Bagliano and Morana estimate the long-run trend in US CPI inflation — "core inflation" — over 1960–2000 using a common trends model. Core inflation is interpreted and constructed as the long-run forecast of inflation conditional on the information in nominal money growth, output fluctuations, and oil-price movements. Unlike exclusion-based or statistical-filter measures, this common-trends core-inflation rate is grounded in the strong long-run link between inflation and monetary growth in the data.
"Core inflation is interpreted and constructed as the long-run forecast of inflation conditional on the information contained in nominal money growth, output fluctuations and movements in the oil price … the common-trends core inflation rate exploits the long-run link between inflation and monetary growth, a strong feature of the data."
A clean example of turning an abstract time-series decomposition into a policy-relevant statistic: "core inflation" is exactly the kind of trend-versus-noise question the common-trends framework is built for, and defining it as a conditional long-run forecast is more disciplined than the ad-hoc ex-food-and-energy convention that central banks actually use. The reliance on the money–inflation long-run link is both the strength and the vulnerability: it is a robust regularity in 1960–2000 US data, but money-demand instability and the post-2008 breakdown of that link would strain the construct out of sample. It rounds out the Bagliano cluster on this wiki — after two papers on identifying monetary-policy shocks, one on measuring the object policy ultimately targets.