Intuitive and Reliable Estimates of the Output Gap from a Beveridge-Nelson Filter

The Beveridge-Nelson (BN) trend-cycle decomposition based on autoregressive
forecasting models of U.S. quarterly real GDP growth produces estimates of the output
gap that are strongly at odds with widely-held beliefs about the amplitude, persistence,
and even sign of transitory movements in economic activity. These antithetical attributes
are related to the autoregressive coefficient estimates implying a very high signal-tonoise
ratio in terms of the variance of trend shocks as a fraction of the overall quarterly
forecast error variance. When we impose a lower signal-to-noise ratio, the resulting BN
decomposition, which we label the “BN filter”, produces a more intuitive estimate of the
output gap that is large in amplitude, highly persistent, and typically increases in
expansions and decreases in recessions. Real-time estimates from the BN filter are also
reliable in the sense that they are subject to smaller revisions and predict future output
growth and inflation better than estimates from other methods of trend-cycle
decomposition that also impose a low signal-to-noise ratio, including deterministic
detrending, the Hodrick-Prescott filter, and the bandpass filter.