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We propose a simple modification of the time series filter by Hamilton (2018) that yields reliable and economically meaningful real-time output gap estimates. The original filter relies on 8-quarter-ahead forecast errors of a simple autoregression of log real GDP. While this approach yields a cyclical component of GDP that is hardly revised with new incoming data due to the one-sided filtering approach, it does not cover typical business cycle frequencies evenly, but short business cycles are muted and medium length business cycles are amplified. Further, the estimated trend is as volatile as GDP itself and can thus hardly be interpreted as potential GDP. A simple modification that is based on the mean of 4- to 12-quarter-ahead forecast errors shares the favorable real-time properties of the Hamilton filter, but leads to a much better coverage of typical business cycle frequencies and a smooth estimated trend. Based on output growth and inflation forecasts and a comparison to revised output gap estimates from policy institutions, we find that real-time output gaps based on the modified Hamilton filter are economically much more meaningful measures of the business cycle than those based on other simple statistical trend-cycle decomposition techniques such as the HP or the Bandpass filter.
Output gap revisions can be large even after many years. Real-time reliability tests might therefore be sensitive to the choice of the final output gap vintage that the real-time estimates are compared to. This is the case for the Federal Reserve’s output gap. When accounting for revisions in response to the global financial crisis in the final output gap, the improvement in real-time reliability since the mid-1990s is much smaller than found by Edge and Rudd (Review of Economics and Statistics, 2016, 98(4), 785-791). The negative bias of real-time estimates from the 1980s has disappeared, but the size of revisions continues to be as large as the output gap itself.
The authors systematically analyse how the realtime reliability assessment is affected through varying the final output gap vintage. They find that the largest changes are caused by output gap revisions after recessions. Economists revise their models in response to such events, leading to economically important revisions not only for the most recent years, but reaching back up to two decades. This might improve the understanding of past business cycle dynamics, but decreases the reliability of real-time output gaps ex post.