Trend-Cycle Decomposition: Implications from an Exact Structural Identification

Abstract

A well-documented property of the Beveridge-Nelson trend-cycle decomposition is the perfect negative correlation between trend and cycle innovations. We show how this may be consistent with a structural model where trend shocks enter the cycle, or cycle shocks enter the trend and that identification restrictions are necessary to make this structural distinction. A reduced form unrestricted version such as Morley, Nelson and Zivot (2003) is compatible with either option, but cannot distinguish which is relevant. We discuss economic interpretations and implications using US real GDP data.

Keywords: trend-cycle decomposition, data revision, state-space form

JEL Classification: C22, C53, C82