How Are Shocks to Trend and Cycle Correlated? A Simple Methodology for Unidentified Unobserved Components Models

In this paper, we propose a simple methodology for investigating how shocks to trend and cycle are correlated in unidentified unobserved components models, in which the correlation is not identified. The proposed methodology is applied to U.S. and U.K. real GDP data. We find that the correlation parameters are negative for both countries. We also investigate how changing the identification restriction results in different trend and cycle estimates. It is found that estimates of the trend and cycle can vary substantially depending on the identification restrictions imposed.