What is the problem with potential output as definined? Here is the definition from WIki:
In economics, potential output (also referred to as "natural gross domestic product") refers to the highest level of real Gross Domestic Product output that can be sustained over the long term. The existence of a limit is due to natural and institutional constraints.
OK, institutions are 40 years long, the long bond is thirty years. It has to be measured over that time span. The IMF measures it over the recession cycle, about eight years. What are they measuring? The ability of economies to adapt to the American recession cycle. Is that a good idea? Well, the US has dominated the world economy, so I guess so. But what a dreary proposition, and it makes the measure useless for much of anything endogenous to the native economy.
Is my method of DSGE spectral decomposition any better? Sure, a bit to the extent it is locally accurate. Spectral decomposition under the adiabatic assumption tells us the relative risk to each component of the DSGE when the economy slows., because it tells which component restructures first, in all probability.