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I realise Drew may have access to some of the work on this stuff? So I guess I shouldn't be too rude about the state of the art in the field, maybe more exists than I know...
I really like the idea of spectrum analysis because there's clearly different kinds of inertia - and they should give clues to different issues.
I'll throw in my usual complaint about "core inflation" which is that "inflation" has very specific meanings... which always need considering before you go from the "inflation" or "core inflation" figure to a policy judgement.
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...
So, in this case, core inflation shows we are heading towards deflation - which does indeed match some other potential measures of the "real economy" - but at the same time the financial economy appears to be inflating again, and with it some commodities that are pretty vital to the real economy (energy? food?)
What does all that mean? I don't know... but I'd be a lot happier if anyone out there can point me to a non-recursive/tautologous definition of inflation that explains what it should mean...
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