Reverse Time-Inconsistency
Serdar Sayman
Ayşe Öncüler
April 2006
_____________________________________________________________________________
Serdar Sayman
Assistant Professor of Marketing
Koç University
Rumeli Feneri Yolu, Istanbul, 34450, Turkey
Phone: +90 (212) 338 1616
Fax:
+90 (212) 338 1653
E-mail: ssayman@ku.edu.tr
Ayşe Öncüler
Assistant Professor of Decision Sciences
INSEAD
Boulevard de Constance, Fontainebleau, 77305, France
Phone: +33 (0) 1 60 724511
Fax:
+33 (0) 1 60 746716
E-mail: ayse.onculer@insead.edu
This research is supported by funds from Koç University, INSEAD, and KÜMPEM. Authors thank seminar
participants at the Marketing Science Conference 2005 Atlanta, ESA 2005 Montreal and SPUDM 2005
Stockholm for their comments, and Demir Çilingir for his contributions at various stages of this research.
Abstract
Individuals preferring a particular future option may change their preference in favor of another one as
time progresses -- a behavior referred to as dynamic or time-inconsistency. Previous empirical findings on
time-inconsistent preferences consistently points to the case where decision-makers prefer a later (and
superior / larger) future prospect over an earlier (and inferior / smaller) one at the outset, but switch their
choice to the smaller prospect when the options become more imminent. In this paper, we provide
evidence for time-inconsistency in the other direction: preferring a smaller-earlier temporal payoff over a
larger-later one at the beginning, but choosing to wait for the latter as both payoffs draw nearer. We use
the term reverse time inconsistency to designate this behavior. This intertemporal preference pattern, to
our knowledge, has not been explicitly identified before. Our findings from a number of empirical studies
suggest that reverse time-inconsistency occurs in a variety of contexts. The results show that the extent of
reverse time-inconsistency depends on payoff sizes and delay times. Furthermore, we also provide some
evidence on gender differences.
Key Words: Time Inconsistency, Dynamic Inconsistency, Time Preference
1
Introduction
Individuals preferring a particular future option may change their preference in favor of another
option as time progresses (e.g. Hoch and Loewenstein 1991, Loewenstein 1996). For instance, a
prospective dieter may decide to eat a chocolate bar (possibly with a feeling of guilt) even though she had
earlier decided to go on a diet. There has been an extensive investigation of time-inconsistent preferences
in the behavioral literature (see Frederick et al. 2002 for a comprehensive review). Empirical evidence
regarding such time-inconsistent preferences consistently points to the case where decision-makers prefer
a later (and superior / larger) future prospect over an earlier (and inferior / smaller) one at the outset, but
switch their choice to the smaller prospect when the options become more imminent.
In this paper, we provide evidence for time-inconsistency in the other direction: preferring a
smaller-earlier temporal payoff over a larger-later one at the beginning, but choosing to wait for the latter
as both payoffs draw nearer. This intertemporal preference pattern, to our knowledge, has not been
explicitly identified before. We will use the term “reverse time-inconsistency” to denote this behavior.
Our findings from four empirical studies suggest that reverse time-inconsistency, like timeinconsistency, is indeed a common behavior under various contexts. Our studies involve: (i) both
hypothetical and real payoffs; and (ii) cases where participants spend effort for the payoffs (loyalty
programs) and cases with effortless payoffs. The results show that the extent of reverse timeinconsistency depends on payoff sizes and delay times. Furthermore, we also provide some evidence on
gender differences.
The paper is planned as follows: The next section involves a brief discussion of the background
research on time-inconsistent preferences. We then present our findings from four empirical studies
followed by a discussion of possible causes or explanations for reverse time-inconsistency. The paper
ends with a summary and concluding remarks.
Background
Time-inconsistency (or dynamic inconsistency), a concept first introduced by Strotz (1955), falls
2
under the broader line of preference reversal research and it implies non-stationarity of preferences. For
example, one may prefer $12 in 31 days over $10 in 30 days; but $10 today is preferred over $12
tomorrow. Discounted Utility Theory (DUT), the standard economic model of choice over time, assumes
that preferences between two temporal payoffs do not depend on the point of time the evaluation is made
(Samuelson 1937; Koopmans 1960; Fishburn and Rubinstein 1982). In other words, if payoffs are
delayed by the same amount of time, the preference ordering should not be affected. This discounting
behavior is modeled by an exponential function, where the discount rate does not change with delay time.
However, this framework has been systematically challenged as a descriptive model. Studies such as
Thaler (1981) and Benzion et al. (1989) suggest that although individuals prefer an earlier payoff to a
delayed one, sensitivity to time delay progressively decreases; that is, the discount rate is not constant.
Hyperbolic discounting has been proposed and modeled in the literature (e.g. Ainslie 1975;
Mazur 1987; Hernnstein 1981; Loewenstein and Prelec 1992) as a discount function that can capture
time-inconsistent preferences. Under hyperbolic discounting, the discounted value of a temporal payoff
falls sharply for small delays but then it flattens out. In other words, there is less discounting (a higher
discount factor, or a lower discount rate per period) for a given time interval if the interval is temporally
remote. Hence, in the above example, hyperbolic discounting can account for the shift in the preferences
because the per-period discount rate moving from 30 days to 31 days is smaller than the rate moving from
today to tomorrow.
There are a few explanations for the decreasing sensitivity towards time delay. One possibility is
that a time interval, if it is evaluated relatively, would be perceived as smaller when it is temporally
further away. Hence, the difference between 30 and 31 days would be perceived as smaller than the
difference between today and tomorrow. This is related to the Weber’s law, or psychophysics of time (see
Keren and Roelofsma 1995). Another explanation is that discounting reflects the implicit uncertainty in
obtaining the payoff in the future (Keren and Roelofsma 1995). This uncertainty increases rapidly for the
near future, and then the rate of increase diminishes. A third possibility is impulsive decision-making and
lack of self-control (Ainslie 1975; Rachlin and Green 1972; Green et al. 1981). If impulsivity plays a role
3
in preference or choice, one would overweigh a smaller-imminent payoff relative to a larger-later one,
even though she had planned to wait for the latter earlier on. Emotions and visceral factors such as
cravings may also play a role in triggering such impulsive or myopic decisions (Loewenstein 1996).
It has been argued that even exponential discounting could account for time-inconsistency if
discounting is not independent of the payoff size (see Green et al. 1981; Kirby and Marakovic 1996;
Kirby 1997). These studies involve exponential discounting, as suggested by DUT, but smaller amounts
are discounted more than larger amounts.1 Such a discounting implies that when both small and large
payoffs are brought forward, the small payoff would become relatively more attractive.
With this background in mind, we hope to contribute to the literature by providing evidence for a
time-inconsistency of a different direction. Previous literature on time- inconsistency focuses mainly on
one direction: preferring a larger-later reward to a smaller-sooner one when both outcomes are in distant
future, but then switching to the smaller-sooner reward when the outcomes become less remote (e.g.
Green et al. 1981, Green et al. 1994, Kirby and Hernnstein 1995). Our experimental results indicate that
there exists some situations where a smaller-earlier temporal payoff may be preferred over a larger-later
one at the outset, but the larger payoff becomes more attractive as both payoffs draw nearer. We designate
this behavior as reverse time-inconsistency. In the next section we present our empirical findings on this
phenomenon. We conducted four studies: Studies 1 and 3 involve payoffs within the context of loyalty
programs, and Studies 2 and 4 use neutral monetary payoffs. Studies 1 and 2 employ cross-sectional
designs; Studies 3 and 4 use longitudinal data with real payoffs. The design specifics of the four studies
are summarized in Figure 1.
----- Insert Figure 1 about here ----
1
This may be explained by the psychophysics of the waiting effort -- for smaller amounts, the return has to be
substantial to make the wait attractive (Thaler 1981).
4
Empirical Studies
Study 1
Method. Our first study involves two choice experiments with 97 and 100 student participants from
INSEAD and Koç University, respectively. Participants answered questions regarding rewards offered by
hypothetical loyalty programs. The rewards were based on accumulated purchases; hence, the payoffs
required (hypothetical) effort. In exchange for participation we offered students in INSEAD and Koç
University a chance to win $100 and $70 gift checks respectively. There were additional sections,
unrelated to our study, in the survey booklets.
Design and Stimuli. We will only describe the details of the session run at INSEAD because the two
sessions are almost identical in structure and stimulus. The experiment involves two hypothetical loyalty
program vignettes: (a) Local supermarket Porcupine offers a $10 check if the buyer makes $100 worth of
purchases. The reward is $25 for a cumulative purchase of $200. Gift checks can be used at any
Porcupine store. (b) Subjects’ favorite movie theater offers one free ticket after purchasing three tickets;
or two free tickets after five tickets. The order of the vignettes is counter-balanced across subjects. There
is no time limit for either of the loyalty programs, and a shopper receiving a reward can pursue additional
reward(s) afterwards. Furthermore, purchases can be recorded by using the student ID (smart) cards, and
there is no additional effort or cost associated with the programs.
Our experimental manipulation is the timing of the reward choice: (i) Students in the “distant”
condition are told that the loyalty program starts today. They are then asked to indicate whether they
would prefer to receive the $10 check or the $25 check after the corresponding purchase volume.
Similarly, for the movie theater vignette, they indicate their choices between one and two free tickets. (ii)
Students in the “immediate” condition are told to assume that the program started a few weeks ago, and
the sales clerk informs them that they have completed $100 worth of purchases. They are asked whether
they would prefer to receive the $10 check immediately, or wait for the $25 check after completing a total
of $200 purchases. For the movie theater loyalty program, they are told to assume that they are buying
their third ticket today, and that they have a choice between receiving a free ticket today or two free
5
tickets later.
Reward choice timing is a between-subjects manipulation. In addition to the choice questions, we
also asked the gender of the participants in both groups. There were 47 participants, with 25 females and
22 males, in the “distant” condition, compared to 50 participants, with 30 females and 20 males, in the
“immediate” condition. Regarding the session run at Koç University, the supermarket vignette was
slightly different: the local supermarket Migros offers a $3 check if consumer spends a total of $30, and
$7.5 if spending reaches $60.2 There were 50 participants (26 females and 24 males) in the “distant”
condition; and 50 (28 females and 22 males) in the “immediate” case.
Results and Discussion. Before presenting our findings, we note that prior research suggests that there
may be gender differences in time preferences. Although studies such as Kirby and Marakovic (1995) and
Harrison et al. (2002) report no gender differences in discounting behavior, others indicate a gender
difference albeit small and domain specific (Bjorklund and Kipp 1996; Silverman 2003). For instance,
Kirby and Marakovic (1996) find that females discount future payoffs less than males do, suggesting that
women are generally better in delaying gratification and resisting temptation or impulsivity. In a recent
study, McLeish and Oxoby (2005) report that males switch to smaller-immediate payoff faster than
females. Hence, there may be some gender differences in time-inconsistency. We will consider gender as
a factor in our analysis of the empirical data regarding reverse time-inconsistency (RTI hereafter), or
time-inconsistency (TI hereafter) thereof.
---- Insert Table 1a and Table 1b about here ----
Table 1a and 1b present the findings from the two experimental sessions. For brevity purposes,
the tables only describe the options SS (smaller-sooner reward) and LL (larger-later reward) in the
2
The figures were stated in local currency terms; at the time of the experiment, one US Dollar was about 1.35 New
Turkish Lira.
6
“distant” rewards condition. In the corresponding “immediate” case, subjects have already spent $100 and
they are to choose between receiving $10 (SS option) or receiving $25 after spending $100 more (LL
option). For instance, the upper panel of Table 1a indicates that 48% of the female participants in the
“distant” supermarket rewards condition preferred to wait for the larger-later reward LL, compared to
20% in the “immediate” case. Hence, a smaller ratio of female subjects preferred to wait when the
rewards were closer in time, indicating a TI behavior. The difference is significant with p  0.05 (2 test,
df = 1). For the movie theater loyalty program presented in the lower panel, 72% of females chose to wait
when both rewards were distant, but only 50% did so when the smaller reward was immediate. This again
indicates TI (p  0.10). For the male participants, on the other hand, there is strong evidence of RTI in the
case of supermarket loyalty program: 32% of males preferred to wait when rewards were distant, 85%
chose to wait when the smaller reward was immediate (difference significant with p  0.01). In the movie
theater scenario, the percentages directionally indicate RTI even though the difference is not statistically
significant. When we look at the aggregate data over all subjects, the corresponding percentages are not
significantly different from each other-- that is, neither TI nor RTI is evident on average.
Our findings from the session at Koç University, presented in Table 1b, are directionally similar
to the above; however, none of the differences between the corresponding percentages is significant.
Hence, there is no statistical evidence of TI or RTI. Taken together, Table 1a and 1b indicate that the
incidence of RTI or TI may depend on the context (type of program, size of the rewards, cultural setting)
and on the individual (gender differences). There is one issue worth noting: In this particular design,
rewards are based on consumer effort or spending. Hence, what we are measuring may not be time
preference per se. Study 2 presented below focuses on (neutral) monetary payoffs to be received over
time, without requiring any effort or spending.
Study 2
Method. There were three experimental sessions in Study 2. Two of these were conducted at Koç
University and the third one at INSEAD, with 130, 116, and 67 subjects in each session respectively.
7
Subjects answered choice questions regarding hypothetical monetary payoffs. We varied the relative sizes
of the payoffs across the experimental sessions and the payoff-delay time combinations within a session.
Participants from Koç University were offered a chance to win a $50 gift check of a department store; in
INSEAD the survey was part of a larger survey and the prize was an MP3 player.
Design and Stimuli. The introduction of the survey stated that the questions were intended to measure the
individual preferences for payoffs over time. Participants then answered eight questions involving choices
between two temporal payoffs (details can be seen in Tables 2a, 2b, and 2c below). Similar to our first
study, we used a between-subjects design. For instance, subjects in the “distant” condition were asked to
indicate their preference between receiving “$7 in 1 day” versus “$10 in 3 days”; whereas in the
corresponding “immediate” case, the choice was between “$7 today” versus “$10 in 2 days”. In both
conditions, the order of the questions was randomized -- picked from one of the predetermined versions.
We also noted in the introduction that there were no right or wrong answers, and each question should be
considered independently. After the choice questions, we also asked the gender of the participants.
---- Insert Table 2a, Table 2b, and Table 2c about here ----
Results and Discussion. As in the first study, the tables describe the options SS and LL for the “distant”
rewards condition; in the corresponding “immediate” condition, SS is immediate and LL is brought
forward.
Study 2a, conducted at Koç University, involved 70 subjects in the “distant” rewards condition
(32 female and 38 male), and 60 subjects in the “immediate” condition (29 female and 31 male). The
results were quite robust in the direction of RTI for both payoff pairs. Except for the pairs where SS was
to be received in two weeks and LL in four weeks, we observed RTI in all cases (p values are given in
Table 2a). This finding holds for both genders and for the overall subject group.
Study 2b was also run at Koç University. The relative sizes of payoffs were modified in order to
provide further evidence on the range of payoff-delay combinations for which RTI or TI is pertinent.
8
There were 59 subjects in the “distant” condition (26 female and 33 male) and 57 subjects in the
“immediate” case (26 female and 31 male). We again observed a strong evidence for RTI, as given in
Table 2b, for all three subject groups.
A third session (Study 2c) was run at INSEAD. The size of the SS and LL rewards were modified
further in this treatment. We had 33 subjects in the “distant” condition (16 female and 17 male) and 34
subjects in the “immediate” condition (15 female and 19 male). Although the number of subjects in each
experimental cell was not large, we still obtained significant differences between the corresponding
percentages (see Table 2c). In general, women exhibited RTI, while men behaved predominantly in the
other direction. All subjects taken together, for smaller payoffs with short delays, evidence is in the
direction of RTI, but not significant; for larger payoffs and / or long delays there is evidence for TI.
Study 3
Most of the empirical work in intertemporal choice involves cross-sectional designs (rather than
longitudinal), where the front-end delay in attaining a reward is manipulated in a single session to
demonstrate time inconsistency (see Read 2004 for a comparative analysis of the two methods).
Longitudinal studies, which elicit preferences in a real-time setting, are quite scarce in the literature.
Harrison et al. (2002) conducted a large-scale field experiment in Denmark over several months in order
to elicit discount rates at different points in time. They report no evidence for TI, except for a particular
segment of the general subject pool (students). In another recent study that compares longitudinal to
cross-sectional designs, Airoldi et al. (2005) found that cross-sectional design overestimates dynamic
inconsistency.
Another experimental design issue is the use of real versus hypothetical payoffs. Most
intertemporal choice experiments use hypothetical rewards for practical reasons-- to have flexibility over
the magnitude of payoffs and over the time horizon. Bohm (1994) provides evidence that an incentivecompatible design can reduce the extent of preference reversal. Evidence in intertemporal choice
literature is mixed: Some studies report no significant difference in discounting behavior with respect to
9
hypothetical and real rewards (Johnson and Bickel 2002; Read et al. 2005), whereas some others show
that real rewards are discounted more heavily than hypothetical ones (Kirby 1997).
Study 1 and 2 presented above involve cross-sectional designs and hypothetical payments,
without any incentive-compatible payment structure. In order to examine whether these design issues
would indeed influence the extent of RTI and/or TI, we conducted two additional studies, Study 3 and 4,
which induce incentive compatibility through real payments. In addition, both are longitudinal studies
conducted with respective subject panels.
Method. Study 3 is a within-subject field experiment conducted on INSEAD campus. In association with
the campus café, a loyalty program was initiated. 47 customers were willing to join the loyalty program
(20 female and 27 male). At the outset, each customer was asked to state their preference between two
rewards offered by the program; later preferences were elicited from actual reward redemptions. Contrary
to Study 1, data is obtained from individuals who actually chose to participate in the program.3
Design and Stimuli. The café offered a two-level reward program: customers could receive a free
croissant when they bought 10 croissants or two free croissants after 15 croissants. At the beginning of
the experiment, the participating customers were given patronage cards, bearing ID numbers and were
asked to indicate their preference between the two promotion levels. During the following few weeks,
they showed these cards when making a croissant purchase, and the purchases were recorded on the card
by means of a stamp. A research assistant at the café counter kept track of the participating customers’
purchase times on a half-hour basis. The experiment lasted 6 weeks, and once the free croissant(s) were
given, the program ended for that customer.4
3
Dhar and Simonson (2003) provide evidence that choice proportions of two options may differ when subjects are
provided with a “no-choice” option.
4
None of the subjects bought more than one croissant at a time. Individual purchase dates and times can be obtained
from the authors.
10
---- Insert Table 3 about here ----
We note that because the measurements are from the same set of subjects, we use the McNemar’s
2 test (Siegal and Castellan 1998). The results in Table 3 show that the majority of the female
participants exhibit RTI. Although men show a tendency for TI, the difference is not significant. At the
aggregate level, there is evidence for RTI: 51% of the participants indicated a preference for LL at the
outset, compared to 72% when SS became imminent. When we analyze the data at the individual level,
there were 9 customers (all male) who preferred LL at the beginning but then received the SS when they
could, indicating TI. There were 19 customers who exhibited RTI behavior, of which 14 are female and 5
are male. The remaining 19 customers, 6 females and 13 males, were time consistent (either chose SS or
LL at the beginning, and received the corresponding reward later on).
Study 4
Method. In Study 4, as in the previous study, we employed a within-subject longitudinal design with real
payments. The experiment was conducted at INSEAD. 38 student participants (17 female, 21 male) stated
their preferences between different pairs of temporal monetary payoffs. When the smaller-earlier payoff
was due, they were asked to state their choices again. The questionnaire was similar to the one in Study 2
but with an addition of incentive compatibility condition since all payments were done in real.
Design and Stimuli. Subjects were students of a negotiations analysis course at INSEAD. The first phase
of the longitudinal study was conducted in a class meeting. During this first meeting, participants
answered 6 choice questions (vignettes) with monetary payoffs. The six temporal payoffs are presented in
Table 4. The choice pairs were the same ones as in Study 2, except for the 2 weeks-4 weeks case.5 The
subjects were told that one payoff level (€7 - €10 or €20 - €25) would be chosen randomly, and each of
the three delay scenarios would be played out for real. When the SS option in each delay scenario became
imminent, subjects were asked to indicate their preference between SS and LL again. In order to minimize
5
Because of practical limitations, we were not able to employ the 2 weeks-4 weeks case.
11
any concerns of consistency on the part of the subjects, they were told that the previous records were not
taken into consideration. After the subjects indicated their choice between SS and LL, payments were
made, if applicable. This was repeated for all three scenarios on the respective days, starting from the
initial experimental day.
---- Insert Table 4 about here ----
Results and Discussion. As in Study 1 and 2, Table 4 only describes the option pairs for when the payoffs
were “distant”. For the payoff pair €7- €10, there is evidence for RTI at the aggregate level in the first two
delay scenarios: 29% of the subjects preferred LL in the “distant” conditions, compared to 71% and 58%
in the “immediate” conditions. Females and males have similar tendencies; however the evidence is weak
for males. Another observation is that the proportion of subjects preferring to wait for LL in the
“immediate” condition decreases as the interval between SS and LL increases. For the payoff pair €20€25, we observe RTI for all subjects group when the delay interval is two days. For longer delays, there is
no evidence in either direction of time inconsistency.
Looking at individual data, 32% of the subjects were consistently showing RTI for both payoff
pairs and for all three delay options; 18% were constantly exhibiting TI, and 21% of the subjects were
time-consistent in all of their choices. The remaining 29% exhibited different behaviors in different
payoff-delay conditions.
General Discussion for Studies 1 - 4
Although Studies 1 through 4 provide substantial evidence for RTI, a simple generalization
regarding the incidence of RTI or TI does not seem to avail itself. Rather, our results suggest that the
extent of time-inconsistency in either direction depends on the context and the decision makers’
characteristics. More specifically, delay times of the payoffs, type and size of the payoffs, and gender
altogether influence the direction of time inconsistency:
12

When payoffs are framed as loyalty program rewards (hence requiring effort), gender, type and
size of the rewards, and incentive compatibility affect the extent of TI or RTI. Male participants
are inclined to exhibit RTI and females exhibit TI when loyalty rewards are hypothetical (Study
1). However, in the case of real rewards (Study 3), RTI seems to be more relevant for females and
TI for males. We should note that Study 3 differs from Study 1 both in terms of incentive
compatibility and the nature of the reward (croissants versus supermarket coupons/movie tickets);
hence, this interpretation is not without reservation. Nevertheless, one key finding from Studies 1
and 3 is that even though RTI / TI is exhibited by males and/or females, it may be overlooked
when only the aggregate data is considered in the data analysis.

Studies 2 and 4 indicate that, in the case of neutral monetary rewards (requiring no effort per se),
the relative size of SS and LL payoffs and the time interval between them affect the degree of
RTI and TI. When the size of the payoffs in options SS and LL are relatively close to one another
(e.g. $7-$10 or $20-$25, as opposed to $4-$10 or $10-$25), RTI is more likely to occur,
especially when the payoff is hypothetical. When the SS reward is relatively smaller than the LL
reward, there is a lower tendency for RTI.
The main conclusion suggested by these findings is that intertemporal preferences are richer than
previously recognized in the literature. In particular, some individuals may exhibit RTI (or TI) in a variety
of settings, but we fail to notice this behavior while examining only the (sample) averages. As a next step
we will discuss some possible explanations that may account for our findings regarding RTI.
1. Utility from Delayed Consumption. One related issue is the additional utility derived from savoring
(Loewenstein 1987). It is possible that savoring about a payoff or a consumption experience may lead
individuals to defer the consumption when it is imminent. There are no clear guidelines as to what type of
products or payoffs are likely to yield such a utility; in our case, croissants may be such a product.
However, this account fails to explain why individuals do not prefer (derive additional utility from
savoring) the larger-later payoff to begin with.
13
2. Effort Uncertainty. A second possible account is that at the outset some individuals may not be sure
whether they could exert the effort or patience for the larger-later payoff, and hence, smaller-earlier
payoff seems more feasible. However, when the smaller-earlier payoff is due, the extra effort required for
the larger-later payoff appears to be more reasonable, compared to what it has taken until then. For
instance, after having bought 10 croissants and qualifying for a free one, the additional 5 croissant
purchases needed for two free croissants may be perceived as easily doable. Our empirical work above
provides two pieces of evidence against the effort explanation. For one, subjects exhibited RTI for
effortless payoffs as well (Studies 2 and 4). Yet, one can still argue that the passage of time per se triggers
some form of mental effort or cost at the outset, which may be disregarded later on (similar to the lack of
a sunk time cost effect, as discussed in Soman 2003). Second, we observed RTI for hypothetical payoffs
in cross-sectional designs (Studies 1 and 2). However, even for hypothetical payoffs, there may be some
perceived or imagined effort linked to temporal investments (Soman 2004). Hence, our empirical analysis
does not quite rule out the effort explanation altogether. A further examination of this problem should
measure the perceived / imagined effort (or any mental cost of waiting).
3. Affect. A third possible explanation is that our findings may reflect affective responses rather than
deliberate or analytical responses. That is, RTI may occur due to the relative affective salience
(evaluability) of information and individual characteristics (see Slovic et al. 2002a, 2002b for a discussion
of affective decision making). It is possible that a payoff may be weakly evaluable when it is immediate,
making it less attractive compared to a very close, but not immediate, payoff. Slovic et al. (2002a) report
a study where a simple gamble with only one possible gain was rated as less attractive than the same
gamble with an additional small loss. A similar finding was reported in Fetherstonhaugh et al. (1997): a
life saving equipment was rated higher when subjects were told that it could save 98% of the passengers
than the case of saving all passengers. The relevance of such an affective mechanism in intertemporal
choice could be examined by looking at the condition where the delay time for the smaller payoff is very
short, for instance one day, rather than immediate.
We ran a follow-up study at INSEAD to examine the role of affect in RTI behavior (Study 5).
14
Participating students received a flat payment. We used $20-$25 as the payoff pair and three delay time
pairs (3 days-1 week, 1 week-2 weeks, and 2 weeks-4 weeks) from Study 2a. In addition to the “distant”
and “immediate” conditions, a “tomorrow” condition is included where SS payoff is to be received in one
day. The “tomorrow” condition involves 1 day-5 days, 1 day-8 days, and 1 day-15 days as the delay times
-- that correspond to the respective cases in the “immediate” and “distant” conditions. 81 subjects
answered all nine choice questions.
---- Insert Table 5 about here ----
If difficulty of evaluating immediacy plays a role in RTI, then the preference for the LL option
should be larger for the case of “immediate” SS condition than for the “tomorrow” and “distant” SS
conditions -- preference for LL in the tomorrow and distant conditions may possibly be similar. The
results are summarized in Table 5. Percentages for “immediate” are larger than those for “tomorrow”
across all groups and delay times, but in only two cases the differences are significant. In addition,
percentages are significantly larger for the “tomorrow” condition than for the “distant” condition in six
cases. Therefore, affect seems have some role in the RTI behavior, but it is limited. We note that our
within-subjects design is a stronger test; a between-subjects design may offer further evidence.
4. Form of Discounting. Finally, RTI may be associated with a discounting function of a particular
characteristic. We noted earlier that TI behavior can be captured by a hyperbolic discount function.
Hyperbolic discounting is characterized by heavier discounting of outcomes that are temporally close to
the current period, compared to distant ones. In contrast, RTI indicates a lower discounting for temporally
close outcomes. The intuition is as follows: In RTI, the smaller payoff is preferred when it is temporally
close to the current period (compared to the distant larger payoff); but as the smaller payoff becomes
immediate and the larger payoff becomes close, the larger payoff is preferred. Lower discounting of
outcomes that are close to the present indicates a discount function that has a smaller slope at first than
later, and then presumably the slope decreases again. A reverse-S form has these characteristics; it is
15
illustrated in Figure 2 below vis-à-vis hyperbolic and exponential forms. In the Appendix we show that a
reverse-S shape discounting function can accommodate RTI.
---- Insert Figure 2 about here ----
It has been long known that the inferred shape of the discount function varies with the elicitation
technique (e.g. Ainslie 1975). In order to further investigate the reverse-S form discounting suggested by
the choice tasks in Studies 1-4, we elicited individual discount functions also by using valuation /
matching tasks. In two studies run at Koç University, presented below, subjects reported the future values
for which they were indifferent with the corresponding present values.
The first study, based on hypothetical payments, was part of a booklet of surveys. There were 120
student participants. Unfortunately we do not have data regarding the gender of the subjects, because the
survey was part of a project unrelated to the current paper. We asked subjects to state future amounts that
would be as attractive as $10 today.6 The time delays used were 1 week, 2 weeks, 4 weeks, and 6 months.
Corresponding discount factors were plotted as a graph, and we examined each subject’s discount
function visually. For benchmarking purposes, we also included exponential discounting curves (for a few
discount factors), as well as an exponential curve fitted to the subject’s discounting data, on the graph.
From the 120 discounting curves, 18 resemble reverse-S shape, 77 hyperbolic, and 9 exponential. 16
subjects had discounting curves that were difficult to label or data was not usable (missing data,
valuations less than $10 etc.).
The second study uses an incentive compatible scheme. 60 student subjects (38 female, 22 male)
received a monetary payment at the end of the experiment. The study involves a web-based interface, and
data was collected in one session in a computer lab. Subjects were asked to provide the smallest future
6
Our decision to use “delayed value of an immediate reward” rather than “immediate value of a delayed reward”
was based on a pretest; in a paper-pencil test, we had found that the latter led to much unusable data.
16
amounts they would accept in the future, instead of receiving a set of present amounts. There were 21
valuation questions using combinations of three present payoffs ($6, $13, and $21) and seven delay times
(1 day, 2 days, 3 days, 4 days, 1 week, 2 weeks, and 4 weeks). We used an incentive-compatibility
scheme adapted from Kirby and Marakovic (1995). At the end of experiment, subjects were paid either
their stated future valuation or the present payoff for one of the questions chosen randomly. Whether the
particular subject received the future or present amount was determined through an auction -- in order to
eliminate the temptation to state large future figures. Participants’ stated future valuations were entered as
bids to an auction. The participant who stated the smallest future amount was to receive that amount in
due time, and the other participants received the present amount.7 After the valuation questions, subjects
completed an unrelated survey. This second part provided us the additional time needed for all subjects to
finish our main study before any of them claimed the payoff. Payments were made for “present payoff $6
- future payoff in 1 week” combination.8
In terms of data analysis, as in the hypothetical payments study, we examined the discount
functions of each subject for each payoff separately. For $6, 8 out of 60 subjects had a reverse-S shape
discount function. There were 19 functions that resembled hyperbolic, and 8 resembled exponential
curves. Data from 25 subjects was either not useful (valuations less than $6, etc.) or could not be
categorized. There were a number of curves with significant ups and downs. This may be due to the fact
that the question order was randomized; and unlike the previous hypothetical payments survey, subjects
were not able to see and adjust their valuations for different future times. For $13, there were 13 subjects
with reverse-S discounting, 15 with hyperbolic, and 9 with exponential forms. Data from 23 subjects was
7
Theoretically, revealing true preferences is the optimal strategy in the second-price auction. The reason for using a
first-price auction is that it is easier to explain to the participants. In any case, efficiency loss compared to secondprice auction is small when number of participants is high, and we are interested in the shape of the discount
function (relative valuations of future payoffs).
8
We actually paid a round figure (in local currency terms) higher than $6.
17
not useful or not categorized. For $21, there were 10 reverse-S, 14 hyperbolic, and 8 exponential discount
functions; and data from 28 subjects was not useful or not categorized. Over all the payoffs ($6, $13, and
$21), the proportion of females with reverse-S-like discounting was slightly higher, but not significantly
different, than of the corresponding males.9 To summarize, our incentive compatible study also provides
evidence that a portion of individuals do exhibit reverse-S discounting.
To summarize the discussion on possible explanations for RTI, we observed that reverse-Sshaped discounting is not an exception and can potentially explain the observed RTI behavior. In
addition, affect seems to have some role in RTI, but the evidence limited. Finally, effort uncertainty as an
explanation needs further investigation.
Conclusion
The main contribution of the current paper is that it is the first study that defines reverse timeinconsistency explicitly as a new anomaly in intertemporal choice. Sholten and Read (2005) observed this
behavior in a subset of their participants, and classified it as an anomalous inconsistency pattern. Airoldi
et al (2005) report that, if anything, people become more impatient over time (a behavior that we label as
the RTI behavior) rather than becoming patient (implying TI). In a recent elicitation study which
introduces time-tradeoff sequences as a new method to measure intertemporal preferences (that does not
require any knowledge about the utility function), Attema et al. (2006) observed increasing impatience
initially and then constant discounting. In our study, we provide extensive empirical evidence that RTI is
indeed a robust phenomenon, rather than a one-time experimental artifact. We also explored possible
explanations for this behavior; affect and reverse-S shape discounting seem to contribute to RTI -- and
there is evidence that individual discount functions are in fact quite diverse.
Our findings have potential implications for decision makers. For instance, a bank may allow
9
When we look at the aggregate of all subjects, hyperbolic discounting seems to prevail for each payoff, and the
overall level of discounting seems to decrease with increasing payoff size. No difference was observed between
females and males.
18
(and offer incentives when profitable) its customers to extend the term of a deposit account when the
original due time approaches. For loyalty programs with multiple reward levels, changing preferences
when consumers qualify for smaller rewards may have implications for planning the reward redemption
process or program profitability.
In terms of future research directions, more evidence on RTI would be much insightful; in
particular, regarding the context where it is more or less likely to be observed. For instance, gender
differences in temporal preferences seem to require further research. In addition, we did a preliminary of
investigation of whether RTI can be explained by the shape of the discounting function. Future research
may consider a more detailed measurement of discount function (with more time points), and a
comparison of discounting forms elicited by different methods from the same subjects -- although such an
approach may have practical difficulties. Finally, future research may examine other possible
explanations of the RTI behavior.
19
Table 1a Results from Study 1a - INSEAD
Percent preferring to wait for LL in
“distant” vs. “immediate” conditions
Females
Option pairs (for “distant”)
N=25
Males
n=30
n=22 n=20
Total
n=47 n=50
SS: $10 after spending $100
LL: $25 after spending $200
48%  20% b
32%  85% a
40%
46%
SS: 1 ticket after 3 tickets
LL: 2 tickets after 5 tickets
72%  50% c
32%
51%
48%
NOTE:
45%
a: difference is significant with p < 0.01; b: with p < 0.05; c: with p < 0.10.
Table 1b Results from Study 1b - Koç University
Percent preferring to wait for LL in
“distant” vs. “immediate” conditions
Females
Males
Total
Option pairs (for “distant”)
N=26
n=28
SS: $3 after spending $30
LL: $7.5 after spending $60
50%
46%
37%
45%
44%
46%
SS: 1 ticket after 3 tickets
LL: 2 tickets after 5 tickets
42%
43%
50%
59%
46%
50%
NOTE:
None of the pairwise differences is significant.
n=24 n=22
n=50 n=50
20
Table 2a Results from Study 2a - Koç University
Percent preferring to wait for LL in
“distant” vs. “immediate” conditions
Option pairs (for “distant”)
Females
Males
Total
n=32 n=29
n=38 n=31
n=70 n=60
SS: $7 in 1 day
LL: $10 in 3 days
38%  72% a
32%  81% a
34%  77% a
SS: $7 in 3 days
LL: $10 in 1 week
19%  45% b
18%  42% b
19%  43% a
SS: $7 in 1 week
LL: $10 in 2 weeks
3%  28% a
11%  26% c
7%  27% a
SS: $7 in 2 weeks
LL: $10 in 4 weeks
6%
11%
9%
SS: $20 in 1 day
LL: $25 in 3 days
44%  72% b
26%  84% a
34%  78% a
SS: $20 in 3 days
LL: $25 in 1 week
19%  52% a
16%  71% a
17%  62% a
SS: $20 in 1 week
LL: $25 in 2 weeks
6%  38% a
8%  29% b
7%  33% a
3%
5%
4%  13% c
SS: $20 in 2 weeks LL: $25 in 4 weeks
NOTE:
14%
14%
a: difference is significant with p < 0.01; b: with p < 0.05; c: with p < 0.10.
10%
13%
12%
21
Table 2b Results from Study 2b - Koç University
Percent preferring to wait for LL in
“distant” vs. “immediate” conditions
Option pairs (for “distant”)
Females
Males
Total
n=26 n=26
n=33 n=31
n=59 n=57
SS: $6 in 1 day
LL: $10 in 3 days
38%  96% a
48%  100% a
44%  98% a
SS: $6 in 3 days
LL: $10 in 1 week
46%  69% c
48%  84% a
47%  77% a
SS: $6 in 1 week
LL: $10 in 2 weeks
27%  62% b
18%  65% a
22%  63% a
SS: $6 in 2 weeks
LL: $10 in 4 weeks
15%
18%  35% c
17%  35% c
SS: $20 in 1 day
LL: $30 in 3 days
50%  92% a
67%  97% a
59%  95% a
SS: $20 in 3 days
LL: $30 in 1 week
52%  88% a
52%  81% b
47%  84% a
SS: $20 in 1 week
LL: $30 in 2 weeks
31%  81% a
39%  94% a
36%  88% a
SS: $20 in 2 weeks LL: $30 in 4 weeks
23%  62% a
21%  68% a
22%  65% a
NOTE:
35%
a: difference is significant with p < 0.01; b: with p < 0.05; c: with p < 0.10.
22
Table 2c Results from Study 2c - INSEAD
Percent preferring to wait for LL in
“distant” vs. “immediate” conditions
Females
Males
Total
Option pairs (for “distant”)
n=16 n=15
n=17 n=19
n=33 n=34
SS: $4 in 3 days
LL: $10 in 1 week
63%  100% a
82%
73%
79%
SS: $4 in 1 week
LL: $10 in 2 weeks
38%  87% a
76%  47% c
58%
65%
SS: $4 in 2 weeks
LL: $10 in 1 month
6%  60% a
71%  37% b
39%
47%
SS: $4 in 1 month
LL: $10 in 2 months
6%  33% c
76%  11% a
42%  21% c
SS: $10 in 3 days
LL: $25 in 1 week
81%
93%
94%  63% b
88%
SS: $10 in 1 week
LL: $25 in 2 weeks
63%
80%
94%  37% a
79%  56% b
SS: $10 in 2 week
LL: $25 in 1 month
44%  73% c
82%  16% a
64%  41% c
6%  53% a
76%  5% a
42%
SS: $10 in 1 month LL: $25 in 2 months
NOTE:
a: difference is significant with p < 0.01; b: with p < 0.05; c: with p < 0.10.
63%
76%
26%
23
Table 3 Results from Study 3
Percent preferring LL (2 croissants) when:
“joining the program” vs. “completing 10 purchases”
Females
Males
Total
n=20
n=27
n=47
25%  95% a
NOTE:
70%
56%
a: difference is significant with p < 0.01; c: with p < 0.10.
51%  72% c
24
Table 4 Results from Study 4
Percent preferring to wait for LL in
“distant” vs. “immediate” conditions
Option pairs (for “distant”)
Females
Males
Total
n=17
n=21
n=38
SS: €7 in 1 day
LL: €10 in 3 days
24%  76% b
33%  67% c
29%  71% a
SS: €7 in 3 days
LL: €10 in 1 week
18%  59% b
38%
57%
29%  58% b
SS: €7 in 1 week
LL: €10 in 2 weeks
18%
29%
38%
43%
29%
SS: €20 in 1 day
LL: €25 in 3 days
41%
59%
29%
57%
34%  58% c
SS: €20 in 3 days
LL: €25 in 1 week
35%
29%
29%
33%
32%
32%
SS: €20 in 1 week
LL: €25 in 2 weeks
29%
18%
29%
29%
29%
24%
NOTE:
a: difference is significant with p < 0.01; b: with p < 0.05; c: with p < 0.10.
37%
25
Table 5 Results from Follow-Up Study 5
Percent preferring to wait for LL in
“distant” vs. “tomorrow” vs. “immediate” conditions
Option pairs (for “distant”)
Females
Males
Total
n=34
n=47
n=81
SS: €20 in 3 days
LL: €25 in 1 week
24%
32%
41%
23%  a 51%  b 64%
23%  a 43%  a 54%
SS: €20 in 1 week
LL: €25 in 2 weeks
6%  b 26%
32%
11%  b 26%
9%  a 26%
32%
SS: €20 in 2 weeks
LL: €25 in 4 weeks
3%
18%
6%
5%  b 13%
17%
NOTE:
12%
a: difference is significant with p < 0.01; b: with p < 0.05.
15%
32%
17%
26
Figure 1 Overview of Experimental Designs
Cross-Sectional
Longitudinal
Loyalty Program
Study 1
Study 3
Neutral Payoff
Study 2
Study 4
Figure 2 Illustrative Discount Functions
discounted
1
reverse-S
w exponential
 hyperbolic

0
delay period
27
Appendix
Consider a decision maker who faces a choice between receiving a payoff R1 in period t1 and payoff R2 in
period t2, where R1  R2.
Figure A1 RTI and Reverse-S Discounting
(t2  t1)
(t1)
(t2)
t2  t1
0
t1
t2
t
Assume that the discounting function (t) is such that in period t = 0 she prefers to receive R1:
U(R1) (t1)  U(R2) (t2)
 U(R1)  U(R2) (t2) / (t1)
(A1)
When R1 is immediate, that is t = t1, she would compare:
U(R1) and U(R2) (t2  t1)
She may change here preference to receiving R2 in t2  t1 periods from that time point only if
(t2) / (t1)  (t2  t1)
If the reverse-S discounting function is such that (t) is steeper in [t1, t2] than in [0, t1], then (t2) / (t1)
could be notably less than 1, and (t2  t1) could be close to 1. In other words,
(t2) / (t1)  (t2  t1) could be satisfied.
28
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