Health Care Spending
The other point from my earlier chart on health care spending worth noting is that in the PCE data health care accounts for around 20% of consumer spending. In contrast, medical care only has a weight of 6.2% in the CPI. Since health care prices generally rise some two to three percentage points faster then overall inflation this implies that the CPI significantly understates reported inflation. If the weight of medicine in the CPI were more like the weight in spending, the reported inflation rate would have been up to a full percentage point higher every year.
Interestingly, when I bring this point up to all the people who argue that the CPI overstates inflation they generally try to change the subject.