On the half-Cauchy prior for a global scale parameter

This paper argues that the half-Cauchy distribution should replace the inverse-Gamma distribution as a default prior for a top-level scale parameter in Bayesian hierarchical models, at least for cases where a proper prior is necessary. Our arguments involve a blend of Bayesian and frequentist reasoning, and are intended to complement the original case made by Gelman (2006) in support of the folded-t family of priors. First, we generalize the half-Cauchy prior to the wider class of hypergeometric inverted-beta priors. We derive expressions for posterior moments and marginal densities when these priors are used for a top-level normal variance in a Bayesian hierarchical model. We go on to prove a proposition that, together with the results for moments and marginals, allows us to characterize the frequentist risk of the Bayes estimators under all global-shrinkage priors in the class. These theoretical results, in turn, allow us to study the frequentist properties of the half-Cauchy prior versus a wide class of alternatives. The half-Cauchy occupies a sensible 'middle ground' within this class: it performs very well near the origin, but does not lead to drastic compromises in other parts of the parameter space. This provides an alternative, classical justification for the repeated, routine use of this prior. We also consider situations where the underlying mean vector is sparse, where we argue that the usual conjugate choice of an inverse-gamma prior is particularly inappropriate, and can lead to highly distorted posterior inferences. Finally, we briefly summarize some open issues in the specification of default priors for scale terms in hierarchical models

Econometric Modelling at the Bank of Greece

At the Bank of Greece econometric modelling started in 1975 when the Bank’s first model of the Greek economy was developed under the leadership of the now Governor of the Bank Nicholas C. Garganas. The model was extensively used for many years in forecasting as well as in policy analysis and proved to be an indispensable tool for the policy decisions of the Bank over a broad spectrum of issues. Model development at the Bank of Greece is an ongoing activity fuelled by the changes in the economy as well as by modelling theoretical advances. This paper describes and documents the use as well as the properties (through a set of standard simulation results) of the current version of the Bank of Greece model.Econometric Modelling; Cointegration Techniques; Simulation Results