Why do measures of inflation disagree?

Inflation as measured by the personal consumption expenditures price index is near historical low levels, below the Federal Reserve’s 2% longer-run goal. Another common inflation measure, the consumer price index, is also historically low, but remains closer to 2%. The recent gap between these two measures is due largely to the cost of shelter, which makes up a larger proportion of the CPI consumption basket. Based on history, the gap between the two inflation measures should close at a rate of 0.05 percentage point per month.