Anticipation and the Valuation of Delayed Consumption

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Anticipation and the Valuation of Delayed Consumption

Author(s): George LoewensteinSource: The Economic Journal, Vol. 97, No. 387 (Sep., 1987), pp. 666-684Published by: Blackwell Publishing for the Royal Economic SocietyStable URL: http://www.jstor.org/stable/2232929

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TheEconomic ournal,97 (September987), 666-684Printed n GreatBritain

ANTICIPATION AND THE VALUATIONOF DELAYED CONSUMPTION*GeorgeLoewenstein

'When calculating the rate at whic-ha futurebenefit isdiscounted, we mustbe careful to make allowance for the pleasuresof expectation.' (Marshall,i89i, p. I78)

Of the various assumptions underlying analyses of intertemporal choice,perhaps the assumption of positive discounting is the most widespread andnoncontroversial. Empirical work which has sought to estimate individualdiscount rates (Hausman, I979; Landsberger, I971) has provided no groundsfor questioning this assumption. In fact, a recent study which explicitlyquestioned the general applicability of positive discountingconcluded that 'thecase for positive time preferenceis absolutely compelling' (Olson and Bailey,I 98 I).Yet it requires ittle effort to think of examples of behaviourin which negativediscounting is apparent. The pleasurable deferralof a vacation, the speedingup of a dental appointment, the prolonged storage of a bottle of expensivechampagne are all instances of this phenomenon. Indeed, if R. H. Strotz hadbegun his work thirty years ago with behaviour such as this in mind, he mighthave developed a critique of Discounted Utility theory (DU) equally ascompelling as his work on myopia but pointing towards researchvery differentfrom what has actually ensuedfromhis work. Instead, in introducing the broadconcept of 'time inconsistency', Strotz devoted his attention exclusively to asubdomain of instances in which the economic actor behaves more myopicallyin the present than he previouslyhad planned. While the focus on impulsivityhas offered important theoretical insights it may have impeded recognition ofthe existence and interest of other phenomena, such as low or negativediscounting. A more inclusive theory of intertemporalchoice should be able toaccount for both extremes of behaviour - myopic and far-sighted. Such amodel is proposed here.The model modifies DU by introducing an insight once recognised byeconomists: that anticipation of the future has an impact on immediatewell-being.1This observation can be traced to Bentham (I789), who includedamong the ingredients of utility, pleasures and pains that derive from antici-pation. For Bentham, anticipation, like consumption itself, was an importantsource of pleasure and pain.

* I thank Robert Abelson, Richard Levin, Sidney Winter,John Geanakoplos, Howard Kunreuther,ColinCamerer, Mark Machina and Robin Pope for their helpful suggestions. The support of the Institute forAdvanced Study, in Princeton. is gratefullv acknowledged.1 In exploring the relationship between anticipation and time discounting, the current paper is akin tothe recent work of Pope (1983), who examined the role of anticipation in risk aversion, and Wolf (1970),who discussed the implications for intertemporalchoice of utility from memory.[ 666 ]


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[SEPT. i987] VALUATION OF DELAYED CONSUMPTION 667Jevons who was one of the first to apply the Benthamite concept of utilityto understanding intertemporal trade-offs, wrote: 'Three distinct ways arerecognisablein which pleasurableor painful feelings are caused:(I) By the memory of past events;(2) By the sensation of present events;(3) By anticipation of future events.' (I905, p. 3)The latter, which Jevons termed 'anticipal pleasure' and 'anticipal pain'were, if anything, the most important for understanding economic behaviour:'The science of economics is very largely occupied in studying man's effortstoobtain anticipal pleasure by the provision of stocks of goods for future use:almost all the complicated practices of production and exchange resolvethemselvesultimately into manifestationsof these efforts' (I 905, p. 65) In whatfollows, the term 'savouring' refers to positive utility derivedfrom anticipationof future consumption; 'dread' refers to negative utility resulting from con-templation of the future.

I. AN ILLUSTRATIVE STUDYFig. I summarisesresultsfroma surveyin which 30 undergraduateswere askedto specifythe 'most you would pay now' to obtain (avoid) each of five outcomes,immediately, and following five different time delays. The outcomes were: (i)obtain fourdollars; (2) avoid losing four dollars; (3) avoid losing one thousand

2 0 -Shock/

(D 1*5-

4- 1.00

0 ~~~~~~~~Lose100000v: Lose$40 5 Gain $4

Immediately 3 hours 24 hours 3 days 1 year 10 yearsTime delay

Fig. i. Maximum payment to obtain/avoid outcomes at selected times. Proportionof currentvalue (N= 30).

dollars; (4) avoid receivinga (non-lethal) one hundredand ten volt shock,and(5) obtain a kiss from the movie star of your choice. Time delays were: (i)immediately (no delay); (2) in twenty-fourhours; (3) in three days; (4) in oneyear; (5) in ten years. Subjectswere asked to specify the most they would pay


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668 THE ECONOMIC JOURNAL [SEPTEMBERfor every combination of outcome and time delay. They were told to assumethat all outcomes were certain to occur at the designated time. Summarystatistics for the study are presented in Appeindix i.It can be seen that the two non-monetary items, the kiss and the shock, bothexhibit unusualpatternsofdevaluation. DU, with positivediscounting, predictsthat people will prefer to consume desired outcomes as soon as possible. Thisprediction is contradicted by the kiss item. Subjects on average were willingto pay more to experience a kissdelayed by 3 days than an immediate kiss orone delayed by three hours or one day. Data presentedlater in this paper showthat the hump-shaped pattern of devaluation evident in Fig. i is common fordesirable consumption that is fleeting.Likewise, DU asserts that people prefer to delay undesirable outcomeswhenever possible. The shock item contrasts sharply with this prediction.Subjects were, on average, willing to pay slightly more to avoid a shock thatwas delayed for3 hoursto 3 days than to avoid an immediate shock.They werewilling to pay substantiallymore to avoid a shockdelayed by one or ten years.In contrast to the patterns of responses for the kiss and shock, the moneyamounts included in the survey appear to be discounted in the normal fashion.Why haven't patterns of intertemporal preference such as those exhibitedtowards the kiss and shock appeared in earlier empiricalworkon intertemporalchoice? Several answersare possible. In some cases,economists have attemptedto infer intertemporal preferencesfrom behaviour in which such preferenceswere irrelevant to behaviour. Hausman's attempt to estimate individualdiscount rates from air-conditioner purchases provides an example. Air con-ditioners vary in purchase price and energy efficiency, thus creating a choicebetween immediate versus deferred payments. Hausman, by observing theprice/efficiency rating of a purchasedair-conditioner, attempted to impute thediscount rate of the purchaser. The problem with this approach is thatindividual discount rates should be irrelevant to what model is purchased. Ifconsumersare able to save and dissave (or borrow) at establishedinterest rates,they should logically purchase the model of air conditioner that minimises atthe desired level of cooling capacity, the net present value of the time streamof payments.2 Similar considerationsmay have caused subjects in the currentexperiment to discount the money amounts in a conventional manner, incontrast to their behaviour towards the kiss and shock.In other cases, economists have attempted to estimate discount rate fromindividual savingbehaviour,but suchattemptsareeven moreproblematicsinceindividuals have little influence on interestrates. The interest rate at which anindividual savesor borrowsgives no information about his or her own discountrate and hence it is necessaryto infer discount rates from level or rate of saving,a process that is extremely sensitive to the specification of the model used torepresent the savings decision. Furthermore,savings behaviour depends on somany factors other than discount rates (e.g. expected future income streams,

2 His finding of substantial differences n discounting between different income groups suggestseither thatunobservedeconomic factors such as liquidity constraintswere operative, or that consumerswere failing tobehave rationally.


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i987] VALUATION OF DELAYED CONSUMPTION 669projected needs) that it is exceedingly difficult to isolate the effect of timepreferenceon saving.In this paper it is argued that patterns of preferencesuch as those exhibitedtowards the kiss and shock, and other DU anomalies discussedbelow, can beexplained by incorporating Jevons' anticipal pleasure and pain into anotherwise standard model of intertemporal choice. In what follows, such amodel is developed in the simplest possible terms, and its implications arediscussed.

II. THE MODELThe following model exploresthe question of how an individual values a singlefuture act of consumption under conditions of certainty. The model depicts aconsumerat time towho anticipates consuming x at time T > to.Consumptionis assumed to yield a constant streamof utility, U(x), beginning at time T andcontinuing for duration L, after which it drops to zero. Formally:

Utf(X,T,L) = U(x) for T < t < T+L, (I)= o otherwisewhere Ut, indicates utility experienced at time t from consumption.At any time t between toand T (when consumption begins) the individualderives utility from anticipation, UtA.Utility from articipation is assumed tobe proportionalto the integral of utility fromconsumptiondiscountedat a rateof 6. 6 is not the conventional discount rate, but a measure of the degree towhich the individual derives immediate utility from anticipated consumption.Thus savouring or dread at each point t is equal to:

rT+LUtA(x, T,L) = e6e-f(T-t) U(x) dT (2)T

- U(x) e-8(T-t) (I -eaL). (3)This formulation has four desirable properties discussed by Jevons in hisenumerationof the laws ofanticipalpleasureand pain. Referringto anticipationof a planned vacation, Jevons wrote:

The intensity of the anticipation will be greater the longer the holiday;greater also, the more intensely one expects to enjoy it when the timecomes. In other words the amount of pleasure expected is one factordetermining the intensity of anticipal pleasure.Again, the nearerthe datefixed for leaving home approaches, the greater does the intensity ofanticipal pleasure become: at first when the holiday is still many weeksahead, the intensity increases slowly; then, as the time grows closer, itincreases faster and faster, until it culminates on the eve of departure(I905, p- 64).In the current formulation, as Jevons proposed, utility from anticipation,

UtA,s a positive function of L, the duration of consumption, a positivefunction


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670 THE ECONOMIC JOURNAL [SEPTEMBERof U(x), the utility that will be derived from consumption, and a negativefunction of (T-t), the time delay prior to consumption. Also, the secondderivativeof UAwith respectto ( T- t) is positive,yielding the acceleratingpathof utility from anticipation suggested by Jevons.

Fig. 2 depicts one possible time path of utility from anticipation andconsumption.

to T T+LFig. 2. Utility from anticipation and consumption.

The individual is assumed to evaluate a delayed act of consumptionaccording to the integral of discounted utility from anticipation and consump-tionthat ityields.Thus, thepresentvalue Y (measured n dollars)ofadelayedact ofconsumption is defined by:CT C T+LU( Y) = J X U(x) e-8(T-t) (i -e-8L) e-r(t-to) dt+ J U(x) e-r(t-to) dt, (4)

utility from utility fromanticipation consumptionwhere r is the conventional discount rate used to discount future utility fromall sources and U(Y) is a 'ratio scale' utility function3with positive first andnegative second derivative. Throughout the following, r is assumed to bepositive.Setting to= o for simplicity, and integrating:

U(Y) = U(X)[8 (e-rTe-T) ( -e r e (i -rL (5)&and ocdefine to the relationship between UA and UC.6 is a measureof anindividual's preoccupation with the future. Someone with a low a savours ordreadseven those outcomes that will occur in the distant future.a is a measureof the 'imaginability' or 'vividness' of a particularoutcome. Factorsthat raisea or lower a increase utility from savouring or dread. (A later section discussesattempts on the partof marketersand policy makersto influence cz.)Since mostpeople take account of future outcomes (e.g. save for their retirement) evenwhen they do not immediately savour or dread those outcomes, it is assumed

that &> r. III. IMPLICATIONS OF THE MODELThe model, as it stands, suggests the conditions under which people will preferto delay desired consumptionorget undesirableconsumptionoverwith quickly.These two cases are explored in turn.

3I.e. invariant with respect to multiplicative transformations.


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I987] VALUATION OF DELAYED CONSUMPTION 67IDelayingof DesiredConsumptionDesired consumption will be delayed when (8Y/IT) > o i.e. when the netpresent value of consumption, taking account of both savouring and consump-tion itself, increases as a function of time delay. Since U(Y) is monotonicallyincreasing, this condition is equivalent to 8U(Y)/8 T> o.Differentiating (5) with respect to T:

er(y = U(X[(_) (4e-11-re-ril)(i -e-1L-1-e-rT (i- e-rL) (6)The first term in the brackets is the marginal benefit from savouring,that would be gained from delaying. The second term is the marginal cost ofdelay, in terms of increased discounting of consumption.

Consumptionwill be deferred when 8U(Y)/DT is positive for T = o. SettingT = o:au(Y) = U(x) a (I-e-L) - U(x) (I - e-rL). (7)AT T=o0

A necessary and sufficient condition for delaying desired consumption is,therefore,t (I-e-L) > i-e-rL. (8)As would be expected, delaying is more likely when a is large and a is small.Fig. 3 illustrates the relationship between Y, the net present value ofconsumption and T, the time at which consumption of x begins, for the casewhen (8Y/I T) is initially positive.

co

zto Tm T: time consumption begins

Fig. 3. Value at time toof an outcome to be consumed at time T.

By reading off the net present value of consumption at any point T on Fig.3, and subtracting it from one, it is possible to derive a crude measure of thevalue of consumption of x at time T relative to the value of immediateconsumption of x. Note that such 'devaluing' (negative or positive) ofconsumption as a function of delay must be distinguishedfrom the individual'sdiscounting of future utility,which is based only on r(.). To avoid confusionbetween theseconceptsa distinctionishenceforthdrawn between 'discounting',which refers to a preferencefor early over later utility,and 'devaluing', whichrefers to a decrease in the outcome's valueat time to as a function of delay.'Devaluing' is also synonymous with the rate of time discount which would


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672 THE ECONOMIC JOURNAL [SEPTEMBERbe estimated by an observer who did not take account of utility fromanticipation. In Fig. 3, it can be seen, devaluing is initially negative and onlyeventually becomespositive even though timepreference s always positive - i.e.r > o.

Point T. in Fig. 3 has special significance. Tm s, for desirableoutcomes, theindividual's most preferred time of consumption. Tmwill be greater than toif(8Y/I T) is positive for T= o (condition 8). When condition 8 is met it willalso be the case that (82Y/I T2) < o, ensuringthat the point T. is a maximum(see Appendix 2). Under the standard approach (in the absence of planningor scarcity effects), T. is always equal to to. T. > tothus constitutes a sharpdistinction between the predictionsof the currentmodel and the standard DUapproach.Conditions onduciveoDelayingof DesiredConsumptionBy totally differentiating (6) (see Appendix 3), it is possible to derive proposit-ions regarding the effect on Tmof changes in the different parametersof themodel.Increasing the duration of consumption, L, raises the marginal cost ofdeferring at Tmmore than it increases the marginal benefit of savouring.Therefore, increasing L discouragesdelaying behaviour (8Tm/IL < o). Con-versely, delayings more ikely whenconsumptionsfleeting.Intuitively this seemsplausible. Those forms of consumption that are commonly delayed typicallyprovide brief but intense pleasure. In such cases anticipation (and sometimesmemory) serves to extend the otherwise fleeting benefit provided byconsumption.Raising a, as would be expected, also encourages delaying behaviour. a, fordesirable outcomes, can be viewed as a measure of the 'savourability' ofconsumption. Outcomes that can be readily imagined and that are pleasurableto contemplate are therefore more likely to be delayed. The effect of changes ina on Tm s ambiguous.The 'kiss from the movie star of your choice' in the study was chosen for itsfleeting quality and high degree of 'savourability', characteristics which arepredicted to promotedelay. It was also chosen to rule out, as much as possible,alternative explanations for delaying behaviour. Two such explanations areworthy of note. The first, the 'planning effect', providesan incentive fordelaywhen, by delaying a desired outcome, preparations can be made that willenhance utility fromconsumption. This is certainly true of food consumption,in which case fasting (within limits) enhances pleasurefromsubsequenteating.In the case of the kissit also seemsreasonable to assume that some preparations(suchas gargling, or moving to a dimly lit room) could intensifythe experience.But it is difficult to see how a delay of threedays, which was generallypreferredto a single-day delay, could add much to such preparations.The second alternative explanation for delaying is the 'scarcity effect'. Thebasis of this argument is that some items are scarcer in the future (e.g.raspberries n winter) than they are in the present and thus should be morehighly valued. The kiss froma movie star of your choice, which is a scarceitem


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I987] VALUATION OF DELAYED CONSUMPTION 673at any time and certainly as scarce in three days as at the present moment, waschosen to avoid this alternative explanation.Accelerating ndesirable onsumptionThe shape of Uto(T) for an undesirable outcome, which is a negative reflectionof its shape fordesirableoutcomes, is shown in Fig. 4. In the case of undesirableoutcomes a different point, Ti,has behavioural significance. Tiis the point atwhich an individual is indifferent between immediate and deferredconsump-tion. If allowed to defer a negative outcome beyond Ti, the individual will doso. If constrained to consume x prior to 7i, however, his preferenceswill bereversed, and he will prefer to get x over with immediately. A common exampleof such behaviour is associated with medical or dental treatment. One puts offvisiting the doctor or dentist as long as possible, but once a maximum delayis imposed - e.g., when one receivesa card in the mail urging a visit - typicallyone asks for the first available appointment. Under the standard approach Tialways equals t0.

to T, T:timeconsumption egins0 I;O.

E 1- ? --1___.z

Fig. 4. Value at time toof consumption at time T.Equation (g) defines Ti.

( -erL) - U(X) ) (e-rT (I-e-L)+ U(x)- erTi -e-rL) (9)

The left-hand side of (g) represents the (negative) utility that would beexperienced if x were consumed beginning immediately. The right-hand sideexpressesdiscounted utility (fromdread and consumption) when consumptionis delayed until T7> to.When these expressionsare equal, the individual at tois indifferent between consuming immediately or at Ti. If constrained toconsume at any point prior to 7i, he would prefer to consume immediately.Again we are interestedin the specificconditions that encourage individualsto get unpleasant outcomes over with quickly - i.e. make T > to. Theseconditions turn out to be analogous to those for Tm seeAppendix 4). The morefleeting an undesirableoutcome - i.e. the shorterL - the greateris the tendencyto get consumption over with quickly. People should therefore be especiallylikely to get fleeting outcomes over with quickly and defer those for whichconsumption is prolonged. This has the sensible implication that people willalways defer outcomes whose effects are prolonged or permanent, e.g. loss of


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674 THE ECONOMIC JOURNAL [SEPTEMBERa leg. It is also the case that 8 7i/8a > o; people are likely to get those outcomesover with quickly that can be vividly imagined beforehand.Thus we should expect that the tendency to get unpleasant outcomes overwith quicklywill be greatestforoutcomes that are fleeting and vivid. The shockitem in the study was chosen to have thesecharacteristics.Lest the survey results,which involve hypothetical responses, be questioned, it should be noted thatseveral other studies involving real shocksproduced similar results (Carlsmith,I962; Barnes and Barnes, I964). In fact even rats, in one experiment, whenfaced with a choice between an immediate or moderately delayed shock, tendedto choose the immediate shock (Knapp et al. I959). Furthermore,when rats areexposed to delayed shocks they typically exhibit physiological signsof fearsuchas elevated heartbeat and blood pressurewhile they wait, suggesting that fearmay be a motivating factor in the choice of the immediate shock.

A problem with the use of the shock item is that it is difficult to generalisethe findings to economic behaviour in naturalistic settings. This particularproblem is avoided in subsequent research n which subjectswere askedamongother questions: 'What is the least amount of money you would accept forcleaning i OOhamstercages at the PsychologyDepartment'sanimal laboratory.You will be paid the money immediately. You should be willing to do the jobfor the amount you specify but not if you were offeredonly one dollar less. Thejob is unpleasantbut takes only 3 hours. How much would you need to be paidto clean the cages: (i) once during the next 7 days; (2) once during the weekbeginning two months fromtoday; (3) once during the weekbeginningone yearfrom now?'The mean reservationwage for cage cleaning in the following week was $30(standard error 3 i). For cleaning the cage in a year respondentsrequired anaverage of $37 in immediate payment (standard error 3-8). In fact, of 37respondentsonly 2 gave a smallerresponse to question (3) than to question (i)!PositiveDevaluationWhen condition (8) is not met - i.e. for consumption that is lasting, or if a issmall - we should not expect to observenegative devaluing. Nevertheless, utilityfrom anticipation will still affect the devaluation of consumption. Fig. 5illustrates the effect of variations in L on devaluation of future consumption.Decreasing L will attenuate devaluing, flatten the slope 8U, /8 T and thus8Y/IT (see Appendix 5, which demonstrates that 82Y/ITOL < o). As Lincreases, therefore, Y(T) will lose its hump and will begin to take on the

> 1- G X~~~Fleetinga) c~~~~~onsumptione) Prolongedconsumption

T: time of consumptionFig. 5.


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I987] VALUATION OF DELAYED CONSUMPTION 675reversed'S' shape depicted in Fig. 5. Savouring, even when it does not causedevaluing to be negative, attenuates devaluing for small delays, bridging thegap between sporadic or short-lived consumption and pleasure of ownership.

IV. ECONOMIC IMPLICATIONSAttemptsto Manipulatea,The concept of 'vividness' or imaginability embodied in the a term played acentral role in historical formulations of intertemporal choice. For example,Bohm-Bawerkcited 'the fragmentary nature of the imaginary picture that weconstruct of the future state of our works' (I889, p. 269) first in his list of causesfor the systematic tendency to undervalue future wants. Marshall noted thata person's willingness... to wait depends on his habit of vividly realising thefuture' (I89I, p. 293). Although modernaccounts of intertemporalchoice havenot included discussionsof vividness, perhaps because vividness is not directlyobservable, its meaning is nevertheless intuitively comprehensible, and thereare numerous examples of attempts to manipulate it.Drivers' education films depict the gruesome consequencesof car accidentsin an effort to make those consequencesmore vivid to young (and presumablymyopic) drivers. But factsand statisticsand even photographsof accidentshaveonly a limited impact. Faced with continuing high accident rates among youngdrivers, several school districts have taken more drastic measures. A deviceintended to demonstrate the violence of even a low-speed collision has beenput into use in several school districts. Students are accelerated down aramp on a wheeled chair which, after gaining a speed of 5 miles per hour, isabruptly halted. It is difficult to understandthis device in purely informationalterms. Rather, the intention is to give immediate emotional significance to anotherwiseabstract outcome. An analogous attempt to counteryouthful myopiathrough manipulation of vividness is depicted in the documentary movie'Scared Straight', in which high-school students thought to be at riskof futuredelinquency toureda maximumsecurity prison,were harassedby inmates, andwere given as vivid an image of prison life as is possiblewithout actually beinglocked up.While the accident simulator and the visit to the prisonwere aimed at youth,such efforts are not limited to teenagers. For example, a recent televisionadvertisementfor a supplementaryretirementplan showed a young couple inthe first frame opting not to participate in the plan, and then showed themphysicallyageing against a backdropof increasing poverty. Each of these effortsat persuasioncan be viewed as attempts to decreaseac o as to raise dread andenhance evaluation of the future consequencesof current actions.Estimationof DiscountRatesThe sensitivity of intertemporal choice behaviour to savouring and dreadsuggests that the standard model may be mis-specified, leading to systematicbias in the estimation of discount rates. Since DU does not ordinarilyincorporate savouring or dread, and since both of these factors attenuate


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676 THE ECONOMIC JOURNAL [SEPTEMBERdevaluation, onventional stimatesof discountratesshouldbe biaseddown-ward, especially n situationswheresavouringor dread significantlyaffectdevaluation.As demonstrated,heseincludesituations n whichfutureout-comesarefleetingor canbe vividly magined.Also,savouring nddreadexerttheir greatest mpact at short and moderatetime delays, so discountratesestimated rom short-term rade-offswill tend to be more biased than ratesestimated rom ong-term rade-offs.The bias n estimation f discount ateswill be especially eriousf savouringand dreadare differentordifferent ategories f consumption.f thiswere thecase, thenthe generalassumptionhat'the discountrate is independent f thecategoryof consumption oodsfor which t is calculated'(Landsberger,97I,p. I35I) would be invalid.Thus, for example,Hausman, n his I979 study,implicitlyassumed hatdiscountrates mputed romair-conditionerurchaseswould alsoapply to other ntertemporalrade-offs.Whathe failedto considerwas thepossibilityhatairconditioners rotherenergy-using pplianceshavespecialcharacteristicshat promote teepdiscounting.Monthlypayments orelectricityarespreadovertimeandmade lesssalientby beingcombinedwithpre-existinglectrical harges, eading o the prediction fhighdevaluing venwhen time discounting s low. In contrast,purchasecost is immediateandlump-sum.This myopia-inducingquality of fuel- or electricity-consumingdurables eems o havebeenrecognised yvariousagenciesofgovernmenthatrequire fficiency atings orappliances, nd estimates f fuelconsumption ndyearlyoperatingcosts,to be affixed o newcars.Savings ehaviourThe concepts of savouringand dread may help to explain the anomalousobservationhat- ratherthandissaving ollowingretirement as is predictedby the permanentincome and life-cycle theories of saving) individualstypicallyincreasetheir rate of savingfollowingretirementand continue toamass ncreasing mountsof wealthuntil they die. A numberof explanationshave been offered or this phenomenon,ncludinguncertain ife expectancyand bequestmotives.4Anotherexplanationofferedby Moore (1978) is thatindividuals eriveutility romwealth tself.The currentmodelbolstersMoore'saccount by providinga reason why wealth may be a source of utility.Accumulations f wealthcanconstitute,n effect,a 'licenceto savour' i.e. toimagineand thus derive mmediatepleasure romtheconsumptionwhichthewealth couldfinance.But the theory also providesa second, perhapseven more plausible,explanationorthe observedailure odissave ollowing etirement.Retirementfor the young is a non-vividevent- perhapspartlybecausethinkingaboutold age is aversiveand tends to be avoided(resultingn a smalla). Youngmiddle-aged ouplesand individuals,possibly or thisreason,often'live likethere's no tomorrow'.As retirementapproaches,however, the prospectofhaving nadequateunds or retirement ecomes ncreasingly ividand causes

4 For a recent summary of this debate see Modigliani (I986).


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I987] VALUATION OF DELAYED CONSUMPTION 677anxiety, anxiety that can be allayed in part by stepping up savings.The onsetof retirement itself, and the sudden loss of wage income, of course, greatlyincreases this anxiety for the future. This anxiety raises the returns, in termsof anxiety reduction, of saving, and counteractsthe savings-discouragingeffectof the loss of income upon retirement.The concept of savouring can also shed light on other anomalous savingsphenomena. In a recent series of interviews with family heads that aimed ata preliminaryunderstandingof saving behaviour, one theme that emergedwasthe ,apparent need of many individuals for highly specific goals to motivatesavings. Such individuals seem incapable of saving for a future retirement inthe abstract; they can, however, save for a retirement condominium or otherconcretegoal that, it is plausible to assume,bringsthem anticipal pleasure.Alsocomprehensible n termsof savouringis the behaviourof misers.In thisextremecase, anticipated consumption exerts so strong a pull that no presentconsumption can compete with it.ReverseTime InconsistencySince the publication of Strotz's well-known I955 article, the phenomenon oftime inconsistency has attracted the attention of social scientists in a numberof disciplines.Time inconsistencyoccurs when an individual makesa long-termplan at time t but systematicallydeparts fromthat plan in later periods.As hasbeen said, subsequent,departures tend to be myopic in character i.e. toallocate greater consumption to the immediate period than was originallyplanned. While not ruling out such forms of time inconsistency, the currentmodel predicts, under certain conditions, a related phenomenon, which couldbe termed 'reverse time inconsistency'.Suppose that an individual at time to, in the light of the characteristicsofa prospective act of consumption, chooses to defer consumption until timeTm> toso as to savour his expectations. Logically, it would seem that whenhe arrivesat T. he has every incentive to deferconsumption once again, sincehe is in the identical situationhe was in earlier.One could imagine thissituationrepeating itself indefinitely. Several factors, however, limit such repeateddelaying and savouring of the same object of consumption.First,concernsabout self-credibilitymay makeplansself-reinforcing.Supposethe individual at TMdecides to delay again, until TM2. The problemis, havingplanned to consume at TMand then failed to do so, he may not be able toconvince himself at TM hat he will follow through on his plan to consume atTM2.Failing to believe that he will consumeat TM2,he will be unable to savourthe prospectof consumption at TM2and he will have no incentive to deferpastTM.Ultimately, therefore,he will consume at TMas he had originallyplanned,without binding himself in any way. Failure to consume as planned mayinterferenot only with the individual's ability to savour the re-deferredobjectbut also with his ability to savour other forms of delayed consumption, thusadding an additional cost to any act of reverse time inconsistency.Second, many decisions concerning future consumption carry with themtheir own enforcement, or at least reinforcementmechanisms- for example,

24 ECS 97


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678 THE ECONOMIC JOURNAL [SEPTEMBERwhen reservationsare made, items are ordered, or plans are made with otherpeople. In addition there are well-known self-control techniques such as thestrategy of making 'side bets' that alter future incentives to encourageconformity with current plans. These have received extensive coverage in theliterature on self-control and time consistency (Strotz, I956; Ainslile, I975;Elster, I979; Schelling, I978).Nevertheless, despite the self-reinforcingcharacter of plans, psychologicalincentives for adherence to plans, and various types of self-controltechniques,people often do exhibit time inconsistency of this reverse form- i.e. repeateddeferral for the purpose of savouring. This pattern is often observed amongchildren at Hallowe'en when some trick-or-treaterscollect then hoard theircandy rather than consuming it. Apparently the pleasure derived fromsavouring future consumption of the candy in some cases outweighs what canbe obtained from immediate consumption. Such behaviour often ultimatelyresultsin the stale candy being thrown out without having been even partiallyconsumed. Similarbehaviourcan be seen among adults towardsbottles of wineand holidays. Often people professto need a vacation desperately,yet they keepputting off actually taking one, preferring nstead to savour their accumulatedvacation days.Violationsf IndependenceLike axiomatic derivations of the Expected Utility Model, derivations of theDiscounted Utility Model (Koopmans, I960; Meyer, I976) have centred onsome type ofindependence axiom. Independence,in thecontextofintertemporalchoice, posits that an individual's preference between two time streams orsequencesofconsumptionshould not be affectedby periods n which the streamsshare identically valued consumption.The following study illustrates a common violation of independence in anintertemporal context. Thirty-seven undergraduateswere given the followingpaired choices. They were asked to ignore scheduling considerations.The first finding of note is that 84 % of the respondentschose option B overoption A in question i. This finding conforms to the prediction made earlierthat people will tend to delay desirable and fleeting consumption for purposesof savouring. More interesting is the fact that 57 % of the respondentschoseoption C over option D in question 2. Note that consumption is equivalent inthe third weekend forA and B and for Cand D. Thus this pattern of responsesQuestion i. Which would you prefer? (circle A or B)

Two weekendsAlternative This weekend Next weekend from nowA Dinner at a fancy Eat at home Eat at homeFrench restaurantB Eat at home Dinner at a fancy Eat at homeFrench restaurant


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1987] VALUATION OF DELAYED CONSUMPTION 679Question 2. Which would you prefer? (circle C or D)

Two weekendsAlternative This weekend Next weekend from nowC Dinner at a fancy Eat at home Fancy lobsterFrench restaurant dinnerD Eat at home Dinner at a fancy Fancy lobsterFrench restaurant dinner

violates the assumptionof independence that has formed the core of axiomaticderivations of DU.These results point to a problem in applying the notion of independence tointertemporal choice. When outcomes are conditional on mutually exclusiveand comprehensive states of nature, as is true in decision-making underuncertainty, it follows that one and only one outcome will occur. In thissituation the independence axiom seems valid, at least as a normative rule. Ifthe state in which pay-offsareequal is revealed, the individual receivesthe samepay-off regardlessof his choice. Thus the common pay-off should not affect hispreference between these alternatives. If any other state occurs, the commonpay-off in the state that did not occur would appear to be irrelevant.In the case of intertemporal choice, however, typically all periodswill occur.Hence if consumption of one outcome affects the usefulness or satisfactionassociated with another there is no reason to expect independence to hold. Thecurrenttheory, generalised to accommodate complex patternsof consumption,5provides a reason why consumption in a later period may affect utility fromconsumption in an earlier period, even when there are no interperiod con-sumption externalities. According to our assumptions, the lobster dinner in week3 provides greater anticipal pleasure in week 2 than in week i. This increasesthe marginal utility of consuming the French dinner in the first week, whenutility is low, even at the cost of forestalling the savouring of the French dinner.When no lobster dinner follows, marginal utility in the first two periods iscomparable, and the anticipal pleasure preceding the French dinner is sufficientto motivate delay. This effect can account for the general preference forspreading discrete acts of consumption over time, even in the absence ofconsumption externalities.

V. DISCUSSIONThe model discussed n thispapermodifiesDU by recognisingthat anticipation,like consumption itself, is a source of utility. That waiting for consumption tooccur can often be pleasurableor painful - indeed, that much of our feeling of

5 The model can be generalised to deal with complex temporal consumption streams or sequences asfollows: 00maxj V(Utc+UtA)(t)dt, (6)where V' > o, V"< o. Uc and UArepresent the sum of utility from consumption and anticipal pleasure fromall sources.

24-2


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68o THE ECONOMIC JOURNAL [SEPTEMBERwell-being and despairarise fromemotionsassociatedwith anticipation - seemsself-evident. The behavioural consequences of these feelings have been thesubject of this paper.When anticipation is a source of utility, the effect of delay on the value ofan objectcan diverge from the predictionsof existing theories.Forconsumptionthat is fleeting and easy to imagine devaluing will often be initially negative.Even if it is not initially negative, it may display a reversed'S' pattern ratherthan the convex shape suggested by DU.The dependenceof discountingon the characteristicsofawaitedconsumptionmeans that discount rates estimated in specific contexts, such as studies ofconsumerdurable purchases(Hausman,,979) or of savingsbehaviour (Lands-berger, I97I), cannot be generalised beyond the domain of behaviour inwhich they were derived. The concepts of anticipal pleasure and pain alsoprovide an explanation for violations of the independence axiom used inaxiomatic derivations of DU. Finally, the model draws attention to thephenomenon of 'reversetime inconsistency' that many people at times exhibit.Universityof ChicagoDate of receiptoffinal typescript:September1986

REFERENCESAinslie, G. (I 975) 'Specious reward:a behaviouraltheory of impulsivenessand impulsecontrol. PsychologicalBulletin,vol. 82, pp. 463-509Barnes,0. and Barnes,L. W. (i964). 'Choice of delay of inevitable shock.' Journalof Abnormal ocialPsychology, ol. 68, pp. 669-72.Bentham,J. (I970). Introductionothe Principles ndMoralsof LegislationI 789). London: Athlone Press.Bohm-Bawerk,E. von (I889). CapitalandInterest.News edition South Holland, Illinois: Libertarian Press,1970.Carlsmith,J. M. (i962). 'Strength of Expectancy: its determinants and effects.' Unpublished doctoraldissertation,Harvard.de Villiers, P. A. and Hernstein, R. J. (I 976). 'Toward a law of responsestrength.' Psychologicalulletin, ol.83, pp. I 131-53-Elster,J. (1979). UlyssesandtheSirens.Cambridge: Cambridge University Press.Hausman, J. (I 979). 'Individual discount rates and the purchase and utilization of energy-usingdurables.'Bell Journalof Economics,ol. IO, pp. 33-54.Jevons, W. S. (1905). Essayson Economics. ondon: Macmillan.Koopmans, T. C. (I960). 'Stationary ordinal utility and impatience.' Econometrica,ol. 28, pp. 207-309.Knapp, R. K., Kause, R. H. and Perkins,C. C. (1959). 'Immediate versus delayed shock in T-mazeperformance.' Journalof Experimentalsychology,ol. 58, pp. 357-62.Landsberger,M. (0975). 'Consumer discount rate and the horizon: new evidence.' Journalof PoliticalEconomy,ol. 79, pp. I346-59.Loewenstein, G. (I985). 'Expectations and intertemporalchoice.' Economics Dissertation,Yale University.Marshall, A. (i89i). Principles f Economics,nd ed. London: Macmillan.Meyer, R. F. (I 976). 'Preferencesover time.' In DecisionswithMultipleObjectives: referencesndValueTradeoffs(R. L. Keeney and H. Raiffa eds.), New York:John Wiley.Modigliani, F. (1986). 'Life cycle, individual thrift,and the wealth of nations.' Americanconomic eview, ol.76 (3), pp. 297-313-Moore, B. J. (I 978). 'Life-cycle saving and bequest behavior.' JournalofPost-Keynesianconomics,ol. i, no.

2.Olson, M. and Bailey, M. (i98i). 'Positive time preference.' Journalof PoliticalEconomy,ol. 89, pp. 1-25.Pareto, V. (I97I). Manualof PoliticalEconomy.New York: A. M. Kelley (translatedfrom French edition of1927).Pope, R. (I983). 'The pre-outcomeperiodand the utility ofgambling.' In Foundationsf UtilityandRisk TheorywithApplicationsed. B. P. Stigum and F. Wenstop), pp. I37-77. Dordrecht: Reidel.


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I987] VALUATION OF DELAYED CONSUMPTION 68IRachlin, H. and Green, L. (I 972). 'Commitment, choice, and self control.' Journal f theExperimentalnalysisof Behavior, ol. 17, pp. 15-22.Schelling, T. C. (I978). Egonomics, or the art of self-management.' AmericanEconomicReview,vol. 68,

pp. 290-4.Strotz, R. H. (I 956). 'Myopia and inconsistency in dynamic utility maximization.' Review f Economictudies,vol. 23, pp. i65-8o.Thaler, R. (I98I). 'Some empirical evidence on dynamic inconsistency.' Economic etters, ol. 8, pp. 20I 7.Wolf, C., Jr (I970). 'The present value of the past.' Journalof PoliticalEconomy,ol. 78, pp. 783-92.APPENDIX I

The following table presents, for each of the five survey outcomes the fraction of theamount that people would pay to obtain or avoid the outcome immediately, that theywould pay to obtain or avoid the outcome after each of the five time delays. Numbersare means across subjects. Standard errors are in parentheses.Fraction f Initial Value

Avoid losing I 20-VoltObtain four Avoid losing one thousand Kiss from electricTime delays dollars four dollars dollars movie star shock3 hours 0o93 0o97 0?97 1 30 I-O

(00-28) (0o023) (o oi6) (o 155) (o0oI5)24 hours o-82 O-9I o096 159 0?99

(0o045) (0o044) (0o021) (0-280) (0o053)3 days o 74 0o75 0?94 1.78 I101

(00-57) (0o072) (0-03 ) (0-487) (O-II)I year 0-46 0?54 O-9I 1-31 1-23

(o0o69) (o-o83) (0?075) (0o295) (0 20)io years 0-2I 0o32 o-68 o-639 I-84(o-o65) (o-o8i) (0-I53) (0-I56) (0o4)

APPENDIX 2This demonstratesthat 02yOT < o at point Tm.

Differentiating (6) a second time with respect to T:aTU= U(x) __ (r2e-rT-82e-T) (i -e-8L) +re-rT( -e-rL) (A )au ax) 6 ~erL] (A 2

at T. 47T= o so 8(8 r) (8e-8T-re-rT) (i -e-L) = e-rT( _e-rL) (A 2)Substituting (A 2) into (A i):

8T2 = U(x)

r)(r2erT82e ) ( -e

+ r (8e-6T-re-rT) (i -e-L) (A 3)

= U(X) a(Q5 ) (I - e-L) (r2e-rT - 82e-6T + r&e-6T - r2e-rT) (A 4)= U(x) a, -e-,M) e-6T (r8_82).


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682 THE ECONOMIC JOURNAL [SEPTEMBERSince by assumption, a > r it follows that (,2U/0 T2) < o. It remains to be demon-strated that (a2U/aT2) < o implies (a2Y/IT2) < o.Proof: Y = U-1 [U(Y)]so

02Y 022U"1[U(Y)] a[U(Y)]12 aU-1[U(Y)] a2U(Y) (A 5)aT2 a U2(Y) taT J aU(Y) aT2But U(Y)/0 T is equal to zero, by the definition of Tm,so the first term is zero, andaU-1[U(Y)]/aU(Y) > o since U(Y) is a motonically increasing function. Sincea2U(Y)/aT2 < o, it follows that (a2Y/aT2) s also < o.

APPENDIX 3Derivation of the partial derivatives of Tmwith respect to L, a, 8 and r: Tm s definedby

? = au(Y) = U(x) - ) (e-TmT- re-rTm) (i - e-L) - e-rTm I - e-rL)]. (A 6)Totally differentiation with respect to T., L, a and 6:

< 00 =dT [ (r2e rTm_2e Tm) (i -e-8L) +rerTm(i-erL)]

0+ da (&e-Tm -re-rTm) (i -e 6L)].

m .The sign of the first term is derived in Appendix 2. The second term is equal to(02U/IOTaL), the sign of which is derived in Appendix 5. The sign of the third termis positive since it is equal to the first term of (A 6) divided by a; the second term of(A 6) is negative, and the first and second term sum to zero.

APPENDIX 4Derivation of the partial derivatives of Tiwith respect to a and L.

* ~~~~~~~~~~~~~rTSs defined by:o = Z (e-ri-e ai) (I -e-L) - (i - erL) (I-e erTi). (A 8)


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I987] VALUATION OF DELAYED CONSUMPTION 683Totally differentiatingwith respect to T7,ax,L:

< 0o = dT[7 - (I-e-8L)8e-8[( ) re-rTi) - e-rTi (I -e-rL

> 0+ dxa8( (e-rT - e-8Tj) (iI- e-L)] (A 9)

< 0+ dL[& (e-rTi-e-Ti) e-L-e-rL (i e-r

The first term is simply the slope ( U/I T) at T7,which will be negative. The sign ofthe second term is straightforward.The sign of the third term can be derived asfollows:from (A 8),

ar (erTi-e-8Ti) (i(-erL) (i -e-rTi) (A io)r ~~~r (i -e-Lsubstituting into the third term of (A 9):

_-&L (i er) (i -rLTi)rTre (I-eL) e ( I.e i) (A ii)= e )e1 - rL](I -e-rTi). (A 12)

Multiplying both sides by r( -e-8L) and dividing by e-rL-8L(i - e-rTi) will not changethe sign.Sign[( e- Lt i;-e- L)(i-erTi)]=sign[r(i-e L)-8(i-erL)] r> o.APPENDIX 5

Derivation of_2 a = Y T)

when AU/@T and Y/I T are both negative.aY aU-1[U(Y)]A-T AT

+ - + +?02Y 02U-1[U(y)] OU(y) OU(y) OU-1[U(Y)] 02U(Y)aTOL OU2(Y) AT AL AU(Y) aTOL (A 4)The signs of each of the terms except the last are self-evident. To demonstrate that

02Y/ITOL < o it is simplynecessaryo provethat02U(Y)/aTOL < o.Differentiating (6) with respect to L:02U(Y) - U [( aX)(8e8T _ re-rT) er-L-re-r(T+L)] (A '5)


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684 THE ECONOMIC JOURNAL [SEPT. I987]Since aU(Y)/aT< o, from (6):

ai(eTre-rT)

Documents

Anticipation and the Valuation of Delayed Consumption