Or is your point that only some stuff is cheaper, but the total standard of living supportable by average wages has nevertheless dropped?
Wage in currency is a lot simpler. The only real manipulation possibility is currency value and some minor tinkering in the definitions.
[1] For example a major criticisms of the euro-zone inflation index is that it excludes housing cost: https://en.wikipedia.org/wiki/Harmonised_Index_of_Consumer_P...
There used to be "white-collar cost of living comparisons", maybe there still is. The headline in the newspaper would be "Copenhagen most expensive city in the world" or somesuch. The major reason for that was that hiring a full-time nanny to look after your children was expensive in Copenhagen, and a full-time nanny was included because that was considered necessary for white-collar professionals in some of the cities om the survey, and for fairness it was included everywhere. But in Copenhagen, there are excellent creches and kindergartens. Only a kook hires a nanny, so those attempts at fair comparisons compared kooky behaviour in Copenhagen with sensible behaviour in, say, Pune or Bangalore, and found that being a kook in Copenhagen is expensive.
But how can you do it better? How can you compute the cost of living (which is tightly connected to purchasing power) so well that you can compare year-over-year and capture 2% changes reliably? If the city provides more/better creches, should you start counting 19.2% of the cost of a nanny instead of 19.4%?
People don't need a car where I live. I know areas nearby where a family like mine would have at least one, perhaps two cars. Cars are cheaper there (renting off-street parking space costs a fortune here) but how would you factor the cost of a car into purchasing power and compare fairly? If the city builds new metro rail, how do you change the weight of the family's first car in your calculation, and the cost of the second car?
This is difficult stuff.
https://www.cbpp.org/blog/census-renters-incomes-still-laggi...
But hey! US$200 4k TVs! Portable handheld computing devices with access to a good chunk of human knowledge (and humanity) ! No problem!
That would be deflation, but we've actually had inflation over the past decades. We can ofcourse discuss how wrll we are measuring it, but generally speaking some life necessities like housing have skyrocketed in price.