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Exogeneity tests and weak identification in IV regressions: Asymptotic theory and point estimation

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  • Doko Tchatoka, Firmin
  • Dufour, Jean-Marie

Abstract

This paper provides new insights on exogeneity tests in linear IV models and their use for estimation, when identification fails or may not be strong. We make two main contributions. First, we show that Durbin–Wu–Hausman (DWH) and Revankar–Hartley (RH) exogeneity tests have correct level asymptotically, even when the first-stage coefficient matrix (which controls identification) is rank-deficient. We provide necessary and sufficient conditions under which these tests are consistent. In particular, we show that test consistency can hold even when identification fails, provided at least one component of the structural parameter vector is identifiable. Second, we study point estimation after estimator (or model) selection, when the outcome of a DWH/RH test determines whether OLS or an IV method is employed in the second-stage. For this purpose, we use (non-local) concepts of asymptotic bias, asymptotic mean squared error (AMSE), and asymptotic relative efficiency (ARE), which remain applicable even when the estimators considered do not have moments (as can happen for 2SLS) or may be inconsistent. We study the asymptotic properties of OLS, 2SLS, and pretest estimators which select OLS or 2SLS based on the outcome of a DWH/RH test. We show that: (i) OLS typically dominates 2SLS estimator asymptotically for MSE across a broad spectrum of cases, including weak identification and moderate endogeneity; (ii) exogeneity-pretest estimators exhibit consistently good performance and asymptotically dominate both OLS and 2SLS. The proposed theoretical findings are documented by Monte Carlo simulations.

Suggested Citation

  • Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2025. "Exogeneity tests and weak identification in IV regressions: Asymptotic theory and point estimation," Journal of Econometrics, Elsevier, vol. 248(C).
  • Handle: RePEc:eee:econom:v:248:y:2025:i:c:s0304407624001660
    DOI: 10.1016/j.jeconom.2024.105821
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    Keywords

    Exogeneity tests; Weak identification; Test consistency; Pretest estimators; Asymptotic MSE; Inference post-selection; Identification-robust procedure;
    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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