Measuring Uncertainty of a Combined Forecast and a New Test for Forecaster Heterogeneity

Using a standard factor decomposition of a panel of forecasts, we have shown that the forecast uncertainty from the standpoint of a policy maker can be expressed as the disagreement among forecasters plus the perceived variability of common aggregate shocks. Thus, the uncertainty of the average forecast is not the variance of the average forecast but rather the average of the variances of the individual forecasts, where the combined forecast is obtained by minimizing the risk averaged over all possible forecasts rather than the risk of the combined forecast. Using a new statistic developed in this paper to test the heterogeneity of idiosyncratic errors under the joint limits with both T and N approaching infinity simultaneously, we show that the previous used uncertainty measures significantly underestimate the correct benchmark forecast uncertainty. JEL classification: C12; C33; E37