Given the limited length of standard macroeconomic datasets relative to the vast number of parameters available, Bayesian methods have become an increasingly popular way of dealing with the problem of over-parameterization.
[1] The general idea is to use informative priors to shrink the unrestricted model towards a parsimonious naïve benchmark, thereby reducing parameter uncertainty and improving forecast accuracy.
The informativeness of the prior can be set by treating it as an additional parameter based on a hierarchical interpretation of the model.
[7] In particular, the Minnesota prior assumes that each variable follows a random walk process, possibly with drift, and therefore consists of a normal prior on a set of parameters with fixed and known covariance matrix, which will be estimated with one of three techniques: Univariate AR, Diagonal VAR, or Full VAR.
Recent research has shown that Bayesian vector autoregression is an appropriate tool for modelling large data sets.