A Bayesian Model Comparison for Trend‐Cycle Decompositions of Output

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.