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. In addition, 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.

SUMMARYWe investigate the issue of model uncertainty in cross-country growth regressions using Bayesian Model Averaging (BMA). We find that the posterior probability is spread widely among many models, suggesting the superiority of BMA over choosing any single model. Out-of-sample predictive results support this claim. In contrast to Levine and Renelt (1992), our results broadly support the more 'optimistic' conclusion of Salai-Martin (1997b), namely that some variables are important regressors for explaining cross-country growth patterns. However, care should be taken in the methodology employed. The approach proposed here is firmly grounded in statistical theory and immediately leads to posterior and predictive inference.

Abstract. We consider the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. We examine the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors and on predictive performance. We illustrate these issues in the context of cross-country growth regressions using three datasets with 41 to 67 potential drivers of growth and 72 to 93 observations. Finally, we recommend priors for use in this and related contexts.

Abstract. We consider the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. We examine the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors and on predictive performance. We illustrate these issues in the context of cross-country growth regressions using three datasets with 41 to 67 potential drivers of growth and 72 to 93 observations. Finally, we recommend priors for use in this and related contexts.

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