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Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression

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  • Tchatoka, Firmin Doko

Abstract

This paper explores the sensitivity of plug-in subset tests to instrument exclusion in structural models. Identification-robust statistics based on the plug-in principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. This paper proposes an analysis of the asymptotic distributions of the limited information maximum likelihood (LIML) estimator and plug-in statistics when potential instruments are omitted. Our results provide several new insights and extensions of earlier studies. We show that the exclusion of instruments can eliminate the first-stage, thus weakening identification and invalidating the plug-in subset inference. However, when instrument omission does not affect LIML consistency, it preserves the plug-in subset test validity, although LIML is no longer asymptotically efficient. Unlike the instrumental variable (IV) estimator, the LIML estimator of the identified linear combination of the nuisance parameter is not asymptotically a Gaussian mixture, even without instrument exclusion.

Suggested Citation

  • Tchatoka, Firmin Doko, 2015. "Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1192-1228, December.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:06:p:1192-1228_00
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    Cited by:

    1. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    2. Wang, Wenjie & Doko Tchatoka, Firmin, 2018. "On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity," Journal of Econometrics, Elsevier, vol. 207(1), pages 188-211.
    3. Firmin Doko Tchatoka & Wenjie Wang, 2015. "On Bootstrap Validity for Subset Anderson-Rubin Test in IV Regressions," School of Economics and Public Policy Working Papers 2015-01, University of Adelaide, School of Economics and Public Policy.
    4. 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.
    5. 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.
    6. Doko Tchatoka, Firmin, 2011. "Testing for partial exogeneity with weak identification," MPRA Paper 39504, University Library of Munich, Germany, revised Mar 2012.
    7. Firmin Doko Tchatoka, 2015. "On bootstrap validity for specification tests with weak instruments," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 137-146, February.
    8. 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).
    9. 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.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • 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
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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