The conventionally used CPI-U is in the middle of the pack.
Figure 1: CPI-urban (bold black), CPI-wage earners and clerical (purple), CPI for 2nd income quintile (pink), chained CPI (tan), HICP (light blue), Everyday Price Index (EPI) (green), all not seasonally adjusted, and PCE deflator – market facing, seasonally adjusted (pink), all in logs 2020M01=0. NBER defined peak-to-trough recession dates shaded gray. Chained CPI, HICP seasonally adjusted by author using X-13 log transform. Source: BLS, BEA via FRED, BLS, European Commission via FRED, AIER, NBER, and author’s calculations.
CPI-wage and CPI 2nd quintile are higher, reflecting the fact that prices have risen faster for those at the lower end of the income distribution (the CPI-U reflects the spending patters of a household roughly at the 70th percentile). Chained CPI is lower because it incorporates substitution effects for broad categories, while CPI-U is quasi-Laspeyres. The HICP differs in many ways from the CPI, but one important distinction is that it does not include housing costs.
Note that the AIER’s Everyday Price Index (EPI) which includes nondelayable items is noticeably higher than the overall CPI (even though it relies on BLS data). To the extent that these expenses are more at the forefront of consumers minds (because they are more frequent), then it would not be surprising if consumers thought that prices had risen substantially more than reported in the CPI (this last point is all surmise on my part).
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