Trend-Cycle Decomposition After COVID

We revisit some popular univariate trend-cycle decomposition methods given the Covid-era data and find that only the output gap estimates from the Beveridge-Nelson filter remain both intuitive and reliable throughout the crisis and its aftermath. The real-time Hodrick-Prescott filter estimates for the output gap just prior to the pandemic are highly unreliable, although the estimated gap during the pandemic is reasonably similar to that of the Beveridge-Nelson filter. The Hamilton filter produces reliable estimates, but suffers from base effects that imply a purely mechanical spike in the output gap exactly two years after the onset of the crisis, in line with the filter horizon. Notably, unlike with the Beveridge-Nelson and Hodrick-Prescott filters, forecasts of the output gap for the Hamilton filter do not settle down to zero given plausible projected values of future output growth and display large spurious dynamics due to base effects given a simulated Covid-like shock in the projection. We also provide some refinements to the original Beveridge-Nelson filter that produce even more intuitive estimates of the output gap, while retaining the same strong revision properties.