Subspace shrinkage in conjugate Bayesian vector autoregressions

Macroeconomists using large datasets often face the choice of working with either a large vector autoregression (VAR) or a factor model. In this paper, we develop a conjugate Bayesian VAR with a subspace shrinkage prior that combines the two. This prior shrinks towards the subspace which is defined by a factor model. Our approach allows for estimating the strength of the shrinkage and the number of factors. After establishing the theoretical properties of our prior, we show that it successfully detects the number of factors in simulations and that it leads to forecast improvements using US macroeconomic data.

Automated summary

This paper proposes a conjugate Bayesian model that combines vector autoregression (VAR) and factor models by shrinking towards the subspace defined by the factor model. The approach allows for estimating the strength of shrinkage and the number of factors. The paper demonstrates the effectiveness of the method in detecting the number of factors and improving macroeconomic forecast using simulations and US macroeconomic data.