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I really like the idea of spectrum analysis because there's clearly different kinds of inertia - and they should give clues to different issues.
You would need to have a clear idea of how you'd expect a frequency spectrum to look like for different kinds of pricing mechanisms before you start mining the data. Ideally, you'd want to calibrate your a priori expectations against several industries that you know to be competitive/monopolistic/oligopolistic.
What you'd want to emphatically not do is chug a lot of data through a frequency decomposition and then mix and match the patterns you get out. That would probably give you turtles all the way down.
This is no minor task, and the calibration in particular will probably involve digging into historical price/volume data that is less complete than we might have wished. Although it is, of course, preferable to using a nonsense index to make serious policy decisions...
The most obvious case is that core inflation was low throughout the finance and housing boom that preceded/caused the current financial crisis. So - there are important things (asset inflation?) that the core inflation (and indeed various other inflation measures) just don't measure...
Yes. The ordinary inflation indices don't touch the balance sheet at all - they only care about the cash flow. What's worse is that it is less than obvious how to construct an inflation index for assets, or that it is even an appropriate thing to try to do.
As a practical matter, that's not a very big problem, because we have a number of other indicators that can tell us whether asset prices are out of line. The problem is the political will to use them (or rather the lack thereof).
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