Forecast uncertainty, disagreement, and the linear pool

The linear pool is the most popular method for combining density forecasts. We analyze the linear pool's implications concerning forecast uncertainty in a new theoretical framework that focuses on the mean and variance of each density forecast to be combined. 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 the linear pool's variance prediction. Moreover, we find that disagreement has no predictive content for ex-post forecast uncertainty under conditions which can be empirically relevant. These findings suggest the removal of the disagreement component from the linear pool. The resulting centered linear pool outperforms the linear pool in simulations and in empirical applications to inflation and stock returns.