A superb note by Yifan Cao and Adam Hale Shapiro of San Francisco Fed.
US has two broad measures for calculating inflation at consumer level – CPI and Fed preferred Personal Consumption Expenditure. They look at reasons for difference between the two measures:
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.
What is amazing is the small gap between the two measures.
Figure 1 shows the year-over-year change in core CPI and PCEPI inflation over the past 10 years. These core measures exclude food and energy prices, reducing volatile short-run movements in the indexes. Core measures are better able to capture the underlying longer-term trends in inflation. The figure shows that core CPI and core PCEPI inflation measures are highly correlated, but that gaps frequently arise between them. Since August 2011, annual core CPI inflation has outpaced annual core PCEPI inflation by a minimum of 0.20 percentage point and an average of 0.34 percentage point. This is the longest sustained gap between these measures in the past 10 years.
Here, we have core WPI and CPI differ by more than 5.5- 6%. Yes there are differences as PCE and CPI are both consumer inflation measures whereas WPI and CPI are not. But still, it is a concern for US researchers whereas it is hardly an issue here..