Reliable Real-Time Output Gap Estimates Based on a Modified Hamilton Filter

We propose a simple modification of Hamilton’s time series filter 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 real GDP. While this approach yields a cyclical component 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 mutes short and amplifies medium length cycles. Further, as the estimated trend contains high-frequency noise, it can hardly be interpreted as potential GDP. A simple modification 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 and the original 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 bandpass filter, and should thus be used preferably.