IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/9804001.html
   My bibliography  Save this paper

Benchmark Priors for Bayesian Model Averaging

Author

Listed:
  • Carmen Fernandez

    (University of Saint Andrews, UK)

  • Eduardo Ley

    (IMF, Washington DC)

  • Mark F.J. Steel

    (University of Kent at Canterbury, UK)

Abstract

In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, "diffuse'' priors on model-specific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective prior information. We aim at providing an ``automatic'' or ``benchmark'' prior structure that can be used in such cases. We focus on the Normal linear regression model with uncertainty in the choice of regressors. We propose a partly noninformative prior structure related to a Natural Conjugate $g$-prior specification, where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter $g_{0j}$. The consequences of different choices for $g_{0j}$ are examined. We investigate theoretical properties, such as consistency of the implied Bayesian procedure. Links with classical information criteria are provided. More importantly, we examine the finite sample implications of several choices of $g_{0j}$ in a simulation study. The use of the MC$^3$ algorithm of Madigan and York (1995), combined with efficient coding in Fortran, makes it feasible to conduct large simulations. In addition to posterior criteria, we shall also compare the predictive performance of different priors. A classic example concerning the economics of crime will also be provided and contrasted with results in the literature. The main findings of the paper will lead us to propose a "benchmark'' prior specification in a linear regression context with model uncertainty.

Suggested Citation

  • Carmen Fernandez & Eduardo Ley & Mark F.J. Steel, 1998. "Benchmark Priors for Bayesian Model Averaging," Econometrics 9804001, EconWPA, revised 08 Oct 2001.
  • Handle: RePEc:wpa:wuwpem:9804001
    Note: Type of Document - PDF; pages: 30 ; figures: included. Published in the Journal of Econometrics,100:2 (February), pages 381-427, 2001.
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/9804/9804001.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters,in: Essays in the Economics of Crime and Punishment, pages 1-54 National Bureau of Economic Research, Inc.
    2. Chib, S. & Osiewalski, J. & Steel, M.F.J., 1990. "Regression models under competing covariance matrices : A Bayesian perspective," Discussion Paper 1990-63, Tilburg University, Center for Economic Research.
    3. Akaike, Hirotugu, 1981. "Likelihood of a model and information criteria," Journal of Econometrics, Elsevier, vol. 16(1), pages 3-14, May.
    4. Richard, J. F. & Steel, M. F. J., 1988. "Bayesian analysis of systems of seemingly unrelated regression equations under a recursive extended natural conjugate prior density," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 7-37.
    5. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    6. Phillips, Peter C. B., 1995. "Bayesian model selection and prediction with empirical applications," Journal of Econometrics, Elsevier, vol. 69(1), pages 289-331, September.
    7. Hoeting, Jennifer & Raftery, Adrian E. & Madigan, David, 1996. "A method for simultaneous variable selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 251-270, July.
    8. Ehrlich, Isaac, 1975. "The Deterrent Effect of Capital Punishment: A Question of Life and Death," American Economic Review, American Economic Association, vol. 65(3), pages 397-417, June.
    9. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
    10. Poirier, Dale J, 1988. "Frequentist and Subjectivist Perspectives on the Problems of Model Building in Economics," Journal of Economic Perspectives, American Economic Association, vol. 2(1), pages 121-144, Winter.
    11. Luc Bauwens, 1991. "The 'pathologie' of the Natural Conjugate Prior Density in the Regression Model," Annals of Economics and Statistics, GENES, issue 23, pages 49-64.
    12. Cornwell, Christopher & Trumbull, William N, 1994. "Estimating the Economic Model of Crime with Panel Data," The Review of Economics and Statistics, MIT Press, vol. 76(2), pages 360-366, May.
    13. repec:adr:anecst:y:1993:i:32:p:04 is not listed on IDEAS
    14. Atkinson, A. C., 1981. "Likelihood ratios, posterior odds and information criteria," Journal of Econometrics, Elsevier, vol. 16(1), pages 15-20, May.
    15. Ehrlich, Isaac, 1973. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 521-565, May-June.
    16. Chow, Gregory C., 1981. "A comparison of the information and posterior probability criteria for model selection," Journal of Econometrics, Elsevier, vol. 16(1), pages 21-33, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Bayes Factors; Markov chain Monte Carlo; Posterior odds; Prior elicitation;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpem:9804001. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: http://econwpa.repec.org .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.