The most important property of reference-dependent preferences is loss aversion—
people dislike losses relative to the reference point more than they like same-sized gains. I illustrate two kinds of evidence on loss aversion, that based on people’s willingness to trade their current position for another one, and that based on choices over risky gambles.
Loss aversion is manifested in the striking endowment effect documented first by Kahneman, Knetsch, and Thaler (1990, 1991) and subsequently by many other researchers: once a person comes to possess a good, she almost immediately values it more than before she possessed it. These experiments usually start by randomly giving half the subjects (often a class) mugs. These subjects become the “owners” or potential sellers, and the others are
“non-owners” or potential buyers. The owners are then asked to examine the mug and think about how useful it might be to them. They are also asked to pass their mug to the closest non-owner, so that they can examine it as well. This is an important part of the design, because it reduces the information asymmetry between owners and non-owners. Buying and selling prices are then elicited in an incentive-compatible way using the Becker-DeGroot-Marschak procedure (Becker, DeGroot and Marschak 1964). Prototypical experiments starting with Kahneman, Knetsch and Thaler (1990), have consistently found a major gap, with selling prices being about twice the buying prices.
The endowment effect—the fact that owners value a good more than other-wise identical non-owners—is usefully conceptualized as a case of loss aversion.
Individuals who are randomly given mugs treat the mugs as part of their ref-erence levels or endowments, and consider not having a mug to be a loss.
Individuals without mugs consider not having a mug as remaining at their reference point, and getting a mug as a gain. Since people are more sensitive to losses than they are to same-sized gains, the sellers “value” the mug more:
by keeping the mug, they avoid a loss, whereas buyers would merely make a gain if they got the mug.
Another important manifestation of loss aversion is in attitudes toward risky gambles. For instance, most people would turn down an immediate fifty-fifty gain $550 or lose $500 gamble. This kind of risk aversion seems such an intuitively obvious fact that for a long time researchers have not even bothered to check it. But recently, Barberis, Huang and Thaler (2006) offered the gamble for real to MBA students, financial analysts, and even very rich investors (with median financial wealth over $10 million!). A majority of all these people, including 71% of the investors, rejected the gamble.
The standard economic explanation for people’s rejection of this gamble is risk aversion or (equivalently for our purposes) diminishing marginal util-ity of wealth. Indeed, diminishing marginal utilutil-ity of wealth is an excellent assumption based on good psychology: people satisfy their most important needs and desires first and the less important ones only if they have something left over, so the first $1,000,000 in wealth generates more utility than the next
$1,000,000. This is a great explanation for large-scale risk aversion, such as the decision to take $4 million for sure rather than $10 million with probability one-half.
But most of the risky decisions we face are not in the $1 million range or even the $100,000 range. They are much smaller. And in a key article, Rabin (2000a) argued that expected-utility-over-wealth maximizers—who care only about final wealth outcomes—should not reject such a gamble unless they turn down phenomenally favorable larger risks. Since most people do take
1.4. REFERENCE DEPENDENCE AND LOSS AVERSION 15
many risks, expected utility is not a reasonable explanation for rejecting the small-scale gamble. Rabin’s mathematical argument centers around proving statements of the following form: “If an individual with expected utility over wealth turns down a fifty-fifty lose $l or gain $g gamble over a range of wealth levels, she also turns down a fifty-fifty lose $L or gain $G gamble,” where G is huge relative to L and Lis not that large (Gis infinite in some examples).
The argument proceeds by using that if a person turns down the g/l gamble for some wealth level, her marginal utility must diminish by some non-trivial amount over the range of the gamble. Using that this is the case for multiple wealth levels, we conclude that over the range of these wealth levels marginal utility diminishes quite a lot. But this implies extreme sensitivity to larger gambles.
Here is an illustration of the precise argument. Suppose Johnny is a clas-sical utility maximizer with diminishing marginal utility of wealth who would turn down a fifty-fifty lose $500 or gain $550 bet for a non-trivial range of initial wealth levels. Let us take a concave, increasing utility function over wealth, u(·). Rejection of this bet means that
1
2u(w+ 550) + 1
2u(w−500)< u(w), which implies
u(w+ 550)−u(w)< u(w)−u(w−500).
But notice that by the concavity ofu(·),u(w)−u(w−500)<500·u0(w−500), and u(w+ 550)−u(w)>550·u0(w+ 550). Therefore,
500·u0(w−500)>550·u0(w+ 550), or
u0(w−500)> 11
10u0(w+ 550).
Now suppose Johnny was $1,050 poorer in lifetime terms. This is a very small change in lifetime wealth, equivalent to something less than $50 per year.
It is implausible that risk aversion would diminish significantly with such small changes in initial wealth, especially for decreases in wealth. If so, then by the same argument as above but now applied to a wealth level of w−1050,
u0(w−1550)> 11
10u0(w−500).
Combining the two
u0(w−1550)>
11 10
2
u0(w+ 550),
and by the same reasoning
u0(w−2100)>
11 10
2
u0(w).
But this implies that marginal utility for wealth skyrockets for larger de-creases in wealth unless there are dramatic shifts in risk attitudes over larger changes in wealth: for every decrease of $1,050 in Johnny’s wealth, his marginal utility of wealth increases by a factor of 11/10. Doing this fifty times... If Johnny became $52,500 poorer in lifetime wealth—which is something less than $2,500 in pre-tax income per year, say—then he would value income at least 117 times (≈ 111050
) as much as he currently does. While none of us know Johnny, we know this is a false fact about Johnny.
Furthermore, such a plummeting marginal utility of money leads to wild risk aversion over large stakes: if Johnny’s marginal utility of wealth increases by a factor of 117 if he were $52,500 poorer, for instance, then—even if he were risk neutral above his current wealth level—then Johnny would turn down a fifty-fifty lose $110,000 or gain $6.4 million bet at his current wealth level.3
By a similar calculation, if Johnny were risk neutral above his current wealth level but averse to 50/50 lose $10 / gain $11 bets below his current wealth level, then he would turn down a 50/50 lose $22,000 / gain $100 billion bet. Rabin gives many further numerical examples.
Since this kind of risk aversion is inconceivable (how many would turn down this last bet?), we can conclude that diminishing marginal utility of wealth cannot reconcile risk aversion over modest stakes with reasonable risk aversion over large stakes. And these results are just bounds, and vastly understate the severity of large-scale risk aversion implied by small-scale risk aversion.
So why do people reject a fifty-fifty lose $500 or gain $550 risk? Most likely because of loss aversion. They dislike the prospect of an unpleasant loss of
$500 much more than they like the prospect of a gain of $500. Loss aversion is not subject to the same critique as diminishing marginal utility over wealth because it does not assume that risk preferences over any level of wealth are determined by a single function. It could be that at any wealth level, a person dislikes a $500 loss much more than she likes a $550 gain—if her reference point is her current wealth. But this does not mean that her utility function is
3To get this number, I used that Johnny’s marginal utility at wealth levels below the current wealth minus $52,500 is at least 117 times that at his current wealth level. A
$110,000 loss is a loss of more than $55,000 extra. He cares about this extra loss at least 117 times as much than about gains from the current wealth level. So even a gain of 6,400,000<117×55,000 would not be enough to compensate him.
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very concave overall, because it does not imply that her utility function must at the same time curve at each of these wealth levels.
In other words, loss aversion gets around the Johnny logic by assigning a special role to current wealth (or another reference point), and making a strong distinction between gains and losses. Because losses are much more painful than equal-sized gains are pleasant, it may well be that a gain of $550 is not as attractive as a loss of $500 is scary. But with loss aversion, it is not necessarily the case that a loss of an extra $500 is worse than the loss of the first $500—since both of these are losses. So the above logic breaks down.