2.3 Gains Are Discounted More Than Losses
whereas a decrease in the monetary reward causes a greater than proportionate decrease in gratification. For example, when the receipt of USD 100 becomes USD 110 due to a 10 % interest rate, the corresponding rate of increase in gratification is not 10 %. Thus, a decision-maker who has a discount rate of 10 % in utility terms (i.e., one who demands a 10 % increment in utility when there is a 1-year delay to receive a reward) would ask for an interest rate higher than 10 % (e.g., 11 %) in monetary terms. In questionnaire research and economic experiments, this 11 % interest rate is termed againdiscount rate. The observedgaindiscount rate is an overestimate of the true discount rate in utility terms. However, when a USD 100 payment increases to USD 110 due to a 10 % interest rate, the corresponding rate of decrease in gratification is greater than 10 %. A decision-maker who has a discount rate of 10 % in utility terms would accept delay only at a lower interest rate (e.g., 9 %) in monetary terms. Thislossdiscount rate (9 %) is an underestimate of the true discount rate in utility terms.
In sum, under the law of decreasing marginal utility, the observed gain discount rate (in monetary terms) is an overestimate of the true personal discount rate (in utility terms), whereas the observed loss discount rate is an underestimate. It thus follows that the gain discount rate is higher than the loss discount rate, as in the sign effect. It is not clear, however, whether the law of decreasing marginal utility applies to small amounts of money (i.e., tens or hundreds of US dollars). In the case of everyday consumption goods (e.g., beer), as the quantity consumed becomes larger, the gratification from additional consumption decreases rapidly. However, a USD 1 increment in a monetary amount (in either direction) will not produce noticeable changes to marginal utility.1 Moreover, the sign effect tends to be more salient for smaller amounts of money, which contradicts the law of decreasing marginal utility.
2.3.3 Loss Bias
To explain the gain-loss asymmetry in discounting, one might assume that there is a systematic difference in the way gains and losses are evaluated. For example, people may be more sensitive to losses than to gains. If so, a decision-maker would evaluate a certain amount of interest more seriously when paying it versus when receiving it; thus, the loss discount rate would differ from the gain discount rate.
To explain the sign effect, Loewenstein and Prelec assumed the following two biases in loss evaluation (Loewenstein and Prelec 1992):
1Assuming that the marginal utility of money was constant, Alfred Marshall used it as the numeraire for the measure of value (Marshall 1890). Ono et al. (2004) empirically showed that there was a lower bound for the marginal utility of money, as hypothesized by Ono (1994).
(1) Loss aversion: The displeasure associated with incurring a loss or making a payment is greater in magnitude than the pleasure associated with receiving the same objective amount.
(2) Excess sensitivity to losses: The loss elasticity of gratification is higher than the gain elasticity.2
In property (1), loss aversion is the preference bias proposed by Daniel Kahne- man and Amos Tversky in prospect theory (see Kahneman and Tversky 1979), the empirical validity of which is well established. Property (2) illustrates that the impact on gratification of a 1 % increase in the amount of a loss is greater than the impact of gain. The two properties capture gain-loss asymmetry in a decision- maker’s evaluation. I refer to them as theloss bias.
Under the loss bias, a 1 % increase in a future loss due to having to pay interest has a greater impact on gratification than a 1 % increase of future gains due to receiving interest. The result is that the payable interest rate required to defer a loss is lower than the required interest rate to defer a gain, as is observed with sign effect.
One important effect of the loss bias is that it reduces intertemporal resource re-allocation between present and future rewards by means of saving and borrow- ing. For example, saving requires one to forego consuming part of a present resource (i.e., a decrease in present consumption so that there can be an increase in future consumption). With the loss bias, people will evaluate the loss due to the present decrease in consumption as larger than the gain of the future increase in consumption. Thus, people should not be likely to save money for the future unless the interest rate for saving is sufficiently high. In contrast, borrowing is an increase in present consumption at the expense of future consumption. Due to the loss bias, the gain from the present decrease in consumption will be evaluated as lower than the loss of future consumption. Thus, people are not likely to borrow unless the interest rate is sufficiently low. Loewenstein and Prelec called this tendency
“borrowing aversion.”
2.3.4 The Sign Effect and Borrowing Aversion
Is the sign effect really associated with borrowing aversion? Can we observe a similar relationship between the sign effect and health-related behavior, as Chap- man suggested, based on a questionnaire survey on hypothetical intertemporal choices related to illness and physical pain (Chapman 2000)? A tentative reply to these questions is shown in Fig.2.1. Using our 2005 questionnaire survey data, the figure compares the debtor ratios, obesity rates, and habitual smoker rates between respondents who displayed the sign effect and those who did not. As predicted by
2The loss (gain) elasticity of gratification represents the percentage the gratification level decreases (increases) in response to a 1 % increase in a loss (gain).
the theory, the sign-effect group included a smaller proportion of debtors, obese people, and habitual smokers compared with the non-sign-effect group. Particularly noteworthy, 20.7 % of the sign-effect group was debtors, which is nearly 7 percent- age points lower than the percentage of the non-sign-effect group (27.3 %). This difference was statistically significant, indicating that the sign effect is indeed negatively associated with borrowing behavior.
Although the data described do indicate a relationship between the sign effect and borrowing behavior, this relationship was detected by just examining a simple correlation between the two variables. A more precise analysis that considers additional factors (e.g., gender, age, income, etc.) is warranted. In Chap.5, I present evidence that the sign effect suppresses behavior that leads to future losses or payments even when these additional variables are included in the analysis.
2.3.5 Delay/Speed-Up Asymmetry
Another anomaly that is thought to be caused by the loss bias described earlier is a behavioral tendency termed “delay/speed-up asymmetry.” This refers to the per- sonal discount rate being differentially affected when the expected delivery time of a reward is changed due to an acceleration or a delay from some pre-scheduled date.
27.3%
19.6%
27.8%
20.9%
16.2%
21.2%
Debtor rate Obesity rate Smoker rate
Sign-Effect Group Non-Sign-Effect Group
Fig. 2.1 The sign effect and self-destructive choices. Note: the differences between the sign- effect group and the non-sign-effect group are all significant at 5 % significance levels. Source:
TheJapan Household Survey on Consumer Preferences and Satisfaction, 2005.N¼2985
For instance, suppose that a consumer has ordered a special cellular phone that is scheduled to arrive in 2 months. If the consumer is then told that the phone’s delivery will be delayed by 1 month, he or she would request a price discount on the phone. This price reduction, required by the consumer as compensation for the delay in receiving the reward (the phone), is called thedelay premium. In contrast, the consumer would be willing to pay a higher price for the phone if the arrival date is brought forward, for instance, from 3 months later to 2 months later. The cost that the consumer is willing to pay for a decrease in the delay to receiving the reward is called thespeed-up cost.
Research has indicated that the delay premium tends to be much higher than the speed-up cost. For example, in Loewenstein’s experiments (Loewenstein 1988), high school students exhibited a USD 1.08 delay premium to accept a 3-week delay for the delivery of a USD 7 disk voucher that was originally scheduled to be delivered in 1 week. In contrast, when the original delivery was scheduled for 4 weeks later, the subjects paid a USD 0.25 speed-up cost in order to receive the delivery in 1 week. That is, the speed-up cost was just a quarter of the delay premium. In both of these scenarios, the time span over which the delivery date changed was the same (3 weeks), yet the delay premium was much greater than the speed-up cost. These two values are the result of making a comparison between the subjective value of receiving the reward at the earlier date and that of the delayed date (in this example, after 1 or 4 weeks). According to standard economic theory, individuals will value receiving the reward after the delay (i.e., 4 weeks in this example) lower than they would value receiving the reward at the earlier time (i.e., 1 week) due to discounting of the 3-week longer delay. Thus, the decrement in the present value caused by the additional delay should equal the increment in the present value caused by the speed up. Differently from this prediction, however, the observed asymmetry between the delay premium and the speed-up cost (i.e., the delay/speed-up asymmetry) shows that the delay premium is usually several times larger than the speed-up cost.
2.3.6 The Framing Effect
The puzzling asymmetry between the delay premium and the speed-up cost can be resolved by applying what behavioral economists call the framing effect. When evaluating an item, people tend to compare it with a reference point that is determined by the context or frame that they are experiencing. New items are evaluated in terms of desirability relative to the reference. Thus, the evaluation and the resulting decision depend on the frame of the choice, even when the choice options are essentially the same.
In the previous example, when evaluating the cost of the 3-week delay to receive the disk voucher originally scheduled to be delivered in 1 week, people would not simply compare the objective value of the voucher at 1 and 4 weeks. Instead, people would evaluate the net cost and benefit of delayed arrival in comparison to the
respective reference values that would have been realized if the voucher arrived at the originally planned time.
Figure2.2aillustrates how the cost and benefit at each point in time are affected by the delay and speed-up of voucher delivery. The benefit flow that would be realized if the voucher had been delivered on the original date represents the reference (see the left flowchart). Given this reference, the voucher’s delay causes
(a)
(b)
1 week later 4 weeks later
delay
Evaluated as larger due to the loss bias.
Evaluated as smaller due to discounting.
Evaluated as larger due to the loss bias, and as smaller due to discounting.
speed up
Small speed-up cost Large delay premium
1 week later 4 weeks later
1 week later 4 weeks later
1 week later 4 weeks later
1 week later
4 weeks later
1 week later
4 weeks later
Fig. 2.2 The delay premium and the speed-up cost. (a) The delay effect. (b) The speed-up effect
the loss in 1 week but also generates the gain of receiving it in 4 weeks (see the right flowchart). For two reasons, the cost in 1 week would have a higher impact in the present than would the benefit in 4 weeks, which leads to the delay premium. First, because the cost occurs 3 weeks earlier than the gain, the cost is discounted less than the benefit. Second, due to the aforementioned loss bias, a USD 1 cost is evaluated as having a greater magnitude than a USD 1 benefit. Since both of these effects jointly operate to make the delay cost larger relative to the benefit, people cannot accept the delay of the voucher’s arrival without a sufficiently large compensation.
This results in the delay premium.
In contrast, when the disk voucher is re-scheduled to be delivered 3 weeks earlier, from 4 weeks later (the reference case) to just 1 week later, one gets the value flow of the gain in 1 week followed by a loss in 4 weeks (i.e., see the right panel of Fig.2.2b). As the gain takes place 3 weeks earlier (hence, is discounted less) than the loss, the speed up of the voucher delivery produces a net gain and leads to the speed-up cost. However, the speed-up cost will not be as large as the delay premium because the gain is evaluated as smaller than the loss due to the loss bias. In sum, in the case of the speed-up cost, the effects of discounting and the loss bias cancel out each other, whereas the two enhance each other for the delay premium. It follows that the speed-up cost is much smaller than the delay premium.
As demonstrated in Sect.3.4, the interest rate for saving tends to be higher than that for borrowing. This phenomenon can be explained in terms of the delay/speed- up asymmetry. Although Fig.2.2ais used to illustrate the effect of delaying the disk voucher delivery in the previous example, it can also illustrate the effect of delaying the timing of consumption by saving. The right panel can represent the changes to the flow of consumption when people save money a week later and thereby consume an item 4 weeks later (from now). Similarly, the right panel of Fig.2.2b can illustrate the effect of accelerating the timing of consumption by borrowing. For the same reasons discussed in the voucher example, the savings interest rate (computed as the rate of the delay premium) will be higher than the borrowing interest rate (measured by the rate of the speed-up cost) due to the combined effects of discounting and the loss bias.