Discussion Paper No. 732

FAT DEBTORS:TIME DISCOUNTING, ITS ANOMALIES,
AND BODY MASS INDEX
Shinsuke Ikeda
Kang Myong-Il
Fumio Ohtake

March 2009

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

Fat Debtors:
Time Discounting, Its Anomalies, andBody Mass Index 1
Ikeda, Shinsuke,2 Myong-Il, Kang,3 and Fumio Ohtake4
ISER, Osaka University
March 6, 2009

1 Our special thanks go to I. Shimomura and T. Hunahashi (Graduate School of

Medicine, Osaka University) for helpful comments from the viewpoint of medical
science. We are also grateful to Y. Fukuta, D. Kawaguchi, K. Hirata, C.Y. Horioka
and participants at the 2008 meeting of the Association of Behavioral Economics
and Finance and the faculty seminars of Hitotsubashi and Osaka Universities forbeneficial discussions. We appreciate financial supports for Ikeda from Grantsin-Aid for Scientific Research (C No. 1553021) from the Japan Society for the
Promotion of Science (JSPS) and the COE and the Global COE Programs from
the Ministry of Education, Culture, Sports, and Science and Technology.
2 Corresponding author: S. Ikeda, The Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. Telephone: 81-6-6879-8568. E-mail: <ikeda@iser.osaka-u.ac.jp>.
3 M. Kang, The Institute of Social and Economic Research, Osaka University,
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. Telephone: 81-6-6879-8568. Email: <myong_il_econ@yahoo.co.jp>.
4 F. Ohtake, The Institute of Social and Economic Research, Osaka University,
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. Telephone: 81-6-6879-8572. Email: <ohtake@iser.osaka-u.ac.jp>.

Abstract
In view of the finding that debtors are likely to be more obese than nondebtors, we investigate whether interpersonal diﬀerences in body mass are,as in the case of debt behavior, related to those in time discounting andtime discounting anomalies. The eﬀects of time discounting on body massindex (BMI) and the probabilities of being obese, severely obese, and underweight are detected by incorporating three properties of intertemporal preferences: (i) impatience, measured by the level of the respondents’ discountrate; (ii) hyperbolic discounting, where discount rates for the discountingof immediate future payoﬀs are higher than those of distant future payoﬀs;and (iii) the sign eﬀect, wherein future negative payoﬀs are discounted ata lower rate than are future positive payoﬀs. We also find that body mass
is non-monotonically correlated with age, income, and working hours. As apolicy implication, body mass can potentially be controlled by changing theintertemporal structure of medical care costs.
Keywords: BMI, obesity, underweight, time preference, discount rate, hyperbolic discounting, procrastination, the sign eﬀect.
JEL classification: I10; Z00.

1

Introduction

As in the case of other advanced countries, the number of obese individuals
in Japan has been increasing, and this has been accompanied by associatedincreases in social costs including health care costs. However, one distinct
feature in Japan is that in addition to obesity, underweight, too, is widely
observed. According to the National Survey of Health and Nutrition 2004
(hereafter, NSHN04), conducted by the Ministry of Health, Labour and Welfare of Japan, the prevalence rate of obesity in Japanese adults amounts
to nearly 30% for males and 20% for females. On the other hand, nearly
5% of male adults and 10% of female adults are underweight. In particular, the prevalence rate of underweight among females in their 20s exceeds
20%. Thus, it is important to examine the causes of these wide interpersonal
diﬀerences in body mass.
According to economic theory, optimal caloric intake is determined by thecondition that the present utility derived from marginal caloric intake nettedof its costs be equal to the discounted future marginal disutility derived
from being overweight (e.g., Cutler et al., 2003). The resulting body mass
would depend on consumers’ preferences regarding time discounting and risk
aversion, lifetime income, and the costs of caloric intake in terms of time andmoney. Among other factors, people’s time preferences or discount rates havebeen focused on as a key determinant of body mass and has been regarded asimportant, especially in explaining the interpersonal diﬀerences in body mass
(e.g., Komlos et al., 2004; Smith et al., 2005; and Borghans and Golsteyn,2006).1 Those less patient, namely, those with higher time preferences, arelikely to discount more intensively the future disutility of obesity, and would
hence be more likely to be obese than those more patient, namely, those withlower time preferences.
As suggested by the title of the paper, there is consistent evidence suggesting that debtors are likely to be more obese than non-debtors. By using
data from a Japanese survey conducted in 2005 (the Japan Household Survey on Consumer Preferences and Satisfaction 2005, which is explained later),Table 1 compares the body mass of debtors and non-debtors while excluding
housing loans from the debts. Body mass index (BMI), the standard measureof body mass, is defined as weight in kilograms divided by height in meterssquared (kg/m2 ). Both for the male and female samples, the table indicatesthat debtors are significantly more obese than non-debtors (the definitions
1

The cost factor is important, especially in explaining the dynamics of peoples’ bodymass. Cutler at al. (2003) and Chou et al. (2004) find that technological progress and theresulting decrease in calorie prices could explain the recent rapid increases in the obesity
prevalence rate in the U.S.

1

of obesity, etc., will be provided later). Because time discounting plays a
key role in determining debt holdings as a result of intertemporal resource
allocation, the significant correlation between body mass and debt holdings
suggests that time discounting may actually aﬀect body mass formation.
Insert Table 1:
Debt holdings and body mass
By using Japanese survey data, this paper aims to examine the determinants of interpersonal diﬀerences in body mass, especially focusing on theempirical validity of the hypothesis that body mass is related to time discounting. The novelty of our study lies in the fact that it investigates theeﬀects of not only impatience, measured by the level of respondents’ discountrate, but also the eﬀects of two time discounting anomalies that have been
empirically reported and predicted to aﬀect debt holding behavior.2 One
time discounting anomaly is hyperbolic discounting or the immediacy eﬀect,under which a person discounts his/her immediate futures more intensively
than his/her distant futures (e.g., Thaler, 1981 and Benzion et al., 1989). Hyperbolic discounting causes consumers to procrastinate saving and thereby
hold excessive debts (e.g., Laibson, 1997, 1998). The other time discounting
anomaly is the sign eﬀect, under which a person discounts positive payoﬀsmore intensively than negative payoﬀs. This anomaly makes consumers reluctant to pay interest in the future, thereby leading to “borrowing aversion”
behavior (Loewenstein and Prelec, 1992).
In view of the strong correlation between debt holdings and body mass,
as shown in Table 1, it would be plausible to apply the same logic of thedebt theory to body mass determination and hence to assume that the twotime discounting anomalies aﬀect body mass. As Cutler et al. (2003) predict, hyperbolic discounting leads people to procrastinate controlling their
immediate appetite and to instead eat excessive cheap, fatty foods. The sign
eﬀect leads people to try and control caloric intake in order to avoid bearing
the future psychological and/or monetary costs of obesity, such as the hardships of dieting, costs of having to buy new larger sized clothes, and medical
services. We hypothesize that, as in the case of debt holdings, body mass isrelated positively to the degrees of impatience and hyperbolic discounting,and negatively to the sign eﬀect. Our main interest involves investigating
the empirical validity of this hypothesis.
2

For a comprehensive survey on time discounting anomalies, see, for example, Frederick,et al. (2002).

2

The relationships between body mass and time preference have been empirically examined in the literature. By using international cross-sectional
macro data, Komlos et al. (2004) find that the prevalence rate of obesity in
the Western advanced countries is negatively correlated with the national savings rate as a reverse proxy for national time preference. Using cross-sectional
data from a National Longitudinal Survey of Youth (NLSY) conducted in the
U.S., Smith et al. (2005) report a significant negative correlation between
BMI and savings, which they used as a reverse proxy for time preference.
From Dutch survey data, Borghans and Golsteyn (2006) construct a variety of proxies for time discounting to show that the respondents’ BMI ispositively correlated with the time preference proxies. However, the proxies
for time preference used in these studies are not very refined. For example,
savings may well depend on variables other than time preference, such as income, age, and especially the magnitudes of the time discounting anomalies.
For savings to be an accurate proxy for time preference, the eﬀects of theother determinants should be controlled for.
To eliminate this problem, we construct two kinds of time preference data.
First, by administering questionnaires on intertemporal monetary choices
under alternative conditions, we obtain individuals’ discount rates. This
enables us (i) to construct time preference data as a measure of impatienceby computing the normalized mean of the elicited discount rates, and (ii) toconstruct indicator variables for hyperbolic discounting and the sign eﬀect.
Second, we construct a time preference proxy from the debt holding data.
This proxy is estimated to be the residual after regressing debt holdings on
the degree of procrastination, the sign eﬀect, income, and the determinants
other than time preference.
After controlling for demographic and economic factors, the main results
reveal that the time discounting anomalies as well as impatience jointly predict respondents’ body mass index and their probabilities of being obese
and underweight; moreover, the significance levels are higher for the female
sample than for the male sample.
Further, body mass is non-monotonically correlated with age, per capita
household income, and working hours. For example, BMI is found to bequadratic in per capita income with a positive coeﬃcient on the income
squared. One important implication of this is that an increase in income
inequality leads to an increase in the social mean of BMI. We will discuss
the implications of these findings for the recent BMI dynamics in Japan.
Definitions of obesity, severe obesity, and underweightDiﬀerent from the international criterion for obesity provided by theWorld Health Organization (WHO), according to which a person is regarded3as obese if he/she has a BMI ≥ 30, the Examination Committee of Criteria
for “Obesity Disease in Japan” (2002), aﬃliated to the Japan Society for
the Study of Obesity (JSSO), provided a new criterion specific to Japan,
according to which a person is regarded as obese if he/she has a BMI ≥25; detailed diﬀerences between the two criteria are summarized in Table
2. The new criterion was provided based on scientific evidence such as thefinding that the average number of obesity-related disorders including hyperglycemia, dylipidemia, and hypertension exceeds 1.0 at a BMI of 25 and that
there is a progressive increase in such disorders at a BMI ≥ 25 (see “New
Criteria,” 2002). Since then, academic research, especially medical research,on the health of the Japanese as well as on the medical care policy of theJapanese government has been conducted based on the JSSO criterion.
In the text that follows, based on the JSSO criterion, we define obesity
as a condition wherein a person has a BMI ≥ 25 and severe obesity as a condition wherein a person has a BMI ≥ 30 (see Table 2). Similarly, individuals
with a BMI < 18.5 are classified as underweight. A BMI of 22, at which
the probability of diseases becomes minimal (see “New Criteria,” 2002), isregarded as standard or ideal.
Insert Table 2:
Definitions of obesity and underweight
The remainder of the paper is structured as follows: In Section 2, the relation between time discounting and caloric intake is discussed from the viewpoint of intertemporal resource allocation. In Section 3, after our Japanesesurvey data are presented, the time discounting data including discount rates
and indicators for time discounting anomalies are constructed. Section 4shows the regression results. Finally, Section 5 provides the conclusion.

2

Time discounting and caloric intake behavior

When we make intertemporal decisions including those on caloric intake, oursubjective discount rate, a measure of time preference, plays a key role indetermining how much of a resource is consumed for present gratification andhow much is saved for future gratification. We hypothesize that interpersonal
diﬀerences in BMI are, in part, related to those in time discounting. To
investigate the eﬀects of time discounting on BMI and hence on the degrees4

of obesity and underweight, we take into account three properties regarding
time discounting: (i) the degree of impatience, (ii) hyperbolic discounting,and (iii) the sign eﬀect.
(i) Impatience
A higher subjective discount rate implies a higher degree of impatienceand hence a stronger preference for present consumption. In advanced countries, where the costs of caloric intake in terms of both money and time areso low that nutrition and calories that are biologically required for subsistence are almost freely available, those less patient with higher discount rates
would tend to have higher BMI values and to have a higher probability of
being obese. As in Komlos et al. (2004) and Smith et al. (2005), we hypothesize that persons with higher discount rates tend to have greater bodymass.
(ii) Hyperbolic discounting
As a stylized fact, it has often been reported that people have high discount rates for very short delays whereas they have considerably lower discount rates for longer delays (e.g., Thaler, 1981 and Benzion et al., 1989).
This implies that people are less patient in the case of immediate gratification than in the case of delayed gratifications in the distant future. Since
the resulting discount factor is better described by a hyperbolic function ofdelay than an exponential one, the phenomenon is referred to as hyperbolic
discounting.3
Hyperbolic discounting tends to lead people lacking adequate self-control
to engage in time-inconsistent procrastination with regard to dieting andhealth care and consequently to overeating, which will harm their long-run
interests (e.g., Ainslie, 2001). In theory, Cutler et al. (2003) stress that reductions in costs pertaining to food consumption due to recent technological advancements have been accelerating this time-inconsistent overeating, thereby
increasing the prevalence rate of obesity. Chapman (1995) also points outthat hyperbolic discounting gives rise to underinvestment in health capital.
We hypothesize that persons with a stronger tendency toward hyperbolic discounting and hence with a stronger propensity toward procrastination tend
to have a greater body mass.
(iii) The sign eﬀect
3

This phenomenon is sometimes referred to as the immediacy eﬀect (e.g., Thaler, 1981;
Benzion et al., 1989).

5

Many studies have reported that losses are discounted at a lower rate thanare gains. For example, Thaler (1981) finds that the discount rates for gains
were 3 to 10 times higher than those for losses. Several of Thaler’s subjects
evidence negative discount rates for loss, implying that an immediate loss
is preferred to a delayed loss of the same value. In Loewenstein (1988), his
subjects’ evaluations reveal that they are indiﬀerent between receiving $100
immediately and receiving $157 in a year and are indiﬀerent between losing$100 immediately and losing $133 in a year. This gain-loss asymmetry isreferred to as the sign eﬀect.
The sign eﬀect makes people reluctant to borrow because persons who
operate under this eﬀect require a more favorable (i.e., lower) interest rate
to borrow than they would to save (e.g., Loewenstein and Prelec, 1992).
Similarly, in the case of the sign eﬀect, people tend to try to control foodconsumption to avoid bearing various obesity-related costs in the future,such as the hardships associated with dieting and costs of medical care. We
hypothesize that subjects operating under the sign eﬀect are likely to have asmaller body mass.

3

The data

Our empirical research is based on the Japan Household Survey on Consumer
Preferences and Satisfaction 2005 (hereafter, JHS05), conducted in February
2005. This survey is a project that is carried out as part of the Osaka
University COE program, sponsored by the Ministry of Education, Culture,
Sports, and Science and Technology of Japan. The JHS05 is a household
survey, in which 6000 randomly selected Japanese respondents who are older
than the age of 20 are requested to fill out questionnaires; out of the 6000
people, 2987 responded, and the proportion of male respondents was 47.0 %,with the average age of the respondents being 49.080. The survey contains
various questions that enable us to elicit information about the respondents’attitudes toward time discounting and risk; their demographic, social, andeconomic attributes; and their health status including height and weight.

3.1

BMI

From the data on height and weight obtained from the JHS05, the respondents’ BMI values are calculated by dividing weight in kilograms by heightin meters squared. Since the JHS05 elicited self-reported data, the resulting
BMI data may well contain an underreporting bias due to respondents’ underreporting of weight and overreporting of height, as in Cawley (2004) and6

Chou et al. (2004). Every year, the Ministry of Health, Labour and Welfareof Japan measures the actual height and weight of thousands of randomly selected Japanese people and summarizes the data obtained from the survey byreporting the BMI distributions, by age, of the males and females. Since thesample sizes of the NSHN04 and JHS05 are suﬃciently large, by comparing
the age-based BMI distributions of our JHS05 data with those of the NSHN
conducted in 2004 (hereafter, NSHN04; sample size: 7689), we could roughly
examine whether or not the JHS05 data contain a self-reporting bias.4 If thepresence of a bias is strongly suggested, it would be necessary to correct forit.
Figures 1(a) and (b) compare the BMI distributions obtained from the
NSHN04 and JHS05 for the male (a) and female (b) samples; the histograms
represent diﬀerences in relative frequencies (the “corrected data” will bedemonstrated later). As seen from the figures, the JHS05 distribution is
thicker than the NSHN04 distribution in the normal range (18.5 5 BMI< 25), whereas for the ranges of underweight and, especially obesity, theJHS05 displays thinner tails than the NSHN04; all these observations suggest the possibilities of the presence of a self-reporting bias in the JHS04
data.
Insert Figures 1(a) and 1(b):BMI distributions: NSHN04, JHS05, and corrected data.
Tables 3(a) through (d) statistically describe and compare the distributions, by age, of BMI and the prevalence rates of obesity, severe obesity, andunderweight as revealed by the NSHN04 and JHS05 data sets, respectively.
From this data, we can observe three tendencies. First of all, consistent with
Figures 1 (a) and (b), the BMI mean, the obesity rate, and the severe obesity rate seem to reflect an underreporting bias. Particularly in the case of
the data for females, the BMI means and the obesity rate as revealed by
the JHS05 are significantly lower in many generations than those as revealedby the NSHN04 data. Consistent with this tendency, the sample standard
deviations (SDs) of the females’ BMI in the JHS05 are significantly smaller
than those in the NSHN04. As for the male sample, although the bias is
not as large as it is in the female sample, the obesity rates are smaller in
the JHS05. Second, there is no diﬀerence between the rates of severe obesity
4

The NSHN04 survey was conducted in November 2004, and the JHS05 survey was
conducted in February 2005; therefore, the systematic diﬀerences in the two BMI data
sets due to time diﬀerence can be regarded as negligible.

7among males in the two data sets. Third, although the prevalence rates ofunderweight in the JHS05 are slightly lower than those in the NSHN04, theirdownward bias does not seem to be substantial.
Insert Tables 3 (a) through (d):By-age distributions of body mass: NSHN04, JHS05, and corrected data
Based on these observations, we correct for the underreporting bias in
the female sample by employing the following procedure, which is a modified
version of the procedure proposed in the literature (e.g., Cawley, 2004; Chouet al., 2004; Cawley and Burkhauser, 2006; and Michaud et al., 2007).5 Fromthe self-reported BMI data in generations i (i = 20, 30, 40, 50, 60) obtained
from the JHS05, we specify a quadratic function, fi (x) = ai x2 + bi x + ci
for x = 22, to obtain corrected BMI data. The coeﬃcients ai , bi , and ci aredetermined such that the function satisfies(1) fi (x∗i ) = 25;(2) fi (x∗∗i ) = 30; and(3) fi (22) = 22,
where x∗i and x∗∗
i represent the critical BMI values by which to define obesityand severe obesity for generation i that equilibrate the prevalence rates ofobesity and severe obesity in JHS05 to the corresponding prevalence rates in
the NSHN04. For the sample of females in their 50s, x∗50 is obtained as 24.24,
which means that for the female obesity rate in the JHS05 data to equal thatin the NSHN04 data, the critical BMI value that defines obesity should belowered from 25 to 24.24. The adjusted critical BMI x∗∗
50 for severe obesity
amounts to 28.67.
Conditions (1) and (2) ensure that the corrected BMI distribution generates the same obesity and severe obesity rates as those in the NSHN04.
5

Chou et al. (2004) followed Cawley’s (2004) procedure when correcting for the underreporting biases in the original self-reported data by (1) estimating the quadratic relations
between actual and self-reported values of weight and height by using the Third National
Health and Nutrition Examination Survey (NHANES III), U.S.A., and (2) applying theestimated relations to their American self-reported data (the BRFSS) pertaining to weightand height to obtain bias-corrected data and to compute bias-corrected BMI. Michaud etal. (2007) applied the quadratic correction function estimated by Cawley and Burkhauser(2006) to their European self-reported data. In Japan, there is no data set that contains
both actually measured and self-reported data of height and weight. However, it might
be questionable to directly apply Cawley and Burkhauser’s estimated correction function
to the Japanese data because the BMI distribution in Japan and the definition of obesity
therein both diﬀer from those in the American or European countries (see the Examination
Committee, 2002).

8

Condition (3) is the assumption that since a BMI of 22 is thought of as
the healthiest from the medical viewpoint,6 people with BMI 5 22 could
be regarded as having no incentive to underreport their weights and/or tooverreport their height, and hence, would have no tendency to underreporttheir BMI values. The corrected values of the female BMI for x = 22 arecomputed by using the quadratic functions obtained for the corresponding
generations, whereas for x < 22, no adjustment is made since no serious bias
is observed for the range of small BMI values.
The male BMI data are adjusted in a similar manner except that no
adjustment is made for x > 30 since, as seen from Table 3(c), the prevalence
rate of severe obesity in the JHS05 does not diﬀer significantly from that in
the NSHN04. There seems to be no strong incentive for severely obese males
to underreport their BMI.
The body mass distributions of the corrected data are depicted in Figures 1(a) and (b) and are summarized statistically in Tables 3(a) through(d). They show that the correction eliminates, to a great extent, the underreporting bias. By construction, the biases in the prevalence rates of obesity
for males and females as well as those in the prevalence rate of severe obesity
for females are almost completely corrected for. The diﬀerences between the
BMI mean revealed by the corrected JHS05 and that revealed by the NSHN04
are statistically insignificant for almost all the generations. The downward
biases in the standard deviation of BMI are also reasonably reduced.7 8

3.2

Eliciting discount rates

In the JHS05, the respondents’ discount rates are measured by asking fivequestions on intertemporal choice under alternative conditions. As in previous surveys (e.g., Harrison et al., 2002 and Borghans and Golsteyn, 2006),
the respondents are told to choose between two options, “A” and “B.” Forexample, they are asked to choose between “A”–receiving JPY 10,000 in 2days and “B”–receiving JPY 10,000 plus a certain amount JPY α, say JPY
10,038, in 9 days. Here, choosing the delayed receipt “B” instead of “A”
implies receiving 20% of the annual interest rate. In each question, eightsuch queries with alternative α values, from small to large, and hence withalternative imputed interest rates, from low to high, were asked in rows of a6

See Examination Committee of JSSO (2002).
However, the corrections of the downward bias in the SDs remain insuﬃcient for males
in their 20s and 30s and for females in their 30s and 40s.
8
The main empirical results that are reported in Section 4 do not diﬀer substantiallyeven when the uncorrected BMI data are used when conducting the regression analysis
below. For the empirical results in the case of the uncorrected data, see the Appendix.
7

9

question table.
Table 4 represents the query QUESTION 1, wherein the amount of receipt for option “A” is specified as JPY 10,000 and the imputed interest rate
for option “B” changes from —10% to 300%. The respondents are expected tochoose option “A” at low interest rates, whereas as the imputed interest rate
rises, they are expected to switch to option “B” at a certain critical high rate.
The individual respondents’ discount rates can be inferred by estimating theinterest rate at which the delayed receipt of option “B” is indiﬀerent to themore immediate receipt of option “A.” Note, however, that the elicited discount rates are associated with the particular choice conditions, for example,
2 days versus 9 days, the amount JPY 10,000 for option “A” in QUESTION
1.
Insert Table 4:
Question to elicit discount rates: An example (QUESTION 1 for DR1 )To detect time discounting anomalies, five questions are developed bycontrolling for (i) money amounts for option “A” as JPY 10,000 or JPY 1
million; (ii) time horizons for “A” as 2 days, 1 month, or 90 days; (iii) timedelays as 7 days or 12 months; and (iv) receipt or payment. In the “payment”
question, QUESTION 5, the respondents are asked to choose either “A” —paying JPY 1 million in 1 month or “B” — paying JPY 1 million + someamount in 13 months, from which acceptable interest rate payments to delay
a 1 million payment for 12 months are elicited.
From each question, we obtain raw response data, which indicate theinterest rates between which each respondent switched his/her choice from
option “A” to “B.” Some subjects, however, stuck to option “A,” regardlessof the interest rates that were oﬀered. To elicit the respondents’ discountrates from these raw data, we follow Kimball et al. (2005) in estimating a
log-normal distribution for the cross-respondent distribution of gross discountrates. From the estimated distribution, each respondent’s gross discount rate
for a certain question, that is, a certain question table, is estimated as an
expected value conditional on the fact that the respondent changes his/her
choice between certain interest rates. The descriptive statistics of the elicited
discount rates, together with the choice conditions under which they are
elicited, are summarized in Table 5, where DRi (i = 1, . . . , 5) represent thediscount rates that are estimated from QUESTION i.
Insert Table 5:
Elicited discount rates under alternative choice conditions
10

To investigate the eﬀect of impatience on body mass, we construct DRSTD,
which represents the simple average of the standardized values of the elicited
discount rates DRi (i = 1, . . . , 5):
DRSTD = (1/5) Σ5i=1 (DRi − E((DRi ))/σ(DRi ),(1)

where E(·) and σ(·) represent sample means and standard deviations. For
E(DRi ) and σ(DRi ), see Table 5. Table 6 summarizes the definitions ofvariables that are used in the analysis below as well as their basic statistics.9
It is hypothesized that, other things being equal, the respondents’ body massdepends positively on the impatience index DRSTD.
Insert Table 6:
Definitions of variables and basic statistics
3.2.1

Time discounting anomalies

By comparing the mean values of the elicited discount rates, we can examine
whether our average respondent displays the aforementioned two anomalies oftime discounting. First, on average, hyperbolic discounting or the immediacy
eﬀect is not observed since the mean of the discount rate DR1 , imputed fromthe immediate future choice (i.e., 2 days or 9 days), is not significantly higher
than DR2 , which is applied to a more distant future choice (i.e., 90 days or 97
days). Second, the discount rate DR4 applied to future receipts is significantly
higher than DR5 , the DR used for the discounting of future payments; this
implies that our average respondent displays the sign eﬀect.10
To examine the eﬀects of the time discounting anomalies on the respondents’ body mass, we construct the binary indicator HYPERBOL for hyperbolic discounting, and the binary indicator SIGN for the sign eﬀect, where,
for example, HYPERBOL = 1 if DR1 > DR2 , and HYPERBOL = 0 otherwise. From the mean values of HYPERBOL and SIGN, shown in Table
6, the proportions of the respondents who display the anomalies are 61.1%(hyperbolic discounting) and 88.5% (the sign eﬀect). Our hypothesis is that,
9

Although the standardized average DRSTD of the elicited discount rates should theoretically satisfy E(DRSTD) = 0 and σ(DRSTD) = 1, neither of the equalities is fulfilled,
as seen in Table 6. This stems from the fact that the number of eﬀective responses diﬀer
in the five discount rate questions.
10
In addition, although we have not included the results of the t test in Table 5, DR3 , thediscount rate for JPY 10,000 is significantly higher than DR4 , applied for JPY 1 million,
implying that people are more patient in the case of larger amounts than in the case ofsmaller amounts. This tendency is called the magnitude eﬀect (e.g., Benzion et al., 1989
and Frederick et al., 2002).

11

other things being equal, the respondents’ body mass is positively related to
HYPERBOL and negatively related to SIGN.
3.2.2

Proxies for impatience and procrastination

To capture the eﬀects of impatience and hyperbolic discounting, we also construct proxy variable DEBTIMP for impatience and PROCR for hyperbolic
discounting. To measure respondents’ degrees of hyperbolic discounting or
procrastination, the JHS05 survey asks them to indicate, on a 5-point scaleranging from 1 to 5, what used to be the extent of their tendency to procrastinate doing homework assignments in the summer vacations during theirhigh school days.11 Variable PROCR represents the response data to thisquestion, wherein a larger value implies a stronger tendency toward procrastination or hyperbolic discounting.
Besides DRSTD, we estimate DEBTIMP, as a proxy measure of the degree of impatience, from the respondents’ debt holding behavior. In the
JHS05, the respondents are asked to indicate whether they have debts otherthan housing loans. Let DEBT denote a binary indicator for the debt holding. The debt holding DEBT is expected to depend on time discounting inthree ways: by means of (i) impatience, where high impatience implies a highprobability of debt holdings; (ii) hyperbolic discounting, which causes people
to procrastinate carrying out saving plans, leading to excessive debt holdings(see Laibson, 1997, 1998); and (iii) the sign eﬀect, which makes people reluctant to pay interest in the future, thereby inducing “borrowing aversion”
behavior (see Loewenstein and Prelec, 1992).
Impatience proxy DEBTIMP is the standardized residual of Prob(DEBT= 1) after regressing it using a probit model on the following: PROCR, as aproxy for (ii); SIGN, the binary indicator for (iii); and other control variables
capturing the degree of risk aversion (RISKAV), per capita household income(INCOME and INCOME^2), the expected percentage change of income in aforthcoming year (∆INCOME), and ages (AGE and AGE squared). The risk
aversion index RISKAV is constructed by subtracting from 100% the respondents’ responses to the question “When you go out, how high a probabilityof rainfall makes you carry an umbrella?” A high RISKAV value, say thatof 90%, implies that the respondent carries an umbrella even when it is very
unlikely to rain, say if there is a 10% probability of rainfall.
The result of the first stage probit regression for Prob(DEBT = 1), together with that of the regression with impatience measure DRSTD added
11

In Japanese elementary and high schools, students are usually given many diﬀerent
homework assignments during the summer vacations.

12to the set of the explanatory variables, are shown in Table 7, where the marginal eﬀect of each explanatory variable on the probability of the respondent
being a debtor is listed. As shown in the second column, which depicts thefirst probit model without DRSTD as a regressor, the coeﬃcients for all the
explanatory variables are significant. In particular, as predicted by theory,debt holding is positively related to the tendency to procrastinate PROCR,
and negatively related to the sign eﬀect SIGN, where both the coeﬃcients are
significant at the 10% level.12 As seen in the third row of the table, the result
is robust, except that the P-value for PROCR becomes a little lower than
10% when we introduce, as an impatience measure, the standardized meanof the elicited discount rates DRSTD to the set of explanatory variables.
Insert Table 7:
Time discounting and debt holdings
The proxy DEBTIMP for impatience is constructed by standardizing theresiduals of the first regression model, that is, the model that does notinclude the impatience variable as a regressor. To check the relevancy ofusing DEBTIMP as an impatience proxy, Table 8 examines correlationsof DEBTIMP with the discount rates elicited from each respondent and
DRSTD. In fact, the impatience proxy shows significant positive correlations
with each of the respondent’s discount rates and DRSTD. This is consistent
with the fact that, as is seen in the third column of Table 7, the impatiencemeasure DRSTD has a positive and highly significant correlation with debt
holdings.
Insert Table 8:
Correlations between impatience proxy (DEBTIMP) and elicited discount
rates

4

Results

For explanatory variables of the respondents’ body mass, we take into account (i) preference factors regarding time discounting and risk aversion; (ii)demographic factors, including gender (MALE), education (UNIV), and age
12

Negative coeﬃcients of risk aversion RISKAV could be interpreted as capturing thetendency that the more risk averse hold smaller debts to avoid the risk of bankruptcy.
Debt holding is shown to be quadratically correlated with age and income.

13

(AGE), where MALE and UNIV are binary indicators for males and university graduates, respectively; and (iii) economic factors such as per capita
household income INCOME and working hours (WORKHOUR). Since there
is uncertainty regarding how much increase in BMI is caused by a certain
amount of excessive caloric intake, we hypothesize that more risk-averse respondents are likely to have a smaller BMI value.
To capture possible non-monotonic correlations, we add AGE squared,
INCOME squared, and the square root of WORKHOUR to the set of explanatory variables. As for working hours, Ohtake (2005) conjectured thatpeople’s BMI is correlated with their working hours under two circumstances.
The first circumstance is that of overworking. Working for long hours isbound to lead to irregular and unhealthy eating–for example, skipping
breakfast, eating dinner late, and eating out frequently–which causes obesity. Second, especially in the case of women who work part-time jobs, working hours function as a means to control caloric intake. With these positive
and negative eﬀects of increases in working hours, BMI may have a nonmonotonic correlation with working hours. The empirical validity of thisassumption is examined by including WORKHOUR and its square root as
explanatory variables.13
We also control for smoking habits SMOKING, which indicates the strengthof the respondents’ smoking habit on a 6-point scale. Since smoking harms
one’s health and thereby reduces body mass, BMI is expected to be negatively correlated with SMOKING. Note that, as is often stressed in theliterature (Becker and Murphy, 1988 and Khwaja et al., 2007), less patient
people are likely to smoke more since the future loss in utility caused by
the unhealthy behavior is likely to be discounted more intensively. Unlessthe smoking habit is controlled for, the correlation between BMI and time
discounting might be underestimated.
We estimate two regression models: model (1) and model (2). In model(1), we use time discounting variables elicited from hypothetical intertemporal monetary choices, namely, DRSTD, as an impatience measure, andHYPERBOL as a measure for hyperbolic discounting (or procrastination).
Due to a domain eﬀect, however, these time discounting variables constructedfrom hypothetical monetary choices might not succeed in capturing the correlation between time discounting and BMI.14 Thus, instead, model (2) re13

By examining Japanese cross-sectional data in 2000, Suzuki (2007) reported that boththe BMI and the probability of being obese are positively and significantly correlated withworking hours, thereby partially supporting Ohtake’s conjecture.
14
For example, Chapman (1995) report that monetary discount rates do not have astrong explanatory power for intertemporal choices regarding health investments. In fact,
in Borghans et al. (2006), monetary discount rates elicited from hypothetical pecuniary

14gresses body mass variables including BMI on the proxies for time discounting, namely, DEBTIMP for impatience and PROCR for hyperbolic discounting (procrastination). Other explanatory variables, including the indicator
SIGN for the sign eﬀect, are common to the two models. The models are
estimated in the all, male, and female samples in order. The OLS method isused for the BMI regression and the binary probit method is used to estimate
the probabilities of being obese, severely obese, and underweight.

4.1

BMI

4.1.1

Preference factors

Table 9 summarizes the results of the OLS regressions for BMI. In model (1),as is predicted by theory, BMI displays significantly positive correlations with
impatience (DRSTD) for the full sample and significantly negative correlations with the sign eﬀect (SIGN) for the full sample and the female sample.
In the full sample, for example, a discount rate that exceeds the average by
one unit of SD, ceteris paribus, leads to a BMI that is around .300 higher than
the average. In this sample, the BMI of the average respondent who displays
the sign eﬀect is around .578 smaller than that of respondents who do notdisplay the sign eﬀect. However, positive eﬀects of hyperbolic discounting
HYPERBOL are not significant in model (1). As a whole, the eﬀects of time
discounting on BMI are not strongly detected from model (1).
Insert Table 9:
BMI regressions
In model (2), in contrast, BMI displays fairly significant correlations withthe three time discounting variables. In particular, for the full and female
samples, the coeﬃcients of all the time discounting variables, namely, impatience (DEBTIMP), procrastination (PROCR), and the sign eﬀect (SIGN),
have expected signs and are fairly significant. Also, in the male sample, thepositive eﬀect of procrastination is significant.
To quantitatively evaluate the impacts of the time discounting variables
reported in Table 9, Table 10 computes the normalized impacts by dividing
the marginal eﬀects in model (2) by the sample mean or the SD of BMI.
The column “∆impatience” reports the impacts of an increase in the averageof the discount rates DRi by one unit of the SD, that is, a unit increase
choices do not display as strong correlations with BMI as do other impatience proxies thatare constructed from responses to behavioral and/or psychological questions.

15

in DRSTD; the column “∆procrastination” shows the eﬀects of an increasein the propensity to procrastinate doing homework from the weakest degree(PROCR = 1) to the strongest degree (PROCR = 5); and the column “∆sign
eﬀect” represents the eﬀects of the presence of the sign eﬀect (SIGN = 1),
compared to the case without the sign eﬀect (PROCR = 0). As seen fromthe table, procrastination and the sign eﬀect have certain impacts on the females’ BMI. Female respondents with the strongest degree of procrastination
are, ceteris paribus, heavier than those with the weakest degree of procrastination by 33.78% of the sample SD. The diﬀerence in BMI between female
respondents who do and do not display the sign eﬀect amounts to -23.58%of the sample SD. Relative to these impacts, those of impatience on BMI are
not so large, though.
Insert Table 10:
Impacts of time discounting variables on BMI: The case of Model (2)In sum, both the models show that, especially for the full and female samples, BMI shows expected correlations with impatience and the sign eﬀect.
A significant positive correlation between BMI and hyperbolic discounting
is also consistently observed in all the samples when the tendency to procrastinate doing homework is used as a proxy for the degree of hyperbolic
discounting.
The dependence of BMI on risk aversion (RISKAV) is, as is expected,
significantly negative for the full and male samples in both models. For
example, the BMI of a male respondent who is risk averse such that his
critical likelihood of carrying an umbrella is 10% higher than the averageis, ceteris paribus, lower than that of the average male by .100 (model (1))
to .103 (model (2)). For the female sample, however, the observed negative
correlations between BMI and RISKAV are insignificant.
4.1.2

Demographic factors

With regard to demographic variables, males are significantly heavier thanfemales, which is in contrast to the case in the American and European
countries.15 In both models and for both samples, BMI quadratically depends
15

By using the U.S. samples, Komlos et al. (2004) show that the average BMI of andthe obesity rate among females are larger than those of males. Borghans and Golsteyn(2006) detect the same tendency in the Dutch samples. By using the U.S. survey data,
Chou et al. (2004) report that males’ BMI is larger than that of females, whereas theobesity rate among females is higher than that among males.

16significantly on age, such that BMI increases with age at decreasing rates
until a critical age, after which it decreases at increasing rates. The criticalpeak is 53.25 (i.e., 0.213/(2*0.002)) years (model (1)) or 52.00 (model (2))
for males, and 64.00 years (model (1)) or 65.75 (model (2)) for females.16 As
seen in Table 3(a), if the other explanatory variables are not controlled for,males’ BMI peaks when they are in their 40s, which is earlier than the age at
which they are at their heaviest (i.e., 53.25 years (model (1)) or 52.00 (model(2)); on the other hand, females’ BMI peaks when they are in their 60s, whichis consistent with the estimate given by the multivariate regression. A highlevel of education (UNIV) is not found to have a significant correlation with
BMI.
4.1.3

Economic factors

In the full and female samples, the coeﬃcients of per capita household income (INCOME) are significantly negative and those of the income squared
are significantly positive in both models, which implies that the BMI-income
correlation could be non-monotonic. In fact, in both samples, the criticalincome level at which BMI reaches its lowest level is higher than the average
income level, but still remains within the observed income range. For example, Figures 2(a) and (b) depict the relations in the female sample between
per capita household income and BMI, estimated by models (1) and (2),respectively, when the eﬀects of other factors considered in the models arecontrolled for. The critical income level estimated from the female sample
regression is 3.785 (i.e., JPY .598/(.079*2)) million for model (1). Since theSD in the female sample is estimated as 1.503, the critical income exceeds
the mean income by an SD of 1.094. For model (2), the critical income levelat which the female BMI reaches its lowest level is estimated as JPY 3.912
million, which exceeds the mean income by an SD of 1.178.
Figure 3 depicts the resulting non-monotonic relation between the female
respondents’ income and the income elasticity of BMI, where the females’
income elasticity of BMI in each income quintile, evaluated at its average
income and average BMI, is plotted.17 In both models (1) and (2), it isshown that the female respondents in the highest income quintile show pos16

For the full sample, BMI peaks at an age of 61.00 years in model (1) and at an age of
60.00 years in model (2); these ages are slightly higher than 57, which Chou et al. (2004)
obtained by using U.S. data.
17
Letting β 1 and β 2 denote the estimated coeﬃcients of INCOME and INCOME^2,
the income elasticities of BMI evaluated at the average in the i th income quintiles(i = 1, · · · , 5) are given by Ei (INCOME)(β 1 + 2β 2 Ei (INCOME))/Ei (BMI), where Ei (·)
represent averages in the i th income quintiles.

17

itive income elasticities of BMI (i.e., 2.8% and 2.7% for models (1) and (2),respectively), whereas those in the lower income classes show negative income
elasticities.18 The non-monotonic income-BMI relation is in contrast with themonotonic, negative correlations between income and BMI that have beenreported in the literature.19
Insert Figures 2(a) and (b):Income and BMI: Females (model (1) and (2), respectively)
Insert Figure 3:
Income Elasticities of BMI in Income Quintiles
It is noteworthy that, with the significant positive eﬀect of per capita
household income squared, the sample mean of BMI depends positively on the
degree of income inequality measuredof per capita in¡ N−1by¢ the sample variance22
come. Because E(INCOME ) = N σ(INCOME) +E(INCOME)2 , where
N denotes the number of samples, the sample mean E(BMI) depends onσ(INCOME)2 . With a positive coeﬃcient of INCOME2 , a mean-preserving
increase in income variance is thus predicted to lead to an increase in thesample mean of BMI. This relation might have an implication in explaining
the recent decline in BMI among females in Japan since there has been adecrease in the income inequality of Japanese females.20 For example, basedon the results of the female sample regression of model (1), a decrease by 0.1
in the variation coeﬃcient of per capita income σ(INCOME)/E(INCOME)
would decrease the females’ mean BMI by 0.054,21 which amounts to a 23.7%
18

The females’ income elasticities of BMI, evaluated at their overall average, are computed as —0.025 for model (1) and —0.031 for model (2), which are close to Chou et al.’s(2004) estimate of —0.03 of the income elasticity of BMI in their full sample. In the caseof the full sample, however, our estimates become around —0.01 for both the models,reflecting the tendency of the males’ BMI to be inelastic to income.
19
Chou at al. (2004) also report that BMI is quadratically related to household income.
In their result, however, the critical income level is so high that BMI almost monotonicallydecreases over the actual range of their income sample.
20
Actually, from our JHS2004 and JHS2005 data, the variation coeﬃcients of the females’ per capita household income are 0.793 in 2004 and 0.702 in 2005, implying that
there was a 0.047 decrease in the variation coeﬃcient during the 2 years.
21
The sample mean of BMI can be expressed in terms of variation coeﬃcient v ≡σ(INCOME)/E(INCOME) as
µ
¶
¢
¡
N −1
E(BM I) = const + βE(INCOME)2 v 2 + 1 + · · · ,Nwhere β denotes the coeﬃcient of INCME^2 in the regression result; and NN−1 ' 1 for oursample size.

18

decrease in females’ BMI from 2003 (average BMI (age ≥ 20): 22.62) to 2004
(22.39).22 In the case of model (2), the decrease in BMI predicted by a 0.1 decrease in σ(INCOME)/E(INCOME) equals 0.063, which amounts to 27.3%of the actual BMI decrease during the 2003—04 period.23 .
In Table 9, the respondents’ BMI values are also shown to have a nonmonotonic correlation with working hours in the full and female samples.
Consistent with what Ohtake (2005) conjectures, with positive coeﬃcientsof WORKHOUR and negative coeﬃcients of its square root, the correlationis negative for small WORKHOUR values, whereas it becomes positive for
WORKHOUR values that are larger than some critical levels. Figure 4 depicts the resulting non-monotonic working hour elasticities of BMI, where thecritical working hour values at which the elasticity of BMI shifts from negative to positive are computed as 12.84 hours a week for model (1) and 12.38
hours a week for model (2). Although the working hour-BMI correlation
is insignificant in the male sample, the significant non-monotonic correlation
between working hours and BMI persists in the full sample, where the criticalworking hour values are 11.21 for model (1) and 11.65 for model (2).
Insert Figure 4:
Females’ working hour elasticities of BMI

4.2

Obesity and severe obesity

Let OBESITY and SEVERE OBESITY be binary indicators for obesity andsevere obesity, respectively. By using binary probit models, we estimate
the marginal eﬀects on the probabilities Prob (OBESITY = 1) and Prob
(SEVERE OBESITY = 1) of the same explanatory variables for BMI as inmodels (1) and (2). Tables 11 and 12 show the results for obesity and serious
obesity, respectively.
As for obesity, the estimated marginal eﬀects of the impatience variables
DRSTD and DEBTIMP are both positive and reasonably significant in bothmodels. In the full sample, the respondents who are less patient by an SD of
one unit than the average are obese with a 5.8% higher probability in model(1) and with a 2.8% higher probability in model (2). Note that these impacts
22

For the Japanese BMI distribution in 2003, see the NSHN03.
However, since a magnitude of 0.1 is unusually large as an increase in the variationcoeﬃcient of income, the eﬀect of income inequality seems quantitatively too small to
explain the recent decrease in the body mass of females. In fact, during the 2003—04
period, a 0.047 decrease in the variation coeﬃcient of income is observed in the JHS data,
which can explain only 7.4% (model 1) to 8.5% (model 2) of the decrease (0.23) in thefemales’ BMI reported by the NSHN during the 2 years.
23

19

are not that small compared with the overall obesity prevalence rate (24.3%),
that is, the unconditional probability of being obese.
With regard to the other discounting variables, the result of model (1)is poor, whereas in model (2), the eﬀect of procrastination (PROCR) on
the obesity probability is positive at the 1% significance level in the fulland female samples. In model (2), the probability of respondents with thestrongest tendency to procrastinate (PROCR = 5) being obese is roughly
10.8% (2.7% times 4) higher than the corresponding probability of thosewith no tendency to procrastinate (PROCR = 1) in the full sample and is
12.0% higher in the female sample. The eﬀects are quantitatively not small,compared with the unconditional probabilities of being obese, measured by
the corresponding obesity prevalence rates (24.3% and 19.5% for the full andfemale samples, respectively). The sign eﬀect, however, is not significant.
As in the BMI regressions, non-monotonic correlations with age, percapita household income (INCOME), and working hours per week (WORKHOUR) are significant for the full and female samples in both models. For
example, the probability of being obese in the full sample is the lowest at JPY
3.389 million of INCOME for model (1) and at JPY 3.526 million for model(2); these values are reasonably close to the corresponding critical values ofincome in the BMI regressions.
Insert Table 11:
Binary probit regressions of obesity
The probability of being severely obese has a significant negative correlation with the sign eﬀect in the full and female samples, implying that
respondents who do not display the sign eﬀect are likely to be severely obese.
For example, in model (1), the probability of respondents who do not display
the sign eﬀect being severely obese is 2.7% higher than the corresponding
probability for those who do display the sign eﬀect in the full sample, andis 4.2% higher than the corresponding probability for those who display thesign eﬀect in the female sample. The increases in the probability due to theabsence of the sign eﬀect are as large as, or even larger than the unconditional probabilities of being severely obese (3.1% and 1.4% for the full andfemale samples, respectively).
Although the eﬀects of hyperbolic discounting in model (1) are insignificant, the eﬀects of homework procrastination PROCR in model (2) are significantly positive for the full and male samples. In particular, comparedwith the males’ unconditional probability of being severely obese (3.6%), the20

marginal eﬀect of PROCR (1.1%) on the probability of being severely obese
is considerable.
Insert Table 12:
Binary probit regressions of severe obesity

4.3

Underweight

Table 13 reports the results on underweight. In the full and female samples,consistent with our hypothesis, models (1) and (2) show that the probabilityof being underweight has a significantly positive correlation with the sign
eﬀect. For both models, respondents displaying the sign eﬀect belong to
the underweight group with a 4% higher probability in the full sample, andwith a 5% higher probability in the female sample, than those who did notdisplay the eﬀect. Again, the eﬀects are large, compared to the corresponding
unconditional probabilities of being underweight (i.e., 8.7% and 9.5% in thefull and female samples, respectively). In model (2), procrastination has asignificant negative eﬀect on the probability of being underweight in the fulland female samples.
Aging has quadratic eﬀects on the underweight probability for the fulland male samples. In the full sample, the probability of being underweight
reaches its lowest level at around 52.5 years (model (1)) or 55.5 years (model(2)). The probability of females being underweight has a significant nonmonotonic correlation with per capita household income INCOME with positive coeﬃcients on INCOME squared, where the probability is the lowest
at an income of JPY 3.455 million for model (1) and JPY 3.422 million formodel (2).24
Insert Table 13:
Binary probit regressions of underweight
Finally, by using the above results in the full sample for model (2), Table
14 summarizes the impacts of diﬀerences in the time discounting variableson the probabilities of being obese, severely obese, and underweight, wherein“∆impatience,” “∆procrastination,” and “∆sign eﬀect” are the same as in
24

The fact that the females’ BMI and obesity also show quadratic curves in INCOME
suggests that the sample SDs of BMI stratified by income classes will form a U-shaped
curve. Actually, the female sample SDs of BMI for the first to fifth income quintile groups
are 3.584, 3.331, 2.761, 3.221, and 3.248, respectively, which form a U-shape, as expected.

21

Table 10. All the impacts have expected signs, and many of them are significant. Compared with the corresponding unconditional probabilities, themagnitudes of the impacts of these time discounting variables are not negligible.25
Insert Table 14:
Impacts of time discounting variables on Probs of being obese, severely
obese, and underweight: The case of Model (2) in the full sample

5Conclusions

Motivated by the empirical fact that debtors are more likely to be obese thannon-debtors, we hypothesized that, as in the case of debt holdings, interpersonal diﬀerences in body mass are related to interpersonal diﬀerences in time
discounting as well as to diﬀerences in other demographic and economic factors. It has been partially (especially in the female sample) confirmed thattime discounting aﬀects body mass through impatience, hyperbolic discounting or procrastination, and the sign eﬀect. Caloric intake behavior and theresulting body mass formation can thus be thought as determined as an intertemporal decision-making. An important policy implication is that theobesity rate can be aﬀected by changing the intertemporal structure of thecosts and benefits of obesity, especially that of medical costs.
Body mass has also been found to have a non-monotonic correlation withage, per capita household income, and working hours. In particular, thequadratic curve estimated between per capita household income and BMI
implies that an increase in income inequality leads to an increase in thesocial average of BMI, whereas an increase in the average income lowers theaverage BMI.
Our regression models, however, do not have high explanatory power. The
adjusted R-squared of the BMI regression is, at most, 11.8%, and the models can explain only around 23% of the observed cross-sectional covariation
between BMI and debt holding, measured by the sample covariance between
BMI and DEBT. One possible reason for this is that genetic factors havedominant eﬀects on BMI (e.g., Cutler and Glaeser, 2005). Another shortcoming may be that we failed to take into account interpersonal or regional
25

These results remain unchanged even when the probabilities of being obese, severely
obese, and underweight are jointly estimated by estimating multivariate probit models
with correlated error terms. For the results of the multivariate probit regression, see the
Appendix.

22

diﬀerences in food prices.26
Future research would need to extend the analysis to a panel analysis so
as to explain recent BMI dynamics in Japan. As reported by Borghans and
Golsteyn (2006), it may be diﬃcult to explain time series changes in BMI
by changes in consumer preferences including time preference. Changes in
economic factors such as income, working hours, food prices, and medical
costs could be considered as more important.

26

However, even when the eﬀects of the regional and occupational diﬀerences are controlled for by adding the prefecture and occupation dummies to the set of the explanatory
variables, the main results do not change substantially. For the estimation results withthe prefecture and occupation dummies, see the Appendix.

23

APPENDIX
To check the robustness of our main results that are obtained in the text,
this Appendix reports the regression results in the following alternative cases:
A Incorporating prefecture and occupation dummies,
B Jointly estimating the probabilities of being obese, severely obese, andunderweight by estimating multivariate probit models that allow correlations among error terms, andC Using the uncorrected body mass data.

A

Incorporating prefecture and occupation
dummies

Our respondents’ body mass could depend on regional and/or occupational
factors. For example, the relative prices of various foods, and hence those ofa calorie diﬀer among regions. In the text, we have not controlled for any
regional or occupational factors. The JHS contains the data of the respondents’ residential prefectures (numbered 1 (Hokkaido) to 48 (Okinawa)) andoccupations (numbered 1 (oﬃce workers) to 13 (others)). By constructing
47 of prefecture dummies and 12 of occupational dummies to add to the setof the explanatory variables, the same models as in Tables 9 (BMI) and 11(OBESITY) to 13 (UNDERWEIGHT) are estimated. The results are reported in Table A1 through A4, where the coeﬃcients of the prefecture andoccupation dummies are omitted.

Insert Table A1:
BMI regression with prefecture and occupation dummies
Insert Table A2:
Obesity probit regression with prefecture and occupation dummies
Insert Table A3:
Severe obesity probit regression with prefecture and occupation dummies
24

Insert Table A4:
Underweight probit regression with prefecture and occupation dummies

Although the significance levels of the estimated coeﬃcients of some variables become weaker (e.g., the coeﬃcients of DEBTIMP and PROCR of the
BMI regression in Table A1), the results, as a whole, do not change considerably from those in the text. In many cases, the values of the R squared or
those of the log-likelihood improve.
One problem in these regressions is that, especially in the case of severe obesity and underweight, compared with the number of severely obese
or underweight respondents, too many explanatory dummy variables are incorporated,27 so that we cannot help excluding redundant dummy variablesfrom the data. Consequently, the number of the samples are unnecessarily
reduced in these regressions (e.g., In Table A3, only 1192 samples are used inModel (1) and only 1131 in Model (2), whereas in Table 12, 1658 and 1629
samples are used in Models (1) and (2), respectively). To avoid this problem,the prefecture and occupation dummies have not been controlled for in theanalysis in text.

B

Estimating multivariate probit models

By construction, the binary indicators OBESITY and SEVERE OBESITY
necessarily have a negative correlation; and UNDERWEIGHT necessarily
has negative correlations with OBESITY and SEVERE OBESITY. These
correlations may well be retained after controlling for the eﬀects of the explanatory variables in the regressions variables, so that the error terms of
the probit regressions regarding OBESITY, SEVERE OBESITY, and UNDERWEIGHT, conducted independently in Sections 4.2 and 4.3, may well becorrelated with each other. Based on the assumption that the error terms arecorrelated with each other, the probabilities of being obese, severely obese,and underweight can be jointly estimated by conducting multivariate probit
regression. The results are reported in Table A6. It can be seen that theresults regarding the signs and the significance levels of the estimated coeﬃcients do not diﬀer largely from those in Tables 11-13. Note that significant
correlations among the error terms remain.
27

For example, among 1658 samples in Table 12 that are used to estimate Model (1) in
the SEVERE OBESITY regression, the number of the severely obese respondents is lessthan 50, whereas the number of the prefecture and occupation dummies amounts to 58.

25Insert Table A5:
Multivariate probit estimation of the prob. of being obesity, severely obese,and underweightC

Using the uncorrected body mass data

We finally report the estimation results when the uncorrected data of BMI,OBESITY, and SEVERE OBESITY, instead of the corrected data, are used
to estimate the same models as estimated in Tables 9, 11, and 12 (note thatthe data of UNDERWEIGHT are not revised from the original data).
Insert Table A6:
OLS regressions of uncorrected BMI
Insert Table A7:
Binary probit regressions of obesity by the uncorrected data
Insert Table A8:
Binary probit regressions of severe obesity by the uncorrected data

26

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27

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28

Table 1: Debt holdings and body mass
All
BMI
Debtors
Nondebtors(t-values)

23.26222.714(3.671) ***BMI

Debtors
Nondebtors(t-values)

23.89823.506(1.880) *BMI

Debtors
Nondebtors(t-values)

22.63522.005(3.084) ***SevereUnderweight
Obesity
0.287
0.045
0.060
0.227
0.027
0.074
(3.153) *** (2.348) ** (-1.240)
MaleSevereObesity
Underweight
Obesity
0.345
0.044
0.027
0.278
0.035
0.043
(2.322) **(0.814)(-1.341)
FemaleSevereObesity
Underweight
Obesity
0.230
0.047
0.093
0.182
0.021
0.102
(1.962) **(2.587) *** (-0.481)
ObesityNotes: The data are those from the Japan Household Survey on Consumer
Preferences and Satisfaction 2005, corrected for the self-reporting biases.
For the correction method, see Section 3.1.
The t-values represent those for mean differences in body mass statuses
between debtors and nondebtors. *, **, *** denote statistical significanceat the 10%, 5%, and 1% levels, respectively.

Table 2: Definitions of obesity and underweight
BMI
BMI <18.5
18.5≦BMI<25
BMI=2225≦BMI<3030≦BMI<35
35≦BMI<40
40≦BMI

WHO criteria

JSSO criteria

This paper

Unnderweight

Underweight

Underweight

Normal range

Normal range

Normal range

Standard (ideal)

Standard (ideal)

Standard (ideal)

Preobese

Obese (degree1)

Obese

Obese (class I)

Obese (degree2)

Obese (class Ⅱ)

Obese (degree3)

Obese (class Ⅲ)

Obese (degree3)

Severe-Obese

Note: The JSSO criteria are based on “New Criteria,” 2002, Japan Society for the Studyof Obesity.

Table 3(a): By-age BMI distributions: NSHN04, JHS05, and corrected data.
Male
JHS05
NSHN04Means
22.52 22.46 (0.448)
20s
S.D.
3.62 3.98 (0.107)
Means
23.42 23.25 (0.284)
30s
S.D.
3.36 3.61 (0.111)
Means
24.07 23.63 (0.045) *40s
S.D.
3.37 3.30 (0.353)
Means
23.69 23.57 (0.262)
50s
S.D.
2.89 2.92 (0.399)
Means
23.75 23.24 (0.002) ***
60-71
S.D.
3.00 2.60 (0.001) ***Means
23.65 23.35 (0.003) ***all
S.D.
3.15 3.14 (0.457)
1368
Obs.
2286
Age

Corrected data
22.66 (0.623)
4.09 (0.054) *23.38 (0.451)
3.69 (0.060) *23.85 (0.202)
3.40 (0.432)
23.76 (0.640)
3.02 (0.169)
23.61 (0.237)
2.99 (0.478)
23.59 (0.298)
3.31 (0.022) **1368

Female
JHS05
Corrected data
NSHN0420.28 20.23 (0.428)
20.29 (0.572)
2.54 2.55 (0.474)
2.64 (0.281)
20.95 20.84 (0.302)
20.85 (0.699)
2.99 2.62 (0.008) *** 2.62 (0.008) ***22.64 22.03 (0.004) *** 22.19 (0.996) *3.57 2.98 (0.000) *** 3.12 (0.004) ***22.97 22.36 (0.001) *** 22.71 (0.999)
3.21 2.80 (0.001) *** 3.21 (0.492)
23.35 22.87 (0.010) ** 23.29 (0.990)
3.47 3.01 (0.001) *** 3.57 (0.273)
22.37 21.94 (0.000) *** 22.17 (1.000) *3.25 2.96 (0.000) *** 3.29 (0.291)
1499
1499
2789

Notes: Values in parentheses represent P-values for the null hypotheses that coresponding statistics equal those of
the NSHN04 data. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table 3(b): By-age obesity distributions: NSHN04, JHS05, and corrected data.

NSHN04
20s
0.199
30s
0.289
40s
0.327

Male
JHS05
0.133 (0.025) **0.252 (0.167)
0.267 (0.012) **Corrected data
0.195 (0.876)
0.292 (0.922)

NSHN040.054
0.083

FemaleJHS05
0.035 (0.261)
0.079 (0.745)

Corrected data
0.049 (0.915)
0.086 (0.782)

0.324 (0.885)
0.179
0.139 (0.016) **0.179 (0.976)
***
***
50s
0.308
0.248 (0.003)
0.305 (0.918)
0.241
0.161 (0.000)
0.240 (0.955)
60-71 0.299
0.237 (0.002) ***0.298 (0.984)
0.298
0.218 (0.000) ***0.297 (0.964)
***
***
all
0.297
0.240 (0.000)
0.296 (0.893)
0.195
0.143 (0.000)
0.195 (0.956)
1368
1368
1499
1499
Obs.
2286
2789
Notes: Values in parentheses represent P-values for the null hypotheses that coresponding statistics equal those of
the NSHN04 data. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table 3(c): By-age severe obesity distributions: NSHN04, JHS05, and corrected data.
NSHN04
20s
0.021

Male
JHS05
0.035 (0.290)

30s

0.030

0.050 (0.052) *

40s

0.034

0.036 (0.960)

Corrected data
0.035 (0.290)

NSHN040.008

0.050 (0.052) **0.036 (0.960)

0.012
0.027

FemaleJHS05
0.007 (0.655)
0.008 (0.523)
0.015 (0.106)

Corrected data
0.007 (0.655)
0.008 (0.523)
0.024 (0.848)
0.032 (0.541)

0.034 (0.780)
0.036
0.015 (0.001) ***0.031 (0.956)
0.045
0.025 (0.013) **0.048 (0.724)
***
all
0.031
0.029 (0.586)
0.036 (0.159)
0.029
0.015 (0.000)
0.027 (0.516)
1368
1368
1499
1499
Obs.
2286
2789
Notes: Values in parentheses represent P-values for the null hypotheses that coresponding statistics equal those of
the NSHN04 data. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

50s
60-71

0.032
0.031

0.034 (0.779)
0.008 (0.000) ***Table 3(d): By-age underweight distributions: NSHN04, JHS05, and corrected data.
Male
Female
NSHN04 JHS05 (Corrected) NSHN04 JHS05 (Corrected)
20s
0.084
0.115 (0.114)
0.214 0.211 (0.913)***
0.156 0.143 (0.431)
30s
0.038
0.074 (0.000)
40s
0.021
0.032 (0.112)
0.066 0.103 (0.000)***
50s
0.020
0.016 (0.523)
0.054 0.057 (0.680)
60-71 0.036
0.036 (0.994)
0.066 0.050 (0.105)
all
0.033
0.042 (0.010) **0.093 0.095 (0.625)
1368
1499
Obs.
2286
2789
Notes: Values in parentheses represent P-values for the null hypotheses that coresponding statistics equal those of
the NSHN04 data. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table 4: Question to elicit discount rates: An example (QUESTION 1 for DR1)
QUESTION 1.
Suppose you have two options to receive some money. You may choose Option “A”, to receive
10,000 JPY in two days; or Option “B”, to receive a different amount in nine days. Compare theamounts and timing in Option “A” with Option “B” and indicate which amount you would
prefer to receive for each of all 8 choices.

Option A (JPY)

Option B (JPY)Interest rate

(Receipt in 2 days)(Receipt in 9 days)(Annual)10,000

9,981

-10%

A

B

10,00010,0000%A

B

10,00010,01910%A

B

10,00010,03820%

A

B

10,00010,09650%

A

B

10,00010,191

100%

A

B

10,00010,383200%

AB

10,000

10,574300%

A

B

Circle A or B.

Note: The Japan Household Survey on Consumer Preferences and Satisfaction, 2005.

Table 5: Elicited discount rates under alternative choice conditions
DR2
DR3
DR4
DR5
DR1
Timings ((A) 2 days or 90 days or 1 month or 1 month or 1 month oror (B))
9 days97 days 13 months 13 months 13 months
ChoiceAmounts for
10,000JPN 10,000JPN 10,000JPN 1millionJPY1millionJPY
conditions(A)
Receipt or
receipt
receipt
receipt
receipt
payment
payment
Mean
1.904
1.892
0.153
0.023
-0.008Descriptive
Median
0.741
0.741
0.080
0.008
0.001
statistics
S.D.
2.390
2.421
0.193
0.042
0.044
Obs.
2737
2768
2790
2771
2331
sign effect:
Time discounting anomalies hyperbolic discounting:
DR4>DR5 (0.00)(P-value)
DR1>DR2 (0.426)
Note: The Japan Household Survey on Consumer Preferences and Satisfaction, 2005.

Table 6: Definitions of variables and basic statistics
Variables
BMI

Definition

Mean

S.D.

Obs.

Body mass index data that are corrected for the self-reporting bias by using the manners

22.846

3.371

2869

explained in Section 3.1
OBESITY

A binary indicator for obesity which equals 1 if BMI ≧ 25 and 0 otherwise

0.243

0.429

2869

SEVERE OBESITY

A binary indicator for severe obesity which equals 1 if BMI ≧ 30 and 0 otherwise

0.031

0.174

2869

UNDERWEIGHTA binary indicator for underweight which equals 1 if BMI < 18.5 and 0 otherwise

0.070

0.255

2869

DRSTD

Simple mean, defined by equation (1), of the standardized values of the elicited discount

0.042

0.688

2202

0.000

1.000

1704

0.621

0.485

2694

3.282

1.300

2910

rates DRi (i = 1,…,5) as a measure of the degree of impatience
DEBTIMPA proxy of the degree of impatience, measured by standardized residuals of debt holding
DEBT after regressing it on explanatory variables other than the degree of impatience(see the first regression in Table 5)

HYPERBOL

A binary indicator for hyperbolic discounting which equals 1 if DR1 > DR2, and 0
otherwise.

PROCR

Response to the question ‘When did you do homework assignments in the summer
vacation in your high school days?’ on a 5-point scale, from 1 (homework was finished at‘the beginning of the vacation’) to 5 (it was not done until ‘the very end of the vacation’),
which is a proxy measure of the degree of procrastination.

SIGN

A binary indicator for the sign effect which equals 1 if DR4 > DR5, and 0 otherwise

0.885

0.319

2289

RISKAV

A variable which measures the degree of risk aversion, constructed by subtracting from

0.505

0.205

2941

100 the respondents' responses to the question: "When you go out, how high probabilityof rainfall makes you bring an umbrella with you?"MALE

A binary indicator for males which equals 1 for male respondents and 0 otherwise

0.470

0.499

2987

UNIV

A binary indicator for university graduates which equals 1 for university graduates and 0

0.204

0.403

2893

otherwise
AGE

Ages of respondents

49.08012.9682983

DEBT

A binary indicator for debt holding other than housing loan which equals 1 for debt

0.251

0.434

2806

holders and 0 otherwise.
INCOMEPer capita household income in million yen

2.213

1.583

2361

ΔINCOMEThe expected percentage change of income in a forthcoming year, estimated from

-0.948

3.914

2707

responses to the question: ‘What is the expected rate of change in your whole householdincome this year?’
WORKHOURWork hours for a week

27.19122.9222879

SMOKINGA ordered variable indicating the strength of smoking habits on a 6-point scale, from 1

2.125

1.713

2972

(smoking no cigarette a day) to 6 (smoking more than two packages of cigarettes a day)

Table 7: Time discounting and debt holdings
Dependent
variable: DEBT
DRSTD
PROCR
SIGN
RISKAV
UNIV
AGE
AGE^2
INCOMEINCOME^2
ΔINCOMELog likelihood#obs

Marginal Effects (t -value)
0.015-0.057-0.174-0.0540.021
0.000-0.0360.004-0.006(1.819) *(-1.724) *(-3.342) ***(-2.141) **(3.315) ***(-4.000) ***(-2.168) **(2.337) **(-2.099) **-928.902
1704

Marginal Effects (t -value)
0.085
0.013
-0.066-0.174-0.0620.021
0.000-0.0430.006-0.007(5.434) ***(1.617)(-1.892) *(-3.228) ***(-2.429) **(3.227) ***(-3.935) ***(-2.441) **(2.708) ***(-2.440) **-875.692
1640

Notes: The probabiltiy of debt holding is estimated by using binary probit models.
*, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table 8: Correlations between impatience proxy (DEBTIMP) and elicited
discount rates.

DEBTIMP(t -values)

DR2
DR3
DR4
DR5
DR1
DRSTD
0.137
0.091
0.071
0.115
0.110
0.080
***
***
***
***
***
(5.583)(3.711) (2.919) (4.762)(4.555) (3.325)***

Notes: Impatience proxy DEBTIMP is construcetd from standardized residuals of thebinary probit estimation of the probability of debt holding (see the first result in Table 7).
*** denotes statistical significance at the 1% level.

Table 9: OLS regressions of BMI
Dependent variable: BMI

ImpatienceDRSTD
DEBTIMP
Hyperbolic discounting HYPERBOL
PROCR
Sign effect
SIGN
Risk aversion
RISKAV
Demographic factors MALE
UNIV
AGE
AGE^2
Economic factors
INCOMEINCOME^2
WORKHOUR
WORKHOUR^(1/2)
OthersSMOKING
Constant
Adj. R^2#obs

All
Coef. (t-value)
0.300 (2.067) **

(1)
Male
Coef. (t-value)
0.277 (1.345)

FemaleCoef. (t-value)
0.303 (1.485)

0.128

0.192

0.047

All
Coef. (t-value)
0.257(0.642)(0.662)(3.301) ***(-2.288) **(-0.859)-0.322-1.001(-0.873)(-1.821) *-0.752-0.482-0.2780.213-0.002-0.1340.027
0.008-0.017-0.05219.172(-1.110)(3.061) ***(-2.740) ***(-0.852)(1.665) *(0.370)0.073 (0.229)
0.256 (3.871) ***-0.002 (-2.859) ***-0.598 (-2.754) ***0.079 (2.745) ***0.042 (1.804) *-0.301 (-1.937) *-0.101 (-1.113)
16.736 (10.919) ***
0.089
840

(-0.102)(-0.870)(12.544) ***
0.018
818

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

0.167(1.489)FemaleCoef. (t-value)
0.332(3.086) ***(3.028) ***(-2.337) **(-1.424)(0.1709)***-0.578 (-2.351) **-0.671 (-1.713) *1.315 (6.768) ***-0.128 (-0.656)
0.242 (5.162) ***-0.002 (-4.237) ***-0.273 (-2.277) **0.040 (2.994) ***0.033 (2.253) **-0.221 (-2.081) **-0.061 (-1.247)
17.026 (15.852) ***
0.092
1658

(2)
Male
Coef. (t-value)

0.225 (3.647)-0.516 (-2.112) **-0.860 (-2.197) **1.219 (6.182) ***-0.148 (-0.747)
0.240 (5.093) ***-0.002 (-4.099) ***-0.303 (-2.436) **0.041 (2.896) ***0.029 (1.945) *-0.198 (-1.841) *-0.074 (-1.497)
16.507 (15.063) ***
0.100
1629

**

0.182
-0.177-1.026(1.993)(-0.495)(-1.884) *0.250-0.776-0.799-0.2740.208-0.002-0.1140.023-0.0060.084-0.04618.544(-1.092)(3.001) ***(-2.658) ***(-0.702)(1.332)(-0.313)(0.509)(-0.778)(11.932) ***
0.020
812

-0.026 (-0.081)
0.263 (3.947) ***-0.002 (-2.868) ***-0.712 (-3.269) ***0.091 (3.143) ***0.053 (2.207) **-0.373 (-2.343) **-0.154 (-1.666) *16.221 (10.448) ***
0.118
817

1.13%
3.94%-2.26%

7.79%
27.25%-15.65%

0.71%
3.09%
-0.75%

5.05%
22.03%-5.34%

1.50%
4.51%-3.50%

10.08%
33.78%-23.58%

Note: The column of "Δimpatience" shows the impacts of an increase in the average of the discount rates DRi 's by one unit of sample S.D. of theaverage discount rate. The column of "Δprocrastination" shows the impacts of an increase in the propensity to procrastinate doing homeworkfrom the weakest degree (PROCR=1) to the strongest (PROCR=5). The column "Δsign effect" summarizes the effect of the presence of the signeffect (SIGN=1), compared with the case without the effect (SIGN=0). The rows of "/average BMI" report the marginal effects relative to theaverage BMI, whereas in the "/BMI S.D." rows the marginal impacts are measured in terms of relative magnitudes to sample S.D. in thecorresponding samples. The impacts are evaluated by the esimation results of model (2).

Δimpatience
Δprocrastination (hyperbolic discounting)Δsign effect

All
Male
Female/average BMI /BMI S.D. /average BMI /BMI S.D. /average BMI /BMI S.D.

Table 10: Impacts of time discounting variables on BMI: The case of Model (2)Table 11: Binary probit regressions of obesity
Dependent variable: OBESITY

ImpatienceDRSTD
DEBTIMP
Hyperbolic discounting HYPERBOL
PROCR
Sign effect
SIGN
Risk aversion
RISKAV
Demographic factors MALE
UNIV
AGE
AGE^2
Economic factors
INCOMEINCOME^2

Others

(1)
(2)
All
Male
FemaleAll
MaleFemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects(t-value)
0.058 (2.961) ***0.045 (1.507)
0.065 (2.588) ***0.028 (2.639) ***0.031 (1.967) **0.022 (1.655) *0.040 (1.494)
0.060 (1.448)
0.020 (0.585)
0.027 (3.166) ***0.020 (1.525)
0.030 (2.820) ***-0.007 (-0.193)
0.006 (0.116)-0.005 (-0.132)-0.003 (-0.089)
0.014 (0.270)-0.008 (-0.178)****-0.063 (-1.184)-0.169 (-2.152)
0.032 (0.461)-0.076 (-1.438)-0.157 (-2.029)-0.001 (-0.008)
0.101 (3.789) ***0.087 (3.214) *******-0.056 (-2.141)-0.058 (-1.615)-0.062 (-1.531)-0.056 (-2.094)-0.054 (-1.503)-0.076 (-1.824) *0.022 (3.231) ***0.017 (1.610)
0.029 (3.007) ***0.023 (3.290) ***0.017 (1.624)
0.032 (3.252) ***0.000 (-2.787) ***0.000 (-1.421)
0.000 (-2.603) ***0.000 (-2.787) ***0.000 (-1.404)
0.000 (-2.812) ***-0.037 (-2.212) **-0.008 (-0.366)-0.103 (-3.800) ***-0.041 (-2.433) **-0.006 (-0.254)-0.118(-4.24) ***0.006 (2.881) ***0.003 (1.1210)
0.014 (3.817) ***0.041 (3.092) ***0.003 (1.055)
0.016 (4.181) ***WORKHOUR

0.004(2.247) **0.001(0.420)0.007(2.310) **0.004(1.907) *-0.001(-0.295)

0.008(2.529) **WORKHOUR^(1/2)-0.030 (-2.068) **-0.003(-0.110)-0.047(-2.392) **-0.026(-1.791) *0.013(0.567)-0.054(-2.640) ***SMOKING-0.004 (-0.585)-875.777-0.003(-0.383)-488.201-0.007(-0.597)-373.459-0.004(-0.583)-863.595-0.002(-0.236)-481.210-0.011(-0.932)-366.513

Log likelihood

1658

#obs

818

840

1629

812

817

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table 12: Binary probit regressions of severe obesity
Dependent variable: SEVERE OBESITY

(1)
All

(2)

Male

FemaleAll

MaleFemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects(t-value)
Impatience

DRSTD-0.003 (-0.377)-0.003(-0.304)-0.003(-0.400)-0.003 (-0.298)-0.012(-0.764)

0.007(0.656)

DEBTIMP
Hyperbolic discounting HYPERBOL

0.006(1.726) *0.004(0.797)0.005(1.696) *0.007(2.310) **0.011(2.051) **0.002(0.933)Sign effect

SIGN-0.027 (-2.008) **-0.005(-0.261)-0.042(-2.585) ***-0.024(-1.954) *-0.001(-0.050)-0.034(-2.552) **Risk aversion

RISKAV
MALE
UNIV
AGE

-0.027 (-1.452)
0.016 (1.665) *-0.006 (-0.687)
0.001 (0.596)-0.040(-1.391)-0.013(-0.610)(-1.438)-0.023(-1.477)(-0.998)(0.339)

0.002
0.003

(0.138)(1.162)(-2.091) **(1.504)(-0.927)(0.252)-0.039-0.0130.001-0.0350.013-0.0080.001-0.0100.000(-0.767)(-0.053)-0.006
0.002(-0.589)(0.721)PROCR

Demographic factors

Economic factors

OthersAGE^20.000 (-0.542)

0.000(-0.378)0.000(-1.064)0.000(-0.085)

INCOME-0.005 (-0.945)

0.001(0.166)-0.013(-1.716) *-0.008(-1.610)*0.000(0.103)0.000(-0.568)-0.002(-0.313)-0.014(-2.256) **0.001(0.722)0.001(1.881) *INCOME^20.001 (1.1919)

0.000(0.292)0.001(1.438)0.001(1.799)

WORKHOUR

0.000(0.438)-0.001(-0.704)

0.001(1.682) *0.000(-0.165)-0.001(-1.152)

0.001(1.427)

WORKHOUR^(1/2)-0.002 (-0.448)

0.005(0.606)-0.010(-1.557)

0.001(0.172)0.009(1.061)-0.006(-1.264)SMOKING-0.003 (-1.262)-200.818-0.004(-1.362)-115.743-0.002(-0.537)-79.642-0.004(-1.606)-196.881-0.003(-1.101)-116.399-0.006(-1.436)-74.069

Log likelihood

1658

#obs

818

840

1629

812

817

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table 13: Binary probit regressions of underweight
Dependent variable: UNDERWEIGHT

(1)
All

(2)

Male

FemaleAll

MaleFemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects(t-value)
Impatience

DRSTD

0.009

(0.863)0.004(0.389)0.011(0.643)0.010(0.702)-0.006(-0.392)

0.030(1.314)

DEBTIMP
Hyperbolic discounting HYPERBOL-0.008(-1.425)-0.005(-0.929)-0.009(-0.988)-0.009(-2.197) **-0.005(-1.419)-0.013(-1.856) *Sign effect

SIGN

0.040

(2.461) **0.023(1.189)0.053(2.116) **0.040(2.538) **0.018(1.471)0.055(2.144) **Risk aversion

RISKAV

0.041(1.422)-0.040(-0.132)

0.116(2.434) **0.034(1.202)-0.004(-0.164)0.104(2.159) **Demographic factors

MALE-0.034 (-2.394) **-0.028(-2.015) **PROCR

Economic factors

OthersLog likelihood
#obs

UNIV

-0.013 (-0.918)

0.002(0.1664)-0.033(-1.439)-0.011(-0.782)

0.002(0.208)-0.031(-1.270)AGE-0.012 (-3.863) ***-0.009(-2.804) ***-0.008(-1.481)-0.012(-4.025) ***-0.007(-3.001) ***-0.009(-1.713) *

AGE^2

0.000

(3.077) ***0.000(2.384) **0.000(0.697)0.000(3.245) ***0.000(2.542) **0.000(0.972)

INCOME-0.004 (-0.492)

0.011(0.766)-0.030(-1.772) *-0.006(-0.655)

0.024(1.397)-0.030(-1.689) *INCOME^20.000(0.290)-0.002(-1.066)

0.004(2.064) **0.000(0.376)-0.006(-1.560)

0.004(1.999) **WORKHOUR-0.002 (-1.768) *-0.002(-1.353)

0.000(0.250)-0.002(-1.739) *-0.001(-1.139)0.000(-0.071)

WORKHOUR^(1/2)

0.014

SMOKING(1.801) *0.008(0.869)0.004(0.354)0.014(1.776) *0.004(0.644)0.008(0.616)0.02 (0.604)-382.243

0.020(0.466)-140.439

0.002(0.309)-228.668

0.002(0.412)-369.856

0.001(0.560)-133.419

0.000(0.035)-223.863

1658

818

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

840

1629

812

817

Notes: The column of "Δimpatience" shows the impacts of an increase in the average of the discount rates DRi 's by one unit of sample S.D. of theaverage discount rate. The column of "Δprocrastination" shows the impacts of an increase in the propensity to procrastinate doing homeworkfrom the weakest degree (PROCR=1) to the strongest (PROCR=5). The column "Δsign effect" summarizes the effect of the presence of the signeffect (SIGN=1), compared with the case without the effect (SIGN=0). The impacts are evaluated by the esimation results of model (2).
*, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table 14: Impacts of time discounting variables on the prob. of being obese, severely obese, and underweight:
The case of Model (2) in the full sample
Obesity
Severe obesity
Underweight
Unconditional probabilities (shares)
24.30%
3.10%
7.00%
***
*
0.60%
-0.80%
Δimpatience
2.80%
***
**
Δprocrastination (hyperbolic discounting)10.80%
2.10%-3.60% **Δsign effect-0.30%-2.40% *4.00% **

Table A1: OLS regression of BMI with prefecture and occupation dummies

All
Coef. (t-value)
0.369 (2.49) **

(1)
Male
Coef. (t-value)
0.332 (1.54)

FemaleCoef. (t-value)
0.252 (1.20)

0.136 (0.66)

0.100 (0.33)-0.017 (-0.06)-0.511 (-2.03) **-0.684 (-1.68) *1.337 ( 5.99) ***-0.187 (-0.90)
0.253 (5.04) ***-0.002 (-4.15) ***-0.298 (-2.37) **0.042 (3.03) ***0.034 (1.80) *-0.260 (-1.43)-0.062 (-1.22)
18.063 (11.89) ***
0.095
1643

-0.210 (-0.54)-0.960 (-1.64)-0.731 (-2.17) **-0.799 (-1.36)-0.530 (-1.91) *0.233 (3.09) ***-0.002 (-2.80) ***-0.158 (-0.95)
0.027 (1.60)
0.009 (0.34)-0.013 (-0.05)-0.052 (-0.84)
18.890 (7.48) ***
0.010
813

0.266 (0.80)
0.296 (4.07) ***-0.002 (-3.19) ***-0.586 (-2.59) ***0.079 (2.67) ***0.066 (2.08) **-0.602 (-2.24) **-0.135 (-1.43)
18.486 (9.17) ***
0.116
830

Dependent variable: BMI

ImpatienceDRSTD
DEBTIMP
Hyperbolic discounting HYPERBOL
PROCR
Sign effect
SIGN
Risk aversion
RISKAV
Demographic factors
MALE
UNIV
AGE
AGE^2
Economic factors
INCOMEINCOME^2
WORKHOUR
WORKHOUR^(1/2)
OthersSMOKING
Constant
Adj. R^2
#obs

(2)
Male
Coef. (t-value)

FemaleCoef. (t-value)

0.253 (3.17) ***0.181 (1.55)

0.266 (2.36)

0.214 (3.32 ) ***-0.521 (-2.01) **-0.756 (-1.80) *1.259 (5.44) ***-0.263 (-1.23)
0.256 (4.94) ***-0.002 (-4.03) ***-0.294 (-2.12) **0.040 (2.51) **0.035 (1.77) *-0.265 (-1.40)-0.073 (-1.40)
17.718 (11.16)***

0.193 (1.96)-0.179 (-0.45)-0.993 (-1.65)

All
Coef. (t-value)

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.
The prefecture dummies (47) and the occupation dummies (12) are added to the set of explanatory variables.
The estimated coefficients of those dummies are not reported in the table.

0.099
1551

**

*

-0.630 (-2.21) **0.231 ( 3.01) ***-0.002 (-2.73 ) ***-0.126 (-0.68)
0.021 (1.06)-0.001 (-0.04)
0.067 (0.23)-0.038 (-0.59)
18.450 (7.14) ***
0.012
772

**

0.215 ( 2.46) **-0.756 (-2.19) **-1.015 (-1.66) *0.211 (0.61)
0.286 (3.85) ***-0.002 (-2.91) ***-0.622 (-2.66) ***0.081 (2.69) ***0.077 (2.33) **-0.671 (-2.40) **-0.207 (-2.09) **18.352 (8.97) ***
0.141
779

Table A2: Binary probit regression of obesity with prefecture and occupation dummies
Dependent variable: OBESITY

(1)
Male

(2)
All
Male
FemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value)
0.071 (3.55 ) ***0.053 (1.70) *0.066 (2.45) **0.027 (2.52) **0.033 (1.99) **0.018 (1.28)
0.045 (1.61)
0.042 (0.95)
0.015 (0.42)
0.023 (1.60)
0.026 (2.27) **0.024 (2.70) ***0.005 (0.13)
0.013 (0.24)-0.011 (-0.25)
0.008 (0.22)
0.017 (0.30)-0.012 (-0.26)-0.004 (-0.05)-0.082 (-1.46)-0.210 (-2.43) **-0.044 (-0.55)-0.070 (-1.27)-0.198 (-2.33) **0.111 (3.65) ***0.099 (3.17) ***-0.069 (-2.50) **-0.097 (-2.43) **-0.040 (-0.90)-0.075 (-2.67) ***-0.109 (-2.69) ***-0.044 (-0.94)
0.024 (3.33) ***0.021 (1.84) *0.033 (3.05) ***0.025 (3.28) ***0.020 (1.74)
0.034 ( 2.98) ***0.000 (-2.84) ***0.000 (-1.56)
0.000 (-2.69 )***
0.000 (-2.78) ***0.000 (-1.51)
0.000 (-2.57) ***-0.041 (-2.32) **-0.014 (0.56)-0.109 (-3.59) ***-0.039 (-2.17) **-0.006 (-0.23)-0.120 (-3.75) ***0.006 (3.00) ***0.003 (1.12)
0.015 (3.74) ***0.006 (2.83) ***0.002 (0.74)
0.017 (3.88) ***All

ImpatienceDRSTD
DEBTIMP
Hyperbolic discounting HYPERBOL
PROCR
Sign effect
SIGN
Risk aversion
RISKAV
Demographic factors
MALE
UNIV
AGE
AGE^2
Economic factors
INCOMEINCOME^2

OthersFemale

WORKHOUR

0.004 (1.74)

0.001 (0.32)

0.008 (2.08) **0.004 (1.52)-0.002 (-0.53)

0.010 (2.36 ) **WORKHOUR^(1/2)-0.027 (-1.11)

0.005 (0.11)-0.067 (-1.96) **-0.025 (-0.97)

0.038 (0.82)-0.080 (-2.26) **SMOKING-0.004 (-0.64)-835.748-0.003 (-0.38)-455.651-0.009 (-0.69)-336.367-0.004 (-0.62)-0.001 (-0.10)-423.651-0.018 (-1.32)-315.694

1643

806

796

765

747

Log likelihood#obs*-789.634
1551

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.
The prefecture dummies (47) and the occupation dummies (12) are added to the set of explanatory variables.
The estimated coefficients of those dummies are not reported in the table.
Table A3: Binary probit regression of severe obesity with prefecture and occupation dummies
Dependent variable: SEVERE OBESITY

(1)
All

(2)

Male

FemaleAll

MaleFemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value)

Impatience

DRSTD-0.001 (-0.16)-0.002 (-0.09)-0.005 (-0.48)-0.002 (-0.20)-0.021 (-0.81)

0.010 (0.71)

DEBTIMP
Hyperbolic discounting HYPERBOL

0.007 (1.93) *0.008(0.87)

0.005 (2.18)

0.009 (2.58) ***0.019(2.18)

Sign effect

SIGN-0.025 (-1.60)

0.004 (0.15)-0.041 (-1.76)-0.026 (-1.81) *0.007(0.25)-0.027 (-1.79) *Risk aversion

RISKAV-0.027 (-1.21)-0.056 (-1.15)-0.023 (-0.77)-0.023 (-1.20)-0.045(-0.98)-0.013 (-0.95)

Demographic factors

MALE

0.016 (1.31)

UNIV-0.005 (-0.43)-0.012 (-0.55)

0.014 (0.72)-0.006 (-0.66)-0.008(0.701)-0.002 (-0.36)

AGE

0.003 (1.00)

0.007 (1.07)

0.004 (1.00)

0.002 (0.90)

0.005(0.83)

0.000 (0.13)AGE^20.000 (-1.02)

0.000 (-1.10)

0.000 (-0.95)

0.000 (-0.82)

0.000(-0.80)0.000 (0.01)

INCOME-0.006 (-1.00)

0.001 (0.09)-0.017 (-1.59)-0.006 (-1.15)

0.000(-0.01)-0.011 (-2.30) **INCOME^20.001 (1.47)

0.001 (0.60)

0.002 (1.46)

0.001 (1.56)

0.001(0.59)

0.001 (2.07)**

WORKHOUR

0.000 (0.46)-0.002 (-0.54)

0.002 (1.69) *0.001 (0.67)-0.002(-0.63)0.001 (1.96)**

WORKHOUR^(1/2)-0.006 (-0.67)

0.011 (0.34)-0.020 (-1.82) *-0.008 (-0.90)

0.014(0.41)-0.010 (-1.98) **SMOKING-0.004 (-1.65) *-171.938-0.009 (-1.76) *-91.510-0.002 (-0.54)-54.227-0.005 (-2.18) **-159.048-0.009(-1.72) *-88.224-0.006 (-1.67) *-41.317

1192

444

391

1131

425

321

PROCR

Economic factors

OthersLog likelihood
#obs

**

**

0.002 (1.34)

0.012 ( 1.12)

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.
The prefecture dummies (47) and the occupation dummies (12) are added to the set of explanatory variables.
The estimated coefficients of those dummies are not reported in the table.
Table A4: Binary probit regression of severe obesity with prefecture and occupation dummies
Dependent variable: UNDERWEIGHT

(1)

(2)

Male

All

FemaleAll

MaleFemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value)

Impatience

DRSTD

0.003 (0.29)-0.002 (-0.78)

0.016 (0.85)

0.007 (0.50)-0.002 (-0.50)

0.032 (1.34)

0.004 (1.38)

0.049 (1.91) *-0.001 (-0.13)

0.133 (2.60) ***DEBTIMP
Hyperbolic discounting HYPERBOL
PROCR
**

Sign effect

SIGN

0.035 (2.33)

Risk aversion

RISKAV

0.040 (1.47)

Demographic factors

MALE-0.043 (-2.89) ***UNIV-0.010 (-0.80)

0.006 (1.65)

AGE-0.010 (-3.22) ***AGE^20.000 (2.52)

INCOME

Economic factors

OthersLog likehood#obs-0.011 (-1.90) *-0.001 (-1.62)-0.009 (-2.15) **-0.001 (-1.52)

0.036 (2.39) **0.002 (1.76)

0.036 (1.27)-0.001 (-0.26)-0.012 (-1.12)-0.013 (-1.69) **0.049 (1.77)*

0.137 ( 2.47) **-0.038 (-2.63) **-0.047 (-2.15) **-0.011 (-0.77)

0.003 (1.81)*-0.052 (-2.11) **-0.002 (-3.10) ***-0.006 (-0.96)-0.011 (-3.34) ***-0.001 (-3.36)***-0.006 (-0.92)

0.000 (2.82)***

0.000 (0.35)

0.000 (2.61) ***0.000 (3.03)***

0.000 ( 0.31)-0.002 (-0.25)

0.005 (1.66)*-0.032 (-1.72) *-0.004 (-0.42)

0.004 (2.11)**-0.038 (-1.90) *INCOME^20.000 (0.22)-0.001 (-1.67) *0.004 (1.99) **0.000 (0.30)-0.001 (-1.97)**

WORKHOUR-0.002 (-1.64) *0.000 (-0.77)-0.001 (-0.44)-0.002 (-1.57)

0.000 (-0.41)***

0.005 (2.20)**-0.002 (-0.51)

WORKHOUR^(1/2)

0.020 (1.63)

0.001 (0.34)

0.027 (1.08)

0.020 (1.55)

0.000 (-0.11)

0.028 (1.04)

SMOKING

0.002 (0.68)-346.028

0.000 (-0.34)-99.237

0.008 (1.15)-195.070

0.002 (0.59)-323.657

0.000 (-0.10)-90.692

0.007 (0.90)-181.899

1528

554

681

1407

531

624

Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.
The prefecture dummies (47) and the occupation dummies (12) are added to the set of explanatory variables.
The estimated coefficients of those dummies are not reported in the table.

Table A5: Multivariate probit estimation of the prob. of obesity, severe obesity, and underweight

Obesity

Model (1)Severe Obesity

Underweight

Obesity

Model (2)Severe Obesity

Underweight

Coef. (t-value)
0.197 (3.03) ***Coef. (t-value)-0.016 (-0.14)

Coef. (t-value)
0.068 (0.75)

Coef. (t-value)

Coef. (t-value)

Coef. (t-value)

0.129 (1.43)

0.000 (0.00)

0.065 (0.50)

Dependent variables:
OBESITY, SEVERE OBESITY,
UNDERWEIGHT
ImpatienceDRSTD
DEBTIMP
Hyperbolic HYPERBOL
discounting PROCR
Sign effect SIGN
Risk aversion RISKAVDemographic MALE
factors
UNIV
AGE
AGE^2
Economic
INCOME
factors
INCOME^2
WORKHOUR
WORKHOUR^(1/2)
OthersSMOKING
Constant
Correlation matrix of error terms

Loglikelihood ratio test:

0.089 (2.62)

0.442 (2.33) **0.318 (1.26)-0.252 (-2.03) **0.335 (3.82) ***-0.190 ( -2.11)-0.094 (-0.74)-0.104 (-3.83) ***0.070 ( 3.14 ) **-0.001 (-2.70) ***0.001 (3.04) ***-0.108 (-2.01) **-0.046 (-0.60)
0.002 (0.26)
0.016 ( 2.71) ***-0.019 (-1.94) **0.014 (2.16) **0.134 (1.94) **-0.095 (-2.00 ) **-0.012 (-0.56 )0.021 (0.66)
0.733 (1.20)-2.459 ( -4.74 ) ***1-0.422 (-6.04) ***-0.252 (-8.66) ***1
H0: all error term correlations = 0,-0.032 (-0.29)-0.356 (-2.12) **-0.559 ( -1.87) *0.202 (1.30)-0.113 ( -0.70)
0.035 ( 0.89)
0.000 (-0.79)-0.079 (-0.93)
0.011 (1.30 )0.005 (0.40)-0.039 (-0.45)-0.035 (-0.88)-2.110 (-2.31) **0.759 (15.61) ***1

χ2(3) = 144.499 Prob > χ2 = 0.000

Log likelihood-1386.588
1658#obs
Notes: *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.
The estimation is conducted by using the "mvprobit" program in the software STATA.

***

0.090 (3.20) ***-0.020 (-0.18)-0.256 (-1.48)
0.276 (3.11) ***-0.189 (-2.08) **0.075 (3.33) ***-0.001 (-2.82) ***-0.123 (-2.26) **0.018 (2.97) ***0.013 (1.95) *-0.088 (-1.84) *-0.011 (-0.51)-2.769 (-5.18 ***1

0.116 (1.94)*-0.084 (-1.60)

0.123 (2.29) **-0.264 (-1.50)-0.679 (-2.24) **(1.48)-0.078 (-0.47)
0.017 (0.42)
0.000 (-0.21)-0.144 (-1.65) *0.017 (1.99) **0.002 (0.17)-0.015 (-0.18)-0.058 (-1.42)-2.197 ( -2.34) **0.748 (14.63) ***1-0.092 (-2.43) **0.481 (2.50) **0.325 (1.27)-0.251 (-2.00)**-0.126 (-0.97)-0.109 (-3.98) ***0.001 (3.21) ***-0.050 (-0.62)
0.003 (0.28)-0.017 (-1.69)
0.125 (1.76)
0.011 (0.34)
1.160 (1.84) *-0.406 (-6.10) ***-0.320 (-3.64) ***1
H0: all error term correlations = 0,

χ2(3) = 137.479 Prob > χ2 = 0.000-1361.592
1629

Table A6: OLS regression of uncorrected BMI

All
Coef. (t-value)
0.273 (2.025) **Model (1)
MaleCoef. (t-value)
0.276 (1.421)

FemaleCoef. (t-value)
0.256 (1.363)

0.105 (0.565)

0.177 (0.647)

0.014 (0.056)-0.550 (-2.400) **-0.659 (-1.805) *1.301 (7.191) ***-0.118 (-0.648)
0.238 (5.470) ***-0.002 (-4.643) ***-0.257 (-2.297) **0.038 (3.000) ***0.030 (2.215) **-0.202 (-2.044) **-0.055 (-1.197)
17.019 (17.013) ***
0.094
1658

-0.300 (-0.863)-0.972 (-1.872) *-0.723 (-2.400) **-0.465 (-0.902)-0.256 (-1.081)
0.230 (3.508) ***-0.002 (-3.244) ***-0.130 (-0.876)
0.026 (1.727) *0.008 (0.426)-0.032 (-0.207)-0.046 (-0.817)
18.705 (12.965) ***
0.021
818

0.059 (0.203)
0.235 (3.865) ***-0.002 (-2.922) ***-0.518 (-2.599) ***0.067 (2.533) **0.037 (1.734) *-0.264 (-1.847) *-0.097 (-1.161)
17.103 (12.145)***
0.079
840

Dependent variable: BMI

Impatience
Hyperbolic
discounting
Sign effectRisk aversion
Demographic factors

Economic factors

OthersDRSTD
DEBTIMP
HYPERBOL
PROCR
SIGN
RISKAV
MALE
UNIV
AGE
AGE^2
INCOMEINCOME^2
WORKHOUR
WORKHOUR^(1/2)
SMOKING
Constant

Adj. R^2#obs

All
Coef. (t-value)
0.246 (3.400)***

0.217 (3.796) ***-0.490 (-2.159) **-0.815 (-2.243) **1.212 (6.622) ***-0.137 (-0.748)
0.238 (5.438) ***-0.002 (-4.542) ***-0.271 (-2.352) **0.037 (2.804) ***0.027 (1.950) *-0.184 (-1.849) *-0.068 (-1.476)
16.458 (16.180) ***
0.102
1629

Model (2)MaleCoef. (t-value)

FemaleCoef. (t-value)***

0.167 (1.574)

0.314 (3.199)

0.179 (2.08) **-0.165 (-0.491)-0.992 (-1.933) *0.240 (3.178) ***-0.743 (-2.447) **-0.725 (-1.412)-0.247 (-1.047)
0.226 (3.468) ***-0.002 (-3.180) ***-0.105 (-0.682)
0.021 (1.336)
0.004 (-0.213)
0.056 (0.357)-0.041 (-0.738)
18.063 (12.337) ***
0.023
812

-0.046 (-0.155)
0.242 (3.971) ***-0.002 (-2.965) ***-0.604 (-3.031) ***0.076 (2.861) ***0.048 (2.197) **-0.337 (-2.310) **-0.149 (-1.759) *16.537 (11.651) ***
0.110
817

Notes: The uncorrected BMI data from JHS05 are used. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table A7: Binary probit regression of obesity by the uncorrected data
Dependent variable: OBESITY

Impatience
Hyperbolic
discounting
Sign effectRisk aversion
Demographic factors

Economic factors

DRSTD
DEBTIMP
HYPERBOL
PROCR
SIGN
RISKAV
MALE
UNIV
AGE
AGE^2
INCOMEINCOME^20.004 (2.412) **0.002 (0.874)

0.006 (2.352) **0.003 (1.926)*

0.000 (-0.046)

0.007 (2.577)

WORKHOUR^(1/2) -0.027 (-2.061) **-0.011 (-0.492)-0.039 (-2.249) **-0.022 (-1.669) *0.008 (0.356)-0.045 (-2.528) **SMOKING-0.005 (-0.884)-762.030-0.004 (-0.536)-439.377-0.011 (-1.056)-316.053-0.005 (-0.798)-748.953-0.002 (-0.206)-428.955-0.016 (-1.475)-310.273

1658

818

840

1629

812

817

WORKHOUR
OthersModel (1)Model (2)
Male
All
All
FemaleMale
FemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects(t-value)**
0.037 (2.093)
0.036 (1.338)
0.032 (1.512)
0.023 (2.470) **0.021 (1.420)
0.023 (2.032) **0.013 (0.543)
0.027 (0.687)
0.001 (0.037)
0.028 (3.616) ***0.029 (2.333) **0.024 (2.613) ***-0.046 (-1.488)-0.018 (-0.357)-0.063 (-1.668) *-0.037 (-1.205)
0.004 (0.079)-0.065 (-1.684) *-0.022 (-0.465)-0.092 (-1.272)
0.045 (0.742)-0.031 (-0.663)-0.070 (-0.992)
0.009 (0.1424)
0.087 (3.675) ***0.069 (2.864) ***-0.030 (-1.286)-0.037 (-1.120)-0.020 (-0.574)-0.028 (-1.170)-0.031 (-0.930)-0.033 (-0.896)
0.019 (3.053) ***0.018 (1.872) *0.020 (2.488) **0.020 (3.148) ***0.019 (1.935) *0.021 (2.592) ***
***
*
**
***
*
0.000 (-2.749)
0.000 (-1.716)
0.000 (-2.229)
0.000 (-2.785)
0.000 (-1.774)
0.000 (-2.261) **-0.035 (-2.493) **-0.021 (-1.021)-0.071 (-3.224) ***-0.040 (-2.752) ***-0.020 (-0.943)-0.081 (-3.634) ***0.004 (2.727) ***0.003 (1.367)
0.009 (3.116) ***0.005 (2.912) ***0.003 (1.276)
0.009 (3.415) ***Log likelihood
#obs

**

Notes: The uncorrected data from JHS05 are used. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Table A8: Binary probit regression of severe obesity by the uncorrected data
Dependent variable: SEVERE OBESITY

Model (1)All

Model (2)

Male

All

FemaleMale

FemaleMarginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects (t-value) Marginal effects(t-value)
Impatience

DRSTD-0.003 (-0.561)-0.005 (-0.638)

0.000 (-0.125)

HYPERBOL-0.004 (-0.616)-0.006 (-0.522)

0.000 (0.039)

PROCR
SIGN
RISKAV
MALE
UNIV
AGE

-0.017 (-1.753) *-0.034 (-2.591) ***0.015 (2.120) **-0.004 (-0.647)
0.002 (1.283)

0.000 (0.018)-0.049 (-2.140) **-0.025 (-2.446) **-0.016 (-1.513)-0.007 (-0.696)
0.005 (1.519)

0.000 (-0.008)
0.001 (0.498)

AGE^20.000 (-1.427)

0.000 (-1.685) *0.000 (-0.476)

0.000 (-1.331)

0.000 (-1.494)

0.000 (-0.369)

INCOME-0.003 (-0.919)

0.001 (0.197)-0.004 (-0.676)-0.005 (-1.676)-0.003 (-0.552)-0.081 (-1.269)

DEBTIMP
Hyperbolic
discounting
Sign effectRisk aversion
Demographic factors

Economic factors

OthersLog likelihood#obs

0.002 (0.753)

0.002 (0.620)

0.001 (0.379)

0.007 (3.180) ***0.011 (-1.665) *-0.031 (-2.878) ***0.008 (1.398)-0.002 (-0.448)
0.002 (1.274)

0.011 (2.447) **0.000 (0.004)-0.037 (-1.960) **0.003 (1.713) *-0.020 (-2.305) **-0.019 (-2.078) **-0.004 (-0.498)
0.004 (1.372)-0.001 (-0.114)
0.001 (0.455)**

INCOME^20.000 (1.257)

0.000 (0.385)

0.000 (0.100)

0.001 (2.051)

0.001 (1.165)-0.005 (0.477)

WORKHOUR

0.000 (0.062)

0.000 (0.1338)

0.000 (0.291)

0.000 (-0.020)

0.000 (0.059)

0.000 (0.053)

WORKHOUR^(1/2)

0.000 (0.0638)-0.002 (-0.278)

0.000 (0.014)

0.000 (0.087)-0.001 (-0.173)

0.000 (0.169)

SMOKING-0.002 (-1.378)-143.284-0.003 (-1.010)-91.649-0.004 (-1.111)-47.110-0.002 (-1.451)-139.330-0.002 (-1.074)-87.161-0.003 (-1.087)-47.890

1658

818

840

1629

812

817

Notes: The uncorrected data from JHS05 are used. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

Figure 1: BMI distribution: NSHN04, JHS05, corrected data
Figure 1(a): Male％
Obesity

JHS05

Underweight

Corrected

NSHN04

NSHN04-JHS05

35−

34−35

33−34

32−33

31−32

30−31

29−30

28−29

27−28

26−27

25−26

24−25

23−24

22−23

21−22

20−21

19−20

18−19

17−18

16−17

15−16

NSHN04-Corrected

-15

0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
-0.01
-0.02
-0.03

BMI

Figure 1(b): Female％
Underweight

Obesity

JHS05

NSHN04
Corrected
NSHN04-JHS05

35−

34−35

33−34

32−33

31−32

30−31

29−30

28−29

27−28

26−27

25−26

24−25

23−24

22−23

21−22

20−21

19−20

18−19

17−18

16−17

15−16

NSHN04-Corrected

-15

0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
-0.01
-0.02
-0.03

BMI

Note: NSHN04, JHS05, and corrected data represent the National Survey of Health and Nutrition
2004, the Japan Household Survey on Consumer Preferences and Satisfaction 2005, and thecorrected data of JHS05, respectively.

Figure 2(a) Income and BMI: Female (model (1))
12average income (2.141)

10

critical income (3.785)

8

BMI(controlled)
BMI (unexplained by otheer variables)

Predicted
6

1 094S D
1.094S.D.
4

2

0
0

1

2

3

4

5

6

7

-2

-4

-6

Per capita household income (million JPY)

8

9

10

Figure 2(b) Income and BMI: Female (Model (2))

1412average income (2.141)

10

BMI (unexplaineed by other variables)

critical income (3.912)

8
BMI(controlled)
1.178S.D.
Predicted

6

4

2

0
0

2

4

6

-2

-4

-6
Per capita household income (million JPY)

810

Figure 3: Females' Income Elasticities of BMI
in Income Quintiles
4.0%

3.0%

2.8%

2.0%

2.7%

model 1model 2

1.0%

0.0%
1

2

3

4

5

‐1.0%
‐1.7%
‐2.0%

‐2.3%

‐2.2%
‐2.6%

‐2.0%

‐2.8%

‐3.0%
‐2.8%
‐4.0%

‐3.2%

Figure 4: Females' Working Hour Elasticities of BMI

14.0%

12.0%

10.0%

Model (1)Working hour elasticity of BMI

Model (2)
8.0%

6.0%

4.0%

Working hour elasticity = 0 at:- working hours = 12.84 for model (1)- working hours = 12.38 for model (2)

2.0%

0.0%
0

‐2.0%

20

40

60

Working hours a week80

100