With August CPI release, we have core, chained core, and supercore. PPI comes tomorrow.
Figure 1: Instantaneous inflation for core CPI (blue), chained core CPI (tan), supercore CPI (pink), PPI core (red), and PCE core (green), per Eeckhout (2023), T=12, a=4. Source: BLS, BEA, and author’s calculations.