Growth, cycles and convergence in US regional time series

This article reports the results of fitting unobserved components (structural) time series models to data on real income per capita in eight regions of the United States. The aim is to establish stylised facts about cycles and convergence. It appears that while the cycles are highly correlated, the two richest regions have been diverging from the others in recent years. A new model is developed in order to characterise the converging behaviour of the six poorest regions. The model combines convergence components with a common trend and cycles. These convergence components are formulated as a second-order error correction mechanism which allows temporary divergence while imposing eventual convergence. After fitting the model, the implications for forecasting are examined. Finally, the use of unit root tests for testing convergence is critically assessed in the light of the stylised facts obtained from the fitted models.