The CPI is kinda fine and should not include interest rates. The CPI is used to measure price inflation and not individual misery and should be left to do just that.
It would have been better to invest in such an index. Here is a simplified example: The US is made of two cities; NYC and midland. Inflation rate is 0% for both and misery is non-existent. midland now has no jobs. None. So people move to NYC and inflate prices there. Inflation in NYC is 20% while deflation in midland is 30%. The Fed works the numbers and says that overall inflation is around 2% for the whole country and so everything is fine.
The reality is that misery is sky high; people are being burnt by prices in NYC and can't find jobs/buyers in midland. They have to move at high personal costs or close their businesses in the midland. On the other hand, they struggle to make a living in the new NYC town.
CPI doesn't measure things like healthcare properly (17% of GDP) as those prices are not paid by consumers. the insurers get their cut straight out of your paycheck.
College either. Tuition is priced as is, but what about people who pay many multiples of the original tuition in interest expenses over the years? not counted in CPI. Tuition inflation for a person with the means to pay out of pocket is much lower than someone who finances their education.
Wait, there is actually a misery index: https://en.wikipedia.org/wiki/Misery_index_(economics)
It would have been better to invest in such an index. Here is a simplified example: The US is made of two cities; NYC and midland. Inflation rate is 0% for both and misery is non-existent. midland now has no jobs. None. So people move to NYC and inflate prices there. Inflation in NYC is 20% while deflation in midland is 30%. The Fed works the numbers and says that overall inflation is around 2% for the whole country and so everything is fine.
The reality is that misery is sky high; people are being burnt by prices in NYC and can't find jobs/buyers in midland. They have to move at high personal costs or close their businesses in the midland. On the other hand, they struggle to make a living in the new NYC town.