Information Sets and Output Gap Estimates from Beveridge-Nelson and Unobserved Components Models

Morley, Nelson and Zivot (2003) show that the Beveridge-Nelson decomposition and an unrestricted unobserved-components model deliver the same cycle for U.S. real GDP once the covariance between trend and cycle innovations is freely estimated. We revisit this result in a narrow replication and then extend it in two directions. First, we repeat the univariate exercise over a longer sample ending in 2026. Second, we add labor-market and real-activity indicators that should be directly informative about the cycle. The narrow replication reproduces the equivalence between the Beveridge-Nelson and unrestricted unobserved-components decompositions in both samples. In the multivariate extension, the two gaps remain closely aligned, with a correlation of 0.995, and the estimated cycle displays persistent contractions around major U.S. recessions. We interpret these results as evidence that the volatile cycle in the unrestricted univariate model mainly reflects the limited cyclical information contained in GDP alone.