Bayesian Multivariate Time Series Methods for Empirical Macroeconomics

Abstract

Macroeconomic practitioners frequently work with multivariate time series models such as VARs, factor augmented VARs as well as timevarying parameter versions of these models (including variants with multivariate stochastic volatility). These models have a large number of parameters and, thus, over-parameterization problems may arise. Bayesian methods have become increasingly popular as a way of overcoming these problems. In this monograph, we discuss VARs, factor augmented VARs and time-varying parameter extensions and show how Bayesian inference proceeds. Apart from the simplest of VARs, Bayesian inference requires the use of Markov chain Monte Carlo methods developed for state space models and we describe these algorithms. The focus is on the empirical macroeconomist and we o¤er advice on how to use these models and methods in practice and include empirical illustrations. A website provides Matlab code for carrying out Bayesian inference in these models.

Bayesian Variable Selection in Spatial Autoregressive Models

“…Conditional on the other parameters, the posterior distribution for ζ has the standard form (see Koop 2003) …”

“…The corresponding draws are stored after discarding a number of burn-in draws (see, for example, Koop 2003).…”

“…The first approach uses stochastic search variable selection (SSVS) priors put forward by George and McCulloch (1993) and George and McCulloch (1997), which have been widely applied especially in the time-series literature (see George et al 2008 andKoop andKorobilis 2010). SSVS priors rely on a mixture of normal priors, where the choice of the prior hyperparameters may have severe effects on posterior inference.…”

A new look at variation in employment growth in Canada: The role of industry, provincial, national and external factors

“…As we noted earlier, one advantage of the Bayesian approach is that assessing model …t is straight forward compared to the minimum distance estimator used in the earlier literature. 4 Since Bayesian MCMC methods for DFMs and VARs are well-established in the literature (see, e.g., Koop and Korobilis, 2009) we will not provide them here. The reader is referred to the online appendix associated with this paper which is available at http://personal.strath.ac.uk/gary.koop/research.htm.…”

“…With VARs and factor models, Bayesian methods are enjoying an increasing popularity and we follow this trend. In addition to standard arguments in favor of Bayesian methods in such high-dimensional models (see, e.g., Koop and Korobilis, 2009), there are some advantages particular to this literature. First, assessing model …t is much more straightforward with Bayesian methods and does not encounter the problems with determining the degrees of freedom for goodness-of-…t tests with minimum distance estimators (e.g., Altonji and Ham, 1990;Clark, 1998).…”