Stock Markets
Rational frenzies?

Few markets are as efficient as the world's largest stock markets, yet prices on them are extremely volatile, and many cite the 1987 crash as strong evidence of markets' inefficiency and irrationality. According to the basic Walrasian model of market clearing, a small piece of new information will have only a small effect on the equilibrium price, so many argue that volatile prices indicate poor market performance. In Discussion Paper No. 593, Jeremy Bulow and Research Fellow Paul Klemperer develop a model in which both surges in trading activity and crashes in market prices may be consistent with the perfect rationality of all buyers and sellers, even when there is no important `news' and traders' valuations of an asset are independent. They argue that rational prospective buyers' decisions to buy now depend not only on their valuations of the good, but also on their expectations of its future prices. Buyers with very different valuations may therefore have a similar willingness to pay. If a small piece of new information then changes many buyers' views of the current price from slightly too high to sufficiently attractive, the first purchase at a given price may then result in a `frenzy' of activity. Since this typically involves a large amount of trading, it reveals a large amount of information, which will either reinforce the frenzy or lead to a discontinuous drop in the market price a `crash'.
Bulow and Klemperer build a simple model of market clearing with rational potential buyers and a single profit-maximizing seller with a fixed supply. The seller begins by asking for a high price, which is then lowered over time, and buyers may purchase at the price named at any moment. This model yields three main results. First, demand will `feed on itself': even a single purchase can make many previously reluctant buyers eager to buy at the same price. Second, frenzies can quickly peter out: while many customers may pay a given price at one moment, it can become common knowledge that no buyer will pay anything close to it the next, which induces a crash. Third, small differences in the underlying demand structure can cause large, unpredictable changes in the price path; so the demand curve of buyers' reservation values may be unambiguously higher and sellers' revenues lower in one market then in another market with the same supply.
Bulow and Klemperer account for these results by arguing that the current `willingness to pay' of buyers with an option to defer purchase may be much more closely related to their expectations of the marketclearing price than to their reservation values. A market's demand curve may therefore be inelastic, while the corresponding `willingness to pay' curve is almost flat in the relevant range. Even a small amount of new information therefore changes many bidders' views and leads to a frenzy of activity. They argue that the model may most closely parallel the manner in which US underwriters sell new securities, although some housing, commodities and currency markets display similar features.

Rational Frenzies and Crashes
Jeremy Bulow and Paul Klemperer

Discussion Paper No. 593, October 1991 (AM)