I don’t want to comment on Posner. He’s a nice guy. But I spend my life trying to understand this stuff. My last two papers, which took me three years, were on determinacy conditions in New-Keynesian models. It took me a lot of time and a lot of math. If Posner can keep with that and with Law and Economics, good for him.
Note he avoids actually confronting anything specific in Posner's argument or providing any argument of his own, and merely points out he knows a lot of math and some parochial modeling expertise. Now, investigating 'determinacy conditions in New-Keynesian models' (see here) seems very high tech, and he does absolutely nothing to explain to the intelligent, but uneducated reader what this means. It is really bad form, using pretentious jargon to avoid argumentation.
In the context of what he investigated 'for the past two years', determinacy conditions just means whether one can say that Fed interest rate targets can moderate inflation by itself, independent of say, the monetary aggregates. We don't have enough data to determine if that is true. Now, given the way interest rates and inflation have behaved, with a long secular trend up from 1950 to 1980, then back down to today, that should be obvious. It's basically two datapoints. Ideally, we need hundreds of such periods. That we don't have enough data to define optimal monetary policy is only an abstruse concept if you are being disingenuous. Every technical debate in economics comes down to a pretty common sensical debate, and if you can't articulate it in such a way, you are either an idiot-savant who does not understand what the models really mean, or you are trying to brow-beat outsiders via intellectual intimidation. As Cochrane wrote a very nice piece on how to write a good economics thesis, he knows better.
There's a famous story about the great mathematician Leonard Euler, and the French philosopher Denis Diderot, who created te first encyclopedia. They were both visiting Russia on Catherine the Great's invitation. The Empress didn't like Diderot's arguments for atheism, and was concerned such arguments were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was informed that a learned mathematician had produced a proof of the existence of God, so he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced, "Sir, (ab+n)/z=x, hence God exists—reply!". Supposedly Diderot stood dumbstruck as laughter erupted from the court. Of course, the 'proof' is total nonsense.
It's not clear how true that story is--surely it's embellished--but it reflects a common tactic by those with specialized skill: hide behind parochial terminology. Some economists like to say you can't have a defensible opinion on the economy unless you fully understand Turnpike theorems, value functions, or set theory. These are model paradigms, and the relation of a model to reality, in economics, has been more hope than reality. All model paradigms in macro have been irrelevant to reality, so the onus is on them to demonstrate they aren't part of parochial status game fancied by academics. Bohr's model of the hydrogen atom isn't 'correct', with an electron circling the nucleus in the way a planet circles the sun, but it gives one some useful intuition. That is really all any economic model can aspire to. The idea that an economic model will allow one to estimate parameters that predict something with the right digit, is the hope of all non-physical sciences, but they haven't been successful.