デロングがポール・ローマーの数学もどき批判Project Syndicate論説取り上げたところ、David Andolfattoが、そのデロングの解釈を皮肉たっぷりに批判するエントリを書いた。その中で彼は以下のように述べている。

For Romer, the issue has to do with (I think) of how to reconcile the costly acquisition of nonrivalous (nonexcludable) ideas with perfect competition. DeLong hints at this when he writes:

Thus Paul Romer sees, in growth theory, the current generation of neoclassical economists grind out paper after paper imposing on the world "the restriction of 0 percent excludability of ideas required for [the] Marshallian external increasing returns" necessary for there to even be a price-taking equilibrium.

But DeLong (and Romer) are (I think) wrong on this dimension, at least, on a technical level. It is in fact possible to write down a growth a model where nonrivalous ideas are partially excludable (subject to costly acquisition) in a competitive equilibrium with price-taking behavior. My paper here (with Glenn MacDonald) constitutes one such example.




The U.S. Department of Energy employs physics Ph.D.s to manage our nuclear weapons. How would you feel if some of them wrote blog posts saying that it is possible to build a perpetual motion machine? What if they did this to signal their loyalty to some club of physicists? Wouldn’t you wonder why membership in this club was important enough get them say that they do not believe the second law of thermodynamics? And what kind of physics club would use an endorsement of the perpetual motion machine as a loyalty oath?
In a recent post, David Andolfatto, who is a Vice President at the Federal Reserve Bank of St. Louis, gives a brazen display of mathiness–brazen because he denies Euler’s theorem, which for economists is about the same as denying the second law of thermodynamics is for physicists.
The type of mathiness that is hardest to root out is the opaque mathiness illustrated by Lucas (2009). It combines math that is hard to understand with verbal claims that can be shown to be misleading, but only after a careful analysis of the math. By taking advantage of ambiguity and misdirection, its verbal claims can mislead without saying anything that is actually false.
Andolfatto’s brazen mathiness involves a verbal statement about a mathematical model that flies in the face of an impossibility theorem. No model can do what he claims his does. No model can have a competitive equilibrium with price-taking behavior and partially excludable nonrival goods.
If you are not an economist, this would be a model in which someone who has a monopoly on an idea can charge for its use, but somehow is unable to influence the price that users have to pay, which should sound implausible at least. If you are an economist, you know that there is a very simple argument based on Euler’s theorem that proves this type of model is impossible. The proof goes back a long way. I know that Karl Shell invoked it in the late 1960s. I restated it in the AER article of mine that Andolfatto quotes, so it was fresh in his memory. Dietz Vollrath has a recent post that works through the logic again.
In its most general form, the proof relies on a step that invokes a fact about production processes: If you double all the rival inputs (the inputs you can touch or stub your toe on) you double the output. Some economists try to evade the theorem by denying the possibility of replication. But Andolfatto’s paper makes the required assumption about production openly–constant returns to scale in rival inputs. So he’s got no wriggle room. I can’t for the life of me see how Andolfatto thinks he can evade Euler’s theorem.
It is certainly possible that he is confused. But if you were confused, wouldn’t you try to understand the proof that says what you want to claim has to be false before you go ahead and claim it anyway?
米エネルギー省は我々の核兵器を管理するために物理学博士を雇っている。もしその中のある者が、永久運動機関を構築することが可能だというブログポストを書いたら、あなたはどう思うだろうか? もしそれが、物理学者のある種のクラブへの忠誠を示すために行われたのだとしたら? 熱力学の第二法則を信じていないと言うほどそのクラブの会員であることがなぜ重要なのか不思議に思うのではないだろうか? そして、一体どんな物理学クラブが永久運動機関の是認を忠誠の誓いに使うのだろうと思うのではないか?



一方、Nick Roweは、間違っているのはローマーの方ではないか、というエントリを書いている