"Paul Krugman Quests for the Minsky Moment
Shleifer, Vishny, Minsky: I’m on a continuing quest to develop a tractable model of Minsky moments. Why? you may ask. Why not go with verbal intuition? Well, I’m enough of a conventional economist to think that there’s no substitute for a model with dotted i’s and crossed t’s; it’s not THE TRUTH, but it really does help clarify your thinking.
So here’s where I am right now. There is a class of models — Shleifer and Vishny is my main inspiration, although other models, like Kiyotaki and Moore, are in the same spirit — in which you can get something like a Minsky moment. The story goes something like this (this isn’t quite how Shleifer-Vishny does it, but not too different):
There are three kinds of investors: ordinary investors who buy when the price is low and sell when it’s high; noise traders, who buy and sell randomly; and highly leveraged informed investors (HLIs), who try to buy low and sell high with other peoples’ money. On average, the HLIs should earn a high rate of return.
However, Shleifer-Vishny assume that there are two periods before the goodness of investments is revealed to all — and in period 2 even good investments can look bad thanks to selling by those noise traders. And if the noise traders drive the price down sufficiently, HLIs can face margin calls, forcing them to liquidate and push prices even lower. This is more or less the Minsky moment.
But how do we make Minsky moments endogenous? Think about playing this game repeatedly, with the number of HLIs varying based on past performance. If there are very few HLIs, expected returns are high and the probability of a Minsky moment (and its severity if it happens) are low; this will tend to bring more HLIs into the picture, until the system is highly vulnerable. A bad draw on noise traders, and there’s an asset price plunge that hits the HLIs very hard. People decide that leverage is a bad thing, and for a while those who do go into leverage do very well. And the cycle begins again.
It’s crude. But I think it does get the nonlinearity Brad DeLong was looking for (though I’d better work up the actual algebra to make sure!).
 In his new book The Myth of the Rational Market Justin Fox traces the lineage of the noise-trade assumption to an unpublished paper by Larry Summers that began, THERE ARE IDIOTS."