Discussion Paper No. 885

TIME DISCOUNTING,PRESENT BIASES,
AND HEALTH-RELATED BEHAVIOR

Myong-Il Kang
Shinsuke Ikeda

September 2013

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Time Discounting, Present Biases, and Health-Related Behavior*

Myong-Il Kang** and Shinsuke Ikeda***Korea University
ISER, Osaka University

9 September 2013

* Our thanks go to participants at the Economics Workshop on Dynamics and Human Behavior held at

Hiroshima University, 2013, for helpful comments. We acknowledge financial supports from: aGrants-in-Aid for Scientific Research (B No. 21330046) from the Japan Society for the Promotion of
Science; the Global COE Program of Osaka University; and the Joint Usage/ Research Center Project of
ISER from the Ministry of Education, Culture, Sports, Science and Technology.
**

Corresponding author: M. Kang, Department of Business Administration, Korea University, 1-700

Ogawa-cho Kodaira, Tokyo 187-8560, Japan. Tel.: 81-42-341-1331. Fax: 81-42-344-1300. E-mail:<mkang@korea-u.ac.jp>*** S. Ikeda, The Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki,

Osaka 560-0047, Japan. Tel.: 81-6-6879-8568. E-mail: <ikeda@iser.osaka-u.ac.jp>

Abstract

Analysis of an original nationwide Internet survey reveals that health-related behavior shows associations
with three aspects of time discounting: (i) impatience, measured by the overall discount rate; (ii) present
bias, measured by the degree of declining impatience in the generalized hyperbolic discount function; and(iii) the sign effect, in that future losses are discounted at a lower rate than future gains. Present-biased
respondents are classified as naïve if the responses are indicative of being a time-inconsistentprocrastinator, and classified as sophisticated otherwise. The health-related indicators that we examine
relate to smoking, health condition, dentition status, and body habitus. We first show that a higher degreeof impatience tends to worsen health-related attributes. Second, respondents with more steeply declining
impatience tend to develop more unhealthy behavior and ill-health conditions, and the tendencies are likely
to be stronger for naïfs than for sophisticates. Third, the sign effect, too, shows an association withhealth-related behavior, although the significance levels are not overly high. Consistent with these findings,
the principal component of the health-related measures shows strong associations with the degrees of
impatience and declining impatience.

Keywords: health, time preference, discount rate, hyperbolic discounting, the sign effect, theprobit model
JEL classification: I1, D03, D90

11. Introduction

This study focuses on the associations of health-related behavior with three aspects of time discounting:(i) impatience, (ii) hyperbolic discounting or declining impatience, and (iii) the sign effect. To do so, we
conduct an original nationwide Internet survey of Japanese adults that includes questions that help us
measure respondents’ behavioral inclinations with respect to time discounting.
Since Grossman (1972) proposes a health investment model, health-related choices are consideredintertemporal decision making, such that, for example, consumers allocate their resources to maximize
their discounted utility under trade-offs between a small and immediate reward (e.g., eating high-calorie
meals) and a larger delayed reward (e.g., enjoying future good health), or between an immediate payment(e.g., exercise or routine medical checkups) and a larger delayed payment (e.g., suffering fromlifestyle-related diseases such as obesity and diabetes). Therefore, the degree of impatience is predicted tocorrelate with current health-related behavior—such as caloric intake, dental care, and smoking—as well
as resulting health statuses, such as BMI, dentition status, and subjective health condition.1
Behavioral economics, in the meanwhile, finds two behavioral properties in people’s time discounting:hyperbolic discounting, where a person applies a higher discount rate in immediate future choices than in
distant future choices, and the sign effect, where a person discounts positive pay-offs more intensely thannegative pay-offs (e.g., Thaler, 1981; Benzion et al., 1989; Chapman, 1996). Hyperbolic discounters would
sacrifice their future health for small immediate pleasures (e.g., Ainslie, 1992; Gruber and Kőszegi, 2001;
Chabris et al., 2008; Ikeda et al., 2010; Kang and Ikeda, 2010). People with the sign effect, in contrast,
would be strongly reluctant to bear the future cost of lost health for immediate gratification (Odum et al.,
2002; Ikeda et al., 2010; Kang and Ikeda, 2010). Despite the fact that logical and testable predictions ofhealth-related behavior are developed, there are few attempts at direct and systematic empiricalconfirmation.
We test the associations between time preferences and health-related behavior by eliciting threemeasures for time-discounting properties (i.e., impatience, declining impatience, and the sign effect) from1

The study of Fuchs (1980) is the first to detect relationships between individual impatience andhealth-related behavior. For brief surveys, see Chapman (2003) and Cawley and Ruhm (2011).
2

four hypothetical questions regarding intertemporal choices. Hyperbolic discounters are sorted into
sophisticates and naïfs by posing questions about planning and doing homework assignments in childhood.
As a result, we show that time-preference measures widely relate to health-related decisions and current
health statuses, such as smoking, being obese or underweight, subjective health status, and dentition status.
The contributions of this study are threefold. First, we specify the discount factor in the form of a“generalized hyperbolic discount function” (Loewenstein and Prelec, 1992), which is characterized by two
parameters: the degree of hyperbolic deviation from exponential discounting (α) and the determinant of theintercept (η). We adduce the two parameters for each individual from responses to hypothetical questions
regarding immediate future choices and distant future choices. Each individual’s α measures his or her
degree of declining impatience. We find that this measure is associated with health-related behavior in themanner predicted. The individual’s degree of impatience is constructed by combining the inferredindividual values of parameter η with other discount rates.
Second, by jointly incorporating the three time-discounting variables as regressors, this researchdetects partial associations between each time-discounting property and health-related behavior. In thissense, the current study sharply contrasts with previous empirical studies, which merely focus on either
aspect of the time-discounting properties.2 This difference is important, because the three time-discounting
properties are not mutually exclusive (e.g., hyperbolic discounters can be less patient in terms of theoverall discount rate and may or may not show a gain–loss asymmetry in discounting).3 Our set ofinquires enables us to focus simultaneously on the multifaceted nature of time discounting.4

2

The study of Grignon (2009) is a typical example: to compare smoking decisions among the types oftime discounting, it classifies respondents into impatient, patient, and present-biased agents. Chabris et al.
(2008) focus on the association between the degree of declining impatience and health behavior, without
incorporating the other time-discounting properties.
3

In our dataset, 28.3% of respondents (N = 543) display below-average discount rates, while showing

both the hyperbolic property and the incidence of the sign effect.
4

Based on a similar motivation, we also detect partial associations of the three time-discounting properties

with body mass index—defined as weight in kilograms divided by height in meters squared (kg/m2),
debt-holding behavior, and cigarette consumption. See Ikeda et al. (2010), Ikeda and Kang (2011), and3

Third, our study partially succeeds in detecting the inclinations of naïve hyperbolic discounters toward
worse health statuses. Economic theory has shown that in many cases, time-inconsistent over-consumption
behavior due to hyperbolic discounting is more salient for naïfs, who misperceive their self-control
problem, than for sophisticates, who incorporate the effect of the problem into their decision making. In
the context of health decisions, it is predicted that naïve hyperbolic discounters have greater inclinations
toward ill health statuses than sophisticated hyperbolic discounters and exponential discounters. 5
Irrespective of the predictions, there have been few attempts to test their empirical validity. By sorting
hyperbolic respondents into naïfs and sophisticates, the current study fills this research gap.
The present research generates the following three findings. First, a higher degree of impatienceworsens health-related attributes; second, steeply declining impatience or a present-biased preference leads
respondents to more unhealthy behavior, or to ill-health conditions, and such behavioral impacts arestronger for naïfs than for sophisticates; and third, the sign effect shows associations with health-related
attributes, consistent with our prediction, although the levels of statistical significance are weak.
The remainder of this paper is constructed as follows. Section 2 briefly discusses the theoretical
relationship between time discounting and health-related behavior, and explains the data. Section 3 showsthe empirical results. Finally, Section 4 concludes the paper.

2. Data and hypotheses

Our research detects the empirical associations between health-related behavior and three aspects of time
discounting: (i) hyperbolic discounting, (ii) impatience, and (iii) the sign effect. To do so, the original
nationwide Internet survey “Japan Internet Survey on Preferences Relating to Time and Risk” (hereafter,
JPTR) is used. The JPTR was conducted from October 21 to 27, 2010, through Nikkei Research, Inc., aKang and Ikeda (2010).
5

Indeed, in the context of the smoking decision, Gruber and Kőszegi (2004) theoretically show that naïve

hyperbolic discounters have a higher smoking propensity than sophisticated hyperbolic discounters and theexponential discounters, whereas the difference in smoking propensity between sophisticated hyperbolic
discounters and exponential discounters is not overly large.
4

representative private research company that handles economic surveys. The respondents are 2,386
Japanese adults aged 20–65 years, selected by stratified random sampling from the Nikkei Research
Access Pane that comprises a total of about 155,000 individuals, such that the age–gender distribution is as
close as possible to that of the Japanese census.6 As incentives, cash vouchers are provided to respondents
by lottery.
Various questions are contained in the JPTR to elicit time and risk preferences, health-related behavior,
health conditions, and respondents’ economic, demographic, and social attributes such as income, asset
holdings, gender, university degree, and age. Panel A of Table 1 shows the summary statistics ofbackground attributes of the respondents: males comprise 49.9% of all respondents, and the average age
overall is 41.8 years.7

Insert Table 1

2.1. Health-related variables

Several health-related questions asked in the JPTR are listed in Table 2. We construct six indicatorvariables from these questions for the explained variables.

Insert Table 2

A smoking indicator, SMOKING, is created from FQ1, such that it equals 1 if respondents report theconsumption of more than 10 cigarettes per day, and 0 otherwise.8 From responses to questions about the6

During the survey period, 11,090 registrants were notified about the survey by e-mail.

7

To elicit the degree of risk aversion, we asked respondents to make three sequential binary choices, as in

Figure 1 for discount rates, on whether they play lottery “A” that pays out JPY100,000 (USD1,233) withprobability 0.5 at given prices, specified as JPY10 to JPY50,000.
8In all, 500 respondents who chose option (vii) in FQ1 (i.e., have quit smoking) are excluded from ouranalysis.
5respondents’ height and weight in FQ2, we calculate BMI values and identify obese and underweight
adults by creating three binary indicators: OBESITY, which takes the value of 1 if BMI ≥ 25, and 0
otherwise; SEVERE OBESITY, which takes the value of 1 if BMI ≥ 30, and 0 otherwise; andUNDERWEIGHT, which takes the value of 1 if BMI < 18.5, and 0 otherwise.9 As an indicator of
subjective health status, HEALTH is created from FQ3, which takes the value of 1 if a respondent selects avalue equal to or greater than six, and 0 otherwise. Finally, a binary indicator, HEALTHYTEETH, takes
the value of 1 if a respondent has such good dentition that he or she has kept all permanent teeth (i.e.,
people select option (i) in FQ4), and 0 otherwise.
Panel B of Table 1 shows the summary statistics of health-related indicators: smokers account for
17.2% of all respondents; obese people, very obese people, and underweight people comprise 18.1%, 3.1%,
and 11.5% of the respondents, respectively; 72.6% of the respondents rate their own health status as being
six points or higher on a 10-point scale, from 1 to 10; and respondents with a healthy dentition statuscomprise 65.2% of the total.

2.2. Time preferences

In the JPTR, four questions on intertemporal choices were asked to determine the nature of the
respondents’ time discounting: two (Q1 and Q2) were designed to detect the degree of declining
impatience; the other two (Q5 and Q6) were asked to detect the incidence of the sign effect. The degree of
impatience is measured by combining the four questions. Respondents are classified as sophisticates ornaïfs, based on the degree of difference between their planned and actual behavior with respect to theirimposed tasks.

2.2.1. Hyperbolic discounting (declining impatience)

Consider that the consumers’ discount factor for future felicity with delay τ is given by the generalized

9

Such criteria regarding bodily habitus are provided by the Examination Committee of Criteria for“Obesity Disease in Japan,” which is affiliated with the Japan Society for the Study of Obesity (JSSO).
6

hyperbolic discount function ƒ(τ):

f (τ ; α ,η ) = (1 + ατ ) −η , τ ≥ 0, α ≥ 0,η ≥ 0 .

(1)

According to the definition of the discount rate ρ that equals –ƒ'(τ) / ƒ (τ), it can be calculated as follows:ρ (τ ; α ,η ) =αη
.
1 + ατ

(2)

In equation (2), the discount rate is declining in delay τ, which represents the usual property ofhyperbolic discounters: such individuals are less patient in immediate future choices than in distant future
choices (e.g., Ainslie, 2001; Benzion et al., 1989). Here, the parameter α indicates the degree of declining
impatience: as α increases, the degree of declining impatience is higher. Especially, the relative discountrates ρ(τ1) / ρ(τ2) (=(1 + ατ2) / (1 + ατ1)) for two distinct delays τ1 and τ2 (τ1 > τ2), which are smaller than 1,
depend solely on α (i.e., a larger α implies a smaller ρ(τ1) / ρ(τ2)), with it leading to a stronger
present-biased preference.
To elicit the degree of declining impatience α, we use the two JPTR questions Q1 and Q2, which
sequentially propose three queries of binary choices on immediate future and distant future trade-offs,
respectively. Figure 1 shows tree diagrams that illustrate the sequential queries.

Insert Figure 1

In Q1, respondents are asked to choose between (A) receiving JPY1,000 (around USD12.33) today,and (B) receiving JPY1,000 plus a certain additional amount one week later. In Q2, on the other hand, theoptions are (A) receiving JPY1,000 one year later, and (B) receiving JPY1,000 plus a certain additionalamount one year and one week later. Let XQ1 and XQ2 be the delayed monetary amounts in Q1 and Q2,
respectively, which are taken as subjectively equivalent to JPY1,000 in options (A). Then, the degree of
declining impatience α in equation (1) is obtained by solving jointly

1,000 = XQ1 ƒ(7, α, η),
1,000 ƒ(365, α, η) = XQ2 ƒ(372, α, η),which are combined into a nonlinear equation of α,7ln(1000) − ln( X Q1 )ln(1000) − ln( X Q 2 )=ln(1 + 7α ).
ln(1 + 365α ) − ln(1 + 372α )The sample mean of estimated α takes the value of 0.018, which differs significantly from 0 (p < 0.00). As
a positive α implies declining impatience or present-biased preferences, it is determined that an average
respondent in our sample is present-biased. Respondents with present-biased preferences (i.e., with apositive α) comprise 40.2% (N = 960) of the 2,386 respondents.

Naïfs and sophisticates

We place hyperbolic discounters into two categories, in terms of their self-awareness of thetime-inconsistent property inherent in their behavior: sophisticated hyperbolic discounters, who are awareof their own time inconsistency which is wrought by hyperbolic discounting, and naïve hyperbolic
discounters, who misconceive themselves as being time-consistent. Economic theory has shown that inmany cases, time-inconsistent over-consumption behavior due to hyperbolic discounting is more salient fornaïfs than for sophisticates. Sophisticates behave time-consistently by incorporating the effect of apreference reversal in time discounting, whereas naïfs do not take their self-control problem into account,and hence, they are likely to consume excessively in a time-inconsistent way.

10

We hypothesize that

hyperbolic discounters are more likely to show inclinations toward ill health than exponential discounters,
and that the tendency is stronger for naïve hyperbolic discounters than for sophisticated hyperbolic
discounters.
To classify each of the hyperbolic respondents as being naïfs or sophisticates, we pose two questions as
to (i) how respondents used to do homework assignments during their childhood vacations, and (ii) how
they had planned to do them:10

Behavioral differences between naïfs and sophisticates are discussed in terms of procrastination

behavior, by O’Donoghue and Rabin (1999); borrowing behavior, by Heidhue and Kőszegi (2010) andIkeda and Kang (2011); and smoking behavior, by Gruber and Kőszegi (2004) and Kang and Ikeda (2010).
8

Q3. Reflecting back on when you were a child and you were given an assignment to be completed
during the school vacation, how early did you usually finish the assignment? (Mark the appropriate
box with an “X.”)(i) Did it right away(ii) Tended to get it done early, before the due date(iii) Worked on it daily up until the due date(iv) Tended to get it done toward the end(v) Got it done at the last minute

Q4. Reflecting back on when you were a child and you were given an assignment to be completed
during school vacation, how early did you plan to finish the assignment? (Mark the appropriate box
with an “X.”)(i) I planned to get it done right away(ii) I planned to get it done rather early, before the due date(iii) I planned to work on it daily up until the due date(iv) I planned to get it done closer toward the end(v) I planned to get it done at the last minute(vi) I didn’t make any plans

After excluding 109 hyperbolic respondents who chose option (vi) in Q4 (i.e., who had not made anyplans), we identify present-biased respondents (that is, those with α > 0) who chose a larger number in Q3
than in Q4 as being naïfs, because they tended to procrastinate on jobs in a time-inconsistent manner. The
nonhyperbolic respondents (α ≤ 0) or respondents who choose a weakly smaller number in Q3 than Q4 are
identified as being sophisticates. The naïfs account for 60.0% (N = 576) of 960 hyperbolic respondents
who used to fail their own plans for doing assignments.

2.2.2. The sign effect9

Many behavioral economists have reported that discount rates for losses are lower than those for gains(e.g., Thaler, 1981; Loewenstein, 1988; Fredrick et al., 2002; Benzion et al., 1989; Chapman, 1996). Thissign effect prompts people to prefer to incur losses immediately rather than delay them, and to have astrong desire to avoid future losses by bearing costs in the present. Indeed, the incidence of the sign effectleads people to consider seriously the future psychological and monetary losses of borrowing, addiction,and ill health.11 We thus hypothesize that a person who exhibits the sign effect is more likely to avoid
unhealthy behavior and likely to maintain a healthy status, compared to those who do not exhibit it.
To detect the sign effect, two discount rates for payments and receipts are elicited from the JPTR.
Table 3 shows the pay-off tables used to elicit discount rates, arranged in terms of the literature (e.g.,Harrison et al., 2002). Each table consists of nine intertemporal trade-offs, where the monetary amounts
with a front-end delay are commonly set at JPY1 million (around USD12,330.76). From the series of
options chosen by respondents, which are expected to change from “A” to “B” in Q5 (from “B” to “A” in
Q6), the individual discount rate ρ (Q5) (ρ (Q6)) can be estimated as the median interest rates ofindifference categories, in which selected options change from “A” to “B” in Q5 (from “B” to “A” in Q6).
The sample mean of ρ (Q5) is 8.8%, whereas that of ρ (Q6) is 1.0%. Since the difference of the twomeans is highly significant (p < 0.000), the average respondent displays the sign effect. Respondents
exhibiting the sign effect (N = 1,859) comprise 81.1% of the total. We construct a binary indicator for thesign effect:

1
Sign effect = 0if ρ(Q5) − ρ(Q6) ≥ E[ ρ (Q5) − ρ(Q6)] + σ[ ρ(Q5) − ρ(Q6)],otherwise

where E(•) and σ(•) represent sample means and standard deviations, respectively.12

11

The predicted relationships between the incidence of the sign effect and actual behavior such as

borrowing, cigarette consumption, and BMI are detected in the studies of Ikeda and Kang (2011), Ikeda etal. (2010), and Kang and Ikeda (2010), respectively.
12

We also define an indicator variable for the sign effect, which takes the value of 1 if ρ (Q5) is greaterthan ρ (Q6), and 0 otherwise. However, the detected associations between the indicator and health-related
attributes are found in our estimations to be insignificant.
10Insert Table 3

2.2.4. Impatience

In equation (2), the discount rate equals αη when τ = 0, which implies that, for any given α, η determines
the discount rate for an infinitesimally short horizon. For given α and τ, therefore, the discount rate ρ has
the same information as η. To ease interpretation, and considering the data availability, we focus on (α, ρ),instead of (α, η), as determinants of health behavior. The discount factor depends negatively on both
declining impatience α and impatience ρ.13
To measure the respondents’ degree of impatience ρ, we take the standardized average of the four
discount rates: Two are discount rates for τ = 7 and 372, elicited from Q1 and Q2, respectively—that is,they are calculated from equation (2); the other two are the discount rates for future receipts and payments,
implied by Q5 and Q6.14

3. Results

3.1. Means in stratified sample

In the first step of our analysis, we examine simple associations between time discounting andhealth-related attributes. Table 4 compares the average values of health-related indicators among
respondents stratified by whether their impatience is declining (α > 0) or not (α ≤ 0); whether impatience ρ
is higher than the average or not; and whether the sign effect is present (θ = 1) or not (θ = 0). The tableshows that health-related attributes relate to the degree of declining impatience and the degree of

13

When we rewrite ƒ(τ; α, η) as F(τ, α, ρ(τ; α, η)), the discount factor F satisfies ∂F(τ, α, ρ) / ∂τ = ƒτ < 0,∂F(τ, α, ρ) / ∂α = ƒα < 0, and ∂F(τ, α, ρ) / ∂ρ = ((1 + ατ) / α)ƒη < 0.
14

Note that daily discount rates are imputed from Q1 and Q2, whereas ρ (Q5) and ρ (Q6) are expressed inannual rates. This difference does not matter, since the average of the four discount rates is calculated fromtheir standardized values.
11impatience, as we hypothesize. First, nonhyperbolic discounters (α ≤ 0) are more likely to develop healthy
behavior and a good health condition than hyperbolic discounters (α > 0). For example, respondents who
maintain healthy teeth comprise 71.3% of nonhyperbolic discounters—a percentage higher than thecorresponding percentages in the samples of naïve hyperbolic discounters (56.1%) and sophisticatedhyperbolic discounters (60.4%).15 Second, naïfs with a positive α value are more likely to develop
unhealthy behavior and an ill-health condition than sophisticated hyperbolic respondents andnonhyperbolic respondents. For example, the smoking rate in the sample of naïfs is 22.5%, which is higher
than the 16.4% figure for the sample of sophisticates and 14.7% for the nonhyperbolic. Third, in all cases,
impatient respondents (ρ > mean) display stronger inclinations toward ill health than patient ones; thedifferences are all significant and with predicted signs. In contrast, associations with the sign effect are
insignificant and unstable, where the observed signs are, in many cases, the opposite of those predicted.

Insert Table 4

3.2. Regression results

To detect associations of time discounting with health-related attributes, we estimate the following probit
models:Pr(Yi = 1 | α i , ρi , θi , xi )Φ (c + βα α i + β ρ ρi + βθ θi + γxi )=Φ (c + βαα i + β Nα i * DNi + β ρ ρi + βθ θi + γxi )for model (A),for model (B),where, for the dependent variable Yi , various health-related indicators, as defined in Section 2.1, areadopted; Φ represents the cumulative normal distribution; and (αί, ρί, θί) indicate time-discounting
attributes: degree of declining impatience, impatience, and the incidence of the sign effect, respectively. Inmodel (B), by adding the interaction term of declining impatience with a naïve indicator, αί*DNi, acoefficient βα captures the partial correlation of present-biased preferences for the sophisticates on the15

Note that the unreported difference of average values of HEALTH between hyperbolic discounters andnonhyperbolic discounters is significant and with the expected sign, although the difference between thenaïve hyperbolic discounters and the sophisticated ones is found to be insignificant.
12

latent variable of Yi, and the corresponding partial correlation for the naïfs is obtained by βα + βN. The
control variables xi contain the following personal attributes: (i) the degree of risk aversion; (ii)demographic factors including age, gender, and college graduation; and (iii) economic factors including
household income, household real asset holdings, and household financial asset holdings.
Table 5 summarizes the marginal effects of declining impatience (α), impatience (ρ), and the sign effect(θ) on the probabilities that health-related indicators will take the value of 1. Corresponding robust
standard errors are given in parentheses.
As we shall explain, our hypotheses are supported in the case of impatience and declining impatience.
First, health-related attributes have significant associations with the degree of impatience, with thepredicted signs. In particular, smoking and teeth condition for males and health condition for females show
strongly significant associations with the degree of impatience: all other personal attributes being equal, a1 increase in impatience from the average induces a 7.9–9.9 percentage-point increase in the probabilityof being a smoker and a 6.3–12.3 percentage-point increase in the probability of having unhealthy teeth,for males; similarly, a 1

increase in impatience induces a 4.9–6.4 percentage-point increase in theprobability of developing ill-health condition, for females.
Second, health-related attributes also show significant associations with the degree of declining
impatience: when the degree of declining impatience α is larger, the probabilities of males being smokers
and being obese and those of females being severely obese and developing ill conditions for both healthand teeth are higher. Importantly, health-related attributes associate significantly with the interaction termsof the declining impatience with the naivety indicator, whereas the associations with the interaction termswith the sophistication indicator are insignificant in almost all the cases. This implies that naivety is likely
to lead respondents with steeply declining impatience toward more unhealthy behavior, whereas
sophistication attenuates such time-inconsistent behavior. Quantitatively, for example, an increase in α by
one unit of the sample standard deviation in the naïve sample leads to a 4.4 percentage-point(=0.066*0.672) higher probability of males being obese and a 0.7 percentage-point (=0.051*0.137) higher
probability of females being severely obese.16
Third, the sign effect shows the predicted signs; however, the significance levels are low.

16

Among the naïfs, the value of the standard deviation of α is 0.066 for males and 0.051 for females.
13Insert Tables 5 (a), (b), and (c)The principal component measure of health-related attributes
To extract the inclination toward healthy behavior, a principal component variable HEALTHRELATED
is created from the binary indicator OBESITY and three ordered variables that take the option number of
responses to health-related questions regarding smoking (FQ1), health status (FQ3), and teeth condition(FQ4).17 The ordinary least squares estimation results using HEALTHRELATED for a regressand aresummarized in Table 6: consistent with our expectations, the degree of impatience and the degree of
declining impatience each displays strongly significant associations with the health-related principal
component measure; also, the sign effect also shows the predicted signs, even though the detected impacts
are insignificant.18

Insert Table 6

4. Conclusion

17

To capture consistently tendencies toward healthy statuses, the binary indicator OBESITY and thesix-scale ordered variable for smoking (Q1) are re-constructed such that their larger values imply healthier
statuses.
18

Although the estimation of the generalized hyperbolic discounting function enables us to detect themarginal effect of a parametric increase in the degree of declining impatience on health-related behavior,
the results may depend on the specification of the discounting function. To focus on the impact of theincidence of present-bias properties without depending on the specification of functional form, instead ofαί, we use as a regressor the present-biased binary indicator, which takes the value of 1 if the respondent ispresent-biased (αί > 0), and 0 otherwise. See Appendices (a), (b), (c), and (d) for the estimation results,
which indicate that the same detected relationships in Section 3 hold in the case of the present-bias
indicator.
14

Based on analyses of data from an original Internet survey, we have shown that personal health-related
attributes have expected correlations with time-discounting properties, including impatience, the present
bias, and the sign effect: impatient respondents are more likely to have inclinations toward unhealthy
behavior; respondents with more steeply declining impatience tend to develop more unhealthy behavior,
where the tendencies are stronger for naïfs than for sophisticates; and the sign effect shows associations
with health-related attributes, although the significance levels are not overly high.
Our research is novel in three respects. First, the parameterized time-discounting properties induced by
the generalized hyperbolic discounting function enable us to detect the empirical associations between the
degree of declining impatience and health-related behavior. Second, hyperbolic discounters are classified
into naïfs and sophisticates, based on the self-reported gap between planning and actual behavior for an
onerous assignment. Third, partial associations between health-related attributes and each of the three
time-discounting properties are detected.

15

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incigarette

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18

Table 1
Summary statistics
Panel A. Background attribute s

Mean(S.D.)N
Age
Male
University grad.
Risk aversion
Household income (in JPY million)
Household's financial assets (in JPY million)
Household's real assets (in JPY million)

41.763(12.46)2386
0.499(0.50)
2386
0.546(0.50)
2386
0.623(0.31)
2386
6.90(4.09)
2361
14.53(23.67)2345
21.15(29.54)2351

Panel B. He alth-re late d attributes
SMOKINGHEALTHTEETHOBESITY
SEVERE OBESITYUNDERWEIGHT

0.172(0.38)
1886
0.726(0.45)
2386
0.652(0.48)
2386
0.181(0.38)
2351
0.031(0.17)
2351
0.115(0.32)
2351

Note : Data source: The original internet survey, The Japan Internet
Survey on Preferences Relating To Time and Risk (JPTR).

19

Table 2: Questions regarding health-related attributes

FQ1. How many cigarettes do you smoke regularly? Select a proximal option from the following:(i) Never smoke(ii) Hardly smoke(iii) Smoke sometimes(iv) About 10 cigarettes per day(v) About a pack per day(vi) More than two packs per day(vii) I used to smoke, but have quit

FQ2. What is your height and weight?

FQ3. How is your health? Using a scale of 1 to 10—where 10 is “good” and 1 is “bad”—choose anumber that describes your present situation.
(Good)
10

(Bad)
9

8

7

6

5

4

3

2

1

FQ4. To which level does your dentition status belong?
(i) All permanent teeth (including treated teeth)(ii) Some missing teeth, but replaced by dental implant or partial denture(iii) More than one missing tooth, without any dental treatment(iv) Wearing a full set of dentures

20

Table 3: Questions to elicit discount rates (Q5 and Q6)Q5. Suppose you have two options to receive some money. You may choose Option “A”, to receive
10,000,000 JPY today; or Option “B”, to receive a different amount in a year. Compare the amounts andtiming in Option “A” with Option “B” and indicate which amount you would prefer to receive for each of all 9
choices.
Option A(Receipt today)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)

Option B(Receipt in a year)
JPY 1,000,000 (USD 12,330.76)
JPY 1,001,000 (USD 12,343.09)
JPY 1,005,000 (USD 12,392.41)
JPY 1,010,000 (USD 12,454.07)
JPY 1,020,000 (USD 12,577.38)
JPY 1,060,000 (USD 13,070.61)
JPY 1,100,000 (USD 13,563.84)
JPY 1,300,000 (USD 16,029.99)
JPY 1,600,000 (USD 19,729.22)

Q6. Suppose you have two options to pay some money. You may choose Option “A”, to pay 1,000,000 JPY
today; or Option “B”, to pay a different amount in a year. Compare the amounts and timing in Option “A”
with Option “B” and indicate which amount you would prefer to pay for each of all 9 choices.

Option A(Pay today)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)
JPY 1,000,000 (USD 12,330.76)

Option B(Pay in a year)
JPY 920,000 (USD 11,344.30)
JPY 970,000 (USD 11,960.84)
JPY 1,000,000 (USD 12,330.76)
JPY 1,001,000 (USD 12,343.09)
JPY 1,005,000 (USD 12,392.41)
JPY 1,010,000 (USD 12,454.07)
JPY 1,050,000 (USD 13,947.30)
JPY 1,100,000 (USD 13,563.84)
JPY 1,300,000 (USD 16,029.99)

Note: The US dollar amounts are computed by using the average JPY/ USD exchange rate, 81.098, in October 21
to 27, 2010.

21

22

2

(0.42)
427
0.698(0.46)
576
0.561(0.50)
576
0.224(0.42)
571
0.040(0.20)
571
0.088(0.28)
571

0.225(12.44)576
0.516(0.50)
576
0.535(0.50)
576
0.636(0.27)
576
7.00(4.32)
565
13.08 (22.17)560
22.46 (28.98)
562

45.68

(0.37)
304
0.729 (0.44)384
0.604 (0.49)384
0.203 (0.40)379
0.029 (0.17)379
0.121 (0.33)
379

0.164

(12.65)384
0.521 (0.50)384
0.534 (0.50)384
0.583 (0.34)384
7.26 (4.11)
381
16.22 (23.03)
380
24.93 (31.57)
382

44.1

Note : Bold digits for χ statistics represent the significance at the 10 % level.

UNDERWEIGHTSEVERE OBESITYOBESITYTEETH

HEALTHSMOKING

Panel B. Health-related attributes

Household's real assets (in JPY million)

Household's financial assets (in JPY million)

Household income (in JPY million)

Risk aversion

University grad.

Male

Age

Panel A. Background attributes

0.147 (0.35)1070
0.744 (0.44)1317
0.713 (0.45)1317
0.151 (0.36)1295
0.026 (0.16)1295
0.127 (0.33)
1295

39.26 (11.87)1317
0.472 (0.50)1317
0.557 (0.50)1317
0.628 (0.32)
1317
6.75
(3.97)
1307
14.86 (24.62)
1298
19.52 (29.31)
1299

Declining impatience (α)
α>0
α≦0
Naif
Sophisticate
Mean(S.D.) Mean (S.D.) Mean (S.D.)
N
N
N

Table 4
Summary statistics stratified by time discounting variables

13.34(0.00)
4.34(0.11)
46.68(0.00)
16.19(0.00)
2.68(0.26)
6.05(0.05)

198.84(0.00)
4.61(0.10)
1.10(0.58)
47.90(0.00)
29.59(0.13)
29.64(0.04)
36.13(0.01)

χ statistics(P-value)2

χ test2

N(S.D.)(0.43)
538
0.692(0.46)
699
0.567(0.50)
699
0.236(0.43)
686
0.048(0.21)
686
0.086(0.28)
686

0.249(12.34)697
0.575(0.49)
697
0.505(0.50)
697
0.629(0.32)
699
6.7082 (4.16)
687
13.994 (24.76)
681
21.407 (30.64)
686

45.23

Mean

ρ>meanNχ test20.139 (0.35)1264
0.746 (0.44)
1582
0.695 (0.46)
1582
0.159 (0.37)
1565
0.024 (0.15)
1565
0.128 (0.33)
1565

31.96
(0.00)
7.03(0.01)
35.63(0.00)
18.97(0.00)
9.47(0.00)
8.40(0.00)

119.69(0.00)
24.81(0.00)
6.59(0.01)
21.12(0.00)
18.27(0.08)
32.65(0.00)
13.51(0.14)(S.D.) χ2 statistics(P-value)(12.19)1584
0.462 (0.50)
1584
0.563 (0.50)
1584
0.623 (0.30)
1582
7.01
(4.07)
1570
15.04 (23.46)
1560
21.46 (29.60)
1562

40.3

Mean

ρ≦meanImpatience (ρ)

N(S.D.)(0.43)
141
0.724(0.45)
181
0.552(0.50)
181
0.261(0.44)
176
0.040(0.20)
176
0.085(0.28)
176

0.241

46.376 (12.16)
181
0.6022 (0.49)
181
0.4199 (0.49)
181
0.659 (0.34)
181
6.0866 (4.29)
179
14.174 (29.57)
174
19.134 (31.85)
176

Mean

θ=1

N

2

χ test0.166(0.37)
1661
0.730(0.44)
2100
0.665(0.47)
2100
0.176(0.38)
2075
0.030(0.17)
2075
0.118(0.32)
2075

5.13(0.02)
0.03(0.86)
9.31(0.00)
7.94(0.00)
0.48(0.49)
6.05(0.05)

61.61(0.05)
4.61(0.10)
1.10(0.58)
66.51(0.00)
29.59(0.13)
29.64(0.04)
36.13(0.01)(S.D.) χ2 statistics(P-value)

θ=041.410 (12.39)
2100
0.488
(0.50)
2100
0.556(0.50)
2100
0.622(0.30)
2100
6.989(4.08)
2078
14.768 (23.32)
2067
21.640 (29.74)
2072

Mean

Sign effects (θ)

Table 5 (a)The marginal effects of time discounting on health-related attributes (all samples)
Model
SMOKING

Declining impatience（α）
0.597 ***

(A)

(B)

(0.18)
Naifs

Sophisticates

0.721 ***
(0.23)

0.538 **
(0.27)

0.308 *(A)

(B)

HEALTH(0.16)
Naifs

Sophisticates

0.426 **
(0.22)

0.200(0.25)-0.429 **

(A)

(B)

(0.20)
Naifs

Sophisticates-0.900 ***(0.26)

0.423(0.34)-0.335 *

(A)

(B)

TEETH

(0.20)
Naifs

Sophisticates-0.720 ***(0.26)

0.423(0.35)-0.704 ***

(A)

(B)

(0.21)
Naifs

Sophisticates-1.008 ***(0.29)-0.620 *(0.34)-0.255(A)(0.22)Naifs(B)

OBESITY-0.161(0.37)
0.615 ***
(0.16)

Naifs

Sophisticates

0.717 ***
(0.21)

0.387(0.27)

0.386 **(A)

(B)

SEVERE OBESITY(0.16)
Naifs

Sophisticates

0.463 **
(0.20)

0.193(0.26)
0.143 **

(A)

(B)

(0.06)
Naifs

Sophisticates

0.163 **
(0.08)

0.053(0.12)
0.117 **(A)

(B)

UNDERWEIGHT(0.06)
Naifs

Sophisticates

0.130 *
(0.07)

0.037(0.10)-0.244(A)(B)(0.18)
Naifs

Sophisticates-0.110(0.22)-0.652 **(0.27)-0.009(A)(B)

Sign effect (θ)

Log pseudolikelihood#obs

Controlled

0.080 ***
(0.02)-0.061 *(0.03)-806.84746

1802

-

0.077 ***
(0.02)-0.053(0.03)-758.09744

1719

-

0.051 ***
(0.02)-0.064 **(0.03)-702.12556

1761

○

0.050 ***
(0.02)-0.054 *(0.03)-661.11236

1680

○

-0.039 **(0.02)

0.062(0.04)-1326.3904

2281

-

-0.028(0.02)

0.047(0.04)-1252.4261

2174

-

-0.029(0.02)

0.073 *
(0.04)-1280.2232

2235

○

-0.019(0.02)

0.065(0.04)-1207.7426

2130

○

-0.101 ***(0.02)

0.061(0.04)-1443.9128

2281

-

-0.104 ***(0.02)

0.072(0.05)-1367.1431

2174

-

-0.042 **(0.02)

0.061(0.05)-1192.1658

2235

○

-0.047 **(0.02)

0.077 *
(0.04)-1134.1001

2130

○

0.026 *
(0.02)

0.022(0.04)-1057.4625

2251

-

0.028 *
(0.02)

0.011(0.04)-1003.4382

2147

-

-0.004(0.02)

0.029(0.04)-960.21508

2212

○

-0.001(0.02)

0.014(0.04)-907.93997

2109

○

0.013 **
(0.01)-0.014(0.01)-306.90501

2251

-

0.014 **
(0.01)-0.019 **(0.01)-290.18041

2147

-

0.010 *
(0.01)-0.013(0.01)-289.47664

2212

○

0.011 *
(0.01)-0.018 ***(0.01)-271.87256

2109

○

-0.032 **(0.02)

0.019(0.04)-800.59426

2251

-

-0.032 **(0.02)

0.017(0.04)-768.81153

2147

-

-0.005(0.01)

0.014(0.04)-707.19834

2212

○

-0.005(0.01)

0.014(0.04)-679.30904

2109

○

Sophisticates-0.473(0.29)(A)(B)

Impatience (ρ)(0.14)
Naifs

Sophisticates

0.097(0.18)-0.271(0.22)

Notes : The estimated marginal effects are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, theuniversity degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%,
and 1% levels, respectively.

23

Table 5 (b)The marginal effects of time discounting on health-related attributes (male samples)
Model
SMOKING

Declining impatience（α）
0.929 ***

(A)

(B)

(0.31)
Naifs

Sophisticates

0.995 **
(0.40)

1.086 **
(0.51)
0.754 **(A)

(B)

HEALTH(0.32)
Naifs

Sophisticates

0.717 *
(0.41)

0.880 *
(0.50)-0.371(A)(B)(0.26)
Naifs

Sophisticates-0.813 **(0.34)

0.582(0.46)-0.259

(A)

(B)

TEETH

(0.27)
Naifs

Sophisticates-0.606 *(0.35)

0.618(0.47)-0.422(A)(0.28)
Naifs(B)-0.314(0.45)-0.146(0.29)Naifs(B)

OBESITY-0.077(0.46)
0.672 ***
(0.25)

Naifs

Sophisticates0.879 ***
(0.32)

0.331(0.42)

0.550 **(A)

(B)

SEVERE OBESITY(0.25)
Naifs

Sophisticates

0.670 **
(0.33)

0.280(0.42)
0.120

(A)

(B)

(0.11)
Naifs

Sophisticates

0.109(0.14)

0.015(0.22)
0.128

(A)

(B)

UNDERWEIGHT(0.10)
Naifs

Sophisticates

0.111(0.13)

0.028(0.20)-0.108(A)(0.13)
Naifs

(B)

(B)

#obs

Controlled

0.099 ***
(0.03)-0.089(0.06)-474.06317

832-

0.097 ***
(0.03)-0.074(0.06)-440.93851

782-

0.080 ***
(0.03)-0.102 *(0.05)-430.84857

815○

0.079 ***
(0.03)-0.086(0.06)-403.38312

767○-0.014(0.03)

0.067(0.05)-681.02099

1133

-

0.003
(0.03)

0.043(0.06)-631.9054

1063--0.004(0.03)

0.080(0.05)-653.65254

1112

○

0.011
(0.03)

0.066(0.06)-604.7578

1044○-0.116 ***(0.03)

0.031(0.06)-734.44813

1133

-

-0.123 ***(0.03)

0.043(0.06)-681.99229

1063

-

-0.063 **(0.03)

0.031(0.06)-621.86298

1112

○

-0.071 **(0.03)

0.047(0.07)-581.56499

1044

○

0.015
(0.02)-0.005(0.06)-654.6877

1127

-

0.019
(0.02)-0.028(0.06)-613.12904

1058

-

-0.005(0.02)-0.004(0.06)-625.37227

1107

○

0.000
(0.03)-0.036(0.06)-583.5051

1039

○

0.016
(0.01)-0.021(0.02)-205.88428

1127

-

0.018 *
(0.01)-0.034 **(0.01)-193.36867

1058

-

0.015 *
(0.01)-0.023 *(0.01)-195.35226

1107

○

0.017 **
(0.01)-0.034 ***(0.01)-181.94022

1039

○

-0.013(0.01)

0.054(0.04)-206.15507

1127

-

-0.013(0.01)

0.061(0.05)-196.8572

1058--0.005(0.01)

0.049(0.04)-180.894

1107○-0.004(0.01)

0.055(0.04)-170.55379

1039

○

Sophisticates-0.124(0.20)-0.046(0.14)-0.016(A)

Log pseudolikelihood

Sophisticates-0.492(0.38)(A)(B)

Sign effect (θ)

Sophisticates-0.929 **(0.38)(A)

Impatience (ρ)(0.09)
Naifs

Sophisticates-0.009(0.13)

0.033(0.11)

Notes : The estimated marginal effects are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, theuniversity degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%,
and 1% levels, respectively.

24

Table 5 (c)The marginal effects of time discounting on health-related attributes (female samples)
Model
SMOKING

Declining impatience（α）
0.115

(A)

(B)

(0.20)
Naifs

Sophisticates

0.280(0.26)-0.076(0.37)-0.102(A)(B)

HEALTH(0.19)
Naifs

Sophisticates

0.162(0.23)-1.011(0.64)-0.501(A)(B)(0.31)
Naifs

Sophisticates-1.034 **(0.41)

0.264(0.52)-0.518 *

(A)

(B)

TEETH

(0.31)
Naifs

Sophisticates-0.969 **(0.42)

0.132(0.54)-1.054 ***

(A)

(B)

(0.35)
Naifs

Sophisticates-1.054 **(0.47)-0.969 *(0.54)-0.437(A)(0.37)Naifs(B)

OBESITY-0.299(0.65)
0.289(0.19)

Naifs

Sophisticates

0.311(0.25)

0.236(0.29)
0.224

(A)

(B)

SEVERE OBESITY(0.19)
Naifs

Sophisticates

0.255(0.24)

0.129(0.30)
0.136 **

(A)

(B)

(0.06)
Naifs

Sophisticates

0.165 **
(0.08)

0.065(0.08)
0.112 **(A)

(B)

UNDERWEIGHT(0.06)
Naifs

Sophisticates

0.137 **
(0.07)

0.054(0.07)-0.131(A)(B)(0.34)
Naifs

Sophisticates

0.134(0.42)-1.239 **(0.60)-0.005(A)(B)

Sign effect (θ)

Log pseudolikelihood#obs

Controlled

0.043 **
(0.02)-0.039(0.03)-282.34039

970-

0.041 **
(0.02)-0.033(0.04)-269.72196

937

-

0.026
(0.02)-0.033(0.03)-264.28625

946

○

0.024
(0.02)-0.029(0.03)-249.38788

913○-0.064 **(0.03)

0.055(0.06)-641.75385

1148

-

-0.059 **(0.03)

0.053(0.06)-616.57141

1111

-

-0.054 *(0.03)

0.059(0.06)-617.29984

1123

○

-0.049 *(0.03)

0.063(0.06)-594.0888

1086○-0.074 **(0.03)

0.098(0.06)-703.82783

1148

-

-0.075 **(0.03)

0.103(0.06)-680.51742

1111

-

-0.008(0.03)

0.076(0.06)-562.013

1123○-0.014(0.03)

0.092(0.06)-545.26143

1086

○

0.005
(0.02)

0.085(0.06)-344.54865

1124

-

0.005
(0.02)

0.090(0.06)-334.11273

1089

-

-0.004(0.02)

0.078(0.06)-330.83656

1105

○

-0.004(0.02)

0.081(0.06)-319.81597

1070

○

0.005
(0.01)-0.003(0.01)-93.731278

1124

-

0.005
(0.01)-0.004(0.01)-88.6025

1089

-

0.004
(0.01)-0.003(0.01)-91.245502

1105

○

0.004
(0.01)-0.004(0.01)-86.222431

1070

○

-0.025(0.03)-0.039(0.06)-538.04786

1124

-

-0.026(0.03)-0.052(0.06)-518.41132

1089

-

-0.006(0.03)-0.054(0.06)-515.49627

1105

○

-0.007(0.03)-0.064(0.06)-496.29253

1070

○

Sophisticates-0.482(0.45)(A)(B)

Impatience (ρ)(0.32)
Naifs

Sophisticates

0.252(0.39)-1.025 *(0.57)

Notes : The estimated marginal effects are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, theuniversity degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%,
and 1% levels, respectively.

25

Table 6
The marginal effects of time discounting on the health-related principal component
Model
HEALTHRELATEDAll

Declining impatience（α）-3.065 ***(A)(0.69)
Naifs(B)(0.65)(0.90)
Naifs

Female(0.91)-1.885(1.53)-2.014 **(0.88)(B)-0.329 ***(0.06)

0.061(0.16)

0.046

1773

-

-0.320 ***(0.06)

0.066(0.16)

0.04851693--0.158 ***(0.06)

0.111(0.14)

0.24211739○-0.155 ***(0.06)

0.129(0.15)

0.24041660○-0.304 ***(0.08)

0.030(0.21)

0.0423826--0.296 ***(0.09)

0.043(0.22)

0.0446777--0.157 *(0.08)

0.125(0.19)

0.2331810○-0.150 *(0.08)

0.137(0.20)

0.2302762○-0.279 ***(0.08)

0.131(0.21)

0.0323947--0.274 ***(0.08)

0.127(0.22)

0.0374916--0.151 **(0.07)

0.104(0.20)

0.1584929○-0.157 **(0.08)

0.132(0.21)

0.1607898○

Sophisticates-3.357 ***(1.06)-0.435(1.23)-1.202(A)

Controlled

Sophisticates-2.612 **(1.23)

Naifs(B)-2.417(1.47)-2.332 **

(A)

#obs

Sophisticates-4.146 ***(1.16)

Naifs(B)-0.754(1.07)-3.188 ***(A)

R-squared

Sophisticates-2.694 ***(0.81)(A)(B)-1.778(1.11)-1.856 ***
Naifs

Male

Sign effect (θ)

Sophisticates-4.137 ***(0.86)(A)(B)

Impatience (ρ)(0.87)
Naifs

Sophisticates-2.627 ***(0.99)

0.462(1.28)

Notes: The estimated coefficients are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, the university
degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%, and 1% levels,
respectively.

26

Q1-1

Q1-3

(A) To get JPY 1,000 today.
(B) To get JPY 3,500 a week later.

(A) To get JPY 1,000 today.
(B) To get JPY 1,200 a week later.

(A) To get JPY 1,000 today.
(B) To get JPY 1,800 a week later.

Q1-3-2(A) To get JPY 1,000 today.
(B) To get JPY 1,050 a week later.

(A) To get JPY 1,000 today.
(B) To get JPY 1,100 a week later.

Q1-3-1Q1-2-2(A) To get JPY 1,000 today.
(B) To get JPY 2,500 a week later.

(A) To get JPY 1,000 today.
(B) To get JPY 1,300 a week later.

Q1-2

Q1-2-1Q1 (Questions on discount rates for immediate future)
Which one do you prefer? Choos one you prefer.

Q2-1

Q2-3

Q2-2-1(A) To get JPY 1,000 a year later.
(B) To get JPY 3,500 a year + a week later.

(A) To get JPY 1,000 a year later.
(B) To get JPY 1,200 a year + a week later.

(A) To get JPY 1,000 a year later.
(B) To get JPY 1,800 a year + a week later.

Q2-3-2(A) To get JPY 1,000 a year later.
(B) To get JPY 1,050 a year + a week later.

(A) To get JPY 1,000 a year later.
(B) To get JPY 1,100 a year + a week later.

Q2-3-1Q2-2-2(A) To get JPY 1,000 a year later.
(B) To get JPY 2,500 a week later + a week later(A) To get JPY 1,000 a year later.
(B) To get JPY 1,300 a year + a week later.

Q2-2

Q2 (Question on discount rates for distant future ）Which one do you prefer? Choos one you prefer.

Figure 1: Questions Q1 and Q2 to elicit the generalized hyperbolic discount factor

27

Appendix (a)The marginal effects on health-related attributes: Estimation with the present bias dummy (all samples)
Model
SMOKING

Present bias (α>0) = 1
0.056 ***

(A)

(B)

(0.02)
Naifs

Sophisticates

0.070 ***
(0.02)

0.023(0.03)

0.027

(A)

(B)

HEALTH(0.02)
Naifs

Sophisticates

0.050 **
(0.02)-0.001(0.02)-0.036 *(A)(0.02)
Naifs(B)-0.015(0.03)-0.031(0.02)

Naifs
(B)

TEETH

(B)

-0.019(0.03)-0.140 ***(0.02)

Naifs

Sophisticates-0.156 ***(0.02)-0.114 ***(0.03)-0.054 **(A)(0.02)Naifs(B)

OBESITY

SEVERE OBESITY(0.02)
Naifs

Sophisticates

0.066 ***
(0.02)

0.051 **
(0.02)

0.036 **
(0.02)
Naifs

Sophisticates

0.041 **
(0.02)

0.034(0.02)
0.007

(A)

(B)

(0.01)
Naifs

Sophisticates

0.010(0.01)-0.001(0.01)
0.006

(A)

(B)

UNDERWEIGHT(0.01)
Naifs

Sophisticates

0.010(0.01)-0.001(0.01)-0.020(A)(B)(0.01)
Naifs

Sophisticates-0.033 **(0.02)

0.003(0.02)
0.004

(A)

(B)

-0.037(0.03)
0.060 ***

(A)

(B)

#obs

Controlled

0.080 ***
(0.02)-0.052(0.03)-807.18862

1802

-

0.078 ***
(0.02)-0.043(0.04)-702.47076

1761

-

0.052 ***
(0.02)-0.060 **(0.03)-758.87998

1719

○

0.051 ***
(0.02)-0.050 *(0.03)-659.9494

1680○-0.040 **(0.02)

0.055(0.04)-1326.9455

2281

-

-0.029(0.02)

0.041(0.04)-1280.3665

2235

-

-0.029(0.02)

0.069 *
(0.04)-1257.9866

2174

○

-0.020(0.02)

0.061(0.04)-1211.6709

2130

○

-0.097 ***(0.02)

0.050(0.04)-1425.0716

2281

-

-0.101 ***(0.02)

0.059(0.05)-1189.7081

2235

-

-0.042 **(0.02)

0.057(0.05)-1350.8305

2174

○

-0.048 **(0.02)

0.073(0.04)-1132.2764

2130

○

0.027 *
(0.02)

0.032(0.04)-1057.6628

2251

-

0.029 *
(0.02)

0.019(0.04)-960.75763

2212

-

-0.003(0.02)

0.036(0.04)-1003.3039

2147

○

0.000
(0.02)

0.019(0.04)-908.07668

2109

○

0.013 **
(0.01)-0.011(0.01)-309.09243

2251

-

0.014 **
(0.01)-0.018 *(0.01)-291.37241

2212

-

0.010 *
(0.01)-0.011(0.01)-291.54504

2147

○

0.011 **
(0.01)-0.017 **(0.01)-272.90882

2109

○

-0.032 **(0.02)

0.015(0.04)-800.55876

2251

-

-0.033 **(0.02)

0.017(0.04)-707.13943

2212

-

-0.006(0.01)

0.014(0.04)-768.43155

2147

○

-0.007(0.01)

0.017(0.04)-678.38265

2109

○

Sophisticates-0.064 **(0.03)(A)(B)

Log pseudolikelihood

Sophisticates-0.030(0.02)(A)

Sign effect (θ)

Sophisticates-0.040 *(0.02)(A)

Impatience (ρ)(0.01)
Naifs

Sophisticates-0.009(0.02)

0.024(0.02)

28

Notes : The estimated marginal effects are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, theuniversity degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%,
and 1% levels, respectively.

Appendix (b)The marginal effects on health-related attributes: Estimation with the present bias dummy (male samples)
Model
SMOKING

Present bias (α>0) = 1
0.081 ***

(A)

(B)

(0.03)
Naifs

Sophisticates

0.109 ***
(0.04)

0.033(0.04)

0.047

(A)

(B)

HEALTH(0.03)
Naifs

Sophisticates

0.085 **
(0.04)

0.003(0.04)-0.024(A)(0.03)
Naifs(B)-0.010(0.04)-0.014(0.03)

Naifs
(B)

TEETH

(B)

-0.008(0.04)-0.137 ***(0.03)

Naifs

Sophisticates-0.164 ***(0.03)-0.091 **(0.04)-0.065 **(A)(0.03)Naifs(B)

OBESITY

SEVERE OBESITY(0.03)
Naifs

Sophisticates

0.096 ***
(0.03)

0.043(0.04)

0.050 *
(0.03)
Naifs

Sophisticates

0.069 **
(0.03)

0.033(0.04)
0.001

(A)

(B)

(0.01)
Naifs

Sophisticates

0.007(0.01)-0.009(0.02)
0.004

(A)

(B)

UNDERWEIGHT(0.01)
Naifs

Sophisticates

0.010(0.01)-0.007(0.02)-0.012(A)(B)(0.01)
Naifs

Sophisticates-0.037 **(0.02)

0.014(0.02)
0.000

(A)

(B)

-0.025(0.04)
0.072 ***

(A)

(B)

#obs

Controlled

0.098 ***
(0.03)-0.070(0.06)-475.27319

832-

0.098 ***
(0.03)-0.057(0.06)-432.82321

815-

0.082 ***
(0.03)-0.086(0.05)-442.13036

782○

0.082 ***
(0.03)-0.072(0.06)-403.97121

767○-0.015(0.02)

0.060(0.05)-681.65579

1133

-

0.001
(0.03)

0.038(0.06)-654.02827

1112

-

-0.005(0.03)

0.075(0.05)-635.68873

1063

○

0.010
(0.03)

0.063(0.06)-607.41528

1044

○

-0.113 ***(0.03)

0.025(0.06)-724.42396

1133

-

-0.121 ***(0.03)

0.035(0.06)-619.84975

1112

-

-0.064 **(0.03)

0.029(0.06)-673.81662

1063

○

-0.073 **(0.03)

0.044(0.07)-579.7625

1044

○

0.016
(0.02)

0.007(0.06)-654.67041

1127

-

0.019
(0.02)-0.018(0.06)-626.13881

1107

-

-0.002(0.02)

0.006(0.06)-612.344

1058

○

0.002
(0.03)-0.028(0.06)-583.52025

1039

○

0.016 *
(0.01)-0.019(0.02)-206.55384

1127

-

0.018 *
(0.01)-0.034 **(0.01)-196.20252

1107

-

0.016 *
(0.01)-0.021(0.01)-193.322

1058○

0.018 **
(0.01)-0.033 ***(0.01)-181.911039○-0.013(0.01)

0.051(0.04)-205.99189

1127

-

-0.012(0.01)

0.065(0.05)-180.90419

1107

-

-0.005(0.01)

0.049(0.04)-193.21934

1058

○

-0.004(0.01)

0.062(0.05)-167.70486

1039

○

Sophisticates-0.086 **(0.04)(A)(B)

Log pseudolikelihood

Sophisticates-0.001(0.03)(A)

Sign effect (θ)

Sophisticates-0.022(0.03)(A)

Impatience (ρ)(0.01)
Naifs

Sophisticates-0.020(0.01)

0.018(0.01)

Notes : The estimated marginal effects are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, theuniversity degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%,
and 1% levels, respectively.

29

Appendix (c)The marginal effects on health-related attributes: Estimation with the present bias dummy (female samples)
Model
SMOKING

Present bias (α>0) = 1
0.027

(A)

(B)

(0.02)
Naifs

Sophisticates

0.035(0.02)

0.010(0.03)
0.015

(A)

(B)

HEALTH(0.02)
Naifs

Sophisticates

0.027(0.02)-0.001(0.02)-0.043 *(A)(0.03)
Naifs(B)-0.015(0.04)-0.048 *(0.03)

Naifs
(B)

TEETH

(B)

-0.025(0.04)-0.139 ***(0.03)

Naifs

Sophisticates-0.146 ***(0.03)-0.137 ***(0.04)-0.044(A)(0.03)Naifs(B)

OBESITY(B)(B)

SEVERE OBESITY(0.02)
Naifs

Sophisticates

0.026(0.02)

0.045 *
(0.03)
0.022(0.02)

Naifs

Sophisticates

0.016(0.02)

0.031(0.02)
0.010

(A)

(B)

(0.01)
Naifs

Sophisticates

0.012(0.01)

0.005(0.01)
0.009

(A)

(B)

UNDERWEIGHT-0.049(0.04)
0.032 *

(A)

(0.01)
Naifs

Sophisticates

0.010(0.01)

0.004(0.01)-0.017(A)(0.02)
Naifs

(B)

(B)

0.043 **
(0.02)-0.038(0.03)-281.41183

970-

0.041 **
(0.02)-0.033(0.03)-264.04591

946

-

0.027
(0.02)-0.034(0.03)-268.9623

937

○

0.026
(0.02)-0.030(0.03)-250.39678

913○-0.064 **(0.03)

0.051(0.06)-641.61333

1148

-

-0.059 **(0.03)

0.047(0.06)-617.04976

1123

-

-0.054 *(0.03)

0.056(0.06)-618.17789

1111

○

-0.050 *(0.03)

0.055(0.06)-595.1549

1086○-0.070 **(0.03)

0.085(0.06)-696.14385

1148

-

-0.070 **(0.03)

0.090(0.07)-561.72643

1123

-

-0.009(0.03)

0.073(0.06)-672.06012

1111

○

-0.014(0.03)

0.089(0.06)-544.72731

1086

○

0.004
(0.02)

0.090(0.06)-343.89642

1124

-

0.003
(0.02)

0.096(0.06)-330.68714

1105

-

-0.004(0.02)

0.082(0.06)-333.06401

1089

○

-0.004(0.02)

0.086(0.06)-319.4515

1070

○

0.005
(0.01)

0.001(0.02)-94.953402

1124

-

0.005
(0.01)

0.002(0.02)-92.263626

1105

-

0.004
(0.01)

0.000(0.02)-90.166184

1089

○

0.004
(0.01)

0.001(0.02)-87.606124

1070

○

-0.023(0.03)-0.040(0.06)-537.88229

1124

-

-0.026(0.03)-0.050(0.06)-515.34629

1105

-

-0.007(0.03)-0.054(0.06)-519.56563

1089

○

-0.011(0.03)-0.062(0.06)-497.24566

1070

○

Sophisticates-0.029(0.03)-0.002(0.03)
0.014(A)

Controlled

Sophisticates-0.046(0.04)(A)#obs

Sophisticates-0.059 *(0.03)(A)

Log pseudolikelihood

Sophisticates-0.056 *(0.03)(A)

Sign effect (θ)

Impatience (ρ)(0.02)
Naifs

Sophisticates

0.003(0.03)

0.030(0.03)

30

Notes : The estimated marginal effects are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, theuniversity degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%,
and 1% levels, respectively.

Appendix (d)The marginal effects of time discounting on the health-related principal component (present bias dummy）
Model
HEALTHRELATED

All

Present bias (α>0) = 1
0.292 ***

(A)

(B)

(0.06)
Naifs

Sophisticates0.320 ***
(0.07)

0.216 ***
(0.08)

0.126 **

(A)

(B)

Male

(0.05)
Naifs

Sophisticates

0.158 **
(0.07)

0.087(0.07)
0.277 ***

(A)

(B)

(0.09)
Naifs

Sophisticates

0.359 ***
(0.12)

0.121(0.13)

0.093

(A)

(B)

Female(0.08)
Naifs

Sophisticates

0.167(0.11)-0.015(0.11)
0.282 ***

(A)

(B)

(0.06)
Naifs

Sophisticates

0.283 ***
(0.08)

0.290 ***
(0.09)

0.160 **(A)

(B)

Impatience (ρ)(0.07)
Naifs

Sophisticates

0.165 **
(0.08)

0.177 **
(0.09)

Sign effect (θ)

R-squared#obs

Controlled

0.325 ***
(0.06)-0.022(0.16)

0.049

1773

-

0.320 ***
(0.06)-0.028(0.16)

0.04761693-

0.161 ***
(0.06)-0.084(0.14)

0.24041739○

0.159 ***
(0.06)-0.103(0.15)

0.23751660○

0.302 ***
(0.09)

0.020(0.21)

0.0402826-

0.299 ***
(0.09)-0.003(0.22)

0.0407777-

0.164 **
(0.08)-0.075(0.20)

0.2275810○

0.160 *
(0.08)-0.104(0.21)

0.2262762○

0.268 ***
(0.08)-0.111(0.21)

0.0468947-

0.265 ***
(0.08)-0.099(0.21)

0.0485916-

0.151 **
(0.07)-0.094(0.20)

0.1623929○

0.157 **
(0.08)-0.111(0.21)

0.1611

898○

Notes: The estimated coefficients are listed with robust standard errors in parentheses. Control variables include: the degree of risk aversion, age, gender, the university
degree, household income, household real asset holding, household financial asset holding. *, **, *** represent statistical significances at the 10%, 5%, and 1% levels,
respectively.

31