In this chapter, I have presented a variety of data and shown that the self-control problems that arise under hyperbolic discounting actually lead to self-destructive choices that undermine long-term interests. A hyperbolic decision-maker tends to
35.3%
16.2%
37.0%
26.1%
23.0%
35.5%
23.5%
14.3%
29.9%
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
% of habitual smokers % of habitual gamblers % of habitual drinkers Naïve hyperbolic discounters Sophisticated hyperbolic discounters Non-hyperbolic discounters
Men
11.1%
7.5%
15.4%
8.0%
4.3%
11.4%
7.5%
4.0%
13.2%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
% of habitual smokers % of habitual gamblers % of habitual drinkers Naïve hyperbolic discounters Sophisticated hyperbolic discounters Non-hyperbolic discounters
Women
Fig. 5.13 Hyperbolic discounting and the habits of smoking, gambling, and drinking. Note:
Prepared based on the data from theJapan Internet Survey on Preferences Relating to Time and Risk 2010. The definitions of each habitual consumer are the same as in Fig.3.8
make choices that lead to overspending and undersaving in various settings, particularly when he or she is naı¨ve in the sense that he or she puts too much faith in his or her own perseverance. Examples include committing the income- consumption cycle where one spends as money comes in, incurring excessive debt through the use of credit cards and unsecured consumer loans, overeating that results in obesity, and excessive (and addictive) gambling and smoking. In contrast, the sign effect, which discounts future loss at a smaller rate than future benefit, leads to borrowing aversion behavior and works to suppress consumption and debt.
Appendix: An Illustrative Model of Hyperbolic Consumers
In this appendix, I theoretically illustrate the borrowing behavior of naı¨ve and sophisticated hyperbolic consumers by using a simple three-period model.
Let me specify the consumers’discount function for future felicity with delayτ by the generalized hyperbolic discount functionf(τ)a la Loewenstein and Prelec (1992) (see the discussions in Sect.3.2.2of Chap.3):
fðτ;α;γÞ ¼ ð1þατÞθ=α forα>0, expðθτÞ forα¼0;
ð5:1Þ
where θ>0. The two function forms are consistent in that limα!0ð1þατÞθ=α¼expðθτÞ. The discount rateρ, which is obtained by com- putingf0ð Þ=τ fð Þ, is given as:τ
ρ τ;ð α;θÞ ¼ θ
1þατ ð5:2Þ
As seen from (5.2), the discount rate is declining in delayτ, which represents the usual property of hyperbolic discounters, that is, they are less patient in immediate future choices than in distant future choices. The degree of declining impatience is higher asαbecomes larger. Especially, for two distinct delaysτ1andτ2(τ1>τ2), the relative discount ratesρ τð Þ=ρ τ1 ð Þ ¼2 ð ð1þατ2Þ=ð1þατ1ÞÞ, which are smaller than 1, depend solely on α: a large α implies a small ρ(τ1)/ρ(τ2). Parameter α thus represents thedegree of hyperbolic discounting or declining impatience.
Let cτ and u(cτ) denote period τ consumption and period utility function, respectively. The gross rate of interestRis constant. When the consumer is naı¨ve,
he or she determines his or her “optimal” consumptionc1in the initial period 1 from the intertemporal optimality conditions,
u0ð Þc1
u0ð Þc2 ð1þαÞθ=α¼R ð5:3Þ u0ð Þc2
u0ð Þc3
1þ2α 1þα θ=α
¼R ð5:4Þ
and the lifetime budget constraint,
c1þc2
Rþc3
R2 ¼W1 ð5:5aÞ
whereW1is initial wealth holding. As 1þα>ð1þ2αÞ=ð1þαÞ, the conditions imply that the consumer puts a greater weight on the immediate gratification from c1than he or she expects to put on the period 2 immediate gratification fromc2. Since this tendency is stronger withα, a largerαresults in larger debt holdings in the period.
In period 2, the naı¨ve consumer re-determines (c2,c3) from the period 2 opti- mality condition,
u0ð Þc2
u0ð Þc3 ð1þαÞθ=α¼R ð5:5bÞ which differs from the period 1 condition (5.4); marginal gratification fromc2is evaluated more highly than in (5.4). The realized c2is thus larger than the level which was planned in the previous period, whereas the opposite is true forc3.
To be more specific, ifu(cτ) is specified by the power function,
u cð Þ ¼c1γ1 1γ ,γ>0
the naı¨ve consumer’s “optimal” consumption rates are given by
c1N¼λ11W1; ð5:6Þ
c2N ¼λ22W2N; ð5:7Þ c3N¼ð1λ22ÞRW2N; ð5:8Þ whereWN2 is wealth in period 2,R W1c1N
, andλ11andλ22represent the realized marginal propensities to consume (MPC) in periods 1 and 2, respectively:
λ11¼ 1
1þR1fR fð Þ1 g1=γþR2R2fð Þ2 1=γ; ð5:9Þ
λ22¼ 1
1þR1fR fð Þ1 g1=γ: ð5:10Þ From these solutions, asf(τ)’s are decreasing inα, a largeαimplies a largecN1 and a smallcN3. In this sense, naı¨ve consumers with stronger hyperbolic discounting are likely to hold larger debts. However, the effect of an increase in α on cN2 is ambiguous because it raises the marginal propensity to consume fromWN2 whereas it reducesWN2 by raisingc1.
When the consumer is a sophisticated person who expects correctly the inci- dence of the preference reversal from (5.4) to (5.5), he or she first solves (5.5) for (c2,c3) by takingc1and hence period 2 wealthW2as given. Once the optimalc2and c3are obtained as functions ofc1, by substituting functionsc2(c1) andc3(c1) into the lifetime utility maximization problem, the consumer determines the optimalc1and hencec2andc3.
In the illustrative model, the sophisticate’s optimal consumptioncSt in period t is obtained as
c1S¼λ011W1; ð5:11Þ c2S ¼λ22W2S; ð5:12Þ c3S¼ð1λ22ÞRW2S; ð5:13Þ whereW2S¼R W1c1S
, and the MPCλ011in period 1 is defined in the same way as in (5.9) by using effective discount factors fSð Þτ ðτ¼1, 2Þ, instead off(τ):
fsð Þ ¼1 λ022fð Þ þ1 ð1λ22Þfð Þ=2 fð Þ;1 fsð Þ ¼2 fð Þ1 fSð Þ:1
The solution differs from the naı¨ve consumer’s solution only in the MPC in period 1; it is defined by using the effective discount functionsfS(τ) instead off(τ).
The effective discount factor fS(1) for period 2 is a weighted average of the corresponding original discount factor f(1) and the original future one-period discount factor for period 3 computed asf(2)/f(1). Since, as is easily seen,fS(2)>f (1) andfS(2)>f(2), which means that the sophisticate behaves as if he or she had a lower discount rate when comparing felicities fromc1and c2and a higher discount rate when comparing felicities fromc2andc3than he or she would if he or she were naı¨ve. Due to these opposite effects, it is theoretically ambiguous whether the sophisticated consumer’s MPC in period 1 (λ011) is smaller than the naı¨ve one’s (λ11).
Nevertheless, it may be natural to hypothesize that the sophisticated consumer would weaken somehow his or her overconsumption/undersaving and
overborrowing because period 1 self has an incentive to use some devices to commit to his or her lifetime consumption plan. From (5.3), (5.4), and the lifetime budget, the solution with commitment devices is obtained as c2S ¼λ21RW1 and c3S¼ð1λ11λ21ÞR2W1, whereλ11is given by (5.9) and
λ21¼ R1fR fð Þ1 g1=γ
1þR1fR fð Þ1 g1=γþR2R2fð Þ2 1=γ:
From this and (5.8), it can be shown that, with commitment devices, c3Sc3N /ƒð Þ2 1=γƒð Þ1 1=γ>0. In sum, the sophisticated consumer’s solution satisfies the following:
c1S¼c1N,c2S<c2N, andc3S >c3N, with commitment devices,
meaning that the sophisticated consumer restrainscS2and mitigates undersaving and/or overborrowing.
Supplement D: Obesity Criteria: Japan and the WHO
To determine whether an individual is obese or underweight, the body mass index (BMI) is usually used. In Western countries, a BMI of 30 or over is considered obese, in accordance with the criteria established by the World Health Organization (WHO). Meanwhile, the Japan Society for the Study of Obesity (JASSO) standards, which regard a BMI of 25 or over as obese, is used in Japan in accordance with the 2000 report released by the Examination Committee of Criteria for “Obesity Disease in Japan,” affiliated with the JASSO. This is because the committee confirmed the tendency that the risk for developing obesity-related health problems (impaired glucose tolerance, hypertension, lipid metabolism abnormality, hyper- uricemia, and heart disease (abnormal electrocardiogram)) dramatically increases among Japanese people whose BMI is 25 or over. In other words, it takes into account that the Japanese have a unique predisposition for obesity-related health problems, even when a BMI value would not be diagnosed as obese by the Western standards.
The differences between these two standards are as shown in Table5.7. Whereas individuals whose BMI is 25 or over but less than 30 are identified as Class I obese based on the JASSO standards, the WHO considers them overweight (preobese), a state that is on the brink of becoming obese. Both the JASSO and WHO standards define underweight as a BMI of less than 18.5; normal, as a BMI of 18.5 or over but less than 25; and standard (ideal) weight—with which the disease risk is mini- mized—as a BMI of 22.
While the body weight criteria in Japan are stricter in the sense that one is considered obese at a lower BMI value, the JASSO separately defines cases in which one develops or is expected to develop a health problem due to being obese as an “obesity disease.” The diagnostic criteria for disease obesity is that an
individual who was determined to be obese (a BMI of 25 or over) meets one of the following:
1. The individual has an obesity-related health problem (e.g., type 2 diabetes, hypertension, hyperuricemia, gout, cardiac infarction, cardiac angina, etc.) that requires him or her to lose weight.
2. The obesity of the individual is a high-risk one, such as visceral fat obesity.
It may be an obesity disease, rather than just obesity, that can be explained well under the framework of choices regarding gains and losses in the present and future, because there are many cases in which an individual is not actually overweight even when his or her BMI is high. This is particularly true among men with a muscular build. In fact, in the case of men (whose muscle proportion is larger), the correlation between the personal discount rate and BMI is not detected as strongly as in the case of women. In this case, it may be because being obese is determined based just on BMI.
Supplement E: “Super Size Me”: The State of Obesity in the United States and Europe
What would happen if you were to eat every single meal at McDonald’s for 30 days? Morgan Spurlock volunteered to be a guinea pig for this ridiculous but interesting experiment and recorded the course of events as a movie. It is in the American documentary film “Super Size Me,” which was released in 2004. The experiment is conducted under rough rules, including the following;
1. He must eat McDonald’s products three times a day.
2. He cannot walk more than 5,000 steps a day, which is the walking distance of an average American.
3. When offered by the clerk, he must accept and eat a “super size” meal.
Table 5.7 Body-weight-status criteria
BMI JASSO criteria WHO criteria
BMI<18.5 Low weight (underweight) Low weight (underweight)
18.5BMI<25 Healthy weight Healthy weight
BMI¼22 Standard (ideal) weight Standard (ideal) weight
25BMI<30 Obese (Class I) Overweight (preobese)
30BMI<35 Obese (Class II) Obese (Class I)
35BMI<40 Obese (Class III) Obese (Class II)
40BMI Obese (Class III) Obese (Class III)
Note: The JASSO criteria are based on the JASSO Obesity Diagnostic Criteria Review Committee (2000)
How was Mr. Spurlock after 30 days of the experiment? His condition was terrible; his weight had increased from 84.1 to 95.2 kg (an increase of 11.1 %, in terms of percentage), a severe inflammation was observed in his liver, and he even began exhibiting manic-depressive tendencies. The title of the movie makes a pun on the McDonald’s “super size” menu items, which are very large in portion size, by turning the phrase into a verb and making the sarcastic and bitter statement that McDonald’s is “trying to make me fat.”
In the background of this movie, there is an explosive increase in the obese population that the United States has been experiencing since the late 1970s. As Fig. 5.14 shows, the percentages of preobese and obese are trending at levels exceeding 30 % after 2000; additionally, as of 2008, two in three individuals aged 20 or older in the United States are categorized as overweight or obese.
In 2002, two minors living in New York City filed a lawsuit for damages against McDonald’s, claiming that they became obese because of McDonald’s food. The federal district court dismissed the complaint, saying that there was no clear causal relationship; however, it was an incident that symbolized just how serious the obesity problem has become in modern American society. Although growth levels vary, this trend of growth in the size of the obese population is a common phenomenon seen in developed countries and East Asia. The United Kingdom, the country with the world’s second highest obesity rate, is developing a system to address this problem by establishing a position called “Minister for Fitness” in 2006, among other things.
31.5 32.3 32.1 32.7 33.6 34.4
33.4
32.2
33.6
13.4 14.5
15
23.2
30.9 31.3 32.9
35.1 34.3
0.9 1.3 1.4
3
5 5.4 5.1 6.2
6
1960–1962 1971–1974 1976–1980 1988–1994 1999–2000 2001–2002 2003–2004 2005–2006 2007–2008 Overweight (25 ≤ BMI < 30) Obese (BMI ≥ 30) Extremely obese (BMI ≥ 40)
(Year)
Fig. 5.14 Changes in the obesity rate in the United States (%). Note: Prepared by the author based on data from the US Department of Health and Human Services (DHHS) and Centers for Disease Control and Prevention (CDC)’s FastStats). The age groups are already adjusted to the US 2000 baseline
Supplement F: Reporting One ’ s Own Weight as Lighter
The two BMI distributions shown in Fig.5.15summarize women’s data obtained from two national surveys conducted 2 months apart, around 2005. The distribution in the dark color contains the results ofthe National Health and Nutrition Survey conducted in November 2004 by the Ministry of Health, Labour and Welfare (MHLW), and the distribution in the light color contains the results of a survey that Osaka University conducted in February 2005 (theJapan Household Survey on Consumer Preferences and Satisfaction 2005). The figure shows the percentage distribution of women in Japan in each range of BMI, as shown in the horizontal axis. Samples in each survey were collected through an appropriate random sam- pling to ensure that there was no regional or age-specific bias. These large-scale surveys had sample sizes exceeding 2,000.
So, how do these two distributions differ from each other? Let us study the graph and offer some thoughts.
The answer is that, whereas the distribution in the dark color is higher in the obese range (where BMI is higher) as well as in the underweight range (where BMI is lower), the distribution in the light color is higher in the range of ideal body type, where the BMI falls between 19 and 25. Why does such a difference occur when both are the results of large-scale national surveys on Japanese women’s body types?
0 2 4 6 8 10 12 14 16 18
Less than 15
15-16 16-17 17-18 18-19 19-20 20-21 21-22 22-23 23-24 24-25 25-26 26-27 27-28 28-29 29-30 30-31 31-32 32-33 33-34 34-35 Larger than 35 Actually measured data (2004) Self-reported data (2005)
BMI (women) (%)
Underweight Obese
Fig. 5.15 Women’s BMI distribution: Actually measured versus self-reported. Note: Range
“15–16” in the horizontal axis represents that 15BMI<16. Prepared by using actually measured data from the2004 National Health and Nutrition Surveyby the Ministry of Health, Labour and Welfare and self-reported data from theJapan Household Survey on Consumer Preferences and Satisfaction 2005conducted by Osaka University
There is actually a large difference between them; whereas the MHLW’s histogram (in dark color) is based on real data obtained by measuring the height and weight of subjects, the graph in the light color is based on self-reported data obtained in the survey.
When surveying weight by using the self-reporting method, many respondents often report their height and weight by adjusting them toward what they consider desirable. Because individuals who are on the heavy side are especially likely to report their weight lighter and height taller than what they truly are, the obesity rate is likely to be underestimated when it is based on self-reported data. These findings thus exhibit what is called self-report bias. We can clearly see that this type of self- report bias is taking place in the example above, since the self-reported data (light color) is particularly lower than the measured data in the obese range (where the BMI is 25 or over) and actually higher in the range of normal weight.
In fact, as shown in Table5.8, calculating the percentages of obese individuals and underweight individuals by gender by using these two datasets yields results that strongly suggest self-report bias. In particular, while the measured data show that 20.1 % of women are obese, our self-report survey indicates only 14.3 % of them are obese. Assuming there is no sampling bias in either dataset, these findings imply that many obese women are reporting their weight as being lighter (or their height as being taller). Based on a simple calculation, it means that 12 % of obese men and more than 28 % of obese women reported themselves as not being obese.
That said, as long as the personal discount rate and the level of hyperbolic discounting do not correlate with self-report bias, there is no statistical issue, even when analyzing the relationship between obesity and either discount rate or hyperbolic discounting by using survey data that might feature self-report bias. For example, I introduced earlier results indicating that the tendency to become obese increases as the individual becomes more hyperbolic. If there is no association between the extent of underreporting one’s own weight and how hyperbolic that individual is, the results can be trusted “as is.” If that is not the case, however, some sort of consideration is needed of the level of detected correlation.
If obese and hyperbolic individuals are more likely to underreport their own weight in a survey, we will not be able to observe a true positive correlation between hyperbolicity and obesity, even if there is one, because underreporting
Table 5.8 Actually measured data and self-reported data
% of obese individuals % of underweight individuals Actually measured
data
Self-reported data
Actually measured data
Self-reported data
Men 27.3 % 24.0 % 7.3 % 5.7 %
Women 20.1 % 14.3 % 15.3 % 14.3 %
Note: Prepared by using actually measured data from the2004 National Health and Nutrition Surveyby the Ministry of Health, Labour and Welfare and self-reported data from theJapan Household Survey on Consumer Preferences and Satisfaction 2005 conducted by Osaka University
will mask the true correlation, or even if we did observe a positive correlation, it would be underestimated.
How one should handle self-report bias is a difficult issue. In the United States, for example, researchers have estimated a simple equation based on the body size data of the same subjects, obtained by measurement and by self-reporting, to correct self-reported data (Burkhauser and Cawley 2008). Therefore, they normally go through a procedure to adjust bias by using such an equation. However, it is not possible to apply that corrective equation to Japanese data, which have a completely different distribution of body type and constitution. Since we still do not have such a dataset in Japan, the only thing we can do is speculate on self-report bias by comparing measured data and self-reported survey results obtained around the same time, as shown above.