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.
Factor models are used in a wide range of areas. Two issues with Bayesian versions of these models are a lack of invariance to ordering of the variables and computational inefficiency. This paper develops invariant and efficient Bayesian methods for estimating static factor models. This approach leads to inference on the number of factors that does not depend upon the ordering of the variables, and we provide arguments to explain this invariance. Beginning from identified parameters which have nonstandard forms, we use parameter expansions to obtain a specification with standard conditional posteriors. We show significant gains in computational efficiency. Identifying restrictions that are commonly employed result in interpretable factors or loadings and, using our approach, these can be imposed ex-post. This allows us to investigate several alternative identifying schemes without the need to respecify and resample the model. We apply our methods to a simple example using a macroeconomic dataset.
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