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Asymptotically Optimal Tests Using Limited Information and Testing for Exogeneity

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  • Smith, Richard J.

Abstract

By appropriately partitioning the joint hypothesis of weak exogeneity and the maintained overidentifying restrictions in the linear dynamic simultaneous equations model and showing that the component subhypotheses are separable, asymptotically optimal tests for the weak exogeneity hypothesis may be constructed using limited information statistics. A necessary and sufficient condition for the separability of parametric hypotheses of the mixed implicit function and constraint equation type is derived which generalizes conditions previously obtained in the literature. Consequently, limited and full information procedures for testing the weak exogeneity hypothesis are asymptotically equivalent. The impact of these results for testing strong exogeneity in the linear dynamic simultaneous equations model is also explored.

Suggested Citation

  • Smith, Richard J., 1994. "Asymptotically Optimal Tests Using Limited Information and Testing for Exogeneity," Econometric Theory, Cambridge University Press, vol. 10(1), pages 53-69, March.
    • Handle: RePEc:cup:etheor:v:10:y:1994:i:01:p:53-69_00
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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. H. Peter Boswijk & Jean-Pierre Urbain, 1997. "Lagrance-multiplier tersts for weak exogeneity: a synthesis," Econometric Reviews, Taylor & Francis Journals, vol. 16(1), pages 21-38.
    3. Parente, Paulo M.D.C. & Smith, Richard J., 2017. "Tests of additional conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 200(1), pages 1-16.
    4. Paulo Parente & Richard Smith, 2012. "Exogeneity in semiparametric moment condition models," CeMMAP working papers 30/12, Institute for Fiscal Studies.
    5. 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.
    6. 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.

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