In July 2008, we surveyed 494 Japanese adults registered with a consumer monitoring investigative company. Our survey was conducted before the radical increase of tobacco in October 2010. We here note that the results may be affected by the small sample properties. The sample was adjusted to reflect Japanese demographics in terms of gender, average age, and geographical features. A total of 150 Japanese Yen (JPY) (1.5 US$, given 100 JPY = 1 US$) was paid to respondents to the basic survey questionnaire and 500 JPY (5 US$) was paid to respondents to the discrete choice experiments questionnaire described below. Respondents who answered in an unrealistically short period of time were excluded from the final sample.
By aggregating the responses, we defined respondents with 0 to 3 points as low cigarette dependence (L-smokers), 4 to 6 points as moderate cigarette dependence (M-smokers), and 7 and over as high cigarette dependence (H-smokers). Altogether, 38.3% of respondents were L-smokers, 43.8% M-smokers, and 17.8% H-smokers. The proportions of female and university graduates were highest for L-smokers, average age was highest for H-smokers, and average income level was highest for M-smokers.
The higher the time preference rate, the higher is smoking probability.
The higher the present bias effect, the higher is smoking probability.
The higher the time preference rate, the higher is cigarette dependence.
The higher the present bias effect, the higher is cigarette dependence.
STEP 1: classifying respondents as time consistent or time inconsistent
The standard theory of decision making over time is based on the exponentially discounted utility model, whose key assumption is a stationarity axiom. This axiom implies that if and only if the utility of 100,000 JPY in the present is preferred to the utility of 150,000 JPY after one year, then the utility of 100,000 JPY after 10 years is preferred to the utility of 150,000 JPY after 11 years, because the implicit discount factor should be the same in both cases.
We assume an intertemporal consumption decision with consumption in the current year (
C0) and in the following year (
C1). This representation makes clear that the marginal rate of substitution (MRS) at an agent’s chosen consumption bundle (or the observed gross rate of time preference) depends on two factors: constant pure time preference (
δ) and diminishing marginal utility (
U′(
C0)/
U′(
C1)) because
(1)
Frederick et al. [
9] pointed out that economists are not comfortable using the term “time preference” to include the effects of differential marginal utility arising from unequal consumption levels between time periods. In that sense, economists tend to focus on the exponentiality of the pure rate of time preference
b.
Assuming here 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:
(2)
Note that ε is a positive constant.
At this point, the exponentially discounted utility model gives
U(X)/(1 + r)
t
≥
U(Y)/(1 + r)
s
for
t and
s. However, the discounted utility anomaly of a present-smaller reward being excessively preferred to a delayed-larger reward indicates the following inconsistent preference orders:
(3)
This anomaly is called
time inconsistency, which is sometimes referred to as
decreasing impatience (Strotz [
10]; Prelec [
11]). For example, Takahashi [
12] demonstrated that time inconsistency is proportional to the Arrow–Pratt concavity of nonlinear time perception (i.e., decreasing impatience).
I asked respondents two hypothetical questions in order to investigate the discounted utility anomaly:
Question 1
Alternative 1: Receive 100,000 JPY (1,000 US$) immediately.
Alternative 2: Receive 150,000 JPY (1,500 US$) after T years.
What T makes the two alternatives equivalent?
Question 2
Alternative 1: Receive 100,000 JPY (1,000 US$) after one year.
Alternative 2: Receive 150,000 JPY (1,500 US$) after S years.
What S makes the two alternatives equivalent?
Based on the exponentially discounted utility model, when the utility of 100,000 JPY in the present equals the utility of 150,000 JPY
after T years, I obtain the following equation:
(4)
Note that r denotes the annual time preference rate.
Further, when the utility of 100,000 JPY
after one year equals the utility of 150,000 JPY
after S years, I obtain the following equation:
(5)
If the time preference rate is constant (
r = q), as the exponentially discounted utility model assumes, then
T/(S – 1) = 1 holds. However, the discounted utility anomaly
T/(S – 1) < 1 is frequently observed, so the time preference rate decreases for time delay (
r > q). The main reason for this is the
present bias effect, wherein people tend to place disproportionally more emphasis on an immediate reward as opposed to a delayed one (Frederick, et al. [
9]). For example, in Question 1, because Alternative 1 consists of an immediate reward, Alternative 2 requires that
T be a relatively small figure (e.g., one year). By contrast, in Question 2, because Alternative 1 consists of a one-year-delayed reward, Alternative 2 requires that
S be a large figure (e.g., three years). The time consistency index is defined as
T/(S – 1). T/(S – 1) = 1 indicates perfect consistency, while
T/(S – 1) = 0 indicates perfect inconsistency. It follows that
T/(S – 1) = 0.5 for the example above. In this way, I classify the samples as time consistent if
T/(S – 1) = 1 and time inconsistent otherwise. One limitation is that I use only two questions to address the discounted utility anomaly. It would be desirable in future research to present a greater number of questions and classify the degree of anomaly into multiple levels.
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 0.330 for L-smokers, 0.324 for M-smokers, and 0.440 for H-smokers, indicating that high cigarette dependence is associated with a less consistent time preference. Moreover, the proportions are 0.297 for those that had never smoked and 0.305 for ex-smokers, showing that the tendency is similar for these groups.
STEP 2: estimating the time and risk preference parameters
The methodology of measuring the preference parameters in this study follows the approach presented by Ida and Goto [
13], who surveyed 692 respondents to simultaneously assess time and risk preferences by using the choice-based DCE model, finding that smokers are more impatient and more risk-prone than non-smokers. However, they failed to differentiate present bias and the constant time preference rate. To address this shortcoming, a new survey was conducted in the present study by adding the STEP 1 questionnaire in August 2008 (Ida [
14]). Respondents were classified as time consistent or time inconsistent based on the exploratory open-ended matching method. I then separately measured the constant time preference and present bias parameters (along with the risk preference coefficients) at the individual level in STEP 2.
Based on the foregoing, the DCE model was used herein to simultaneously measure the time and risk preferences of the 494 respondents, given that an alternative is a profile composed of attributes. In Alternative 1, the baseline alternative, the levels of the reward, probability, and delay were fixed across profiles, whereas these attributes varied across profiles in Alternative 2. After conducting several pretests, I thus determined the alternatives, attributes, and levels presented in Table
2.
Table 2
Attributes and levels
Attributes | Levels |
Reward: | 100,000 JPY |
(1,000 US$) |
Winning probability: | 100% |
Time delay: | None |
Alternative 2
|
Attributes | Levels |
Reward: | 150,000 JPY | 200,000 JPY | 250,000 JPY | 300,000 JPY |
(1,5000 US$) | (2,000 US$) | (2,500 US$) | (3,000 US$) |
Winning probability: | 40% | 60% | 80% | 90% |
Time delay: | 1 month | 6 months | 1 year | 5 years |
Because the number of profiles would become unmanageable if all possible combinations were considered, an orthogonal planning method was adopted. The 16 questions were divided into two versions, and respondents were asked to answer either version. Therefore, I posed eight questions to each respondent.
Next, in the quasi-hyperbolic discount function (Laibson [
2]), lifetime utility from present period 0 onwards is given by
(6)
where
μ
t
is periodic utility, the parameter
β denotes present bias, and
δ is the standard exponential discount factor.
Time-consistent samples
Let the utility of alternative
i be
V
i
(reward
i, probability
i, timedelay
i). The exponentially discounted and expected utility model is assumed for time-consistent samples to derive the functional form of
V
i
as follows:
(7)
where
δ denotes the constant rate of time preference.
I specify the functional form of utility as the
γ-th power of reward. Such a utility function is called the constant relatively risk-averse form, where the coefficient of relative risk aversion is denoted by 1-
γ. By taking the logarithm of both sides, I obtain
(8)
Time-inconsistent samples
The following quasi-hyperbolically discounted and expected utility model is assumed for the time-inconsistent sample:
(9)
where
β denotes present bias, 1[timedelay
i] is an index function for a delayed reward in alternative 2, and
δ is the constant rate of time preference.
Again, by taking logarithms and assuming a constant relative risk-averse form (
γ), I obtain
(10)
Thus, δ is estimated for both the time-consistent and the time-inconsistent samples, while β is estimated only for the time-inconsistent sample.
Finally, conditional logit (CL) models, which assume the independent and identical distribution (IID) of random terms, have been widely used in previous studies. Recently, the most appropriate scheme to adopt has been a random parameters (or mixed) logit (RPL) model, which can accommodate differences in the variance of random coefficients. Such models are flexible enough to overcome the limitations of CL models by allowing random taste variation, unrestricted substitution patterns, and the correlation of random terms by choice situation. Fiebig et al. [
15] argued, furthermore, that much of the heterogeneity in attribute coefficients is accounted for by scale heterogeneity and thus that the scale of their error term is allowed to be larger for some consumers than others by fixing the attributes’ coefficients. A generalized mixed (or scaled random parameters) logit model that includes a free-scale parameter to be estimated was adopted in this work. See Appendix for the technical details.
It is assumed here that the random parameters follow a normal distribution. One can demonstrate variety in the parameters at the individual level by using the maximum simulated likelihood method for estimation with 200 Halton draws. Further, as respondents answered eight questions as part of the DCE analysis, the resultant data form a panel that offers the option of applying a standard random effect estimation. Hence, the estimator of the conditional means of the random parameters can be calculated at the individual level (denoted by subscript n), β
n
, δ
n
, and γ
n
. These individual-level preference parameters are used as explanatory variables in the STEP 3 estimation.
Table
3 summarizes the measurement results. First, the basic fact that smokers are more impatient than non-smokers is observed: the measured
constant monthly time preference rates (
δ
n
) are 6.8% for smokers and 5.6% for non-smokers. Specifically, these rates are 5.9% for L-smokers, 8.0% for M-smokers, and 8.6% for H-smokers, indicating that heavier smokers are more impatient.
Table 3
Impatience, present bias, and risk parameters
Non-smoker | -587.7 | 0.3299 (0.1197) | Mean | -0.0556 (0.0098)*** | 0.4578 (0.1909)*** | -0.2283 (0.2065) |
(N = 241) | S.D. | 0.0346 (0.0101)*** | 0.0617 (0.0790) | 0.4064 (0.2101)* |
Never-smoker | -440.1 | 0.2318 (0.1652) | Mean | -0.0542 (0.0131)*** | 0.4207 (0.1956)** | -0.2172 (0.2438) |
(N = 182) | S.D. | 0.0261 (0.0120)** | 0.0875 (0.0976) | 0.0207 (0.7300) |
Ex-smoker | -140.1 | 0.2718 (0.2341) | Mean | -0.0700 (0.0253)*** | 0.5365 (0.5339) | -0.3697 (0.4689) |
(N = 59) | S.D. | 0.2077 (0.1219)* | 0.0562 (0.0316)* | 0.8366 (0.4635)* |
Smoker | -57105 | 0.3575 (0.1073)*** | Mean | -0.0683 (0.0133)*** | 0.3619 (0.1137)*** | -0.3658 (0.2186) |
(N = 253) | S.D. | 0.0421 (0.0127)*** | 0.0276 (0.1055) | 0.6265 (0.2108)*** |
L-smoker | -226.2 | 0.3900 (0.2694) | Mean | -0.0587 (0.0211)*** | 0.2685 (0.1076)** | -0.4843 (0.3617) |
(N = 97) | S.D. | 0.0341 (0.0192)** | 0.0072 (0.1253) | 0.6083 (0.3096)** |
M-smoker | -255.6 | 0.3575 (0.1461)** | Mean | -0.0802 (0.0226)*** | 0.5677 (0.5316) | -0.2035 (0.3468) |
(N = 111) | S.D. | 0.0465 (0.0188)** | 0.1129 (0.3377) | 0.7142 (0.3870)* |
H-smoker | -93.8 | 0.3575 (0.1908)* | Mean | -0.0855 (0.0365)** | 0.2876 (0.1597)* | -0.5267 (0.5171) |
(N = 45) | S.D. | 0.0639 (0.0334)* | 0.0305 (0.1605) | 0.3395 (1.1399) |
Note that the measured time preference rates are very high compared with those presented in the economic literature, partly because I estimated the preferences using a hypothetical survey and because the absent income constraints framework leads to biased responses. Further, the discount factor is a function of the time horizon, which I partly address by the present bias effect, and this is conspicuous when I consider intertemporal choices within one year. Fredrick et al. [
9] also pointed out the huge variability in discount rate estimation (from negative to infinity).
However, simultaneously measuring the constant time preference (δ
n
) and present bias parameters (exp(β
n
)) leads to some unexpected results. Although smokers (0.36) have higher present bias than non-smokers (0.46), M-smokers (0.57) have lower present bias than L-smokers (0.27) and H-smokers (0.29). This finding may mean that M-smokers suffer the least from present bias.
Another counterintuitive result is that the measured risk values (1-
γ
n
) are negative. However, none of the coefficients of relative risk aversion is statistically significant. This finding may occur because the functional forms assumed herein are so specific that any unobserved interdependencies among the parameters are insufficiently addressed. Indeed, although many studies have investigated the relationship between smoking and attitudes toward risk, this issue remains inconclusive (Mitchell [
16]; Reynolds et al. [
17]; Ohmura et al. [
18]).
STEP 3: estimating smoking decision and cigarette dependency
The smoking decision can be divided into two steps: (i) the decision to start smoking and (ii) the degree of cigarette dependence. This two-step decision is considered to be an ordered probit model (in which cigarette dependence is classified into three groups depending on FTCD scores) with a binomial probit model (in which smoking is denoted by 1 and non-smoking by 0).
The selection equation is a binominal probit model written as follows (McKelvey, and Zavoina [
19]):
(11)
The structural equation is an ordered probit model written as follows:
(12)
As definitions of variables,
d
n
denotes the decision to start smoking,
y
n
denotes the degree of cigarette dependence, and
X
n
includes constant time preference, present bias, gender, age, age squared, the year of education, household income, and relative risk aversion. The system [
y
n
,
X
n
] is observable if and only if
d
n
= 1 holds. Selectivity matters if
ρ is not equal to zero:
(13)
The elasticities in the ordered probit model (w.r.t.
Χ
n
) can be calculated as the effects of changes in the covariates on each range of probability:
(14)
where
j = 0, 1, and
2 and
ϕ denotes normal density.
Elasticities are measured around the mean values.
The full information maximum likelihood method is then used to estimate the parameters, including ρ. This method reduces to the limited information maximum likelihood 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, while in the ordered probit model, the variable for cigarette dependence ranges from 0 (low) to 2 (high).
The explanatory variables are the present bias effect, the rate of time preference, and the rate of risk preference. Note that the present bias effect is measured as 1 − exp(β
n
) rather than exp(β
n
) at this point. The individual characteristic variables are dummy variables for gender (GENDER = 0 for male), age (AGE), age squared (AGESQ), year of education (EDUCATION), and annual household income (INCOME, million JPY).