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 Markov switching models to measure the strength of synchronization between business cycles. Synchronization is defined by the fraction of time in which two country’s business cycles are in the same state (concordance) and by the degree to which turning points cluster together (correlation). We use a Bayesian, Gibbs sampling approach to estimate a univariate Markov switching model of GDP growth for several countries. We obtain posterior distributions of business cycle states by simulating data from the posterior distributions of the model parameters, then censoring the simulated data using the Bry-Boschan algorithm. The business cycle states are then mapped into posterior distributions of concordance and correlation statistics. We compare these posterior distributions with the point estimates of concordance and correlation of cycles in the data. As a point of reference, we repeat this exercise using simulated data from a heteroskedastic AR(1) model. Posterior odds ratios overwhelmingly favor the Markov switching model. While the model performs well in describing the concordance of the data, it performs quite poorly in capturing the correlation of business cycles across countries; the actual correlations lie far in the tails of the posterior distributions. Mapping the priors on the parameters of the univariate Markov switching model into priors on the synchronization statistics, we find that the implied priors on the concordance statistics are quite flat. However, the priors on the correlation statistics are fairly tight around zero. This may be a consequence of the diffuseness of the concordance prior but may also be attributable to our univariate modeling framework. ∗We are grateful to Don Harding, Adrian Pagan and Christopher Sims for many helpful comments, but retain all responsibility for any remaining errors. This work was sponsored in part by Australian Research Council grant C79930704.