Abstract
SummaryThe 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.
Highlights
There is a growing recognition that measuring forecast uncertainty matters for economic policy
We provide a simple example in which the linear pool opinion (LP) violates one or both of the implications of an optimal variance forecast stated in Equations (4) and (5)
The QP's tendency to, generate a and variance given by combined density with lower variance than the LP holds beyond the Gaussian case
Summary
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. 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
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