Time Discounting and Time Preference: A Critical RevieFrederick, Loewenstein, and O ’Donoghue: Time Discounting 353 The anticipatory-utility and absti-nence perspectives share the

Journal of Economic LiteratureVol XL (June 2002) pp 351ndash401

Frederick Loewenstein and OrsquoDonoghue Time DiscountingJournal of Economic Literature Vol XL (June 2002)

Time Discounting and TimePreference A Critical Review

SHANE FREDERICK GEORGE LOEWENSTEINand TED OrsquoDONOGHUE1

1 Introduction

INTERTEMPORAL CHOICESmdashdecisionsinvolving tradeoffs among costs and

benefits occurring at different timesmdashare important and ubiquitous Such deci-sions not only affect onersquos health wealthand happiness but may also as AdamSmith first recognized determine theeconomic prosperity of nations In thispaper we review empirical research onintertemporal choice and present anoverview of recent theoretical formula-tions that incorporate insights gainedfrom this research

Economistsrsquo attention to intertempo-ral choice began early in the history ofthe discipline Not long after AdamSmith called attention to the impor-tance of intertemporal choice for the

wealth of nations the Scottish economistJohn Rae was examining the sociologi-cal and psychological determinants ofthese choices In section 2 we brieflyreview the perspectives on intertempo-ral choice of Rae and nineteenth- andearly twentieth-century economists anddescribe how these early perspectivesinterpreted intertemporal choice asthe joint product of many conflictingpsychological motives

All of this changed when Paul Sam-uelson proposed the discounted-utility(DU) model in 1937 Despite Samuel-sonrsquos manifest reservations about thenormative and descriptive validity ofthe formulation he had proposed theDU model was accepted almost in-stantly not only as a valid normativestandard for public policies (eg in cost-benefit analyses) but as a descriptivelyaccurate representation of actual behav-ior A central assumption of the DUmodel is that all of the disparate mo-tives underlying intertemporal choice canbe condensed into a single parametermdashthe discount rate In section 3 we exam-ine this and many other assumptionsunderlying the DU model We do notpresent an axiomatic derivation of themodel but instead focus on thosefeatures that highlight the implicitpsychological assumptions underlyingthe model

351

1 Frederick Sloan School of Management Mas-sachusetts Institute of Technology LoewensteinDepartment of Social and Decision SciencesCarnegie Mellon University OrsquoDonoghue De-partment of Economics Cornell University Wethank Colin Camerer David Laibson JohnMcMillan Drazen Prelec Daniel Read NachumSicherman Duncan Simester and three anony-mous referees for useful comments We thankCara Barber Rosa Blackwood Mandar Oak andRosa Stipanovic for research assistance For finan-cial support Frederick and Loewenstein thank theIntegrated Study of the Human Dimensions ofGlobal Change at Carnegie Mellon University(NSF Grant SBR-9521914 ) and OrsquoDonoghuethanks the National Science Foundation (AwardSES-0078796)

Samuelsonrsquos reservations about thedescriptive validity of the DU modelwere justified Section 4 reviewsthe growing list of ldquoDU anomaliesrdquomdashpatterns of choice that are inconsistentwith the modelrsquos theoretical predic-tions Virtually every assumption under-lying the DU model has been testedand found to be descriptively invalid inat least some situations Moreover aswe discuss at the end of the sectionthese anomalies are not anomalies in thesense that they are regarded as errorsby the people who commit them Unlikemany of the better-known expected-utility anomalies the DU anomalies donot necessarily violate any standard orprinciple that people believe theyshould uphold

The insights about intertemporalchoice gleaned from this empirical re-search have led to the proposal of nu-merous alternative theoretical modelswhich we review in section 5 Some ofthese modify the discount function per-mitting for example declining discountrates or ldquohyperbolic discountingrdquo Oth-ers introduce additional arguments intothe utility function such as the utilityof anticipation Still others depart fromthe DU model more radically by in-cluding for instance systematic mis-predictions of future utility Many ofthese new theories revive psychologicalconsiderations discussed by Rae andother early economists that were extin-guished with the adoption of the DUmodel and its expression of intertem-poral preferences in terms of a singleparameter

In section 6 we review attempts toestimate discount rates While the DUmodel assumes that people are charac-terized by a single discount rate thisliterature reveals spectacular variationacross (and even within) studies Thefailure of this research to converge to-ward any agreed-upon average discount

rate stems partly from differences inelicitation procedures But it also stemsfrom the faulty assumption that the var-ied considerations that are relevant inintertemporal choices apply equally todifferent choices and thus that they canall be sensibly represented by a singlediscount rate

Throughout the paper we stress theimportance of distinguishing among thevaried considerations that underlie in-tertemporal choices We distinguishtime discounting from time preferenceWe use the term time discountingbroadly to encompass any reason forcaring less about a future consequenceincluding factors that diminish the ex-pected utility generated by a futureconsequence such as uncertainty orchanging tastes We use the term timepreference to refer more specifically tothe preference for immediate utilityover delayed utility In section 7 wepush this theme further by examiningwhether time preference itself mightconsist of distinct psychological traitsthat can be separately analyzed Section8 concludes

2 Historical Origins of the DiscountedUtility Model

The historical developments that cul-minated in the formulation of the DUmodel help to explain the modelrsquos limi-tations Each of the major figures in thedevelopment of the DU modelmdashJohnRae Eugen von Boumlhm-Bawerk IrvingFisher and Paul Samuelsonmdashbuiltupon the theoretical framework of hispredecessors drawing on little morethan introspection and personal obser-vation When the DU model eventuallybecame entrenched as the dominanttheoretical framework for modeling in-tertemporal choice it was due largely toits simplicity and its resemblance to thefamiliar compound interest formula

352 Journal of Economic Literature Vol XL (June 2002)

and not as a result of empirical researchdemonstrating its validity

Intertemporal choice became firmlyestablished as a distinct topic in 1834with John Raersquos publication of The So-ciological Theory of Capital Like AdamSmith Rae sought to determine whywealth differed among nations Smithhad argued that national wealth was de-termined by the amount of labor allo-cated to the production of capital butRae recognized that this account was in-complete because it failed to explainthe determinants of this allocation InRaersquos view the missing element wasldquothe effective desire of accumulationrdquomdashapsychological factor that differed acrosscountries and determined a societyrsquoslevel of saving and investment

Along with inventing the topic of in-tertemporal choice Rae also producedthe first in-depth discussion of the psy-chological motives underlying inter-temporal choice Rae believed thatintertemporal-choice behavior was thejoint product of factors that either pro-moted or limited the effective desire ofaccumulation The two main factorsthat promoted the effective desire ofaccumulation were the bequest motive(ldquothe prevalence throughout the societyof the social and benevolent affectionsrdquop 58) and the propensity to exerciseself-restraint (ldquothe extent of the intel-lectual powers and the consequentprevalence of habits of reflection andprudence in the minds of the mem-bers of societyrdquo p 58) One limitingfactor was the uncertainty of humanlife

When engaged in safe occupations and livingin healthy countries men are much more aptto be frugal than in unhealthy or hazardousoccupations and in climates pernicious to hu-man life Sailors and soldiers are prodigalsIn the West Indies New Orleans the EastIndies the expenditure of the inhabitants isprofuse The same people coming to residein the healthy parts of Europe and not get-

ting into the vortex of extravagant fashionlive economica lly War and pestilence havealways waste and luxury among the other evilsthat follow in their train (Rae 1834 p 57)

A second factor that limited the ef-fective desire of accumulation was theexcitement produced by the prospect ofimmediate consumption and the con-comitant discomfort of deferring suchavailable gratifications

Such pleasures as may now be enjoyed gener-ally awaken a passion strongly prompting tothe partaking of them The actual presence ofthe immediate object of desire in the mind byexciting the attention seems to rouse all thefaculties as it were to fix their view on it andleads them to a very lively conception of theenjoyment s which it offers to their instantpossession (Rae 1834 p 120)

Among the four factors that Rae iden-tified as the joint determinants of timepreference one can glimpse two funda-mentally different views One which waslater championed by William S Jevons(1888) and his son Herbert S Jevons(1905) assumes that people care onlyabout their immediate utility and ex-plains farsighted behavior by postulat-ing utility from the anticipation offuture consumption On this view de-ferral of gratification will occur only ifit produces an increase in ldquoanticipalrdquoutility that more than compensates forthe decrease in immediate consumptionutility The second perspective assumesequal treatment of present and future(zero discounting) as the natural base-line for behavior and attributes theoverweighting of the present to themiseries produced by the self-denialrequired to delay gratification N WSenior the best-known advocate of thisldquoabstinencerdquo perspective wrote ldquoToabstain from the enjoyment which is inour power or to seek distant ratherthan immediate results are among themost painful exertions of the humanwillrdquo (Senior 1836 p 60)

Frederick Loewenstein and OrsquoDonoghue Time Discounting 353

The anticipatory-utility and absti-nence perspectives share the idea thatintertemporal tradeoffs depend on im-mediate feelingsmdashin one case the im-mediate pleasure of anticipation and inthe other the immediate discomfort ofself-denial The two perspectives how-ever explain variability in intertemporal-choice behavior in different ways Theanticipatory-utility perspective attrib-utes variations in intertemporal-choicebehavior to differences in peoplersquosabilities to imagine the future and todifferences in situations that promoteor inhibit such mental images The ab-stinence perspective on the other handexplains variations in intertemporal-choice behavior on the basis of individ-ual and situational differences in thepsychological discomfort associated withself-denial In this view one shouldobserve high rates of time discountingby people who find it painful to delaygratification and in situations in whichdeferral is generally painfulmdasheg whenone is as Rae worded it in the ldquoactualpresence of the immediate object ofdesirerdquo

Eugen von Boumlhm-Bawerk the nextmajor figure in the development of theeconomic perspective on intertemporalchoice added a new motive to the listproposed by Rae Jevons and Seniorarguing that humans suffer from asystematic tendency to underestimatefuture wants

It may be that we possess inadequate powerto imagine and to abstract or that we are notwilling to put forth the necessary effort butin any event we limn a more or less incom-plete picture of our future wants and espe-cially of the remotely distant ones Andthen there are all those wants that nevercome to mind at all (Boumlhm-Bawerk 1889 pp268ndash69)2

Boumlhm-Bawerkrsquos analysis of time pref-erence like those of his predecessorswas heavily psychological and much ofhis voluminous treatise Capital andInterest was devoted to discussions ofthe psychological constituents of timepreference However whereas the earlyviews of Rae Senior and Jevons ex-plained intertemporal choices in termsof motives that are uniquely associatedwith time Boumlhm-Bawerk began model-ing intertemporal choice in the sameterms as other economic tradeoffsmdashas aldquotechnicalrdquo decision about allocating re-sources (to oneself) over different pointsin time much as one would allocateresources between any two competinginterests such as housing and food

Boumlhm-Bawerkrsquos treatment of inter-temporal choice as an allocation of con-sumption among time periods was for-malized a decade later by the Americaneconomist Irving Fisher (1930) Fisherplotted the intertemporal consumptiondecision on a two-good indifferencediagram with consumption in the cur-rent year on the abscissa and consump-tion in the following year on the ordi-nate This representation made clearthat a personrsquos observed (marginal)rate of time preferencemdashthe marginalrate of substitution at her chosen con-sumption bundlemdashdepends on twoconsiderations time preference and di-minishing marginal utility Many econo-mists have subsequently expressed dis-comfort with using the term ldquotimepreferencerdquo to include the effects of dif-ferential marginal utility arising fromunequal consumption levels betweentime periods (see in particular MancurOlson and Martin Bailey 1981) InFisherrsquos formulation pure time prefer-ence can be interpreted as the marginal

2 In a frequently cited passage from The Eco-nomics of Welfare Arthur Pigou (1920) proposeda similar account of time preference suggestingthat it results from a type of cognitive illusion ldquoour

telescopic faculty is defective and we thereforesee future pleasures as it were on a diminishedscalerdquo


rate of substitution on the diagonalwhere consumption is equal in bothperiods

Fisherrsquos writings like those of hispredecessors included extensive discus-sions of the psychological determinantsof time preference Like Boumlhm-Bawerkhe differentiated ldquoobjective factors rdquosuch as projected future wealth andrisk from ldquopersonal factorsrdquo Fisherrsquoslist of personal factors included the fourdescribed by Rae ldquoforesightrdquo (the abil-ity to imagine future wantsmdashthe inverseof the deficit that Boumlhm-Bawerk postu-lated) and ldquofashionrdquo which Fisher be-lieved to be ldquoof vast importance inits influence both on the rate of interestand on the distribution of wealth itselfrdquo(Fisher 1930 p 88)

The most fitful of the causes at work is prob-ably fashion This at the present time actson the one hand to stimulate men to saveand become millionaires and on the otherhand to stimulate millionaires to live in anostentatious manner (Fisher 1930 p 87)

Hence in the early part of the twen-tieth century ldquotime preferencerdquo wasviewed as an amalgamation of variousintertemporal motives While the DUmodel condenses these motives into thediscount rate we will argue that resur-recting these distinct motives is crucialfor understanding intertemporal choices

3 The Discounted Utility Model

In 1937 Paul Samuelson introducedthe DU model in a five-page articletitled ldquoA Note on Measurement of Util-ityrdquo Samuelsonrsquos paper was intended tooffer a generalized model of intertem-poral choice that was applicable to mul-tiple time periods (Fisherrsquos graphicalindifference-curve analysis was difficultto extend to more than two time peri-ods) and to make the point that repre-senting intertemporal tradeoffs re-quired a cardinal measure of utility But

in Samuelsonrsquos simplified model all thepsychological concerns discussed over theprevious century were compressed intoa single parameter the discount rate

The DU model specifies a decisionmakerrsquos intertemporal preferences overconsumption profiles (ctcT) Underthe usual assumptions (completenesstransitivity and continuity) such pref-erences can be represented by an in-tertemporal utility function Ut(ctcT)The DU model goes further by as-suming that a personrsquos intertemporalutility function can be described by thefollowing special functional form

Ut(ctcT) = aringk = 0

T t

D(k)u(ct + k)

where D(k) = aeligccedilegrave

11 + r

oumldivideoslash

k

In this formulation u(ct + k) is often inter-preted as the personrsquos cardinal instanta-neous utility functionmdashher well-being inperiod t + kmdashand D(k) is often inter-preted as the personrsquos discount func-tionmdashthe relative weight she attaches inperiod t to her well-being in period t + kr represents the individualrsquos pure rateof time preference (her discount rate)which is meant to reflect the collectiveeffects of the ldquopsychologicalrdquo motivesdiscussed in section 23

Samuelson did not endorse the DUmodel as a normative model of in-tertemporal choice noting that ldquoanyconnection between utility as discussedhere and any welfare concept is dis-avowedrdquo (p 161) He also made noclaims on behalf of its descriptive valid-ity stressing ldquoIt is completely arbitraryto assume that the individual behaves soas to maximize an integral of the formenvisaged in [the DU model]rdquo (p 159)However despite Samuelsonrsquos manifest

3 The continuous-time analogue is Ut(ctt Icirc[tT]) =ogravet = t

T e r(t t)u(ct) For expositional ease we shallrestrict attention to discrete-time throughout


reservations the simplicity and ele-gance of this formulation was irresist-ible and the DU model was rapidlyadopted as the framework of choice foranalyzing intertemporal decisions

The DU model received a scarcelyneeded further boost to its dominanceas the standard model of intertemporalchoice when Tjalling C Koopmans(1960) showed that the model could bederived from a superficially plausibleset of axioms Koopmans like Samuel-son did not argue that the DU modelwas psychologically or normativelyplausible his goal was only to show thatunder some well-specified (though ar-guably unrealistic) circumstances in-dividuals were logically compelled topossess positive time preference Pro-ducers of a product however cannotdictate how the product will be usedand Koopmansrsquo central technical mes-sage was largely lost while his axiom-atization of the DU model helped tocement its popularity and bolster itsperceived legitimacy

In the remainder of this section wedescribe some important features of theDU model as it is commonly used byeconomists and briefly comment on thenormative and positive validity of theseassumptions These features do not rep-resent an axiom systemmdashthey are nei-ther necessary nor sufficient conditionsfor the DU modelmdashbut are intendedto highlight the implicit psychologicalassumptions underlying the model4

31 Integration of New Alternatives with Existing Plans

A central assumption in most modelsof intertemporal choicemdashincluding theDU modelmdashis that a person evaluates

new alternatives by integrating themwith her existing plans To illustrateconsider a person with an existing con-sumption plan (ctcT) who is offeredan intertemporal-choice prospect Xwhich might be something like an op-tion to give up $5000 today to receive$10000 in five years Integration meansthat prospect X is not evaluated in isola-tion but in light of how it changes thepersonrsquos aggregate consumption in allfuture periods Thus to evaluate theprospect X the person must choose whather new consumption path (ccenttfrac14ccentT)would be if she were to accept prospectX and should accept the prospect ifUt(ccenttfrac14ccentT) gt Ut(ctfrac14cT)

An alternative way to understand in-tegration is to recognize that intertem-poral prospects alter a personrsquos budgetset If the personrsquos initial endowment isE0 then accepting prospect X wouldchange her endowment to E0 Egrave X Let-ting B(E) denote the personrsquos budgetset given endowment Emdashie the set ofconsumption streams that are feasiblegiven endowment Emdashthe DU modelsays that the person should acceptprospect X if

max(ctcT) IcircB(E0 Egrave X)

aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)

gt max(ctcT) IcircB(E0)

aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)

While integration seems normativelycompelling it may be too difficult toactually do A person may not havewell-formed plans about future con-sumption streams or be unable (or un-willing) to recompute the new optimalplan every time she makes an intertem-poral choice Some of the evidence wereview below supports the plausiblepresumption that people evaluate theresults of intertemporal choices inde-pendently of any expectations they have

4 There are several different axiom systems forthe DU modelmdashin addition to Koopmans seePeter Fishburn (1970) K J Lancaster (1963)Richard F Meyer (1976) and Fishburn and ArielRubinstein (1982)


regarding consumption in future timeperiods

32 Utility Independence

The DU model explicitly assumes thatthe overall valuemdashor ldquoglobal utilityrdquomdashof a sequence of outcomes is equal tothe (discounted) sum of the utilities ineach period Hence the distribution ofutility across time makes no differencebeyond that dictated by discountingwhich (assuming positive time prefer-ence) penalizes utility that is experi-enced later The assumption of utilityindependence has rarely been discussedor challenged but its implications arefar from innocuous It rules out anykind of preference for patterns of utilityover timemdasheg a preference for a flatutility profile over a roller-coaster util-ity profile with the same discountedutility5

33 Consumption Independence

The DU model explicitly assumes thata personrsquos well-being in period t + k isindependent of her consumption in anyother periodmdashie that the marginalrate of substitution between consump-tion in periods t and tcent is independentof consumption in period tsup2

Consumption independence is analo-gous to but fundamentally different fromthe independence axiom of expected-utility theory In expected-utility the-ory the independence axiom specifiesthat preferences over uncertain pros-

pects are not affected by the conse-quences that the prospects sharemdashiethat the utility of an experienced out-come is unaffected by other outcomesthat one might have experienced (butdid not) In intertemporal choice con-sumption independence says that pref-erences over consumption profi les arenot affected by the nature of consump-tion in periods in which consumption isidentical in the two profilesmdashie thatan outcomersquos utility is unaffected byoutcomes experienced in prior or futureperiods For example consumption in-dependence says that a personrsquos prefer-ence between an Italian and Thai res-taurant tonight should not depend onwhether she had Italian last night norwhether she expects to have it tomor-row As the example suggests and asSamuelson and Koopmans both recog-nized there is no compelling rationalefor such an assumption Samuelson(1952 p 674) noted that ldquothe amountof wine I drank yesterday and will drinktomorrow can be expected to have ef-fects upon my todayrsquos indifferenceslope between wine and milkrdquo Simi-larly Koopmans (1960 p 292) acknowl-edged that ldquoOne cannot claim a highdegree of realism for [the indepen-dence assumption] because there is noclear reason why complementarity ofgoods could not extend over more thanone time periodrdquo

34 Stationary Instantaneous Utility

When applying the DU model to spe-cific problems it is often assumed thatthe cardinal instantaneous utility func-tion u(ct) is constant across time so thatthe well-being generated by any activityis the same in different periods Mosteconomists would acknowledge that sta-tionarity of the instantaneous utilityfunction is not sensible in many situ-ations because peoplersquos preferences doin fact change over time in predictable

5 ldquoUtility independencerdquo has meaning only ifone literally interprets u(ct + k) as well-being expe-rienced in period t + k We believe that this is infact the common interpretation For a model thatrelaxes the assumption of utility independencesee Benjamin Hermalin and Alice Isen (2000)who consider a model in which well-being inperiod t depends on well-being in period t ndash 1mdashie they assume ut = u(ct ut ndash 1) See also DanielKahneman Peter Wakker and Rakesh Sarin(1997) who propose a set of axioms that wouldjustify an assumption of additive separabili ty ininstantaneous utility


and unpredictable ways Though thisunrealistic assumption is often retainedfor analytical convenience it becomes lessdefensible as economists gain insightinto how tastes change over time (seeLoewenstein and Angner forthcomingfor a discussion of different sources ofpreference change)6

35 Independence of Discountingfrom Consumption

The DU model assumes that the dis-count function is invariant across allforms of consumption This feature iscrucial to the notion of time preferenceIf people discount utility from differentsources at different rates then the no-tion of a unitary time preference ismeaningless Instead we would need tolabel time preference according to theobject being delayedmdashrdquobanana timepreferencerdquo ldquovacation time prefer-encerdquo and so on In section 7 we dis-cuss in more detail the validity of theassumption that the same rate of timepreference applies to all forms ofconsumption

36 Constant Discounting and TimeConsistency

Any discount function can be written inthe form D(k) = Pn = 0

k 1 aeligccedilegrave

1

1 + rn

oumldivideoslash where rn rep-

resents the per-period discount ratefor period nmdashthat is the discount rateapplied between periods n and n + 1Hence by assuming that the discountfunction takes the form D(k) = aelig

ccedilegrave

1

1 + roumldivideoslash

kthe DU model assumes a constant per-

period discount rate (rn = r for alln)7

Constant discounting entails an even-handedness in the way a person evalu-ates time It means that delaying oraccelerating two dated outcomes by acommon amount should not changepreferences between the outcomesmdashifin period t a person prefers X at t to Yat t + d for some t then in period t shemust prefer X at t to Y at t + d for all tThe assumption of constant discountingpermits a personrsquos time preference tobe summarized as a single discountrate If constant discounting does nothold then characterizing onersquos timepreference requires the specification ofan entire discount function

Constant discounting implies that apersonrsquos intertemporal preferences aretime-consistent which means that laterpreferences ldquoconfirmrdquo earlier prefer-ences Formally a personrsquos preferencesare time-consistent if for any two con-sumption profiles (ctcT) and (ccenttccentT)with ct = ccentt Ut(ctct + 1cT) sup3 Ut(ccenttccentt + 1ccentT) if and only if Ut + 1(ct + 1cT) sup3Ut + 1(ccentt + 1ccentT)8 For an interesting dis-cussion that questions the normative va-lidity of constant discounting see MartinAlbrecht and Martin Weber (1995)

37 Diminishing Marginal Utilityand Positive Time Preference

While not core features of the DUmodel virtually all analyses of intertem-poral choice assume both diminishing

6 As we discuss in section 5 endogenous prefer-ence changes due to things such as habit forma-tion or reference dependence are best understoodin terms of consumption interdependence and notnonstationary utility In some situations nonsta-tionarities clearly play an important role in behav-iormdasheg Steven Suranovic Robert Goldfarb andThomas Leonard (1999) and OrsquoDonoghue andMathew Rabin (1999a 2000) discuss the impor-tance of nonstationarities in the realm of addictivebehavior

7 An alternative but equivalent definition of con-stant discounting is that D(k)D(k + 1) is indepen-dent of k

8 Constant discounting implies time-consis tentpreferences only under the ancillary assumptionof stationary discounting for which the dis-count function D(k) is the same in all periods As acounterexample if the period-t discount functionis Dt(k) = aelig

ccedilegrave

1

1 + r

oumldivideoslash

k while the period-t + 1 discountfunction is Dt + 1(k) = aelig

ccedilegrave

1

1 + rcent

oumldivideoslash

k for some rcent sup1 r thenthe person exhibits constant discounting at bothdates t and t + 1 but nonetheless has time-inconsistent preferences


marginal utility (that the instantaneousutility function u(ct) is concave) and posi-tive time preference (that the discount rater is positive)9 These two assumptionscreate opposing forces in intertemporalchoice diminishing marginal utility mo-tivates a person to spread consumptionover time while positive time prefer-ence motivates a person to concentrateconsumption in the present

Since people do in fact spread con-sumption over time the assumption ofdiminishing marginal utility (or someother property that has the same effect)seems strongly justified The assump-tion of positive time preference on theother hand is more questionable Sev-eral researchers have argued for posi-tive time preference on logical grounds(Jack Hirshleifer 1970 Koopmans 1960Koopmans Peter A Diamond andRichard E Williamson 1964 Olson andBailey 1981) The gist of their argu-ments is that a zero or negative timepreference combined with a positivereal rate of return on saving wouldcommand the infinite deferral of allconsumption10 But this conclusion as-sumes unrealistically that individualshave infinite life-spans and linear (orweakly concave) utility functions Never-theless in econometric analyses of sav-ings and intertemporal substitution posi-tive time preference is sometimes treatedas an identifying restriction whose vio-lation is interpreted as evidence ofmisspecification

The most compelling argument sup-porting the logic of positive time pref-

erence was made by Derek Parfit (19711976 1982) who contends that there isno enduring self or ldquoIrdquo over time towhich all future utility can be ascribedand that a diminution in psychologicalconnections gives our descendent fu-ture selves the status of other peoplemdashmaking that utility less than fullyldquooursrdquo and giving us a reason to count itless11

We care less about our further future because we know that less of what we arenowmdashless say of our present hopes or plansloves or idealsmdashwill survive into the furtherfuture [if] what matters holds to a lesserdegree it cannot be irrational to care less(Parfit 1971 p 99)

Parfitrsquos claims are normative not de-scriptive He is not attempting to ex-plain or predict peoplersquos intertemporalchoices but is arguing that conclusionsabout the rationality of time preferencemust be grounded in a correct view ofpersonal identity However if this is theonly compelling normative rationale fortime discounting it would be instruc-tive to test for a positive relation be-tween observed time discounting andchanging identity Frederick (2002)conducted the only study of this type

9 Discounting is not inherent to the DU modelbecause the model could be applied with r pound 0However the inclusion of r in the model stronglyimplies that it may take a value other than zeroand the name discount rate certainly suggests thatit is greater than zero

10 In the context of intergenerational choiceKoopmans (1967) called this result the paradox ofthe indefinite ly postponed splurge See also Ken-neth J Arrow (1983) S Chakravart y (1962) andRobert M Solow (1974)

11 As noted by Frederick (2002) there is muchdisagreement about the nature of Parfitrsquos claim Inher review of the philosophical literature JenniferWhiting (1986 p 549) identifies four different in-terpretations (1) the strong absolute claim that itis irrational for someone to care about their futurewelfare (2) the weak absolute claim that there isno rational requirement to care about onersquos futurewelfare (3) the strong comparative claim that it isirrational to care more about onersquos own futurewelfare than about the welfare of any other per-son and (4) the weak comparative claim that oneis not rationally required to care more about theirfuture welfare than about the welfare of any otherperson We believe that all of these interpretationsare too strong and that Parfit endorses only aweaker version of the weak absolute claim That ishe claims only that one is not rationally requiredto care about onersquos future welfare to a degree thatexceeds the degree of psychological connectednessthat obtains between onersquos current self and onersquosfuture self


and found no relation between mone-tary discount rates (as imputed fromprocedures such as ldquoI would be indiffer-ent between $100 tomorrow and $____in five yearsrdquo) and self-perceived stabil-ity of identity (as defined by the follow-ing similarity ratings ldquoCompared tonow how similar were you five yearsago [will you be five years fromnow]rdquo) nor did he find any relationbetween such monetary discount ratesand the presumed correlates of identitystability (eg the extent to which peo-ple agree with the statement ldquoI am stillembarrassed by stupid things I did along time agordquo)

4 DU Anomalies

Over the last two decades empiricalresearch on intertemporal choice hasdocumented various inadequacies of theDU model as a descriptive model of be-havior First empirically observed dis-count rates are not constant over timebut appear to declinemdasha pattern oftenreferred to as hyperbolic discountingFurthermore even for a given delaydiscount rates vary across differenttypes of intertemporal choices gainsare discounted more than losses smallamounts more than large amounts andexplicit sequences of multiple outcomesare discounted differently than outcomesconsidered singly

41 Hyperbolic Discounting

The best documented DU anomalyis hyperbolic discounting The termldquohyperbolic discountingrdquo is often usedto mean in our terminology that a per-son has a declining rate of time prefer-ence (in our notation rn is declining inn) and we adopt this meaning hereSeveral results are usually interpretedas evidence for hyperbolic discountingFirst when subjects are asked to com-pare a smaller-sooner reward to a

larger-later reward (see section 6 for adescription of these procedures) theimplicit discount rate over longer timehorizons is lower than the implicit dis-count rate over shorter time horizonsFor example Richard Thaler (1981)asked subjects to specify the amount ofmoney they would require in [onemonthone yearten years] to make themindifferent to receiving $15 now Themedian responses [$20$50$100] implyan average (annual) discount rate of345 percent over a one-month horizon120 percent over a one-year horizonand 19 percent over a ten-year hori-zon12 Other researchers have found asimilar pattern (Uri Benzion AmnonRapoport and Joseph Yagil 1989Gretchen B Chapman 1996 Chapmanand Arthur S Elstein 1995 John LPender 1996 Daniel A Redelmeier andDaniel N Heller 1993)

Second when mathematical functionsare explicitly fit to such data a hyper-bolic functional form which imposesdeclining discount rates fits the databetter than the exponential functionalform which imposes constant discountrates (Kris N Kirby 1997 Kirby and NinoMarakovic 1995 Joel Myerson and Leon-ard Green 1995 Howard Rachlin AndresRaineri and David Cross 1991) 13

Third researchers have shown that12 That is $15 = $20 (endash(345)(112)) = $50 (endash(120)(1)) =

$100 (endash(019)(10)) While most empirical studies re-port average discount rates over a given horizon itis sometimes more useful to discuss average ldquoper-periodrdquo discount rates Framed in these termsThalerrsquos results imply an average (annual) discountrate of 345 percent between now and one monthfrom now 100 percent between one month fromnow and one year from now and 77 percentbetween one year from now and ten yearsfrom now That is $15 = $20 (endash(345)(112)) =$50 (endash(345)(112) endash(100)(11 12)) = $100 (endash(345)(1 12)

endash(100)(11 12)endash(0077)(9))13 Several hyperbolic functional forms have

been proposed George Ainslie (1975) suggestedthe function D(t) = 1t Richard Herrnstein (1981)and James Mazur (1987) suggested D(t) = 1(1 + at)and George Loewenstein and Drazen Prelec (1992)suggested D(t) = 1(1 + at)ba


preferences between two delayed re-wards can reverse in favor of the moreproximate reward as the time to bothrewards diminishesmdasheg someone mayprefer $110 in 31 days over $100 in 30days but also prefer $100 now over$110 tomorrow Such ldquopreference re-versalsrdquo have been observed both inhumans (Green Nathaniel Fristoe andMyerson 1994 Kirby and Herrnstein1995 Andrew Millar and DouglasNavarick 1984 Jay Solnick et al 1980)and in pigeons (Ainslie and Herrnstein1981 Green et al 1981) 14

Fourth the pattern of declining dis-count rates suggested by the studiesabove is also evident across studies Insection 6 we summarize studies that es-timate discount rates Figure 1a plotsthe average estimated discount factor(= 1(1 + discount rate)) from each ofthese studies against the average timehorizon for that study15 As the regres-sion line reflects the estimated dis-count factor increases with the time ho-rizon which means that the discountrate declines We note however thatafter excluding studies with very shorttime horizons (one year or less) fromthe analysis (see figure 1b) there is no

evidence that discount rates continue todecline In fact after excluding the stud-ies with short time horizons the corre-lation between time horizon and discountfactor is almost exactly zero (ndash00026)

Although the collective evidence out-lined above seems overwhelmingly tosupport hyperbolic discounting a re-cent study by Daniel Read (2001)points out that the most common typeof evidencemdashthe finding that implicitdiscount rates decrease with the timehorizonmdashcould also be explained byldquosubadditive discountingrdquo which meansthe total amount of discounting over atemporal interval increases as the inter-val is more finely partitioned16 To dem-onstrate subadditive discounting anddistinguish it from hyperbolic discount-ing Read elicited discount rates for a two-year (24-month) interval and for its threeconstituent intervals an eight-monthinterval beginning at the same time aneight-month interval beginning eightmonths later and an eight-month inter-val beginning sixteen months later Hefound that the average discount ratefor the 24-month interval was lower thanthe compounded average discount rateover the three eight-month subintervalsmdasha result predicted by subadditive dis-counting but not predicted by hyper-bolic discounting (or any type of discountfunction for that matter) Moreoverthere was no evidence that discount ratesdeclined with time as the discountrates for the three eight-month inter-vals were approximately equal Similarempirical results were found earlier byJ H Holcomb and P S Nelson (1992)

14 These studies all demonstrate preference re-versals in the synchronic sensemdashsubjects simulta-neously prefer $100 now over $110 tomorrow andprefer $110 in 31 days over $100 in 30 days whichis consistent with hyperbolic discounting Butthere seems to be an implicit belief that such pref-erence reversals would also hold in the diachronicsensemdashthat if subjects who currently prefer $110in 31 days over $100 in 30 days were brought backto the lab thirty days later they would prefer $100at that time over $110 one day later Under theassumption of stationary discounting (as discussedin footnote 8) synchronic preference reversals im-ply diachronic preference reversals To the extentthat subjects anticipate diachronic reversals andwant to avoid them evidence of a preference forcommitment could also be interpreted as evidencefor hyperbolic discounting (we discuss this issuemore in section 511)

15 In some cases the discount rates were com-puted from the median respondent In othercases the mean discount rate was used

16 Readrsquos proposal that discounting is subaddi-tive is compatible with analogous results in otherdomains For example Amos Tversky and DerekKoehler (1994) found that the total probability as-signed to an event increases the more finely theevent is partitionedmdasheg the probabili ty ofldquodeath by accidentrdquo is judged to be more likely ifone separately elicits the probabili ty of ldquodeath byfirerdquo ldquodeath by drowningrdquo ldquodeath by fallingrdquo etc


although they did not interpret theirresults the same way

If Read is correct about subadditivediscounting its main implication foreconomic applications may be to providean alternative psychological underpin-ning for using a hyperbolic discountfunction because most intertemporaldecisions are based primarily on dis-counting from the present17

42 Other DU Anomalies

The DU model not only dictates thatthe discount rate should be constant forall time periods it also assumes that thediscount rate should be the same for alltypes of goods and all categories ofintertemporal decisions There are sev-eral empirical regularities that appear tocontradict this assumption namely(1) gains are discounted more thanlosses (2) small amounts are discountedmore than large amounts (3) greaterdiscounting is shown to avoid delayof a good than to expedite its receipt(4) in choices over sequences ofoutcomes improving sequences areoften preferred to declining sequencesthough positive time preference dic-tates the opposite and (5) in choicesover sequences violations of indepen-dence are pervasive and people seemto prefer spreading consumption overtime in a way that diminishing marginalutility alone cannot explain

421 The ldquoSign Effectrdquo (gains arediscounted more than losses)

Many studies have concluded thatgains are discounted at a higher ratethan losses For instance Thaler (1981)

17 A few studies have actually found increasingdiscount rates Frederick (1999) asked 228 respon-dents to imagine that they worked at a job thatconsisted of both pleasant work (ldquogood daysrdquo) andunpleasant work (ldquobad daysrdquo) and to equate theattractiveness of having additional good days thisyear or in a future year On average respondentswere indifferent between 20 extra good days thisyear 21 the following year or 40 in five yearsimplying a one-year discount rate of 5 percent anda five-year discount rate of 15 percent A possibleexplanation is that a desire for improvement isevoked more strongly for two successive years(this year and next) than for two separated years(this year and five years hence) Rubinstein (2000)asked students in a political science class to choosebetween the following two payment sequences

AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000

Then two weeks later he asked them to choosebetween $997 on November 1 and $1000 onDecember 1 Fifty-four percent of respondentspreferred $997 in November to $1000 in Decem-ber but only 34 percent preferred sequence A tosequence B These two results suggest increasingdiscount rates To explain them Rubinstein specu-lated that the three more proximate additional ele-

ments may have masked the differences in thetiming of the sequence of dated amounts whilemaking the differences in amounts more salient

10

08

06

04

02

00

Figure 1a Discount Factor as a Function of TimeHorizon (all studies)

0

impu

ted

disc

ount

fact

or

5time horizon (years)

10 15

10

08

06

04

02

00

Figure 1b Discount Factor as a Function of TimeHorizon (studies with avg horizons gt 1 year)

0

impu

ted

disc

ount

fact

or


10 15


asked subjects to imagine they had re-ceived a traffic ticket that could be paideither now or later and to state howmuch they would be willing to pay ifpayment could be delayed (by threemonths one year or three years) Thediscount rates imputed from these an-swers were much lower than the discountrates imputed from comparable questionsabout monetary gains This pattern isprevalent in the literature Indeed in manystudies a substantial proportion of sub-jects prefer to incur a loss immediatelyrather than delay it (Benzion Rapoportand Yagil 1989 Loewenstein 1987 L DMacKeigan et al 1993 Walter MischelJoan Grusec and John C Masters 1969Redelmeier and Heller 1993 J FrankYates and Royce A Watts 1975)

422 The ldquoMagnitude Effectrdquo (smalloutcomes are discounted more than large ones)

Most studies that vary outcome sizehave found that large outcomes arediscounted at a lower rate than smallones (Ainslie and Varda Haendel 1983Benzion Rapoport and Yagil 1989 GreenFristoe and Myerson 1994 GreenAstrid Fry and Myerson 1994 Hol-comb and Nelson 1992 Kirby 1997Kirby and Marakovic 1995 KirbyNancy Petry and Warren Bickel 1999Loewenstein 1987 Raineri and Rachlin1993 Marjorie K Shelley 1993 Thaler1981) In Thalerrsquos (1981) study for ex-ample respondents were on averageindifferent between $15 immediatelyand $60 in a year $250 immediatelyand $350 in a year and $3000 immedi-ately and $4000 in a year implying dis-count rates of 139 percent 34 percentand 29 percent respectively

423 The ldquoDelay-Speeduprdquo Asymmetry

Loewenstein (1988) demonstratedthat imputed discount rates can bedramatically affected by whether the

change in delivery time of an outcomeis framed as an acceleration or a delayfrom some temporal reference pointFor example respondents who didnrsquotexpect to receive a VCR for anotheryear would pay an average of $54 to re-ceive it immediately but those whothought they would receive it immedi-ately demanded an average of $126 todelay its receipt by a year BenzionRapoport and Yagil (1989) and Shelley(1993) replicated Loewensteinrsquos findingsfor losses as well as gains (respondentsdemanded more to expedite paymentthan they would pay to delay it)

424 Preference for Improving Sequences

In studies of discounting that involvechoices between two outcomesmdasheg Xat t vs Y at tcentmdashpositive discounting isthe norm Research examining prefer-ences over sequences of outcomes how-ever has generally found that peopleprefer improving sequences to declin-ing sequences (for an overview seeAriely and Carmon in press Frederickand Loewenstein 2002 Loewenstein andPrelec 1993) For example Loewen-stein and Nachum Sicherman (1991)found that for an otherwise identicaljob most subjects prefer an increasingwage profile to a declining or flat one(see also Robert Frank 1993) Christo-pher Hsee Robert P Abelson andPeter Salovey (1991) found that an in-creasing salary sequence was rated ashighly as a decreasing sequence thatconferred much more money CarolVarey and Kahneman (1992) found thatsubjects strongly preferred streams ofdecreasing discomfort to streams of in-creasing discomfort even when the over-all sum of discomfort over the intervalwas otherwise identical Loewensteinand Prelec (1993) found that respon-dents who chose between sequences oftwo or more events (eg dinners or


vacation trips) on consecutive weekendsor consecutive months generally pre-ferred to save the better thing for lastChapman (2000) presented respondentswith hypothetical sequences of head-ache pain that were matched in termsof total pain that either gradually less-ened or gradually increased with timeSequence durations included one hourone day one month one year fiveyears and twenty years For all se-quence durations the vast majority(from 82 percent to 92 percent) of sub-jects preferred the sequence of painthat lessened over time (See also W TRoss Jr and I Simonson 1991)

425 Violations of Independenceand Preference for Spread

The research on preferences over se-quences also reveals strong violations ofindependence Consider the followingpair of questions from Loewenstein andPrelec (1993)

Imagine that over the next five weekends you mustdecide how to spend your Saturday nights From eachpair of sequences of dinners below circle the one youwould prefer ldquoFancy Frenchrdquo refers to a dinner at afancy French restaurant ldquoFancy Lobsterrdquo refers to anexquisite lobster dinner at a four-star restaurant Ignorescheduling considerations (eg your current plans)

As discussed in section 33 consump-tion independence implies that prefer-ences between two consumption pro-files should not be affected by thenature of the consumption in periods in

which consumption is identical in thetwo profiles Thus anyone preferringprofile B to profile A (which share thefifth period ldquoEat at Homerdquo) should alsoprefer profile D to profi le C (whichshare the fifth period ldquoFancy Lobsterrdquo)As the data reveal however manyrespondents violated this predictionpreferring the fancy French dinner onthe third weekend if that was the onlyfancy dinner in the profile but prefer-ring the fancy French dinner on thefirst weekend if the profile containedanother fancy dinner This result couldbe explained by the simple desire tospread consumption over timemdashwhichin this context violates the dubious as-sumption of independence that the DUmodel entails

Loewenstein and Prelec (1993) pro-vide further evidence of such a prefer-ence for spread Subjects were asked toimagine that they were given two cou-pons for fancy ($100) restaurant din-ners and were asked to indicate whenthey would use them ignoring consid-erations such as holidays birthdays andsuch Subjects either were told thatldquoyou can use the coupons at any timebetween today and two years from to-dayrdquo or were told nothing about anyconstraints Subjects in the two-yearconstraint condition actually scheduledboth dinners at a later time than thosewho faced no explicit constraintmdashtheydelayed the first dinner for eight weeks(rather than three) and the second din-ner for 31 weeks (rather than thirteen)This counterintuitive result can be ex-plained in terms of a preference forspread if the explicit two-year intervalwas greater than the implicit time hori-zon of subjects in the unconstrainedgroup

43 Are These ldquoAnomaliesrdquo Mistakes

In other domains of judgment andchoice many of the famous ldquoeffectsrdquo

firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]


that have been documented are re-garded as errors by the people whocommit them For example in the ldquocon-junction fallacyrdquo discovered by Tverskyand Kahneman (1983) many people willmdashwith some reflectionmdashrecognize that aconjunction cannot be more likely thanone of its constituents (eg that it canrsquotbe more likely for Linda to be a femi-nist bank teller than for her to beldquojustrdquo a bank teller) In contrast thepatterns of preferences that are re-garded as ldquoanomaliesrdquo in the contextof the DU model do not necessarily vio-late any standard or principle that peo-ple believe they should uphold Evenwhen the choice pattern is pointed outto people they do not regard them-selves as having made a mistake (andprobably have not made one) Forexample there is no compelling logicthat dictates that one who prefers todelay a French dinner should also pre-fer to do so when that French dinnerwill be closely followed by a lobsterdinner

Indeed it is unclear whether any ofthe DU ldquoanomaliesrdquo should be regardedas mistakes Frederick and Read (2002)found evidence that the magnitude ef-fect is more pronounced when subjectsevaluate both ldquosmallrdquo and ldquolargerdquoamounts than when they evaluate eitherone Specifically the difference in thediscount rates between a small amount($10) and a large amount ($1000) waslarger when the two judgments weremade in close succession than whenthey were made separately Analogousresults were obtained for the sign ef-fect as the differences in discountrates between gains and losses wereslightly larger in a within-subjectsdesign where respondents evaluateddelayed gains and delayed losses thanin a between-subjects design wherethey evaluate only gains or only lossesSince respondents did not attempt to

coordinate their responses to conformto DUrsquos postulates when they evaluatedrewards of different sizes it suggeststhat they consider the different dis-count rates to be normatively appropri-ate Similarly even after Loewensteinand Sicherman (1991) informed respon-dents that a decreasing wage profile($27000 $26000 $23000 ) would(via appropriate saving and investing)permit strictly more consumption inevery period than the correspondingincreasing wage profile with an equiv-alent nominal tota l ($23000 $24000 $27000 ) respondents still pre-ferred the increasing sequence Perhapsthey suspected that they could notexercise the required self control tomaintain their desired consumptionsequence or felt a general leerinessabout the significance of a decliningwage either of which could justifythat choice As these examples illus-trate many DU ldquoanomaliesrdquo exist asldquoanomaliesrdquo only by reference to a modelthat was constructed without regardto its descriptive validity and whichhas no compelling normative basis

5 Alternative Models

In response to the anomalies justenumerated and other intertemporal-choice phenomena that are inconsistentwith the DU model a variety of alter-nate theoretical models have beendeveloped Some models attempt toachieve greater descriptive realism byrelaxing the assumption of constantdiscounting Other models incorporateadditional considerations into the in-stantaneous utility function such asthe utility from anticipation Still othersdepart from the DU model moreradically by including for instancesystematic mispredictions of futureutility


51 Models of Hyperbolic Discounting

In the economics literature R HStrotz (1955ndash56) was the first to con-sider alternatives to exponential dis-counting seeing ldquono reason why anindividual should have such a specialdiscount functionrdquo (p 172) MoreoverStrotz recognized that for any discountfunction other than exponential aperson would have time-inconsistentpreferences18 He proposed two strate-gies that might be employed by a per-son who foresees how her preferenceswill change over time the ldquostrategy ofprecommitmentrdquo (wherein she commitsto some plan of action) and the ldquostrat-egy of consistent planningrdquo (whereinshe chooses her behavior ignoring plansthat she knows her future selves willnot carry out)19 While Strotz did notposit any specific alternative functionalforms he did suggest that ldquospecialattentionrdquo be given to the case ofdeclining discount rates

Motivated by the evidence discussedin section 41 there has been a recentsurge of interest among economists inthe implications of declining discountrates (beginning with David Laibson1994 1997) This literature has used aparticularly simple functional form whichcaptures the essence of hyperbolicdiscounting

D(k) =igraveiacuteicirc

1bdk

if h = 0if k gt 0

This functional form was first introducedby E S Phelps and Pollak (1968) tostudy intergenerational altruism and wasfirst applied to individual decision mak-

ing by Jon Elster (1979) It assumes thatthe per-period discount rate betweennow and the next period is 1 bd

bdwhereas

the per-period discount rate betweenany two future periods is 1 d

dlt 1 bd

bd

Hence this (bd) formulation assumes adeclining discount rate between this pe-riod and next but a constant discountrate thereafter The (bd) formulation ishighly tractable and captures many ofthe qualitative implications of hyperbolicdiscounting

Laibson and his collaborators haveused the (bd) formulation to explorethe implications of hyperbolic discount-ing for consumption-saving behaviorHyperbolic discounting leads a personto consume more than she would likefrom a prior perspective (or equiva-lently to under-save) Laibson (1997)explores the role of illiquid assets suchas housing as an imperfect commit-ment technology emphasizing how aperson could limit overconsumption bytying up her wealth in illiquid assetsLaibson (1998) explores consumption-saving decisions in a world without illiq-uid assets (or any other commitmenttechnology) These papers describe howhyperbolic discounting might explainsome stylized empirical facts such asthe excess comovement of income andconsumption the existence of asset-spe-cific marginal propensities to consumelow levels of precautionary savings andthe correlation of measured levels ofpatience with age income and wealthLaibson Andrea Repetto and JeremyTobacman (1998) and George-MariosAngeletos et al (2001) calibrate modelsof consumption-saving decisions usingboth exponential discounting and (bd)hyperbolic discounting By comparingsimulated data to real-world data theydemonstrate how hyperbolic discount-ing can better explain a variety ofempirical observations in the consump-tion-saving literature In particular

18 Strotz implicitly assumes stationary discount-ing

19 Building on Strotzrsquos strategy of consistentplanning some researchers have addressed thequestion of whether there exists a consistent pathfor general non-exponential discount functions See in particular Robert Pollak (1968) BezalelPeleg and Menahem Yaari (1973) and StevenGoldman (1980)


Angeletos et al (2001) describe howhyperbolic discounting can explainthe coexistence of high preretirementwealth low liquid asset holdings (rela-tive to income levels and illiquid assetholdings) and high credit-card debt

Carolyn Fischer (1999) andOrsquoDonoghue and Rabin (1999c 2001)have applied (bd) preferences to pro-crastination where hyperbolic discount-ing leads a person to put off an onerousactivity more than she would like from aprior perspective20 OrsquoDonoghue andRabin (1999c) examine the implicationsof hyperbolic discounting for contract-ing when a principal is concerned withcombating procrastination by an agentThey show how incentive schemes withldquodeadlinesrdquo may be a useful screeningdevice to distinguish efficient delay frominefficient procrastination OrsquoDonoghueand Rabin (2001) explore procrastina-tion when a person must not onlychoose when to complete a task butalso which task to complete They showthat a person might never carry out avery easy and very good option becausethey continually plan to carry out aneven better but more onerous optionFor instance a person might never takehalf an hour to straighten the shelves inher garage because she persistentlyplans to take an entire day to do a majorcleanup of the entire garage Extendingthis logic they show that providing peo-ple with new options might make pro-crastination more likely If the personrsquosonly option were to straighten theshelves she might do it in a timelymanner but if the person can eitherstraighten the shelves or do the majorcleanup she now may do nothingOrsquoDonoghue and Rabin (1999d) applythis logic to retirement planning

OrsquoDonoghue and Rabin (1999a 2000) Jonathan Gruber and BotondKoszegi (2000) and Juan D Carrillo(1999) have applied (bd) preferencesto addiction These researchers de-scribe how hyperbolic discounting canlead people to overconsume harmfuladdictive products and examine thedegree of harm caused by such over-consumption Carrillo and ThomasMariotti (2000) and Roland Benabouand Jean Tirole (2000) have examinedhow (bd) preferences might influence apersonrsquos decision to acquire informa-tion If for example a person is decid-ing whether to embark on a specificresearch agenda she may have the op-tion to get feedback from colleaguesabout its likely fruitfulness The stan-dard economic model implies that peo-ple should always choose to acquire thisinformation if it is free However Car-rillo and Mariotti show that hyperbolicdiscounting can lead to ldquostrategic igno-rancerdquomdasha person with hyperbolic dis-counting who is worried about with-drawing from an advantageous course ofaction when the costs become imminentmight choose not to acquire free infor-mation if doing so increases the risk ofbailing out

511 Self Awareness

A person with time-inconsistent pref-erences may or may not be aware thather preferences will change over timeStrotz (1955ndash56) and Pollak (1968)discussed two extreme alternatives Atone extreme a person could be com-pletely ldquonaiumlverdquo and believe that herfuture preferences will be identicalto her current preferences At theother extreme a person could be com-pletely ldquosophisticatedrdquo and correctlypredict how her preferences willchange over time While casual observa-tion and introspection suggest that

20 While not framed in terms of hyperbolic dis-counting George Akerlofrsquos (1991) model of pro-crastination is formally equivalent to a hyperbolicmodel


people lie somewhere in between thesetwo extremes behavioral evidence re-garding the degree of awareness isquite limited

One way to identify sophistication isto look for evidence of commitmentSomeone who suspects that her prefer-ences will change over time might takesteps to eliminate an option that seemsinferior now but might tempt her laterFor example someone who currentlyprefers $110 in 31 days to $100 in 30days but who suspects that in a monthshe will prefer $100 immediately to$110 tomorrow might attempt to elimi-nate the $100 reward from the laterchoice set and thereby bind herselfnow to receive the $110 reward in 31days Real-world examples of commit-ment include ldquoChristmas clubsrdquo or ldquofatfarmsrdquo

Perhaps the best empirical demon-stration of a preference for commit-ment was conducted by Dan Ariely andKlaus Wertenbroch (2002) In thatstudy MIT executive-education stud-ents had to write three short papersfor a class and were assigned to oneof two experimental conditions In onecondition deadlines for the three pa-pers were imposed by the instructorand were evenly spaced across the se-mester In the other condition eachstudent was allowed to set her owndeadlines for each of the three papersIn both conditions the penalty fordelay was 1 percent per day late re-gardless of whether the deadline wasexternally or self-imposed Althoughstudents in the free-choice conditioncould have made all three papers due atthe end of the semester many did infact choose to impose deadlines onthemselves suggesting that they ap-preciated the value of commitmentFew students chose evenly spaceddeadlines however and those whodid not performed worse in the course

than those with evenly spaced dead-lines (whether externally imposed orself-imposed)21

OrsquoDonoghue and Rabin (1999b) ex-amine how peoplersquos behaviors dependon their sophistication about their owntime inconsistency Some behaviors suchas using illiquid assets for commit-ment require some degree of sophisti-cation Other behaviors such as over-consumption or procrastination aremore robust to the degree of aware-ness though the degree of misbehaviormay depend on the degree of sophisti-cation To understand such effectsOrsquoDonoghue and Rabin (2001) intro-duce a formal model of partial naiumlveteacutein which a person is aware that she willhave future self-control problems butunderestimates their magnitude Theyshow that severe procrastination cannotoccur under complete sophisticationbut can arise even if the person is onlya little naiumlve For more discussion onself-awareness see OrsquoDonoghue andRabin (in press)

The degree of sophistication versusnaiveteacute has important implications forpublic policy If people are sufficientlysophisticated about their own self-control problems providing commit-ment devices may be beneficial How-ever if people are naiumlve policiesmight be better aimed at either edu-cating people about loss of control(making them more sophisticated) orproviding incentives for people touse commitment devices even ifthey donrsquot recognize the need forthem

21 A similar ldquonaturalrdquo experiment was recentlyconducted by the Economic and Social ResearchCouncil of Great Britain They recently eliminatedsubmission deadlines and now accept grant pro-posals on a ldquorollingrdquo basis (though they are stillreviewed only periodical ly) In response to thispolicy change submissions have actually declinedby about 15ndash20 percent (direct correspondencewith Chris Caswill at ESRC)


52 Models That Enrich theInstantaneous Utility Function

Many discounting anomalies espe-cially those in section 42 can be un-derstood as a misspecification of theinstantaneous utility function Similarlymany of the confounds we discuss insection 6 are caused by researchers at-tributing to the discount rate aspects ofpreference that are more appropriatelyconsidered as arguments in the instan-taneous utility function As a resultalternative models of intertemporalchoice have been advanced that add ad-ditional arguments such as utility fromanticipation to the instantaneous utilityfunction

521 Habit-Formation Models

James Duesenberry (1952) was thefirst economist to propose the idea ofldquohabit formationrdquomdashthat the utility fromcurrent consumption (ldquotastesrdquo) can beaffected by the level of past consump-tion This idea was more formally devel-oped by Pollak (1970) and Harl Ryderand Geoffrey Heal (1973) In habit for-mation models the period-t instantane-ous utility function takes the formu(ctct 1ct 2) where para2u curren paract paract cent gt 0for tcent lt t For simplicity most suchmodels assume that all effects of pastconsumption for current utility enterthrough a state variable That is theyassume that period-t instantaneous util-ity function takes the form u(ctzt)where zt is a state variable that is in-creasing in past consumption andpara2 curren paractparazt gt 0 Both Pollak (1970) andRyder and Heal (1973) assume that zt isthe exponentially weighted sum of pastconsumption or zt = aring i = 1

yen g ict iAlthough habit formation is often

said to induce a preference for an in-creasing consumption profile it canunder some circumstances lead a per-son to prefer a decreasing or even non-

monotonic consumption profi le The di-rection of the effect depends on thingssuch as how much one has already con-sumed (as reflected in the initial habitstock) and perhaps most importantlywhether current consumption increasesor decreases future utility

In recent years habit-formation mod-els have been used to analyze a varietyof phenomena Gary Becker and KevinMurphy (1988) use a habit-formationmodel to study addictive activities andin particular to examine the effects ofpast and future prices on the currentconsumption of addictive products22

Habit formation can help explain asset-pricing anomalies such as the equity-premium puzzle (Andrew Abel 1990 JohnCampbell and John Cochrane 1999George M Constantinides 1990) Incor-porating habit formation into business-cycle models can improve their abilityto explain movements in asset prices(Urban Jermann 1998 Michele BoldrinLawrence Christiano and Jonas Fisher2001) Some recent papers have shownthat habit formation may help explainother empirical puzzles in macro-economics as well Whereas standardgrowth models assume that high savingrates cause high growth recent evi-dence suggests that the causality canrun in the opposite direction Christo-pher Carroll Jody Overland and DavidWeil (2000) show that under conditionsof habit formation high growth ratescan cause people to save more JeffreyFuhrer (2000) shows how habit forma-tion might explain the recent findingthat aggregate spending tends to have agradual ldquohump-shapedrdquo response to

22 For rational-choice models building onBecker and Murphyrsquos framework see AthanasiosOrphanides and David Zervos (1995) Ruqu Wang(1997) and Suranovic Goldfarb and Leonard(1999) For addiction models that incorporatehyperbolic discounting see OrsquoDonoghue andRabin (1999a 2000) Gruber and Koszegi (2000)and Carrillo (1999)


various shocks The key feature of habitformation that drives many of these re-sults is that after a shock consumptionadjustment is sluggish in the short termbut not in the long term

522 Reference-Point Models

Closely related to but conceptuallydistinct from habit-formation modelsare models of reference-dependent util-ity which incorporate ideas from pros-pect theory (Kahneman and Tversky1979 Tversky and Kahneman 1991)According to prospect theory outcomesare evaluated using a value function de-fined over departures from a referencepointmdashin our notation the period-t in-stantaneous utility function takes theform u(ctrt) = v(ct ndash rt) The referencepoint rt might depend on past con-sumption expectations social compari-son status quo and such A secondfeature of prospect theory is that thevalue function exhibits loss aversionmdashnegative departures from onersquos refer-ence consumption level decrease utilityby a greater amount than positive de-partures increase it A third feature ofprospect theory is that the value func-tion exhibitsmdashdiminishing sensitivity forboth gains and losses which means thatthe value function is concave over gainsand convex over losses23

Loewenstein and Prelec (1992) ap-plied a specialized version of such avalue function to intertemporal choiceto explain the magnitude effect thesign effect and the delay-speedup

asymmetry They show that if the elas-ticity of the value function is increasingin the magnitude of outcomes peoplewill discount smaller magnitudes morethan larger magnitudes Intuitively theelasticity condition captures the insightthat people are responsive to both dif-ferences and ratios of reward amountsIt implies that someone who is indiffer-ent between say $10 now and $20 in ayear should prefer $200 in a year over$100 now because the larger rewardshave a greater difference (and the sameratio) Consequently even if a personrsquostime preference is actually constantacross outcomes she will be more will-ing to wait for a fixed proportional in-crement when rewards are larger andthus her imputed discount rate will besmaller for larger outcomes Similarlyif the value function for losses is moreelastic than the value function for gainsthen people will discount gains morethan losses Finally such a model helpsexplain the delay-speedup asymmetry(Loewenstein 1988) Shifting consump-tion in any direction is made less desir-able by loss aversion since one losesconsumption in one period and gains itin another When delaying consump-tion loss aversion reinforces time dis-counting creating a powerful aversionto delay When expediting consumptionloss aversion opposes time discountingreducing the desirability of speedup(and occasionally even causing anaversion to it)

Using a reference-dependent modelthat assumes loss aversion in consump-tion David Bowman Deborah Mine-hart and Rabin (1999) predict thatldquonewsrdquo about onersquos (stochastic) futureincome affects onersquos consumptiongrowth differently than the standardPermanent Income Hypothesis predictsAccording to (the log-linear version of)the Permanent Income Hypothesischanges in future income should not

23 Reference-point models sometimes assumethere is a direct effect of the consumption level orreference level so that u(ctrt) = v(ct rt) + w(ct) oru(ctrt) = v(ct rt) + w(rt) Some habit-formationmodels could be interpreted as reference-pointmodels where the state variable zt is the refer-ence point Indeed many habit-formation modelssuch as Pollak (1970) and Constantinides (1990)assume instantaneous utility functions of the formu(ct zt) although they typically assume neitherloss aversion nor diminishing sensitivity


affect the rate of consumption growthFor example if a person finds out thather permanent income will be lowerthan she formerly thought she wouldreduce her consumption by say 10 per-cent in every period leaving her con-sumption growth unchanged If how-ever this person were loss averse incurrent consumption she would be un-willing to reduce this yearrsquos consump-tion by 10 percentmdashforcing her to re-duce future consumption by more than10 percent and thereby reducing thegrowth rate of her consumption Twostudies by John Shea (1995a b) supportthis prediction Using both aggregateUS data and data from teachersrsquounions (in which wages are set one yearin advance) Shea finds that consump-tion growth responds more strongly tofuture wage decreases than to futurewage increases

523 Models Incorporating Utility from Anticipation

Some alternative models build on thenotion of ldquoanticipalrdquo utility discussed bythe elder and younger Jevons If peoplederive pleasure not only from currentconsumption but also from anticipatingfuture consumption then current in-stantaneous utility will depend posi-tively on future consumptionmdashthat isthe period-t instantaneous utility func-tion would take the form u(ctct + 1ct + 2frac14) where parau curren paract cent gt 0 for tcent gt tLoewenstein (1987) advanced a formalmodel which assumes that a personrsquos in-stantaneous utility is equal to the utilityfrom consumption in that period plussome function of the discounted utilityof consumption in future periods Spe-cifically if we let v(c) denote utilityfrom actual consumption and assumethis is the same for all periods then

u(ctct + 1ct + 2frac14) = v(ct) + a[gv(ct + 1) + g 2v(ct + 2) + frac14] for some g lt 1

Loewenstein describes how utilityfrom anticipation may play a role inmany DU anomalies Because near-termconsumption delivers only consumptionutility whereas future consumption de-livers both consumption utility and an-ticipatory utility anticipatory utilityprovides a reason to prefer improve-ment and for getting unpleasant out-comes over with quickly instead ofdelaying them as discounting wouldpredict It provides a possible explana-tion for why people discount differentgoods at different rates because utilityfrom anticipation creates a downward biason estimated discount rates and this down-ward bias is larger for goods that createmore anticipatory utility If for instancedreading future bad outcomes is astronger emotion than savoring futuregood outcomes which seems highlyplausible then utility from anticipationwould generate a sign effect24

Finally anticipatory utility gives riseto a form of time inconsistency that isquite different from that which arisesfrom hyperbolic discounting Instead ofplanning to do the farsighted thing(eg save money) but subsequently do-ing the shortsighted thing (splurging)anticipatory utility can cause people torepeatedly plan to consume a good aftersome delay that permits pleasurableanticipation but then to delay againfor the same reason when the plannedmoment of consumption arrives

Loewensteinrsquos model of anticipatoryutility applies to deterministic out-comes In a recent paper Caplin andLeahy (2001) point out that many an-ticipatory emotions such as anxiety or

24 Waiting for undesirable outcomes is almostalways unpleasant but waiting for desirable out-comes is sometimes pleasurable and sometimesfrustrating Despite the manifest importance forintertemporal choice of these emotions associatedwith waiting we are aware of no research that hassought to understand when waiting for desirableoutcomes is pleasurable or aversive


suspense are driven by uncertaintyabout the future and they propose anew model that modifies expected-utility theory to incorporate such antici-patory emotions They then show thatincorporating anxiety into asset-pricingmodels may help explain the equity pre-mium puzzle and the risk-free rate puz-zle because anxiety creates a taste forrisk-free assets and an aversion to riskyassets Like Loewenstein Caplin andLeahy emphasize how anticipatory util-ity can lead to time inconsistencyKoszegi (2001) also discusses someimplications of anticipatory utility

524 Visceral Influences

A final alternative model of the utilityfunction incorporates ldquovisceralrdquo influ-ences such as hunger sexual desirephysical pain cravings and suchLoewenstein (1996 2000b) argues thateconomics should take more seriouslythe implications of such transientfluctuations in tastes Formally visceralinfluences mean that the personrsquosinstantaneous utility function takesthe form u(ctdt) where dt representsthe vector of visceral states in period tVisceral states are (at least to someextent) endogenousmdasheg a personrsquoscurrent hunger depends on how muchshe has consumed in previous periodsmdashand therefore lead to consumptioninterdependence

Visceral influences have importantimplications for intertemporal choicebecause by increasing the attractive-ness of certain goods or activities theycan give rise to behaviors that look ex-tremely impatient or even impulsiveIndeed for every visceral influence itis easy to think of one or more associ-ated problems of self-controlmdashhungerand dieting sexual desire and variousldquoheat-of-the-momentrdquo behaviors crav-ing and drug addiction and so on Vis-ceral influences provide an alternate

account of the preference reversals thatare typically attr ibuted to hyperbolictime discounting because the temporalproximity of a reward is one of thecues that can activate appetitive visceralstates (see Laibson 2001 Loewenstein1996) Other cuesmdashsuch as spatial prox-imity the presence of associated smellsor sounds or similarity in current set-ting to historical consumption sitesmdashmay also have such an effect Thusresearch on various types of cues mayhelp to generate new predictions aboutthe specific circumstances (other thantemporal proximity) that can triggermyopic behavior

The fact that visceral states areendogenous introduces issues ofstate-management (as discussed byLoewenstein 1999 and Laibson 2001under the rubric of ldquocue managementrdquo)While the model (at least the rationalversion of it) predicts that a personwould want herself to use drugs if shewere to experience a sufficiently strongcraving it also predicts that she mightwant to prevent ever experiencingsuch a strong craving Hence visceralinfluences can give rise to a preferencefor commitment in the sense that theperson may want to avoid certainsituations

Visceral influences may do more thanmerely change the instantaneous utilityfunction First there is evidence thatpeople donrsquot fully appreciate the effectsof visceral influences and hence maynot react optimally to them (Loewen-stein 1996 1999 2000b) When in a hotstate people tend to exaggerate howlong the hot state will persist and whenin a cold state people tend to underesti-mate how much future visceral influ-ences will affect their future behaviorSecond and perhaps more importantlypeople often would ldquopreferrdquo not to re-spond to an intense visceral factor suchas rage fear or lust even at the


moment they are succumbing to its in-fluence A way to understand such ef-fects is to apply the distinction pro-posed by Kahneman (1994) betweenldquoexperienced utilityrdquo which reflectsonersquos welfare and ldquodecision utilityrdquowhich reflects the attractiveness of op-tions as inferred from onersquos decisionsBy increasing the decision utility of cer-tain types of actions more than theexperienced utility of those actions vis-ceral factors may drive a wedge be-tween what people do and what makesthem happy Douglas Bernheim andAntonio Rangel (2001) propose a modelof addiction framed in these terms

53 More ldquoExtremerdquo AlternativePerspectives

The alternative models discussedabove modify the DU model by alteringthe discount function or adding addi-tional arguments to the instantaneousutility function The alternatives dis-cussed next involve more radicaldepartures from the DU model

531 Projection Bias

In many of the alternative models ofutility discussed above the personrsquosutility from consumptionmdashher tastesmdashchange over time To properly make in-tertemporal decisions a person mustcorrectly predict how her tastes willchange Essentially all economic modelsof changing tastes assume (as econo-mists typically do) that such predictionsare correctmdashthat people have ldquorationalexpectationsrdquo However LoewensteinOrsquoDonoghue and Rabin (2000) proposethat while people may anticipate thequalitative nature of their changingpreferences they tend to underestimatethe magnitude of these changesmdashasystematic misprediction they labelprojection bias

Loewenstein OrsquoDonoghue and Rabinreview a broad array of evidence that

demonstrates the prevalence of projec-tion bias and then model it formallyTo illustrate their model consider pro-jection bias in the realm of habit forma-tion As discussed above suppose theperiod-t instantaneous utility functiontakes the form u(ctzt) where zt is a statevariable that captures the effects of pastconsumption Projection bias arises whena person whose current state is zt mustpredict her future utility given futurestate zt Projection bias implies that thepersonrsquos prediction u~(ctzt | zt) will liebetween her true future utility u(ctzt)and her utility given her current stateu(ctzt) A particularly simple functionalform is u~(ctzt | zt) = (1 a)u(ctzt) + au(ctzt)for some a Icirc[01]

Projection bias may arise whenevertastes change over time whetherthrough habit formation changing ref-erence points or changes in visceralstates It can have important behavioraland welfare implications For instancepeople may underappreciate the degreeto which a present consumption splurgewill raise their reference consumptionlevel and thereby decrease their enjoy-ment of more modest consumption lev-els in the future When intertemporalchoices are influenced by projection biasestimates of time preference may bedistorted

532 Mental-Accounting Models

Some researchers have proposed thatpeople do not treat all money as fungi-ble but instead assign different types ofexpenditures to different ldquomental ac-countsrdquo (see Thaler 1999 for a recentoverview) Such models can give rise tointertemporal behaviors that seem oddwhen viewed through the lens of theDU model Thaler (1985) for instancesuggests that small amounts of moneyare coded as spending money whereaslarger amounts of money are codedas savings and that a person is more


willing to spend out of the former ac-count This accounting rule would pre-dict that people will behave like spend-thrifts for small purchases (eg a newpair of shoes) but act more frugallywhen it comes to large purchases (ega new dining-room table)25 ShlomoBenartzi and Thaler (1995) suggest thatpeople treat their financial portfol ios asa mental account and emphasize theimportance of how often people ldquoevalu-aterdquo this account They argue that ifpeople review their portfolios once ayear or so and if people experience joyor pain from any gains or losses as as-sumed in Kahneman and Tverskyrsquos(1979) prospect theory then such ldquomy-opic loss aversionrdquo represents a plausi-ble explanation for the equity premiumpuzzle

Prelec and Loewenstein (1998) pro-pose another way in which mental ac-counting might influence intertemporalchoice They posit that payments forconsumption confer immediate disutil-ity or ldquopain of payingrdquo and that peoplekeep mental accounts that link the con-sumption of a particular item with thepayments for it They also assume thatpeople engage in ldquoprospective account-ingrdquo According to prospective account-ing when consuming people think onlyabout current and future payments pastpayments donrsquot cause pain of payingLikewise when paying the pain of pay-ing is buffered only by thoughts offuture but not past consumption Themodel suggests that different ways of fi-nancing a purchase can lead to different

decisions even holding the net presentvalue of payments constant Similarly aperson might have different financingpreferences depending on the con-sumption item (eg they should preferto prepay for a vacation that is con-sumed all at once vs a new car that isconsumed over many years) The modelgenerates a strong preference for pre-payment (except for durables) for get-ting paid after rather than before doingwork and for fixed-fee pricing schemeswith zero marginal costs over pay-as-you-go schemes that tightly couple mar-ginal payments to marginal consumptionThe model also suggests that interindi-vidual heterogeneity might arise fromdifferences in the degree to which peo-ple experience the pain of paying ratherthan differences in time preference Onthis view the miser who eschews afancy restaurant dinner is not doing sobecause she explicitly considers thedelayed costs of the indulgence butrather because her enjoyment of thedinner would be diminished by theimmediate pain of paying for it

533 Choice Bracketing

One important aspect of mental ac-counting is that a person makes at mosta few choices at any one time and gen-erally ignores the relation betweenthese choices and other past and futurechoices Which choices are consideredat the same time is a matter of whatRead Loewenstein and Rabin (1999)label ldquochoice bracketingrdquo Intertempo-ral choices like other choices can beinfluenced by the manner in which theyare bracketed because different brack-eting can highlight different motivesTo illustrate consider the conflict be-tween impatience and a preference forimprovement over time Loewensteinand Prelec (1993) demonstrate that therelative importance of these two mo-tives can be altered by the way that

25 While it seems possible that this conceptual -ization could explain the magnitude effect as wellthe magnitude effect is found for very ldquosmallrdquoamounts (eg between $2 and $20 in Ainslie andHaendel 1983) and for very ldquolarge amountsrdquo (egbetween $10000 and $1000000 in Raineri andRachlin 1993) It seems highly unlikely that re-spondents would consistent ly code the loweramounts as spending and the higher amounts assavings across all of these studies


choices are bracketed They asked onegroup of subjects to choose betweenhaving dinner at a fine French restau-rant in one month vs two months Mostsubjects chose one month presumablyreflecting impatience They then askedanother group to choose between eatingat home in one month followed by eatingat the French restaurant in two monthsvs eating at the French restaurant in onemonth followed by eating at home in twomonths The majority now wanted theFrench dinner in two months For bothgroups dinner at home was the mostlikely alternative to the French dinnerbut it was only when the two dinnerswere expressed as a sequence that thepreference for improvement became abasis for decision

Analyzing how people frame orbracket choices may help illuminate theissue of whether a preference for im-provement merely reflects the com-bined effect of other motives such asreference dependence or anticipatoryutility or whether it is somethingunique Viewed from an integrateddecision-making perspective it perhapsseems natural to conclude that the pref-erence for improvement is derivative ofthese other concepts because it is notclear why improvement for its own sakeshould be valuable But when viewedfrom a choice-bracketing perspectivewherein a person must have some choiceheuristic for evaluating sequences itseems possible that improvement maybe valued for its own sake Specificallya preference-for-improvement choiceheuristic may have originated from con-siderations of reference dependence oranticipatory utility but a person usingthis choice heuristic may come to feelthat improvement for its own sake hasvalue26

Loewenstein and Prelec (1993) de-velop a (choice-heuristic) model for howpeople evaluate choices over sequencesThey assume that people consider asequencersquos discounted utility its degreeof improvement and its degree ofspread The key ingredients of themodel are ldquogestaltrdquo definitions for im-provement and spread In other wordsthey develop a formal measure of thedegree of improvement and the degreeof spread for any sequence They showthat their model can explain a widerange of sequence anomalies includingobserved violations of independenceand that it predicts preferences be-tween sequences much better thanother models that incorporate similarnumbers of free parameters (even amodel with an entirely flexible timediscount function)

534 Multiple-Self Models

An influential school of theorists haveproposed models that view intertempo-ral choice as the outcome of a conflictbetween multiple selves Most multiple-self models postulate myopic selves whoare in conflict with more farsightedones and often draw analogies betweenintertemporal choice and a variety ofdifferent models of interpersonal strate-gic interactions Some models (egAinslie and Nick Haslam 1992 Thomas

26 Thus to the extent that the preference forimprovement reflects a choice heuristic it shouldbe susceptible to framing or bracketing effects

because what constitutes a sequence is highly sub-jective as noted by Loewenstein and Prelec 1993and by John G Beebe-Center (1929) several de-cades earlier

What enables one to decide whether a givenset of affective experiences does or does notconstitute a unitary temporal group what of series involving experiences of differ-ent modalitiesmdash visual and auditory ex-periences for instance And what ofsuch complex events as ldquoarising in the morn-ingrdquo or ldquoeating a good mealrdquo or ldquoenjoying agood bookrdquo (Beebe-Center 1929 p 67emphasis added)


C Schelling 1984 Gordon C Winston1980) assume that there are two agentsone myopic and one farsighted who al-ternately take control of behavior Themain problem with this approach is thatit fails to specify why either type ofagent emerges when it does Further-more by characterizing the interactionas a battle between the two agentsthese models fail to capture an impor-tant asymmetry farsighted selves oftenattempt to control the behaviors of my-opic selves but never the reverse Forinstance the farsighted self may pourvodka down the drain to prevent to-morrowrsquos self from drinking it but themyopic self rarely takes steps to ensurethat tomorrowrsquos self will have access tothe alcohol he will then crave

Responding in part to this problemThaler and Hersh Shefrin (1981) pro-posed a ldquoplanner-doerrdquo model thatdraws upon principal-agent theory Intheir model a series of myopic ldquodoersrdquowho care only about their own immedi-ate gratification (and have no affinityfor future or past doers) interact with aunitary ldquoplannerrdquo who cares equallyabout the present and future Themodel focuses on the strategies em-ployed by the planner to control thebehavior of the doers The model high-lights the observation later discussed atlength by Loewenstein (1996) that thefarsighted perspective is often muchmore constant than the myopic perspec-tive For example people are often con-sistent in recognizing the need to main-tain a diet Yet they periodically violatetheir own desired course of actionmdashoften recognizing even at the momentof doing so that they are not behavingin their own self-interest

Yet a third type of multiple-selfmodel draws connections between inter-temporal choice and models of multi-person strategic interactions (Elster1985) The essential insight that these

models capture is that much like coop-eration in a social dilemma self-controloften requires the cooperation of a se-ries of temporally situated selves Whenone self ldquodefectsrdquo by opting for immedi-ate gratification the consequence canbe a kind of unraveling or ldquofalling offthe wagonrdquo when subsequent selvesfollow the precedent

Few of these multiple-self modelshave been expressed formally and evenfewer have been used to derive testableimplications that go much beyond theintuitions that inspired them in the firstplace However perhaps it is unfair tocriticize the models for these short-comings These models are probably bestviewed as metaphors intended to high-light specific aspects of intertemporalchoice Specifically multiple-self mod-els have been used to make sense ofthe wide range of self-control strategiesthat people use to regulate their ownfuture behavior Moreover these mod-els provided much of the inspiration formore recent formal models of sophisti-cated hyperbolic discounting (followingLaibson 1994 1997)

535 Temptation Utility

Most models of intertemporal choicemdashindeed most models of choice in anyframeworkmdashassume that options notchosen are irrelevant to a personrsquos well-being In a recent paper Gul andPesendorfer (2001) posit that peoplehave ldquotemptation preferencesrdquo whereinthey experience disutility from notchoosing the option that is most enjoy-able now Their theory implies that aperson might be better off if someparticularly tempting option were notavailable even if she doesnrsquot choosethat option As a result she may be will-ing to pay in advance to eliminate thatoption or in other words she may havea preference for commitment


536 Conclusion Combining Insightsfrom Different Models

Many behavioral models of intertem-poral choice focus on a single modifica-tion to the DU model and explore theadditional realism produced by thatsingle modification But many empiricalphenomena reflect the interaction ofmultiple phenomena For instance apreference for improvement may inter-act with hyperbolic discounting to pro-duce preferences for U-shaped sequencesmdasheg for jobs that offer a signing bonusand a salary that increases graduallyover time As discussed by Loewensteinand Prelec (1993) in the short termthe preference-for-improvement motiveis swamped by the high discount ratesbut as the discount rate falls over timethe preference-for-improvement motivemay gain ascendance and cause a netpreference for an increasing paymentsequence

As another example introducing vis-ceral influences into models of hyper-bolic discounting may more fully accountfor the phenomenology of impulsivechoices Hyperbolic-discounting modelspredict that people respond especiallystrongly to immediate costs and benefitsand visceral influences have powerfultransient effects on immediate utilitiesIn combination the two assumptions couldexplain a wide range of impulsive choicesand other self-control phenomena

6 Measuring Time Discounting

The DU model assumes that a per-sonrsquos time preference can be capturedby a single discount rate r Over thepast three decades there have beenmany attempts to measure this rateSome of these estimates are derivedfrom observations of ldquoreal-worldrdquo be-haviors (eg the choice between elec-trical appliances that differ in theirinitial purchase price and long-run op-

erating costs) Others are derived fromexperimental elicitation procedures(eg respondentsrsquo answers to the ques-tion ldquoWhich would you prefer $100today or $150 one year from todayrdquo)Table 1 summarizes the implicit dis-count rates from all studies that wecould locate in which discount rateswere either directly reported or easilycomputed from the reported data

Figure 2 plots the estimated discountfactor for each study against the publi-cation date for that study where the dis-count factor is d = 1(1 + r)27 This figurereveals three noteworthy observationsFirst there is tremendous variability inthe estimates (the corresponding im-plicit annual discount rates range fromndash6 percent to infinity) Second in con-trast to estimates of physical phenom-ena such as the speed of light there isno evidence of methodological progressthe range of estimates is not shrinkingover time Third high discountingpredominates as most of the datapoints are well below 1 which repre-sents equal weighting of present andfuture

In this section we provide an over-view and critique of this empirical lit-erature with an eye toward under-standing these three observations Wefirst discuss a variety of confoundingfactors such as intertemporal arbitrageuncertainty and expectations of chang-ing utility functions These considera-tions typically are not regarded as legiti-mate components of time preferenceper se but they can affect both experi-mental responses and real-world choicesWith these confounding factors inmind we then review the proceduresused to estimate discount rates Thissection reiterates our general theme Totruly understand intertemporal choices

27 In some cases the estimates are computedfrom the median respondent In other cases theauthors reported the mean discount rate


TABLE 1EMPIRICAL ESTIMATES OF DISCOUNT RATES

Study Type Good(s) Real or Hypo Elicitation Method

Maital amp Maital 1978 experimental money amp coupons hypo choiceHausman 1979 field money real choiceGateley 1980 field money real choiceThaler 1981 experimental money hypo matchingAinslie amp Haendel 1983 experimental money real matchingHouston 1983 experimental money hypo otherLoewenstein 1987 experimental money amp pain hypo pricingMoore and Viscusi 1988 field life years real choiceBenzion et al 1989 experimental money hypo matchingViscusi amp Moore 1989 field life years real choiceMoore amp Viscusi 1990a field life years real choiceMoore amp Viscusi 1990b field life years real choiceShelley 1993 experimental money hypo matchingRedelmeier amp Heller 1993 experimental health hypo ratingCairns 1994 experimental money hypo choiceShelley 1994 experimental money hypo ratingChapman amp Elstein 1995 experimental money amp health hypo matchingDolan amp Gudex 1995 experimental health hypo otherDreyfus and Viscusi 1995 field life years real choiceKirby amp Marakovic 1995 experimental money real matchingChapman 1996 experimental money amp health hypo matchingKirby amp Marakovic 1996 experimental money real choicePender 1996 experimental rice real choiceWahlund amp Gunnarson 1996 experimental money hypo matchingCairns amp van der Pol 1997 experimental money hypo matchingGreen Myerson amp McFadden 1997

experimental money hypo choice

Johanneson amp Johansson 1997

experimental life years hypo pricing

Kirby 1997 experimental money real pricingMadden et al 1997 experimental money amp heroin hypo choiceChapman amp Winquist 1998 experimental money hypo matchingHolden Shiferaw amp Wik 1998

experimental money amp corn real matching

Cairns amp van der Pol 1999 experimental health hypo matchingChapman Nelson amp Hier 1999

experimental money amp health hypo choice

Coller amp Williams 1999 experimental money real choiceKirby Petry amp Bickel 1999 experimental money real choicevan der Pol amp Cairns 1999 experimental health hypo choiceChesson amp Viscusi 2000 experimental money hypo matchingGaniats et al 2000 experimental health hypo choiceHesketh 2000 experimental money hypo choicevan der Pol amp Cairns 2001 experimental health hypo choiceWarner amp Pleeter 2001 field money real choiceHarrison Lau amp Williams 2002

experimental money real choice

TABLE 1 (Cont)

Study Time Range Annual Discount Rate(s)Annual Discount

Factor(s)

Maital amp Maital 1978 1 year 70 059Hausman 1979 undefined 5 to 89 095 to 053Gateley 1980 undefined 45 to 300 069 to 025Thaler 1981 3 mos to 10 yrs 7 to 345 093 to 022Ainslie amp Haendel 1983 undefined 96000 to yen 000Houston 1983 1 yr to 20 yrs 23 081Loewenstein 1987 immediately to 10 yrs ndash6 to 212 106 to 032Moore and Viscusi 1988 undefined 10 to 12 091 to 089Benzion et al 1989 6 mos to 4 yrs 9 to 60 092 to 063Viscusi amp Moore 1989 undefined 11 090Moore amp Viscusi 1990a undefined 2 098Moore amp Viscusi 1990b undefined 1 to 14 099 to 088Shelley 1993 6 mos to 4 yrs 8 to 27 093 to 079Redelmeier amp Heller 1993 1 day to 10 yrs 0 100Cairns 1994 5 yrs to 20 yrs 14 to 25 088 to 080Shelley 1994 6 mos to 2 yrs 4 to 22 096 to 082Chapman amp Elstein 1995 6 mos to 12 yrs 11 to 263 090 to 028Dolan amp Gudex 1995 1 month to 10 yrs 0 100Dreyfus and Viscusi 1995 undefined 11 to 17 090 to 085Kirby amp Marakovic 1995 3 days to 29 days 3678 to yen 003 to 000Chapman 1996 1 yr to 12 yrs negative to 300 101 to 025Kirby amp Marakovic 1996 6 hours to 70 days 500 to 1500 017 to 006Pender 1996 7 mos to 2 yrs 26 to 69 079 to 059Wahlund amp Gunnarson 1996 1 month to 1 yr 18 to 158 085 to 039Cairns amp van der Pol 1997 2 yrs to 19 yrs 13 to 31 088 to 076Green Myerson amp McFadden 1997

3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097

Kirby 1997 1 day to 1 month 159 to 5747 039 to 002Madden et al 1997 1 week to 25 yrs 8 to yen 093 to 000Chapman amp Winquist 1998 3 months 426 to 2189 019 to 004Holden Shiferaw amp Wik 1998

1 yr 28 to 147 078 to 040

Cairns amp van der Pol 1999 4 yrs to 16 yrs 6 094Chapman Nelson amp Hier 1999

1 month to 6 mos 13 to 19000 088 to 001

Coller amp Williams 1999 1 month to 3 mos 15 to 25 087 to 080Kirby Petry amp Bickel 1999 7 days to 186 days 50 to 55700 067 to 000van der Pol amp Cairns 1999 5 yrs to 13 yrs 7 093Chesson amp Viscusi 2000 1 year to 25 yrs 11 090Ganiats et al 2000 6 mos to 20 yrs negative to 116 101 to 046Hesketh 2000 6 mos to 4 yrs 4 to 36 096 to 074van der Pol amp Cairns 2001 2 yrs to 15 yrs 6 to 9 094 to 092Warner amp Pleeter 2001 immediately to 22 yrs 0 to 71 0 to 058Harrison Lau amp Williams 2002

1 month to 37 mos 28 078

one must recognize the influence ofmany considerations besides pure timepreference

61 Confounding Factors

A wide variety of procedures havebeen used to estimate discount ratesbut most apply the same basic ap-proach Some actual or reported in-tertemporal preference is observed andresearchers then compute the discountrate that this preference implies usinga ldquofinancialrdquo or net present value (NPV)calculation For instance if a persondemonstrates indifference between 100widgets now and 120 widgets in oneyear the implicit (annual) discountrate r would be 20 percent becausethat value would satisfy the equation100 = (1(1 + r))120 Similarly if aperson is indifferent between an ineffi-cient low-cost appliance and a moreefficient one that costs $100 extra butsaves $20 a year in electricity over thenext ten years the implicit discountrate r would equal 151 percent be-cause that value would satisfy theequation 100 = St = 1

10 (1 curren (1 + r)) t20Although this is an extremely wide-

spread approach for measuring discountrates it relies on a variety of additional(and usually implicit) assumptions and issubject to several confounding factors

611 Consumption Reallocation

The calculation outlined above as-sumes a sort of ldquoisolationrdquo in decisionmaking Specifically it treats the ob-jects of intertemporal choice as dis-crete unitary dated events it assumesthat people entirely ldquoconsumerdquo the re-ward (or penalty) at the moment it isreceived as if it were an instantaneousburst of utility Furthermore it assumesthat people donrsquot shift consumptionaround over time in anticipation of thereceipt of the future reward or penaltyThese assumptions are rarely exactlycorrect and may sometimes be badapproximations Choosing between $50today versus $100 next year or choos-ing between 50 pounds of corn todayversus 100 pounds next year are notthe same as choosing between 50 utilstoday and 100 utils on the same daynext year as the calculations implyRather they are more complex choicesbetween the various streams of con-sumption that those two dated rewardsmake possible

612 Intertemporal Arbitrage

In theory choices between tradablerewards such as money should not re-veal anything about time preferencesAs Victor Fuchs (1982) and others havenoted if capital markets operate effec-tively (if monetary amounts at differenttimes can be costlessly exchanged at aspecified interest rate) choices be-tween dated monetary outcomes can bereduced to merely selecting the rewardwith the greatest net present value(using the market interest rate)28 To

10

08

06

04

02

00

Figure 2 Discount Factor by Year of Study Publication

1975

impu

ted

disc

ount

fact

or

1980year of publication

1985 1990 1995 2000

28 Meyer (1976) expresses this point ldquo if wecan lend and borrow at the same rate thenwe can simply show that regardless of the funda-mental orderings on the crsquos [consumptionstreams] the induced ordering on the xrsquos [se-quences of monetary flows] is given by simple dis-counting at this given rate We could say thatthe market assumes command and the market rateprevails for monetary flowsrdquo


illustrate suppose a person prefers$100 now to $200 ten years from nowWhile this preference could be ex-plained by imputing a discount rate onfuture utility the person might bechoosing the smaller immediate amountbecause she believes that throughproper investment she can turn it intomore than $200 in ten years and thusenjoy more than $200 worth of con-sumption at that future time The pres-ence of capital markets should causeimputed discount rates to converge onthe market interest rate

Studies that impute discount ratesfrom choices among tradable rewardsassume that respondents ignore oppor-tunities for intertemporal arbitrageeither because they are unaware ofcapital markets or unable to exploitthem29 The latter assumption maysometimes be correct For instance infield studies of electrical-appliance pur-chases some subjects may have facedborrowing constraints that preventedthem from purchasing the more expen-sive energy-efficient appliances Moretypically however imperfect capitalmarkets cannot explain choices theycannot explain why a person who holdsseveral thousand dollars in a bank ac-count earning 4-percent interest shouldprefer $100 today over $150 in oneyear Because imputed discount ratesdo not in fact converge on the prevail-

ing market interest rates but insteadare much higher it seems that many re-spondents are neglecting capital mar-kets and basing their choices on someother consideration such as time pref-erence or the uncertainty associatedwith delay

613 Concave Utility

The standard approach to estimatingdiscount rates assumes that the utilityfunction is linear in the magnitude ofthe choice objects (eg amounts ofmoney pounds of corn duration of somehealth state) If instead the utilityfunction for the good in question isconcave estimates of time preferencewill be biased upward For exampleindifference between $100 this year and$200 next year implies a dollar discountrate of 100 percent However if theutility of acquiring $200 is less thantwice the utility of acquiring $100 theutility discount rate will be less than100 percent This confound is rarelydiscussed perhaps because utility is as-sumed to be approximately linear overthe small amounts of money commonlyused in time-preference studies Theoverwhelming evidence for reference-dependent utility suggests howeverthat this assumption may be invalidmdashthat people may not be integrating thestated amounts with their current andfuture wealth and therefore that curva-ture in the utility function may besubstantial even for these smallamounts (see Ian Bateman et al 1997David W Harless and Colin F Camerer1994 Kahneman and Tversky 1979Rabin 2000 Rabin and Thaler 2001Tversky and Kahneman 1991)

Three techniques could be used toavoid this confound (1) One could re-quest direct utility judgments (eg at-tractiveness ratings) of the same conse-quence at two different times Thenthe ratio of the attractiveness rating of

29 Arguments about violations of the discountedutility model assume as Pender (1996 pp 282ndash83) notes ldquothat the results of discount rate ex-periments reveal something about intertemporalpreferences directly However if agents are opti-mizing an intertemporal utility function their op-portunities for intertemporal arbitrage are alsoimportant in determining how they respond tosuch experiments when tradable rewards areoffered one must either abandon the assumptionthat respondents in experimental studies are opti-mizing or make some assumptions (either implicitor explicit) about the nature of credit markets Theimplicit assumption in some of the previous stud-ies of discount rates appears to be that there areno possibilities for intertemporal arbitrage rdquo


the distant outcome to the proximateoutcome would directly reveal the im-plicit discount factor (2) To the extentthat utility is linear in probability onecan use choices or judgment tasks in-volving different probabilities of thesame consequence at different times(Alvin E Roth and J Keith Murnighan1982) Evidence that probability isweighted nonlinearly (see eg Starmer2000) would of course cast doubt onthis approach (3) One can separatelyelicit the utility function for the good inquestion and then use that function totransform outcome amounts into utilityamounts from which utility discountrates could be computed To our knowl-edge Chapman (1996) conducted theonly study that attempted to do this Shefound that utility discount rates weresubstantially lower than the dollar dis-count rates because utility was stronglyconcave over the monetary amountssubjects used in the intertemporalchoice tasks30

614 Uncertainty

In experimental studies subjects aretypically instructed to assume that de-layed rewards will be delivered withcertainty It is unclear whether subjectsdo (or can) accept this assumption becausedelay is ordinarilymdashand perhaps un-avoidablymdashassociated with uncertaintyA similar problem arises for field stud-ies in which it is typically assumed thatsubjects believe that future rewardssuch as energy savings will materializeBecause of this subjective (orldquoepistemicrdquo) uncertainty associated withdelay it is difficult to determine towhat extent the magnitude of imputed

discount rates (or the shape of the dis-count function) is governed by timepreference per se versus the diminu-tion in subjective probability associatedwith delay31

Empirical evidence suggests that in-troducing objective (or ldquoaleatoryrdquo) un-certainty to both current and future re-wards can dramatically affect estimateddiscount rates For instance GideonKeren and Peter Roelofsma (1995)asked one group of respondents tochoose between 100 florins (a Nether-lands unit of currency) immediately and110 florins in one month and anothergroup to choose between a 50-percentchance of 100 florins immediately and a50-percent chance of 110 florins in onemonth While 82 percent preferred thesmaller immediate reward when bothrewards were certain only 39 percentpreferred the smaller immediate rewardwhen both rewards were uncertain32

Also Albrecht and Weber (1996) foundthat the present value of a future lottery(eg a 50-percent chance of receiving250 deutsche marks) tended to exceed thepresent value of its certainty equivalent

615 Inflation

The standard approach assumes thatfor instance $100 now and $100 in fiveyears generate the same level of utility atthe times they are received However

30 Chapman also found that magnitude effectswere much smaller after correcting for utilityfunction curvature This result supports Loewen-stein and Prelecrsquos (1992) explanation of magnitudeeffects as resulting from utility function curvature(see section 522)

31 There may be complicated interactions be-tween risk and delay because uncertainty aboutfuture receipt complicates and impedes the plan-ning of onersquos future consumption stream (MichaelSpence and Richard Zeckhauser 1972) For exam-ple a 90-percent chance to win $10000000 infifteen years is worth much less than a guaranteeto receive $9000000 at that time because to theextent that the person cannot insure against theresidual uncertainty there is a limit to how muchshe can adjust her consumption level during thosefifteen years

32 This result cannot be explained by a magni-tude effect on the expected amounts because 50percent of a reward has a smaller expected valueand according to the magnitude effect should bediscounted more not less


inflation provides a reason to devaluefuture monetary outcomes because inthe presence of inflation $100 worth ofconsumption now is more valuable than$100 worth of consumption in fiveyears This confound creates an upwardbias in estimates of the discount rateand this bias will be more or less pro-nounced depending on subjectsrsquo ex-periences with and expectations aboutinflation

616 Expectations of Changing Utility

A reward of $100 now might also gen-erate more utility than the same amountfive years hence because a person ex-pects to have a larger baseline con-sumption level in five years (eg due toincreased wealth) As a result the mar-ginal utility generated by an additional$100 of consumption in five years maybe less than the marginal utility gener-ated by an additional $100 of consump-tion now Like inflation this confoundcreates an upward bias in estimates ofthe discount rate

617 Habit Formation AnticipatoryUtility and Visceral Influences

To the extent that the discount rate ismeant to reflect only time preferenceand not the confluence of all factorsinfluencing intertemporal choice themodifications to the instantaneous util-ity function discussed in section 5 rep-resent additional biasing factors be-cause they are typically not accountedfor when the discount rate is imputedFor instance if anticipatory utility moti-vates one to delay consumption morethan one otherwise would the imputeddiscount rate will be lower than thetrue degree of time preference If aperson prefers an increasing consump-tion profi le due to habit formation thediscount rate will be biased downwardFinally if the prospect of an immediatereward momentarily stimulates visceral

factors that temporarily increase thepersonrsquos valuation of the proximate re-ward the discount rate could be biasedupward33

618 An Illustrative Example

To illustrate the difficulty of sepa-rating time preference per se fromthese potential confounds consider aprototypical study by Benzion Rapoportand Yagil (1989) In this study respon-dents equated immediate sums of moneyand larger delayed sums (eg theyspecified the reward in six months thatwould be as good as getting $1000 im-mediately) In the cover story for thequestionnaire respondents were askedto imagine that they had earned money(amounts ranged from $40 to $5000) butwhen they arrived to receive the paymentthey were told that the ldquofinanciallysolidrdquo public institute is ldquotemporarilyshort of fundsrdquo They were asked tospecify a future amount of money (de-lays ranged from six months to fouryears) that would make them indiffer-ent to the amount they had been prom-ised to receive immediately Surely thedescription ldquofinancially solidrdquo couldscarcely be sufficient to allay uncertain-ties that the future reward would actu-ally be received (particularly given thatthe institute was ldquotemporarilyrdquo short offunds) and it seems likely that re-sponses included a substantial ldquoriskpremiumrdquo Moreover the subjects inthis study had ldquoextensive experiencewith a three-digit inflation raterdquo

33 It is unclear whether visceral factors shouldbe considered a determinant of time preference ora confoundin g factor in its estimation If visceralfactors increase the attractiveness of an immediatereward without affecting its experienced enjoy-ment (if they increase wanting but not liking)they are probably best viewed as a legitimatedeterminant of time perference If howevervisceral factors alter the amount of utility that acontemplated proximate reward actually deliversthey might best be regarded as a confoundingfactor


and respondents might well have con-sidered inflation when generating theirresponses Even if respondents assumedno inflation the real interest rate dur-ing this time was positive and theymight have considered intertemporalarbitrage Finally respondents may haveconsidered that their future wealthwould be greater and that the later re-ward would therefore yield less mar-ginal utility Indeed the instructionscued respondents to consider this asthey were told that the questions didnot have correct answers and that theanswers ldquomight vary from one individ-ual to another depending on his or herpresent or future financial assetsrdquo

Given all of these confounding fac-tors is it unclear exactly how much ofthe imputed annual discount rates(which ranged from 9 percent to 60 per-cent) actually reflected time prefer-ence It is possible that the responses inthis study (and others) can be entirelyexplained in terms of these confoundsand that once these confounds are con-trolled for no ldquopurerdquo time preferencewould remain

62 Procedures for Measuring DiscountRates

We discussed above several con-founding factors that greatly complicatethe assignment of a discount rate to aparticular choice or judgment Withthese confounds in mind we next dis-cuss the methods that have been usedto measure discount rates Broadlythese methods can be divided into twocategories field studies in which dis-count rates are inferred from economicdecisions that people make in their or-dinary life and experimental studies inwhich people are asked to evaluate styl-ized intertemporal prospects involvingreal or hypothetical outcomes The dif-ferent procedures are each subject tothe confounds discussed above and as

we shall discuss are also influencedby a variety of other factors that aretheoretically irrelevant but which cangreatly affect the imputed discountrate

621 Field Studies

Some researchers have estimated dis-count rates by identifying real-worldbehaviors that involve tradeoffs be-tween the near future and more distantfuture Early studies of this type exam-ined consumersrsquo choices among differ-ent models of electrical applianceswhich presented purchasers with atradeoff between the immediate pur-chase price and the long-term costs ofrunning the appliance (as determined byits energy effic iency) In these studiesthe discount rates implied by consum-ersrsquo choices vastly exceeded market in-terest rates and differed substantiallyacross product categories The implicitdiscount rate was 17ndash20 percent for airconditioners (Jerry Hausman 1979) 102percent for gas water heaters 138 per-cent for freezers 243 percent for elec-tric water heaters (H Ruderman M DLevine and J E McMahon 1987) andfrom 45 percent to 300 percent forrefrigerators depending on assump-tions made about the cost of electricity(Dermot Gately 1980) 34

34 These findings illustrate how people seem toignore intertemporal arbitrage As Hausman(1979) noted it does not make sense for anyonewith positive savings to discount future energy sav-ings at rates higher than the market interest rateOne possible explanation for these results is thatpeople are liquidity constrained Consistent withsuch an account Hausman found that the discountrate varied markedly with incomemdashit was 39 per-cent for households with under $10000 of incomebut just 89 percent for households earning be-tween $25000 and $35000 However conflictingwith this finding a study by Douglas Houston(1983) that presented individuals with a decisionof whether to purchase a hypothetical ldquoenergy-savingrdquo device found that income ldquoplayed no sta-tistically significant role in explaining the level ofdiscount raterdquo


Another set of studies imputes dis-count rates from wage-risk tradeoffs inwhich individuals decide whether toaccept a riskier job with a higher salarySuch decisions involve a tradeoff be-tween quality of life and expected lengthof life The more that future utility isdiscounted the less important is lengthof life making risky but high-payingjobs more attractive From such trade-offs W Kip Viscusi and Michael Moore(1989) concluded that workersrsquo implicitdiscount rate with respect to future lifeyears was approximately 11 percentLater using different econometric ap-proaches with the same data set Mooreand Viscusi (1990a) estimated the dis-count rates to be around 2 percent andMoore and Viscusi (1990b) concludedthat the discount rate was somewherebetween 1 percent and 14 percentMark Dreyfus and Viscusi (1995) ap-plied a similar approach to auto-safetydecisions and estimated discount ratesranging from 11 percent to 17 percent

In the macroeconomics literature re-searchers have imputed discount ratesby estimating structural models of life-cycle saving behavior For instanceEmily Lawrence (1991) used Eulerequations to estimate household timepreferences across different socioeco-nomic groups She estimated the dis-count rate of median-income house-holds to be between 4 percent and 13percent depending on the specificationChristopher Carroll (1997) criticizesEuler-equation estimation on thegrounds that most households tend toengage mainly in ldquobuffer-stockrdquo savingearly in their livesmdashthey save primarilyto be prepared for emergenciesmdashandonly conduct ldquoretirementrdquo saving lateron Recent papers have estimated richcalibrated stochastic models in whichhouseholds conduct buffer-stock savingearly in life and retirement saving laterin life Using this approach Carroll and

Andrew Samwick (1997) report pointestimates for the discount rate rangingfrom 5 percent to 14 percent andPierre-Olivier Gourinchas and JonathanParker (2001) report point estimates of40ndash45 percent Field studies of thistype have the advantage of not assum-ing isolation because integrated deci-sion making is built into the model Butsuch estimates often depend heavily onthe myriad assumptions included in thestructural model35

Recently John Warner and SaulPleeter (2001) analyzed decisions madeby US military servicemen As part ofmilitary downsizing over 60000 mili-tary employees were given the choicebetween a one-time lump-sum pay-ment and an annuity payment The sizesof the payments depended on the em-ployeersquos current salary and number ofyears of servicemdasheg an ldquoE-5rdquo withnine years of service could choose be-tween $22283 now vs $3714 everyyear for eighteen years In general thepresent value of the annuity paymentequaled the lump-sum payment for adiscount rate of 175 percent Althoughthe interest rate was only 7 percent atthe time of these decisions over half ofall military officers and over 90 percentof enlisted personnel chose the lump-sum payment36 This study is particu-larly compelling in terms of credibilityof reward delivery magnitude of stakesand number of subjects37

35 These macroeconomi cs studies are not in-cluded in the tables and figures which focus pri-marily on individual level choice data

36 It should be noted however that the guaran-teed payments in the annuity program were notindexed for inflation which averaged 42 percentduring the four years preceding this choice

37 Warner and Pleeter (2001) noted that ifeveryone had chosen the annuity payment thepresent value of all payments would have been$42 billion Given the choices however thepresent value of the government payout was just25 billion Thus offering the lump-sum alternativesaved the federal government $17 billion dollars


The benefit of field studies as com-pared with experimental studies istheir high ecological validity There isno concern about whether estimateddiscount rates would apply to real be-havior because they are estimated fromsuch behavior But field studies are sub-ject to additional confounds due to thecomplexity of real-world decisions andthe inability to control for some impor-tant factors For example the high dis-count rates implied by the widespreaduse of inefficient electrical appliancesmight not result from the discounting offuture cost savings per se but fromother considerations including (1) alack of information among consumersabout the cost savings of the more effi-cient appliances (2) a disbelief amongconsumers that the cost savings will beas great as promised (3) a lack of ex-pertise in translating available informa-tion into economically efficient deci-sions or (4) hidden costs of the moreefficient appliances such as reducedconvenience or reliability or in the caseof light bulbs because the more effi-cient bulbs generate a less aestheticallypleasing light spectra38

622 Experimental Studies

Given the difficulties of interpretingfield data the most common methodol-ogy for eliciting discount rates is to so-licit ldquopaper-and-pencilrdquo responses tothe prospect of real and hypothetical re-wards and penalties Four experimentalprocedures are commonly used choicetasks matching tasks pricing tasks andratings tasks

Choice tasks are the most commonexperimental method for eliciting dis-count rates In a typical choice tasksubjects are asked to choose between a

smaller more immediate reward and alarger more delayed reward Of coursea single choice between two intertem-poral options only reveals an upper orlower bound on the discount ratemdashforexample if a person prefers 100 unitsof something today over 120 units ayear from today the choice merely im-plies a discount rate of at least 20 per-cent per year To identify the discountrate more precisely researchers oftenpresent subjects with a series of choicesthat vary the delay or the amount of therewards Some studies use real rewardsincluding money rice and corn Otherstudies use hypothetical rewards includ-ing monetary gains and losses and moreor less satisfying jobs available atdifferent times (See table 1 for a list ofthe procedures and rewards used in thedifferent studies)

Like all experimental elicitation pro-cedures the results from choice taskscan be affected by procedural nuancesA prevalent problem is an anchoringeffect when respondents are asked tomake multiple choices between imme-diate and delayed rewards the firstchoice they face often influences sub-sequent choices For instance peoplewould be more prone to choose $120next year over $100 immediately if theyfirst chose between $100 immediatelyand $103 next year than if they firstchose between $100 immediately and$140 next year In general imputed dis-count rates tend to be biased in the di-rection of the discount rate that wouldequate the first pair of options to whichthey are exposed (see Donald Green etal 1998) Anchoring effects can beminimized by using titration proceduresthat expose respondents to a series ofopposing anchorsmdasheg (1) $100 todayor $101 in one year (2) $100 today or$10000 in one year (3) $100 today or$105 in one year and so on Becausetitration procedures typically only offer

38 For a criticism of the hidden-costs explana-tion however see Jonathan Koomey and AlanSanstad (1994) and Richard Howarth and Sanstad(1995)


choices between an immediate rewardand a greater future reward howevereven these procedures communicate torespondents that they should be dis-counting and potentially bias discountrates upward

Matching tasks are another popularmethod for eliciting discount rates Inmatching tasks respondents ldquofill in theblankrdquo to equate two intertemporaloptions (eg $100 now = _____ inone year) Matching tasks have beenconducted with real and hypotheticalmonetary outcomes and with hypotheti-cal aversive health conditions (again seetable 1 for a list of the procedures andrewards used in different studies)Matching tasks have two advantagesover choice tasks First because sub-jects reveal an indifference point anexact discount rate can be imputedfrom a single response Second becausethe intertemporal options are not fullyspecified there is no anchoring prob-lem and no suggestion of an expecteddiscount rate (or range of discount rates)Thus unlike choice tasks matching taskscannot be accused of simply recoveringthe expectations of the experimentersthat guided the experimental design

Although matching tasks have someadvantages over choice tasks there arereasons to be suspicious of the re-sponses obtained First responses oftenappear to be governed by the applica-tion of some simple rule rather than bytime preference For example whenpeople are asked to state the amount inn years that equals $100 today a verycommon response is $100 n Secondthe responses are often very ldquocoarserdquomdashoften multiples of two or ten of the im-mediate reward suggesting that respon-dents do not (or cannot) think verycarefully about the task Third andmost importantly there are large differ-ences in imputed discount rates amongseveral theoretically equivalent proce-

dures Two intertemporal options couldbe equated or matched in one of fourways Respondents could be asked tospecify (1) the amount of a delayed re-ward that would make it as attractiveas a given immediate reward (which isthe most common technique) (2) theamount of an immediate reward thatmakes it as attractive as a given delayedreward (Albrecht and Weber 1996) (3)the maximum length of time they wouldbe willing to wait to receive a larger re-ward in lieu of an immediately availablesmaller reward (Ainslie and Haendel1983 Roelofsma 1994) or (4) the latestdate at which they would accept asmaller reward in lieu of receiving alarger reward at a specified date that islater still

While there is no theoretical basis forpreferring one of these methods overany other the small amount of empiri-cal evidence comparing different meth-ods suggests that they yield very differ-ent discount rates Roelofsma (1994)found that implicit discount rates variedtremendously depending on whether re-spondents matched on amount or timeOne group of subjects was asked to in-dicate how much compensation theywould demand to allow a purchased bi-cycle to be delivered nine months lateThe median response was 250 florinsAnother group was asked how long theywould be willing to delay delivery of thebicycle in exchange for 250 florins Themean response was only three weeksimplying a discount rate that is twelvetimes higher Frederick and Read (2002)found that implicit discount rates weredramatically higher when respondentsgenerated the future reward that wouldequal a specified current reward thanwhen they generated a current rewardthat would equal a specified future re-ward Specifically when respondentswere asked to state the amount in thirtyyears that would be as good as getting


$100 today the median response was$10000 (implying that a future dollar is1100 th as valuable) but when asked tospecify the amount today that is as goodas getting $100 in thirty years the me-dian response was $50 (implying that afuture dollar is 12 as valuable)

Two other experimental proceduresinvolve rating or pricing temporal pros-pects In rating tasks each respondentevaluates an outcome occurring at aparticular time by rating its attractive-ness or aversiveness In pricing tasks each respondent specifies a willingnessto pay to obtain (or avoid) some real orhypothetical outcome occurring at aparticular time such as a monetary re-ward dinner coupons an electric shockor an extra year added to the end ofonersquos life (Once again see table 1 for alist of the procedures and rewards usedin the different studies) Rating andpricing tasks differ from choice and match-ing tasks in one important respectWhereas choice and matching tasks callattention to time (because each respon-dent evaluates two outcomes occurring attwo different times) rating and pricingtasks permit time to be manipulated be-tween subjects (because a single respon-dent may evaluate either the immediateor delayed outcome by itself)

Loewenstein (1988) found that thetiming of an outcome is much less im-portant (discount rates are much lower)when respondents evaluate a single out-come at a particular time than whenthey compare two outcomes occurringat different times or specify the valueof delaying or accelerating an outcomeIn one study for example two groupsof students were asked how much theywould pay for a $100 gift certificate atthe restaurant of their choice Onegroup was told that the gift certificatewas valid immediately The other wastold it could be used beginning sixmonths from now There was no signifi-

cant difference in the valuation of thetwo certificates between the two groupswhich implies negligible discountingHowever when asked how much theywould pay [have to be paid] to use it sixmonths earlier [later] the timing be-came importantmdashthe delay group waswilling to pay $10 to expedite receipt ofthe delayed certificate while the imme-diate group demanded $23 to delay thereceipt of a certificate they expected tobe able to use immediately39

Another important design choice inexperimental studies is whether to usereal or hypothetical rewards The use ofreal rewards is generally desirable forobvious reasons but hypothetical re-wards actually have some advantages inthis domain In studies involving hypo-thetical rewards respondents can bepresented with a wide range of rewardamounts including losses and largegains both of which are generally infea-sible in studies involving real outcomesThe disadvantage of hypothetical choicedata is the uncertainty about whetherpeople are motivated to or capable ofaccurately predicting what they woulddo if outcomes were real

To our knowledge only two studieshave compared discounting betweenreal and hypothetical rewards Kirbyand Marakovic (1995) asked subjects tostate the immediate amount that wouldmake them indifferent to some fixed de-layed amount (delayed reward sizeswere $1475 $1725 $2100 $2450 $2850 delays were 3 7 13 17 23 and29 days) One group of subjects an-swered all thirty permutations for realrewards and another group of subjects

39 Rating tasks (and probably pricing tasks aswell) are subject to anchoring effects Shelley andThomas Omer (1996) Mary Kay Stevenson (1992)and others have found that a given delay (eg sixmonths) produces greater time discounting whenit is considered alongside shorter delays (eg onemonth) than when it is considered alongsidelonger delays (eg three years)


answered all thirty permutations forhypothetical rewards Discount rateswere lower for hypothetical rewards40

Maribeth Coller and Melonie Williams(1999) asked subjects to choose be-tween $500 payable in one month and$500 + $x payable in three monthswhere $x was varied from $167 to$9094 across fifteen different choicesIn one condition all choices were hypo-thetical in five other conditions oneperson was randomly chosen to receiveher preferred outcome for one of herfifteen choices The raw data suggestagain that discount rates were consid-erably lower in the hypothetical condi-tion although they suggest that thisconclusion is not supported after con-trolling for censored data demographicdifferences and heteroskedasticity(across demographic differences andacross treatments)41 Thus there is asof yet no clear evidence that hypotheti-cal rewards are discounted differentlythan real rewards42

63 Conclusion What Is TimePreference

Figure 2 reveals spectacular disagree-ment among dozens of studies that allpurport to be measuring time prefer-ence This lack of agreement likely re-flects the fact that the various elicita-tion procedures used to measure timepreference consistently fail to isolatetime preference and instead reflect tovarying degrees a blend of both puretime preference and other theoreticallydistinct considerations including (a)intertemporal arbitrage when tradeablerewards are used (b) concave utility (c)uncertainty that the future reward orpenalty will actually obtain (d) inflationwhen nominal monetary amounts are used(e) expectations of changing utility and(f) considerations of habit formationanticipatory utility and visceral influences

Figure 2 also reveals a predominanceof high implicit discount ratesmdashdis-count rates well above market interestrates This consistent finding may alsobe due to the presence of the variousextra-time-preference considerations listedabove because nearly all of these workto bias imputed discount rates upwardmdashonly habit formation and anticipatoryutility bias estimates downward If theseconfounding factors were adequatelycontrol led we suspect that many in-tertemporal choices or judgments wouldimply much lowermdashindeed possiblyeven zeromdashrates of time preference

Our discussion in this section high-lights the conceptual and semantic am-biguity about what the concept of ldquotimepreferencerdquo ought to includemdashaboutwhat properly counts as time prefer-ence per se and what ought to be calledsomething else (for further discussion

40 The two results were not strictly comparablehowever because they used a different procedurefor the real rewards than for the hypothetical re-wards An auction procedure was used for thereal-rewards group only Subjects were told thatwhoever of three subjects stated the lowest im-mediate amount would receive the immediateamount and the other two subjects would receivethe delayed amount Optimal behavior in such asituation involves overbidding Since this createsa downward bias in discount rates for the real-rewards group however it does not explain awaythe finding that real discount rates were higherthan hypothetical discount rates

41 It is hard to understand which control elimi-nates the differences that are apparent in the rawdata It would seem not to be the demographi cdifferences per se because the hypothetical condi-tion had a ldquosubstantially higher proportion of non-white participantsrdquo (p 121) and ldquonon-whites on av-erage reveal discount rates that are nearly 21percentage points higher than those revealed bywhitesrdquo (p 122)

42 There has been considerable recent debateoutside of the context of intertemporal choiceabout whether hypothetical choices are repre-sentative of decisions with real consequences Thegeneral conclusion from this debate is that the twomethods typically yield qualitatively similar results

(see Camerer and Robin Hogarth 1999 for a re-cent review) though systematic differences havebeen observed in some studies (Ronald CummingsGlenn Harrison and Elisabet Rutstrom 1995Yoram Kroll Haim Levy and Rapoport 1988)


see Frederick 1999) We have arguedhere that many of the reasons for caringwhen something occurs (eg uncer-tainty or utility of anticipation) are nottime preference because they pertainto the expected amount of utility conse-quences confer and not to the weightgiven to the utility of different moments(see figure 3 adapted from Frederick1999) However it is not obvious whereto draw the line between factors thatoperate through utilities and factorsthat make up time preference

Hopefully economists will eventuallyachieve a consensus about what isincluded in and excluded from theconcept of time preference Until thendrawing attention to the ambiguity ofthe concept will hopefully improve thequality of discourse by increasing aware-ness that in discussions about timepreference different people may be usingthe same term to refer to significantlydifferent underlying constructs43

7 Unpacking Time Preference

As detailed in section 2 early twentieth-century economistsrsquo conceptions of inter-temporal choice included detailedaccounts of disparate underlying psy-chological motives With the adventof the DU model in 1937 howevereconomists eschewed considerations ofspecific motives proceeding as if all in-tertemporal behavior could be explainedby the unitary construct of time prefer-ence In sections 5 and 6 we highlightedseveral factors that influence intertem-poral decisions but which would not beconsidered time preference as the termis ordinarily used In this section we turnour focus inward and question whethereven time preference itself should beregarded as a unitary construct

Issues of this type are hotly debatedin psychology For example psycholo-gists debate the usefulness of conceptu-alizing intelligence in terms of a singleunitary ldquogrdquo factor Typically a positedpsychological construct (or ldquotraitrdquo) isconsidered useful only if it satisfiesthree criteria (1) it remains relativelyconstant across time within a particularindividual (2) it predicts behavioracross a wide range of situations and(3) different measures of it correlatehighly with one another The concept ofintelligence satisfies these criteria fairlywell44 First performance in tests of

43 Not only do people use the same term to re-fer to different concepts (or sets of concepts) theyalso use different terms to represent the sameconcept The welter of terms used in discussionsof intertemporal choice include discount factordiscount rate marginal private rate of discountsocial discount rate utility discount rate marginalsocial rate of discount pure discounting timepreference subjective rate of time preferencepure time preference marginal rate of time pref-erence social rate of time preference overall timepreference impatience time bias temporal orien-tation consumption rate of interest time positivityinclination and ldquothe pure futurity effectrdquo JohnBroome (1995 pp 128ndash29) notes that some of the

controversy about discounting results from differ-ences in how the term is used ldquoOn the face of it typical economists and typical philosophersseem to disagree But actually I think there ismore misunderstanding here than disagreement When economists and philosophers think ofdiscounting they typically think of discounting dif-ferent things Economists typically discount thesorts of goods that are bought and sold in markets[whereas] philosophers are typically thinking of amore fundamental good peoplersquos well-being It is perfectly consistent to discount commoditie sand not well-beingrdquo

44 Debates remain however about whethertraditional measures exclude important dimen-sions and whether a multidimensional account of

Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth

future consequenceconfers less utility

Amountof utility

future utility isless important

diminishedidentity

impulsivity

Weightingof utility

d


cognitive ability at early ages correlateshighly with performance on such testsat all subsequent ages Second cogni-tive ability (as measured by such tests)predicts a wide range of important lifeoutcomes such as criminal behaviorand income Third abilities that we re-gard as expressions of intelligence correlatestrongly with each other Indeed whendiscussing the construction of intelligencetests Herrnstein and Charles Murray(1994 p 3) note that ldquoIt turned out tobe nearly impossible to devise itemsthat plausibly measured some cognitiveskill [which] were not positively corre-lated with other items that plausiblymeasured some cognitive skillrdquo

The posited construct of time prefer-ence does not fare as well by these cri-teria First no longitudinal studies havebeen conducted to permit any conclu-sions about the temporal stability oftime preference45 Second correlationsbetween various measures of time pref-erence or between measures of time

preference and plausible real-worldexpressions of it are modest at bestChapman and Elstein (1995) and Chap-man Richard Nelson and Daniel Hier(1999) found only weak correlationsbetween discount rates for money andfor health and Chapman and Elstein(1995) found almost no correlation be-tween discount rates for losses and forgains Fuchs (1982) found no correlationbetween a prototyp ical measure of timepreference (eg ldquoWould you choose$1500 now or $4000 in five yearsrdquo) andother behaviors that would plausibly beaffected by time preference (eg smok-ing credit-card debt seat-belt use andthe frequency of exercise and dentalcheckups) Nor did he find much corre-lation among any of these reported be-haviors (see also Nyhus 1995) 46 Chap-man and Elliot Coups (1999) found thatcorporate employees who chose to re-ceive an influenza vaccination did havesignificantly lower discount rates (as in-ferred from a matching task with mone-tary losses) but found no relationbetween vaccination behavior andhypothetical questions involving healthoutcomes Lalith Munasinghe andSicherman (2000) found that smokerstend to invest less in human capital(they have flatter wage profi les) andmany others have found that for stylizedintertemporal choices among monetaryrewards heroin addicts have higher dis-count rates (eg Leanne Alvos R AGregson and Michael Ross 1993 KirbyPetry and Bickel 1999 Gregory Mad-den et al 1997 Thomas Murphy andAlan De Wolfe 1986 Petry Bickel andMartha Arnett 1998)

Although the evidence in favor of asingle construct of time preferenceis hardly compelling the low cross-behavior correlations do not necessarily

intelligence would have even greater explanatorypower Robert Sternberg (1985) for example ar-gues that intelligence is usefully decomposed intothree dimensions (1) analytical intelligencewhich includes the ability to identify problemscompute strategies and monitor solutions and ismeasured well by existing IQ tests (2) creativeintelligence which reflects the ability to generateproblem-solving options and (3) practical intelli-gence which involves the ability to implementproblem-solving options

45 Although there have been no longitudinalstudies of time preference per se Mischel and hiscolleagues did find that a childrsquos capacity to delaygratification was significantly correlated with othervariables assessed decades later including aca-demic achievemen t and self esteem (Ozlem Ayduket al 2000 Mischel Yuichi Shoda and Peake1988 Shoda Mischel and Peake 1990) Of coursethis provides evidence for construct validity onlyto the extent that one views these other variablesas expressions of time preference We also notethat while there is little evidence that intertempo-ral behaviors are stable over long periods there issome evidence that time preference is not strictlyconstant over time for all people Heroin addictsdiscount both drugs and money more steeplywhen they are craving heroin than when they arenot (Louis Giordano et al 2001)

46 A similar lack of intraindividual consistencyhas been observed in risk-taking (KennethMacCrimmon and Donald Wehrung 1990)


disprove the existence of time prefer-ence Suppose for example that some-one expresses low discount rates on aconventional elicitation task yet indi-cates that she rarely exercises While itis possible that this inconsistency re-flects true heterogeneity in the degreeto which she discounts different typesof utility perhaps she rarely exercisesbecause she is so busy at work earningmoney for her future or because shesimply cares much more about her fu-ture finances than her future cardiovas-cular condition Or perhaps she doesnrsquotbelieve that exercise improves healthAs this example suggests many factorscould work to erode cross-behavior cor-relations and thus such low correlationsdo not mean that there can be no singleunitary time preference underlying allintertemporal choices (the intertempo-ral analog to hypothesized construct of ldquogrdquoin analyses of cognitive performance)However notwithstanding this dis-claimer in our view the cumulative evi-dence raises serious doubts about whetherthere is in fact such a constructmdasha sta-ble factor that operates identically on andapplies equally to all sources of utility47

To better understand the pattern ofcorrelations in implied discount ratesacross different types of intertemporalbehaviors we may need to unpack timepreference itself into more fundamentalmotives as illustrated by the segmenta-tion of the delta component of figure 3Loewenstein et al (2001) have pro-posed three specific constituent mo-tives which they labeled impulsivity(the degree to which an individual actsin a spontaneous unplanned fashion)compulsivity (the tendency to make

plans and stick with them) and inhibi-tion (the ability to inhibit the automaticor ldquoknee-jerkrdquo response to the appetitesand emotions that trigger impulsive be-havior)48 Preliminary evidence sug-gests that these subdimensions of timepreference can be measured reliablyMoreover the different subdimensionspredict different behaviors in a highlysensible way For example repetitivebehaviors such as flossing onersquos teethexercising paying onersquos bills on timeand arriving on time at meetings wereall predicted best by the compulsivitysubdimension Viscerally driven behav-iors such as reacting aggressively tosomeone in a car who honks at you at ared light were best predicted by impul-sivity (positively) and behavioral inhibi-tion (negatively) Money-related behav-iors such as saving money havingunpaid credit-card balances or beingmaxed out on one or more credit cardswere best predicted by conventionalmeasures of discount rates (but impul-sivity and compulsivity were also highlysignificant predictors)

Clearly further research is needed toevaluate whether time preference isbest viewed as a unitary construct or acomposite of more basic constituentmotives Further efforts hopefully willbe informed by recent discoveries ofneuroscientists who have identified re-gions of the brain whose damage leadsto extreme myopia (Antonio R Damasio1994) and areas that seem to play animportant role in suppressing the be-havioral expression of urges (Joseph E

47 Note that one can also overestimate thestrength of the relationship between measuredtime preference and time-related behaviors or be-tween different time-related behaviors if thesevariables are related to characteri stics such as in-telligence social class or social conformity thatare not adequately measured and controlled for

48 Recent research by Roy Baumeister ToddHeatherton and Diane Tice (1994) suggests thatsuch ldquobehavioral inhibitionrdquo requires an expendi-ture of mental effort that like other forms ofeffort draws on limited resourcesmdasha ldquopoolrdquo ofwillpower (Loewenstein 2000a) Their researchshows that behavioral inhibition in one domain(eg refraining from eating desirable food) re-duces the ability to exert willpower in another do-main (eg completing a taxing mental or physicaltask)


LeDoux 1996) If some behaviors arebest predicted by impulsivity some bycompulsivity some by behavioral inhi-bition and so on it may be worth theeffort to measure preferences at thislevel and to develop models that treatthese components separately Of coursesuch multidimensional perspectives willinevitably be more difficult to opera-tionalize than formulations like the DUmodel which represent time preferenceas a unidimensional construct

8 Conclusions

The DU model which continues tobe widely used by economists has littleempirical support Even its developersmdashSamuelson who originally proposed themodel and Koopmans who providedthe first axiomatic derivationmdashhad con-cerns about its descriptive realism andit was never empirically validated as theappropriate model for intertemporalchoice Indeed virtually every core andancillary assumption of the DU modelhas been called into question by empiri-cal evidence collected in the past twodecades The insights from this empiri-cal research have spawned new theoriesof intertemporal choice that revive manyof the psychological considerations dis-cussed by early students of intertempo-ral choicemdashconsiderations that were ef-fectively dismissed with the introductionof the DU model Additionally some ofthe most recent theories show that in-tertemporal behaviors may be dramaticallyinfluenced by peoplersquos level of under-standing of how their preferenceschangemdashby their ldquometaknowledgerdquo abouttheir preferences (see eg OrsquoDonoghueand Rabin 1999b LoewensteinOrsquoDonoghue and Rabin 2000)

While the DU model assumes that in-tertemporal preferences can be charac-terized by a single discount rate thelarge empirical literature devoted to

measuring discount rates has failed toestablish any stable estimate There isextraordinary variation across studiesand sometimes even within studiesThis failure is partly due to variations inthe degree to which the studies take ac-count of factors that confound the com-putation of discount rates (eg uncer-tainty about the delivery of futureoutcomes or nonlinearity in the utilityfunction) But the spectacular cross-study differences in discount rates alsoreflect the diversity of considerationsthat are relevant in intertemporalchoices and that legitimately affect dif-ferent types of intertemporal choicesdifferently Thus there is no reasonto expect that discount rates should beconsistent across different choices

The idea that intertemporal choicesreflect an interplay of disparate andoften competing psychological motiveswas commonplace in the writings ofearly twentieth-century economists Webelieve that this approach should beresurrected Reintroducing the multiple-motives approach to intertemporal choicewill help us to better understand andbetter explain the intertemporal choiceswe observe in the real world Forinstance it permits more scope forunderstanding individual differences(eg why one person is a spendthriftwhile his neighbor is a miser or whyone person does drugs while herbrother does not) because people maydiffer in the degree to which they ex-perience anticipatory utility or areinfluenced by visceral factors

The multiple-motive approach may beeven more important for understandingintra-individual differences When onelooks at the behavior of a single individ-ual across different domains there isoften a wide range of apparent attitudestoward the future Someone may smokeheavily but carefully study the returnsof various retirement packages Another


may squirrel money away while at thesame time giving little thought to elec-trical effic iency when purchasing an airconditioner Someone else may devotetwo decades of his life to establishing acareer and then jeopardize this long-term investment for some highly tran-sient pleasure Since the DU model as-sumes a unitary discount rate thatapplies to all acts of consumption suchintra-individual heterogeneities pose atheoretical challenge The multiple-motive approach by contrast allows usto readily interpret such differences interms of more narrow more legitimateand more stable constructsmdasheg thedegree to which people are skeptical ofpromises experience anticipatory util-ity are influenced by visceral factors orare able to correctly predict their futureutility

The multiple-motive approach maysound excessively open-ended We havedescribed a variety of considerationsthat researchers could potentially incor-porate into their analyses Includingevery consideration would be far toocomplicated while picking and choos-ing which considerations to incorporatemay leave one open to charges of beingad hoc How then should economistsproceed

We believe that economists shouldproceed as they typically do Economicshas always been both an art and a sci-ence Economists are forced to intuitto the best of their abilities which con-siderations are likely to be important ina particular domain and which are likelyto be largely irrelevant When econo-mists model labor supply for instancethey typically do so with a utility func-tion that incorporates consumption andleisure but when they model invest-ment decisions they typically assumethat preferences are defined overwealth Similarly a researcher investi-gating charitable giving might use a

utility function that incorporates altru-ism but not risk aversion or time prefer-ence whereas someone studying inves-tor behavior is unlikely to use a utilityfunction that incorporates altruism Foreach domain economists choose theutility function that is best able to in-corporate the essential considerationsfor that domain and then evaluatewhether the inclusion of specific con-siderations improves the predictive orexplanatory power of a model Thesame approach can be applied tomultiple-motive models of intertemporalchoice For drug addiction for exam-ple habit formation visceral factorsand hyperbolic discounting seem likelyto play a prominent role For extendedexperiences such as health states ca-reers and long vacations the prefer-ence for improvement is likely to comeinto play For brief vivid experiencessuch as weddings or criminal sanctionsutility from anticipation may be animportant determinant of behavior

In sum we believe that economistsrsquounderstanding of intertemporal choiceswill progress most rapidly by continuingto import insights from psychology byrelinquishing the assumption that thekey to understanding intertemporalchoices is finding the right discountrate (or even the right discount func-tion) and by readopting the view thatintertemporal choices reflect many dis-tinct considerations and often involvethe interplay of several competing mo-tives Since different motives may beevoked to different degrees by differentsituations (and by different descriptionsof the same situation) developing de-scriptively adequate models of in-tertemporal choice will not be easy Butwe hope this paper will help

REFERENCES

Abel Andrew 1990 ldquoAsset Prices Under HabitFormation and Catching Up with the JonesesrdquoAmer Econ Rev 80 pp 38ndash42


Ainslie George 1975 ldquoSpecious Reward A Be-havioral Theory of Impulsiveness and ImpulseControlrdquo Psych Bull 824 pp 463ndash96

Ainslie George and Varda Haendel 1983 ldquoTheMotives of the Willrdquo in Etiologic Aspects of Al-cohol and Drug Abuse E Gottheil K DurleyT Skodola and H Waxman eds SpringfieldIL Charles C Thomas pp 119ndash40

Ainslie George and Nick Haslam 1992 ldquoHyper-bolic Discountingrdquo in Choice Over TimeGeorge Loewenstein and Jon Elster eds NYRussell Sage pp 57ndash92

Ainslie George and Richard J Herrnstein 1981ldquoPreference Reversal and Delayed ReinforcementrdquoAnimal Learning Behavior 94 pp 476ndash82

Akerlof George A 1991 ldquoProcrastination andObedience rdquo Amer Econ Rev 812 pp 1ndash19

Albrecht Martin and Martin Weber 1995 ldquoHy-perbolic Discounting Models in PrescriptiveTheory of Intertemporal Choicerdquo ZeitschriftFur Wirtschafts-U Sozialwissenschaften 115Spp 535ndash68

mdashmdashmdash 1996 ldquoThe Resolution of Uncertainty AnExperimental Studyrdquo J Inst Theoretical Econ1524 pp 593ndash607

Alvos Leanne R A Gregson and Michael WRoss 1993 ldquoFuture Time Perspective in Cur-rent and Previous Injecting Drug Usersrdquo DrugAlcohol Depend 31 pp 193ndash97

Angeletos George-Marios David Laibson AndreaRepetto Jeremy Tobacman and Stephen Wein-berg 2001 ldquoThe Hyperboli c ConsumptionModel Calibration Simulation and EmpiricalEvaluation rdquo J Econ Perspect 153 pp 47ndash68

Ariely Daniel and Ziv Carmon 2002 ldquoPrefer-ences over Sequences of Outcomesrdquo in Timeand Decision Economic and Psychological Per-spectives on Intertemporal Choice GeorgeLoewenstein Daniel Read and Roy Baumeistereds NY Russell Sage (in press)

Ariely Daniel and Klaus Wertenbroch 2002ldquoProcrastination Deadlines and Performance Using Precommitment to Regulate Onersquos Be-haviorrdquo Psych Sci (in press)

Arrow Kenneth J 1983 ldquoThe Trade-Off BetweenGrowth and Equityrdquo in Social Choice and Jus-tice Collected Papers of Kenneth J ArrowKenneth J Arrow ed Cambridge MA BelknapPress pp 190ndash200

Ayduk Ozlem Rodolfo Mendoza-Denton WalterMischel G Downey Philip K Peake andMonica Rodriguez 2000 ldquoRegulating the Inter-personal Self Strategic Self-Regulation forCoping with Rejection Sensitivityrdquo J Personal-ity Social Psych 795 pp 776ndash92

Bateman Ian Alistair Munro Bruce RhodesChris Starmer and Robert Sugden 1997 ldquoATest of the Theory of Reference-DependentPreferencesrdquo Quart J Econ 1122 pp 479ndash505

Baumeister Roy F Todd F Heatherton and Di-ane M Tice 1994 Losing Control How andWhy People Fail at Self-Regulation San DiegoAcademic Press

Becker Gary And Kevin M Murphy 1988 ldquoATheory of Rational Addictionrdquo J Polit Econ964 pp 675ndash701

Beebe-Center John G 1929 ldquoThe Law of Affec-tive Equilibriumrdquo Amer J Psych 41 pp 54ndash69

Benabou Roland and Jean Tirole 2000 ldquoSelf-Confidence Intrapersonal Strategiesrdquo Prince-ton U discuss paper 209

Benartzi Shlomo and Richard H Thaler 1995ldquoMyopic Loss Aversion and the Equity Pre-mium Puzzlerdquo Quart J Econ 1101 pp 73ndash92

Benzion Uri Amnon Rapoport and Joseph Yagil1989 ldquoDiscount Rates Inferred From Deci-sions An Experimental Studyrdquo ManagementSci 35 pp 270ndash84

Bernheim Douglas and Antonio Rangel 2001ldquoAddiction Conditioning and the VisceralBrainrdquo Stanford U

Boumlhm-Bawerk Eugen Von (1889) 1970 Capitaland Interest South Holland Libertarian Press

Boldrin Michele Lawrence Christiano and JonasFisher 2001 ldquoHabit Persistence Asset Re-turns and the Business Cyclerdquo Amer EconRev 91 pp 149ndash66

Bowman David Deborah Minehart and MatthewRabin 1999 ldquoLoss Aversion in a Consumption-Savings Modelrdquo J Econ Behav Org 382 pp155ndash78

Broome John 1995 ldquoDiscounting the FuturerdquoPhilosophy and Public Affairs 20 pp 128ndash56

Cairns John A 1992 ldquoDiscounting and HealthBenefitsrdquo Health Econ 1 pp 76ndash79

mdashmdashmdash 1994 ldquoValuing Future Benefitsrdquo HealthEcon 3 pp 221ndash29

Cairns John A and Marjon M van der Pol 1997ldquoConstant and Decreasing Timing Aversion forSaving Livesrdquo Social Sci Med 4511 pp 1653ndash59

mdashmdashmdash 1999 ldquoDo People Value Their Own Fu-ture Health Differently Than Othersrsquo FutureHealthrdquo Med Decision Making 194 pp 466ndash72

Camerer Colin F and Robin M Hogarth 1999ldquoThe Effects of Financial Incentives in Experi-ments A Review and Capital-Labor ProductionFrameworkrdquo J Risk Uncertainty 19 pp 7ndash42

Campbell John and John Cochrane 1999 ldquoByForce of Habit A Consumption-Based Explana-tion of Aggregate Stock Market Behaviorrdquo JPolit Econ 107 pp 205ndash51

Caplin Andrew and John Leahy 2001 ldquoPsycho-logical Expected Utility Theory And Anticipa-tory Feelingsrdquo Quart J Econ 166 pp 55ndash79

Carrillo Juan D 1999 ldquoSelf-Control ModerateConsumption and Cravingrdquo CEPR discusspaper 2017

Carrillo Juan D and Thomas Mariotti 2000ldquoStrategic Ignorance as a Self-DiscipliningDevicerdquo Rev Econ Stud 673 pp 529ndash44

Carroll Christopher 1997 ldquoBuffer-Stock Savingand the Life CyclePermanent Income Hy-pothesisrdquo Quart J Econ 112 pp 1ndash55

Carroll Christopher Jody Overland and David


Weil 2000 ldquoSaving and Growth with HabitFormationrdquo Amer Econ Rev 90 pp 341ndash55

Carroll Christopher and Andrew Samwick 1997ldquoThe Nature of Precautionary Wealthrdquo JMonet Econ 40 pp 41ndash71

Chakravarty S 1962 ldquoThe Existence of an Opti-mum Savings Programrdquo Econometrica 301 pp178ndash87

Chapman Gretchen B 2000 ldquoPreferences for Im-proving and Declining Sequences of HealthOutcomesrdquo J Behav Decision Making 13 pp203ndash18

mdashmdashmdash 1996 ldquoTemporal Discounting and Utilityfor Health and Moneyrdquo J Exper Psych Learn-ing Memory Cognition 223 pp 771ndash91

Chapman Gretchen B and Elliot J Coups 1996ldquoTime Preferences and Preventive Health Be-havior Acceptance of the Influenza VaccinerdquoMed Decision Making 193 pp 307ndash14

Chapman Gretchen B and Arthur S Elstein1995 ldquoValuing the Future Temporal Discount-ing of Health and Moneyrdquo Med DecisionMaking 154 pp 373ndash86

Chapman Gretchen Richard Nelson and DanielB Hier 1999 ldquoFamiliarity and Time Prefer-ences Decision Making about Treatments forMigraine Headaches and Crohnrsquos Diseaserdquo JExper Psych Applied 51 pp 17ndash34

Chapman Gretchen B and Jennifer R Winquist1998 ldquoThe Magnitude Effect Temporal Dis-count Rates and Restaurant Tipsrdquo PsychonomicBull Rev 51 pp 119ndash23

Chesson Harrell and W Kip Viscusi 2000 ldquoTheHeterogeneity of Time-Risk Tradeoffsrdquo J Be-hav Decision Making 13 pp 251ndash58

Coller Maribeth and Melonie B Williams 1999ldquoEliciting Individual Discount Ratesrdquo ExperEcon 2 pp 107ndash27

Constantinides George M 1990 ldquoHabit Forma-tion A Resolution of the Equity Premium Puz-zlerdquo J Polit Econ 983 pp 519ndash43

Cummings Ronald G Glenn W Harrison and EElisabet Rutstrom 1995 ldquoHomegrown Valuesand Hypothetical Surveys Is the DichotomousChoice Approach Incentive-CompatiblerdquoAmer Econ Rev 85 pp 260ndash66

Damasio Antonio R 1994 Descartesrsquo Error Emo-tion Reason and the Human Brain NY G PPutnam

Dolan Paul and Claire Gudex 1995 ldquoTime Pref-erence Duration and Health State ValuationsrdquoHealth Econ 4 pp 289ndash99

Dreyfus Mark K and W Kip Viscusi 1995ldquoRates Of Time Preference and ConsumerValuations of Automobile Safety and Fuel Effi-ciencyrdquo J Law Econ 381 pp 79ndash105

Duesenberry James 1952 Income Saving andthe Theory of Consumer Behavior CambridgeMA Harvard U Press

Elster Jon 1979 Ulysses and the Sirens Studiesin Rationality and Irrationality CambridgeUK Cambridge U Press

mdashmdashmdash 1985 ldquoWeakness of Will and the Free-Rider Problemrdquo Econ Philosophy 1 pp 231ndash65

Fischer Carolyn 1999 ldquoRead This Paper EvenLater Procrastination with Time-InconsistentPreferencesrdquo Resources for the Future discusspaper 99ndash20

Fishburn Peter C 1970 Utility Theory and Deci-sion Making NY Wiley

Fishburn Peter C and Ariel Rubinstein 1982ldquoTime Preferencerdquo Int Econ Rev 232 pp677ndash94

Fisher Irving 1930 The Theory of Interest NYMacmillan

Frank Robert 1993 ldquoWages Seniority and theDemand for Rising Consumption Profilesrdquo JEcon Behav Org 21 pp 251ndash76

Frederick Shane 1999 ldquoDiscounting Time Prefer-ence and Identityrdquo PhD Thesis Dept Social amp De-cision Sci Carnegie Mellon U

mdashmdashmdash 2002 ldquoTime Preference and PersonalIdentityrdquo in Time and Decision Economic andPsychological Perspectives on IntertemporalChoice George Loewenste in Daniel Read andRoy Baumeister eds NY Russell Sage (inpress)

Frederick Shane and George Loewenstein 2002ldquoThe Psychology of Sequence Preferencesrdquowork paper Sloan School MIT

Frederick Shane and Daniel Read 2002 ldquoTheEmpirical and Normative Status of HyperbolicDiscounting and Other DU Anomaliesrdquo workpaper MIT and London School Econ

Fuchs Victor 1982 ldquoTime Preferences andHealth An Exploratory Studyrdquo in Economic As-pects of Health Victor Fuchs ed Chicago UChicago Press pp 93ndash120

Fuhrer Jeffrey 2000 ldquoHabit Formation in Con-sumption and Its Implications for Monetary-Policy Modelsrdquo Amer Econ Rev 90 pp 367ndash90

Ganiats Theodore G Richard T Carson RobertM Hamm Scott B Cantor Walton SumnerStephen J Spann Michael Hagen and Christo-pher Miller 2000 ldquoHealth Status and Prefer-ences Population-Based Time Preferences forFuture Health Outcomerdquo Medical DecisionMaking An Int J 203 pp 263ndash70

Gately Dermot 1980 ldquoIndividual Discount Ratesand the Purchase and Utilization of Energy-Using Durables Commentrdquo Bell J Econ 11pp 373ndash74

Giordano Louis A Warren Bickel GeorgeLoewenstein Eric Jacobs Lisa Marsch andGary J Badger 2001 ldquoOpioid Deprivation Af-fects How Opioid-Dependent Outpatients Dis-count the Value of Delayed Heroin andMoneyrdquo work paper U Vermont BurlingtonPsychiatry Dept Substance Abuse TreatmentCenter

Goldman Steven M 1980 ldquoConsistent PlansrdquoRev Econ Stud 473 pp 533ndash37

Gourinchas Pierre-Olivier and Jonathan Parker2001 ldquoThe Empirical Importance of Precau-tionary Savingrdquo Amer Econ Rev 912 pp406ndash12

Green Donald Karen Jacowitz Daniel Kahneman


and Daniel Mcfadden 1998 ldquoReferendum Con-tingent Valuation Anchoring and Willingnessto Pay for Public Goodsrdquo Resource EnergyEcon 20 pp 85ndash116

Green Leonard E B Fischer Jr Steven Perlowand Lisa Sherman 1981 ldquoPreference Reversaland Self Control Choice as a Function of Re-ward Amount and Delayrdquo Behav Anal Letters11 pp 43ndash51

Green Leonard Nathanael Fristoe and Joel Myer-son 1994 ldquoTemporal Discounting and Prefer-ence Reversals in Choice Between DelayedOutcomesrdquo Psychonomic Bull Rev 13 pp383ndash89

Green Leonard Astrid Fry and Joel Myerson1994 ldquoDiscounting of Delayed Rewards ALife-Span Comparison rdquo Psychological Sci 51pp 33ndash36

Green Leonard Joel Myerson and EdwardMcFadden 1997 ldquoRate of Temporal Discount-ing Decreases with Amount of Rewardrdquo Mem-ory amp Cognition 255 pp 715ndash23

Gruber Jonathan and Botond Koszegi 2000 ldquoIsAddiction lsquoRationalrsquo Theory and EvidencerdquoNBER work paper 7507

Gul Faruk and Wolfgang Pesendorfer 2001ldquoTemptation and Self-Controlrdquo Econometrica69 pp 1403ndash35

Harless David W and Colin F Camerer 1994 ldquoThePredictive Utility of Generalized Expected Util-ity Theoriesrdquo Econometrica 626 pp 1251ndash89

Harrison Glenn W Morten I Lau and MelonieB Williams 2002 ldquoEstimating Individual Dis-count Rates in Denmarkrdquo Amer Econ Rev 92(in press)

Hausman Jerry 1979 ldquoIndividual Discount Ratesand the Purchase and Utilization of Energy-Using Durablesrdquo Bell J Econ 101 pp 33ndash54

Hermalin Benjamin and Alice Isen 2000 ldquoTheEffect of Affect on Economic and Strategic De-cision Makingrdquo mimeo U C Berkeley andCornell U

Herrnstein Richard 1981 ldquoSelf-Control as Re-sponse Strengthrdquo in Quantification of Steady-State Operant Behavior Christopher M Brad-shaw Elmer Szabadi and C F Lowe edsElsevierNorth-Holland

Herrnstein Richard J George F LoewensteinDrazen Prelec and William Vaughan 1993ldquoUtility Maximization and Melioration Inter-nalities in Individual Choicerdquo J Behav Deci-sion Making 63 pp 149ndash85

Herrnstein Richard J and Charles Murray 1994The Bell Curve Intelligence and Class Struc-ture in American Life NY Free Press

Hesketh Beryl 2000 ldquoTime Perspective inCareer-Related Choices Applications of Time-Discounting Principlesrdquo J Vocational Behav57 pp 62ndash84

Hirshleifer Jack 1970 Investment Interest andCapital Englewood Cliffs NJ Prentice-Hall

Holcomb J H and P S Nelson 1992 ldquoAnother

Experimental Look at Individual Time Prefer-encerdquo Rationality Society 42 pp 199ndash220

Holden Stein T Bekele Shiferaw and Mette Wik1998 ldquoPoverty Market Imperfections and TimePreferences of Relevance for EnvironmentalPolicyrdquo Environ Devel Econ 3 pp 105ndash30

Houston Douglas A 1983 ldquoImplicit DiscountRates and the Purchaes of Untried Energy-Saving Durable Goodsrdquo J Consumer Res 10pp 236ndash46

Howarth Richard B and Alan H Sanstad 1995ldquoDiscount Rates and Energy Efficiencyrdquo Con-temp Econ Pol 133 pp 101ndash109

Hsee Christopher K Robert P Abelson and Pe-ter Salovey 1991 ldquoThe Relative Weighting ofPosition and Velocity in Satisfactionrdquo PsychSci 24 pp 263ndash66

Jermann Urban 1998 ldquoAsset Pricing in Produc-tion Economies rdquo J Monet Econ 41 pp 257ndash75

Jevons Herbert S 1905 Essays on EconomicsLondon Macmillan

Jevons William S 1888 The Theory of PoliticalEconomy London Macmillan

Johannesson Magnus and Per-Olov Johansson1997 ldquoQuality of Life and the WTP for an In-creased Life Expectancy at an Advanced AgerdquoJ Public Econ 65 pp 219ndash28

Kahneman Daniel 1994 ldquoNew Challenges to theRationality Assumptionrdquo J Inst TheoreticalEcon 150 pp 18ndash36

Kahneman Daniel and Amos Tversky 1979ldquoProspect Theory An Analysis of Decision Un-der Riskrdquo Econometrica 47 pp 263ndash92

Kahneman Daniel Peter Wakker and RakeshSarin 1997 ldquoBack to Bentham Explorations ofExperienced Utilityrdquo Quart J Econ 112 pp375ndash405

Keren Gideon and Peter Roelofsma 1995 ldquoIm-mediacy and Certainty in IntertemporalChoicerdquo Org Behav Human Decision Proc633 pp 287ndash97

Kirby Kris N 1997 ldquoBidding on the Future Evi-dence Against Normative Discounting of De-layed Rewardsrdquo J Experiment Psych General126 pp 54ndash70

Kirby Kris N and Richard J Herrnstein 1995ldquoPreference Reversals due to Myopic Discount-ing of Delayed Rewardrdquo Psych Sci 62 pp83ndash89

Kirby Kris N and Nino N Marakovic 1995ldquoModeling Myopic Decisions Evidence for Hy-perbolic Delay-Disco unting with Subjects andAmountsrdquo Org Behav Human Decision Proc64 pp 22ndash30

mdashmdashmdash 1996 ldquoDelay-Disco unting ProbabilisticRewards Rates Decrease as Amounts IncreaserdquoPsychonomic Bull Rev 31 pp 100ndash104

Kirby Kris N Nancy M Petry and WarrenBickel 1999 ldquoHeroin Addicts Have HigherDiscount Rates for Delayed Rewards than Non-Drug-Using Controlsrdquo J Exper Psych Gen-eral 1281 pp 78ndash87

Koomey Jonathan G and Alan H Sanstad 1994


ldquoTechnical Evidence for Assessing the Perfor-mance of Markets Affecting Energy EfficiencyrdquoEnergy Pol 2210 pp 826ndash32

Koopmans Tjalling C 1960 ldquoStationary OrdinalUtility and Impatiencerdquo Econometrica 28 pp287ndash309

mdashmdashmdash 1967 ldquoObjectives Constraints and Out-comes in Optimal Growth Modelsrdquo Econo-metrica 351 pp 1ndash15

Koopmans Tjalling C Peter A Diamond andRichard E Williamson 1964 ldquoStationary Utilityand Time Perspectiverdquo Econometrica 32 pp82ndash100

Koszegi Botond 2001 ldquoWho Has AnticipatoryFeelingsrdquo work paper econ dept U CalBerkeley

Kroll Yoram Haim Levy and Amnon Rapoport1988 ldquoExperimental Tests of the SeparationTheorem and the Capital Asset Pricing ModelrdquoAmer Econ Rev 78 pp 500ndash19

Laibson David 1994 ldquoEssays in Hyperbolic Dis-countingrdquo PhD dissertation MIT

mdashmdashmdash 1997 ldquoGolden Eggs and Hyperbolic Dis-countingrdquo Quart J Econ 112 pp 443ndash77

mdashmdashmdash 1998 ldquoLife-Cycle Consumption and Hy-perbolic Discount Functionsrdquo Europ EconRev 42 pp 861ndash71

mdashmdashmdash 2001 ldquoA Cue-Theory of ConsumptionrdquoQuarterly J Econ 116 pp 81ndash119

Laibson David Andrea Repetto and Jeremy To-bacman 1998 ldquoSelf-Control and Saving for Re-tirementrdquo Brookings Pap Econ Act 1 pp 91ndash196

Lancaster K J 1963 ldquoAn Axiomatic Theory ofConsumer Time Preferencerdquo Int Econ Rev 4pp 221ndash31

Lawrence Emily 1991 ldquoPoverty and the Rate ofTime Preference Evidence from Panel DatardquoJ Polit Econ 119 pp 54ndash77

Ledoux Joseph E 1996 The Emotional BrainThe Mysterious Underpinnings of EmotionalLife NY Simon amp Schuster

Loewenstein George 1987 ldquoAnticipation and theValuation of Delayed Consumptionrdquo Econ J97 pp 666ndash84

mdashmdashmdash 1988 ldquoFrames of Mind in IntertemporalChoicerdquo Manage Sci 34 pp 200ndash14

mdashmdashmdash 1996 ldquoOut of Control Visceral Influenceson Behaviorrdquo Org Behav Human DecisionProc 65 pp 272ndash92

mdashmdashmdash 1999 ldquoA Visceral Account of Addictionrdquoin Getting Hooked Rationality and AddictionJon Elster and Ole-Jorgen Skog eds Cam-bridge UK Cambridge U Press pp 235ndash64

mdashmdashmdash 2000a ldquoWillpower A Decision-TheoristrsquosPerspectiverdquo Law Philos 19 pp 51ndash76

mdashmdashmdash 2000b ldquoEmotions In Economic Theoryand Economic Behaviorrdquo Amer Econ RevPap Proceed 90 pp 426ndash32

Loewenstein George and Erik Angner 2002ldquoPredicting and Honoring Changing Prefer-encesrdquo in Time and Decision Economic andPsychological Perspectives on IntertemporalChoice George Loewenstein Daniel Read and

Roy Baumeister eds NY Russell Sage (inpress)

Loewenste in George Ted OrsquoDonoghue and Mat-thew Rabin 2000 ldquoProjection Bias in the Pre-diction of Future Utilityrdquo work paper

Loewenstein George and Drazen Prelec 1991ldquoNegative Time Preferencerdquo Amer Econ Rev81 pp 347ndash52

mdashmdashmdash 1992 ldquoAnomalies in IntertemporalChoice Evidence and an InterpretationrdquoQuart J Econ 1072 pp 573ndash97

mdashmdashmdash 1993 ldquoPreferences for Sequences of Out-comesrdquo Psych Rev 1001 pp 91ndash108

Loewenste in George and Nachum Sicherman1991 ldquoDo Workers Prefer Increasing WageProfilesrdquo J Labor Econ 91 pp 67ndash84

Loewenste in George Roberto Weber JanineFlory Stephen Manuck and Matthew Muldoon2001 ldquoDimensions of Time Discountingrdquo pre-sented at Conference on Survey Research onHousehold Expectations and Preferences AnnArbor Nov 2ndash3

Maccrimmon Kenneth R and Donald A Weh-rung 1990 ldquoCharacteri stics of Risk-TakingExecutivesrdquo Manage Sci 364 pp 422ndash35

Mackeigan L D L N Larson J R DraugalisJ L Bootman and L R Burns 1993 ldquoTimePreference for Health Gains vs Health LossesrdquoPharmacoecon 35 pp 374ndash86

Madden Gregory J Nancy M Petry Gary JBadger and Warren Bickel 1997 ldquoImpulsiveand Self-Control Choices in Opioid-DependentPatients and Non-Drug-Us ing Control Partici-pants Drug and Monetary Rewardsrdquo ExperClinical Psychopharmacology 53 pp 256ndash62

Maital S and S Maital 1978 ldquoTime PreferenceDelay of Gratification and IntergenerationalTransmission of Economic Inequality A Behav-ioral Theory of Income Distributionrdquo in Essaysin Labor Market Analysis Orley Ashenfelterand Wallace Oates eds NY Wiley

Martin John L 2001 ldquoThe Authoritar ian Person-ality 50 Years Later What Lessons Are Therefor Political Psychology rdquo Polit Psych 221 pp1ndash26

Mazur James E 1987 ldquoAn Adjustment Procedurefor Studying Delayed Reinforcementrdquo in TheEffect of Delay and Intervening Events on Rein-forcement Value Michael L Commons JamesE Mazur John A Nevin and Howard Rachlineds Hillsdale NJ Erlbaum

Meyer Richard F 1976 ldquoPreferences OverTimerdquo in Decisions with Multiple ObjectivesRalph Keeney and Howard Raiffa eds NYWiley pp 473ndash89

Millar Andrew and Douglas Navarick 1984 ldquoSelf-Control and Choice in Humans Effects ofVideo Game Playing as a Positive ReinforcerrdquoLearning and Motivation 15 pp 203ndash18

Mischel Walter Joan Grusec and John C Mas-ters 1969 ldquoEffects of Expected Delay Time onSubjective Value of Rewards and PunishmentsrdquoJ Personality Soc Psych 114 pp 363ndash73


Mischel Walter Yuichi Shoda and Philip KPeake 1988 ldquoThe Nature of Adolescent Com-petencies Predicted by Preschool Delay ofGratificat ionrdquo J Personality Soc Psych 544pp 687ndash96

Moore Michael J and W Kip Viscusi 1988 ldquoTheQuantity-Adjusted Value of Liferdquo Econ Inq263 pp 369ndash88

mdashmdashmdash 1990a ldquoDiscounting EnvironmentalHealth Risks New Evidence and Policy Impli-cationsrdquo J Environ Econ Manage 18 ppS51ndashS62

mdashmdashmdash 1990b ldquoModels for Estimating Discount Ratesfor Long-Term Health Risks Using LaborMarket Datardquo J Risk Uncertainty 3 pp 381ndash401

Munasinghe Lalith and Nachum Sicherman2000 ldquoWhy Do Dancers Smoke Time Prefer-ence Occupationa l Choice and Wage Growthrdquowork paper Columbia U and Barnard Col-lege

Murphy Thomas J and Alan S Dewolfe 1986ldquoFuture Time Perspective in Alcoholics Pro-cess and Reactive Schizophrenics and Nor-malsrdquo Int J Addictions 20 pp 1815ndash22

Myer R F 1976 ldquoPreferences Over Timerdquo inDecisions with Multiple Objectives R Keeneyand H Raiffa eds pp 473ndash89

Myerson Joel and Leonard Green 1995 ldquoDis-counting of Delayed Rewards Models of Indi-vidual Choicerdquo J Exper Anal Behav 64 pp263ndash76

Nisan Mordecai and Abram Minkowich 1973ldquoThe Effect of Expected Temporal Distance onRisk Takingrdquo J Personality Soc Psych 253pp 375ndash80

Nyhus E K 1995 ldquoItem and Non Item-Speci ficSources of Variance in Subjective DiscountRates A Cross Sectional Studyrdquo 15th Confer-ence on Subjective Probability Utility and De-cision Making Jerusalem

OrsquoDonoghue Ted and Matthew Rabin 1999aldquoAddiction and Self Controlrdquo in Addiction En-tries and Exits Jon Elster ed NY RussellSage pp 169ndash206

mdashmdashmdash 1999b ldquoDoing It Now or Laterrdquo AmerEcon Rev 891 pp 103ndash24

mdashmdashmdash 1999c ldquoIncentives for ProcrastinatorsrdquoQuart J Econ 1143 Pp 769ndash816

mdashmdashmdash 1999d ldquoProcrastination in Preparing forRetirementrdquo in Behavioral Dimensions of Re-tirement Economics Henry Aaron ed Brook-ings Institution and Russell Sage pp 125ndash56

mdashmdashmdash 2000 ldquoAddiction and Present-Biased Pref-erencesrdquo Cornell U and U C Berkeley

mdashmdashmdash 2001 ldquoChoice and ProcrastinationrdquoQuart J Econ 1161 pp 121ndash60

mdashmdashmdash 2002 ldquoSelf Awareness and Self Controlrdquoforthcoming in Time and Decision Economicand Psychological Perspectives on Intertempo-ral Choice George Loewenstein Daniel Readand Roy Baumeister eds NY Russell Sage inpress

Olson Mancur and Martin J Bailey 1981 ldquoPosi-

tive Time Preferencerdquo J Polit Econ 891 pp1ndash25

Orphanides Athanasios and David Zervos 1995ldquoRational Addiction with Learning and RegretrdquoJ Polit Econ 1034 pp 739ndash58

Parfit Derek 1971 ldquoPersonal Identityrdquo Philo-sophical Rev 801 pp 3ndash27

mdashmdashmdash 1976 ldquoLewis Perry and What Mattersrdquoin The Identities of Persons Amelie O Rortyed Berkeley U California Press

mdashmdashmdash 1982 ldquoPersonal Identity and RationalityrdquoSynthese 53 pp 227ndash41

Peleg Bezalel and Menahem E Yaari 1973 ldquoOnthe Existence of a Consistent Course of ActionWhen Tastes Are Changingrdquo Rev Econ Stud403 pp 391ndash401

Pender John L 1996 ldquoDiscount Rates and CreditMarkets Theory and Evidence from Rural In-diardquo J Devel Econ 502 pp 257ndash96

Petry Nancy M Warren Bickel and Martha MArnett 1998 ldquoShortened Time Horizons andInsensitivity to Future Consequences in HeroinAddictsrdquo Addiction 93 pp 729ndash38

Phelps E S and Robert Pollak 1968 ldquoOnSecond-Bes t National Saving and Game-Equilibrium Growthrdquo Rev Econ Stud 35 pp185ndash99

Pigou Arthur C 1920 The Economics of WelfareLondon Macmillan

Pollak Robert A 1968 ldquoConsistent PlanningrdquoRev Econ Stud 35 pp 201ndash208

mdashmdashmdash 1970 ldquoHabit Formation and Dynamic De-mand Functionsrdquo J Polit Econ 784 pp 745ndash63

Prelec Drazen and George Loewenstein 1998ldquoThe Red and the Black Mental Accounting ofSavings and Debtrdquo Marketing Sci 171 Pp 4ndash28

Rabin Matthew 2000 ldquoRisk Aversion andExpected-Utility Theory A Calibration Theo-remrdquo Econometrica 685 pp 1281ndash92

Rabin Matthew and Richard H Thaler 2001ldquoAnomalies Risk Aversionrdquo J Econ Perspect151 pp 219ndash32

Rachlin Howard Andres Raineri and DavidCross 1991 ldquoSubjective Probability and De-layrdquo J Exper Anal Behav 552 pp 233ndash44

Rae John 1834 The Sociological Theory ofCapital (reprint 1834 ed) London Macmil-lan

Raineri Andres and Howard Rachlin 1993 ldquoTheEffect of Temporal Constraints on the Value ofMoney and Other Commodities rdquo J Behav De-cision Making 6 pp 77ndash94

Read Daniel 2001 ldquoIs Time-Discounting Hyper-bolic or Subadditiverdquo J Risk Uncertainty 23pp 5ndash32

Read Daniel George F Loewenstein and Mat-thew Rabin 1999 ldquoChoice Bracketingrdquo J RiskUncertainty 19 pp 171ndash97

Redelmeier Daniel A and Daniel N Heller1993 ldquoTime Preference in Medical DecisionMaking and Cost-Effectiveness Analysisrdquo Medi-cal Decision Making 133 pp 212ndash17


Roelofsma Peter 1994 ldquoIntertemporal ChoicerdquoFree U Amsterdam

Ross Jr W T and I Simonson 1991 ldquoEvalu-ations of Pairs of Experiences A Preference forHappy Endingsrdquo J Behav Decision Making 4pp 155ndash61

Roth Alvin E and J Keith Murnighan 1982ldquoThe Role of Information in Bargaining An Ex-perimental Studyrdquo Econometrica 505 pp1123ndash42

Rubinstein Ariel 2000 ldquoIs It lsquoEconomics and Psy-chologyrsquo The Case of Hyperbolic DiscountingrdquoTel Aviv U and Princeton U

Ruderman H M D Levine and J E Mcmahon1987 ldquoThe Behavior of the Market for EnergyEfficiency in Residential Appliances IncludingHeating and Cooling Equipmentrdquo Energy J81 pp 101ndash24

Ryder Harl E and Geoffrey M Heal 1973 ldquoOp-timal Growth with Intertemporally Depen-dent Preferencesrdquo Rev Econ Stud 40 pp 1ndash33

Samuelson Paul 1937 ldquoA Note on Measurementof Utilityrdquo Rev Econ Stud 4 pp 155ndash61

mdashmdashmdash 1952 ldquoProbability Utility and the Inde-pendence Axiomrdquo Econometrica 204 pp 670ndash78

Schelling Thomas C 1984 ldquoSelf-Command inPractice in Policy and in a Theory of RationalChoicerdquo Amer Econ Rev 742 pp 1ndash11

Senior N W 1836 An Outline of the Science ofPolitical Economy London Clowes amp Sons

Shea John 1995a ldquoMyopia Liquidity Constraintsand Aggregate Consumptionrdquo J Money CreditBanking 273 pp 798ndash805

mdashmdashmdash 1995b ldquoUnion Contracts and the Life-CyclePermanent-Income Hypothesis rdquo AmerEcon Rev 851 pp 186ndash200

Shelley Marjorie K 1993 ldquoOutcome Signs Ques-tion Frames and Discount Ratesrdquo Manage Sci39 pp 806ndash15

mdashmdashmdash 1994 ldquoGainLoss Asymmetry in Risky In-tertemporal Choicerdquo Org Behav Human Deci-sion Proc 59 pp 124ndash59

Shelley Marjorie K and Thomas C Omer 1996ldquoIntertemporal Framing Issues in ManagementCompensati onrdquo Org Behav Human DecisionProc 661 pp 42ndash58

Shoda Yuichi Walter Mischel and Philip KPeake 1990 ldquoPredicting Adolescent Cognitiveand Self-Regulatory Competencie s from Pre-school Delay of Gratificationrdquo Develop Psych266 pp 978ndash86

Solnick Jay Catherine Kannenberg David Ecker-man and Marcus Waller 1980 ldquoAn Experimen-tal Analysis of Impulsivity and Impulse Controlin Humansrdquo Learning and Motivation 11 pp61ndash77

Solow Robert M 1974 ldquoIntergenerational Equityand Exhaustible Resourcesrdquo Rev Econ Stud41Symposiu m Econ Exhaustible Resources pp 29ndash45

Spence Michael and Richard Zeckhauser 1972ldquoThe Effect of Timing of Consumption Deci-

sions and Resolution of Lotteries on Choiceof Lotteriesrdquo Econometrica 402 pp 401ndash403

Starmer Chris 2000 ldquoDevelopments in Non-Expected Utility Theory The Hunt for aDescriptive Theory of Choice Under RiskrdquoJ Econ Lit 382 pp 332ndash82

Sternberg Robert J 1985 Beyond IQ A TriarchicTheory of Human Intelligence NY CambridgeU Press

Stevenson Mary Kay 1992 ldquoThe Impact of Tem-poral Context and Risk on the Judged Value ofFuture Outcomesrdquo Org Behav Human Deci-sion Proc 523 pp 455ndash91

Strotz R H 1955ndash56 ldquoMyopia and Inconsistencyin Dynamic Utility Maximizationrdquo Rev EconStud 233 pp 165ndash80

Suranovic Steven Robert Goldfarb and ThomasC Leonard 1999 ldquoAn Economic Theory ofCigarette Addictionrdquo J Health Econ 181 pp1ndash29

Thaler Richard H 1981 ldquoSome Empirical Evi-dence on Dynamic Inconsistencyrdquo Econ Let-ters 8 pp 201ndash07

mdashmdashmdash 1985 ldquoMental Accounting and ConsumerChoicerdquo Manage Sci 4 pp 199ndash214

mdashmdashmdash 1999 ldquoMental Accounting Mattersrdquo J Be-hav Decision Making 12 pp 183ndash206

Thaler Richard H and Hersh M Shefrin 1981ldquoAn Economic Theory of Self-Controlrdquo J PolitEcon 892 pp 392ndash410

Tversky Amos and Daniel Kahneman 1983 ldquoEx-tensional vs Intuitive Reasoning The Conjunc-tion Fallacy in Probability Judgmentrdquo PsychRev 90 pp 293ndash315

mdashmdashmdash 1991 ldquoLoss Aversion in Riskless Choice AReference Dependent Modelrdquo Quart J Econ106 pp 1039ndash61

Tversky Amos and Derek J Koehler 1994 ldquoSup-port Theory Nonextensional Representation ofSubjective Probabilityrdquo Psych Rev 1014 pp547ndash67

van der Pol Marjon M and John A Cairns 1999ldquoIndividual Time Preferences for Own HealthApplication of a Dichotomous Choice Questionwith Follow Uprdquo Appl Econ Letters 610 pp649ndash54

mdashmdashmdash 2001 ldquoEstimating Time Preferences forHealth Using Discrete Choice ExperimentsrdquoSocial Sci Med 52 pp 1459ndash70

Varey C A and D Kahneman 1992 ldquoExperi-ences Extended Across Time Evaluation ofMoments and Episodesrdquo J Behav DecisionMaking 53 pp 169ndash85

Viscusi W Kip and Michael J Moore 1989ldquoRates of Time Preference and Valuation of theDuration of Liferdquo J Public Econ 383 pp 297ndash317

Wahlund Richard and Jonas Gunnarsson 1996ldquoMental Discounting and Financial StrategiesrdquoJ Econ Psych 176 pp 709ndash30

Wang Ruqu 1997 ldquoThe Optimal Consumptionand Quitting of Harmful Addictive Goodsrdquowork paper Queens U


Warner John T and Saul Pleeter 2001 ldquoThe Per-sonal Discount Rate Evidence from MilitaryDownsizing Programsrdquo Amer Econ Rev 911pp 33ndash53

Whiting Jennifer 1986 ldquoFriends and FutureSelvesrdquo Philosophical Rev 954 pp 547ndash580

Winston Gordon C 1980 ldquoAddiction and Back-sliding A Theory of Compulsive ConsumptionrdquoJ Econ Behav Org 1 pp 295ndash324

Yates J Frank and Royce A Watts 1975 ldquoPrefer-ences for Deferred Lossesrdquo Org Behav Hu-man Perform 132 pp 294ndash306


Samuelsonrsquos reservations about thedescriptive validity of the DU modelwere justified Section 4 reviewsthe growing list of ldquoDU anomaliesrdquomdashpatterns of choice that are inconsistentwith the modelrsquos theoretical predic-tions Virtually every assumption under-lying the DU model has been testedand found to be descriptively invalid inat least some situations Moreover aswe discuss at the end of the sectionthese anomalies are not anomalies in thesense that they are regarded as errorsby the people who commit them Unlikemany of the better-known expected-utility anomalies the DU anomalies donot necessarily violate any standard orprinciple that people believe theyshould uphold

The insights about intertemporalchoice gleaned from this empirical re-search have led to the proposal of nu-merous alternative theoretical modelswhich we review in section 5 Some ofthese modify the discount function per-mitting for example declining discountrates or ldquohyperbolic discountingrdquo Oth-ers introduce additional arguments intothe utility function such as the utilityof anticipation Still others depart fromthe DU model more radically by in-cluding for instance systematic mis-predictions of future utility Many ofthese new theories revive psychologicalconsiderations discussed by Rae andother early economists that were extin-guished with the adoption of the DUmodel and its expression of intertem-poral preferences in terms of a singleparameter

In section 6 we review attempts toestimate discount rates While the DUmodel assumes that people are charac-terized by a single discount rate thisliterature reveals spectacular variationacross (and even within) studies Thefailure of this research to converge to-ward any agreed-upon average discount

rate stems partly from differences inelicitation procedures But it also stemsfrom the faulty assumption that the var-ied considerations that are relevant inintertemporal choices apply equally todifferent choices and thus that they canall be sensibly represented by a singlediscount rate

Throughout the paper we stress theimportance of distinguishing among thevaried considerations that underlie in-tertemporal choices We distinguishtime discounting from time preferenceWe use the term time discountingbroadly to encompass any reason forcaring less about a future consequenceincluding factors that diminish the ex-pected utility generated by a futureconsequence such as uncertainty orchanging tastes We use the term timepreference to refer more specifically tothe preference for immediate utilityover delayed utility In section 7 wepush this theme further by examiningwhether time preference itself mightconsist of distinct psychological traitsthat can be separately analyzed Section8 concludes

2 Historical Origins of the DiscountedUtility Model

The historical developments that cul-minated in the formulation of the DUmodel help to explain the modelrsquos limi-tations Each of the major figures in thedevelopment of the DU modelmdashJohnRae Eugen von Boumlhm-Bawerk IrvingFisher and Paul Samuelsonmdashbuiltupon the theoretical framework of hispredecessors drawing on little morethan introspection and personal obser-vation When the DU model eventuallybecame entrenched as the dominanttheoretical framework for modeling in-tertemporal choice it was due largely toits simplicity and its resemblance to thefamiliar compound interest formula




























T t

D(k)u(ct + k)


11 + r

oumldivideoslash

k














aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)


aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)





















1

1 + rn



ccedilegrave

1











ccedilegrave

1

1 + r

oumldivideoslash


ccedilegrave

1

1 + rcent

oumldivideoslash














4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES






































































































































































































































































T t

D(k)u(ct + k)


11 + r

oumldivideoslash

k














aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)


aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)





















1

1 + rn



ccedilegrave

1











ccedilegrave

1

1 + r

oumldivideoslash


ccedilegrave

1

1 + rcent

oumldivideoslash














4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES





























































































































































































































































T t

D(k)u(ct + k)


11 + r

oumldivideoslash

k














aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)


aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)





















1

1 + rn



ccedilegrave

1











ccedilegrave

1

1 + r

oumldivideoslash


ccedilegrave

1

1 + rcent

oumldivideoslash














4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES





















































































































































































































































T t

D(k)u(ct + k)


11 + r

oumldivideoslash

k














aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)


aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)





















1

1 + rn



ccedilegrave

1











ccedilegrave

1

1 + r

oumldivideoslash


ccedilegrave

1

1 + rcent

oumldivideoslash














4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES




















































































































































































































































aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)


aring t = t

T aeligccedilegrave

11 + r

oumldivideoslash

t t

u(ct)





















1

1 + rn



ccedilegrave

1











ccedilegrave

1

1 + r

oumldivideoslash


ccedilegrave

1

1 + rcent

oumldivideoslash














4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES





























































































































































































































































1

1 + rn



ccedilegrave

1











ccedilegrave

1

1 + r

oumldivideoslash


ccedilegrave

1

1 + rcent

oumldivideoslash














4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES


















































































































































































































































1

1 + rn



ccedilegrave

1











ccedilegrave

1

1 + r

oumldivideoslash


ccedilegrave

1

1 + rcent

oumldivideoslash














4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES























































































































































































































































4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES













































































































































































































































4 DU Anomalies


























AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES



























































































































































































































































AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES



















































































































































































































































AMarch 1$997

June 1$997

Sept 1$997

Nov 1$997

BApril 1$1000

July1$1000

Oct 1$1000

Dec 1$1000



10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15

10

08

06

04

02

00


0

impu

ted

disc

ount

fact

or


10 15




















firstweekend

secondweekend

thirdweekend

fourthweekend

fifthweekend

Option AFancy

FrenchEat athome

Eat athome

Eat athome

Eat athome

[11]

Option BEat athome

Eat athome

FancyFrench

Eat athome

Eat athome

[89]

Option CFancy

FrenchEat athome

Eat athome

Eat athome

FancyLobster

[49]

Option DEat athome

Eat athome

FancyFrench

Eat athome

FancyLobster

[51]












1bdk

if h = 0if k gt 0



bdwhereas


dlt 1 bd

bd









511 Self Awareness



















































531 Projection Bias






















































TABLE 1 (Cont)


Factor(s)


3 mos to 20 yrs 6 to 111 094 to 047


6 yrs to 57 yrs 0 to 3 097


1 yr 28 to 147 078 to 040


1 month to 6 mos 13 to 19000 088 to 001












10

08

06

04

02

00


1975

impu

ted

disc

ount

fact

or


1985 1990 1995 2000






613 Concave Utility






614 Uncertainty





615 Inflation





















621 Field Studies





















































Figure 3

opportunity costs

uncertainty

changing tastes

increased wealth


Amountof utility


diminishedidentity

impulsivity

Weightingof utility

d


















8 Conclusions












REFERENCES












































































































































































































































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