This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. Default prior choices fixing Zellner's g are predominant in the Bayesian Model Averaging literature, but tend to concentrate posterior mass on a tiny set of models. The paper demonstrates this supermodel effect and proposes to address it by a hyper-g prior, whose data-dependent shrinkage adapts posterior model distributions to data quality. Analytically, existing work on the hyper-g-prior is complemented by posterior expressions essential to fully Bayesian analysis and to sound numerical implementation. A simulation experiment illustrates the implications for posterior inference. Furthermore, an application to determinants of economic growth identifies several covariates whose robustness differs considerably from previous results.

This article describes the BMS (Bayesian model sampling) package for R that implements Bayesian model averaging for linear regression models. The package excels in allowing for a variety of prior structures, among them the "binomial-beta" prior on the model space and the so-called "hyper-g" specifications for Zellner's g prior. Furthermore, the BMS package allows the user to specify her own model priors and offers a possibility of subjective inference by setting "prior inclusion probabilities" according to the researcher's beliefs. Furthermore, graphical analysis of results is provided by numerous built-in plot functions of posterior densities, predictive densities and graphical illustrations to compare results under different prior settings. Finally, the package provides full enumeration of the model space for small scale problems as well as two efficient MCMC (Markov chain Monte Carlo) samplers that sort through the model space when the number of potential covariates is large.

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Vector autoregressive (VAR) models are frequently used for forecasting and impulse response analysis. For both applications, shrinkage priors can help improving inference. In this paper we derive the shrinkage prior of Griffin et al. (2010) for the VAR case and its relevant conditional posterior distributions. This framework imposes a set of normally distributed priors on the autoregressive coefficients and the covariances of the VAR along with Gamma priors on a set of local and global prior scaling parameters. This prior setup is then generalized by introducing another layer of shrinkage with scaling parameters that push certain regions of the parameter space to zero. A simulation exercise shows that the proposed framework yields more precise estimates of the model parameters and impulse response functions. In addition, a forecasting exercise applied to US data shows that the proposed prior outperforms other specifications in terms of point and density predictions.

We use Bayesian Model Averaging (BMA) to evaluate the robustness of determinants of economic growth in a new dataset of 255 European regions in the 1995-2005 period. We use three different specifications based on (1) the cross-section of regions, (2) the cross-section of regions with country fixed effects and (3) the cross-section of regions with a spatial autoregressive (SAR) structure. We investigate the existence of parameter heterogeneity by allowing for interactions of potential explanatory variables with geographical dummies as extra regressors. We find remarkable differences between the determinants of economic growth implied by differences between regions and those within regions of a given country. In the cross-section of regions, we find evidence for conditional convergence with speed around two percent. The convergence process between countries is dominated by the catching up process of regions in Central and Eastern Europe (CEE), whereas convergence within countries is mostly a characteristic of regions in old EU member states. We also find robust evidence of positive growth of capital cities, a highly educated workforce and a negative effect of population density.

In this paper we put forward a Bayesian Model Averaging method dealing with model uncertainty in the presence of potential spatial autocorrelation. The method uses spatial ltering in order to account for dierent types of spatial links. We contribute to existing methods that handle spatial dependence among observations by explicitly taking care of uncertainty stemming from the choice of a particular spatial structure. Our method is applied to estimate the conditional speed of income convergence across 255 NUTS-2 European regions for the period 1995-2005. We show that the choice of a spatial weight matrix -and in particular the choice of a class thereof -can have an important eect on the estimates of the parameters attached to the model covariates. We also show that estimates of the speed of income convergence across European regions depend strongly on the form of the spatial patterns which are assumed to underlie the dataset. When we take into account this dimension of model uncertainty, the posterior distribution of the speed of convergence parameter appears bimodal, with a large probability mass around no convergence (0% speed of convergence) and a rate of convergence of 1%, approximately half of the value which is usually reported in the literature.

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Introduction 2 The Effects of the Crisis on the Real Economy 2.1 Measures of Crisis Severity 2.2 Potential Drivers of Crisis Severity: Vulnerabilities and Transmission Channels 3 The Econometric Model 4 The Determinants of Crisis Severity 4.1 Short-Run Impact of the Crisis on the Real Economy 4.2 Long-Run Deviations from Trend Output 4.3 Robustness Checks 5 Conclusions References