Multivariate models with dual cycles: implications for output gap and potential growth measurement

Structural time series models applied to the factor inputs of a production function often lead to small output gaps and to erratic measures of potential growth. We introduce a dual cycle model which is an extension to the multivariate trend plus cycle model with phase shifts à la Rünstler. The dual cycle model is a combination of two types of model: the trend plus cycle model and the cyclical trend model, where the cycle appears in the growth rate of a variable. This property enables hysteresis to be taken into account. Hysteresis is likely to show up in unemployment, but it can also affect the capital stock due to the existence of long investment cycles. In the proposed model, hysteresis may affect all the factor inputs of the production function and phase shifts are extended to the dual cycles. Genuine measures of potential growth can be computed that are hysteresis-free and less prone to volatility. A complementary measure of the output gap that takes hysteresis into account can be derived.