I mentioned this last week, but Susan Fleck, John Glaser, and Shawn Sprague have a much better illustration (PDF) of the divergence between the GDP deflator (a measure of inflation for all the things the American economy produces) and the Consumer Price Index (a measure of inflation for all the things American households buy).
This sounds extremely wonky and boring, but it's important for a couple of reasons. One is that about a third of the divergence between productivity and real wages is accounted for by this divergence. American workers are getting better at making stuff, but it's not necessarily the stuff that American workers buy. Computers, for example, have seen a productivity explosion. But a lot of that is for export or for the enterprise market. High-tech products are a pretty small share of the typical household's spending. It's also important for monetary policy. For decades, the different ways of calculating inflation all tended to converge over the medium term, so the precise choice of target index wasn't that important. Recently that hasn't been the case. Inflation targeting using the GDP deflator would have led to slightly but systematically looser monetary policy throughout the "Great Moderation" and to a much more accommodative approach during 2008.