Nick Rowe sent me his response and gave me the permission to post it. You find my remarks at the end of his reply. So here we go:
Thanks for your response. I've got several different things I want to say in response, so i will just number them for clarity:
1. Yes, you understood what I'm saying. That's always a relief. I wasn't sure if I was clear enough.
2. As you say, my critique about fragility in the limit is different from Peter Howitt's critique about dynamic instability under learning. But my intuition (OK, my "gut") tells me that the two are closely related. That if a model is very fragile in my sense it will be unlearnable in Peter's sense. Because if they haven't learned it yet that will cause big changes in how the model behaves, so what they learn from observing the model will be very different from the RE equilibrium.
3. OK, if half the agents make one mistake, and the other half make the exact opposite mistake, the model might behave exactly like an RE model in aggregate. But what if 49.9% make one mistake, and the other 50.1 make the exact opposite mistake? If it's a robust model, that's no big deal. The predictions will be almost identical to full RE. But if the model is "fragile in the limit", that small difference will cause a big bang in the predictions.
4. OK, I concede your main point! A model that is "fragile in the limit" might still be a "useful" model in some sense. But that's a very different sense from the one that we usually have in mind when we talk about models being "useful". Normally we mean something like "there's some sort of rough correspondence between the world and the model". But models can sometimes be "useful" in another way. The Modigliani Miller Theorem would be my favourite example. Someone could argue that the MM model is totally useless as a theory of how the world works, but is still a really useful theory because it tells us what assumptions we need to reject if we want to understand firms' financing.
5. Now I want to go totally off-topic. Well, not totally, but close. Whatever are you guys doing learning that stuff about stability of equilibrium in a Walrasian (OK, Arrow-Debreu, but same difference) economy? We live in a monetary exchange economy with n-1 markets (2 goods each, one of which is the medium of exchange), not a Walrasian economy with one big market where all n goods are traded simultaneously. So Walras' Law is misspecified, because there are n-1 different excess demands for money. Plus, if prices are at disequilibrium levels, either buyers or sellers will be rationed (they won't be able to buy or sell as much as they want), so will reformulate their notional demands and supplies taking those quantity constraints into account. So Walras' Law can't apply anyway, because their demands and supplies in each market are based on the quantity constraints in all the *other* markets, so the sum of the excess demands don't conform to any unified decision-making process based on a single (budget) constraint. We (old) guys learned that in the 1980's. It was called "disequilibrium macro". Then Lucas came along, and (almost) everyone forgot it. But doing stability proofs in a non-monetary economy with a Walrasian auctioneer with "notional" excess demand functions that ignore quantity constraints....now that really is useless. As well as "fragile in the limit"! ;-)Since it's quite late in good old Germany, I will only comment on #5. Well, perhaps my recourse to the SMD results becomes more comprehensible if I tell you that I'm a historian of economics. So my job is to cope with the 'wrong ideas of dead men' (or at least quite old men). That may explain my focus on Arrow-Debreu models. Yet note that I used the SMD results only as an example to make my point. You could find other frameworks to make the same point. I'm just writing about SMD, so it seemed natural to use it. Actually, I would be pleased if SMD results would figure more prominently in our curricula. Since it is a highly negative result, applied economists should be aware of it. In particular when you are a Arrow-Debreu sceptic, you should welcome higher awareness of the generic impossibility to establish global uniqueness and stability by means of 'proper microfoundations'. This is because Arrow-Debreu reasoning is not as dead as perhaps it should be. Be it as it may, I'm happy that you concede my main argument (#4).
Actually, I concede your point about Walras' Law. Right because I'm a historian of economics, I'm well aware of the precious results by Clower and Leijonhuvfud that you "(old) guys" studied some hundred years ago (more or less), and that unfortunately disappeared from modern curricula. In concrete, I concede that in a monetary economy it is crucial to distinguish between notational and effective demand and, hence, to know of Clower's dual decision hypothesis. Consequently, I do accept that Walras' Law applies if and only if effective demands coincide with notational demands and that this do not have to be the case. So you preach to the converted!
