A four-page American Statistical Association (ASA) proceedings address presenting the conceptual case for Bayesian vector autoregressions (BVARs). Litterman argues that unrestricted VARs overfit noise because standard methods offer only two options—exclude a variable (too restrictive) or include it without a prior (too diffuse)—and that a Bayesian prior encoding the belief that most coefficients are near zero resolves the overparameterization problem without sacrificing lag coverage. The paper closes with an actual BVAR forecast of U.S. GNP growth made in mid-1985.
"The approach taken by the BVAR technique is to solve the overparameterization problem by specifying in a Bayesian framework the likely values for all of the coefficients. Instead of setting lots of coefficients to zero, the prior that we use specifies that most coefficients are likely to be close to zero."
"Specifying the value of such a hyperparameter is a difficult issue, similar in some ways to the problem of choosing a lag length k; but the important point is that the model generated by choosing any reasonable value for the hyperparameter will reflect the prior information available to the modeler much more accurately than the prior implicit in any choice of k."
This is a companion piece to Litterman (1986b), aimed at a broader statistical audience. Its value is conceptual clarity: the framing of "exclude vs. include" as an implicit and inadequate prior choice is the most memorable argument in the BVAR literature. The actual 1985 GNP forecast (notably bullish relative to consensus) serves as a live demonstration of what a BVAR with genuine uncertainty quantification produces.