With the core PCE deflator, we have these measures of what’s happening to core.

Figure 1: Instantaneous inflation for core CPI (blue), chained core CPI (tan), supercore CPI (pink), services supercore (light green), PPI core (red), and PCE core (green), per Eeckhout (2023), T=12, a=4. Source: BLS, BEA, Pawel Skrzypczynski,  and author’s calculations.