How Well Do Markov Switching Models Describe Actual Business Cycles? The Case of Synchronization

The objective of this paper is to evaluate the effectiveness of using a Markov switching model to measure the synchronization of business cycles. We use a Bayesian, Gibbs sampling approach to estimate a multivariate Markov switching model of GDP growth for several countries. We look for evidence of synchronization across countries in the sense of common Markov states, covariance of impulses and a long-run co-integrating relationship. We then use the fitted data implied by the posterior distribution of the Markov switching VAR, in conjunction with a dating rule, to obtain the posterior distribution of binary business cycle states. We use these to investigate the posterior distributions of non-parametric measures of synchronization described by Harding and Pagan (2003) and compare them with similar measures obtained from standard reference chronologies. As a point of reference, we repeat this exercise using simulated data from a linear VAR. We find no evidence of a common Markov state, but some evidence of the propagation of country-specific disturbances across countries and of a co-integrating relationship between the United States and Canada. Posterior odds ratios overwhelmingly favor the Markov switching model over the linear VAR and we find that the posterior distributions of the non-parametric measures of synchronisation produced by the Markov switching VAR match the data more closely than those produced by the linear VAR.