Benchmark priors for Bayesian model averaging

Citation
C. Fernandez et al., Benchmark priors for Bayesian model averaging, J ECONOMET, 100(2), 2001, pp. 381-427
Citations number
64
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Economics
Journal title
JOURNAL OF ECONOMETRICS
ISSN journal
0304-4076 → ACNP
Volume
100
Issue
2
Year of publication
2001
Pages
381 - 427
Database
ISI
SICI code
0304-4076(200102)100:2<381:BPFBMA>2.0.ZU;2-R
Abstract
In contrast to a posterior analysis given a particular sampling model, post erior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, 'diffus e' priors on model-specific parameters can lead to quite unexpected consequ ences. 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 'automat ic' 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 re gressors. We propose a partly non-informative prior structure related to a natural conjugate g-prior specification, where the amount of subjective inf ormation requested from the user is limited to the choice of a single scala r hyperparameter g(0j). The consequences of different choices for g(0j) are examined, We investigate theoretical properties, such as consistency of th e implied Bayesian procedure. Links with classical information criteria are provided. More importantly, we examine the finite sample implications of s everal choices of g(0j) in a simulation study. The use of the MC3 algorithm of Madigan and York (Int. Stat. Rev. 63 (1995) 215), combined with efficie nt coding in Fortran, makes it feasible to conduct large simulations. In ad dition to posterior criteria, we shall also compare the predictive performa nce of different priors. A classic example concerning the economics of crim e 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 spec ification in a linear regression context with model uncertainty. (C) 2001 E lsevier Science S.A. All rights reserved. JEL classification: C11; C15.