general that forecasters ought to pay attention to this result, even without necessarily
understanding exactly what is so effective about this particular form of shrinkage.
The result that equal weighted averaging gives the best forecasts is however odd.
Indeed it cannot be correct as a general principal that equal weighted averaging of
forecasts is always optimal. For example, one can always just average the first two
forecasts, call that a new forecast, and throw that back in the set of forecasts being
considered. If equal weighting is always best, then this new forecast will get an equal
weight. But this changes the weights on the original forecasts, which are no longer all
equal. While it is easy to say this, it is much harder to come up with a concrete
alternative forecasting strategy that actually does better than simple averaging in terms of
out-of-sample prediction of inflation. That is the goal of this paper.
This paper considers the prediction of US inflation by Bayesian Model
Averaging, a technique which was not considered by Stock and Watson (2001, 2002a).
Bayesian Model Averaging has been developed mainly, but not exclusively, by
statisticians as opposed to econometricians. The idea is to consider prediction when the
researcher does not know the true model, but has several candidate models. A forecast
can be constructed putting weights on the predictions from each model. If these weights
are all equal, then this is simple forecast averaging. The researcher can however start
from the prior that all the models are equally good, but then estimate the posterior
probabilities of the models, which can be used as weights instead.