The paper considers the efficient estimation of opinion pools with regularization in the Bayesian paradigm and extends their application to cases where the number of competing models exceeds the number of observations. A Bayesian-inspired formulation and estimation algorithm is proposed whose 1) conditional density accommodates any proper scoring rule and 2) different priors allow weight shrinkage towards equality, extreme weights or any combinations under the Lasso, Ridge and Entropy penalty. Specifically, the Dirichlet prior allows shrinkage towards extreme weights which is useful for model selection applications. The simulation study explores and identifies situations where average log score is highest for opinion pools under shrinkage towards equality or extreme weights. An application involving the Survey of Professional Forecasters demonstrates that the Bayesian opinion pool’s inflation forecast competes well with the equal-weight aggregated inflation forecast
post 2013.
