Disentangling Time and Forecaster Effects in Probabilistic Forecasts: Bayesian Hierarchies and Latent Mixtures for Predictive Uncertainty

Probabilistic forecasts encode both expected outcomes and uncertainty, but these need not arise from the same sources of variation. We study this distinction using 4,040 one-quarter-ahead real-GDP density forecasts from 174 participants in the Survey of Professional Forecasters over 112 quarters (1992-2019). We develop a hierarchical framework that separates common Time effects from persistent Forecaster effects in forecast location and uncertainty. Classical benchmarks are complemented by Bayesian hierarchical Gaussian models, bivariate hierarchies for dependence between location and uncertainty, and heteroskedastic specifications for time-varying residual variability. We further investigate a sparse Bayesian finite-mixture extension that replaces individual forecaster effects with latent classes, testing whether persistent heterogeneity can be summarized by a small number of recurring uncertainty profiles. The framework provides an interpretable decomposition of predictive uncertainty across time and heterogeneous forecasting agents.