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Property taxes, food, copays and deductibles even if you have healthcare insurance, highway tolls, ...

They diddle what is in the list of "standard stuff" to keep the indicated CPI low, so they need not pay increases in social security and medicare.

Think of it this way:

Bob has money in his pocket which is not losing value rapidly.
That's because there is no appreciable monetary inflation in recent years: the dollar really has held most of its purchasing power.

But... Bob spends most of his money on specific things that happen to be rising in price a lot lately.
Bill lives next door and buys a lot of computers, so he doesn't see the same problem.
CPI is designed to capture the experience of the "average" person like Bob and Bill.

This is an impossible task. No measure can do that because experiences vary so widely, and it definitely can't also tell you a good measure of monetary inflation.
It's also almost impossible to handle product substitutions (buy apples if pears get expensive) and improvements (faster CPUs for the same price) correctly.
So anybody that says CPI is well implemented is kinda right. And everybody who says it's measuring things incorrectly is also kinda right.
It depends on the question you are expecting it to be able to answer.

The US CPI appears to be designed to measure the monetary portion of inflation as it shows up in the average consumer's expenditure basket.
The monetary slant comes from using the median, not average, price rise in the basket: it tries to avoid things with product-specific and possibly transient big price moves.
But the basket itself is built up from consumer spending habits, so it hits the middle of the pack from among what people actually buy. Or tries to.

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