Trend in Cycle or Cycle in Trend? New Structural Identifications for Unobserved-Components Models of U.S. Real GDP

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 permanent innovations enter the cycle or transitory innovations enter the trend, and that identification restrictions are necessary to make this structural distinction. A reduced-form unrestricted version is compatible with either option, but cannot distinguish which is relevant. We discuss economic interpretations and implications using U.S. real GDP data.

Trend–cycle–seasonal Interactions: Identification and Estimation

“…In particular, Cecchetti and Kashyap (1996) observe that seasonal cycles in production are less marked in business cycle booms, implying negative correlation between these components. As noted by Proietti (2006) negative correlations lead to higher weights on future observations in the Kalman smoother, resulting in relatively large revisions to filtered estimates; see also Dungey et al (2015).…”

“…As discussed by Weber (2011), the economic rationale for such correlation can include real business cycle theories, nominal rigidities, hysteresis, policy responses to temporary shocks, and so on. Estimates of the correlation between the innovations of the trend and cycle for output 4 or related series (such as employment) are negative and relatively close to −1; for example, MNZ, Sinclair (2010), Weber (2011), Dungey et al (2015.…”

“…Seasonal adjustment is based on the unobserved component approach, of which the key assumption is that the components (typically trend, cycle and seasonal) are mutually uncorrelated. However, a growing recent literature strongly suggests that the trend and cycle can be correlated; see Morley, Nelson and Zivot (2003), MNZ hereafter, Dungey, Jacobs, Tian and van Norden (2015) and others. While this has important implications for economic analyses that employ detrended data, the consequences of the uncorrelated assumption for seasonality are much more pervasive.…”

Trend-Cycle-Seasonal Interactions: Identification and Estimation

“…As discussed by Weber (2011), the economic rationale for such correlation can include real business cycle theories, nominal rigidities, hysteresis, policy responses to temporary shocks, and so on. Estimates of the correlation between the innovations of the trend and cycle for output or related series (such as employment) are negative and relatively close to −1; for example, MNZ, Sinclair (2010), Weber (2011), Dungey et al (2015).…”

Modeling Multivariate Data Revisions

“…These are situations in which we have fewer underlying true values than we 5 See Dungey et al (2013b).…”