In Loewenstein and Thaler, the authors discuss a change in a West Virginia law that substantially reduced the number of high school dropouts. Briefly discuss this change, explain why it is surprising from a rational standpoint, and appear to suggest "extremely high discount rates".

Examples of extremely high discount rates are also easy to nd. A recent change in West Virginia law provides an example. Students under the age of 18 who drop out of school lose their driving pennits. The rst year results indicate that this law has reduced the dropout rate by one-third. It seems implausible that one-third of the high school dropouts were so close to the margin that the loss of driving privileges for a year or two (or more precisely, the expected costs of driving illegally for this period) could tip a rational human capital investment decision toward completing high school. Rather, the behavior seems to reveal extremely myopic preferences. A similar - myopia is evident in the lament of a dermatologist that her warnings about the risk of skin cancer have little effect, but \"My patients are much more compliant about avoiding the sun when I tell them that it can cause large pores and blackheads.\" I It is not just teenagers and sun lovers who display high discount rates. Most homeowners have too little insulation in their attics and walls, and fail to buy more expensive energy-efcient appliances even when the pay-back period for the extra expense is less than a year. Hausman's (1979) study of air conditioner purchases, which examined consumer tradeoffs between purchase price and delayed energy payments, estimated an average consumer discount rate of about 25 percent. A subsequent study by Gately (1980) comparing pairs of refrigerators differing only in energy use and initial purchase price revealed that the implicit discount rates associated with purchasing the cheaper models were incredibly high: from 45 to 130 percent assuming an electricity cost of 3.8 cents per kilowatt hour, and from 120 to 300 percent at 10 cents per kilowatt hour. Most recently, Ruderman, Levine and McMahan (1986) computed the discount rates implicit in several different kinds of appliances (for the average model on the market, relative to the most efficient): space heaters, air conditioners, water heaters, refrigerators and freezers. They found that the implicit discount rate for room air conditioners was 17 percent, somewhat lower than Hausman's estimate. However, the discount rates for other appliances were much higher, e.g., gas water heater, 102 percent; electric water heater, 243 percent; and freezer, 138 percent. Economic theory has a clear prediction about these inefficient appliances-they will not be produced. But they are produced, and purchased.' So, as usual, where there are testable predictions, there are anomalies. The remainder of this column examines a number of situations in which people do not appear to discount money flows at the market rate of interest or any other single discount rate. Discount rates observed in both laboratory and field decision-making environments are shown to depend on the magnitude and sign of what is being discounted, on the time delay, on whether the choice is cast in terms of speed-up or delay, on the way in which a choice is framed, and on whether future benefits or costs induce savoring or dread. Variations in the Discount Rate for an Individual An experiment that investigated the first three of these effects was presented in Thaler (1981). Subjects (mostly students) were asked to imagine that they had won some money in a lottery conducted by their bank. They could take the money now or wait until later. They were asked how much they would need to be paid to make waiting as attractive as immediate payment. Each subject received a 3 X 3 table to fill in with amounts of money varied along one dimension and length of time along the other. Four versions of the questionnaires were used, three involving gains, and one involving losses. In the losses version, subjects were asked to imagine that they had been issued a traffic fine that could either be paid at face value now or at an increasedNon-Exponential Discounting. Soum: Ainslie (1975). demonstrated, if the discount rate declines over time, then people will always consume more in the present than called for by their previous plans. The problem of dynamic inconsistency raises questions about consumer sovereignty. Who is sovereign. the self who sets the alarm clock to rise early, or the self who shuts it off the next morning and goes back to sleep? It is instructive that we normally see the far-sighted self take actions which constrain or alter the behavior of the myopic self. Dieters pay money to stay on \"fat farms\" whose main appeal is that they guarantee to underfeed their guests; alcoholics taloe antabuse which causes nausea and vomiting if they take a drink; smokers buy cigarettes by the paclt (rather than by the carton which is cheaper). And, though no longer fashionable, for many years Christmas clubs were extremely popular in the U.S. These savings plans offered the unusual combination of inconvenience (deposits were made in person every week), illiquidity (funds could not be withdrawn until late Nevember), and low interest (in some cases, zero interest). 0! course, iiliquidity was the Christmas club's raison d'Etre since customers wanted to assure themselves of funds to pay for Christmas presents. Recognizing the limited ability of conventional decision models to account for self-binding behavior and other forms of intrapersonal conict, a number of authors have proposed models that view economic behavior as an internal struggle between multiple selves with conicting preferences (Ainslie 19?5, forthcoming; Elster, 1979; Schelling, [984; Thole:- and Shefrin, 1981; Winston, 1980). Discounting as a Function of Time Delay and Money Amount. 0.5 0.45 0.4 -$40 0.35 0.3 $200 Discount Rate 0.25 $1,000- 0.2 -$5,000 0.15 0.1 0.05 0.5 No Delay in years Source: Benzion et al. (1989). which occurs at ,, and a bigger later reward B, which occurs at 2.* The lines represent the present utility of the rewards as perceived by the individual at different points in time. If the individual discounts the future at a constant rate, that is, if discounting is constant for different time delays, then the curves will never cross. However, if discounting decreases as a function of time delay, as the empirical research suggests, then the curves may cross, leading to a reversal of preference. When both rewards are sufficiently distant, the individual prefers B, but as S becomes more proximate, its relative value increases until at *, S abruptly comes to dominate B in terms of present utility. The significance of the crossing curves is that behavior will not generally be consistent over time. In the morning, when temptation is remote, we vow to go to bed early, stick to our diet, and not have too much to drink. That night we stay out until 3:00 a.m., have two helpings of chocolate decadence, and sample every variety of Aquavit at a Norwegian restaurant. Applied to saving, as Strotz (1956)