What the GOP tax scheme did was adopt the chained consumer price index (chained CPI). Chained CPI is the measurement of CPI that understates inflation’s effects on our standard of living by assuming inflation has not reduced Americans’ standard of living.
No. The chained CPI measures the average change in prices at a constant standard of living. Most price indexes do. A Laspeyres index overstates inflation by assuming no future substitutions due to relative changes in prices and a Paasche index understates inflation by assuming no past substitutions. The chained CPI averages both types using a Tornqvist index (initially, it uses a geometric means index until later expenditure data is available.
I know what it is. Chained CPI assumes inflation has not reduced Americans’ standard of living.
Wrong. It measures what the price change would be to maintain the same standard of living. You can substitute goods based on price changes and maintain the same standard of living.
For example, you can buy hamburgers when you can no longer afford steak. That full substitution ignores the fact that if individuals viewed hamburgers as a full substitute for steak they would have bought hamburgers before Fed-created inflation made steak unaffordable.
Which is why that is NOT what the chained CPI does.
Simplistic example. There are 2 kinds of candy bars: peanut bars and chocolate bars. Both cost $1/ea. Julie buys 2 peanut and 2 chocolate for a total candy budget of $4. But, oh no! There's a cacao blight and chocolate bars go up to $4 ea. Peanut bars don't change. A Laysperes index would assume no change in quantity and calculate the price change as ($1*2+$4*2)/($1*2+$1*2)=2.5.which is an increase of 150%. This assumes no substitution.
You seem to be asking about the case where Julie can't change her budget and switches to 4 peanut bars. To calculate the chained CPI, we need to look at the price differentials and the expenditure shares. In the base period peanut bars share was $2/$4 and chocolate's share was $2/$4, so .5 for each. In the current period, peanut bars are $4/$4 and chocolate is $0/$4. So 1 and 0. Peanut bars average share is (.5+1)/2 = .75 and chocolate bars average share is (.5+0)/2 =.25
Price differential: peanut bar is no change so $1/$1 =1 and chocolate bar went from $1 to $4 so $4/$1=4
The tornqvist index then is 1^.75 * 4^.25 = 1*1.414 = 41.4% change.
Note that while Julie is not actually spending more, the CPI would show inflation of 41.4%
More realistically, Julie might give up 1 chocolate bar and substitute 2 peanut bars for 4 peanut bars and 1 chocolate and spending $8 on candy instead of $4...Less chocolate, but more candy....about the same standard of living. And the expenditure shares would stay the same. The tornqvist index would be 1^.5 * 4^.5 = 2 A 100% increase in prices, accurately reflecting the price change she experiences at the same standard of living.