Modelling the dynamic convergence of business cycles

This paper proposes a new non-linear parametric model, called the Dynamic Cyclical Convergence Model (DCCM), to measure and test the convergence between two cycles. This model combines unobserved component models with time-varying parameter models. The convergence is characterised by two time-varying indicators, the shift and the amplitude ratios between the two cycles. A Kalman filter-based iterative procedure is developed for the model estimation. The procedure is assessed on simulated time series. The time-domain approach is compared with a frequency-domain approach, using techniques from the bivariate spectral analysis. DCCM models are applied to British, German, and American business cycles over a period ranging from 1970 to 2003. The empirical result of this method is twofold: on the one hand, since 1996, the British cycle progressively synchronises with the German one: at the end of the period, both cycles have a lag equal to 4 quarters relative to American fluctuations. On the other hand, it appears that the British cycle amplitude has stood around 40% of the German one since 1996: shocks have asymmetric effects and the euro adoption would require an improved fiscal co-ordination.