With US HICP out today:
Figure 1: Instantaneous inflation (T=12, a=4) for CPI (bold blue), PCE deflator (brown), and HICP (green), per Eeckhout (2023). Tan dashed horizontal line at 2% target for PCE deflator, blue dashed line corresponding target for CPI, HICP, assuming 0.5 ppts difference. Source: BLS, BEA, Economic Commission, and author’s calculations.
A key difference between US CPI and US HICP is that the latter does not include cost of shelter.