Reliable real-time output gap estimates based on a modified Hamilton filter

We propose a simple modification of the time series filter by Hamilton (2018b) that yields reliable and economically meaningful real-time output gap estimates. The original filter relies on 8-quarter ahead forecasts errors of an autoregression. 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 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 cycles than those based on other simple statistical trend-cycle decomposition techniques such as the HP or the Bandpass filter.