A Bayesian Model Comparison for Trend‐Cycle Decompositions of Output

Abstract

We compare a number of widely used trend‐cycle decompositions of output in a formal Bayesian model comparison exercise. This is motivated by the often markedly different results from these decompositions—different decompositions have broad implications for the relative importance of real versus nominal shocks in explaining variations in output. Using U.S. quarterly real GDP, we find that the overall best model is an unobserved components model with two features: (i) a nonzero correlation between trend and cycle innovations and (ii) a break in trend output growth in 2007. The annualized trend output growth decreases from about 3.4% to 1.2%–1.5% after the break. The results also indicate that real shocks are more important than nominal shocks. The slowdown in trend output growth is robust when we expand the set of models to include bivariate unobserved components models.

Reconciling output gaps: Unobserved components model and Hodrick–Prescott filter

“…Specifically, the annualized trend growth rate fluctuates between 3.5% and 4% from 1950 to 1970; remains stable at about 3% from the mid-1970s to 2000; and starts a gradual decline to about 1.7% in the middle of the Great Recession. These estimates are comparable to those reported in Perron and Wada (2009) and Grant and Chan (2016)-all obtained using UC models with breaks in the trend growth rate.…”

“…In particular, we present results from the correlated unobserved components (UCUR) model of Morley et al (2003). Moreover, given the findings in Perron and Wada (2009), Luo and Startz (2014) and Grant and Chan (2016), we also consider a version in which the trend growth rate has a break at t 0 . More precisely, we replace (3) with…”

“…For example, using US real GDP from 1947Q1 to 1998Q2, Perron and Wada (2009) find a break in trend growth at 1973Q1. Using more recent data, Luo and Startz (2014) and Grant and Chan (2016) find a break at 2006Q1 and 2007Q1, respectively. One way to relax this restrictive assumption is to allow for a time-varying growth rate, as considered in Harvey (1985) and Clark (1987), replacing (3) by…”

“…The aim of this paper is similar to Perron and Wada (2009) and Grant and Chan (2016) in that we assess the support of different trend output specifications. However, while they focus on random walk trend output models with a deterministic break in the growth rate, we consider models with both stochastic trend output and stochastic growth.…”

Estimating the U.S. output gap with state‐level data

“…Hence it does not seem that aggregate inflation could make a significant difference to the results obtained with real GDP and unemployment rate data at the state level. 20 Morley, Nelson, and Zivot (2003), Basistha and Nelson (2007), Sinclair (2009), and Grant and Chan (2017), among others, postulate UC models to decompose GDP into its trend and cycle allowing for correlated trend-cycle disturbances. In general, the results indicate that there is an appreciable degree of comovement between trend and cycle disturbances and that the estimated cycle may not have the conventional features of amplitude and frequency, in particular when compared with the features of the CBO-implied output gap, for example.…”