From this month's edition of Economic Trends, published by the Federal Reserve Bank of Cleveland (page 3):
What information households base their inflation expectations on is the topic of frequent academic debate. Rather crude correlations, which examine the relationship between realized inflation rates and households’ expectations, indicate that their year-ahead expectations are most closely correlated with the headline CPI inflation rate, and are especially sensitive to this measure over longer time horizons. Interestingly, expectations for the inflation rate over the next five to 10 years are more closely correlated with the core CPI inflation rate than with headline CPI. The correlation also grows stronger as the underlying core CPI inflation trend becomes more persistent. Indeed, the divergence between short- and long-term inflation expectations is correlated to the divergence between headline and core CPI inflation rates; this may indicate that households see through the same transitory fluctuations in prices that the core inflation measure is designed to isolate.
At a minimum, this means that the FOMC has been pretty successful at getting the public to focus on core inflation as a reasonable measure of the longer-term inflation trend. But it is unlikely that this situation could persist without a central bank that generally delivers the goods, and as I suggested once before, it does appear that, over the medium term, core inflation is a better predictor of headline inflation than is headline inflation itself.
To the extent that stabilizing inflation expectations is the really important part of getting monetary policy right, these sorts of results begin a persuasive case for the use of core inflation as a guide.