GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.19

Time Discounting: Delay Effect and Procrastinating Behavior

Shunichiro Sasaki
Shiyu Xie
Shinsuke Ikeda
Jie Qin
Yoshiro Tsutsui

January 2009; revised March 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Time Discounting:
Delay Effect and Procrastinating BehaviorShunichiro Sasaki1(Nagoya University of Commerce and Business)
Shiyu Xie2
(Fudan University)
Shinsuke Ikeda3(Oasaka University)
Jie Qin4(Ritsumeikan University)
Yoshiro Tsutsui5（Osaka University and University of Amsterdam）

This research was supported by the 21st Century Centre of Excellence (COE) program at Osaka
University and Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports,
Science, and Technology in Japan.
1

Faculty of Economics, Nagoya University of Commerce and Business, 4-4 Sagamine,
Komenoki-cho, Nisshin, Aichi 470-0193, Japan. E-mail: ssasaki@nucba.ac.jp
2
Department of World Economics, Fudan University, 220 Handan Road, Shanghai 200433, P. R.
China. E-mail: syxie@fudan.edu.cn
3
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka
567-0047, Japan. E-mail: ikeda@iser.osaka-u.ac.jp
4
Faculty of Economics, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu,Shiga 525-8577,
Japan. E-mail: jieqinjp@yahoo.co.jp
5Corresponding author, Graduate School of Ecoonmics, Osaka University, 1-7 Machikaneyama,
Toyonaka 560-0043 Japan. E-mail: tsutsui@econ.osaka-u.ac.jp, Phone: +81-6-6850-5223, Fax:
+81-6-6850-5274

Abstract
This paper pursues two aims by conducting economic experiments in Shanghai. One aim of
this paper is to investigate the following three anomalies on time discounting: the delay,interval, and magnitude effects. We confirmed all the three anomalies. Particularly, by
separating the delay effect from the interval effect, the delay effect is found when the delay
is relatively short, which has seldom been reported in former studies. Another feature of ourexperiment is that it is immune to the criticism that the subjects recruited for the experiment
did not have sufficient incentives to report their true preferences because the highest rewardthat was offered to the subjects was approximately equivalent to their monthly householdincomes. The second aim of this paper is its explanation of the subjects’ procrastinating
behaviors by their time discount rates and the degrees of the delay effect. Our analysis
suggested that higher time discounting always promotes procrastination; however, the delay
effect is negatively associated with procrastination. An interpretation of the latter result canbe that our subjects, i.e., the students of Fudan University, are sophisticates rather thannaïfs.

JEL classification numbers: C91, D91
Keywords: discount rate, economic experiment in China, delay effect, naïfs andsophisticates, procrastination

11. Introduction
This study examines an economic experiment that was conducted in China for exploring
the manner in which people discount future values. Specifically, we focus on the following
two topics: one is whether the existence of the delay effect is actually independent of theinterval effect, and the other is whether procrastinating behavior can be explained with thetime discount rate and delay effect.
Although traditional economics has relied on the assumption of “exponential
discounting,” i.e., the time discount rate is constant over the time horizon, numerous
experimental studies have rejected the validity of the assumption (Ainslie 1975, Benzion etal. 1989, Kirby 1997, Kirby and Marakovic 1995, and Thaler 1981). This anomaly of
discounting, i.e., the discount rate is not constant over the time horizon, is termed the delay
effect, diminishing impatience, present bias, or hyperbolic discounting. In addition, it is awell-known fact that discount rates depend on the value to be discounted; the smaller thevalue, the more intensively it is discounted, and this is termed “the magnitude effect”(Benzion et al. 1989, Kirby and Marakovic 1995, Kirby 1997, and Thaler 1981).
However, most studies on delay effect encounter a problem. In experiments thus far,subjects were typically asked which of following two options they preferred: option A,
wherein the subjects will receive a reward in the near future, or option B, wherein thesubjects will receive a (usually larger) reward in the distant future. All options that wereshown in the question could neatly be identified with the following four experimental
conditions: date s and receipt of amount X in option A; and date t (t > s) and receipt ofamount Y (usually larger than X) in option B. With respect to these conditions, the delay2was termed s and the difference between the two points of time, t  s , was termed intervalh. In what follows, we termed the phenomenon where discount rates depended on the delay,“the delay effect,” on the interval, “the interval effect,” and on the reward amount, “themagnitude effect.”Thus, the two concepts of time, delay s and interval h, must be distinguished as thefactors that characterize intertemporal choices. Delay s is, among other things, the focal
point because if time discounting depends on the delay, a plan made by such a person will
be time-inconsistent. Nonetheless, most studies thus far have not separated the delay fromthe interval, and subjects have been asked to specify the amount of money that they would
require, at some future date, in order to make them indifferent to receiving a certain amountnow. In these studies, since the receipt time of the earlier option is fixed at now, their resultsmust be interpreted as an investigation of the interval effect rather than the delay effect or,at least, as a combination of these two effects.
Read (2001) was the first to highlight this problem. He conducted an experimentthat separated the delay from the interval. Although he observed a form of the interval
effect, he did not confirm the delay effect.1 However, although the delay effect exists evenwith a rather short delay (Frederick et al. 2002), the shortest delay used by Read was six

1

Recently, Read and Roelofsma (2003) and Read et al. (2005) reported that the delay effect isfound in experiments wherein subjects are asked questions in ways that differ from those in Read
(2001). Read and Roelofsma (2003) utilized the matching method, which asks subjects regarding
the amount at a specified date, which makes them indifferent to a specified option. This is different
from the choice method used in Read (2001) and in this study, which asks subjects to select thebetter of two specified options. On the other hand, Read et al. (2005) focused on how the timings ofthe two options are described and specified the timing with respect to the calendar dates. Thismethod is different from the method used in Read (2001) and this paper, which specified the lengthof the delay.

3months. Thus, whether subjects show the delay effect within a six-month delay period
remains an open question. Given these arguments, the primary aim of this study is to
re-examine whether the delay effect is in fact found when the delay and the interval are
explicitly distinguished. Our experiment differs from that of Read (2001) in that weinvestigated the delay effect using a much shorter delay than that used by Read (2001). 2
The second aim of this study is to explain the subjects’ procrastinating tendencies in
performing onerous activities (e.g., doing homework assignments) using their time discountrates and degrees of their delay effects. Although correlation between the delay effect (orthe present bias) and procrastination has often been predicted in literature (e.g.,
O’Donophue and Rabin, 1999), there is no empirical research on this important issue. This
study attempts to fill this gap. In order to do so, we measure the subjects’ degrees ofprocrastinating tendencies by asking them how often they procrastinated doing homeworkassignments in their childhood.
Intuitively, the delay effect is expected to lead to procrastinating behaviors becausewith delay effect people tend to always overweight immediate costs more than delayed
costs. The prediction in fact holds for naïve people who do not expect the future incidenceof preference reversal (see O’Donophue and Rabin, 1999). In contrast, in the case ofsophisticated people, who make decisions by incorporating preference shifts of future
selves, know that making future selves make decisions causes harmful procrastination andhave incentives to do onerous jobs earlier. As indicated by O’Donophue and Rabin (1999),
2

Kinari et al. (2009) examined the delay effect independent of the interval effect with Japanese
subjects and reported that the delay effect is found for a short delay. The current paper differs fromtheirs with respect to the method of presenting options. We present pairs of options in sequential
order of discount rates, whereas Kinari et al. (2009) presented them in random order.

4

if this incentive effect, called the sophistication effect, is sufficiently strong, thensophisticated people perform jobs earlier than exponential discounters would, and hence thedelay effect can be negatively correlated with procrastination.
One merit of our study is that in our experiments, we give the Chinese subjects strong
incentives, by offering high rewards to induce them to reveal their true preferences. This
study examines whether real payments to all subjects is indispensable for eliciting the true
preferences when some subjects are actually paid a larger reward.
The remainder of this paper is organized as follows. The subsequent section
explains our experimental design. Section 3 reports the results of the experiment andexamines whether the delay, interval, and magnitude effects are confirmed by using the testof the same mean, and a regression analysis. Section 4 examines whether the discount rate
and the degree of the delay effect of the subjects can explain their procrastinating behaviors.
Section 5 presents our conclusion.

2. Design of the experiment
We attempt to measure subjective time discounting by asking subjects to select one of thetwo options that they prefer: option A, to receive a reward X with a shorter delay s, andoption B, to receive a (usually larger) reward Y with a longer delay t. On the basis of these
conditions, the rate of compensation for postponement R is defined as

1 YX
, and
X ts

interval h is defined as t  s .
We specified four values for s (2 days, 1 month, 90 days, and 10 months), three values
for h (7 days, 3 months, and 12 months), and three values for the reward amount (240,5

2,800, and 800,000 yuan). We also controlled for whether the reward specified in the
pay-off tables would be paid in reality, which was denoted as P = (YES, NO). Combining
these four conditions, we specified twelve sets of conditions (s, h, X, and P), as shown in
Table 1. Thus, the experiment consisted of twelve rounds, each of which corresponded to
one set of conditions.
Each set of conditions comprised 32 pairs of options, each of which were specified
with a value of the rate of compensation, R, by changing the value of the reward of thesubsequent option, Y. Thirty-two pairs of options were arranged in ascending order of R,
which varied from a rather low value of −20% to a rather high value of 300% (annual rate)
in a table that we termed the “payoff table.” 3 The subjects were expected to select theearlier receipt A when R is small and the subsequent receipt B when R becomes sufficiently
large. Subsequently, we defined the time discount rate TDij for condition j = (s, h, X, P) andsubject i with the value of R at which the subject switched from A to B.4
The experiment was conducted on March 11, 2005 at Fudan University, Shanghai. 5
The subjects were 29 undergraduate students recruited from the Department of World
Economics at Fudan University. They were either 20 or 21 years old, and 25 of the 29
subjects (86%) were female. The reward was paid in the following manner: At the end of
the experiment, we randomly selected one pair of options, starting from round one, to be
paid from the payoff table. Subsequently, we randomly selected one subject as a recipient3

An example of the payoff table is presented in the Appendix.
If a subject selects A (B) for all 32 pairs, then we regard the highest (lowest) value of R in the
payoff table as TDij. If a subject switches multiple times, then we discard the data because thesubject had probably misunderstood the question.
5
Before conducting the experiment on the time discount rate, we conducted an experiment on risk
aversion on the same day. For the experiment on risk aversion, see Sasaki et al. (2008).
4

6

of the reward amount on the date specified in the option that the subject had selected.6 The
highest reward presented in the payoff tables was 3,920 yuan (800,000 yuan would not bepaid), which was a relatively large amount, considering that the annual household incomeof the subjects was 20,000−40,000 yuan. This enabled us to provide the subjects with an
incentive to express their true preferences. Including a 120 yuan (approximately US$14)
participation fee, the average payoff for both the experiments, on time discounting and risk
aversion, was 788 yuan (approximately US$106). After we selected the winners, thesubjects were required to complete a detailed questionnaire indicating their preferences,opinions, and attributes.

3. Results of the experiment
3.1 Time discount rates elicited by the experiment
The bottom row of Table 1 presents the averages and standard errors of the discount rates,
which reveals that the discount rates changed substantially (from 1.0% to 44% in the annualrate) depending on the parameters of the experimental conditions. Since the discount rates
would remain unchanged if all the subjects followed exponential discounting, then it would
strongly suggest that the conventional assumption of exponential discounting is notsupported by the data. In other words, there existed anomalies that were probably
associated with the delay, interval, and reward amount. In this section, we have examinedthe delay, interval, and magnitude effects. We also investigated whether the results
depended on the promise of the payment of a reward.
6

Since this payment procedure was explained in the instructions and was rehearsed twice, thesubjects were expected to clearly understand that what they would receive depended entirely on
their choice.

7

3.2 Examination of the three anomalies in time discounting using tests of the same mean
In our framework, the discount rates probably depended on the following four experimental
conditions: delay, s, interval, h, reward amount, X, and whether the payment is promised, P.
In this subsection, each round held three of the four conditions constant and the fourth
condition variable, and we tested whether the mean discount rate varied with the t-test of
the same mean.

The delay effect
In order to test the delay effect, we compared the rounds wherein the interval and amountare the same but the delay differs. 7 The rounds are indicated as follows:
1) Round 2 (30 days, 90 days, 240 yuan) vs. Round 4 (10 months, 90 days, 240 yuan)
2) Round 5 (2 days, 7 days, 2,800 yuan) vs. Round 6 (90 days, 7 days, 2,800 yuan)
3) Round 7 (1 month, 3 months, 2,800 yuan) vs. Round 9 (10 months, 3 months, 2,800
yuan)4) Round 10 (1 month, 3 months, 800000 yuan) vs. Round 12 (10 months, 3 months,
800,000 yuan)
Table 2 presents the P-values of the mean-difference tests. In all the combinations, thenull hypothesis that the means are the same is not rejected. Thus, the delay effect is notobserved by the mean difference test.

7

Whether the payment would be made or not is also controlled.

8

The interval effect
For the interval effect, three comparison tests, round 2 vs. 3, round 7 vs. 8, and round 10 vs.
11, are possible and Table 3 presents the test results. When the reward amount is set at 240
or 2,800 yuan, the discount rates were significantly higher in the shorter intervals than in
the longer intervals, and this confirmed the interval effect. However, when the reward
amount was set at 800,000 yuan, the null of the same mean was not rejected. This isprobably because people select sufficiently low discount rates for an extremely large
amount such as 800,000 yuan; therefore, the difference in the other conditions no longer
changes the discount rates. The result of the interval effect is generally consistent with thesubadditivity found by Read (2001).

The magnitude effect
Table 4 presents the results of the tests of the magnitude effect. The top panel shows threetest results comparing the rewards of 240 and 2,800 yuan. The middle panel presents theresults comparing the rewards of 2,800 and 800,000 yuan, and the bottom panel presents
those comparing the rewards of 240 and 800,000 yuan. In all the combinations, the time
discount rate was significantly higher for the smaller reward amount. Thus, the magnitude
effect, wherein the discount rates were inversely related to the reward amount, wassignificantly observed. This is consistent with the results of previous studies (Benzion et al.
1989, Kirby 1997, Kirby and Marakovic 1997, and Thaler 1981).

The payment effectFinally, we examined whether the promise of payment influences the discount rates.

9

Rounds 1 and 7 were designed to have the same condition (s, h, X), and they differed onlyin that the reward was actually paid in round 5 and not in round 1. Table 5 presents the test
result of the same mean, which reveals that the null of the same mean is not rejected. As
noted above, the reward of 2,800 yuan was relatively large in China; therefore, this result
has a strong implication: as long as a few of the subjects will actually be paid a large
reward for a few rounds that are selected randomly in the same experiment, whether the
reward is actually paid to the subjects is unrelated to the time discount rates reported bythem. This provides grounds for the validity of our experimental result with respect to thefollowing: (1) although we did not pay rewards to all subjects except the winner of eachround, the overall results are trustworthy, and (2) the results of rounds 10–12, where thereward of 800,000 yuan was only imaginary, are reliable.

3.3 Regression analysis for the investigation of the three anomalies
In the previous subsection, although we did not confirm the delay effect, we determined theinterval and magnitude effects. This is consistent with Read’s (2001) conclusion, and it
creates uncertainty regarding the empirical validity of the delay effect reported bynumerous previous studies because they did not separate the delay from the interval.
However, we must be careful, because the comparison tests in the previous subsection may
suffer from the problem of a small sample, and this may lead to a small power to reject thenull of the same mean. A careful analysis of Table 2 indicates that the rounds of the 2-day
delay report a discount rate of 30.6%, which is substantially higher than the discount rate of
22% for the 90-day delay in round 6. Although the P-value is only 32%, this may be a10

result of the small sample of 29. In order to avoid this weakness, we pool all the 348
samples, and conduct a regression analysis using these samples.
The regression equation essentially controlled all the experimental conditions: thedelay, s, interval, h, reward amount, X, and whether the reward is actually paid, P. In
particular, we adopted the following variables: For the variables standing for the delay, weused dummy variables HOR 2 j , HOR 30 j , and HOR 90 j , which were equal to unity if
the delay is 2 days, 1 month, and 3 months in round j, respectively, and 0 otherwise. The
dummy variable representing 10 months was deleted for the benchmark. For the amount of
the reward, we used dummy variables AMT 240 j and AMT 2800 j , which were equal tounity for the reward amounts of 240 and 2,800 yuan, respectively, in round j , and 0
otherwise. The dummy variable representing 800,000 yuan was deleted for the benchmark.
For the interval, we used a variable INT j , which was equal to the length of the interval inround j . Since the interval dummies and delay dummies were perfectly collinear and not
all the dummies could be included at once, we did not use the interval dummies. Finally,
we used a dummy variable PAYj , which was equal to unity if the reward would be paid inround j , and 0 otherwise. Thus, the regression equation is
LNTDij   0  1 HOR2 j   2 HOR30 j   3 HOR90 j   4 INTj   5 AMT240 j  6 AMT2800 j   7 PAYj   ij,

(1)where LNTD ij represents the logarithm of subject i’s time discount rate in round j. The
logarithm of time discount rates were considered because the time discount rates were11

essentially positive, and therefore, the lognormal distribution was expected to fit better thannormal distribution. It was probably owing to this fact that the fits of any estimation below
became substantially worse when time discount rates were used instead of their logarithms.
Table 6 presents the results of the random effect model. For the variables of thedelay dummies, although the estimated coefficient of HOR 2 j was significantly positive,
those of HOR 30 j and HOR 90 j were insignificant, thereby indicating that the delay
effect operates only in 2-day delays, but not in the rounds where the delay is over 30 days.
This implies that the delay effect is found between delays of two days and 30 days
(approximately four weeks). This non-linear property of the delay effect is close to that of
the quasi-hyperbolic discount model, wherein people discount much of the future value
between the present and the very near future, whereas they discount it only moderately afterthat period (Laibson 1997). The result does not contradict Read (2001), who reported thatthe delay effect is not observed in the case of 6-month and 8-month delays, which are bothsubstantially longer periods of delay than that considered in our study. It is also consistent
with Kinari et al. (2009), who reported the delay effect between two and four weeks (wheninterval is set at four weeks) or zero and two weeks (when interval is set at two weeks).
Let us briefly examine other anomalies. The estimated coefficients of AMT 240 j
and AMT 2800 j were significantly positive, and that of INT j were significantly negative.
These results confirm the magnitude and interval effects, which have already been
confirmed by us using the test of the same mean. The estimated coefficient of PAYj was
insignificant, which is also consistent with the results in the previous subsection. Thus,

12when a part of the subjects are randomly selected, and are actually paid a large reward
amount for certain rounds, the subjects honestly answer the questions even when the reward
is imaginary.
Subsequently, we considered the attributes of the subjects, i.e., gender, andhousehold income. In particular, we added a dummy variable, MALE, which was equal tounity for male subjects and zero otherwise, and a dummy variable HINCOME, which wasequal to unity if the subject’s annual household income was over 14,000 yuan and zerootherwise. Four subjects were classified as high income and 20 as low income. Since fivesubjects who did not report household income were excluded, there were 24 observations
for this regression. The right column of Table 6 indicate the estimates. Both coefficients of
MALE and HINCOME were not significant at the 5% level. Thus, for our subjects, thediscount rates were independent of these attributes. On the other hand, the three anomalies
were clearly confirmed with this specification. The result that PAY had no effect also
remains unchanged. 8

4. Time discounting and procrastinating behavior
4.1 Analytical framework
It is not common to behave as we had originally planned: we tend to postpone experiencing
discomfort and enjoy pleasure earlier. In this section, we investigate whether the subjects’

8

The questions that were included in the questionnaire, which the subjects were asked to completeat the end of the experiment, were similar to those in the experiment. Thus, we computed thediscount rates from these questions in order to compare them with those in experiment. Although
the discount rates elicited by the questionnaire and the experiment were not exactly the same, they
were rather close in numerous cases. This also supports the conclusion regarding the effect of thepayment of the rewards.

13

time preference and the delay effect, as revealed in the experiment, can explain theirprocrastinating behavior.
As an example of an unpleasant task that people tend to procrastinate, we adopted
homework assignments in childhood. In the questionnaire that was distributed at the end of
the experiment, we asked the respondents the following question in order to determine
when they did their assignments:“Thinking about the time when you were a child and were given an assignment inschool, when did you usually do the assignment?” (Circle ONE number)
1. Got it done right away
2. Tended to get it done early, before the due date
3. Worked on it daily up until the due date
4. Tended to get it done toward the end
5. Got it done at the last minuteOn the basis of their answers, we defined HWK i as the number that was chosen by subject
i. This is a proxy for procrastinating behavior, a larger value of HWK i implies a stronger
propensity to procrastinate.
Our interest was to empirically examine the manner in which the subjects’procrastinating propensities, measured by HWK i , related to their following two attributes
regarding time discounting: the degree of impatience, measured by the mean discount rate,
and the degree of the delay effect. Since lesser patient subjects would select theperformance of onerous activities at a subsequent stage, we hypothesized that the time
discount rate is positively correlated to procrastinating propensity.

14

The impact of the delay effect on when to perform onerous tasks depends on whether
the decision maker is naïve or sophisticated. 9 With the delay effect, naïve people, who do
not expect a future upward shift of impatience, repeatedly procrastinate the performance ofcostly jobs. Therefore, in this case, procrastination is expected to be positively correlatedwith the delay effect.
In contrast, sophisticated people, who make decisions by incorporating preference
shifts of future selves, understand that making future selves make decisions leads toharmful procrastination and have incentives to perform onerous tasks earlier. The incentive
effect, termed the sophistication effect, mitigates procrastination. In particular, as shown by
O’Donophue and Rabin (Proposition 2, 1999), if the sophistication effect is sufficiently
strong, sophisticated people perform tasks earlier than exponential discounters would. Insuch an extreme case, the delay effect is negatively correlated with procrastination.
Overall, these arguments may be summarized in the following manner: (i) if thesubjects are naïfs, the delay effect will enhance their procrastination; however, (ii) if thesubjects are sophisticates, the delay effect may not evidently promote procrastination; it
may even suppress procrastination. Here, it must be noted that although theory does notpredict any signs of correlation between the delay effect and procrastination, a negative
correlation between them implies that the subjects are sophisticated.
We regressed procrastination (HWK) over the time discount rate and the degree of thedelay effect. The coefficient of the discount rate is expected to be positive regardless ofnaïfs or sophisticates. If most of the subjects are naïfs, the coefficient of delay effect must9

See O’Donophue and Rabin (1999).

15

be positive. However, if they are sophisticates, it can take any sign.

4.2 Definition of variables used in the regression
For the time discount rate of subject i, we used the standardized average AVSTDTD i ofthe logarithmic discount rates in all rounds LNTDij (j = 1, …, 12) such that

12

AVSTDTDi   STDTDij / 12 ,

(2)

j 1

where STDTD ij represents the standardized value of TD ij , which is calculated as

STDTDij  (LNTD ij   j

j) , where  j and  j are the means and standard deviations oflogarithmic time discount rates, respectively, in round j over the subjects. It must be notedthat the standardization was necessary for ruling out biases owing to the cross-rounddifferences in the averages of the discount rate.10
In the same token, we define the degree of the delay effect of subject i, STDDLYi, as
the average of the differences in standardized time discount rates among the cases where all
the conditions other than the delay are the same (see Table 2), i.e.,
STDDLYi  [(STDTDi 2  STDTDi 4 )  (STDTDi 5  STDTDi 6 )( STDTDi 7  STDTDi 9 )  (STDTDi10  STDTDi12 )] / 4.

(3)

4.3 Estimation results on procrastination
10

For example, a simple average would underestimate the contribution of the discount rates in caseof the larger reward amount, wherein the discount rates are rather small. However, the conclusions
essentially remain unchanged when we use non-standardized discount rates and delay effects.

16

We estimated the relationship using ordered probit because the dependent variable HWK itakes on integers from one to five, and a larger value represents stronger procrastination.11
In the left column of Table 7, HWK i is regressed only over the time discount rate,
AVSTDTD, which reveals that higher discount rates enhance procrastination. In the rightcolumn of Table 7, we indicate the results including both AVSTDTD and STDDLY.
Although the time discount rates have a positive coefficient, the coefficient of STDDLY issignificantly negative. The result that the coefficient of the delay effect is not positive
contradicts that the subjects are naïfs, thereby suggesting that our subjects may besophisticates. This is an intuitively natural result since the students of Fudan University are
undoubtedly the top elite in China.12

4.4 Further examination of the naïfs-sophisticates model
It may be suspected, however, that our results were merely obtained by chance and are thus
not reliable. In order to address this concern, we conducted an additional analysis on therelationship between the delay effect and procrastination. If all the subjects are naïfs, larger
delay effects result in greater procrastination. On the other hand, if all the subjects are
essentially sophisticates, then what can be expected? The correlation between the delay
effect and procrastination may depend on the size of the delay effects displayed by the
subjects: The regret experienced by those whose delay effect is weak is not strong enough
11

It must be noted that the estimated coefficients do not represent the marginal effect on the valueof HWK. They represent the effect on the continuous latent variable corresponding to the HWK.
12
It was reported in the media that “according to the results of a respected exam, the students inShanghai have surprised experts by outscoring their counterparts in dozens of other countries inreading as well as in math and science” (New York Times, December 7, 2010). The news offers
evidence that education level in Shanghai is generally rather high.

17

to prevent further procrastination, whereas those who have strong delay effects will stop
procrastinating because of a strong sophistication effect.
In order to substantiate our hypothesis, we divided the subjects into two groups, highand low degrees of delay effects. Subsequently, we defined a variable representing thedegree of the delay effect of the higher group, HSTDDLYi, and a variable representing thatof the lower group, LSTDDLYi, in the following manner:
 STDDLYi
HSTDDLYi  0

if STDDLYi  STDDLY,
otherwise(4)

 STDDLYiLSTDDLYi  0

if STDDLYi  STDDLY,
otherwise(5)

where STDDLY denotes a critical value dividing the subjects into two groups that are
specified below. The regression equation now becomes

HWK i    AVSTDTD i   H HSTDDLY i   L LSTDDLY i   i , i  1, ... , 29 .

(6)

If our subjects are naïfs, then  H   L  0 will be obtained. On the contrary, if thesubjects are sophisticates,  H and  L can take any sign. However, the following may be
a probable case: when the critical value STDDLY is set at an adequately low level,sophisticates who have weaker delay effects do not regret that they are procrastinating;therefore, they behave as if they are naïfs. On the other hand, those who have stronger
delay effects attempt to stop procrastination; therefore, their increase in the level ofprocrastination is lesser than proportional to their degree of delay effect. Therefore, thesensitivity to the delay effect,  H , becomes smaller than  L . In this case,  H   L  0 is18

expected. This does not necessarily mean that procrastination is weaker for the higher delay
effect group. However, in case it is weaker for the higher delay effect group, then  H is
negative.
In order to determine the critical value, STDDLY , let us study the histogram of
STDDLY in Figure 1. It reveals that 17 out of 29 subjects do not report the delay effect.
Thus, we first stratify all the subjects who report negative STDDLY as the low-delay-effectgroup and all others as the high-delay-effect group. The left column of Table 8 presents theestimates in this case, which reveal that the high group (HSTDDLY) has a significant
negative coefficient and the low group (LSTDDLY) has an insignificant coefficient. Thus,
we obtain  H  0 and  L  0 .
When the critical value is increased to 0.2, it is confirmed that we obtain the same
results, i.e.,  H  0 and  L  0 . The results in Table 8 contradict the notion that the
subjects are naïfs; however, it is consistent with the hypothesis considered forsophisticates. 13

5. Conclusion
This study used an economic experiment in order to investigate the time discounting of
human beings. Economic experiments are often termed unreliable because the subjects thatare recruited do not have sufficient incentives to report their true preferences. Our
experiment is immune to such criticism because in our study, the highest reward that was
13

When the non-standardized time discount rate and delay effect were used, we obtained the same
results, wherein  H is significantly negative and  L is insignificant.

19

indicated to the subjects was close to their monthly household incomes.
This study achieved two goals. First, the delay effect owing to which people discountthe near future more than the remote future was substantiated by explicitly separating thedelay from the interval. 14 A majority of the previous studies have not separated these two
experimental conditions; however, Read (2001) identified these two conditions andreported that the delay effect was not found. By setting shorter delays than that set by Read
(2001), we substantiated the delay effect for a delay of less than 90 days. This finding isimportant because the delay effect induces people to make time-inconsistent plans andsubsequently regret their decision.
Another contribution of this study is its explanation of the subjects’ procrastinating
behavior on the basis of their time discount rates and the degree of the delay effect. Higher
time discounting always promotes procrastination; however, the impact of the delay effectdepends on whether the subjects are naïfs or sophisticates. If they are naïfs, a higher delay
effect promotes procrastination. However, if they are sophisticates, it involves twocompeting effects on procrastination, i.e., the positive present-bias effect and the negative
sophistication effect, so that the direction of the effect is not known a priori. We
hypothesized that the effect of the delay effect is weaker when the delay effect is strong
than when it is not strong. Our results contradicted the notion that our subjects are naïfs andare consistent with our hypothesis on sophisticates.
However, we must note that this study found that the naïfs-sophisticates model holds

14

Simultaneously, we confirmed the interval effect, wherein subjects discount the future more in
shorter intervals than in longer intervals, and the magnitude effect, wherein subjects discount the
future more for smaller amounts of money than larger amounts of money.

20

for a specific sample of the students at Fudan University. On the other hand, Hiruma and
Ikeda (2007) and Tsutsui et al. (2007) had found a positive correlation between the degreeof the delay effect and the loan amount. Considering that the loan amount is a good proxy
for the behavior of the procrastination of unpleasant things, their results contradict those ofthis paper. The naïfs-sophisticates model interprets the results of our study for sophisticatesand naïfs; however, this interpretation may seem arbitrary. Determining more direct
evidences for identifying sophisticates and naïfs is a potential area for future research.

21

References
Ainslie, G. (1975). Specious Reward: A Behavioral Theory of Impulsiveness and Impulse
Control. Psychological Bulletin, 82 (4), 463496.
Benzion, U., Rapaport, A., & Yagil, J. (1989). Discount Rates Inferred from Decisions: An
Experimental Study. Management Science, 35, 270284.
Frederick, S., Loewenstein, G., & O’Donoghue, T. (2002). Time Discounting and Time
Preference: A Critical Review. Journal of Economic Literature, 40, 351401.
Hiruma, F., & Ikeda, S. (2007). A Study on Time Discounting Based on Experiments.
Review of Monetary and Financial Studies, 25, 1225. (in Japanese)
Kinari, Y., Ohtake, F., & Tsutsui, Y. (2009). “Time Discounting: Declining Impatience andInterval Effect,” Journal of Risk and Uncertainty, 39, 87112.
Kirby, K. N. (1997). Bidding on the Future: Evidence Against Normative Discounting of
Delayed Rewards. Journal of Experimental Psychology: General, 126, 5470.
Kirby, K. N., & Marakovic, N. N. (1995). Modeling Myopic Decisions: Evidence forHyperbolic Delay-Discounting with Subjects and Amounts. Organizational Behavior
and Human Decision Processes, 64, 2230.
Laibson, D. (1997). Golden Eggs and Hyperbolic Discounting. Quarterly Journal of
Economics, 112, 443477.
O’Donoghue, T., & Rabin, M., (1999). Doing It Now or Later. American Economic Review,
89 (1), 103124.
Read, D. (2001). Is Time Discounting Hyperbolic or Subadditive? Journal of Risk andUncertainty, 23, 532.
Read, D., &. Roelofsma P. H. M. P. (2003). Subadditive versus Hyperbolic Discounting: A
Comparison of Choice and Matching. Organizational Behavior and Human Decision
Process, 91, 140153.
Read, D., Frederick, S., Orsel, B., & Rahman, J. (2005). Four Score and Seven Years from
Now: The Date/Delay Effect in Temporal Discounting. Management Science, 51,13261335.

22

Sasaki, S., Xie, S., Ohtake, F., Qin, J., & Tsustui, Y. (2008). Experiments on Risk Attitude:
the Case of Chinese Students, China Economic Review, 19 (2), 245259.
Thaler, R. H. (1981). Some Empirical Evidence on Dynamic Inconsistency. Economic
Letters, 8, 201207.
Tsutsui, Y., Hiruma, F., Ohtake, F., & Ikeda, S. (2007). An Analysis of the Impact ofInterest Rate Ceilings to the Consumer Credit: Behavioral Economic Approach.
Gendai Finance, 22, 2573. (in Japanese)

23

Table 1. Twelve sets of experimental conditions and their mean discount rates
Round
Delay (s)Interval (h)Rewards (X)Payment (P)Mean discount rate
Standard error

1
1 month
3 months
2,800
No
9.586
2.085

2
1 month
3 months
240
Yes
40.0347.520

3
1 month
1 year240
Yes
23.7933.770

410 months
3 months
240
Yes
43.8288.630

5
2 days7 days2,800
Yes
30.6389.160

690 days
7 days2,800
Yes
22.121
7.027

Round
Delay (s)Interval (h)Rewards (X)Pay (P)
Mean discount rate
Standard error

7
1 month
3 months
2,800
Yes
8.276
1.275

8
1 month
1 year
2,800
Yes
5.819
0.948

9
10 months
3 months
2,800
Yes
9.034
2.040

10
1 month
3 months
800,000
No
1.103
0.378

11
1 month
1 year800,000
No
1.491
0.655

12
10 months
3 months
800,000
No
0.959
0.299

Note: This table shows the experimental conditions of twelve rounds and the mean and standard errors of the discount rate ofeach round.

24

Table 2. Results of the t-test of the same mean in the case that delays are different
Round
Delay (s)Interval (h)Rewards (X)Payment (P)Observations
Mean discount rate
95% upper bound
95% lower boundP-value2
4
1 month 10 months
3 months 3 months
240
240
Yes
Yes
29
29
40.03443.82824.63026.14955.43961.5060.617

5
6
2 days90 days
7 days7 days
2,800
2,800
Yes
Yes
29
29
30.63822.12111.8757.727
49.40136.5140.317

7
9
1 month300
3 months
3 months
2,800
2,800
Yes
Yes
29
29
8.276
9.034
5.664
4.855
10.88713.2140.455

Note: P-values indicate the probability with which the null of the same mean is rejected.

25

10
12
1 month
10 months
3 months
3 months
800,000
800,000
No
No
29
29
1.103
0.959
0.329
0.346
1.876
1.573
0.638

Table 3. Results of the t-test of the same mean in the case that the intervals are different
Round
Delay (s)Interval (h)Rewards (X)Payment (P)Observations
Mean discount rate
95% upper bound
95% lower boundP-value2
3
1 month
1 month
3 months
1 year
240
240
Yes
Yes
29
29
40.03423.79324.63016.07055.43931.516
0.003

7
8
10
11
1 month 1 month 1 month
1 month
3 months
1 year3 months
1 year2,800
2,800
800,000
800,000
Yes
Yes
No
No
29
29
29
29
8.276
5.819
1.103
1.491
5.664
3.877
0.329
0.151
10.887
7.761
1.876
2.832
0.003
0.538

26

Table 4. Results of the t-test of the same mean in the case that reward amounts aredifferent
2
7
3
8
4
9
Round
30
30
30
30
300
300
Delay (s)
90
90
365
365
90
90
Interval (h)
240
2,800
240
2,800
240
2,800
Rewards (X)
Yes
Yes
Yes
Yes
Yes
Yes
Payment (P)
29
29
29
29
29
29
Observations
Mean discount40.0348.276
23.7935.819
43.828
9.034
rate
24.63
5.664
16.07
3.877
26.1494.855
95% upper bound10.88731.5167.761
61.50613.21495% lower bound 55.439
0.000
0.000
0.000
P-value
Round
Delay (s)Interval (h)Rewards (X)Payment (P)Observations
Mean discountrate
95% upper bound
95% lower boundP-value
Round
Delay (s)Interval (h)Rewards (X)Payment (P)Observations
Mean discountrate
95% upper bound
95% lower boundP-value

7
30
90
2,800
Yes
29
8.276

10
30
90
800,000
No
29
1.103

8
30
365
2,800
Yes
29
5.819

11
30
365
800,000
No
29
1.491

9
300
90
2,800
Yes
29
9.034

5.664
0.329
10.887
1.876
0.000

3.877
7.761

0.151
2.832

4.855
0.346
13.214
1.573
0.001

2
30
90
240
Yes
29
40.034

3
30
365
240
Yes
29
23.7931130
365800,000
No
29
1.491

4
300
90
240
Yes
29
43.8281030
90800,000
No
29
1.103

24.63
0.329
55.439
1.876
0.000

0.001

16.07
0.151
31.516
2.832
0.000
27

12
300
90
800,000
No
29
0.959

12
300
90
800,000
No
29
0.959

26.1490.346
61.5061.573
0.000

Table 5. Results of the t-test of the same mean for the cases that the reward is paid or not
Round
Delay (s)Interval (h)Rewards (X)Payment (P)Observations
Mean discount rate
95% upper bound
95% lower boundP-value

1
7
30
30
90
90
2,800
2,800
No
Yes
29
29
9.586
8.276
5.315
5.664
13.857
10.8870.461

28

Table 6. Result of the regression analysis on three anomalies

Constant
HOR2
HOR30
HOR90
AMT240
AMT2800
INT
PAY
MALE
HINCOME
Number ofobservations
Number of
subjects
R2

Estimated
P-valuecoefficient−1.074
0.000
0.765
0.004
0.077
0.651
0.336
0.203
4.413
0.000
2.941
0.000
−0.001
0.018
0.001
0.997

Estimatedcoefficient

P-value-1.140
0.822
0.160
0.342
4.485
2.957
-0.0020.028-0.304
0.817

0.000
0.004
0.382
0.230
0.000
0.000
0.016
0.920
0.491
0.064

348

288

29

24

0.62840.6581

Note: The regression equation is given by
LNTDij   0  1 HOR2 j   2 HOR30 j   3 HOR90 j   4 INT j   5 AMT240 j  6 AMT2800 j   7 PAYj   i , jResults are presented according to the random effect model.

29

Table 7. How procrastination depends on time discount rate and delay effect

AVSTDTDSTDDLY
Cut1
Cut2
Cut3
Cut4
Log likelihood
Pseudo R2
Number of observations

Estimatedcoefficient

P-value

0.855

0.014

-1.434-0.0540.577
1.669-39.1380.073
29

Estimatedcoefficient

P-value

1.147
0.003
-1.3620.015-1.362
0.012
0.699
1.815
-35.9860.148
29

Note: This table presents the estimates by ordered probit. It must be noted that the estimatedcoefficients are not for the marginal effect. Cut 1 to Cut 4 are estimated cutpoints on the latentvariable for classifying HWK i into values from 1 to 5, which represent the propensity ofprocrastination.

30

Table 8. Analysis on Naïfs-Sophisticates model
Estimatedcoefficient
AVSTDTD
HSTDDLY
LSTDDLY
Cut1
Cut2
Cut3
Cut4
Log likelihood
Pseudo R2
Number of observations
Critical value of STDDLY(High group, Low group)

P-value

1.059
0.007
-2.856
0.008
0.672
0.607
-2.4
-0.5440.131
1.311-34.4850.183229
0(12, 17)

Note: Refer to Table 7’s footnote.

31

Estimatedcoefficient

P-value

1.049
0.008
-2.2330.016-0.1960.858-2.06-0.2730.401
1.55-35.218
0.165929
0.2(8, 21)

Figure 1. Histogram of the standardized degree of the delay effect, STDDLY

32

Appendix: An example of Payoff table used in the experiment (Round 1)① Payoff table (2,800.00 yuan, 1 month vs. 4 months, reward is not actually paid)

Number of theoption pair
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

Option A (yuan)(receipt at 1
month later)
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00
2,800.00

Option B(yuan)(receipt at 4
month later)
2,730.00
2,765.04
2,772.00
2,779.04
2,786.00
2,793.04
2,800.00
2,807.04
2,814.00
2,821.04
2,828.00
2,835.04
2,842.00
2,849.04
2,856.00
2,863.04
2,870.00
2,877.04
2,884.00
2,891.04
2,898.00
2,905.04
2,912.00
2,919.04
2,926.00
2,933.04
2,940.00
2,975.04
3,010.00
3,080.00
3,150.00
3,220.00

Rate of return(annual rate)
−10%
−5%
−4%
−3%
−2%
−1%
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
25%
30%
40%
50%
60%

Notes: 1. Please circle A or B, whichever you prefer.
2. If you circled a wrong option, correct the answer with a double line.

33

Answers
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A

B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B