH Pretest; Instrumental Variable; Asymptotic Size; Bootstrap; Bonferroni-based Size-correction; Uniform Inference.;
    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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