Combining Large Numbers of Density Predictions with Bayesian Predictive Synthesis

Abstract: Bayesian Predictive Synthesis is a flexible method of combining density predictions. The flexibility comes from the ability to choose an arbitrary synthesis function to combine predictions. I study choice of synthesis function when combining large numbers of predictions – a common occurrence in macroeconomics. Estimating combination weights with many predictions is difficult, so I consider shrinkage priors and factor modelling techniques to address this problem. These techniques provide an interesting contrast between the sparse weights implied by shrinkage priors and dense weights of factor modelling techniques. I find that the sparse weights of shrinkage priors perform well across exercises.