Trend-cycle decomposition in the presence of large shocks

We introduce some refinements of the Beveridge-Nelson filter to help address possible distortions from large shocks. We then compare how the Beveridge-Nelson filter and other popular univariate trend-cycle decomposition methods perform given the extreme outliers associated with the Covid recession. Real-time estimates of the output gap based on the Hodrick-Prescott filter are highly unreliable in the years just prior to the pandemic, although the revised estimates during the pandemic are similar to those of the more reliable Beveridge-Nelson filter. The Hamilton filter suffers from base effects that produce a mechanical spike in the estimated output gap exactly two years after the onset of the pandemic, in line with the filter horizon. Given projected data with a simulated Covid-like shock, both the Hodrick-Prescott and Hamilton filters overstate the true reduction in the output gap and fail to capture the implied movements in trend output. The Hodrick-Prescott filter generates a spurious transitory boom just prior to the simulated shock, while the Hamilton filter produces another mechanical spike exactly two years after the simulated shock, as well as an ongoing divergence in forecasted values of the output gap away from zero. Only the Beveridge-Nelson filter correctly forecasts trend and cycle movements when faced with a Covid-like shock.