Implications of Two Measures of Persistence for Correlation Between Permanent and Transitory Shocks in U.S. Real GDP

Conventionally, shocks to permanent and transitory components in the unobserved components (UC) model for the log of real GDP are assumed to be uncorrelated. This assumption is mainly for identification of model parameters. In this paper, we show important implications of two popular measures of persistence for the correlation between permanent and transitory shocks in the UC model, and demonstrate that the correlation is negative for the log of U.S. real GDP under a very general specification of the cycle process.