Hierarchical shrinkage priors for dynamic regressions with many predictors

This paper examines the properties of Bayes shrinkage estimators for dynamic regressions that are based on hierarchical versions of the typical normal prior. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using a single hierarchical Bayes formulation. Using 129 US macroeconomic quarterly variables for the period 1959–2010, I extensively evaluate the forecasting properties of Bayesian shrinkage in macroeconomic forecasting with many predictors. The results show that, for particular data series, hierarchical shrinkage dominates factor model forecasts, and hence serves as a valuable addition to the existing methods for handling large dimensional data.