Quick post; I went back and re-did the inflation rate calculations using seasonally adjusted data (this takes out some of the noisy yearly cycle stuff that was in the picture in the last post). I also show where "QE1", "QE2" and "QE3" occur on the graph (gray bars). Model is in blue, CPI is in dark gray:
Here we zoom in on 1960-2008 (leaving off the last bit where QE starts):
I note that the CPI data seems biased against inflation rates < 0.
I also did some smoothing to see the general trend; interestingly the biggest deviations of the CPI data (gray) from the model (blue) come at times when monetary policy was ... unconventional? The Volcker disinflation and the latest rounds of QE under Bernanke (marked with gray bars).
I'd call this a major success; we derive the inflation rate from nominal GDP and the monetary base with a single parameter (a normalization of the monetary base).