BARBERIS AND THALER
if x 0 if x 0
π i w P i ( * ) , ( ) w P i
Pγ w(P) (Pγ (1 P)γ )1/γ
Here, Pi (Pi*) is the probability that the gamble will yield an outcome at least as good as (strictly better than) xi. Tversky and Kahneman (1992) use experimental evidence to estimate α 0.88, λ 2.25, and γ 0.65. Note that λ is the coefficient of loss aversion, a measure of the relative sensitivity to gains and losses. Over a wide range of experimental contexts λ has been estimated in the neighborhood of 2.
Earlier in this section, we saw how prospect theory could explain why people made different choices in situations with identical final wealth lev- els. This illustrates an important feature of the theory, namely that it can accommodate the effects of problem description, or of framing. Such effects are powerful. There are numerous demonstrations of a 30 to 40 percent shift in preferences depending on the wording of a problem. No normative theory of choice can accommodate such behavior since a first principle of rational choice is that choices should be independent of the problem de- scription or representation.
Framing refers to the way a problem is posed for the decision maker. In many actual choice contexts the decision maker also has flexibility in how to think about the problem. For example, suppose that a gambler goes to the race track and wins $200 in his first bet, but then loses $50 on his sec- ond bet. Does he code the outcome of the second bet as a loss of $50 or as a reduction in his recently won gain of $200? In other words, is the utility of the second loss υ(50) or υ(150) υ(200)? The process by which peo- ple formulate such problems for themselves is called mental accounting (Thaler 2000). Mental accounting matters because in prospect theory, υ is nonlinear.
One important feature of mental accounting is narrow framing, which is the tendency to treat individual gambles separately from other por- tions of wealth. In other words, when offered a gamble, people often evaluate it as if it is the only gamble they face in the world, rather than merging it with pre-existing bets to see if the new bet is a worthwhile addition.