The Fed targets PCE. CPI gets the headlines. They measure the same thing differently, and PCE runs about 0.3 to 0.5 percentage points below CPI on a structural basis.
CPI comes from the Bureau of Labor Statistics around the middle of each month. PCE comes from the Bureau of Economic Analysis near the end. The structural gap between them comes from how they build the basket.
CPI uses a fixed basket of goods and services, reweighted every two years. PCE uses a basket that updates every quarter to reflect what people actually bought. When the price of beef rises and shoppers switch to chicken, PCE captures the switch in real time. CPI does not.
The weights themselves differ too. Shelter is roughly 33 percent of CPI but only about 15 percent of PCE. Health care is the reverse: small in CPI, large in PCE, because PCE includes spending paid by employers and Medicare, not just out-of-pocket. When shelter inflation runs hot and health care inflation runs cool, CPI will print higher than PCE. When the situation reverses, so does the gap.
The Fed targets 2 percent on PCE. A 2 percent PCE world is usually a 2.3 to 2.5 percent CPI world.
If you want to know what the Fed will do, watch PCE, especially core PCE excluding food and energy. If you want to know what your grocery bill will look like next month, CPI is closer to the experience because of the fixed basket and the heavier weight on the things households actually shop for.
Both indexes are correct. They are measuring different questions.