I don't have as strong of an opinion about living standards as I do about inaccurate inflation because I haven't been around long enough to run a household and buy groceries in the 80's, but from someone who talks about facts and feelings a lot, I was hoping for some more facts.
As for CPI, there are two fundamental issues that all result in lower-than-actual reported CPI.
1. If a household spends all of its money, and prices at the grocery store rise, it has to change which items it buys, likely switching to items which experienced lower inflation during that period. The BLS weights are determined by a survey of what median households bought, not what they bought last year before prices rose. That's a mistake that leads to lower reported inflation numbers.
2. Hedonic adjustments are free rein for arbitrary adjustments. For example, new vehicles did not go up in hedonic-adjusted price from 1997 to 2020 according to the BLS [0]. An automatic Toyota Corolla was $12373 brand new in 1997. It was $19700 in 2020. While operating expenses have decreased somewhat (due to better fuel economy), does that cover the 60% price spike to the median purchaser? They throw in a bunch of other nonsense justifications like that new cars have bluetooth and other features that counter-act the price change. Our inflation numbers over those years did not incorporate a price increase AT ALL, so it's a fair assessment that real inflation was higher based on that alone. The Big Mac index has probably always been the most accurate assessment, free of political pressures.
And I agree with this. When we talk about "inflation adjusted", we need a benchmark to compare the value of dollars across time. Typically CPI is used, but it has major issues. One major issue for the "median worker" is that real estate values are not included. Obviously many workers want to buy a house to live in so this is a glaring omission. Similarly, things like stock values are not included, even though the value of equities has a massive impact on a dollar's buying power. E.g. if consumer prices at time A and B are the same, but the value of GOOG is X at time A and 2X at time B, doesn't the dollar at time A has more buying power than at time B? Finally, CPI heavily weights things like consumer electronics and automobile. These are important, but people buy these things once in a blue moon and movement in these prices generally doesn't impact people that much.
The only reason why college attendance is slightly lower today is because the college wage premium is lower today. It's not cost, which has slightly decreased recently. Housing is the only thing getting more expensive because we don't build enough but yet the median American is still a homeowner.
To me, this seems like a misleading framing. When you say "consumer prices at time A and B are the same", you can point at a basket of concrete goods which we can agree are the same (a dozen eggs, a gallon of gas, etc). But if the value of GOOG is 2X at time B ... are shares the same? How would you know? Does GOOG at time B have more revenue or a different revenue growth trajectory, or is the competitive landscape different at time B, or did they buy a bunch of other firms? Absolute vs relative is not quite the right distinction, but a share is a portion of a whole whose value can change, and so not a clear unit for evaluating purchasing power. Perhaps slightly more concrete, shares of a REIT are going to change over time, but that can be because the stuff being held changed (they bought more property) or because the value of the stuff they already held changed.
One way of thinking of share ownership is the price being paid for a share of future cash flows. That’s already kind of normalized
There is no evidence for this other than vague gut feelings
This chart demonstrates the inaccuracy concisely: [0]. According to FRED, the median worker should be living much more comfortably now than at previous times in recent history, when a median worker could, you know, buy a house with a yard, support a family, and retire. All because of some fundamental errors in how CPI is calculated that the government has no incentive to fix (combined with fundamental errors in how (un)employment is measured, but that's a different issue).
[0] https://fred.stlouisfed.org/series/LES1252881600Q