Adaptive Shrinkage in Bayesian Vector Autoregressive Models

ABSTRACT

Vector autoregressive (VAR) models are frequently used for forecasting and impulse response analysis. For both applications, shrinkage priors can help improving inference. In this article, we apply the Normal-Gamma shrinkage prior to the VAR with stochastic volatility case and derive its relevant conditional posterior distributions. This framework imposes a set of normally distributed priors on the autoregressive coefficients and the covariance parameters of the VAR along with Gamma priors on a set of local and global prior scaling parameters. In a second step, we modify this prior setup by introducing another layer of shrinkage with scaling parameters that push certain regions of the parameter space to zero. Two simulation exercises show that the proposed framework yields more precise estimates of model parameters and impulse response functions. In addition, a forecasting exercise applied to U.S. data shows that this prior performs well relative to other commonly used specifications in terms of point and density predictions. Finally, performing structural inference suggests that responses to monetary policy shocks appear to be reasonable.

Key words:

• Density predictions
• Hierarchical modeling
• Normal-Gamma prior
• Stochastic volatility.

ACKNOWLEDGMENTS

The authors thank the editor, Todd Clark, an anonymous associate editor as well as three anonymous referees for constructive comments that significantly improved the article. The authors thank Clara De Luigi for excellent research assistance and Sylvia Frühwirth-Schnatter and Gregor Kastner for helpful comments and suggestions. The research of the first author was partly funded by the Jubiläumsfonds of the Oesterreichische Nationalbank (project number 16244). Any views expressed in this article represent those of the authors only and not necessarily of the Oesterreichische Nationalbank or the Eurosystem.