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-to-noise 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 positive in expansions and negative 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 for 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.

JEL classification: C18, E17, E32

Keywords: Beveridge-Nelson decomposition, output gap, signal-to-noise ratio