A recent post, On Bayesian DSGE Modeling with Hard and Soft Restrictions, ended with: "A related issue is whether 'theory priors' will supplant others, like the 'Minnesota prior'. I'll save that for a later post." This is that later post. Its title refers to Ingram and Whiteman's 1994 classic, entitled "Supplanting the 'Minnesota' Prior: Forecasting Macroeconomic Time Series Using Real Business Cycle Model Priors."

So, shrinking VAR's using DSGE theory priors improves VAR forecasts. Sounds like a victory for economics, with the headline "Using Economic Theory Improves Economic Forecasts!" We'd all like that. We all want that.

But the "victory" is misleading, and more than a little hollow. Lots of shrinkage directions improve forecasts. Indeed

*almost all*shrinkage directions improve forecasts. Real victory would require theory-inspired priors to deliver clear extra improvement relative to other shrinkage directions, but they usually don't. In particular, the Minnesota prior, centered on a simple vector random walk, remains competitive. (See Del Negro and Schorfheide (2004) and Del Negro and Schorfheide (2007).) Sometimes theory priors beat the Minnesota prior by a little, sometimes they lose by a little. It depends on the dataset, the variable, the forecast horizon, etc.

The bottom line: Theory priors seem to be roughly as good as anything else, including the Minnesota prior, but certainly they've not led us to anything resembling wonderful new forecasting success. This seems at best a small forecasting victory for theory priors, but perhaps a victory nonetheless, particularly given the obvious appeal of using a theory prior for Bayesian VAR forecasting that coheres with the theory model used for policy analysis.