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Specification Tests with Weak and Invalid Instruments

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  • Firmin Doko Tchatoka

    (School of Economics, University of Adelaide)

Abstract

We focus on the classical linear simultaneous equations models and study the sensitivity to instrument endogeneity of six alternative versions of Durbin-Wu-Hausman (DWH) tests of exogeneity. To address this issue, we consider two setups for instrument endogeneity: (i) fixed instrument endogeneity, i.e., the parameter that controls instrument invalidity is fixed (does not depend on the sample size); (ii) local-to-zero instrument endogeneity, i.e., this parameter goes to zero at rate [n^1/2] as the sample size n increases [similar to Staiger and Stock (1997)]. In the first setup, we show that all tests have size converging to 1, as the sample size increases, no matter how weak the instruments are. In the second setup, we provide a characterization of the null limiting distribution of the statistics, which clearly shows that all statistics converge asymptotically to non-degenerated noncentral x^2 under the null hypothesis. This means that all tests have size greater than their nominal level asymptotically if the usual x^2 critical values are used, despite the fact that instrument endogeneity vanishes as the sample size increases. We propose size correction based on bootstrap techniques. Our analysis of the proposed bootstrap tests provides some new insights. More precisely, we show that even for moderate instrument endogeneity, the bootstrap provides a first-order approximation of the asymptotic size of the DWH tests, no matter how weak the instruments are. We present a Monte Carlo experiment that confirms our theoretical findings.

Suggested Citation

  • Firmin Doko Tchatoka, 2014. "Specification Tests with Weak and Invalid Instruments," School of Economics and Public Policy Working Papers 2014-05, University of Adelaide, School of Economics and Public Policy.
  • Handle: RePEc:adl:wpaper:2014-05
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    1. Firmin Doko Tchatoka & Jean‐Marie Dufour, 2014. "Identification‐robust inference for endogeneity parameters in linear structural models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 165-187, February.
    2. 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.
    3. Doko Tchatoka, Firmin, 2012. "On the validity of Durbin-Wu-Hausman tests for assessing partial exogeneity hypotheses with possibly weak instruments," Working Papers 15061, University of Tasmania, Tasmanian School of Business and Economics, revised 06 Jul 2012.

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    More about this item

    Keywords

    DWH tests; weak instruments; exclusion restrictions; instrument endogeneity; bootstrap.;
    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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