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Not to mention CPI calculation changes regularly
CPI changes every two years. Regularly, but not that frequently.
Also doesn't measure substitutions, like choosing to buy a cheapo brand of the same product to save money.
Speaking of, in the age of mass surveillance and data collection I have no idea why inflation is limited to a basket of goods. It seems trivial to just measure the cost of everything everywhere.
Using substitution for CPI leads to counterintuitive effects.
If the price of gas increases 5%, and you respond by biking to work instead of driving, then you have substituted something else for gasoline. When people argue that CPI should take substitution into account, they are arguing that you aren't actually spending 5% more on gas. Since you are buying less gas, maybe you are only spending 2% more on gas. That's inflation with substitution taken into account.
In other words, taking substitution into account makes inflation appear less bad. That's why consumer activists don't want to take substitution into account: if prices increase 5%, then inflation is 5% regardless of how people respond.
There is an alternative form of CPI called "chained CPI" that tries to account better for substitution. Every month, chained CPI changes according to how people are responding to inflation. Chained CPI is generally lower than regular CPI, and when people want to use chained CPI they are usually trying to pay people less for their cost-of-living increases in wages/benefits. In other words, they are arguing "Hey, why should I adjust your pay for CPI when you can just substitute for cheaper stuff?"
TLDR: Substitution is how employers justify stiffing employees.