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A New Form of the Information Matrix Test


  • Russell Davidson
  • James G. MacKinnon


We develop a new form of the information matrix test for a wide variety of statistical models, and present full details for the special case of univariate nonlinear regression models. Chesher (1984) showed that the implicit alternative of the information matrix test is a model with random parameter variation. We exploit this fact by constructing the test against an explicit alternative of this type. The new test is computed using a double-length artificial regression, instead of the more conventional outer product of the gradient regression, which, although easy to use, is known to give test statistics with distributions very far from the asymptotic nominal distribution even in rather large samples. The new form on the other hand performs remarkably well, at least in the context of regression models. Some approximate finite-sample distributions are calculated and lend support to the use of the new form of the test.

Suggested Citation

  • Russell Davidson & James G. MacKinnon, 1988. "A New Form of the Information Matrix Test," Working Papers 724, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:724

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    References listed on IDEAS

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    Cited by:

    1. Chesher, Andrew & Dumangane, Montezuma & Smith, Richard J., 2002. "Duration response measurement error," Journal of Econometrics, Elsevier, vol. 111(2), pages 169-194, December.
    2. Stomberg, Christopher & White, Halbert, 2000. "Bootstrapping the Information Matrix Test," University of California at San Diego, Economics Working Paper Series qt158451cr, Department of Economics, UC San Diego.
    3. Teodosio Perez Amaral, 1994. "Una aplicación de los contrastes M y de la matriz de información dinámica: el caso de la demanda de dinero norteamericana 1960-1984," Investigaciones Economicas, Fundación SEPI, vol. 18(1), pages 193-201, January.
    4. Davidson, R. & MacKinnon & J.G., 1999. "Artificial Regressions," G.R.E.Q.A.M. 99a04, Universite Aix-Marseille III.
    5. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    6. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    7. Dhaene, Geert & Hoorelbeke, Dirk, 2004. "The information matrix test with bootstrap-based covariance matrix estimation," Economics Letters, Elsevier, vol. 82(3), pages 341-347, March.
    8. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    9. Francisco Cribari-Neto, 1996. "On the Corrections to Information Matrix Tests," Econometrics 9601001, EconWPA.
    10. Choi, Hwan-sik, 2016. "Information theory for maximum likelihood estimation of diffusion models," Journal of Econometrics, Elsevier, vol. 191(1), pages 110-128.
    11. Joachim Zietz, 2006. "Detecting neglected parameter heterogeneity with Chow tests," Applied Economics Letters, Taylor & Francis Journals, vol. 13(6), pages 369-374.
    12. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    13. Dirk Hoorelbeke, 2004. "Bootstrap correcting the score test," Econometric Society 2004 North American Summer Meetings 228, Econometric Society.
    14. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, Open Access Journal, vol. 4(4), pages 1-24, November.
    15. Kaiser, Ulrich & Spitz, Alexandra, 2000. "Quantification of qualitative data using ordered probit models with an application to a business survey in the German service sector," ZEW Discussion Papers 00-58, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.


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