Trend-Cycle Decomposition in the Presence of Large Shocks

We introduce some refinements of the Beveridge-Nelson filter to produce more intuitive estimates of the output gap and address possible distortions from large shocks. We then compare how the Beveridge-Nelson filter and other popular univariate trend-cycle decomposition methods performed given the extreme outliers in the Covid-era data. Real-time estimates of the output gap based on the Hodrick-Prescott filter turn out to have been highly unreliable in the years just prior to the pandemic, although the estimated gap during the pandemic is similar to that 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 that includes 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 prior to the shock, while the Hamilton filter produces another mechanical spike two years after the shock and also 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.