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\title{Can asymmetric subjective opportunity cost effect explain impatience in intertemporal choice? A replication study}

\author{
Si-Chu Shen\thanks{CAS Key Laboratory of Behavioral Science, Institute
of Psychology, Beijing 100101, China, and Department of Psychology, University of Chinese
Academy of Sciences, Beijing 100049, China.}
\and
Yuan-Na Huang\footnotemark[1]
\and
Cheng-Ming Jiang\thanks{Corresponding author. School of Management, Zhejiang University of
  Technology, Hangzhou 310023, China. Email: jiangchengming@zjut.edu.cn.}
\and
Shu Li\thanks{Corresponding author. CAS Key Laboratory of Behavioral
Science, Institute of Psychology, Chinese Academy of Sciences, Beijing
100101, China; Department of Psychology, University of Chinese Academy
of Sciences, Beijing 100049, China; and Department of Psychology and Behavioral Sciences,
Zhejiang University, Hangzhou 310028, China. Email:
lishu@psych.ac.cn. ORCID: 0000--0003--4402--1674}
}

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\begin{onecolabstract}
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In “The value of nothing: asymmetric attention to opportunity costs
drives intertemporal decision making”
Read, Olivola and Hardisty (2017) proposed an asymmetric subjective
opportunity cost (ASOC) effect to explain and predict why impatience
can be detected in intertemporal choice. This work deserves to be
replicated and extended for its novel and potentially important
findings. The present study aimed to examine the reliability and
robustness of the evidence presented by Read et al.\ 
by conducting precise replications of their key findings in
Study 1. The ASOC effect (Read, et al., 2017) was
important for expanding its application and reported to be typically
stronger when baseline larger-but-later option (LL) and
smaller-but-sooner option (SS) preferences were closer to 50\% in the
authors’ original condition. Therefore, the present study also aimed to
replicate and test the ASOC effect when baseline LL preferences were
higher or lower than those in the original condition. We intended to
set two additional conditions wherein either LL or SS is more obviously
favored (i.e., baseline LL preferences were higher or lower than those
in the original condition) by respectively applying the common
difference effect (Kirby \& Herrnstein, 1995) and the unit effect
(Burson, Larrick \& Lynch Jr., 2009; Pandelaere, Briers \& Lembregts,
2011). Having successfully generated two more obviously favored
conditions, the ASOC effect was replicated and confirmed under the
original condition and one additional condition wherein SS was more
obviously favored. However, the ASOC effect was not detected under the
other additional condition wherein LL was more obviously favored. The
implications of these findings were discussed.

\smallskip
\noindent
Keywords: intertemporal choice, asymmetric subjective opportunity cost
effect, replication, more obviously favored condition
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]
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{\renewcommand{\thefootnote}{}

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\footnotetext{

This study was partly supported by the National Natural Science
Foundation of China (31471005, 71761167001, 71571164) and the CAS Key
Laboratory of Behavioral Science, Institute of Psychology, Chinese
Academy of Sciences (Y5CX052003). We wish to thank Li-Lin Rao for her
assistance with the data analysis.

Copyright: \copyright\ 2019.
The authors license this article under the terms of the
\href{http://creativecommons.org/licenses/by/3.0/}{Creative Commons
  Attribution 3.0 License.}
}}

\saythanks

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\section{Introduction}

Individuals tend to be impatient when making intertemporal choices.
Various decision effects have been investigated to identify ways to
reduce impulsive choice behavior. Notable among recent efforts is the
asymmetric subjective opportunity cost (ASOC) effect proposed to
account for impatience (Read, Olivola \& Hardisty, 2017).

The ASOC effect indicated that people are less likely to choose a
smaller-but-sooner option (SS) over a larger-but-later option (LL) when the
stimulus explicitly notes that getting SS now means getting \$0 later; that
is, the choice of SS goes down when the stimulus highlights its later
opportunity cost (Read, Olivola \& Hardisty, 2017).\footnote{ We are
  grateful to a reviewer for suggesting this well-written rephrase of the
  ASOC effect. } However, when the opportunity costs of choosing LL rewards
are highlighted, no effect is observed. The ASOC effect assumes that,
although the opportunity costs of the LL option are naturally salient, the
opportunity costs of its SS counterpart are often neglected or
underweighted in intertemporal choice. In Study 1 of Read et al.\ (2017),
opportunity costs were made explicit by providing people with subtle
framing “nudges” (adding “£0”). For example, the SS zero frame was
presented by describing the SS option as offering zero at the time when the
LL outcome would occur. The LL choice proportions were then compared across
four core frames: the Explicit zero frame (which makes both opportunity
costs explicit), Hidden zero frame (with no explicit opportunity costs), SS
zero frame (with the opportunity cost of choosing SS made explicit), and LL
zero frame (with the opportunity cost of choosing LL made explicit). The
ASOC effect was supported given a significant effect of the SS zero frame
on patience. In the succeeding seven experiments, the generalizability of
the ASOC effect was enhanced by changing the sizes or signs of the payoffs,
adding delays, using an incentive-compatible procedure, and utilizing
alternative reminders. Evidence provided by Read et al.\ (2017) indicates
that the prediction of the ASOC effect can adequately account for the
Hidden zero phenomenon, which suggests that making zero outcomes explicit
decrease impatience (Magen, Dweck \& Gross, 2008), whereas other
alternative explanations may not. The ASOC effect is then suggested as a
possible effective means to prompt people to make patient choices. Read,
Olivola and Hardisty’s (2017) study deserves to be replicated and expanded
for its novel and potentially important findings.

The so-called ASOC effect was first reported by Wu and He (2012, as
indicated by Read et al., 2017). However, Wu and He focused on assessing
the relationship between time perspective and the salience of future
outcomes instead of directly investigating the ASOC effect
itself. Considering that the ASOC effect was first found using a Chinese
sample, a replication study testing whether this effect holds in a
country with a high savings rate, such as China, would be interesting.

We also noticed that the ASOC effect was typically detected when baseline
LL preferences were closer to 50\% in Read et al.'s (2017) original
condition. We conjectured that the ASOC effect might prompt people to be
patient only when neither choice option clearly dominates in the standard
Hidden zero frame. The ASOC effect could be absent when baseline LL
preferences in the standard Hidden zero frame are away from 50\%. This
concern was acknowledged by Read et al.\ (2017) in their Discussion
section. However, they did not manipulate the baseline preferences in the
Hidden zero frame, so empirical evidence is lacking.

The present study aimed to examine the reliability and robustness of the
evidence presented by Read et al.\ (2017) by conducting a precise
replication of Study 1. The ASOC effect was observed under a condition
wherein neither LL nor SS option was obviously favored (i.e., when baseline
LL preferences were closer to 50\%) by using Magen et al.’s (2008) 15
choice items. This replication study also aimed to test the ASOC effect
when participants showed their obvious preference for either LL or SS
option (in conditions where either LL or SS is more obviously favored). To
be specific, we intended to set two additional more obviously favored
conditions (i.e., baseline LL preferences higher or lower than those in the
original condition) by respectively applying the common difference effect
(Kirby \& Herrnstein, 1995) and unit effect (Burson, Larrick \& Lynch Jr.,
2009; Pandelaere, Briers \& Lembregts, 2011).\footnote{ The unit effect can
  be an instance of the magnitude effect (Thaler, 1981).} Between the two
additional conditions, the common difference effect would increase patience
by changing relative differences between two options on the \textbf{delay}
dimension (adding a constant delay to both payoff dates of options),
whereas the unit effect would decrease patience by changing relative
differences between two options on the \textbf{outcome} dimension (changing
the magnitude of payoffs of both options). This approach allowed us to
perform additional replication and verification studies of these two
effects on intertemporal choice.

To ensure interpretable results, we obtained original materials from Table
3 and the supplemental materials of the original paper by Read et al.,
(2017) (the same experimental materials were derived from Magen et al.,
2008). In addition, we completed a replication checklist recipe (Brandt et
al., 2014) and planned informative samples in advance (Simonsohn,
2015). Our materials and data are available on the Open Science Framework
(\url{https://osf.io/4ebzs/}).\footnote{ In this article, we report how we
  determined our sample size, all data exclusions (if any), all
  manipulations, and all measures used in the study (Simmons, Nelson \&
  Simonsohn, 2012). }

\subsection{Testing the ASOC effect in conditions where either SS or LL is
  more obviously favored}

This study attempted to replicate the ASOC effect by adopting the original
materials and investigating this effect in conditions wherein either SS or
LL is more obviously favored. A 4 × 3 mixed design was employed in
replicating the ASOC effect and testing it in more obviously favored
conditions, with the zero frame as a between-subjects variable and the
baseline condition as a within-subjects variable. On the basis of the
findings of Read et al.\ (2017), we expected that, when the opportunity
costs of choosing the SS option were highlighted, people would become more
patient when baseline LL preferences were closer to 50\% when using Magen
et al.’s (2008) 15 choice items. Moreover, we aimed to test whether the
ASOC effect would be reinforced or weakened when baseline LL preferences
were higher or lower than those in the original condition.

\subsection{Participants}
In Read et al.’s (2017) Study 1, participants were recruited through
Maximiles. They were randomly assigned to the four core frames and the
Middle zero frame.\footnote{ The “Middle zero” frame is the frame with
  zeros occurring halfway (in time) between the SS and LL outcomes. This
  frame was used to provide evidence supporting the ASOC effect rather than
  other accounts for explaining the Hidden zero effect.} The calculation of
the main effect of SS zero on patience reported in the original Study 1
involved only four frame groups of participants, excluding those who were
assigned to the Middle zero frame group. Therefore, the sample size of the
original reported ASOC effect was 563. The main effect of SS zero was
reported (\textit{F }(1, 561) = 30.65, \textit{p} {\textless} .001,
\textit{$\eta $}\textit{\textsubscript{p}}² = .05). The confidence intervals
of the reported effect size were calculated on the basis of the method
provided by Smithson (2001): 90\% CI [0.026, 0.084].

As suggested by Simonsohn (2015), a replication needs 2.5 times the
original sample size to have approximately 80\% power. Given the
reported original sample size of 563 participants, a goal was set to
recruit at least 1,408 participants for informative replication sample
sizes.

The sample of the present replication study was recruited online via
Sojump (\url{http://www.Wjx.cn}), an online platform similar to Mechanical Turk or
Qualtrics, which is used to launch nationwide e-surveys in China and is
widely employed in behavioral and psychological studies. To rule out
the participants who we assumed did not take the task seriously, 130\%
of the target was recruited to accommodate the exclusion criteria
(Calin-Jageman, 2018). We thus placed an order of 1,830 participants
with Sojump, with the request that all participants pass four attention
check items. Participants from the sample of 1,830 respondents who gave
nonsensical answers (always chose SS or LL) in all 45 choice items or
who showed an inconsistent discount rate\footnote{ Take the paired of
choice “£4.50 today or £7.70 in 28 days” and “£4.70 today or £5.40 in
92 days” as an example, if LL was chosen in the pair of “£4.70 today or
£5.40 in 92 days”, then LL in the pair of “£4.50 today or £7.70 in 28
days” should be dominantly favored and chosen according to a
discounting model in intertemporal choice. Otherwise, an inconsistent
discount rate was revealed.} were excluded. The final valid dataset
consisted of 1,730 Chinese respondents (51\% female; mean age = 30.56
years) and contained nearly 433 participants per between-subjects cell.
The participants were paid ¥ 9 for their participation. 

\subsection{Procedures}

The procedure of this replication study was modeled after the original,
with the same instructions and similar choice items translated into
Chinese. The only difference in the current procedure was that participants
were required to make hypothetical choices in two additional more obviously
favored conditions (i.e., baseline LL preference was supposed to be higher
or lower than that in original condition). Participants in the original
study needed to make hypothetical choices only in the baseline condition
using Magen et al.’s (2008) 15 choice items.

As in the original study, participants were randomly assigned to one of the
four core frame groups: Explicit zero frame, Hidden zero frame, SS zero
frame, and LL zero frame.\footnote{ Compared with the original study, the
  middle zero frame was omitted in the present research.}  Participants in
each group needed to complete all three sets of choice items presented in
the assigned frame, with each set containing 15 choice items. The choice
items in the baseline condition were presented first, then the presentation
order of two additional sets of paired choice items was counterbalanced
within the group. The presentation order of choice items was randomized
within each set for each participant. In the study by Read et al.\ (2017),
patience was found to be unaffected by the presentation format of
options. Therefore, the choice items were presented individually (i.e., one
pair of options at a time), and the options of each item were presented
vertically. Finally, demographic information, including age and gender, was
collected.

\subsection{Materials}

Choice items were presented in four zero frames as in the original
study. Below are four corresponding examples:
\begin{quote}
Hidden zero frame: £2.00 today OR £8.50 in 18 days;

Explicit zero frame: £2.00 today and £0 in 18 days OR \$0 today and £8.50 in
18 days;

SS zero frame: £2.00 today and \$0 in 18 days OR £8.50 in 18 days;

LL zero frame: £2.00 today OR \$0 today and £8.50 in 18 days.
\end{quote}

%Table 1
\begin{table}[t!]\centering
\caption{Delay lengths and payoff magnitudes for the 15 items
drawn from Magen et al.\ (2008). (Payments were in “£” for the present study.)}
\begin{tabular}{C{1in}C{1in}C{1in}}\toprule
Smaller, sooner (SS) amount & Larger, later (LL) amount & Delay (days)\\\midrule
£2.00 & £8.50 & 18\\
£3.10 & £8.50 & 7\\
£3.30 & £8.00 & 14\\
£4.10 & £7.50 & 20\\
£4.30 & £7.50 & 22\\
£4.50 & £7.70 & 28\\
£4.70 & £5.40 & 92\\
£4.90 & £5.80 & 42\\
£5.00 & £7.20 & 34\\
£5.40 & £8.00 & 30\\
£5.50 & £7.50 & 61\\
£6.00 & £8.50 & 46\\
£6.70 & £7.50 & 119\\
£6.90 & £8.70 & 102\\
£8.00 & £8.40 & 140\\\bottomrule
\end{tabular}
\end{table}

Three sets of paired choice items were used to examine the reliability
and robustness of the ASOC effect and investigate it in conditions
wherein either SS or LL is more obviously favored.

%Figure 1
\begin{figure*}[t!]\centering
\includegraphics[clip=true,width=4.5in]{Fig1.eps}
\caption{Mean level of patience (proportion of LL choices) as a function of zero
framing in the original baseline condition The horizontal axis indicates
the presence or absence of the SS zero. The solid line indicates the
presence of the LL zero, and the dotted line indicates its absence.}
\end{figure*}

\paragraph{Original baseline condition:} 15 choice items drawn from Magen
et al.\ (2008), which were the same materials adopted in Study 1 of Read et
al.\ (2017).
\begin{quote}
Example of original items:

Choose between

£2.00 today OR £8.50 in 18 days
\end{quote}

\paragraph{Common Delay condition:} 15 newly generated choice items with LL
preferences that were supposed to be higher than those in the original
condition. The common difference effect (Kirby \& Herrnstein, 1995) suggests that
adding a constant delay to both payoff dates of options would shift
preference from SS to LL option. Accordingly, we added a common
constant additional delay to both original options, in the hope that a
stronger preference for the LL option could be reached.
\begin{quote}
Example of generated items (adding a common delay interval of 100 days
to both original choice options):

Choose between

£2.00 in 100 days OR £8.50 in 118 days
\end{quote}

\paragraph{Money Unit condition:} 15 newly generated choice items with LL
preferences that were supposed to be lower than those in the original
condition. The Unit effect (Burson, Larrick \& Lynch Jr., 2009; Pandelaere,
Briers \& Lembregts, 2011) suggests that expressing quality information in
a currency unit that has a lower value makes the perceived relative
difference between two options on the \textbf{outcome} dimension
smaller. Accordingly, we replaced the payoffs’ unit of “pound” with the
unit of “Thai Baht” in both original options (e.g., replacing £2.00 with
฿2.00), in the hope that a stronger preference for the SS option could be
reached.
\begin{quote}
Example of generated items (the familiarity of “฿”might be similar to
that of “£” for Chinese participants, ฿1 ${\approx}$ £0.02):

Choose between

฿2.00 today OR ฿8.50 in 18 days
\end{quote}

Patience was measured in terms of the proportion of LL choices in each
of the three sets of pairs of intertemporal choice items.

\section{Results}

%Figure 2: 
\begin{figure*}[t!]\centering
\includegraphics[clip=true,width=4.5in]{Fig2.eps}
\caption{Mean level of patience (proportion of LL choices) as a
function of zero framing in the Common Delay condition
The horizontal axis indicates the presence or absence of
the SS zero. The solid line indicates the presence of the LL zero, and
the dotted line indicates its absence.}
\end{figure*}

First, we intended to replicate and test the ASOC effect. Read et al.\
(2017) predicted an ordering of LL choice proportions across the four
conditions as follows: SS zero = Explicit zero {\textgreater} Hidden zero =
LL zero.\footnote{ Compared with the original study, the middle zero frame
  was omitted in the present study.} As in the original study, we
calculated patience (the proportion of LL responses) for each
participant. Then we compared the effects of the four core zero frames on
the proportion of the LL choices in the \textbf{original} condition (Figure
1). The results indicated that participants were more patient in the SS
zero frame than in the Hidden zero frame (41.61\% vs.\ 31.11\%,\textit{ t
}(870) = 6.10, \textit{p} {\textless} .001, \textit{d} = .41, 95\% CI
[0.279, 0.547]), which is consistent with the original study. No
significant differences in patience were noted between the SS and Explicit
zero frames (\textit{p} = .68) as well as the LL and Hidden zero frames
(\textit{p} = .09).

We then conducted a 2 (SS zero: present vs.\ absent) × 2 (LL zero: present
vs.\ absent) × 3 (Condition: original condition, Common Delay condition,
and Money Unit condition) ANOVA, with condition as a within-subjects factor
and SS zero frame and LL zero frame as between-subjects factors. The ANOVA
revealed a main effect of SS zero (\textit{F }(1, 1725) = 59.06, \textit{p
}{\textless} .001, $\eta_p^2$ = .033, 90\% CI [0.021, 0.048]), and a main
effect of conditions (\textit{F }(2, 1724) = 354.16, \textit{p }{\textless}
.001, $\eta_p^2$ = .291, 90\% CI [0.262, 0.318]). Moreover, the ANOVA
revealed a significant condition-by-SS zero interaction (\textit{F }(2,
1724) = 20.02, \textit{p }{\textless} .001, $\eta_p^2$ = .023, 90\% CI
[0.012, 0.035]), and a significant condition-by-LL zero interaction
(\textit{F }(2, 1724) = 3.08, \textit{p }= .05, $\eta_p^2$ = .004, 90\% CI
[0.000, 0.009]). No other significant effect was found (\textit{ps
}${\geq}$ .15).

Simple effect analysis of condition-by-SS zero interaction showed that
under original condition, patience in the presence of SS zero frame
(\textit{M} = 41.99\%) was significantly higher than that in the
absence of SS zero frame (\textit{M} = 32.60\%) (\textit{p} {\textless}
.001) (Figure 1). Under Money Unit condition, patience in the presence
of SS zero frame (\textit{M} = 39.12\%) was significantly higher than
that in the absence of SS zero frame (\textit{M} = 29.08\%) (\textit{p}
{\textless} .001) (Figure 3). However, no significant difference
between the presence and absence of SS zero frames was found under
Common Delay condition (\textit{p} = .13) (Figure 2). Simple effect
analysis of condition-by-LL zero interaction showed that no significant
difference between the presence and absence of LL zero frames was found
in each of three conditions (\textit{ps }${\geq}$ .07). 

%Figure 3
\begin{figure*}[t!]\centering
\includegraphics[clip=true,width=4.5in]{Fig3.eps}
\caption{Mean level of patience (proportion of LL choices) as a function of
  zero framing in the Money Unit condition. The horizontal axis indicates
  the presence or absence of the SS zero. The solid line indicates the
  presence of the LL zero, and the dotted line indicates its absence.}
\end{figure*}

The results of the present study supported the ASOC effect of Read, Olivola
and Hardisty (2017) in their original condition. Specifically, people
became more patient when the opportunity cost of the SS option was
highlighted, whereas patience remained constant when the opportunity cost
of the LL option was highlighted. The effect sizes found in the present
study were comparable to those observed in the original study ($\eta_p^2$ =
.05, 90\% CI [0.017, 0.049]), though slightly weaker in our Chinese
sample. A statistically significant main effect of SS zero frame on the
proportion of LL choices with the same direction as the original study were
detected, which indicated that this replication were as successful as the
results in the original study (Camerer et al., 2016; Open Science
Collaboration, 2015).

Having successfully replicated the ASOC effect under the original
condition in the present study, we found mixed results of the ASOC
effect in the two additional more obviously favored conditions. First,
ASOC effect was obtained in Money Unit condition when baseline
LL preferences were \textit{lower} than those in the original condition
(by applying unit effect). Second, little to no effect of SS zero
framing on patience were detected in Common Delay condition
when baseline LL preferences were higher than those in the original
condition (by applying the common difference effect).

\subsection{Replication and verification of the common difference effect and
unit effect}

% correct heading?

To generate two additional conditions for investigating the ASOC effect
in the more obviously favored conditions, we chose to apply the common
difference effect and unit effect respectively to the original baseline
condition. Therefore, the robustness of the common difference effect
(Kirby \& Herrnstein, 1995) and unit effect (Burson, Larrick \& Lynch
Jr., 2009; Pandelaere, Briers \& Lembregts, 2011) could be replicated
and verified separately as byproducts in this study.

Regarding the common difference effect, a paired-sample \textit{t} test
was performed for participants assigned to the Hidden zero frame group
to compare the differences in patience between the original
condition and Common Delay condition. Patience in the Common Delay
condition was significantly higher than that in the original condition
(52.41\% vs.\ 31.11\% LL choice, \textit{t }(446) = 16.65, \textit{p}
{\textless} .001, \textit{d} = 1.12, 95\% CI [0.964, 1.265]).

As for unit effect, a paired-sample \textit{t} test was performed for
participant assigned to the Hidden zero frame group to compare the
differences in patience between the original condition and Money Unit
condition. Participants were less patient in Money Unit condition than in
the original condition (26.88\% vs.\ 31.11\% LL choice, \textit{t }(444) =
$-$3.70, \textit{p} {\textless} .001, \textit{d} = .25, 95\% CI [0.115,
0.380]).

%Figure 4: 
\begin{figure*}[t!]\centering
\includegraphics[clip=true,width=5.5in]{Fig4.eps}
\caption{Proportion of individuals choosing LL option in each of the 15
items, as a function of the common difference effect (in red) and unit
effect (in green).\protect\footnote{}}
\end{figure*} 

The analysis investigated the common difference effect and the unit effect
based on the proportion of LL option (Figure 4). We have further analyzed
participants’ choice at the item level. Table 2 provides a close look at
the item-level data.

%Table 2.
\begin{table*}[t!]\centering
\caption{Choice results from the 15 pairs of choices in the
original condition, Common Delay condition, and Money Unit condition, with
McNemar $\chi^2$ tests.}
\begin{tabular}{@{}L{.6in}l*{8}{cc@{\hspace{4mm}}}@{}}\toprule
 &  & \mc{16}{l}{Original Condition}\\
 &  & \mc{2}{c}{Item 1} & \mc{2}{c}{Item 2} & \mc{2}{c}{Item 3} & \mc{2}{c}{Item 4} & \mc{2}{c}{Item 5} & \mc{2}{c}{Item 6} & \mc{2}{c}{Item 7} & \mc{2}{c}{Item 8}\\
&  & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL\\\midrule
\multirow{3}{.6in}{Common delay condition} & SS & 101 & 86 & 71 & 105 & 108 & 75 & 220 & 78 & 290 & 93 & 353 & 96 & 1313 & 102 & 1182 & 107\\
 & LL & 302 & 1241 & 256 & 1298 & 369 & 1178 & 580 & 852 & 553 & 794 & 584 & 697 & 218 & 97 & 269 & 172\\
 &  & \mc{2}{l}{$\chi^2$=119.14} & \mc{2}{l}{$\chi^2$=62.33} & \mc{2}{l}{$\chi^2$=193.35} & \mc{2}{l}{$\chi^2$=381.46} & \mc{2}{l}{$\chi^2$=326.13} & \mc{2}{l}{$\chi^2$=348.78} & \mc{2}{l}{$\chi^2$=41.33} & \mc{2}{l}{$\chi^2$=68.94}\\
 &  & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l@{}}{ \textit{p }{\textless} .001}\\\cmidrule{3-18}

 &  & \mc{2}{c}{Item 9} & \mc{2}{c}{Item 10} & \mc{2}{c}{Item 11} & \mc{2}{c}{Item 12} & \mc{2}{c}{Item 13} & \mc{2}{c}{Item 14} & \mc{2}{c@{}}{Item 15}\\
&  & SS & LL & SS & LL & SS &  LL & SS & LL & SS & LL & SS & LL & SS & LL\\\cmidrule{3-16}
\multirow{3}{.6in}{} & SS & 714 & 106 & 527 & 121 & 1063 & 99 & 921 & 96 & 1387 & 57 & 1307 & 79 & 1432 & 66\\
 & LL & 476 & 434 & 483 & 599 & 312 & 256 & 370 & 343 & 186 & 100 & 197 & 147 & 160 & 72\\
 &  &  \mc{2}{l}{$\chi^2$=233.95} & \mc{2}{l}{$\chi^2$=215.76} & \mc{2}{l}{$\chi^2$=109.35} & \mc{2}{l}{$\chi^2$=159.93} & \mc{2}{l}{$\chi^2$=67.42} & \mc{2}{l}{$\chi^2$=49.60} & \mc{2}{l}{$\chi^2$=38.27}\\
 &  & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l@{}}{ \textit{p }{\textless} .001}\\\midrule

 &  & \mc{2}{c}{Item 1} & \mc{2}{c}{Item 2} & \mc{2}{c}{Item 3} & \mc{2}{c}{Item 4} & \mc{2}{c}{Item 5} & \mc{2}{c}{Item 6} & \mc{2}{c}{Item 7} & \mc{2}{c}{Item 8}\\
&  & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL\\\midrule
\multirow{3}{.6in}{Money unit condition} & SS & 227 & 265 & 173 & 193 & 261 & 265 & 543 & 326 & 592 & 350 & 699 & 330 & 1412 & 136 & 1316 & 190\\
 & LL & 176 & 1062 & 154 & 1210 & 216 & 988 & 257 & 604 & 251 & 537 & 238 & 463 & 119 & 63 & 135 & 89\\
 &  & \mc{2}{l}{$\chi^2$=17.56} & \mc{2}{l}{$\chi^2$=4.16} & \mc{2}{l}{$\chi^2$=4.79} & \mc{2}{l}{$\chi^2$=7.93} & \mc{2}{l}{$\chi^2$=15.98} & \mc{2}{l}{$\chi^2$=14.58} & \mc{2}{l}{$\chi^2$=1.00} & \mc{2}{l@{}}{$\chi^2$=8.97}\\
 &  & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }= .041} & \mc{2}{l}{ \textit{p }= .029} & \mc{2}{l}{ \textit{p =} .005} & \mc{2}{l}{ \textit{p {\textless}} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }= .316} & \mc{2}{l@{}}{ \textit{p =} .003}\\\cmidrule{3-18}

 &  & \mc{2}{c}{Item 9} & \mc{2}{c}{Item 10} & \mc{2}{c}{Item 11} & \mc{2}{c}{Item 12} & \mc{2}{c}{Item 13} & \mc{2}{c}{Item 14} & \mc{2}{c@{}}{Item 15}\\
&  & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL & SS & LL\\\cmidrule{3-16}
\multirow{3}{.6in}{} & SS & 1000 & 270 & 798 & 317 & 1224 & 198 & 1107 & 248 & 1467 & 101 & 1381 & 143 & 1502 & 97\\
 & LL & 190 & 270 & 212 & 403 & 151 & 157 & 184 & 191 & 106 & 56 & 123 & 83 & 90 & 41\\
 &  &  \mc{2}{l}{$\chi^2$=13.57} & \mc{2}{l}{$\chi^2$=20.45} & \mc{2}{l}{$\chi^2$=6.06} & \mc{2}{l}{$\chi^2$=9.19} & \mc{2}{l}{$\chi^2$=.08} & \mc{2}{l}{$\chi^2$=1.36} & \mc{2}{l}{$\chi^2$=.19}\\
 &  & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }{\textless} .001} & \mc{2}{l}{ \textit{p }= .014} & \mc{2}{l}{ \textit{p }= .002} & \mc{2}{l}{ \textit{p }= .781} & \mc{2}{l}{ \textit{p }= .244} & \mc{2}{l@{}}{ \textit{p }= .661}\\\bottomrule
% \mc{18}{@{}p{6.5in}}{\textit{Notes.} The underlined data are consistent with the
% prediction of the common difference effect in the Common Delay
% condition or the unit effect in the Money Unit condition.}
\end{tabular}
\end{table*}

% maybe note not needed

In the Common Delay condition, the item-level data analysis revealed that,
for all the 15 pairs of choices (100\% of all the choice items), the
choices of participants shifted in the expected direction (i.e., shifting
choices from SS into LL). In addition, all the McNemar $\chi^2$ values were
statistically significant (\textit{ps} {\textless} .001), indicating that
applying the common difference effect to prompt people to be \textbf{more}
patient is successful. In the Money Unit condition, item-level data
analysis revealed that for 11 out of the 15 pairs of choices (73\% of all
the choice items), the choices of participants shifted in the expected
direction from that in the original condition (i.e., shifting choices from
LL into SS) and the McNemar $\chi^2$ values were statistically significant
(\textit{ps} {\textless} .05), indicating that applying the unit effect to
prompt people to be \textbf{less} patient is similarly successful.

The common difference effect and the unit effect were also
replicated and verified. This result made generating two more
obviously favored conditions possible and feasible by applying these
two effects separately.

\section{Discussion}
The goal of this study was to assess the replicability of the research
presented by Read, Olivola and Hardisty (2017) in support of the ASOC
effect. Consistent with the original findings, the present replication of
Study 1 confirmed that the ASOC effect was robust when using Magen et al.’
s (2008) 15 choice items adopted by Read et al.\ (2017). The resulting
effect size of the SS zero frame on patience in our experiment was
comparable to but weaker than that reported in the original study. The ASOC
effect observed using a Chinese sample in the present study, together with
those found using Western (American and British) and Indian samples
reported in the original study, adds to the accumulating evidence that the
ASOC effect is a general human tendency rather than the product of culture.

Our Chinese participants showed lower than expected patience in the
original condition (around 30\% in the present study, 50\% in the
original study). The reason our results differed from our expectations
might be that the hypothetical payoff and delay adopted in this study
were relatively smaller and shorter compared with the large magnitude
outcome and long delay of real-world saving behavior. Interval effect
(Read, 2001; Read \& Roelofsma, 2003) suggested that small
payoff/short-term intertemporal preference might not sufficiently
describe and predict the large payoff/long-term saving behaviors.

To expand the application of the ASOS effect, the common difference effect
(Kirby \& Herrnstein, 1995) and unit effect (Burson et al., 2009;
Pandelaere et al., 2011) were applied separately to generate two additional
more obviously favored conditions. The common difference effect was
successfully demonstrated to prompt people to select more LL options,
whereas unit effect was also demonstrated to be able to prompt people to
select more SS options.

\footnotetext{We acknowledge Editor Jonathan Baron for suggesting that we apply this analysis.}

The common difference effect was verified in the present study to generate
conditions wherein the LL option was more obviously favored.  However, no
significant ASOC effect was observed in our Common Delay condition,
suggesting it might be a condition beyond which further manipulations
(e.g., the ASOC effect) have no additional effect on improving patience. A
strong ASOC effect was detected in a front-end delay condition included in
Study 3 in the original paper by Read et al.\ (2017). Nonetheless, the
front-end delay effect was not obtained in their study. The front-end delay
and the common difference effect suggest that adding delays to original
options could increase patience. However, a few differences were observed
between the original paper and the present study. First, from the
perspective of adding time intervals, a constant delay of 100 days was
added to both SS ad LL options in the present study, whereas the original
LL delay to both SS and LL options were added in each choice item in
original paper of Read, Olivola and Hardisty (2017). Second, from the
perspective of selecting choice items, all 15 choice items drawn from Magen
et al.\ (2008) were used in the present study, whereas 11 out of 15 choice
items were selectively adopted in the original paper. Third, the baseline
patience of participants differed between the two studies.

The unit effect was successfully replicated, in order to generate
conditions wherein the SS option was more obviously favored in this
study, although the effect was not as strong as the common difference
effect on patience. We speculated that the reason might be that
familiarity with the “Thai Baht” was not as high as expected in our
Chinese sample. Consequently, participants had to convert the outcomes’
unit of “Thai Baht” (฿) into “British Pound” (£) and then into “Chinese
Yuan” (¥), which might have caused additional difficulty for our
Chinese participants.

More generally, to reach a more obvious preference for the LL option, the
common difference effect was applied in the present study to change the
perceived relative differences between two options on the \textit{delay}
dimension. We conjectured that any other effects, such as date/delay effect
(see Read, Frederick, Orsel \& Rahman, 2005), that might play a similar
role in changing the perceived relative differences between two options on
the delay dimension could be applied to improve patience in the
intertemporal choice. To reach a more obvious preference for the SS option,
the unit effect was employed in the present study to change the perceived
relative differences between two options on the \textit{outcome} dimension.
Future research may consider 1) re-examining the unit effect by directly
replacing the unit of payoffs with “Chinese Yuan” or using other currency
of even lower value (e.g., Japanese Yen) and 2) enhancing impulsive~choice
by using any other effects, such as magnitude effect (Thaler, 1981), that
might play similar roles in changing the perceived relative differences
between two options on the outcome dimension.

In view of the balanced evidence, an asymmetry in the ASOC effect on
prompting the patience was observed in this study. That is, little to no
ASOC effect was observed in the Common Delay condition, but the ASOC effect
was detected in the Money Unit condition with a slightly larger effect size
than that in the original condition. It leaves the possibility that the
failure to find the ASOC effect in the condition wherein the LL option was
more obviously favored was due to a change in baseline patience or a change
in the framing of options. An overall explanation might be that the room
for improvement (from SS to LL) determined the asymmetry in the ASOC effect
on prompting patience. The baseline LL preferences in the Money Unit
condition by applying unit effect were relatively low, leaving adequate
room for the ASOC effect or other effects to prompt people into making more
patient choices. By contrast, the baseline LL preferences in the Common
Delay condition by applying the common difference effect were relatively
high, therefore leaving little room for the ASOC effect or other effects to
play a role in improving patience. This asymmetry feature will pose a
challenge for future researchers who may be interested in conducting
additional research on prompting patient choices.

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\end{hangparas}

\end{document}

