SWL: Accepting the concept of the NAIRU does not mean you have to agree with their judgements. But if you want to argue that they could be doing something better, you need to use the language of macroeconomics.As an applied mathematician, Brian showed how macroeconomists don't know what they are talking about with respect to NAIRU when using the language of macroeconomics because the concept is empty.
And no advanced math required to do it. Just basic logic and philosophy of science.
Philosophy is a battle against the bewitchment of our intelligence by means of our language. — Ludwig Wittgenstein, Philosophical Investigations, § 109There are many parallels between economics and philosophy, one of the most evident is unfounded assumptions presumed to be self-evident. Scientific method was developed to circumvent this.
BR: The whole point of the standard NAIRU definition is that it is easy to observe: you just need to back out the acceleration of inflation (keeping in mind there may be other variables whose influence needs to be isolated). However, in the real world, the observed unemployment rate is affected by institutional factors -- which do not exist in a NAIRU model. Since the end result is that NAIRU estimates are inherently unreliable, the concept is wrong by definition.
This is why most mainstream macro has retreated to discussing output gaps of various types. Output gaps have to be inferred via various statistical techniques, and they are inherently fuzzier. It may be that Professor Wren-Lewis has some of these more recent models in mind when he is referring to NAIRU; but that makes as much sense as referring to post-1990 Fed Policy as monetary base targeting.
If you want to use standard academic terms, NAIRU is falsifiable, and was in fact falsified. The generalised output gaps that popped up to replace NAIRU are pretty much unfalsifiable.To a philosopher standing outside economics looking in, it appears that many economists are so intellectually committed to finding a solutions that they convince themselves and each other that they have found one when they have not.
We have got on to slippery ice where there is no friction and so in a certain sense the conditions are ideal, but also, just because of that, we are unable to walk. We want to walk: so we need friction. Back to the rough ground! — Ludwig Wittgenstein, Philosophical Investigations, § 107