Without at all denigrating Paul Krugman’s goodness as a human being, I can amply testify to Noah’s goodness.
I also love Paul’s definition of an irrational bubble:
… what do we mean when we talk about bubbles? Basically, I’d argue, we mean that people are basing their decisions on beliefs about the future that are based on recent experience but can’t be fulfilled. …
The point, whether prices are involved or not, is that the expectations of individuals add up to an aggregate impossibility.
Note that Paul does not venture a definition of a rational bubble at all, but reserves the term “bubble” for an irrational bubble.
It is clear to me why we would want a definition of an irrational bubble–we are interested in knowing that something is bound to pop sooner or later. The purpose of defining a rational bubble is less clear to me, except to distinguish it from an irrational bubble. Clarifying the purpose of distinguishing a “rational bubble” from things that aren’t bubbles at all, should help in choosing a good definition of a “rational bubble.”
Multiple rational expectations equilibria are perennially fascinating. (Indeed, I have often warned graduate students to beware of the danger that this particular fascination might distract them from the optimal choice of research topic for advancing their careers; studying the intricacies of multiple equilibria can easily absorb enormous amounts of time, often far out of proportion to the useful knowledge won.) Thus, one possible purpose for the term “rational bubble” is using it as a way of talking about multiple equilibria that differ first and foremost in a particular asset’s price.
As Paul says, money is clearly not an irrational bubble. Whether money is a “rational bubble” or not depends on the definition of “rational bubble.” Here is one reasonable definition:
An asset price exhibits a rational bubble if there are multiple rational expectations equilibria (within a given class) that have different prices for the asset, and the asset price is above its minimum price over those equilibria.
By that definition, money looks like a rational bubble, for quite relevant classes of rational expectations equilibria. In particular, the equilibrium in which paper money has zero value has substantial historical relevance.
As I say in that exchange, let me remind everyone that given my settings, anything said on my Facebook wall is totally public, just as comments on this blog are.