Choosing Prior Hyperparameters: With Applications to Time-Varying Parameter Models

Abstract

Time-varying parameter models with stochastic volatility are widely used to study macroeconomic and financial data. These models are almost exclusively estimated using Bayesian methods. A common practice is to focus on prior distributions that themselves depend on relatively few hyperparameters such as the scaling factor for the prior covariance matrix of the residuals governing time variation in the parameters. The choice of these hyperparameters is crucial because their influence is sizeable for standard sample sizes. In this article, we treat the hyperparameters as part of a hierarchical model and propose a fast, tractable, easy-to-implement, and fully Bayesian approach to estimate those hyperparameters jointly with all other parameters in the model. We show via Monte Carlo simulations that, in this class of models, our approach can drastically improve on using fixed hyperparameters previously proposed in the literature. Supplementary materials for this article are available online.

KEY WORDS:

• Bayesian inference
• Bayesian VAR
• Time variation.

ACKNOWLEDGMENTS

The authors thank Luca Benati, Fabio Canova, Minsu Chan, Todd Clark, Frank Diebold, Luca Gambetti, Thomas Lubik, Frank Schorfheide, Mark Watson, Alexander Wolman, and seminar participants at the University of Pennsylvania as well as conference participants at the EUI workshop on time-varying parameter models and the 9th Rimini Bayesian econometrics workshop for helpful comments. Andrew Owens and Daniel Tracht provided excellent research assistance. The views expressed in this article are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal Reserve System.