State Space Model with Mixtures of Normals: Specifications and Applications to International Data

This paper first generalizes the trend-cycle decomposition framework of Perron and Wada (2005) based on an unobserved components model with innovations having a mixture of Normal distribution, which is able to handle sudden level and slope changes to the trend function as well as outliers. We investigate how important are the differences in the implied trend and cycle compared to the popular decomposition based on the Hodrick and Prescott (HP) (1997) filter. Our results show important qualitative and quantitative differences in the implied cycles for both real GDP and consumption series for the G7 countries. Most of the differences can be ascribed to the fact that the HP filter does not handle well slope changes, level shifts and outliers, while our method does so. Third, we assess how such different cycles affect some so-called “stylized facts†about the relative variability of consumption and output across countries. Our results show again important differences. In particular, the cross-country consumption correlations are generally higher than the output correlations, except for the period from 1975 to 1985, provided Canada is excluded. Our results therefore provide a partial solution to this puzzle. The evidence is particularly strong for the most recent period.