Measuring Uncertainty of a Combined Forecast and Some Tests for Forecaster Heterogeneity

From the standpoint of a policy maker who has access to a number of expert forecasts, the uncertainty of a combined or ensemble forecast should be interpreted as that of a typical forecaster randomly drawn from the pool. This uncertainty formula should incorporate forecaster discord, as justified by (i) disagreement as a component of combined forecast uncertainty, (ii) the model averaging literature and (iii) central banks’ communication of uncertainty via fan charts. Using new statistics to test for the homogeneity of idiosyncratic errors under the joint limits with both T and n approaching infinity simultaneously, we find that some previously used measures can significantly underestimate the conceptually correct benchmark forecast uncertainty.