Time Varying Dimension Models

Time varying parameter (TVP) models have enjoyed an increasing popularity in empirical macroeconomics. However, TVP models are parameter-rich and risk over-…tting unless the dimension of the model is small. Motivated by this worry, this paper proposes several Time Varying dimension (TVD) models where the dimension of the model can change over time, allowing for the model to automatically choose a more parsimonious TVP representation, or to switch between di¤erent parsimonious representations. Our TVD models all fall in the category of dynamic mixture models. We discuss the properties of these models and present methods for Bayesian inference. An application involving US in‡ation forecasting illustrates and compares the di¤erent TVD models. We …nd our TVD approaches exhibit better forecasting performance than several standard benchmarks and shrink towards parsimonious speci…cations. Acknowledgements: Koop, Leon-Gonzalez and Strachan are Fellows of the Rimini Centre for Economic Analysis. We would like to thank the Leverhulme Trust and the Australian Research Council for …nancial support under Grant F/00 273/J and Grant DP0987170, respectively. Contact address: Gary Koop, Department of Economics, Strathclyde University, Glasgow, G4 0GE, United Kingdom, [email protected]