A question for New Keynesians - InvestingChannel

A question for New Keynesians

As you know, I often argue that inflation doesn’t play a useful role in macroeconomics.  In places where economists put inflation into their models, NGDP growth would be much more useful.  Obviously lots of people don’t agree with me, and this post is aimed at those people.  Here’s my question:

Which inflation rate is appropriate in NK models?  The average change in the price of goods sold, or the average change in the quality-adjusted price of goods sold? I.e., according to NK theory, what role should hedonics play in the construction of price indices?  Why?  What specific aspect of the NK model points to the need for a specific hedonic adjustment?

I hope it goes without saying that in NK models there is no role for the concept of a price index that in some sense accurately reflects changes in the ‘cost of living’, whatever that nebulous terms means.  So then what is the optimal price index, according to the NKs?  In addition, how would your optimal index treat the cost of housing?  What about monthly payments made under long-term rental agreements?  Are they “prices”?  How about payments made to pay off long-term car loans?  Are they “prices”?  (Hint:  The BLS treats apartment rents as prices, but not payments on car loans.)

In other words, what the hell is this “inflation” concept (which you think is so important) actually trying to measure?

Second hint:  Think about things like menu costs, and then also think about how they relate to the way the government actually measures the (quality-adjusted) cost of living.

I’m not worried about perfection—I understand that no data series are perfect.  I’m just trying to figure out what you think “inflation” should be trying to measure, in a perfect world.  In case my question still is not clear, suppose there were no new products being invented, but existing products rose in price at 4% per year in unit terms, and 2.5% per year in quality-adjusted terms.  That’s because the quality of each product improved at 1.5% per year.  In that case, which inflation number belongs in NK models, 4% or 2.5%?