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Uniform Inference after Pretesting for Exogeneity

Author

Listed:
  • Firmin Doko Tchatoka

    (School of Economics, University of Adelaide)

  • Wenjie Wang

    (Division of Economics, School of Social Sciences, Nanyang Technological University)

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 residual 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 in the sense that it yields a two-stage test with correct asymptotic size. Monte Carlo simulations confirm ourtheoretical 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

  • Firmin Doko Tchatoka & Wenjie Wang, 2020. "Uniform Inference after Pretesting for Exogeneity," School of Economics and Public Policy Working Papers 2020-05, University of Adelaide, School of Economics and Public Policy.
  • Handle: RePEc:adl:wpaper:2020-05
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    References listed on IDEAS

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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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