PCE Inflation vs CPI Inflation
A comparison of the trends in PCE vs CPI inflation meausures for the US, based on Fred data.
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PCE Inflation is published by U.S. Bureau of Economic Analysis is based on implied prices and weights by surveying businesses selling to consumers. It uses a Fisher index to construct updates for each period.
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CPI Inflation is published by U.S. Bureau of Labor Statistics and is based on a survey of prices for a representative basket of goods and services and weighted by a direct survey consumer expenditure. It uses a Laspeyres index to construct updates for each period.
For detailed discussion of differences see the BLS.