A Mechanism for Reducing Delay Discounting by Altering Temporal Attention

A MECHANISM FOR REDUCING DELAY DISCOUNTING BY ALTERING TEMPORAL ATTENTION

PETER T. RADU1, RICHARD YI

2, WARREN K. BICKEL3, JAMES J. GROSS

1, AND SAMUEL M. MCCLURE1

1STANFORD UNIVERSITY2UNIVERSITY OF MARYLAND

3VIRGINIA TECH UNIVERSITY

Rewards that are not immediately available are discounted compared to rewards that are immediatelyavailable. The more a person discounts a delayed reward, the more likely that person is to have a rangeof behavioral problems, including clinical disorders. This latter observation has motivated the search forinterventions that reduce discounting. One surprisingly simple method to reduce discounting is an‘‘explicit-zero’’ reframing that states default or null outcomes. Reframing a classical discounting choiceas ‘‘something now but nothing later’’ versus ‘‘nothing now but more later’’ decreases discount rates.However, it is not clear how this ‘‘explicit-zero’’ framing intervention works. The present studiesdelineate and test two possible mechanisms to explain the phenomenon. One mechanism proposes thatthe explicit-zero framing creates the impression of an improving sequence, thereby enhancing thepresent value of the delayed reward. A second possible mechanism posits an increase in attentionallocation to temporally distant reward representations. In four experiments, we distinguish betweenthese two hypothesized mechanisms and conclude that the temporal attention hypothesis is superiorfor explaining our results. We propose a model of temporal attention whereby framing affectsintertemporal preferences by modifying present bias.

Key words: delay discounting, hidden-zero effect, temporal attention, reward sequences, priming,humans

_______________________________________________________________________________

We frequently face choices between out-comes that may be realized at different pointsin time. For example, we may use vacationtime to take a needed day off work, but savingthose hours would afford the luxury of anextended future vacation. When faced withsuch choices—those that pit an immediatereward against larger alternatives availableafter some delay—we often opt for immediategratification, even when doing so conflicts withour longer-term interests. Procrastination is aclear example: despite a self-professed prefer-

ence for the timely completion of a task,we often postpone it in favor of immediatedistraction. Temptation hints at another com-mon problem; sometimes, despite the fullexpectation of later regret, momentary hedo-nism beckons us to indulge in one more glassof wine or one more piece of cake. In general,we are prone to disregarding our longer-terminterests in favor of immediate gratification,often despite our better intentions (Ainslie &Haslam, 1992; Rachlin, 2000).

Formally, these behaviors may be quantifiedby expressing how subjective value dependson delay. Mazur (1987) developed the highlysuccessful hyperbolic discount function, ex-pressed as

V ~X

i

ri

1zktið1Þ

for rewards indexed by i with magnitudes andtime to delivery given by ri and ti, respectively.Discount rates (k) from this function arefrequently used as a measure of impulsivity(Ainslie, 1975); high discount rates corre-spond to a greater preference for immediacy.Critically, this function allows for the phenom-enon of time-dependent preference reversals.If a larger, delayed reward is preferred to asmaller but more proximate reward when both

Peter T. Radu, James J. Gross, and Samuel M. McClure:Department of Psychology, Stanford University; Richard Yi:Department of Psychology, University of Maryland; andWarren K. Bickel: Carilion Research Institute, VirginiaTech University.

This research was supported by the John Philip CoghlanFellowship (SMM), National Institute on Drug AbuseGrants R01DA024080 and R01DA022386, 1UL1RR029884,Wilbur Mills Chair Endowment, and the Arkansas Biosci-ences Institute (WKB), National Institute on Drug AbuseGrant R01 DA011692-11 (RY), and National Institute ofHealth Grant R01MH76074 ( JJG). Thanks especially tomembers (and friends) of the Decision NeuroscienceLaboratory for their immensely helpful feedback andideas.

Correspondence concerning this article should beaddressed to Samuel M. McClure, Department of Psychol-ogy, Stanford University, 450 Serra Mall, Stanford,California 94305 (e-mail: [email protected]).

doi: 10.1901/jeab.2011.96-363

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2011, 96, 363–385 NUMBER 3 (NOVEMBER)

363

are delayed, then preference reversals arisewhen the smaller, proximate reward becomesimmediately available due to the passage of theintervening time (Ainslie & Haslam, 1992). Toillustrate, we may prefer to skip dessert whenthe prospect is remote but impulsively suc-cumb when the cake is brought to the table.

For most people, selection of the immediatereward is an occasional and largely inconse-quential behavior. However, for some, prefer-ence for proximate rewards is pathologicallypersistent. Indeed, a variety of clinical disor-ders, including substance abuse (Bickel &Marsch, 2001; Kirby, Petry, & Bickel, 1999;Reynolds, 2006), attention-deficit hyperactivitydisorder (Barkley, Edwards, Laneri, Fletcher,& Metevia, 2001; Critchfield & Kollins, 2001),obesity (Epstein, Salvy, Carr, Dearing, &Bickel, 2010), and pathological gambling(Petry, 2001; Reynolds, 2006), are associatedwith a heightened preference for smaller butimmediately available rewards. That highdiscounting characterizes so many disorderssuggests it may function as a trans-diseaseprocess (Bickel & Mueller, 2009). Consequent-ly, interventions that reduce discounting are ofbroad clinical interest.

In prescribing methods to ameliorate myopicintertemporal choice, dominant theories to datehave largely posited some degree of intrapsychicconflict between immediate, pleasure-seekingimpulses and future-oriented, regulatory or inhi-bitory control mechanisms (Ainslie & Haslam,1992; Baumeister & Heatherton, 1996; Metcalfe& Mischel, 1999). Shifting preferences to favorlong-term outcomes, such a view holds, requireseither suppressing or ignoring one’s latent desirefor the immediate reward or down-regulating itsvalue through cognitive reconstrual (Fujita &Han, 2009; Magen & Gross, 2007; Metcalfe &Mischel, 1999). However, emerging data offerinterventions that may effectively preemptthe need for such cognitively demandingtechniques. For instance, discount rates can bereduced simply by reframing questions toincrease the subjective value of larger, distant(LD) outcomes over smaller, proximate (SP)alternatives (Magen, Dweck, & Gross, 2008; Read,Frederick, Orsel, & Rahman, 2005). Little to notraditional ‘‘self-control’’ efforts may be requiredif the presentation format itself alters rewardprocessing in favor of larger, later outcomes.

One such framing manipulation, whichexpresses immediate outcomes as ‘‘something

now but nothing later’’ and deferred out-comes as ‘‘nothing now but more later,’’ hasbeen labeled the ‘‘hidden-zero effect’’ byMagen et al. (2008). In their experiment,Magen and colleagues contrasted two condi-tions, whose format and terminology we alsoemploy herein. In the hidden-zero condition,choices take the form, ‘‘$5.00 today, OR $8.20in 26 days.’’ The explicit-zero condition presentschoices as ‘‘$5.00 today and $0 in 26 days, OR$0 today and $8.20 in 26 days’’ and promotesreduced discounting. Loewenstein and Prelec(1993) conducted a similar experiment withnonmonetary rewards (dinners at fancy res-taurants versus dinners at home) and arrivedat the same conclusion: Explicitly statingdefault outcomes associated with each choicealters intertemporal preferences.

That reframing of intertemporal optionscan increase patience is of great potentialinterest to clinicians and theorists alike. Assuch, the aim of the present article is toelucidate the psychological mechanism under-lying the hidden-zero effect. Below, we presenttwo possible hypotheses, delineating the re-spective processes by which each would ex-plain the effect of reduced discounting. Forease of reference, we refer throughout to theeffect of reduced discounting as the ‘‘hidden-zero effect’’ and the inclusion of zero-dollaroutcomes in discount questions as ‘‘explicit-zero framing.’’

Improving Sequence Hypothesis

In general, people tend to prefer scenariosin which their prospects improve, rather thandecline, as time progresses (Loewenstein &Prelec, 1993). This preference can be mea-sured in various ways. For example, peopleprefer salary profiles that gradually increasewith years of job experience (Loewenstein &Sicherman, 1991) and experiences that endon positive rather than sour notes (Ross &Simonson, 1991), independent of cumulativegains. In the case of the hidden-zero effect, theinclusion of null outcomes may similarly createthe impression of a sequence. Specifically, ‘‘$5today and $0 in 26 days’’ is a decliningsequence, whereas ‘‘$0 today and $8.20 in26 days’’ is improving. When discountingoptions are thus construed as successive eventsrather than isolated outcomes, the net result isgreater relative preference for delayed op-

364 PETER T. RADU et al.

tions. Notably, Equation 1 cannot account forthis phenomenon.

With this in mind, the value function inEquation 1 may be amended to include themere impression of sequences (followingLoewenstein & Prelec, 1993):

V ~X2

i~1

ri

1zk tij jzIsc(r2{r1) ð2Þ

(see Appendix 1 for the derivation of thisequation.) Here, Is is an indicator variable thatis 1 when each component reward ri isexpressed as a sequence (explicit-zero condi-tion) and 0 when it is not (hidden-zerocondition). r1 and r2 are the rewards availableat times t1 and t2 (where the choice is betweenr1 at time t1 and r2 at time t2, t1 , t2 and eitherr1 or r2 is $0). We use the absolute value fortime to account for the recent finding,addressed below, that k is the same whendiscounting rewards in the future (t . 0) andin the past (t , 0) (Yi, Gatchalian, & Bickel,2006). Importantly, the free parameter cindicates an individual’s valuation of sequenc-es: Positive c implies preference for improvingsequences, whereas negative c favors decliningsequences. According to the improving sequencehypothesis, positive c adds overall utility to thevalue function when considering the delayedoption in an explicit-zero discounting frame.

Temporal Attention Hypothesis

Recent data have challenged traditionalconceptions of discounting, suggesting thatit may reflect time perspective rather thantraditional notions of self-control (Bickel,Kowal, & Gatchalian, 2006; Ebert & Prelec,2007; Zauberman, Kim, Malkoc, & Bettman,2009). Consider the case of substance addic-tion, a powerful example of suboptimal inter-temporal choice. One study asked heroin-dependent individuals and matched controlsto complete a story beginning, ‘‘After awaken-ing, Bill began to think about his future. Ingeneral, he expected to…’’ (Petry, Bickel, &Arnett, 1998). Of interest was not the subjectmatter of each participant’s response, butrather the time frame in which it was set:Whereas controls projected stories an averageof 4.7 years into the future, heroin addictsconsidered futures of only 9 days. With futuretime perspectives this truncated, it is perhaps

no wonder that addicted individuals repeated-ly ingest drugs despite the long-term legal,interpersonal, and economic hardships theyportend—such delayed consequences maysimply fall outside the restricted range of theirtemporal attention (Bickel et al., 2006).

Following this reasoning, future-minded re-ward responding may reflect not an exercisein delay of gratification per se, but rather aproficiency in episodic future thinking (cf.Peters & Buchel, 2010). Accumulating datasuggest that the ability to self-project into thefuture in such a fashion relies on a neural systeminvolving prefrontal, parietal, and mediotem-poral sites; interestingly, this very network hasalso been linked to recalling the past (Buckner& Carroll, 2007). Shifting attentional resourcesfrom ‘‘now’’ to ‘‘not now’’—that is, either thefuture or the past—seems to involve similarneural and psychological processes (Addis,Wong, & Schacter, 2007; Okuda et al., 2003),so much so that past memory and futureprojection have been called ‘‘two sides of thesame coin, two mutually complementary aspectsof temporal integration’’ (Fuster, 1989). Indeed,just as the consideration of future outcomes isinconsistent with respect to time—hyperbolicdiscounting yields steep discounting for the nearfuture and progressively less discounting in thefar future—so, too, is the process of memorydecay inconsistent across the past. Up to 50% ofan event is likely to be forgotten within 20 min,and up to 75% forgotten after 24 hr, yet theremainder decays much more slowly (Baddeley,1990; Hammersley, 1994). Given this similarity,studying the valuation of past rewards may helpelucidate the mechanisms underlying intertem-poral choice in general.

Recent work has begun examining currentpreferences for past rewards in both healthyand clinical populations (Bickel, Yi, Kowal, &Gatchalian, 2008; Dixon & Holton, 2009; Yiet al., 2006). In this paradigm, participants areasked to rate satisfaction for rewards justreceived (SP past rewards; e.g., ‘‘$5 one hourago’’) compared with larger but temporallydistant alternatives (LD past rewards; e.g.,‘‘$8.20 26 days ago’’). Preferences for thesechoices are well fitted by a hyperbolic func-tion, and notably, past and future rewarddiscount rates (k) are correlated. Furthermore,cigarette smokers discount the past and futuresymmetrically and, in both cases, more thancontrols (Bickel et al., 2008).

DELAY DISCOUNTING AND TEMPORAL ATTENTION 365

Traditional explanations, which posit impul-sive inabilities to delay gratification, cannotaccount for hyperbolic past discounting, sinceregulating tempting impulses is unnecessaryfor events that have already transpired. Weposit that temporal attention contributes toboth past and future outcomes and that, ineither case, selection of the LD alternativedepends in part on increased attention alloca-tion away from ‘‘now.’’ Since natural inclina-tion is attentional myopia for the present (asevidenced by preference reversals in hyperbol-ic discounting), the addition of a delayed $0outcome to an immediate reward mitigates itsvalue by placing it in the same timeframe as itsdelayed, larger alternative. This hypothesis,which we refer to as the temporal attentionhypothesis, suggests that explicit-zero framingincreases patience by emphasizing the un-pleasant distant consequences associated withpresent responding.

To formalize the temporal attention hypoth-esis, we begin from the conceptual similarity totwo-systems models of temporal discounting(Laibson, 1997; Loewenstein, 1996; McClure,Ericson, Laibson, Loewenstein, & Cohen, 2007;McClure, Laibson, Loewenstein, & Cohen, 2004;Thaler & Shefrin, 1981). We recently proposed asimplified mathematical formulation as a weight-ed sum of two processes that differ in temporalhorizon (McClure et al., 2007):

V ~X

i

ri v’d tij jz 1{v’ð Þb tij jh i

ð3Þ

One system, described by the value function bt, ismyopic in temporal focus, sharply discountingthe value of rewards that are not availableimmediately. The other system values rewardsat all time points with a moderate discount rate;its value is given by dt (1 $ d . b $ 0). Therelative activity of these separate systems deter-mines whether a smaller, proximate or larger,distant reward is selected (McClure et al., 2004,2007). Crucially, the d parameter has beencorrelated with activity in the frontal-parietalnetwork associated with past and future self-projection (Buckner & Carroll, 2007; McClureet al., 2004). We therefore believe that it mayreflect the allocation of attention to temporallydistant (past or future) scenarios. Finally, theweighting term, v9, captures the relative impactof each system in the overall valuation. If con-sidering distant time perspectives is hypothesized

to depend on d, then expanding temporalattention amounts to enhancing the relativeimportance (v9) of this process by some amount e:

v’~vzIse ð4Þ

As in Equation 2, Is is an indicator variable that is 1when zeros are explicit and 0 when they arehidden. From this formulation, explicit-zeroframes change temporal attention by directlyshifting processing in favor of a far-sightedattentional (d) system.

The Present Experiments

The two hypotheses outlined above (theimproving sequence hypothesis and temporalattention hypothesis) can both account for thehidden-zero effect described by Magen andcolleagues (2008). However, future discountingalone in this format cannot be employed todelineate a precise psychological mechanism, asboth hypotheses predict increased selection ofLD rewards when framed with explicit zeros.However, as we detail below, the hypothesesmake opposite predictions regarding the hidden-zero effect for past temporal discounting. Wetake advantage of this fact and, in four experi-ments, examine these hypotheses and theirrespective behavioral implications in greaterdetail. We conclude that the temporal attentionhypothesis is superior for explaining our results.

In Experiments 1 and 2, we extend thehidden-zero effect to the discounting of pastrewards, demonstrate its relatedness to thefuture hidden-zero effect, and argue that thephenomena cannot be explained by a prefer-ence for improving sequences. However, inevaluating the two hypotheses, a potentialconfound arises from our formulation of Equa-tion 2. Although we specify the absolute value oftime in the hyperbolic term, we do notsimultaneously require that |t1| , |t2| in the past,but simply that t1 , t2. Essentially, Equation 2assumes a unidirectional perception of timepassage. (For simplicity, we always refer tosequences with respect to unidirectional timepassage; therefore, ‘‘$0 an hour ago and $8.2026 days ago’’ would be a past decliningsequence.) While this assumption is consistentwith other work in psychology (see Boroditsky,2001), previous work offers no direct empiricalbasis for our formulation. Furthermore, ourassumption on this point has direct implicationsfor preferences among sequences of rewards in


the past: If the absolute value of time were usedin the sequence term of Equation 2, then wewould expect preferences for improving se-quences in the future but declining sequencesin the past. In our formulation, preferences arefor improving sequences in both the future andpast. Our assumption is therefore an empiricalquestion; we test it directly in Experiment 3and demonstrate preferences for improvingsequences in the past. This effect is oppositethat of the past hidden-zero effect and thusprovides further evidence against the improvingsequence hypothesis. Finally, in Experiment 4,we demonstrate that priming the distant past—and thus drawing attention away from the‘‘now’’—increases preferences for temporallydistant past rewards, providing additional sup-port for the feasibility of the temporal attentionhypothesis.

EXPERIMENT 1: THE PAST HIDDEN-ZERO EFFECT

The improving sequence and temporal atten-tion hypotheses suggest different explanationsfor the reduction in discounting rates observedwhen questions are framed with explicit zeros.However, these hypotheses cannot be discrimi-nated on the basis of future discounting alone,as both predict an increased preference forlarger, distant (LD) over smaller, proximate(SP) rewards (see the ‘‘Future’’ panels ofFigures 1B and 1C). To demonstrate this, notethe pattern in Figure 1A: both hypothesespredict that adding explicit zeros to a futurediscounting choice (e.g., ‘‘[option i] $5.00 todayand $0.00 in 26 days, OR [option ii] $0.00 todayand $8.20 in 26 days’’) should increase thesubjective valuation of the larger, distant (LD)reward (thick line for option ii, an improvingsequence) and decrease subjective valuation ofthe smaller, proximate (SP) reward (broken linefor option i, a declining sequence). Therefore,in order to differentiate between the twohypotheses, we extend explicit-zero framings tothe discounting of past rewards (Bickel et al.,2008; Yi et al., 2006). The two hypotheses makeopposite predictions for past discounting (seeFigure 1A and ‘‘Past’’ panels of Figures 1B and1C), which we describe in turn below.

Improving Sequence Hypothesis

Extending Loewenstein and Prelec’s (1993)formulation for valuing sequences (Equation

2) to the past suggests that the effect ofexplicit-zero framing should be opposite tothe effect for future valuation. For example,see Figure 1A, which presents a choice be-tween ‘‘(option iii) $5.00 one hour ago and$0.00 26 days ago, OR (iv) $0.00 one hour agoand $8.20 26 days ago.’’ In both instances thereward from 26 days ago (t1) is the earliestin a sequence of two rewards over time andtherefore corresponds to r1 in Equation 2; thereward from one hour ago comes next in time(t2) and thus corresponds to r2.

The lynchpin of this hypothesis is Loewen-stein and Prelec’s (1993) finding that individ-uals prefer improving sequences (i.e. c . 0).According to an objective, linear conceptionof time, option iii represents an improvingtemporal sequence, and option iv represents adeclining sequence. Equation 2, therefore,predicts that the SP reward (option iii) shouldpreferentially benefit from the explicit-zeroframing, since it results in (r2 2 r1) . 0,adding overall utility to the option (thick linefor option iii). Conversely, the value of the LDreward (option iv) decreases with the explicit-zero framing, as in this case (r2 2 r1) , 0(broken line for option iv). Overall, a prefer-ence for increasing sequences should increasepreference for temporally near outcomes inthe past with explicit-zero frames.

Temporal Attention Hypothesis

The temporal attention account of the hid-den-zero effect posits reduced present bias withthe inclusion of null (zero-dollar) outcomes.Accordingly, this hypothesis predicts that fram-ing past options with explicit zeros will increasepreferences for LD options in the past (thickline for option iv in Figure 1A) and decreasepreference for SP past options (broken line foroption iii). Notably, such a preference wouldrepresent a preference for declining sequencesin the past, directly contradicting an improvingsequence account of the hidden-zero effect.

METHOD

Participants

Twenty-seven undergraduates were recruit-ed from an introductory psychology courseat Stanford University and compensated withcourse credit. One subject was excluded fromall analyses for a stated suspicion of hypothesis.The remaining 26 participants (18 females, 8


males) ranged in age from 17 to 22 years (M 518.8 years; SD 5 0.88). One individual indicat-ed a prior psychiatric diagnosis and currentuse of psychiatric medication. None indicatedany prior history of substance use disorders.

Materials

All discounting questions were presented inrandomized order on a computer, immediatelyfollowing a set of on-screen instructions. Re-sponses were recorded with keystrokes. Themoney amounts and their corresponding rela-tive delays were taken directly from the set used

by Magen et al. (2008); we altered only thedirection of the temporal delays, such that theynow projected into the past: SP options werepresented as having occurred ‘‘one hour ago’’(Yi et al., 2006), whereas LD options werepresented as having occurred (for example)‘‘26 days ago.’’ The full set of past discountingoptions is presented in Appendix 2.

Procedure

After providing consent, participants wereled to the computer on which the task wasprogrammed and were told by the experimenter

Fig. 1. Hypotheses for Experiments 1 and 2. (A) Predictions of the improving sequence and temporal attentionhypotheses for effects of explicit-zero framing on intertemporal reward valuation. (B) Model simulation for theimproving sequence hypothesis (Equation 2), starting with arbitrary initial parameter values (k 5 .04, c 5 .2, m 5 10) and100 iterations of the maximum likelihood estimation procedure. This model predicts a decrease in SP choices in thefuture explicit-zero condition but a decrease in past explicit-zero SP choices. (C) Model simulation for the temporalattention hypothesis (Equation 3), starting with arbitrary initial parameter values (b 5 .85, d 5 .998, v 5 .5, e 5 .1, m 510) and 100 iterations of the maximum likelihood estimation procedure. This model predicts a decrease in SP explicit-zero choices in both past and future and no difference in effect between past and future.


to complete the task at their own pace.Participants were then presented with thefollowing computerized instructions:

‘‘This is a study about money preferences. You will beasked to choose between different sums of money. Pleaseread the following instructions carefully. You may askthe experimenter questions at any time if anything isunclear. Take a moment to get comfortable in yourchair. Please also take a moment to gently rest yourhands on the keyboard so that your left index fingerrests on the ‘F’ key, your right index finger rests on the‘J’ key, and your thumbs rest on the spacebar. All set?‘‘For each money choice that follows, please indicatethe option you WOULD PREFER TO HAVERECEIVED, if the money had been available to youat that point in time. Press the ‘F’ key (your left indexfinger) if you would prefer the option on the left-handside of the screen. Press the ‘J’ key (your right indexfinger) if you would prefer the option on the right-hand side of the screen.‘‘Let’s take a moment to practice the task. Remember,press the ‘F’ key if you would prefer the option on theleft side of the screen, and press the ‘J’ key if youwould prefer the option on the right side of the screen.Ready to practice?’’

Participants then made three practice choic-es (none of which had explicit zeros) to ensurefamiliarity with the choice-selection proce-dure. Finally, they read the following beforemoving on to the test phase of the experiment:

‘‘You are now ready to begin the experiment. Again,for each of the following choices, please select theoption you would prefer to have received. Please makeyour choices as thoughtfully as you can.’’

We employed a within-subject design inwhich all participants completed 15 past hid-den-zero questions and 15 past explicit-zeroquestions. These two blocks of 15 questionswere counterbalanced in presentation orderacross participants, and the order of choices wasrandomized within each block. Reward pairswere presented individually on the screen; inaccordance with common practice, the SP andLD options always appeared on the left andright sides of the screen, respectively.

Model Fitting

A simple way to determine participant behavioris by summarizing the number of smaller,proximate rewards chosen in each of the hidden-and explicit-zero conditions; these analyses arepresented below. Nevertheless, there is a cruciallimitation to this approach. Consider the possi-bility that explicit-zero framing does not lower

discount rates per se, but that this novel questionformat merely increases randomness in partici-pant responding. A decrease in the meannumber of SP choices across the hidden- andexplicit-zero conditions (towards a 50-50 split inresponses) might then be misinterpreted asreduced discounting, when in fact it wouldmerely reflect higher degrees of ‘‘noise’’ orrandom responding to explicit-zero frames.Importantly, this possibility would not be detect-able from a simple count of binary responses toeach question.

Although an F test revealed no difference inthe variance of responses across experimentalconditions, F(25,25) 5 0.68, p . .34, we morerigorously addressed this concern by fittingEquation 2 to all participants’ individualchoices (from both conditions combined).We used a maximum likelihood process toestimate free parameters from Equation 2, k, c,and m (see Equations 5, 6 below), for eachsubject individually. For any value of k and c,there is an estimated value of the SP option,V1, and of the LD option, V2. We assume thatchoices follow a softmax decision functionwhere the probability of selecting the smallerreward is

PSP ~ 1z exp {mDVð Þ½ �{1 ð5Þ

and

DV ~VSP k,cð Þ{VLD k,cð Þ: ð6Þ

The likelihood of the observed sequence ofchoices is then given by the product of theprobabilities for all choices and depends on k,c, and m. We used a simplex procedure with100 randomly selected initial parameter valuesto maximize this likelihood function. Thisprocedure also allowed us to determine thesignificance of the fit for each subject using alikelihood ratio test, indicating good modelfits relative to an intercept-only (binomial)model. We calculated the likelihood of thebinomial model from each subject’s observednumber of SP choices alone. All subjects’model fits passed this likelihood ratio test: allx2 (3) . 11.81, all ps , .009.

RESULTS

We found no effects of demographic vari-ables (age, gender, ethnicity) or psychiatric


status on the primary outcome of interest:Namely, the difference in SP choices in thepast hidden- and past explicit-zero conditions:all Fs , 1, all ps . .37. Hence, we do notconsider demographics further.

Our aim was to determine whether explicitlystating zero-dollar outcomes alters preferencesfor past rewards. For the 26 participantsretained for analyses, we found fewer SPchoices in the past explicit-zero condition (M5 9.04) than in the past hidden-zero condition(M 5 9.81), t(25) 5 2.04, p 5 .05, paired (seeFigure 2). The difference in choices acrossconditions did not differ as a function of blockpresentation order (Wilcoxon rank sum test; W5 75, p . .6). These results demonstrate thatthe hidden-zero effect indeed extends to pastoutcomes, and contradicts the improving se-quence hypothesis as expressed in Equation 2.

Recall from Equation 2 that the parametersummarizing the behavioral hidden-zero effect(i.e., the difference in discounting acrossexplicit- and hidden-zero conditions) is c,which captures the impact of improvingsequences on valuation (and hence choice).When fitting Equation 2 to the data, we foundthat the estimated mean value of c across allparticipants was negative (M 5 20.10, SD 50.25, range 5 20.54–0.35) and was significant-ly different from zero, t(25) 5 22.07, p , .05,implying a significant framing effect irrespec-tive of response noise.

DISCUSSION

Experiment 1 is the first demonstration ofthe hidden-zero effect for past discounting:Participants chose the larger, distant outcomemore frequently when presented with theexplicit-zero frame. We also found initialevidence against the improving sequencehypothesis: In our sample, subjects preferredpast sequences that declined through time (i.e.c , 0). Importantly, preference for decliningsequences is normatively correct (assumingnonzero inflation or the possibility of positiveinterest rate). However, as discussed, individ-uals tend to prefer future sequences andimpressions of sequences (i.e., explicit-zeroframes) that improve through time. It istherefore important to test for a within-subjectrelationship between past and future hidden-zero effects. Evidence for simultaneous valua-tion of past declining sequences and futureimproving sequences would challenge the

improving sequence hypothesis. In Experi-ment 2, we explored the past and futurehidden-zero relationship and test the alterna-tive model of temporal attention.

EXPERIMENT 2: RELATIONSHIP OF PASTAND FUTURE HIDDEN-ZERO EFFECTS

Our next experiment extended the findingfrom Experiment 1 by replicating the original(future) hidden-zero effect and relating it tothe discounting of past hidden- and explicit-zero rewards. We predicted that past andfuture hidden-zero effects would be positivelycorrelated (in other words, that explicit-zeroframing would increase the number of LDchoices in both the past and the future). If astrong preference for improving sequencesin the future were simultaneously associatedwith a strong preference for declining sequenc-es in the past, we would have strong evidenceagainst the improving sequence hypothesis.

In this experiment, we assessed our twocompeting hypotheses by fitting Equations 2and 3 to the data. To facilitate interpretationof the results, we conducted simulations acrosspast and future choices for the improvingsequence hypothesis (Equation 2; Figure 1B)and the temporal attention hypothesis (Equa-tion 3; Figure 1C). We used arbitrary param-eter values for the models, as we were onlyinterested in qualitative differences in model

Fig. 2. Behavioral results from Experiment 1: identifi-cation of the past hidden-zero effect, with fewer SP choicesin the explicit-zero relative to the hidden-zero condition(out of 15 options per condition; * p 5 .05, paired).


predictions. The number of SP choices calcu-lated for Figure 1 is the mean numberexpected for each condition. The improvingsequence hypothesis (see Figure 1A, B), pre-dicts increased preference for SP options inthe past explicit-zero condition but a de-creased preference for SP options in the futureexplicit-zero condition (with c . 0; the sign onboth differences changes with c , 0). For thetemporal attention hypothesis (Figure 1C),the model predicts that explicit-zero frameswill decrease preference for SP choices equallyin both past and future choices.

METHOD

Participants

Participants were 47 undergraduates in anintroductory psychology course at StanfordUniversity who completed the experiment forcourse credit. These participants (28 females,19 males) ranged in age from 17 to 22 years (M5 18.8, SD 5 .95). None indicated a psychiat-ric diagnosis, although one participant report-ed currently taking psychiatric medication.None indicated any past history of substanceuse disorders.

Materials

The past discounting questions were identi-cal to those described in Experiment 1 (seeAppendix 2). For the future hidden-zerodiscounting questions, we used the set fromMagen et al. (2008) (the full set is presentedin Appendix 2). All money amounts werepresented as hypothetical to create proceduralsymmetry across past and future conditions.

Procedure

Participants adhered to the same protocoland instructions as described in Experiment 1,completing 15 explicit-zero and 15 hidden-zero past discounting questions (blocked,counterbalanced, and randomized in orderacross participants). They then went on tocomplete blocks of 15 future hidden-zero and15 future explicit-zero questions, again coun-terbalanced and randomized in order acrossparticipants. All participants completed pastdiscounting questions first.

Model Fitting

The improving sequence model (Equation2) was fitted twice (once for past and once

for future choices) to each participant’s dataindividually (hidden- and explicit-zero condi-tions combined). We used the maximumlikelihood estimation procedure describedin Experiment 1. Doing so required droppingparticipants who selected either all SP or allLD choices. This pattern of choices precludesaccurate estimation of discounting parame-ters, suggesting that the task was not appro-priately calibrated to determine these partici-pants’ true indifference point. As such, wedropped 8 participants from the followinganalyses1. All remaining participants’ modelfits were submitted to a likelihood ratio test forgoodness of fit; 1 additional participant wasdropped from all analyses because of a failureto meet significance at the p 5 .05 level in bothfits—past: x2 (3) 5 7.46, p 5 0.06; future: x2

(3) 5 3.80, p 5 .28. Post hoc inspection of thisparticipant’s choices using the Kirby scoringprocedure (Kirby et al., 1999) revealed seem-ingly random responding. All other model fitspassed [all x2 (3) . 7.95, all ps , .05]. Thisleft a final sample of 38 participants for allreported model-based analyses.

To fit the temporal attention model (Equa-tion 3), we again used a maximum likelihoodprocess to estimate the free parameters v, e, b,and d, and m (see Equation 7 below) for eachparticipant individually (and separately forpast and future). To allow for formal modelcomparisons, we retained the 38 participantsfor whom we also fitted Equation 2 (seeabove). We assumed that choices follow asoftmax decision function (Equation 5) with

DV ~VSP (v,e,b,d){VLD(v,e,b,d): ð7Þ

The likelihood of the observed choices is thengiven by the product of the probabilities for allchoices and depends on v, e, b, d and m. Weused a simplex procedure with 100 randomlyselected initial parameter values to maximizethis likelihood function. To determine good-ness of fit, we submitted the fits to a likelihoodratio test relative to an intercept-only (binomi-al) model based on number of SP choicesalone. In general, results indicated that the

1 Dropping these 8 participants did not affect thebehavioral results reported in Experiment 2. If anything,it led to a more conservative analysis; in both the past,t(37) 5 4.40, p , .00008, and future, t(37) 5 2.41, p , .03,conditions, the hidden-zero effect was slightly weakerwhen excluding these participants.


model summarized behavior quite well, allx2 (4) . 14.6, all ps , .006, for all but 1participant, for whom the model fitted to pastchoices was only marginally significant, x2 (4) 58.25, p 5 0.083. Nonetheless, we retained thisparticipant for the analyses below in order todirectly compare the fits for Equations 2 and 3.

RESULTS

Demographics

As in Experiment 1, we found no effects ofdemographics or psychiatric status (all ps ..18) on either the past (all Fs , 1) or future(all Fs , 2) hidden-zero effect, and so we donot consider these variables further.

Behavioral Demonstration of the Hidden Zero Effect

Replicating our result from Experiment 1, wefound that the past hidden-zero effect was highlysignificant, t(46) 5 4.60, p , .00004, paired;participants (N 5 47) made fewer smaller,proximate choices when past options wereframed with explicit zeros. There was a differenceacross conditions for the future choices as well,t(46) 5 3.05, p , .004, paired, replicating theoriginal finding of Magen and colleagues (2008).These findings are presented in Figure 3A. Aswith Experiment 1, order of block presentationhad no effect in either the past, t(42.27) 5 20.96,p . .3, or future condition, t(43.55) 5 20.13,p . .8, and the variance in responses was

Fig. 3. Behavioral results from Experiment 2. (A) Similarity of past and future hidden-zero effect (Expt. 2),resembling the predictions of the temporal attention hypothesis (see Figure 1C) (out of 15 options per condition; ** p ,.00004, paired; * p , .004, paired). (B) Hidden-zero effect magnitude: in both past and future, D SP choices [(# hidden-zero SP choices) 2 (# explicit-zero SP choices)] is significantly greater than 0. Error bars 5 standard error of the mean.(C) Correlation between past and future hidden-zero effects, where D SP choices 5 (# hidden-zero SP choices) 2 (#explicit-zero SP choices).


homogeneous across hidden- and explicit-zeroconditions: future, F(46,46) 5 1.20, p . .54; past,F(46,46) 5 1.03, p . .91.

Numerically, we summarized the hidden-zeroeffect by calculating delta scores for smaller,proximate choices ([number of SP choices,hidden condition] – [number of SP choices,explicit condition]) in both the past and futurediscounting sets. As shown in Figure 3B, thesedelta scores did not differ across past and futureconditions, t(46) 5 1.56, p . .12, paired.Finally, these delta scores were modestly but

positively correlated, r 5 .29, p 5 .05, acrossthe past and future conditions, hinting at acommon mechanism that is sensitive to manip-ulation (see Figure 3C).

Improving Sequence Model Fits

We first assessed the relationship betweenpast and future discounting in general byfitting Equation 1. As distributions of k wereskewed in both the past and future, we used alog-transform to normalize the fitted parame-ter values. Past and future values of k did not

Fig. 4. Model-fitting results from Experiment 2. (A) Correlation between log-transformed k values in the past andfuture discounting conditions. (B) Mean estimate of c for past discounting options only, future options only, and acrossthe entire choice set (both past and future options). Error bars 5 standard error of the mean. (C) Mean parameterestimates from Equation 3 for past and future discounting choices (both hidden- and explicit-zero). Error bars (whereappropriate) 5 standard error of the mean. (D) Mean estimates of e for past discounting options only, future optionsonly, and across the entire choice set (both past and future options). Error bars 5 standard error of the mean.


differ, t(37) 5 1.77, p . .08, and weresignificantly correlated, r 5 .65, p , .00001,(see Figure 4A), replicating the finding thatthe hyperbolic discount factor is related forpast and future discounting (Bickel et al.,2008; Yi et al., 2006).

Figure 4B summarizes the c fits for eachcondition. We found negative values of c (M 520.14, SD 5 0.19, range 5 2.66–.15) for pastdiscounting; the mean was significantly differ-ent from 0, t(37) 5 24.33, p 5 .0001.Additionally, we found positive values of c (M5 0.08, SD 5 0.20, range 5 20.26–0.65) forfuture discounting; this mean was also signif-icantly different from 0, t(37) 5 2.43, p 5 .02.Values of c were significantly and negativelycorrelated across the past and future condi-tions, r 5 2.34, p , .04, converging withthe behavioral correlation between the deltascores (see above) and demonstrating arelationship between past and future hidden-zero effects.

Importantly, these results imply that partic-ipants preferred declining sequences (c , 0)in the past while concurrently preferringimproving (c . 0) future sequences. Behav-iorally, this is demonstrated by a mirror-symmetric hidden-zero effect (see Figure 3A).We thus expected to find that, when fittingEquation 2 across past and future choicescombined, c would no longer express thisbehavioral symmetry (as positive future andnegative past values of the parameter wouldcancel to zero). We fitted the model a thirdtime to both choice sets concurrently (poolingall 60 future and past questions); all modelspassed a likelihood ratio test for goodness offit relative to a binomial model, all x2 (3) .16.95, all ps , .0008. As expected, we foundthat c was not significantly different from zero,t(37) 5 0.39, p 5 .7, (see Figure 4B). An

estimated value of c 5 0 implies that thereshould be no hidden-zero effect, furtherdemonstrating the inadequacy of Equation 2(and hence the improving sequence hypothe-sis) in describing the data.

Temporal Attention Model Fits

These model fits contrast with those forthe temporal attention hypothesis, which weassessed by fitting Equation 3 to these partic-ipants’ choices (two separate times, once forthe past and once for the future options).We report results from nonparametric testswherever distributions showed evidence ofnonnormality.

Figure 4C compares parameter values acrosspast and future choice sets. Paired-sample testsfound no significant differences for b, d, or theweighting parameter v (b: t(37) 5 20.94, p ..35; d: W 5 274, p . .22; v: t(37) 5 1.26, p ..21), indicating similarity in the temporalattention domain. In other words, the additionof explicit zeros affects temporal attention (asapproximated by model parameters) similarlyfor past and future outcomes2.

Figure 4D summarizes e fits for each condi-tion. Estimates of e were positive for both thefuture (M 5 0.13, SD 5 0.33, range: 20.78–0.99) and past (M 5 0.18, SD 5 0.41, range:21–1), significantly different from zero: fu-ture, t(37) 5 2.45, p , .02; past, t(37) 5 2.71,p 5 .01, and not different from one another,t(37) 5 0.68, p . .5, paired. Behaviorally, thisreveals a similar effect of explicit-zero framingon both past and future discounting. However,the correlation between past and future e,though positive, was not significant, r 5 .24, p5 0.14. This may mean that, while attentionalallocation mechanisms operate similarly fordistant past and future outcomes, the effect isidiosyncratic across individuals.

To determine whether the explicit-zeroframe widened temporal attention across allchoices (irrespective of past or future), wefitted Equation 3 to both choice sets (past andfuture combined) concurrently; this result ispresented in Figure 4D. All models passed alikelihood ratio test for goodness of fit, relativeto a binomial model based on SP choicesalone: all x2 (4) . 24.27, all ps , .000083.When examining values of e (M 5 0.18, SD 50.34), we found they were significantly differ-ent from 0, t(37) 5 3.29, p , .003, indicatingthat increases in e, and its corresponding

2 Wilcoxon-Mann-Whitney tests on data from all subjects(N 5 47) found similar results for the estimates of b [t(46)5 21.36, p 5 .18], d (W 5 392, p . .35), and e [t(46) 521.14, p . .26]. Estimates of v, however, did differ slightlyacross past and future conditions, t(46) 5 2.05, p , .05.We note that this result mirrors the behavioral data, inwhich group differences in SP choices revealed a slightlylarger hidden-zero effect in the past condition. Accord-ingly, we found that v estimates across all participants wasslightly larger in the future (M 5 .62, SD 5 .31) than in thepast (M 5 .50, SD 5 0.34), corresponding to a smallerweighting on b (see Equation 3) and hence a smallereffect. Excluding the data of 8 participants who choseeither all SP or all LD rewards produced this slightdiscrepancy.


effects on the relative weights placed on b andd, widen temporal attention and decreasediscounting for explicit-zero frames. To thispoint, estimates of e were positively correlatedwith delta scores for number of SP choicesacross conditions in both the past (r 5 .40, p ,.02) and future (r 5 .32, p , .05) choice sets.This demonstrates a scaling of e with behavior:The less one chooses immediate (past orfuture) choices in the explicit-zero condition,the more e is affecting temporal attention.

Model Comparison

One critical difference between the improv-ing sequence and temporal attention models isthe number of free parameters. The temporalattention model explains the behavioral re-sults better than does the improving sequencemodel, but a formal comparison is necessary todetermine whether this improvement is signif-icant relative to the increased number ofmodel parameters. To determine this, wecollapsed across all participants’ data toprovide a representative fit for Equations 2and 3. The observed hidden-zero effect, (i.e,,the mean difference in SP choices [#SPhidden – #SP explicit]) across past and futureconditions was 1.1 for the 38 participants. Foreach model, we determined the likelihood ofobserving a mean effect of this magnitude byrunning a Monte Carlo simulation, with 10,000iterations and using the mean parametervalues from the fits for combined past andfuture choices reported above. As expected,Equation 3 (Bayesian information criterion[BIC] 5 24.58) accounted for the hidden-zeroeffect better than Equation 2 (BIC 5 26.54).This indicates that the reduction in discount-ing promoted by explicit-zero frames is betterexplained as a shift in temporal attention thanas a preference for improving sequences.

DISCUSSION

The results of this experiment demonstrate arelationship between past and future hidden-zero discounting: Explicit-zero framing reduces

SP choice preference for both future and pastoutcomes. Importantly, we found evidence forsimilarity in the temporal attention domain forboth past and future rewards, consistent withrecent evidence that consideration of past andfuture involves overlapping neural systems(Buckner & Carroll, 2007). The similarity ofpast and future hidden-zero effects suggeststhat discounting may be reduced throughframing effects that preempt the need forcognitively demanding techniques such astemptation inhibition. After all, there is noth-ing to inhibit in the past (Bickel et al., 2008).

For a sequence account, these findingsindicate that if one prefers improving sequenc-es in the future, one also prefers decliningsequences in the past. Since Equation 2predicts uniform preference for improvingsequences across time, in both past and future(see Figure 1C), we conclude that the resultsdo not support the improving sequencehypothesis but rather follow directly fromthe temporal attention hypothesis. However,a simple alternative explanation (to a changein temporal attention) is that individuals favordeclining sequences in the past while concur-rently favoring improving sequences in thefuture. In other words, our finding in Exper-iments 1 and 2 that c , 0 in the past mayactually reflect inherent preferences.

To see this, note that a central argument forthe temporal attention hypothesis is the factthat past and future discounting are mirror-symmetric (Bickel et al., 2008; Yi et al., 2006).To reflect this fact, we have amended Mazur’s(1987) hyperbolic equation by indicating |t| inexpressing Equation 2. The sequence term,however, does not require that |t1| , |t2|, butsimply that t1 , t2. For our formulation ofEquation 2, we assumed a linear, unidirection-al perception of time passage (see, forexample, Boroditsky, 2001). In other words,time passage may be mapped onto a numberline, with the origin (0) corresponding to‘‘now,’’ negative numbers corresponding tothe past, and positive numbers correspondingto the future. To return to our runningexample, ‘‘26 days ago’’ (226, or t1) is indeedless than ‘‘now’’ (0, or t2) according to thisconception of time passage. This formulationpredicts that improving sequences should bepreferred when considering both past andfuture explicit-zero frames. Experiments 1

3 Notably, log-likelihood tests on the model fits of allparticipants (N 5 47) revealed a much stronger perfor-mance when past and future choices were aggregated; allparticipants passed, all x2 (4) . 12.01, all ps , .02, exceptfor one, x2 (4) 5 6.07, p 5 .2. Overall, then, Equation 3describes behavior best when past and future choices areaggregated, adding further support to the conclusion thattemporal attention is similar for past and future outcomes.


and 2 have demonstrated that this predictioncontradicts actual behavior.

Nevertheless, our stipulation that t1 , t2remains open to empirical inquiry. Instead ofunidirectional time passage, it may be thatindividuals demonstrate relative perception ofpast and future time passage (i.e., that timeincreases positively towards the distant futureas well as towards the distant past). This wouldimply a preference for sequences that improvetowards the distant future as well as the distantpast, a pattern that would be consistent withthe data in Experiment 2. Were this the case,the sequence term in Equation 2 would needto stipulate |t1| , |t2|, making Equation 2 anadequate summary of behavior. The aim ofExperiment 3 is to explicitly explore thispossibility—that is, we assessed whether indi-viduals actually prefer sequences that improverelative to the distant past.

EXPERIMENT 3: PREFERENCE FOR PASTIMPROVING SEQUENCES

To test participant preferences for sequencesof rewards in the past, we extended a paradigmemployed by Loewenstein and Sicherman(1991), who asked workers to select between arange of salary profiles that increased, decreased,or remained constant with years of experience onthe job. Given this scenario, individuals preferredincreasing payment sequences in the future. Weemployed the same procedure to determinewhether people prefer declining sequences inthe past. Participants were told to imagine that,6 years ago, they had won a $150,000 lottery, to bepaid in yearly increments over the following6 years (thus leading up to the present). Theythen ranked preferences for various paymentsequences—some that improved from 6 years agoto last year, some that declined, and one thatremained constant. If participants prefer se-quences that increase from the distant to themore recent past—but nonetheless prefer the LDoption in past explicit-zero discounting—animproving-sequence account can be ruled outas the explanatory mechanism for the hidden-zero effect.

METHOD

Participants

Participants were 123 introductory psychol-ogy students (from Stanford University) and

community sample participants (from the SanFrancisco Bay Area). Thirty-two participantshad to be dropped because we discovered anexperimenter error in task programming,resulting in useless data for these participants.An additional 11 participants were droppedfrom analyses for providing incomplete data.This left a final sample size of 80 participants(42 females, 38 males) who ranged in age from18 to 52 years (M 5 20.9, SD 5 5.90). Sixparticipants indicated a prior psychiatric diag-nosis, 3 indicated that they were currentlytaking psychiatric medications, and 1 indicat-ed a substance use disorder. As compensation,participants received $5 or course credit.

Materials

We presented participants with a slide on thecomputer screen containing seven bar graphs,adapted from Loewenstein and Sicherman(1991), that summarized yearly payment se-quences over 6 years, leading up to ‘‘last year.’’Three of these sequences declined towards therecent past (with slopes of varying steepness),three improved towards the recent past (again,with varying slopes), and one remained con-stant (flat slope). The graphs varied in yearlyincremental differences between payment se-quences, but each added to a total of $150,000.Each graph’s component values were takenfrom Loewenstein and Sicherman (1991).

Procedure

After providing consent, participants wereseated at the computer and told to workthrough the upcoming instructions and taskat their own pace. They then read thefollowing computerized instruction set:

‘‘Imagine that five years ago, you won a lottery andwere awarded a total of $150,000 to be paid in yearlyincrements over the past five years. This money waspaid to you in a sequence of yearly increments thatvaried according to which of the following optionsyou selected.‘‘On the following slide, you will see a series ofgraphs, labeled A-G, which depict the paymentincrements you were provided at the time you won.‘‘Please rank the following payment sequencesaccording to how satisfied each of them would makeyou today, with the first being the sequence thatmakes you the most satisfied today, and the last beingthe sequence that makes you the least satisfied today.‘‘PLEASE RANK EVERY GRAPH. In other words,you should make an entry for ALL 7 of the followinggraphs.’’


Once they had finished this task, they wenton to complete Experiment 4.

RESULTS

To assess participant preferences, we as-signed a within-participant rank score, rangingfrom 1 (least preferred) to 7 (most preferred),to each of their selected graphs. Using thismetric, we were able to summarize how highlyparticipants, on average, tended to rank eachof the improving and declining past sequences(see Figure 5A). We report results fromnonparametric tests because of the nonnorm-ality of these rank distributions.

We examined whether mean rankings givento improving and declining sequences variedby gender, age, and psychiatric diagnosis. Wefound that females were slightly more likelythan males to rank declining sequences astheir least preferred, Kruskal-Wallis rank sumtest, x2 (1, N 5 80) 5 5.41, p 5 .02. As no priorresearch of which we are aware has reportedgender effects on sequence preferences, wehad no a priori reason to expect a difference,and so we do not discuss this result further. Noother demographic variable influenced thesequence preferences (Kruskal-Wallis ranksum test; all ps . .05).

Results revealed a pattern of overwhelmingrank preference for improving sequences. Themost sharply improving sequence was rankedhigher than the most sharply declining se-quence (Wilcoxon-Mann-Whitney test; U 52271, p , .001) and the third most sharplydeclining sequence, U 5 2628, p , .05, and itshowed a trend for a higher ranking than thesecond most sharply declining sequence, U 52712.5, p , .10. Furthermore, the second mostsharply improving sequence was ranked morehighly than all of the declining sequences, allUs , 2450, all ps , .01, as was the third mostsharply improving sequence, all Us , 2298, allps , .003. Finally, when the mean ranks of allthree improving sequence graphs and all threedeclining sequence graphs were averaged intosingle vectors (see Figure 5B), the improvingsequences (M 5 4.38, SD 5 1.73) were rankedmore highly than the declining sequences (M5 3.4, SD 5 1.79), U 5 2297, p , .001.

Interestingly, the uniform sequence re-ceived a high average rank (M 5 4.69, SD 51.48). Nevertheless, while it was ranked morehighly than all of the declining sequences, allUs , 1951, all ps , .00002, it was not ranked

differently than the improving sequencegraphs, all Us . 2984, all ps . .4. Therefore,while individuals may not distinguish be-tween improving and evenly distributedinstallments of past payments, they over-whelmingly prefer both to payment sequenc-es that decline. In terms of the improvingsequence model (Equation 2), this is clearevidence that c should not be negative forpast rewards.

DISCUSSION

These results provide evidence that individ-uals prefer past sequences that improve (or,at the least, that do not change) as timeprogresses from the distant past towards thepresent. This rules out the hypothesis thatdeclining sequences might be preferred in thepast. Instead, individuals prefer to experiencelarger rewards in the more immediate past,despite the fact that this represents aneconomically irrational preference (it decreas-es the time over which large financial gainscould have been invested and compounded).Rather, the still-tangible positive emotionassociated with having recently received alarger reward (a ‘‘warm glow’’ of rewardenjoyment) may drive this pattern of choices(see Ekman & Lundberg, 1971; Elster &Loewenstein, 1992). Notably, the high prefer-ence assigned to the uniform sequence isconsistent with prior research (Frederick &Loewenstein, 2008), in which allocation fram-ings were shown to increase preferences forequal distributions over time. Since ourexperiment asked participants to allocatepayments from a $150,000 windfall over 6 years,we believe this framing likely accounts for thefinding. Nevertheless, the crucial fact remains:Decreasing sequences were not endorsed byour participants.

Altogether, these data demonstrate that alinear, unidirectional conception of time—asis assumed in Equation 2—is justified and that,consequently, an improving-sequence basedexplanation does not account for the hidden-zero effect. Rather, we suggest that explicit-zero framings operate by biasing participants’attention towards the past and the future. Todirectly examine the feasibility of this atten-tion-based model, we manipulated temporalattention in Experiment 4 by priming pastevents and subsequently assessing past dis-counting.


EXPERIMENT 4: ALTERING PAST DIS-COUNTING WITH TEMPORAL PRIMING

Recent experiments by Zauberman andcolleagues (2009) have demonstrated thatpriming of various durations of time decreaseshyperbolic discounting. Participants who esti-mated the amount of time it would take tocomplete each of a set of activities (such aslearning a new language or studying for adifficult exam) requested less money to delaythe use of a hypothetical gift certificate thanparticipants who guessed the calorie contentof various food items. This demonstrates thatcertain attentional manipulations can alterdiscount rates, a finding that converges withthe present temporal attention hypothesis.

Importantly, Zauberman and colleagues’(2009) manipulation focused on increasingattention to durations, hence altering howtheir participants construed the passage oftime. In this experiment, we tested a primingmanipulation more akin to the hidden-zeroeffect: namely, drawing attention away fromthe present to some other specific point intime. We hypothesized that drawing attentionto specific events in one’s past (and henceincreasing v9), would reduce preference forproximate past rewards. Because of the inher-ent uncertainty associated with predicting theoccurrence of future life events, we focused

solely on past outcomes (and past discount-ing), as uncertainty is known to affect dis-counting (e.g. Rachlin, Raineri, & Cross,1991).

METHOD

Participants

We collected data from 123 participants (thecohort for Experiment 3). We dropped 12from the following analyses (1 for statedfailure to understand the priming manipula-tion, and 11 for providing incomplete data).This left a final sample of 111 (62 females, 49males), who ranged in age from 18 to 52 years(M 5 20.4, SD 5 5.09). Of these 111participants, 8 reported a prior psychiatricdiagnosis, 4 reported currently taking psychi-atric medication, and 1 reported a priorsubstance abuse disorder. Participants werecompensated with either course credit or a $5cash payment.

Materials

For the control condition, we borrowed thecalorie estimation procedure directly fromZauberman and colleagues (2009). Partici-pants were asked to estimate the caloriecontent for each of seven food items (oneslice of a large one-topping pizza, a bowl ofsalad, a quarter-pound cheeseburger, one

Fig. 5. (A) Mean rank score for each graph in Experiment 3 (1 5 lowest ranked; 7 5 highest ranked). (B) Meanaggregate rank score for all the improving and declining sequences in Experiment 3. Values derived from averaging theranks of all graphs with increasing and decreasing slopes, respectively. (* p , .01, ** p , .001).


serving of chicken wings, a six-inch turkeysandwich with cheese, six pieces of Californiaroll sushi, and one beef burrito). In the targetcondition, we presented participants with aseries of seven common life events and askedthem to indicate how long ago they hadexperienced them. These events were all pre-sumed to have occurred at some memorablepoint in their past, but one whose exact time ofoccurrence would need to be effortfully recalled(‘‘Last time you went to the zoo,’’ ‘‘Your firstcavity,’’ ‘‘Last time you did your laundry,’’ ‘‘Lasttime you were sick and vomited,’’ ‘‘Openingyour first bank account,’’ ‘‘Last time you got ahaircut,’’ ‘‘First learning to ride a bike’’). Weopted for a distribution of events that, presum-ably, would have occurred at both relativelydistant and relatively recent times in the past.

The subsequent discounting reward pairswere presented with E-Prime, with the SP pastoption and the LD past option always appear-ing on the left and right sides of the screen,respectively. We constructed five past discount-ing pairs (all with hidden zeros) that spanneda wide range of discount rates. SP options, allavailable ‘‘one hour ago,’’ were $5.10 to $5.90.LD options (from $5.90 to $9.30) wereavailable after delays ranging from 4 to 94 daysago. The full set is provided in Appendix 3.

Procedure

After providing consent, participants wereled to the computer and were assigned, inalternating order, to one of two conditions. Inthe control condition, they were asked toestimate the calorie content for each of sevenfood items. They read the following comput-erized instructions:

‘‘In this task, we ask you to consider the typical fooditems you would consume and estimate how manycalories each of the food items would contain.‘‘Please think about each of the following food itemsand provide your most accurate estimate of the totalnumber of calories each would contain.‘‘In your answers, please type in ‘calories’ after eachof your estimates.’’

In the target (temporal priming) condition(the time estimation condition), participantswere asked to estimate, as accurately as theycould remember, how long ago they experi-enced or engaged in each of seven commonevents (see above). They were presented withthe following computerized instructions:

‘‘In this task, we ask you to think about severalevents and estimate, to the best you can remember,how long ago they happened to you.‘‘Please think about each of the following events andprovide your best estimate of how long ago each ofthese events happened to you. Try your hardest toremember each event, and give your best estimate ofhow long ago it occurred.‘‘ROUND YOUR ANSWERS to the nearest unit oftime from the following list: hours, days, weeks,months, or years. For example, one of your answersmight be ‘5 years.’’’

All target and control condition stimuliappeared one at a time on the screen, andtheir order of appearance was randomizedacross participants.

After making entries for the seven estima-tion prompts, participants then moved on tothe critical phase of the experiment. Theywere presented with the following computer-ized instructions:

‘‘The following questions are about money preferences.You will be presented with two sums of money, one onthe left side of the screen, and one on the right side.‘‘For each pair of sums, please select the option youprefer more.‘‘Press the ‘F’ key if you prefer the option on the left-hand side of the screen.‘‘Press the ‘J’ key if you prefer the option on the right-hand side of the screen.’’

All participants made five past discountingselections (all with hidden zeros), the presen-tation order of which was randomized acrossparticipants. Finally, they provided demo-graphic information before being thanked,compensated, and dismissed.

RESULTS

No demographic variable differed by exper-imental condition, all x2 (1, N 5 111) , 3.30,all ps . .07, and so we do not consider thesevariables in our analyses.

Figure 6 summarizes our results. We foundthat the mean number of SP choices in thetime estimation (target) condition (n 5 56)was 2.18 (SD 5 1.72) and was significantlyfewer than the number of SP choices made inthe calorie estimation (control) condition (n5 55), which was 2.85 (SD 5 1.60), t(109) 52.14, p , .04.

DISCUSSION

The results indicate that individuals are lessinclined to select temporally proximate past


rewards when their attention is drawn awayfrom the present through a priming manipu-lation. In this experiment, all past rewardswere necessarily hypothetical so that nobehavioral suppression of or cognitive distrac-tion from tempting impulses was involved asparticipants made their discounting choices.We posit that the results were a direct result ofa broadening of temporal attention followingrecollection of temporally distant past events;the data thus further support the feasibility ofthe temporal attention hypothesis.

GENERAL DISCUSSION

These studies examined two candidatehypotheses for the mechanism by which asimple manipulation, the hidden-zero effect,reduces temporal discounting. The extensionof the hidden-zero effect to past discounting,in which participants preferred reward se-quences that decreased through time, contra-dicts an account of the phenomenon thatrelies on preferences for improving sequencesof rewards. Importantly, Experiment 3 explic-itly rules out mirror-symmetric sequence pref-erences as an alternative explanation of theeffect. Instead, we posit that an increase intemporal attention to distant past and futureevents is sufficient to reduce discounting. Thatis, when attention is drawn away from‘‘now’’—through either the hidden-zero effect(Experiments 1 and 2) or through priming(Experiment 4)—behavior becomes less fo-cused on immediate gratification. Model fitsconfirm that the hidden-zero effect, which iscorrelated across past and future, is betterexplained by an increased reliance on far-sighted attentional processes through whichrewards are valuated (Equation 3) than bya preference for time-dependent sequences(Equation 2).

These results converge with recent evidencesuggesting that focus on the temporal domaincan alter delay discounting (Ebert & Prelec,2007; Zauberman et al., 2009) and represent anovel approach to the study of intertemporalchoice. By demonstrating the hidden-zeroeffect for discounting of past outcomes, thepresent results provide further evidence thattemporally distant reward values can be en-hanced with no concurrent need to ‘‘control’’a latent desire for the proximate alternative.After all, no behavioral suppression of or

cognitive distraction from tempting impulsescan be realistically implicated in explainingchoices involving past rewards. A more likelyexplanation is that similar cognitive processesconsider both the past and the future (Bickelet al., 2008), often demonstrate bias forimmediate over temporally distant outcomes,and are sensitive to attentional manipulationsthat reduce this bias. Below, we highlight anumber of future directions and clinicalimplications this hypothesis engenders. Wefocus on the issue of substance abuse, as it isamong the most costly public health problemsin the United States (Office of National DrugControl Policy, 2004).

First and foremost, it remains to be seenwhether temporal attention reallocation canreduce present bias among clinical popula-tions who repeatedly struggle to avoid imme-diate rewards. Cigarette smokers represent aparticularly challenging case. Although up to80% of smokers report some desire to quit,there is a 78% relapse rate within the first6 months of cessation (Sigmon, Lamb, &Dallery, 2008), underscoring the fact that

Fig. 6. Reduction in the mean number of past smaller,proximate (SP) choices after priming of past events. Errorbars 5 standard error of the mean.


dynamic inconsistency in reward preferenceis a large contributor to smoking relapse(Herrnstein & Prelec, 1992). It will be impor-tant to investigate whether explicit-zero framescan reduce preference for immediate rewardsin both the future and the past among nicotine(and other substance) addicts. High rates ofdelay discounting have already been identifiedas a risk factor for poor smoking abstinenceoutcome (Dallery & Raiff, 2007; MacKillop &Kahler, 2009; Yoon et al., 2007); an intriguingquestion is whether the hidden-zero effectpredicts cessation outcome at treatment intake,or whether the magnitude of the effect changesas a function of abstinence duration. If so,public health campaigns might successfullyemploy framing manipulations to heightenfocus on the delayed financial consequencesassociated with purchasing cigarettes. As amajority of smokers are aware of the healthrisks associated with smoking (Weinstein, Slo-vic, Waters, & Gibson, 2004) but continue tosmoke nonetheless, such an approach may bemore salient and impactful in the decision toquit (or even to initiate) smoking.

Additionally, the present results align con-ceptually with recent interventions developedto reduce discount rates. Specifically, increas-ing focus on the future and past has success-fully been shown to decrease present biasamong substance abusers. Smokers in a recentlaboratory study, for example, were able toreduce cravings for cigarettes by focusingon the long-term future effects of smoking(Kober, Kross, Mischel, Hart, & Ochsner,2010). Furthermore, extensive working mem-ory training results in a reduction of discountrates among stimulant users seeking treatment(Bickel, Yi, Landes, Hill, & Baxter, 2010). Asworking memory recruits the same frontal-parietal network implicated in intertemporalprojection (Buckner & Carroll, 2007), thistraining intervention may reduce discountingin part by targeting the very networks requiredfor far-sighted episodic reflection. Finally,addiction may be considered a disorder ofreward-related learning and memory (Hyman,2007) that results in hyporesponsivity tonatural reinforcers and hyperresponsivity todrug stimuli (Volkow, Fowler, Wang, Swanson,& Telang, 2007). As suggested by our resultsfrom Experiment 4, then, improving theability to recall positive past experiences thatdid not involve drug use may help reduce past

discounting rates—and may also have benefi-cial effects on future reward valuation. Ele-ments of this latter approach are currentlyemployed in traditional cognitive-behavioraltherapy for substance abuse (Beck, Wright,Newman, & Liese, 1993), but remain to betested within a temporal attention framework.

Nevertheless, we caution against the unwa-vering conclusion that temporal attention tothe past and future is identical, such thatreallocating attention to the past automaticallyresults in quantitatively equivalent reallocationof attention to the future (and vice-versa).Recall that, in our formulation of the temporalattention hypothesis (Equation 3), the eparameter quantified the attentional shiftresulting from explicit-zero framing. Althoughestimates of e in the past and future were notsignificantly different, they failed to correlateat a significant level. This may be a statisticalartifact (possibly resulting from a trend for alarger mean hidden-zero effect in the pastthan in the future), but it may also reflectindividual differences in the ease with whichone’s attention can be drawn to the past orfuture. Indeed, research on time perspectiveindicates that there are multiple temporalorientations and that orienting to the futureand the past loads on separate factors (Zim-bardo & Boyd, 1999). If one is especially apt toconsider the future but not as inclined toconsider the past, it may be easier to focusattention to the former. Accordingly, theextent to which trait individual differencesin time perspective mediate the hidden-zeroeffect in past and future is an important futureresearch question.

Finally, we posit that temporal attention maybe the mechanism by which some existingsubstance abuse interventions gain effect. Inparticular, contingency management (CM) hasa conceptually similar structure to the explicit-zero framing that we have investigated (seeHiggins, Silverman, & Heil, 2008). Contingencymanagement provides incremental reinforce-ment (in the form of vouchers or other tangiblerewards) that is contingent upon verifiableabstinence from the target substance; as such,it pits a choice between ‘‘using now and earningno reward later’’ and ‘‘not using now andearning reward later.’’ Although the techniquewas initially inspired by evidence that drinkingand drug use could be reduced with traditionaloperant techniques (Higgins & Silverman,


2008), it is conceivable that CM achieves itshigh success rate by changing temporal atten-tion in people with a pathologically hyperactive‘‘impulsive’’ system (Bickel et al., 2007). Inaccordance with this hypothesis, a brief (2 week)contingency management intervention wasshown to increase preference for delayedhypothetical money over smaller values ofimmediately available cigarettes (Yoon, Hig-gins, Bradstreet, Badger, & Thomas, 2009).Reduced discounting of hypothetical moneyhas also been shown in cigarette smokersundergoing CM treatment (Yi et al., 2008). Atpresent, research into the psychological mech-anisms by which CM interventions promoteabstinence is lacking. Based on the results inExperiments 1, 2, and 4, we hypothesize thatthe promise of tangible rewards in the futurepartially ameliorates the temporal myopia ofdrug addiction.

Overall, we have developed a novel hypoth-esis by which delay discounting may be alteredthrough changes in attention. Although thishypothesis is suggested by our studies, it hasnot been conclusively validated. We haveassayed temporal attention only indirectly,through a temporal priming manipulation(Experiment 4). Importantly, we have notattempted to actually measure a correlate oftemporal attention (such as implicit behavior-al measures or physiological measures such aseye-tracking). This is certainly a crucial nextstep in advancing this theory, but the methodswill need to be developed anew and validated.As such, this remains beyond the scope of thecurrent report.

Temporal attention is an under-investigat-ed mode by which delay discounting may bemanipulated. In four experiments, we havedemonstrated that temporal attention altersbehavior in a phenomenon that had previ-ously been explained by a different mecha-nism (i.e., improving sequences). The tem-poral attention model additionally offers anew interpretation of some of the literatureon temporal discounting and the clinicaldisorders with which it is associated. Thismodel should be submitted to future inves-tigation to determine its usefulness in de-scribing other aspects of intertemporal re-ward valuation. Doing so will enhance thegrowing arsenal of approaches aimed athelping us refrain from the tyranny of theimmediate.

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Received: March 9, 2011Final Acceptance: July 5, 2011

APPENDIX 1

Here we derive Equation 2 from the modelof preferences for sequences proposed byLoewenstein and Prelec (1993; LP). We beginwith Equation 7 from LP, which separatestemporal discounting (in time-dependentweights wt) from sequence preference. The totalvalue of a sequence of rewards, X, is given by

V Xð Þ~Xn

t~1

wtutzXn{1

t~1

st dtj j LP, Equation 7

In deriving Equation 2, we substitute thehyperbolic equation (Equation 1) for wt:

wt~1

1zktt:

LP define dt as

dt~t

n

Xn

i~1

ui{Xt

i~1

ui LP, Equation 2

With sequences of length 2 (n52), as in ourexperiments,

sXn{1

t~1

dtj j~sd1~s

2u1zu2ð Þ{u1~

s

2u2{u1ð Þ:

We arrive at Equation 2 by letting c 5 s/2 andassuming a linear utility function.

APPENDIX 2

Past discounting options (employed in Exper-iments 1 and 2):

Explicit-zero condition:

1. A. $5.50 one hour ago and $0 61 days agoB. $0 one hour ago and $7.50 61 days ago















Hidden-zero condition:

1. A. $5.50 one hour agoB. $7.50 61 days ago
















Future discounting options (employed inExperiment 2):Explicit-zero condition:

1. A. $5.50 today and $0 in 61 daysB. $0 today and $7.50 in 61 days















Hidden-zero condition:

1. A. $5.50 todayB. $7.50 in 61 days

2. A. $6.90 todayB. $8.70 in 102 days

3. A. $3.30 todayB. $8.00 in 14 days

4. A. $5.40 todayB. $8.00 in 30 days

5. A. $3.10 todayB. $8.50 in 7 days

6. A. $6.70 todayB. $7.50 in 119 days

7. A. $6.00 todayB. $8.50 in 46 days

8. A. $4.30 todayB. $7.50 in 22 days

9. A. $5.00 todayB. $7.20 in 34 days

10. A. $4.90 todayB. $5.80 in 42 days

11. A. $4.50 todayB. $7.70 in 28 days

12. A. $2.00 todayB. $8.50 in 18 days

13. A. $8.00 todayB. $8.40 in 140 days

14. A. $4.70 todayB. $5.40 in 92 days

15. A. $4.10 todayB. $7.50 in 20 days

APPENDIX 3

Past discounting set used in Experiment 4:







A Mechanism for Reducing Delay Discounting by Altering Temporal Attention

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