Bayesian Mixture Models with Applications in Macroeconomics

Abstract

A vast empirical literature has documented the widespread nature of structural instability in many macroeconomic time series. In order to accommodate such a feature, there has been an increasing interest in models that allow time-variation in the parameters. One important issue for modeling this time-variation is to decide which type of time-varying processes is more suitable in applications. For instance, one might want to choose between a model where the parameters are gradually evolving over time or one in which there are a small number of abrupt change-points. The objective of this thesis is to investigate the performance of Bayesian mixture models in modeling such changes in macroeconomic time series.

First, we examine the performance of two basic types of mixture models, a scale mixture of Gaussian models and a finite Gaussian mixture model, in forecasting inflation rates of G7 countries. Since it is well-known that many heavy-tailed distributions can be represented as a scale mixture of Gaussian distributions, we build upon the frequently employed stochastic volatility (SV) models and allow the error terms to have different distributional assumptions, such as the $t$ distribution and double exponential (or Laplace) distribution. The results suggest that allowing for heavy-tailed distributed error terms is as important as allowing stochastic volatility in improving point and density forecast accuracy.

Next, we propose a Gaussian mixture innovation model with time-varying mixture probabilities to detect the in-sample breaks in the relationship between inflation and inflation uncertainty. By allowing the time-variation in the mixture probabilities, we find that the proposed model produces more robust estimates and better in-sample fit. Our empirical study provides strong evidence of the existence of breaks in the relationship between inflation and inflation uncertainty in the last few decades.

Finally, we develop a class of vector autoregressive (VAR) models with infinite hidden Markov structures. We first improve the computational efficiency by developing a new Markov chain Monte Carlo method built upon the precision-based algorithms. We then investigate the performance of these infinite hidden Markov models with various dynamics to predict the US inflation, GDP growth and interest rate. The results show that it is better to model separately the time variation in the conditional mean coefficients and that in the variance process.