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Exogeneity tests, weak identification, incomplete models and non-Gaussian distributions: Invariance and finite-sample distributional theory

Author

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  • Firmin Doko Tchatoka

    (School of Economics, University of Adelaide)

  • Jean-Marie Dufour

    (McGill University)

Abstract

We study the distribution of Durbin-Wu-Hausman (DWH) tests for exogeneity from a finite-sample viewpoint, under the null and alternative hypotheses. We consider linear structural models with possibly non-Gaussian errors, where structural parameters may not be identified and where reduced forms can be incompletely specified (or nonparametric). On level control, we characterize the null distributions of all the test statistics. Through conditioning and invariance arguments, we show that these distributions do not involve nuisance parameters. In particular, this applies to several test statistics for which no finite-sample distributional theory is yet available, such as the standard statistic proposed by Hausman (1978). The distributions of the test statistics may be non-standard – so corrections to usual asymptotic critical values are needed – but the characterizations are sufficiently explicit to yield finite-sample (Monte-Carlo) tests of the exogeneity hypothesis. The procedures so obtained are robust to weak identification, missing instruments or misspecified reduced forms, and can easily be adapted to allow for parametric non-Gaussian error distributions. We give a general invariance result (block triangular invariance) for exogeneity test statistics. This property yields a convenient exogeneity canonical form and a parsimonious reduction of the parameters on which power depends. In the extreme case where no structural parameter is identified, the distributions under the alternative hypothesis and the null hypothesis are identical, so the power function is flat, for all the exogeneity statistics. However, as soon as identification does not fail completely, this phenomenon typically disappears. We present simulation evidence which confirms the finite-sample theory. The theoretical results are illustrated with two empirical examples: the relation between trade and economic growth, and the widely studied problem of the return of education to earnings.

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  • 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 and Public Policy Working Papers 2016-01, University of Adelaide, School of Economics and Public Policy.
    • Handle: RePEc:adl:wpaper:2016-01
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    3. Firmin Doko Tchatoka & Lauren Slinger & Virginie Masson, 2020. "Revisiting empirical studies on the liquidity effect: An identication-robust approach," School of Economics and Public Policy Working Papers 2020-02, University of Adelaide, School of Economics and Public Policy.

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    More about this item

    Keywords

    Exogeneity; Durbin-Wu-Hausman test; weak instrument; incomplete model; non-Gaussian; weak identification; identification robust; finite-sample theory; pivotal; invariance; Monte Carlo test; power;
    All these keywords.

    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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