Forecast uncertainty, disagreement, and the linear pool

The linear pool is the most popular method for combining density forecasts. We analyze its implications concerning forecast uncertainty, using a new framework that focuses on the means and variances of the individual and combined forecasts. Our results show that, if the variance predictions of the individual forecasts are unbiased, the well-known “disagreement” component of the linear pool exacerbates the upward bias of its variance prediction. This finding suggests the removal of the disagreement component from the linear pool. The resulting centered linear pool outperforms the linear pool in simulations and an empirical application to inflation.