Project Center, Graduate School of Economics, Kyoto University, Working Paper No.11-10

IMPATIENCE AND IMMEDIACY: A QUASI-HYPERBOLICDISCOUNTING APPROACH TO SMOKING BEHAVIOR

TAKANORI IDA
Graduate School of Economics, Kyoto University, Yoshida, Sakyo, Kyoto 606-8501,
Japan; Tel. & Fax: +81-75-753-3477; E-mail: ida@econ.kyoto-u.ac.jp

Abstract
This paper investigates smoking status, including nicotine dependence, on the basis of aquasi-hyperbolic discounting approach. This approach reconciles the traditional rational
addiction model and the bounded rational addiction model. The paper measures two key
parameters: impatience, in line with the former model, and immediacy, in line with thelatter model. There are two main conclusions. First, the impatience and immediacy
parameters are positively associated with smoking probability. Second, they are
positively associated with nicotine dependence.
Keywords: smoking, nicotine dependence, time preference, impatience, immediacy
JEL classifications: D81, D91, I12

1. INTRODUCTION
Addiction has attracted considerable attention in health and behavioral economics, andeconomists have tried to understand addiction from the viewpoint of decision making
over time (Chaloupka and Warner 2000). This viewpoint is relevant because consumers
believe that an addictive product such as tobacco increases their current satisfaction,although it actually decreases their future utility by damaging their health. Furthermore,
Fehr and Zych (1998) reported that addicts systematically consumed too muchcompared to the optimal consumption decision and explained this systematic excess
consumption in terms of the psychologically salient features of addictive goods. It
follows that reinforcement matters for addiction, because a larger stock of past
consumption raises the marginal utility of current consumption (Becker and Murphy
1988, Gruber and Koszegi 2001). This paper investigates smoking, including nicotine
dependence, the most common form of addiction, on the basis of the quasi-hyperbolic
discounting approach proposed by Laibson (1997).
I now briefly describe smoking trends in Japan, where the percentage of smokers in

the general population remains higher than the percentages of smokers in otherdeveloped nations. In fact, the prevalence rate of smoking among people aged 20 years

and over was around 26.3% in Japan in 2006, still higher than the average figure of
24.0% among OECD countries. Although from 1990 to 2006, the smoking prevalence

rate for males in Japan dropped from 53.1% to 41.3%, for females, it actually increased
from 9.4% to 12.4%. As in other countries, reduction of the smoking rate has been acentral issue in Japanese public health policy. Healthy Japan 21, a program establishedby the Ministry of Health, Labour, and Welfare, has promoted risk education, theeradication of smoking among teenagers, the establishment of nonsmoking areas, andeffective support for smoking cessation as its four main measures for tobacco control.

Nevertheless, the factors that successfully account for smoking behavior still remain
undetermined.1
1

Cutler and Glaeser (2009) analyzed why there was a big difference in smoking rates

between the U.S. and Europe. Interestingly, they discussed that the most importantfactor would be differences in beliefs about the health consequences of smoking
between residents of the U.S. and of Europe.
1There are two lines of research in the literature on addictive behaviors such as
smoking: rational addiction models and bounded rational addiction models (Messinis1999). A model of the first type was advocated by Becker and Murphy (1988); in thismodel, utility-maximizing consumers consider the future consequences of their past andcurrent consumptions of addictive substances. The rational addiction model is thus
compatible with such traditional economic models as the discounted utility schemes.
Considerable research on time preference has reported that smokers are more impatientthan non-smokers, and that they more frequently choose earlier-smaller rewards overlater-larger rewards.2 Examples of such studies include Mitchell (1999), Bickel et al.

(1999), Odum et al. (2002), Baker et al. (2003), Reynolds et al. (2003), and Ohmura etal. (2005).
The second type of model is the bounded rational addiction model, an example ofwhich is the model developed by Gruber and Koszegi (2001). In their model, theexponentially discounted utility hypotheses were systematically violated: some smokers
neither recognized the true difficulty of quitting nor searched for self-control devices tohelp themselves quit. Gruber and Koszegi (2001) included strikingly different
normative implications, because they suggested that government policy should consider
not only the externalities imposed by smokers on others but also the internalities
imposed by smokers on themselves (see also Winston 1980, Akerlof 1991, Kan 2007).
Are these two addiction models related? If so, are they complements or substitutes?
Further, it is necessary to verify whether an addict is both impatient and present-biased.
Note that estimating smoking behavior separately based on either a rational or bounded
rational addiction model would result in omitted variable bias. These questions will be
investigated in this paper. Very few studies, however, have focused on these aspects.
One exception is Blondel et al. (2007), who compared the behavior of drug addicts withthe behavior of a control group and discovered that the decisions of the drug users werelargely consistent with standard decision-making theories. Furthermore, they found nodifferences in the estimated discount rates between the drug users and the control group.
2

On the other hand, addiction can be interpreted as decision making under risk because

the future health damage is stochastic. Although many studies have investigated therelationship between smoking and attitudes toward risk, the issue remains inconclusive(Mitchell 1999, Reynolds et al. 2003, Ohmura et al. 2005).
2

These conclusions are interesting, although the size of the sample was only 34.
Expanding on Blondel et al. (2007), I draw a large sample to examine the relationshipbetween the rationality and bounded-rationality approaches in the context of smoking.
Next, I discuss two points regarding measurement of the economic-psychologicalparameters adopted in this paper. First, most previous studies measured the time
preference rate and risk preference coefficient separately when they examined smoking
from the economic-psychological perspective.3 Ida and Goto (2009) and Ida (2010),
however, simultaneously measured the time preference rate and risk preference
coefficient at the individual level using discrete choice experiments (DCE) and mixed
logit (ML) model analysis. They found that smokers were more impatient andrisk-prone than non-smokers, which was first reported by Viscusi and Hirsh (2001). I
will use this simple model to simultaneously measure the parameters.
Second, and more importantly, I elucidate how likely it is that the stationarity axioms,
which are required by discounted utility theory, are violated. I then assume that the
time-inconsistent smokers have a quasi-hyperbolic discount function (Laibson 1997), sothat lifetime utility from period τ onwards is given byUτ = uτ + β ∑ Tt = τ +1δ t − τ ut ,where ut is the periodic utility; the parameter β denotes present bias, or immediacyeffect; and δ denotes the standard exponential discount factor, which reflects
impatience4. I investigate whether these β − δ parameters can successfully predict
smoking status, including nicotine dependence.
3

As Rachlin and Siegel (1994) suggest, the nature of the interaction between theseparameters remains controversial because most previous studies measured themseparately. This is analytically unsatisfactory. A few studies have integrated themeasurements of time and risk preferences—for instance, Rachlin et al. (1991), Kerenand Roelofsma (1995), Anderhub et al. (2001), and Yi et al. (2006).
4

Most recently, however, Van der Pol and Cairns (2011) have sounded an alarm for theeasy popularity of quasi-hyperbolic discount model. They have tested whether thequasi-hyperbolic model provides a better description of individual time preference forhealth outcomes when stationarity is violated, concluding that the quasi-hyperbolicmodel may not be appropriate as an intertemporal model.
3This paper’s main conclusions can be summarized as follows. First, I analyze
whether the quasi-hyperbolic discounting parameters are associated with smoking. The
analysis reveals that a 1% increase in the immediacy parameter (relatedly, β )significantly increases smoking probability by 0.2753%, while a 1% increase in theimpatience parameter (relatedly, δ ) increases smoking probability by 0.9384%. Second,
I investigate how these parameters elucidate nicotine dependence. The analysis showsthat a 1% increase in the immediacy parameter decreases the proportion of the low
nicotine-dependent smokers by 0.5444% but increases that of the highly
nicotine-dependent smoker by 0.4259%. Furthermore, a 1% increase in the impatienceparameter decreases the proportion of the low nicotine-dependent smokers by 0.9324%
but increases that of the highly nicotine-dependent smokers by 0.9522%. Thus, one cansee that the quasi-hyperbolic discounting parameters function as good predictors ofsmoking status as a whole.
The paper is organized as follows. Section 2 explains the method of sampling data
and discusses the characteristics of the sample. Section 3 proposes the strategy for
estimating the quasi-hyperbolic discounting parameters and illustrates an ML model
analysis. Section 4 explains the estimation models and their results, and Section 5
proposes four hypotheses and discusses the results. Section 6 provides concluding
remarks.

2. SURVEY AND DATAThis section explains the survey method and describes the data. In July 2008, I surveyed
494 Japanese adults registered with a consumer-monitoring investigative company.5
Note that 150 Japanese Yen (JPY) (1.5 US$, given 100 JPY = 1 US$) were paid torespondents who replied to the Fagerström Test for Nicotine Dependence (FTND), and
500 JPY (5 US$) were paid to respondents who replied to the conjoint questionnairethat I describe below. Respondents who answered in an unrealistically short period of
5

The samples were adjusted to reflect Japanese demographics for gender, average age,and geographical features of the sampling. Still, the size of sample (494) is limited, and,thus, it will be an important future topic of research to increase the sample and checkthe robustness.
4

time were excluded in advance.
Of those sampled, 253 were smokers, in which category the 59 ex-smokers were
included, and 241 were non-smokers. In terms of demographics, the proportion ofsmokers who were female was 36.4%, and the proportion of non-smokers who werefemale was 51.5%. The average ages of the smokers and non-smokers were 40.5 and38.1 years, respectively. Similarly, 46.2% of the smokers and 69.7% of the non-smokers
were university or junior college graduates, and the annual household incomes were 5.9
million JPY (59 thousand US$) for smokers and 6.3 million JPY (63 thousand US$) for
non-smokers.
	  I defined nicotine dependence as follows. On the basis of the FTND, current smokers
were classified as heavy smokers (H), moderate smokers (M), or light smokers (L).
FTND comprises the following six questions (Heatherton et al. 1991):

1. How soon after you wake up do you smoke your first cigarette? (1) Within 5
minutes (3 points), (2) 6–30 minutes (2 points), (3) 31–60 minutes (1 point), (4)After 60 minutes (0 points)
2. Do you find it difficult to refrain from smoking in places where it is forbidden,e.g., in church, at the library, at the cinema, etc.? (1) Yes (1 point), (2) No (0points)3. Which cigarette would you hate most to give up? (1) The first one in themorning (1 point), (2) All others (0 points)
4. How many cigarettes do you smoke a day? (1) 10 or less (0 points), (2) 11–20 (1point), (3) 21–30 (2 points), (4) more than 30 (3 points)
5. Do you smoke more frequently during the first hours after waking than during
the rest of the day? (1) Yes (1 point), (2) No (0 points)
6. Do you smoke even if you are so ill that you are in bed most of the day? (1) Yes(1 point), (2) No (0 points)

By aggregating the responses, I defined respondents with 0 to 3 points as having low

5nicotine dependence (L-smokers); with 4 to 6 points, as having moderate nicotine
dependence (M-smokers); and with 7 or more points, as having high nicotine
dependence (H-smokers). I found that 38.3% of the respondents were L-smokers;
43.8% M-smokers; and 17.8% H-smokers. The proportion female and the proportion
university graduates are highest for L-smokers, and the average age is highest for
H-smokers. Further, the average income level is highest for M-smokers. The basic
statistics are summarized in Table 1.
<Table 1>

3. MEASURING THE IMPATIENCE AND IMMEDIACYPARAMETERS
In this section, I explain the derivation of the impatience and immediacy parameters andshow the estimation results. The research strategy was composed of the following two
steps. First, I conducted an experimental survey to check whether smokers displayed thediscounted utility anomalies. Then, I classified the samples as time consistent or time
inconsistent. Second, I used conjoint analysis to measure the immediacy parameter(relatedly, β ) for the time-inconsistent samples and the impatience parameter(relatedly, δ ) for both the time-consistent and time-inconsistent samples. I depict thisstrategy in Figure 1.
<Figure 1>

3.1. Discounted utility anomaly
Next, I address the discounted utility anomaly. The standard theory of decision making
over time is the exponentially discounted utility model, whose key assumption is astationarity axiom. This implies that if and only if the utility of 100,000 JPY in thepresent is indifferent with the utility of 150,000 JPY in one year, then the utility of
100,000 JPY in ten years is indifferent with the utility of 150,000 JPY in eleven years.

6Assuming that X and Y denote payoffs (X < Y) and t and s denote time delay (t < s),the axiom is more formally defined as follows:(X,t) ≥ (Y,s) and (X,t+ε) ≥ (Y,s+ε).
Note that ε is a positive constant.
At this point, the discounted utility model gives U(X)/(1 + r)t ≥ U(Y)/(1 + r)s for t
and s.6 However, the discounted utility anomaly of a present-smaller reward being
excessively preferred to a delayed-larger reward indicates the following inconsistentpreference orders:(X,t) ≥ (Y,s) and (X,t + ε) ≤ (Y,s + ε).
This anomaly is called time inconsistency (Strotz 1956, Prelec 2004). Interestingly, it isobserved even in animals, such as pigeons (Ainslie 1975).
I asked the respondents two hypothetical questions in order to investigate thediscounted utility anomaly:
Question 1
Alternative 1: Receive 100,000 JPY (1,000 US$) immediately.
Alternative 2: Receive 150,000 JPY (1,500 US$) in X years.
What X makes the two alternatives equivalent?
Question 2
Alternative 1: Receive 100,000 JPY (1,000 US$) in one year.
Alternative 2: Receive 150,000 JPY (1,500 US$) in Y years.
What Y makes the two alternatives equivalent?
On the basis of the exponentially discounted utility model, when the utility of
100,000 JPY in the present equals the utility of 150,000 JPY in X years, I obtain the6

For continuous time, the exponentially discounted utility model is represented byexp(-rt)U(X) ≥ exp(-rs)U(Y).
7following equation:
Utility of 100,000 JPY = Utility of 150,000 JPY/(1 + r)X.
Note that r denotes the annual time preference rate.
And when the utility of 100,000 JPY in one year equals the utility of 150,000 JPY in
Y years, I obtain the following equation:
Utility of 100,000 JPY/(1 + s) = Utility of 150,000 JPY/(1 + s)Y.
If the time preference rate is constant (r = s), as the exponentially discounted utility
model assumes, then X/(Y – 1) = 1 holds. However, the discounted utility anomaly X/(Y– 1) < 1 is frequently observed, so the time preference rate decreases for time delay (r >s). The main reason for this is the immediacy effect, wherein people tend to lay moreemphasis on an immediate reward as opposed to a delayed one (Fredrick et al. 2002).
For example, in Question 1, because Alternative 1 consists of an immediate reward,
Alternative 2 requires that X be a relatively small figure (for example, one year). On theother hand, in Question 2, because Alternative 1 consists of a one-year-delayed reward,
Alternative 2 requires that Y be a large figure (for example, three years). The time
consistency index is defined as X/(Y – 1). X/(Y – 1) = 1 indicates perfect consistency,
while X/(Y – 1) = 0 indicates perfect inconsistency. It follows that X/(Y – 1) = 0.5 forthe example above. In this way, I classify the samples as time consistent if X/(Y – 1) = 1
and time inconsistent otherwise.
Table 1 (right row) summarizes the proportions of the samples that are time
inconsistent. The proportions are 0.299 for non-smokers and 0.352 for smokers,
indicating that the behaviors of non-smokers are more consistent with the discounted
utility hypothesis than those of smokers. For smokers, the proportions are as follows:
0.330 for L-smokers, 0.324 for M-smokers, and 0.440 for H-smokers, indicating thathigh nicotine dependence is associated with a less consistent time preference. The
proportions are 0.297 for never-smokers and 0.305 for ex-smokers, showing that thetendency is similar for these groups.

8

3.2. Impatience and immediacy parameters
I now simultaneously measure the impatience and immediacy parameters (along withthe risk preference coefficients) at the individual level using the DCE and ML model
analysis. An advantage of simultaneously measuring the time preference rate and risk
preference coefficient is that the time preference rate can be identified without assuming
a utility functional form (risk preference coefficient) ad hoc. Andersen et al. (2008)
argued that allowing for risk preference leads to a significant difference in the elicited
discount rates.
The stated preference method (conjoint analysis) was used to simultaneously measuretime and risk preferences for 494 valid respondents. Conjoint analysis assumes that aservice is a profile composed of attributes. If I include too many attributes and levels,
respondents find it difficult to answer the questions. On the other hand, if I include toofew, the description of the alternatives becomes inadequate. After conducting several
pretests, I determined the following alternatives, attributes, and levels.
Alternative 1
Reward, probability, and delay are fixed across profiles.
Reward: 100,000 JPY (1,000 US$)
Winning probability: 100%
Time delay: None
Alternative 2
Reward, probability, and delay vary across profiles.
Reward is either 150,000 JPY (1,500 US$), 200,000 JPY (2,000 US$), 250,000
JPY (2,500 US$), or 300,000 JPY (3,000 US$).
The winning probability is 40, 60, 80, or 90%.
The time delay is 1 month, 6 months, 1 year, or 5 years.
Because the number of profiles would become unmanageable if I considered all
possible combinations, I avoid this problem by adopting an orthogonal planning method.
Figure 2 depicts a representative questionnaire. I posed eight questions to each
respondent.
9<Figure 2>
Next, I explain the basic models for estimating the impatience and immediacy
parameters for the time-consistent and time-inconsistent samples, respectively.
Time-Consistent Samples
Let the utility of alternative i be Vi (rewardi, probabilityi, timedelayi). The
exponentially discounted and expected utility model is assumed for time-consistentsamples to derive the functional form of Vi as follows:
Discounted utility: exp(–IMPATIENCE*timedelayi)*utility (rewardi),
where IMPATIENCE denotes the constant rate of time preference.
Expected utility7: probabilityi*utility (rewardi).
Accordingly, rewriting Vi, I obtain
Vi (rewardi, probabilityi, timedelayi)= exp(–IMPATIENCE *timedelayi)*probabilityi*utility(rewardi).
At this point, I simply specify the functional form of utility as the RISK-th power ofreward. Such a utility function is called the constant relatively risk-averse form, where
the coefficient of the relative risk aversion is denoted by 1-RISK. Taking the logarithmof both sides, I obtainln Vi (rewardi, probabilityi, timedelayi)= –IMPATIENCE*timedelayi + ln probabilityi + RISK*ln rewardi.

7

If we consider index s as the state of nature (s = 1,…, S), the expected utility is written

as Σ s = 1,…, S probabilitys*utility(rewards). Note that here we simply assume that eachalternative has only one state of nature other than the state of zero reward.
10

Time-Inconsistent Samples
Next, the quasi-hyperbolically discounted and expected utility model is assumed fortime-inconsistent samples as follows:
Discounted utility:
IMMEDIACY*exp(–IMPATIENCE*timedelayi)*utility(rewardi),
where IMMEDIACY indicates the immediacy effect, while IMPATIENCE
denotes the constant rate of time preference.
Expected utility: probabilityi*utility(rewardi).
Accordingly, rewriting Vi, I obtain
Vi (rewardi, probabilityi, timedelayi)= IMMEDIACY*exp(–IMPATIENCE*timedelayi)*probabilityi*utility(rewardi).
Again, taking the logarithm of both sides, I obtainln Vi (rewardi, probabilityi, timedelayi)= ln IMMEDIACY – IMPATIENCE*timedelayi + ln probabilityi + RISK*ln rewardi.
Thus, IMPATIENCE is estimated for both the time-consistent and time-inconsistentsamples, while IMMEDIACY is estimated only for the time-inconsistent samples. (Idelete ln before IMMEDIACY for simplification for the moment.)
Finally, I explain the estimation models. Conditional logit (CL) models, whichassume independent and identical distribution (IID) of random terms, have been widelyused in previous studies. However, the property of independence from the irrelevantalternatives (IIA), which is derived from the IID assumption of the CL model, is toostrict to allow for flexible substitution patterns. The most appropriate scheme is an ML
model that accommodates differences in the variance of random components (orunobserved heterogeneity). Such models are flexible enough to overcome thelimitations of CL models by allowing random taste variation, unrestricted substitution
patterns, and the correlation of random terms over time. See the Appendix for details on
11

the ML models.
In what follows, I assume that the preference parameters—IMMEDIACY,
IMPATIENCE, and 1-RISK—follow a normal distribution. One can demonstrate variety
in the parameters at the individual level with the maximum simulated likelihood (MSL)
method for estimation using 100 Halton draws. 8 Furthermore, as the respondents
answered eight questions as part of the conjoint analysis, the resultant data form a panelthat offers the option of applying a standard random effect estimation. One can now
calculate the estimator of the conditional mean of the random parameters at theindividual level.
Table 2 summarizes the measurement results; the values represent the means andstandard deviations. They are seemingly too complicated and difficult to interpret. The
basic fact that smokers are more impatient than non-smokers is observed. The measured
IMPATIENCE values, or monthly time preference rates, are 6.2% for smokers and 5.6%
for non-smokers. The detailed results for smokers are as follows: 4.8% for L-smokers,
6.3% for M-smokers, and 6.4% for H-smokers, indicating that the heavier smokers are
more impatient.
<Table 2>
Note that the measured time preference rates are very high compared with the rates inthe economic literature. This is partly because I estimated the preferences using the
hypothetical survey; the absent income constraints framework leads to biased responses.
Furthermore, the discount factor is a function of the time horizon, which I partly addressby the immediacy effect, and this is conspicuous when I consider intertemporal choicewithin one year. Fredrick et al. (2002) pointed out that there has been tremendous
variability in discount rate estimation (from negative to infinity).
It can be seen, on the other hand, that simultaneously measuring the impatience andimmediacy parameters leads to some unexpected results. Although smokers (0.98) havehigher IMMEDIACY than non-smokers (0.85), M-smokers (0.69) have lower
8

The adoption of the Halton sequence draw is an important issue to be examined(Halton 1960). Bhat (2001) found that 100 Halton sequence draws are more efficientthan 1,000 random draws for simulating an ML model.
12

IMMEDIACY than L-smokers (1.32) and H-smokers (1.28). This may mean thatM-smokers suffer the least from present bias.
Another anomaly is observed in that the measured 1-RISK values are negative,
indicating that the samples are somewhat risk-prone. This is a counter-intuitive result.
However, all the coefficients of relative risk aversion are not statistically significant,and therefore, the respondents are totally risk-neutral. It may be because the functional
forms that I have assumed are so specific that the unobserved interdependencies among
the parameters are not sufficiently addressed.9
Although many studies have investigated the relationship between smoking andattitudes toward risk, the issue remains inconclusive (Mitchell 1999, Reynolds et al.
2003, Ohmura et al. 2005)10. I reserve final judgment on the results for the moment,
because my purpose is to investigate whether the impatience and immediacy parameters
are associated with smoking, including nicotine dependence.

4. ESTIMATION MODEL AND RESULTS
In this section, I explain the ordered probit model with a sample selection equation andthen discuss the estimation results.

4.1. Estimation model
I begin by explaining the estimation model that I adopted. The decision to smoke can be
decomposed into two steps. First, one simply decides whether to smoke. Next, one
decides how much to smoke, namely, one’s degree of nicotine dependence. This
two-step decision is considered an ordered probit model (in which nicotine dependence
9

It will be a topic for future research to consider the general approaches that recent

research has advocated. For example, Andersen et al. (2008) simultaneously measured
time and risk preferences and allowed the discounted utility function to take many
alternative functional forms (e.g., exponential, hyperbolic, and so on).
10Gerking and Khaddaria (2011) have interestingly reported that perceived risk deters
smoking among young people who have the good belief about the health damage fromsmoking but do not affect the smoking status of those who hold the opposite belief.
13

is classified into three groups, depending on FTND scores) with a binomial probit
model (in which smoking is denoted by 1 and non-smoking by 0). I now comment on
the ordered probit model with the sample selection equation.
The selection equation is a binominal probit model written as follows:
di* = α ' Zi + ui ,(1)

di = 1 if di* > 0 and 0 otherwise.

The structural equation is an ordered probit model written as follows:

yi* = β ' Xi + ε i , ε i  F(ε i | θ ), E[ε i ] = 0, Var[ε i ] = 1,

yi = 0 if yi * ≤ 0,(2)

= 1 if 0 ≤ yi * ≤ µ,

= 2 if µ ≤ yi * .

The system [yi , Xi ] is observable if and only if di = 1 holds. Selectivity matters if

ρ is not equal to zero:[ε i ,ui ]  N[0, 0,1,1, ρ ].

(3)

The full information maximum likelihood (FIML) method is used to estimate theparameters, including ρ . FIML reduces to the limited information maximum
likelihood (LIML) method if ρ = 0 holds.
The explained variables are given as follows. In the binomial model, the dummy
variable is 1 for smoking and 0 for non-smoking; in the ordered probit model, thevariable for nicotine dependence ranges from 0 (low) to 2 (high).
The explanatory variables are given as follows. First, the individual characteristic
variables are a female dummy variable (GENDER = 0 for male, 1 for female), age(AGE), age squared (AGESQ), school history (SCHOOL = 1 for junior high school, 2
for high school, 3 for university, and 4 for graduate school), and annual householdincome (INCOME, million JPN). Next, the following are the economic-psychologicalparameters that were previously introduced: the immediacy effect (IMMEDIACY), therate of time preference (IMPATIENCE), and the rate of risk preference (1-RISK).
14

4.2. Estimation Results
I begin the discussion of the estimation results, which are shown in Table 3, with theresults of the binomial probit model.11 The female dummy and school history are
negatively associated with smoking probability, while the age variable is reverse
U-shaped (with the peak around 51 years old). Further, annual household income does
not influence smoking probability. The risk preference rate does not have a significant
influence. Turning to the two key parameters, both IMPATIENCE and IMMEDIACY aresignificantly associated with smoking probability. In the following section, I investigate
the detailed influence of those parameters on smoking behavior.
Then, I discuss the results of the ordered probit model. The female dummy andschool history are negatively associated with nicotine dependence, while age ispositively associated with nicotine dependence. Further, annual household income does
not influence nicotine dependence. The risk preference rate positively influences
nicotine dependence. Similar to the results of the binomial probit model, both
IMPATIENCE and IMMEDIACY are significantly associated with nicotine dependence.
<Table 3>

5. DISCUSSIONSIn this section, I investigate the comprehensive effects of the time preference rate
(IMPATIENCE) and the immediacy effect (IMMEDIACY) on the decision to smoke andon nicotine dependence.
The elasticities of smoking probability for these parameters are displayed in Table 4.
Note that the elasticities are measured around the mean values. The first hypothesis isestablished for the elasticities of smoking probability with respect to the time preference
rate.

11

At first, I conducted the FIML estimation, but I could not reject the null hypothesis(i.e. ρ = 0 ). Then, I carried out the LIML estimation.
15

<Table 4>
Hypothesis 1: IMPATIENCE and smoking probability
The higher the time preference rate, the higher the smoking probability.
I tested this hypothesis and obtained the following result.
Result 1: Hypothesis 1 is verified.
A 1% increase in the time preference rate significantly increased smoking probability
by 0.9384% with 1% significance.
Smoking involves considerations such as current stress relief and future healthdamage. This explains the positive correlation between the time preference rate andsmoking probability. The finding that smokers are more impatient than non-smokers
with regard to delay discounting is consistent with previous research (Mitchell 1999,
Bickel et al. 1999, Odum et al. 2002, Baker et al. 2003, Reynolds et al. 2004, Ohmura etal. 2005).
At this point, a reservation must be noted. This research only investigated therelationship between smoking and time preferences. I reserve judgment about causality
because I cannot determine whether an impatient person tends to smoke or whether asmoker tends to become impatient. A detailed study of causality lies outside the scopeof this paper. This is the most crucial area for future research12.
The second hypothesis is established for the elasticities of smoking probability withrespect to the immediacy effect.
Hypothesis 2: IMMEDIACY and smoking probability
The higher the immediacy effect, the higher the smoking probability.

12

Education is considered to be an important predictor of health. Van der Pol (2011) has

investigated the role of time preference in the relationship between education and health,concluding that the effect of education reduces but does not disappear after controlling
for time preference rates.
16

I obtained the following result.
Result 2: Hypothesis 2 is verified.
A 1% increase in the immediacy effect increased the smoking probability by
0.2753% with 5% significance.
Consequently, the immediacy effect also successfully accounts for smoking decisions.
This is the most important finding of the paper. If one supposes that smoking resultsfrom discounted utility anomalies, higher consistency naturally leads to lower smoking
probability. Several studies have regarded addiction as time-inconsistent behavior. For
example, Gruber and Koszegi (2001) demonstrated that some smokers failed torecognize

the

true

difficultyofquitting.

Kan(2007)

empiricallystudiedtime-inconsistent preferences in the context of cigarette smoking behavior andconcluded that some smokers who wanted to quit had a demand for control devices, e.g.,smoking bans in public areas or hikes in cigarette taxes. Result 2 is consistent with thesestudies.
Next, the elasticities of nicotine dependence with respect to the impatience andimmediacy parameters are displayed in Table 5. The third hypothesis is established forthe elasticities of nicotine dependence with respect to the time preference rate.
<Table 5>
Hypothesis 3: IMPATIENCE and nicotine dependence
The higher the time preference rate, the higher the nicotine dependence.
I tested the above hypothesis and obtained the following result.
Result 3: Hypothesis 3 is verified.
A 1% increase in the time preference rate decreased the proportion of low
nicotine-dependent smokers by 0.9324% with 5% significance but increased the
proportion of highly nicotine-dependent smokers by 0.9522% with 1% significance.
However, a 1% increase in the time preference rate did not influence the proportionof moderately nicotine-dependent smokers.
17

In light of this result, the time preference rate accounts for the higher and lower
degree of nicotine dependence, which is consistent with the findings of previous
research. For example, Reynolds et al. (2004) reported a significant positive correlation
between the number of cigarettes smoked daily and the time preference rate, andOhmura et al. (2005) suggested that both the frequency of nicotine self-administration
as well as the dosage were positively associated with greater delay discounting.
The fourth hypothesis is established for the elasticities of nicotine dependence withrespect to the immediacy effect.
Hypothesis 4: IMMEDIACY and nicotine dependence
The higher the immediacy effect, the higher the nicotine dependence.
I obtained the following result.
Result 4: Hypothesis 4 is verified.
A 1% increase in the immediacy effect decreased the proportion of low
nicotine-dependent smokers by 0.5444% with 10% significance but increased the
proportion of highly nicotine-dependent smokers by 0.4259% with 5% significance.
However, a 1% increase in the immediacy effect did not influence the proportion ofmoderately nicotine-dependent smokers.
The immediacy effect also successfully accounts for nicotine dependence; thisfinding is consistent with previous research. For example, Gruber and Koszegi (2001)
developed a new model of time inconsistency and argued that government policy should
consider not only the externalities that smokers impose on others but also theinternalities imposed by smokers on themselves. In this context, we can consider theconcept of libertarian paternalism advocated by Thaler and Sunstein (2008). They insist
that with bounded rationality, it is preferable to maintain freedom of choice on the one
hand, as well as to design private and public institutions for improving people’s welfare
on the other hand13. In conclusion, both impatience and immediacy can suitably account13

It is important to distinguish the welfare effects of happy and unhappy addicts. De
18

for smoking and nicotine dependence.

6. CONCLUSIONSThis paper investigated smoking status, including nicotine dependence, on the basis of aquasi-hyperbolic discounting approach, which reconciled the rational addiction modeland the bounded rational addiction model. First, from the analysis of whether theimpatience parameter was associated with smoking, it was found that the time
preference rate significantly increased smoking probability. Furthermore, it was foundthat the higher the immediacy effect, the higher is the smoking probability. Second,from the investigation into how immediacy can elucidate nicotine dependence, it was
discovered that immediacy, along with impatience, was positively associated with
nicotine dependence. Thus, it became clear that both impatience and immediacyfunction as good predictors of smoking status.
The above results mark a breakthrough in smoking research. However, someunsolved problems remain. As this research investigated only the relationship between
smoking and time preferences, I reserve judgment about causality because I cannot
determine whether an impatient person tends to smoke or whether a smoker tends tobecome impatient. A detailed study of causality lies outside the scope of this paper. Thisis a crucial area for future research. Furthermore, I assumed that delay and risk weredistinguished by the questionnaires. However, the literature, including Rachlin et al.
(1991) and Sozou (1998), has demonstrated that both risk and delay of reward elicitedthe same underlying form of intolerance, because the value of a future reward should be
discounted such that there exists a risk that the reward will not be realized. On the other
hand, other studies such as Green and Myerson (2004) have shown that time andprobability discounting are different and dissociable processes. I consider these issues
as potential topics for future research.

Chaisemartin et al. (2011) have recently discussed that workplace smoking ban may
improve happy addicts’ welfare.
19

APPENDIX. ML MODEL
Assuming that parameter β n is distributed with density function f ( β n ) , the ML
specification allows for repeated choices by each sampled decision maker in such a waythat the coefficients vary over people but are constant over choice situations for each
person (Train 2003). The logit probability of decision maker n choosing alternative i inchoice situation t is expressed as
Lnit ( β n ) = ∏ t =1[exp(Vnit ( β n )) / ∑ j =1 exp(Vnjt ( β n ))] ,JTwhich is the product of normal logit formulas, given parameter β n , the observable
portion of utility function Vnit , and alternatives j=1, …, J in choice situations t = 1, …, T.
Therefore, the ML choice probability is a weighted average of logit probability
Lnit ( β n ) evaluated at parameter β n with density function f ( β n ) , which can be written

asPnit = ∫ Lnit ( β n ) f ( β n )dβ n .
In the linear-in-parameter form, the utility function can be written as
U nit = β n ' xnit + ε nit ,where xnit denotes observable variables, β n denotes a random parameter vector, andε nit denotes an independently and identically distributed extreme value (IIDEV) term.
Since ML choice probability is not expressed in closed form, simulations need to be
performed for the ML model estimation (see Train 2003, p. 148 for details). One canalso calculate the estimator of the conditional mean of the random parameters,
conditioned on individual specific choice profile yn , given ash( β | yn ) = [P( yn | β ) f ( β )] / ∫ P( yn | β ) f ( β )d β .
Here, I assume that the preference parameters—IMPATIENCE, IMMEDIACY, and
RISK—follow a normal distribution.

20

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24

TABLE 1: Basic Demographics

38.14

UNIVERSITYGRADUATION
RATIO
0.697

AVERAGEHOUSEHOLD
INCOME (JPY)
6.3 M

TIME
INCONSISTENT
RATIO
0.299

35.26

0.714

6.1 M

0.297

0.644

7.2 M

0.305

40.48

0.462

5.9 M

0.352

0.485

38.30

0.505

5.7 M

0.330

111

0.315

40.86

0.450

6.3 M

0.324

45

0.222

44.22

0.400

5.5 M

0.467

SAMPLE NO.

FEMALERATIO

AVERAGEAGE

NON-SMOKER

241

0.515

NEVER-SMOKER

182

0.566

EX-SMOKER

59

0.356

SMOKER

253

0.364

L-SMOKER

97

M-SMOKER
H-SMOKER

25

FIGURE 1: Research Strategy
At the 1st StageClassifying the samples:

Time-consistent samples

Time-inconsistent samples

Impatience parameter

Impatience parameterAt the 2nd Stage
Measuring the parameters:

Immediacy parameter

26

FIGURE 2: Representative Questionnaire	
 ALTERNATIVE 1	 ALTERNATIVE 2

REWARD	 JPY 100,000	 JPY 250,000

TIME DELAY

	
 

NOW

	
 

1 MONTH LATER

WINNING PROBABILITY

	
 

100%

	
 

80%

CHOOSE ONE

↓

↓

	
 

	
 

27

TABLE 2: Impatience, Immediacy, and Risk Parameters

NON-SMOKER
NEVER-SMOKER
EX-SMOKER
SMOKER
L-SMOKER
M-SMOKER
H-SMOKER

IMPATIENCE

ln IMMEDIACY

1-RISK

MEAN

0.0564 (0.0136) ***0.8453 (0.4424) *-0.2356 (0.2686)

S.D.

0.0336 (0.0146) ***0.0087 (0.4748)

0.4383 (0.3676)

MEAN

0.0497 (0.0101) ***0.8909 (0.3852) **-0.1816 (0.2112)

S.D.

0.0238 (0.0099) **0.0085 (0.4093)

0.2502 (0.3594)

MEAN

0.0325 (0.0075) ***0.70475 (0.6188)-0.0832 (0.4456)

S.D.

0.00018 (0.01585) **0.0095 (0.6767)

1.0970 (0.4257) **MEAN

0.0622 (0.0221) ***0.9797 (0.5332) *-0.3244 (0.3634)

S.D.

0.0358 (0.0230) *0.1071 (0.6233)

0.7130 (0.4050) *MEAN

0.0484 (0.0147) ***1.3246 (0.5045) ***-0.4076 (0.3236)

S.D.

0.0250 (0.0198)

0.0053 (0.4272)

0.6328 (0.3400) *MEAN

0.0625 (0.0139) ***0.6938 (0.4735)-0.1486 (0.3156)

S.D.

0.0310 (0.0147) **0.1089 (0.4572)

0.8685 (0.2689) **MEAN

0.0643 (0.0384) *1.2779 (0.6470) **-0.5779 (0.5605)

S.D.

0.0428 (0.0445)

0.0380 (0.6297)

0.7008 (0.7525)

Note1: The values in parentheses denote the standard errors of MEAN and S.D. estimates for the randomparameters. *** 1% significant level (p<0.01), ** 5% significant level (p<0.05), * 10% significant level(p<0.1).
Note2: IMPATIENCE and 1-RISK are estimated for both time-consistent and time-inconsistent samples,while ln IMMEDIACY is estimated only for the time-inconsistent samples.

28

TABLE 3: Estimation Results
SAMPLE NO.

494

LOG LIKELIHOOD-535.02089
Coefficient

S.E.

IMPATIENCE

21.88592.90418***

ln IMMEDIACY

0.445960.20906**

GENDER-0.44718

0.12007***AGE

0.048930.01851***

AGE SQUARED-0.00048

0.00023**SCHOOL-0.58687

0.09891***

INCOME (M JPY)
1-RISK-0.0105
0.123170.01771
0.16209

IMPATIENCE

19.5937

7.0520***ln IMMEDIACY

0.5696

0.2660**GENDER-0.5938

0.2189***AGE

0.03900.0191**AGE SQUARED-0.0001

0.0002SCHOOL-0.46630.2477

INCOME (M JPY)

0.01170.01881-RISK
THRESHOLD PARAMETER

0.50691.848190.15570.12452

BINOMIAL PROBIT MODEL

ORDERED PROBIT MODEL

*
***
***

Note: *** 1% significant level (p<0.01), ** 5% significant level (p<0.05), * 10% significant level(p<0.1).

29

TABLE 4: Smoking Probabilities Elasticities for Binomial Probit Model

IMPATIENCEIMMEDIACY

Elasticity

S.E.

0.93840.27530.12380.1292

Note 1: *** 1% significant level (p<0.01), ** 5% significant level (p<0.05).
Note 2: The IMMEDIACY elasticities are calculated only for the time-inconsistent samples.

30

TABLE 5: Nicotine Dependence Elasticities for Ordered Probit Model

L-SMOKER
IMPATIENCEIMMEDIACY

M-SMOKER
IMPATIENCEIMMEDIACY

H-SMOKER
IMPATIENCEIMMEDIACY

Elasticity-0.9324-0.5444S.E.
0.44610.3058

Elasticity
0.83410.3117

S.E.
0.68930.2735

Elasticity
0.95220.4259S.E.
0.26380.1812







Note 1: *** 1% significant level (p<0.01), ** 5% significant level (p<0.05).
Note 2: The IMMEDIACY elasticities are calculated only for the time-inconsistent samples.

31