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Bartlett Identities Tests

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  • Andrew Chesher

    (Crest)

  • Geert Dhaene

    (Crest)

  • Christian Gourieroux

    (Crest)

  • Olivier Scaillet

    (Crest)

Abstract

In this note we propose a general testing procedure for parametric models based on Bartlett Identities. A well-known example is the Information Matrix test, which is based on the Bartlett Identity of order 1. The Identities are shown to induce a sequenceof testable restrictions on the data generating process. When all the restrictions are considered jointly, they are often complete, in the sense that they are satisfied if and only if the model is correctly specified. We show that this is the case for normal, exponential and Poisson models. A test of the joint validity of an arbitrarily chosen subset of restrictions is proposed, and its first order asymptotic properties are presented. An interpretation of the test as a score test for neglected parameter heterogeneity is also given.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 99-32.

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Date of creation: 1999
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Handle: RePEc:crs:wpaper:99-32

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References

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  1. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Universite de Montreal, Departement de sciences economiques.
  2. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  3. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
  4. Gourieroux, Christian & Jasiak, Joanna, 1999. "Nonlinear innovations and impulse responses," CEPREMAP Working Papers (Couverture Orange) 9906, CEPREMAP.
  5. Takesi Hayakawa, 1977. "The likelihood ratio criterion and the asymptotic expansion of its distribution," Annals of the Institute of Statistical Mathematics, Springer, vol. 29(1), pages 359-378, December.
  6. Andrew Chesher & Richard J. Smith, 1997. "Likelihood Ratio Specification Tests," Econometrica, Econometric Society, vol. 65(3), pages 627-646, May.
  7. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
  8. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
  9. Jean-Marie Dufour, 2005. "Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and non-standard asymptotics," CIRANO Working Papers 2005s-02, CIRANO.
  10. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-53, July.
  11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  12. Gourieroux, C. & Monfort, A., 1986. "Testing non-nested hypotheses," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 44, pages 2583-2637 Elsevier.
  13. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1983. "Testing nested or non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 21(1), pages 83-115, January.
  14. Chesher, Andrew & Dumangane, Montezuma & Smith, Richard J., 2002. "Duration response measurement error," Journal of Econometrics, Elsevier, vol. 111(2), pages 169-194, December.
  15. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  16. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-72, July.
  17. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & GARDIOL, Lucien, 1998. "Simulation-Based Finite-Sample Normality Tests in Linear Regressions," Cahiers de recherche 9811, Universite de Montreal, Departement de sciences economiques.
  18. Geert Dhaene & Christian Gourieroux & Olivier Scaillet, 1998. "Instrumental Models and Indirect Encompassing," Econometrica, Econometric Society, vol. 66(3), pages 673-688, May.
  19. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-78, May.
  20. Gurmu, Shiferaw, 1991. "Tests for Detecting Overdispersion in the Positive Poisson Regression Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 215-22, April.
  21. Breusch, T.S. & Pagan, A.R., . "The Lagrange multiplier test and its applications to model specification in econometrics," CORE Discussion Papers RP -412, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
  1. Fernandes, Marcelo & Grammig, Joachim, 2003. "Nonparametric specification tests for conditional duration models," Economics Working Papers (Ensaios Economicos da EPGE) 502, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  2. Bontemps, Christian & Meddahi, Nour, 2007. "Testing Distributional Assumptions: A GMM Approach," IDEI Working Papers 486, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. J.L. Prigent & O. Renault & O. Scaillet., 1999. "Option pricing with discrete rebalancing," THEMA Working Papers 99-41, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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