I was going to do a long post explaining why Scott Sumner’s attempt to nihilate the concept of inflation was going too far.
However, Scott has accepted the crux of my argument making the whole thing a lot easier. He says
I said “almost every use” because there is one valid use of inflation. Take the rate of NGDP growth per capita and subtract out your subjective estimate of how much NGDP growth would have left us equally happy as before. The difference is inflation. But inflation still doesn’t have practical value, it’s merely your personal estimate of how much of the increase in NGDP is not “real.”
So we can do the same thing, but take all people in society and allow side payments so as to determine which NGDP growth path is Kaldor-Hicks preferable.
We then have a relation defined over all possible NGDP growth paths such that Growth Path A is equal to or superior to Growth Path B if and only if there exists some set of side payments that would make all parties at least as well satisfied with path A as Path B.
This is then a partial ordering over the possible NGDP growth paths. There then exists some F mapping NGDP paths into the real numbers such that F(NGDP Path A) is
greater less than or equal to F(NGDP Path B) if and only if NGDP Path A is equal to or superior to NGDP Path B.
This mapping F is what we call the inflation function and it is well defined.
What is not immediately clear is if we can meaningfully pass lotteries through F such that the partial ordering is maintained. Though it seems to me that you could.
If you can then you have a cardinal mapping. That is, a price index, and it is fundamental and well defined.
Even if we can’t we have a meaningful measure of ordinal inflation.