The common converging trend-cycle model: estimation, modeling and an application to European convergence

This paper discusses multivariate time series models based on unobserved components with dynamic converging properties. We define convergence in terms of a decrease in dispersion over time and model this decrease via mechanisms that allow for gradual reductions in the ranks of covariance matrices associated with the disturbance vectors driving the unobserved components of the model. The inclusion of such convergence mechanisms within the formulation of unobserved components makes the identification of various types of convergence possible. For example, in a panel of macroeconomic time series for different countries, convergence in rates of growth, in cyclical behaviour and in overall volatility can be modelled separately and jointly. Each convergence mechanism introduces two, or in the case of overall volatility, three additional parameters. These parameters can be estimated simultaneously with the other parameters of the model. A mix of EM and numerical maximisation methods are used to obtain maximum likelihood estimates. The multivariate unobserved common converging component model is applied to the per capita gross domestic product for five European countries: Germany, France, Italy, Spain and the Netherlands.