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Benchmark Priors for Bayesian Model Averaging

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Author Info

  • 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.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9804001.

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Length: 30 pages
Date of creation: 02 Apr 1998
Date of revision: 31 Jul 1999
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.
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Web page: http://128.118.178.162

Related research

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

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References

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  1. Peter C.B. Phillips, 1992. "Bayesian Model Selection and Prediction with Empirical Applications," Cowles Foundation Discussion Papers 1023, Cowles Foundation for Research in Economics, Yale University.
  2. BAUWENS, Luc, . "The "pathology" of the natural conjugate prior density in the regression model," CORE Discussion Papers RP -962, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. 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.
  4. 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.
  5. Gary S. Becker, 1968. "Crime and Punishment: An Economic Approach," Journal of Political Economy, University of Chicago Press, vol. 76, pages 169.
  6. 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.
  7. Jacek OSIEWALSKI & Mark F.J. STEEL, 1993. "Regression Models under Competing Covariance Structures: A Bayesian Perspective," Annales d'Economie et de Statistique, ENSAE, issue 32, pages 65-79.
  8. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
  9. Min, C.K. & Zellner, A., 1992. ""Bayesian and Non-Bayesian Methods for Combining Models and Forecasts with Applications to Forecasting International Growth Rates"," Papers 90-92-23, California Irvine - School of Social Sciences.
  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 121-44, Winter.
  11. Akaike, Hirotugu, 1981. "Likelihood of a model and information criteria," Journal of Econometrics, Elsevier, vol. 16(1), pages 3-14, May.
  12. Ehrlich, Isaac, 1973. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 521-65, May-June.
  13. Atkinson, A. C., 1981. "Likelihood ratios, posterior odds and information criteria," Journal of Econometrics, Elsevier, vol. 16(1), pages 15-20, May.
  14. 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 360-66, May.
  15. 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.
  16. 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.
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