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On Bootstrap Validity for Specification Tests with Weak Instruments

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  • Firmin Doko Tchatoka

    () (School of Economics, University of Adelaide)

Abstract

We investigate the asymptotic validity of the bootstrap for Durbin-Wu-Hausman (DWH) tests of exogeneity in linear IV regressions, with or without identification. Our analysis of the properties (size and power) of the proposed bootstrap tests provides some new insights and extensions of earlier studies. More precisely, we show that when identification is strong, the bootstrap: (1) provides an asymptotic refinement of the size of the DWH tests under exogeneity, and (2) is consistent under the alternative hypothesis if the endogeneity parameter is fixed. However, the bootstrap only provides a first-order approximation of the asymptotic distributions of these statistics when instruments are weak. Moreover, we characterize the necessary and sufficient condition under which the proposed bootstrap DWH tests exhibit power under fixed endogeneity and weak instruments. The latter condition may still hold over a wide range of cases, provided that at least one instrument is not irrelevant. But all bootstrap tests have low power when all instruments are irrelevant, a case of little interest in empirical work. We present a Monte Carlo experiment that confirms our theoretical findings.

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  • Firmin Doko Tchatoka, 2014. "On Bootstrap Validity for Specification Tests with Weak Instruments," School of Economics Working Papers 2014-06, University of Adelaide, School of Economics.
  • Handle: RePEc:adl:wpaper:2014-06
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    File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2014-06.pdf
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    Cited by:

    1. Firmin DOKO TCHATOKA & Jean-Marie DUFOUR, 2016. "Exogeneity Tests, Incomplete Models, Weak Identification and Non-Gaussian Distributions : Invariance and Finite-Sample Distributional Theory," Cahiers de recherche 14-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Kiviet, Jan F. & Pleus, Milan, 2017. "The performance of tests on endogeneity of subsets of explanatory variables scanned by simulation," Econometrics and Statistics, Elsevier, vol. 2(C), pages 1-21.
    3. Firmin Doko Tchatoka & Jean-Marie Dufour, 2016. "Exogeneity tests, weak identification, incomplete models and non-Gaussian distributions: Invariance and finite-sample distributional theory," School of Economics Working Papers 2016-01, University of Adelaide, School of Economics.
    4. Doko Tchatoka, Firmin, 2012. "Specification tests with weak and invalid instruments," Working Papers 15063, University of Tasmania, Tasmanian School of Business and Economics, revised 26 Jun 2012.
    5. Firmin Doko Tchatoka & Wenjie Wang, 2015. "On Bootstrap Validity for Subset Anderson-Rubin Test in IV Regressions," School of Economics Working Papers 2015-01, University of Adelaide, School of Economics.

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    Keywords

    Exogeneity testing; Durbin-Wu-Hausman tests; weak instruments; bootstrap validity; asymptotic refinement.;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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