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 "We need to find a way to make these CPI numbers look better."

"OK, jettison canned tomatoes, coffee, and vegetable oil. That'll do it!"

https://m.primal.net/IGUv.png  
 CP-lie 🤡
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 They get rid of things that consumers dont use. In 2020 is was cars and baby stuff in 2024 is seed oils! See we are winning 🏆. We memes seed oil’s out of CPI. 
 So, in a few years time, what will be the last item on the list?

I would go for bread sticks. 
 Bug protein  
 Not to mention the price of coffee 
 It doesn't make sense to measure inflation against "stable items" anyway! Who thought that made any sense?

Inflation impacts those with the greatest need, who are and have been the vast majority of persons, so we ought to measure it against that on which they spend their money. Then, we ought to normalize against their wages. That then affords a real understanding of what inflation actually does to the populace. The bankers and big money investors don't need the CPI, because they gather their own numbers.  
 Idea - good or bad?

Personalized CPI tracker based on your past Amazon purchases.

- scrape / or request data from Amazon order history
- look up today's price of the products (if the very same ones still exist!)
- calculate the inflation

Would you expect it to be useful given the caveat of dropping the missing data and no (hedonic) adjustments? 
 I don’t wanna call it good or bad, but it’s really interesting. 

Another thing to factor though is what were you planning on purchasing but didn’t.   One good example is a Home, for many … CPI through the roof on that one. 
 Good point. I expect real estate would be a whole level up. This one would be just a personalized consumer goods category.

Maybe if crowdsourced, then you can get a public datasets of prices od many goods over the time, that would be some cool hard data to have access to for anyone.