The two big commodity price shocks of the 70s did, in fact, feed quickly into core inflation. Since then, however, nada.
Here's the picture he posted.
There's even a smaller third shock around '69-'70 that he doesn't mention. What a stark difference: from 1968 to '80 the two inflation measures move almost in lock-step. Since then, the sticky measure has been very unresponsive to price shocks - i. e. -- sticky.
I'm not sure I buy the COLA explanation - though I can't really say how or why. It does seem to be at least consistent with the expectations view of inflation that David Beckworth and many other economist (including Krugman) put a lot of stock in.
Of course, in an environment where inflation expectations get unanchored, like the 1965-1979 period, nominal spending shocks will have a greater impact on the price level and less influence on real economic activity.
Steve is ahead of me here, and thinks he's sussed it. More to come, I'm sure. Stay tuned.