The Clark Model with Correlated Components

Abstract

This paper is an extension of "Why are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP so Different?" (Morley, Nelson, and Zivot, 2003) to Clark's double-drift unobserved components model. We show that the reduced-form of the double-drift model is an ARIMA(2,2,3) model, and we discuss various restrictions for identifying the parameters of the double-drift model with correlated components. When shocks to the smooth trend and cycle are allowed to be correlated but forced to be uncorrelated with shocks to the drift, the Kalman Filter estimates of the trend and cycle are identical to the estimates from the Beveridge-Nelson decomposition from the ARIMA(2,2,3) model and are similar to the estimates from Morley, Nelson and Zivot. We also find that alternative identification schemes are not supported by the data.

Keywords: Beveridge-Nelson Decomposition, identification, Trend-Cycle Decomposition, Unobserved Components Model

JEL Classification: C22, E32