Priors for the Long Run

ABSTRACT

We propose a class of prior distributions that discipline the long-run behavior of vector autoregressions (VARs). These priors can be naturally elicited using economic theory, which provides guidance on the joint dynamics of macroeconomic time series in the long run. Our priors for the long run are conjugate, and can thus be easily implemented using dummy observations and combined with other popular priors. In VARs with standard macroeconomic variables, a prior based on the long-run predictions of a wide class of theoretical models yields substantial improvements in the forecasting performance. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

KEYWORDS:

• Bayesian vector autoregression
• Forecasting
• Hierarchical model
• Initial conditions
• Overfitting

Acknowledgments

The authors thank Gianni Amisano, Francesco Bianchi, Todd Clark, Gary Koop, Dimitris Korobilis, Ulrich Müller, Chris Sims, Jim Stock, Harald Uhlig, Herman van Dijk, Mark Watson, Tao Zha as well as seminar and conference participants for comments and suggestions, and Patrick Adams and Brandyn Bok for research assistance. The views expressed in this article are those of the authors and are not necessarily reflective of views at the European Central Bank, the Eurosystem, the Federal Reserve Bank of New York, or the Federal Reserve System.