IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20000035.html
   My bibliography  Save this paper

The Bayesian Score Statistic

Author

Listed:
  • Frank Kleibergen

    (University of Amsterdam)

  • Richard Kleijn

    (Erasmus University Rotterdam)

  • Richard Paap

    (Erasmus University Rotterdam)

Abstract

We propose a novel Bayesian test under a (noninformative) Jeffreys'priorspecification. We check whether the fixed scalar value of the so-calledBayesian Score Statistic (BSS) under the null hypothesis is aplausiblerealization from its known and standardized distribution under thealternative. Unlike highest posterior density regions the BSS isinvariantto reparameterizations. The BSS equals the posterior expectation oftheclassical score statistic and it provides an exact test procedure,whereasclassical tests often rely on asymptotic results. Since the statisticisevaluated under the null hypothesis it provides the Bayesiancounterpart ofdiagnostic checking. This result extends the similarity of classicalsampling densities of maximum likelihood estimators and Bayesianposteriordistributions based on Jeffreys' priors, towards score statistics. Weillustrate the BSS as a diagnostic to test for misspecification inlinearand cointegration models.

Suggested Citation

  • Frank Kleibergen & Richard Kleijn & Richard Paap, 2000. "The Bayesian Score Statistic," Tinbergen Institute Discussion Papers 00-035/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20000035
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/00035.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
    2. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
    3. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
    4. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, December.
    5. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    6. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
    7. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    8. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
    9. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
    10. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Division of Economics, School of Business, University of Leicester.
    2. Kleibergen, Frank, 2004. "Invariant Bayesian inference in regression models that is robust against the Jeffreys-Lindley's paradox," Journal of Econometrics, Elsevier, vol. 123(2), pages 227-258, December.
    3. van Dijk, H.K., 2002. "On Bayesian structural inference in a simultaneous equation model," Econometric Institute Research Papers EI 2002-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Rodney Strachan & Herman K. van Dijk, "undated". "Bayesian Model Averaging in Vector Autoregressive Processes with an Investigation of Stability of the US Great Ratios and Risk of a Liquidity Trap in the USA, UK and Japan," MRG Discussion Paper Series 1407, School of Economics, University of Queensland, Australia.
    5. David Ardia & Lukasz T. Gatarek & Lennart Hoogerheide & Herman K. Van Dijk, 2016. "Return and Risk of Pairs Trading Using a Simulation-Based Bayesian Procedure for Predicting Stable Ratios of Stock Prices," Econometrics, MDPI, vol. 4(1), pages 1-19, March.
    6. Warne, Anders, 2006. "Bayesian inference in cointegrated VAR models: with applications to the demand for euro area M3," Working Paper Series 692, European Central Bank.
    7. Kleibergen, F., 1996. "Reduced Rank of Regression Using Generalized Method of Moments Estimators," Other publications TiSEM 5caf1c0c-d988-4184-acf7-d, Tilburg University, School of Economics and Management.
    8. Urbain, Jean-Pierre, 1995. "Partial versus full system modelling of cointegrated systems an empirical illustration," Journal of Econometrics, Elsevier, vol. 69(1), pages 177-210, September.
    9. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    10. Hoogerheide, Lennart & Kleibergen, Frank & van Dijk, Herman K., 2007. "Natural conjugate priors for the instrumental variables regression model applied to the Angrist-Krueger data," Journal of Econometrics, Elsevier, vol. 138(1), pages 63-103, May.
    11. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
    12. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
    13. Onur Ozsoy, 2008. "Defence Spending And The Macroeconomy: The Case Of Turkey," Defence and Peace Economics, Taylor & Francis Journals, vol. 19(3), pages 195-208.
    14. Chew Lian Chua & Sarantis Tsiaplias, 2014. "A Bayesian Approach to Modelling Bivariate Time-Varying Cointegration and Cointegrating Rank," Melbourne Institute Working Paper Series wp2014n27, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    15. Chuanming Gao & Kajal Lahiri, 2000. "A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments," Econometric Society World Congress 2000 Contributed Papers 0230, Econometric Society.
    16. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
    17. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics.
    18. Richard Kleijn, 2000. "Bayesian Testing in Cointegration Models using the Jeffreys' Prior," Econometric Society World Congress 2000 Contributed Papers 1445, Econometric Society.
    19. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911.
    20. de Pooter, M.D. & Ravazzolo, F. & Segers, R. & van Dijk, H.K., 2008. "Bayesian near-boundary analysis in basic macroeconomic time series models," Econometric Institute Research Papers EI 2008-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20000035. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.