ISSN (Print) 0473-453X

Discussion Paper No. 1237

ISSN (Online) 2435-0982

FRAMING EFFECTSON TIME PREFERENCES:
THE IMPACT OF INVESTMENT
AND LOAN CONTEXTSIN INTERTEMPORAL CHOICES

Shohei Yamamoto
Shotarao Shiba

April 2024

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

Framing Effects on Time Preferences: The Impact of Investment and Loan Contexts inIntertemporal Choices

Shohei Yamamoto1 and Shotarao Shiba2
Abstract
Our decisions frequently involve the combinations of gains and losses occurring at different points intime, such as enduring early losses for future gains (investments), or enjoying immediate gains at theexpense of future losses (loans). This study introduces novel experiments that examine how binaryintertemporal payment options, framed as either investments or loans, influence decision-making.
Each option comprised two payment components: common payments, which are identical between
the options, and main payments, which vary between the options. Through strategic manipulation ofthese payments, the study explores how investment or loan frames affect time preferences. Our studies
consistently indicate that the common payments tend to be disregarded, thus the preferences areaffected by framing. Notably, this remained true even when common payments were substantial(Study 2), and the framing effect was also found in scenarios where decisions carried real financial
consequences (Study 3).
Keywords: time preferences, framing, cancellation

1

Graduate School of International Corporate Strategy, Hitotsubashi University, Tokyo, Japan (ORCID:
0000-0002-8136-6842). Correspondence concerning this article should be addressed to Shohei Yamamoto.
Email: syamamoto@ics.hub.hit-u.ac.jp
2
Faculty of Economics, Toyo University, Tokyo, Japan (ORCID: 0000-0002-7494-531X)

1

Acknowledgements: This research has benefited from the financial support of (a) the Joint
Usage/Research Center, the Institute of Social and Economic Research (ISER), Osaka University,and (b) Grants-in-aid for Scientific Research No. 21K13257 from the Japan Society for the
Promotion of Science. The experiments reported in this paper has been approved by IRB at
Hitotsubashi University (No. 2021A011).

2

Framing Effects on Time Preferences: The Impact of Investment and Loan Contexts inIntertemporal Choices
Time preferences involving gains and losses are crucial in many decision-making processes.
Researchers have extensively studied the discounting behaviors associated with time preferences ingain and loss domains, and findings suggest that these preferences differ. Individuals tend to
discount future outcomes more heavily in gain domains compared to loss domains (e.g., Benzion etal., 1989; Ikeda et al., 2010; MacKeigan et al., 1993; Molouki et al., 2019; Thaler, 1981). Thisphenomenon is commonly referred to as the sign effect (Frederick et al., 2002).
Intertemporal decision-making often entails trade-offs between gains and losses, which we canclassify into two distinct domains in this paper: the investment domain and the loan domain. The
investment domain involves losses sooner and gains later. Such situations include instances whereindividuals forego immediate consumption of enjoyable goods or services to save money, with the
expectation of receiving greater benefits in the future. This is commonly observed in contexts suchas pension plans and investment portfolios. Conversely, the loan domain involves gains sooner andlosses later. Such situations include instances where individuals make purchases using credit,
enjoying immediate gains in the form of goods or services, but incurring future losses when theymust repay the borrowed amount, as seen in contexts like credit card debt and mortgages. Despite
the apparent importance of these domains, the difference in time preferences between them has notbeen thoroughly explored, except in a few studies (Meissner & Albrecht, 2022; Schleich et al.,2021; Walters et al., 2016). These studies have shown that debts from loans are discounted at alower rate than returns from investments, a phenomenon referred to as saving-borrowing
asymmetry or debt aversion. Meissner and Albrecht (2022) allowed participants to accept or reject
various debt and saving contracts with an incentivized experiment. They systematically observedthat participants consistently preferred saving contracts over debt contracts, even after controlling3

for time preferences, risk aversion, and loss aversion. Their structural estimation revealed that asubstantial majority (89%) of participants exhibited aversion to being in debt.
Given the substantial influence of domains on time preferences, it is reasonable to consider thatthe framing of intertemporal choices across different domains may also impact preferences. The
framing effect was a well-established phenomenon in economics, psychology, and other disciplines(Tversky & Kahneman, 1981). This effect suggests that decisions are affected by how choices arepresented, even when the final consequences of the options remain unchanged.
Loewenstein (1988) highlighted that the way intertemporal options are presented as either
speeding up or delaying outcomes influences choices significantly. For instance, individuals who
anticipated receiving a VCR in a year were willing to pay an average of $54 to get it right away,
whereas those expecting it immediately required an average of $126 to agree to a one-year delay.
Additionally, the strength of framing effects can even reverse the sign effect, showing that
individuals are more inclined to discount future outcomes by merely changing the frames of theintertemporal choices decisions, e.g., an acceleration frame in which the default is to realize theoutcomes in the future and a delayed frame in which the default is to realize the outcomes today(Appelt et al., 2011; Benzion et al., 1989; Shelley, 1993, 1994; Yamamoto et al., 2020).
Framing choices as multiple events has been shown to have an impact on preferences, as
demonstrated by Thaler (1985) and Thaler and Johnson (1990). Thaler's study involved framing
outcomes as multiple events, and participants were asked to evaluate which frames they considered
to be more favorable. For instance, they were presented with a choice between receiving $100 andthen paying $80, or receiving $20 as a single outcome. The majority of participants strictlypreferred for the single outcome of receiving $20, despite the total outcomes being identical. Thaler
and Johnson (1990) showed another evidence that separating outcomes has an impact on
preferences. Participants perceived greater happiness when gains were temporally separated,4

indicating a preference for receiving multiple gains separately. Linville and Fischer (1991) also
found similar results which the subjects preferred to temporally separate two positive events.
This paper specifically focuses on the specific type of framing similar to Thaler (1985), which
involves dividing outcomes into multiple components or manipulating the values of various
outcomes to highlight common components in choices. In these kinds of situations, individuals havea tendency to disregard shared components when making decisions. This phenomenon, known ascancellation, was demonstrated by Kahneman and Tversky (1979). Participants in their study were
presented with two choice options following a prior bonus. In the first scenario, participants were
given a bonus of 1,000 and subsequently had to choose between Lotteries A and B:⚫

Lottery A: a 50% chance of winning 1,000, with no win otherwise⚫

Lottery B: a guaranteed win of 500

In the second scenario, participants received a bonus of 2,000 and then had to choose between
Lotteries C and D:⚫

Lottery C: a 50% chance of a loss of 1,000, with no loss otherwise⚫

Lottery D: a guaranteed loss of 500

Interestingly, despite equivalent overall outcomes between Lotteries A and C, as well as B and D,
the majority favored Lottery B in the first scenario and Lottery C in the second. These results
suggest that individuals tend to overlook the common prior bonus and instead focus on the specificoutcomes of the lotteries.
Wu (1994) study also observed the occurrence of cancellation in risky decision-making andrevealed that participants exhibit a tendency to disregard outcomes that are transparently common
in lottery choices. For instance, when given the choice between a risky lotteries, X and Y:⚫

Lottery X: a 32% chance of winning $3,600, a 1% chance of winning $3,500 and no win
otherwise5⚫

Lottery Y: a 32% chance of winning $3,600, a 2% chance of winning $2,000 and no win
otherwise

participants overlooked the shared chance of winning $3,600, focusing instead on the distinct
outcomes to determine their preferable lottery.
Weber and Kirsner (1997) conducted a similar experiment investigating choices between a safer
lottery and a riskier lottery. Each lottery consisted of three outcomes, with one outcome being
common between both lotteries. By varying the magnitude of this common outcome, they found no
significant impact on the selection of the riskier option, reinforcing the cancellation concept.
Cancellation has been documented in ambiguity choices as well (Schneider et al., 2018). The
consistent observation of this phenomenon across different studies and variations in common
outcome magnitudes attesting to its durability in decision-making processes.
Given these findings, it is plausible to influence intertemporal decisions by manipulating
common outcomes and framing intertemporal choices across various domains. This is due toindividuals' tendency to ignore common outcomes, potentially leading to shifts in preferences.
Related literature, such as Abraham et al. (2020), found a significant framing effect on choices
between income-driven loan repayment plans and standard fixed-amount repayment plans byemphasizing cost aspects of the plans. However, their framing approach differs from ours, which
involves presenting outcomes in multiple components. To our knowledge, no previous studies havedemonstrated the impacts of investment or loan frames on decisions due to cancellation.
Our novel experiments presented binary intertemporal payment choices framed as investments
and loans. Initially, we devised options that offered payments at both sooner and later dates, andthen we divide the payments for each option into two components: common payments (CPs), where
the payment amounts are common to both choices, and main payments (MPs), where the payment
amounts differ between choices. Consequently, each option has two distinct payments at both

6

sooner and later dates (see Figure 1 for an example question). By varying the CP amounts, we cancreate different frames without altering total outcomes, effectively transforming the MPs into either
investment and loan domains. This led us to hypothesize that CPs are disregarded and decisions are
based solely on MPs, thus the Investment frame or Loan frame affects time preferences.
We conducted three online studies in which participants were presented with realistic scenarios
requiring them to choose between projects offering different payments at sooner and later dates. In
Study 1, we observed distinct differences in individual discount factors (IDFs) between the framed
scenarios and a control (No frame) scenario, showing a pronounced framing effect. This finding
suggests that participants likely overlooked the common payments (CPs), concentrating instead on
the main payments (MPs) when making their decisions.
Study 2 showed that the observed framing effect was both substantial and consistent. Study 2delved deeper into the extent of this effect, revealing that even significantly larger CPs—sufficient
to change the total outcome's domain—seemed to be disregarded by participants.
Study 3, based on the experimental design of Study 1, introduced incentives for the decisionmaking process, also demonstrated a significant framing effect from the Loan frame, akin to Study
1’s findings. Moreover, the comparison of IDFs between Study 1 and Study 3 revealed nosignificant differences, affirming the reliability of decisions made in the hypothetical scenarios.

Study 1: Influence of Investment and Loan Frames on Intertemporal Choices
Our first study was designed to test how Investment and Loan frames affect time preferences in
Gain and Loss sections. In these scenarios, total outcomes are positive for the Gain section andnegative for the Loss section. We will also confirm whether individuals ignore common payments(CPs) when making these decisions.

7

Method
Participants. In Study 1, we recruited 300 participants for our experiment through the online
platform Prolific (39% female, mean age = 40 years, age range: 18-73 years, nationality: UK). Our
target was collecting around 100 participants each for three treatments: No frame, Investment frameand Loan frame. The study took an average of 7 minutes and 18 seconds to complete andparticipants received a fixed compensation of £1.
Design and procedure. The participants were randomly assigned to one of three framing
treatments, each sharing identical total outcomes. Each participant went through two sections, Gainsection and Loss section. Participants were presented with hypothetical scenarios involving a choice
between two project sets, AC and BC, which included taking on Projects A and C or Projects B andC, respectively. Set AC and BC are assumed to be equally difficult and take an equal amount oftime to complete. The projects could be successful or unsuccessful, meaning that they directly get
the profits or suffer losses from the projects. The payments for the projects will be made today andin 2 months. After they read the scenario, participants were presented with the specific payments ofthe projects at the moment of making intertemporal choices. Note that both sets include Project C,
hence the payments from Project C are the CPs. The parameters in the first question that theparticipants saw for each frame are shown in Table 1 (See Figure 1 for an example of the actual
question that the participants saw).
Insert Table 1 about here.
Insert Figure 1 about here.
The payments in the study are denoted as (𝑀0 , 𝑀2 ), where 𝑀0 represents an immediate payment
and 𝑀2 denotes a payment realized in 2 months. In the No frame, the CPs were set to £8 today and£8 in 2 months, thus expressed as (8, 8). Positive values of M describe the amount of payment
subjects receive, while negative values of M indicate the amount of payments subjects lose. They8

chose between Set AC, with payments of (16,16) plus the CPs (8, 8), and Set BC, with payments of(X, 24) plus the CPs (8, 8). The value of X (varying from £0.1 to £16 in the No frame) started at 8
and varies based on the previous choices to identify indifference points where the options appeared
equally attractive. This method followed the modified Parameter Estimation by Sequential Testing(PEST) algorithm (Findlay, 1978; Walters et al., 2016): (1) The initial step size is 4; (2) The step
size was reduced each time the direction of change was reversed; (3) the step size remained thesame otherwise; (4) terminate the procedure when the step size becomes less than 1. The advantageof the PEST procedure is that the early choices do not constrain the range of possible indifference
points, as is the case with other titration methods.
In the Investment frame, the total outcomes mirrored those of the No frame, but the CPs weremanipulated to (32, 8) to reflect an investment context. This configuration resulted in MPs being
negative today and positive in 2 months. In the Loan frame, the CPs were set to (8, 48) to align MPs
with a loan context, resulting in MPs being positive today and negative in 2 months.
The Loss section was a reverse mirror of the Gain section, with all parameter signs reversed. For
example, in the No frame for the Loss section, choices were between Set AC, with (-16, -16) plus
the CPs (-8, -8), and Set BC, comprising (X, -24) plus the CPs (-8, -8). Notice that the MPs in theInvestment and Loan frames remain consistent between the Gain and Loss sections to becomparable. The order of the section was randomized.
To make sure that the participants understand the scenario, they need to pass the comprehension
question about the instructions before making the intertemporal choices. As most of the previous
papers investigating time preferences of losses (e.g., Abdellaoui et al., 2018), we utilized
hypothetical scenarios due to ethical and logistical concerns associated with subjects experiencing
financial losses at different times. The issue of incentivizing decisions is revisited in Study 3.
Detailed experimental instructions are available in the Online Appendix.

9

Exclusion criteria
We will exclude two types of extreme responses from our analysis. The first type of extreme caseis when participants consistently choose Project A, even when Project B (weakly) dominates A. For
instance, in the Gain section under the No frame treatment, a participant might choose Set BC,
which yields £24 today and £32 in two months, over Set AC, which provides £24 today and £24 in
two months. Such choices violate the principle of monotonicity, a fundamental property ofpreference theory, leading to the exclusion of these participants.1 The other type of extreme case isthat participants always choose Set BC. In that case, they would see, for example, Set AC (receive£24 today and £24 in 2 months) and Set BC (receive £8.1 today and £32 in 2 months in Gainsection in No frame treatment, thus the sooner date of project B is £0.1 in this option).2 Although
there is no theoretical reason to exclude the observations that participants choosing Set BC in theexample above, such choices indicate that the value in the sooner date of Project B (remember, Set
BC consists of project B and C) must be negative to make Set AC and BC indifferent. But now thisframe of the question would be no longer the same anymore (Investment frame in this example).
Therefore, we will exclude observations choosing B in the extreme question above. Anyway, suchpreferences infer the extreme monthly individual discount factor (IDF) of more than 1.40,
indicating that they chose extremely patient options. Similarly, in the Loss section, exclusion
criteria are based on violations of monotonicity and the exhibition of extreme IDFs that fall outside
the intended frames.

1

There was an additional question in which Set BC (receiving £24.1 today and £32 in two months)
unambiguously dominates Set AC (receiving £24 today and £24 in two months). Participants who select Set
BC in this question will be considered in our supplementary analysis (refer to Appendix B).
2
According to the rule of the modified PEST, it should be £0. However, we show £0.1 instead only in thisspecial case to keep all the payments positive.

10

Debt Aversion Measure (DAM) scale
After the intertemporal choices, the participants answered the Debt Aversion Measure (DAM;
Schleich et al., 2021) consisting of seven questions on a 6-point scale to measure the level of debt
aversion. The questions include, for example, “If I have debts, I like to pay them as soon as
possible” (1 = very much like me to 6 = not at all like me). We then created the variable DAM
describing the average score of the questions. This measure could potentially correlate with thevariations in decisions between the Loan and Investment frames. Walters et al. (2016) showed that
individuals with higher levels of debt aversion, as measured by the DAM, exhibited a more
pronounced saving-borrowing asymmetry. At the end of the experiment, they answered thequestions about their demographics, including age, gender and education.
Results and discussion
The demographic variables including age, gender and education across the treatments are notstatistically different, indicating the randomization properly works in this study (Table 2). We
report our analyses in this section, excluding the observations by following the rules above.3
However, we replicate the analyses including the observations which weakly violated monotonicity
in Appendix B. The overall results do not change indicating our results are robust.
Insert Table 2 about here.
Figure 2 presents the boxplot of monthly individual discount factors (IDFs) for each treatment.
The IDFs are calculated from the indifference points derived using the elicitation method outlinedin the preceding section. We employ the assumption of an additive utility function and a standard
linear model in intertemporal decisions to estimate them. For example, if the indifference value of
X is 12 in the No frame in the Gain section, the participant is indifferent between receiving £24

3

We have 6.33% of the observations that violate monotonicity and 1.33% of the observations that exhibit
extreme discounting in the Gain section and have 1.33% of the observations that violate monotonicity and 8%of the observations that exhibit extreme discounting in the Loss section.

11

today and £24 in 2 months and receiving £20 today and £32 in 2 months (24 + 𝛿 2 24 = 20 +
𝛿 2 32). Therefore, the monthly IDF (𝛿) is about 0.71 with the assumptions above. Lower IDFs areinterpreted as indicative of less patience.
In Figure 2, the IDFs appear to be lower in the No frame than the other frames in the Gainsection, suggesting that frames affect the decisions. Due to the non-normal distribution of IDFs
(Shapiro-Wilk test for each frame: p < .001), we employed non-parametric tests. The IDF in No
frame significantly differed from that in the Investment frame (Mann-Whitney U test; p = .02) andthe Loan frame (p < .001). In the Loss section, the IDF was appeared to be higher in the No frame
than in the other domains in the graph, suggesting the framing effect in the opposite direction
compared to the Gain section. Indeed, the IDF in the No frame was different from that in theInvestment frame (p < .01) and the Loan frame (p = .04). These findings support our hypothesis thatframing influences time preferences in both sections.
Insert Figure 2 about here.
In addition, the IDF in the Loan frame significantly differed from that in the Investment frame in
the Gain section (Mann-Whitney test; p < .01), aligning with the concept of saving-borrowing
asymmetry. However, the difference was not significant in the Loss section (p = .54).
Debt aversion, as measured by the Debt Aversion Measure (DAM),4 was investigated by Walters
et al. (2016) and found to be more pronounced in individuals with higher levels of debt aversion.
Our regression analysis, including only observations from the Investment and Loan frames in theGain section, introduced a Loan dummy variable (1 for Loan frame, 0 otherwise). The regression of
IDFs against DAM, Loan, and their interaction term revealed that the interaction term was not
significant, diverging from Walters et al. (2016)'s findings.

4

The mean score of the DAM in this study was 33.1, with 86.7% of participants reporting debt aversion
above the midpoint of the scale, echoing results of the previous studies.

12

Next, we compare the IDFs between the Gain and Loss sections. In the No frame, median IDFs
are higher in the Loss section (Wilcoxon signed-rank test; p < .001) aligning with the sign effect. In
contrast, in both the Investment and Loan frames, the IDFs were not significantly different (p = .07;
p = .11). These outcomes in the two frames support the cancellation hypothesis: despite constantMPs, the varying CPs did not significantly affect decisions, indicating that participants focused on
the MPs and disregarded the CPs in their decision-making process.
Nonetheless, the variation was not limited to the CPs; the total outcomes between the Gain and
Loss sections also differed. Therefore, decisions were influenced by both CPs and total outcomes,
potentially counterbalancing each other, cannot be entirely ruled out. However, this scenario seems
unlikely given the observed differences in IDFs between the No frame and the other frames in both
sections, despite identical total outcomes.
Study 2: Investigating the Boundary Condition of Common Payments Ignorance
We have thus far observed that time preferences are influenced by the Investment or Loanframes. This framing effect seems to arise from participants overlooking common payments
between options.
Study 1 tested only one specific CP for each treatment in each section. Furthermore, the CPs
were not large enough to change the domain of the total outcomes; total outcomes for all questionsin the No, Investment and Loan frames in the Gain section fell within the gain domain, and those in
the Loss section were within the loss domain. Different values of CPs or total outcomes mightsignificantly influence decisions. Higher values of CPs increase their relative importance,
particularly if they are large enough to shift the domain of the total outcomes, making it less likely
for the CPs to be ignored.
In Study 2, we use various CPs for each treatment while keeping the MPs constant (thus, the total
outcomes are no longer identical between main treatments) in the main treatments. The highest

13absolute values of CPs in this study were £32 today and £76 in 2 months, higher than in Study 1,
and some CPs were large enough to alter the domain of total outcomes.
Therefore, the aim of this study is to explore the framing effect's boundary conditions bymanipulating CPs. The cancellation hypothesis posits that preferences should remain consistent aslong as the MPs are identical. Conversely, if the domains of total outcomes or the magnitude of CPs
influence decisions, we should observe variations in the IDFs in such scenarios.5
MethodParticipants. We recruited 800 participants for our experiment via Prolific (48% female, mean
age = 43 years, age range: 18-84 years, nationality: UK). The study took an average of 6 minutes
and 4 seconds to complete and participants received a fixed fee of £0.8.
Design and procedure. This study replicated the scenario from Study 1, but exclusively focusedon the Gain section, so no Loss section in this study. Participants were randomly assigned to one ofeight treatments, with the initial parameters for each detailed in Table 3.
Insert Table 3 about here.
Six main treatments
Six main treatments featured identical MPs: (16, 20) for Project A and (8, 28) for Project B. The
experiment encompassed three domains of total outcomes: gain, investment and loan. Each domain
within the main treatments had two distinct CPs. Specifically:⚫

In the gain domain, gain_no had no CP, whereas gain_CP included a CP of (-6, -10).

⚫

In the investment domain, inv_CP presented a CP of (-32, 16), and inv_CPD offered adoubled CP of (-64, 36).

5

In Study 2, we also fixed the locations of options for MPs. In the main treatments, the left option isalways (16,20) and the right option is always (8, 28) in the first questions.

14⚫

In the loan domain, loan_CP involved a CP of (16, -32), with loan_CPD providing adoubled CP of (32, -76).

According to the cancellation hypothesis, the IDFs for all main treatments should be identical.
However, should the domain of the total outcome exert an influence on decision-making, the IDFs
across varying domains of total outcomes are expected to differ. For example, use gain_no as abaseline, the CP in loan_CP is sufficiently large to alter its domain from that of gain. Consequently,
if the domain of the total outcome impacts decisions, differences in IDFs between these two
conditions may be observed.
Furthermore, analyses within the same domain, such as inv_CP and inv_CPD, which both fallunder the investment domain, are conducted to assess whether larger CPs have a discernible effecton decision-making choices.
Two additional treatments
The remaining two domains were included to examine the effect of total outcomes. The
inv_CPD’ treatment, representing a specific frame of inv_CPD, shares the same total outcome as
inv_CPD but without CPs. Similarly, loan_CPD’, a specific frame of loan_CPD presents identical
total outcomes as loan_CPD but without CPs.
Following the intertemporal decision-making tasks, participants completed the Debt Aversion
Measure (DAM) and demographic questions including age, gender and education, as in Study 1.

15Results and discussion.
The demographic variables including age, gender and education across the treatments are notstatistically different, indicating the randomization properly works in this study (Table 4). We
applied the same exclusion criteria as in Study 1.6
Insert Table 4 about here.
Figure 3 displays the boxplot of IDFs for each treatment, which aligns with the cancellation
hypothesis. The IDFs of the six main treatments with different CPs did not show significant
differences (Kruskal-Wallis test; p = .59). This outcome supports the cancellation hypothesis andsuggests that participants primarily focused on the MPs while making decisions, overlooking theCPs.
We will examine a possibility that preferences are influenced by both CPs and total outcomes,
with these effects potentially neutralizing each other, although this is unlikely, as discussed in Study
1. To assess the impact of total outcomes, we analyzed two additional treatments.
The IDFs between inv_CPD and gain_no (treatments with identical MPs) were not significantly
different (Mann-Whitney test; p = 0.13). However, substituting inv_CPD with inv_CPD’ andretesting these treatments showed that the IDFs between inv_CPD’ and gain_no (treatments withdifferent MPs) were significantly different (p < .001). Similarly, the IDFs between loan_CPD and
gain_no (treatments with identical MPs) showed no significant difference (p = .56), while the IDFs
between loan_CPD’ and gain_no (treatments with different MPs) differ significantly (p < .001).
The findings further suggest the participants’ primary focus on MPs rather than total outcomes.
Insert Figure 3 about here.

6

We excluded 5.38% of the observations for violating monotonicity and 1.63% for extreme discounting. In
Appendix B, we replicate the analysis including the observations which weakly violated monotonicity as inStudy 1. The overall results remain unchanged, indicating the robustness of our findings.

16

In addition, the IDFs between inv_no and loan_no are different (p = .02). This is in line with theborrowing-saving asymmetry. We conducted the similar regression analysis to see the relationshipbetween the borrowing-saving asymmetry and DAM as in Study 1, but our findings are again
different from the results of Walters et al. (2016).7
Study 3: Incentivizing Choices in the Gain Section
The aforementioned studies consistently demonstrate that framing exerts significant influences on
individual time preferences. However, it is important to note that the decisions examined in thesestudies were not incentivized. While certain prior research papers have reported no disparity indiscount factors between real and hypothetical rewards (Johnson & Bickel, 2002; Madden et al.,2003), others have raised concerns regarding the hypothetical bias in intertemporal decisions.
Frederick et al. (2002) argued that uncertainty exists as to whether individuals, when presented withhypothetical rewards, are sufficiently motivated or capable of accurately predicting their actions if
the outcomes were real. Furthermore, Kirby and Maraković (1995) discovered that individuals
exhibited higher IDFs when the rewards were hypothetical.
Thus, we decided to incentivize the decisions only in the Gain section of Study 1 to examine theframing effect under such conditions. Incentivizing the Gain section is feasible because the overall
payment of the section is positive. However, we decided not to incentivize the Loss section of Study
1 due to some serious problems. Letting participants lose money in the future is ethicallychallenging since participants must be compensated after participating in experiments. To
circumvent this issue, we could provide endowments or allow participants to earn some money tocover the losses by completing tasks. However, that procedure also has significant flaws. If

7

The mean score of the DAM was 32.5, with 83.7% of participants reporting debt aversion above the
midpoint of the scale. To conduct the analysis, we only used the observations of treatments inv_no andloan_no. The dummy variable loan_no takes a value of 1 if the observations are in loan_no and 0, otherwise.
We regress IDFs on DAM, loan_no and the interaction term of these two variables. The interaction term was
not significant.

17

participants receive additional rewards not derived from the intertemporal questions, the rewards
can be considered as another common payment. Since we cannot differentiate these additional
rewards from CPs in our analysis, we decided to incentivize only the Gain section of Study 1.
MethodParticipants. We recruited 300 participants for our experiment via Prolific (52% female, mean
age = 44 years, age range: 18-81 years, nationality: UK). The study took an average of 7 minutes
and 32 seconds to complete.
Design and procedure. This study mirrored the Gain section from Study 1, with the key
distinction being the incentivization of intertemporal payment decisions. One in ten participants was
randomly chosen for actual payment at the study's conclusion.
After the intertemporal decisions, we asked the demographic questions similar to that in Studies 1
and 2. Additionally, we included exploratory questions that are potentially correlated withintertemporal decisions according to the previous studies. These questions include householdincome, McArthur scales of subjective social status (Adler et al., 2000) and DAM (Schleich et al.,2021).
For the participants selected for actual payment, the amounts were directly tied to the choices
they made during the experiment, and any show-up fees were not provided to them. One option was
randomly selected for payment on its scheduled date, with immediate payments issued on theexperiment day and deferred payments exactly two months from the experiment day. Those notselected for actual payment received a show-up fee of £0.8.
Results and discussion
The demographic variables including age, gender, education, income and McArthur scales,
examined across the treatments showed no significant differences for these four factors, with18

income being the sole exception. This outcome indicates that the randomization process was mostly
effective, as evidenced by the consistency in the four variables (Table 5).8
Insert Table 5 about here.
Figure 4 displays a boxplot of monthly IDFs for each treatment. Consistent with Study 1, we
found significant differences between the Loan frame and No frame (Mann-Whitney test; p = .02).
However, no significant difference was observed between the No frame and Investment frame (p= .37). In addition, the IDF in the Loan frame was not significantly different from that in theInvestment frame (Mann-Whitney test; p = .13).
Insert Figure 4 about here.
We compared the results with those from the Gain section in Study 1. The IDFs between thesestudies are not statistically different (Mann-Whitney test; No frame, p = .56; Investment frame, p= .43; Loan frame, p = .08), indicating that the results from incentivized and non-incentivized
experiments are not different. Repeating the regression analysis on the DAM from Study 1, ourfindings were consistent with those of Study 1 and did not reveal a stronger saving-borrowing
asymmetry among individuals with higher DAM.
We also analyzed the data based on participants' income levels, categorized observations by the
median income level: those earning at or above the median were classified into the higher income
group, while those earning below the median were placed in the lower income group. Notably, asignificant impact of the Loan frame was observed among lower-income participants (MannWhitney test; p = .03), whereas such an effect was absent among higher income participants (p= .2).

8

We excluded 10% of the observations that violate monotonicity and 4.67% of the observations thatexhibit extreme discounting by following the same rules used in the previous Studies 1 and 2. In Appendix B,
we replicate the analysis including the observations which weakly violated monotonicity as in Study 1. The
overall results remain unchanged, indicating the robustness of our findings.

19

The results clearly demonstrate that the impact of the Loan frame on intertemporal decisions in
the incentivized experiment and corroborate the findings from Study 1's Gain section, enhancing thecredibility of results from non-incentivized studies.
General discussion
Our series of three experiments investigated the impact of Investment and Loan frames on time
preferences, uniquely demonstrating that common payments (CPs) tend to be disregarded inintertemporal decisions.
In Study 1, we manipulated the presentation of monetary outcomes by dividing the payments
into CPs, which are identical between the option, and main payments (MPs), which payments
amounts differ between the options. This manipulation allowed the MPs to represent an investment
domain or a loan domain, termed the Investment frame and the Loan frame, respectively. Notably,individual discount factors (IDFs) differed between these frames and a control treatment (Noframe), illustrating a significant framing effect. Furthermore, the results suggest that participantstended to disregard the CPs, focusing primarily on the MPs in their decision-making.
Study 2 further examined the robustness and strength of the framing effect, demonstrating thateven large CPs, sufficient to change the domain of the total outcome, were generally disregarded.
Study 3 introduced incentives for intertemporal payment decisions, yet the significant framing
effect from the Loan frame persisted, aligning with Study 1's findings. Moreover, IDFs for overall
decisions did not differ from those in Study 1, suggesting that the results of non-incentivized
experiments were reliable.
Notably, in the incentivized experiment, no difference in IDFs was observed between the No
frame and Investment frame, which diverges from the findings of Study 1. The cause of thisdiscrepancy is not immediately apparent, but it does not seem to be attributable to the
incentivization, as the IDFs did not vary significantly between the Studies 1 and 3. This raises the20possibility that the lack of observable effect in the Investment frame may be due to a Type II error,
despite our relatively large sample size of 300, which was maintained consistently across Studies 1
and 3.
There might be an alternative explanation for the framing effect other than the cancellation
hypothesis. Both positive and negative payments were presented in the Investment and Loanframes. Furthermore, these frames included a mix of positive and negative payments for bothsooner and later dates, differentiating them from the No frame treatment, which exclusively
displayed either positive or negative payments. An auxiliary experiment, as detailed in Appendix A,
shows that exposure to a combination of positive and negative payments does not significantly
impact decision-making.
Our results were different from the unpublished work of Walters et al. (2016), who suggested thatborrowing-saving asymmetry is driven by individuals more averse to debt, as measured by the Debt
Aversion Measure (DAM). This difference could be due to our use of a single question and a
between-subjects design, as opposed to Walters et al.'s multiple-question, within-subjects approach.
Implications
Our findings have practical implications, showing that time preferences can be influenced
without changing total outcomes. This insight is applicable across various fields. In the stock
market, for instance, the framing effect might lead investors to prefer certain stocks over others,
despite identical total outcomes. Stocks typically generate profit through dividends and priceincreases. Our results imply that, despite identical total returns from different stocks, investors may
exhibit preferences. To illustrate, consider two hypothetical stocks: Stocks A and B. Both yield
identical dividends, whereas their prices fluctuate over time. The dividends in this scenario are akinto CPs, and the price changes resemble MPs in our experimental framework. By adjusting thecommon dividend values without changing the total outcomes, Stocks A and B can mimic21

Investment or Loan frames as in our experiments. Our findings suggest that these frames
significantly influence investor preferences, as they tend to overlook the common dividend
components and focus instead on fluctuations in stock prices. Nevertheless, this illustration does notaccount for the inherent uncertainty of stock prices, thus incorporating uncertain elements into ourexperimental design will be a potential future extension of our research.
Likewise, the framing effect could influence user preferences between opting for free accounts
or upgrading to premium memberships on platforms like Freelancer.com, a prominent freelancing
and crowdsourcing marketplace. This type of platform requires an upfront payment for premium
memberships that later offer additional benefits, resembling the structure of our Investment frame.
Even though overall advantages for premium and free members might be similar, users may show apreference for one over the other.
Our findings are also relevant to experiments where participants receive participation fees inadvance and then make financial decisions. A potential concern is that participants might factor inthese fees when making decisions. This is particularly problematic in experiments that incentivize
decisions about losses. In such cases, integrating the participation fee into the decision-making
process effectively transforms a decision about a loss into one about a gain. However, our results
indicate that participants tend to make their decisions without considering these upfront fees.

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26

Appendix A: Displaying a Combination of Positive and Negative Payments in the No Frame
Treatment
The observed framing effect in our studies appears to stem from the cancellation of common
payments in intertemporal questions, although alternative explanations may be viable. Notably, in
the Investment and Loan frames, each question displayed both positive and negative payments.
Moreover, these frames presented a mix of positive and negative payments for both sooner and later
dates, which contrasts with the No frame treatment, where only positive or negative payments wereshown. This exposure to a combination of positive and negative payments could influence decisionmaking, a phenomenon potentially described as the mixed-outcome effect.
First, the introduction of losses can provoke emotional reactions that impact decision-making
processes. Individuals are typically loss-averse, meaning losses are perceived as more significant
than equivalent gains (Kahneman & Tversky, 1979; Tversky & Kahneman, 1991). This loss
aversion is often driven by negative emotions such as fear or anxiety (Camerer, 2005). Furthermore,
people tend to disproportionately react to minor losses (Loewenstein et al., 2001).
Second, making decisions in the Investment and Loan frames could be more cognitively
demanding than in the No frame if participants aim for rational choices. To ascertain the overalloutcomes, participants in the No frame need to perform basic calculations: simple addition for the
No frame (simple subtraction in the gain_CP treatment in Study 2), versus both addition andsubtraction in the other frames to calculate the total amounts of sooner and later payments.
Thus, the framing effect found in our studies could be attributed to the simultaneous presence of
positive and negative payments at both sooner and later dates in the Investment and Loan frames.
This effect may be due to negative emotions or cognitive burdens associated with mixed outcomes.
This hypothesis, termed the mixed-outcome effect, is investigated in this auxiliary experiment.

27

Method
Participants. We recruited 500 participants for our experiment via Prolific (44% female, mean
age = 40 years, age range: 18-77 years, nationality: UK). The study took an average of 7 minutes
and 21 seconds to complete and participants received a fixed fee of £1.
Design and procedure.
This study utilized the same scenario as Study 1, with each participant going through Gain and
Loss sections. However, unlike Study 1, This study comprises five treatments, all of which are No
frame treatments. This means that MPs in sooner and later dates are consistently positive in theGain section and negative in the Loss section. The five treatments include four main treatments andone additional treatment. The four main treatments were designed to test the mixed-outcome
effects; hence, the values of the MPs are fixed, but the sign of the CPs in sooner and later dates ismanipulated to create either non-mixed or mixed outcomes. In non-mixed-outcome scenarios, eachquestion displayed only positive or negative payments, while in mixed-outcome scenarios, acombination of positive and negative payments was shown. The distinction between thesetreatments lies not only in the presence or absence of mixed payments but also in the total
outcomes. Therefore, the additional treatment was introduced to determine whether participants'
decisions were influenced by the total outcomes despite previous results from Studies 1 and 2
suggesting that total outcomes are unlikely to be a significant factor. The parameters of eachtreatment in the first question are detailed in Table A1.
Insert Table A1 about here.
Four main treatments and an additional treatment
The four main treatments in the Gain section presented the same MPs: (32, 32) for Project A and(16, 48) for Project B in the first question. The sooner payment of the Project A varies insubsequent questions to find indifference values, using the same method as in Studies 1, 2 and 3.

28

Each treatment featured distinct CPs. The treatments named No CP and Base represent non-mixedoutcome scenarios, while Mixed 1 and Mixed 2 correspond to mixed-outcome scenarios.
Specifically:⚫

No CP treatment (non-mixed-outcome) has no CPs, represented as (0,0).

⚫

Base treatment (non-mixed-outcome) includes CPs of (12, 12).

⚫

Mixed 1 treatment (mixed-outcome) includes CPs of (-12, 12).

⚫

Mixed 2 treatment (mixed-outcome) includes CPs of (12, -12)

An additional treatment, named Base’, representing a specific frame of Base, shares the same
total outcome as Base but without CPs. In the Loss section, the sign of all payments for each option
is inverted (see Table A1).
The mixed-outcome effect hypothesis posits that preferences between Base and Mixed 1, as well
as between Base and Mixed 2, should differ. Conversely, the cancellation hypothesis predicts that
preferences across all main treatments should be identical. Additionally, to ascertain if the total
outcomes influence preferences, we examine differences between Base’ and No CP. Following theintertemporal questions, participants completed the same demographic questions as in Study 1.
Results and discussion.
The demographic variables including age, gender and education across the treatments are notstatistically different, indicating the randomization properly works in this study (Table A2).9Insert Table A2 about here.

9

We excluded 2.4% of the observations for violating monotonicity and 1.8% for exhibiting extreme
discounting in the Gain section, as well as 2.4% of the observation for violating monotonicity and 6.4% forexhibiting extreme discounting in the Loss section, applying the same criteria as in our earlier studies. In
Appendix B, we replicate the analysis including the observations that weakly violated monotonicity,
consistent with the approach in Study 1. The overall results remain unchanged, indicating the robustness of
our findings.

29

Figure A1 presents a boxplot of the monthly discount factors for each treatment. The results
support the cancellation hypothesis and do not endorse the mixed-outcome effect hypothesis. The
IDFs did not significantly differ between the Base and Mixed 1 treatments, nor between Base andMixed 2 in the Gain section (Mann-Whitney test; p = .62 and p = .48, respectively). The IDFs
between Base and No CP were not significantly different either (p = .77).
Subsequently, further analysis was conducted to examine the effect of total outcomes asmentioned in the Method section. We showed that the IDFs between Base and No CP (treatmentswith identical MPs) were not significantly different in the above analysis. However, replacing Basewith Base’ and retesting these treatments revealed a significant difference between Base’ and No
CP (treatments with different MPs) (p < .01). The result further illustrates the participantspredominantly focused on MPs rather than total outcomes.
Similar findings were observed in the Loss section. The IDFs between the three pairs (Base vs.
Mixed 1, Base vs. Mixed 2, and Base vs. No CP) showed no significant differences (p = .91; p = .88;
p = .78, respectively), not supporting the mixed-outcome effect hypothesis either. However, thedifference in IDFs between Base’ and No CP was not statistically significant (p = .57), suggestingthat the difference of MPs between the two does not impact decisions in the Loss section. We
maintained the same absolute numbers between the Gain and Loss sections for comparability.
However, the magnitude of difference in MPs between Base’ and No CP in the Loss section might
not be substantial enough to yield statistically significant results. Adjusting these values potentiallyreveal significant differences. Furthermore, the time spent on decision-making between thesetreatments showed no significant difference (Kruskal-Wallis test; p = .47), indicating that presenting
mixed outcomes does not necessarily complicate the decision-making process.

30

Insert Figure A1 about here.

31

Appendix B: Robustness check
In our main analysis, we omitted observations that either weakly or strictly violated the principleof monotonicity across all studies, aligning with conventional methodologies for assessing
individual preferences. However, for this robustness check, we have included observations thatweakly violate monotonicity and have replicated the main analysis regarding IDFs. Table B1
illustrates the proportion of observations that weakly violate monotonicity in each study. The
subsequent analysis demonstrates that the inclusion of these observations does not alter the overall
results, thereby affirming the robustness of the findings reported in the main analysis.
Insert Table B1 about here.
Study 1
In line with the main analysis, framing effects were observed in both the Gain and Loss sectionsin Study 1. Specifically, the IDF in the No frame was statistically distinct from that in theInvestment frame (Mann-Whitney test; p < .01) and the Loan frame (p < .001). In the Loss section,
significant differences were found between the IDF in the No frame and those in the Investment
frame (p = .01) and the Loan frame (p = .04).
The comparative analysis of IDFs between the Gain and Loss sections is consistent with theresults of the main analysis. In the No frame, median IDFs were higher in the Loss section(Wilcoxon signed-rank test; p < .001), whereas in the Investment and Loan frames, the IDFs did not
significantly differ (p = .07; p = .12).
Study 2The overall findings from Study 2 are consistent with those of the main analysis as well andfurther confirm that the framing effect was substantial and robust. First, the outcomes support thecancellation hypothesis, as no significant differences were observed in the IDFs across the six main
treatments (Kruskal-Wallis test; p = .64). The subsequence analysis further suggests that32

participants focused on MPs rather than total outcomes in their decisions. Specifically, no
significant difference was observed in the IDFs between loan_CPD and gain_no (p = .63), while asignificant difference was found between loan_CPD’ and gain_no (Mann-Whitney test; p < .001).
Similarly, there was no significant difference in IDFs between inv_CPD and gain_no (p = .17),
while a significant difference was found between inv_CPD’ and gain_no (Mann-Whitney test; p< .01).
Study 3
The findings from Study 3 also align with those of the main analysis, demonstrating that the IDF
in the Loan frame is significantly different from that in the No frame (p < .01). Additionally, there
was no significant difference between the IDF in the No frame and that in the Investment frame(sign-rank test; p = .22).
Subsequently, we compared the results with those from the Gain section in Study 1. The IDFs
between these studies are not statistically different in the No frame and Investment frame (MannWhitney test; No frame, p = .80; Investment frame, p = .21), consistent with the main analysis.
However, the IDFs between the two studies are significantly different in the Loan frame (p = .04).
While this specific result differs from the main analysis, it does not detract from the overall patternof results, which affirm the replicability and stability of the framing effects identified in our
research.
Auxiliary Study
The findings from Auxiliary study align with those of the main analysis confirming thecancellation hypothesis. Our replication test does not support the mixed-outcome effect hypothesis.
The IDFs between the Base condition and the other three main conditions (Mixed 1, Mixed 2 and NoCP) showed no significant differences (p = .54, .28 and .77, respectively) in the Gain section.
Similarly, IDFs between Base and the other three main conditions were not significant (p = .91, .88

33

and .78, respectively) in the Loss section. Subsequent analysis on the effect of total outcomes is
consistent with the main analysis as well. The IDF was significantly different between the Base’and No CP treatments in the Gain section (p < .01) but not in the Loss section (p = .57).

34

Table 1
Parameters in the First Questions for each Treatment in Gain and Loss Sections (Study 1)
MP
SectionName

CP

Total outcome
Project A or Project B

Gain

No frame(8,8)(16,16) or (8,24)(24,24) or (16,32)

Gain

Investment(32,8)(-8,16) or (-16,24)(24,24) or (16,32)

Gain

Loan

(8,48)(16,-24) or (8,-16)(24,24) or (16,32)

Loss

No frame(-8,-8)(-16,-16) or (-8,-24)(-24,-24) or (-16,-32)

Loss

Investment(-8,-48)(-16,24) or (-8,16)(-24,-24) or (-16,-32)

Loss

Loan

(-32,-8)(8,-16) or (16,-24)(-24,-24) or (-16,-32)

Notes: The payments in the experiments are denoted as (𝑀0 , 𝑀2 ), where 𝑀0 represents animmediate payment and 𝑀2 signifies a payment realized in 2 months. After the first question, thesooner payment of Project B is varied for each question based on the previous answers while theother payments remain fixed to identify their indifference points.

35

Table 2
The Summary Table of Demographic Variables (Study 1)

Variables

No

Investment

Loan

F

p

(12.94)

.71

.49

0.65

(0.48).86.43(0.49)

0.55(0.50)

1.19.31(7.49)

32.75(7.64)

.29

.75

Mean

SD

Mean

SD

Mean

SD

Age

38.67

(12.75)40.47(13.78)40.67

Female0.61(0.49)

0.56(0.50)

College

0.51(0.50)

0.62

DAM

33.08

(6.98)

33.54

N

102

99

99

Notes: The dummy variable College is assigned a value of 1 for subjects holding a college degree and 0 for those without. The variable
DAM represents the total scores from the Debt Aversion Measure, which includes seven questions on a 6-point scale to assess the level ofdebt aversion.

36

Table 3
Parameters in the First Questions for each Treatment (Study 2)
MP
Name

CP

Domain of total
Total outcome

Project A or Project B

outcomegain_no(0,0)(16,20) or (8,28)(16,20) or (8,28)

Gaingain_CP(-6,-10)(16,20) or (8,28)(10,10) or (2,18)

Gain

inv_CP(-32,16)(16,20) or (8,28)(-16,36) or (-24,44)

Investment

inv_CPD(-64,36)(16,20) or (8,28)(-48,56) or (-56,64)

Investment

inv_CPD’(0,0)(-48,56) or (-56,64)(-48,56) or (-56,64)

Investment

loan_CP(16,-32)(16,20) or (8,28)(32,-12) or (24,-4)

Loanloan_CPD(32,-76)(16,20) or (8,28)(48,-56) or (40,-48)

Loanloan_CPD’(0,0)(48,-56) or (40,-48)(48,-56) or (40,-48)

LoanNotes: The payments in the experiments are denoted as (𝑀0 , 𝑀2 ), where 𝑀0 represents animmediate payment and 𝑀2 signifies a payment realized in 2 months. After the first question, thesooner payment of Project A is varied for each question based on the previous answers while theother payments remain fixed to identify their indifference points.

37

Table 4
The Summary Table of Demographic Variables (Study 2)

Variables

Age

FemaleCollege

DAM

N

gain_nogain_CP

inv_noinv_CP

inv_CPD

loan_noloan_CP

loan_CPD

ANOVA

Mean

Mean

Mean

Mean

Mean

Mean

Mean

Mean

F

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(SD)

(p)

43.80

45.49

41.83

40.20

41.96

44.97

41.49

42.63

1.61

(13.57)(14.62)(14.96)(14.20)(13.93)(14.02)(13.31)(14.70)

(.13)

0.56

0.56

0.52

0.51

0.53

0.47

0.48

0.50

0.5

(0.50)(0.50)(0.50)(0.50)(0.50)(0.50)(0.50)(0.50)

(.84)

0.13

0.14

0.13

0.17

0.12

0.20

0.16

0.12

0.72

(0.33)(0.35)(0.34)(0.38)(0.33)(0.40)(0.37)(0.32)

(.65)

32.91

30.59

32.49

32.55

32.41

32.26

32.60

33.12

0.8

(8.16)(9.52)(8.30)(7.70)(8.62)(8.60)(7.56)(6.53)

(.59)

87

87

104

105

105

103

105

104

Notes: The dummy variable College is assigned a value of 1 for subjects holding a college degree and 0 for those without. The variable
DAM represents the total scores from the Debt Aversion Measure, which includes seven questions on a 6-point scale to assess the level ofdebt aversion.

38

Table 5
The Summary Table of Demographic Variables (Study 3)

Variables

No

Investment

Loan

F

p

(14.79)

0.71

.49

0.43

(0.50)

1.63.2(0.50)

0.57(0.50)

0.35.7149400.00(25655.84)

42926.83(24819.74)

3.35

.04

(1.58)

5.19(1.46)

5.14(1.61)

1.1.34(9.01)

31.89(7.30)

31.96(7.83)

0.1

.99

Mean

SD

Mean

SD

Mean

SD

Age

45.42

(13.73)45.05(14.85)

43.05

Female0.56(0.50)

0.50(0.50)

College

0.51(0.50)

0.52

Income (£)

53653.85(32472.77)

McArthur

5.44

DAM

31.83

N

109

107

84

Notes: The dummy variable College is assigned a value of 1 for subjects holding a college degree and 0 for those without. The variable
Income represents the annual gross income in GBP. The variable McArthur describes the average scores from the McArthur scales ofsubjective social status. The variable DAM represents the total scores from the Debt Aversion Measure, which includes seven questions
on a 6-point scale to assess the level of debt aversion.

39

Figure 1. The Screenshot of the Question (No frame, Gain section; Study 1).
The payments from Project C in the question are common payments (CPs) because they are identical forboth options. The remaining payments in the questions are main payments (MPs).

40

Figure 2. The Monthly Discount Factors across Treatments in Gain and Loss Sections (Study 1).
Each dot represents one observation. The bold horizontal line inside each box is the median; the bottom andtop of the box are the first and third quartile, respectively.

41

Figure 3. The Monthly Discount Factors across Treatments (Study 2).
Each dot represents one observation. The bold horizontal line inside each box is the median; the bottom andtop of the box are the first and third quartile, respectively.

42

Figure 4. The Monthly Discount Factors across the Treatments (Study 3).
Each dot represents one observation. The bold horizontal line inside each box is the median; the bottom andtop of the box are the first and third quartile, respectively.

43

Table A1Parameters in the First Questions for each Treatment in Gain and Loss Sections (Auxiliary
Study)
MP
SectionName

CP

Total outcome
Project A or Project B

Gain

No CP

(0,0)

(32,32) or (16,48)(32,32) or (16,48)

Gain

Base

(12,12)(32,32) or (16,48)(44,44) or (28,60)

Gain

Mixed 1(-12,12)(32,32) or (16,48)(20,44) or (4,60)

Gain

Mixed 2(12,-12)(32,32) or (16,48)(44,20) or (28,36)

Gain

Base’

(0,0)

(44,44) or (28,60)(44,44) or (28,60)

Loss

No CP

(0,0)

(-32,-32) or (-16,-48)(-32,-32) or (-16,-48)

Loss

Base

(-12,-12)(-32,-32) or (-16,-48)(-44,-44) or (-28,-60)

Loss

Mixed 1

(12,-12)(-32,-32) or (-16,-48)(-20,-44) or (-4,-60)

Loss

Mixed 2(-12,12)(-32,-32) or (-16,-48)(-44,-20) or (-28,-36)

Loss

Base’

(0,0)

(-44,-44) or (-28,-60)(-44,-44) or (-28,-60)

Notes: The payments in the experiments are denoted as (𝑀0 , 𝑀2 ), where 𝑀0 represents animmediate payment and 𝑀2 signifies a payment realized in 2 months. After the first question, thesooner payment of Project A is varied for each question based on the previous answers while theother payments remain fixed to identify their indifference points.
44

Table A2
The Summary Table of Demographic Variables (Auxiliary Study)

Variables

Age

FemaleCollege

N

No CP

Base

Mixed 1

Mixed 2

Addition

ANOVA

Mean

Mean

Mean

Mean

Mean

F

(SD)

(SD)

(SD)

(SD)

(SD)

(p)

39.68

41.00

39.92

38.50

38.73

0.57

(14.68)(13.10)(12.63)(13.08)(13.08)

(.68)

0.56

0.49

0.56

0.55

0.59

0.52

(0.50)(0.50)(0.50)(0.50)(0.50)

(.72)

0.22

0.22

0.21

0.25

0.18

0.33

(0.42)(0.41)(0.41)(0.43)(0.39)

(.86)

98

102

100

101

99

Notes: The dummy variable College is assigned a value of 1 for subjects holding a college degree and 0 for those without.

45

Table B1
The Proportion of the Observations that Weakly Violate Monotonicity
Gain

Loss

Study 1

3.33%

0.67%

Study 2

3.25%-

Study 3

3.67%-

Auxiliary

0.8%

1.8%

46

Figure A1. The Monthly Discount Factors across Treatments in Gain and Loss Sections(Auxiliary Study).
Each dot represents one observation. The bold horizontal line inside each box is the median; the bottom andtop of the box are the first and third quartile, respectively.

47