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BARBERIS AND THALER

fewer than 50 percent of the balls in Urn 1 are red, while the choice of b_{2 }implies the opposite.

The experiment suggests that people do not like situations where they are uncertain about the probability distribution of a gamble. Such situations are known as situations of ambiguity, and the general dislike for them, as ambiguity aversion.^{14 }SEU does not allow agents to express their degree of confidence about a probability distribution and therefore cannot capture such aversion.

Ambiguity aversion appears in a wide variety of contexts. For example, a researcher might ask a subject for his estimate of the probability that a cer- tain team will win its upcoming football match, to which the subject might respond 0.4. The researcher then asks the subject to imagine a chance ma- chine, which will display 1 with probability 0.4 and 0 otherwise, and asks whether the subject would prefer to bet on the football game—an ambigu- ous bet—or on the machine, which offers no ambiguity. In general, people prefer to bet on the machine, illustrating aversion to ambiguity.

Heath and Tversky (1991) argue that in the real world, ambiguity aver- sion has much to do with how competent an individual feels he is at as- sessing the relevant distribution. Ambiguity aversion over a bet can be strengthened by highlighting subjects’ feelings of incompetence, either by showing them other bets in which they have more expertise, or by mention- ing other people who are more qualified to evaluate the bet (Fox and Tver- sky 1995).

Further evidence that supports the competence hypothesis is that in situ- ations where people feel especially competent in evaluating a gamble, the opposite of ambiguity aversion, namely a “preference for the familiar,” has been observed. In the example above, people chosen to be especially knowl- edgeable about football often prefer to bet on the outcome of the game than on the chance machine. Just as with ambiguity aversion, such behavior cannot be captured by SEU.

# 4. Application: The Aggregate Stock Market

Researchers studying the aggregate U.S. stock market have identified a num- ber of interesting facts about its behavior. Three of the most striking are:

The Equity Premium. The stock market has historically earned a high ex- cess rate of return. For example, using annual data from 1871 to 1993, Campbell and Cochrane (1999) report that the average log return on the

An early discussion of this aversion can be found in Knight (1921), who defines risk as a gamble with known distribution and uncertainty as a gamble with unknown distribution, and suggests that people dislike uncertainty more than risk. 14

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