Bayesian Inference in High Dimensions for Economic Time Series

• Applicant: Dr. Jan Prüser
• Subject Area: Statistics and Econometrics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 468814087

The increasing availability of new large datasets enables empirical macroeconomists to use a large number of predictors, but usually only a few hundred observations are available. This raises problems for conventional methods of econometric inference. Intuitively, there is not enough information in the data to estimate large models in an unrestricted fashion. Additional information can formally be incorporated using global-local hierarchical shrinkage priors. As the name suggests, global-local priors introduce both global and local variance components into their prior distribution. The global shrinkage component places substantial probability mass near the prior mean, while the local shrinkage component induces fat-tailed behaviour in the marginal prior distribution. Set in this manner, global-local priors heavily regularize the model parameters while retaining enough flexibility to prevent possibly weak signals from being forced to zero.Our first aim is to improve forecasting in high dimensions. In particular, we exploit the information contained in “new” data sets (e.g. textual data) by using them as predictors in addition to traditional macroeconomic variables. In such an environment, we provide a large-scale study comparing the empirical performance of a wide range of global-local priors. In addition, we develop a range of novel global-local priors that capture the well-known prior beliefs of the Minnesota prior. To facilitate and speed up computation in high dimensions, we compare a range of existing algorithms and develop some new algorithms.Our second aim is to perform structural analysis in high dimensions. Specifically, we propose the use of multi-country VARs to study spillover effects between European countries and compare the relative importance of common and country specific shocks. In order to provide accurate inference we combine panel VAR shrinkage priors with global-local priors. Finally, we propose a statistical measure to compare multi-country VARs with individual country VARs.

• DFG Programme: Research Grants