Projection Bias in Predicting Future Utility* George Loewenstein Ted O'donoghue Matthew Rabin

PROJECTION BIAS INPREDICTING FUTUREUTILITY*

GEORGE LOEWENSTEIN TED O’DONOGHUE MATTHEW RABIN

Peopleexaggerate the degree to which their future tastes will resemble their current tastes.We present evidence from a varietyof domains which demon- stratesthe prevalence of such projectionbias, developa formalmodel of it,and use thismodel to demonstrate its importance in economic environments. We show that,when people exhibit habit formation, projection bias leads people to consume toomuch early in life,and to decide, as time passes, to consume more— and save less—than originally planned. Projection bias can also lead to misguided purchasesof durable goods. We discuss a numberof additional applications and implications.

Thegreat source of both the misery and disordersof human life,seems to arise from over-rating the difference between onepermanent situation and another.Avarice over-rates the differencebetween poverty and riches:ambition, that be- tweena private and apublic station:vain-glory, that between obscurityand extensivereputation— Adam Smith, The The- oryof Moral Sentiments [2002, p. 173; III,iii,31].

I. INTRODUCTION Optimal decision-makingoften requires a predictionof futuretastes, and futuretastes may differ fromcurrent tastes due tosuch factors as habit formation,day-to-day mood uctuations, socialin uences, maturation, and changesin theenvironment.

*Forhelpful comments, we are grateful to Erik Eyster, ChristopherHarris, andmembers of theRussell Sage Foundation Behavioral Economics Roundtable; seminarparticipants at Cornell University, Yale University, Harvard University, Universityof Michigan,University of Texas,Syracuse University, London School ofEconomics, University of Zurich, the Toulouse Conference on Psychology and Economics,and the Jerome Levy Institute;and Lawrence Katz, Edward Glaeser, andan anonymousreferee. We especiallythank Colin Camerer and Drazen Prelec forvery helpfuldiscussions at theformative stages of this project. Forresearch assistance,we thank Kitt Carpenter,Erik Eyster, JeffreyHolman, David Huff- man,Christopher Meissner, and Mandar Oak. For nancialsupport, Loewenstein thanksthe Center for the Study ofHuman Dimensions of Global Change at CarnegieMellon University (NSF Grant SBR-9521914),O’ Donoghueand Rabin thankthe National Science Foundation (Awards SBR-9709485,SES-0078796, andSES-0079266), and Rabin thanks the Russell Sage, MacArthur, andSloan Foundations.This research was started while Loewenstein and Rabin were Fel- lowsat theCenter for Advanced Study inthe Behavioral Sciences, supported by NSF Grant SBR-960123,and they are very gratefulfor the Center’ s hospitality andthe National Science Foundation’ s support.

1209 1210 QUARTERLY JOURNALOF ECONOMICS

Whenmaking summer vacation plans during thecold of winter, peoplemust predict what vacationswill bemost enjoyable during theheat of summer. When ordering food at thebeginning of a meal,people must predict howhungry they will beat theend of themeal. When contemplating smoking cigarettes or indulging in otherhabit-forming substances,people must predict howthis consumptionwill affect theirfuture desire for and enjoymentof thesesubstances. In this paper weprovide evidence for, formalize, and explore theimplications of a generalbias in theprediction of future tastes:people tend tounderstand qualitatively thedirections in whichtheir tastes will change,but systematicallyunderestimate themagnitudes of thesechanges. Hence, they tend toexaggerate thedegree to which their future tastes will resembletheir current tastes.Such projectionbias maycause people making summer vacationplans in thewinter to chooseoverly warm destinations, dinersto order too much food at thebeginning of meals, and peopleunaddicted tocigarettes to underestimate the power of and drawbacks ofaddiction. In SectionII wereview evidence from a varietyof domains supporting theexistence of projectionbias. Peopleunderappreci- atethe effects of long-term changes in tastes,such as thosethat resultfrom adaptation toa shifting standard ofliving.People also underappreciatethe effects of frequently uctuating tastes,such as uctuating hunger.Indeed, virtually all evidencewe are fa- miliarwith onmisprediction of future tastes is consistentwith projectionbias. In SectionIII wedevelop a formalmodel of projectionbias. To xideas,suppose that aperson ’sinstantaneousutility canbe written as u(c,s), where c is herconsumption and s is a “state” that parameterizesher tastes. Suppose furtherthat theperson with currentstate s9 mustpredict hertastes at atimein the futurewhen her state will be s.Consistentwith evidencethat peopletend tounderstand thequalitative natureof changes in tastes,but underestimatethe degree of change, we assume that the person’spredictionof her own future preferences, u˜ (c,sus9), liessomewhere “in between” hertrue future tastes u(c,s) and her currenttastes u(c,s9).Ourformal analysis in this paper assumes that u˜ (c,sus9)is asimplelinear combination of u(c,s) and u(c,s9), whichwe refer to as simple projectionbias. Becauseprojection bias leads todiscrepancies between predicted and subsequentlyrealized utilities, it impliesthat aperson’sbehaviorneed not correspond to correct intertemporal util- PROJECTION BIAS 1211 ity maximization.For instance, if currentconsumption has dele- teriouseffects on futurewell-being, and projectionbias leads the personto underappreciate these effects, she may overconsume relativeto what would maximizeher true intertemporal utility. Moreover,as tasteschange over time in ways shedoes not predict, apersonmakes plans that shemay end up notcarrying out; that is,projection bias can lead todynamic inconsistency.A stressedundergraduate who underappreciates the addictiveness ofcigarettes, for instance, might start smokingwith theplan of quitting upongraduation, only to continue smoking after gradu- ationonce she becomes addicted. Todemonstratethe potential economic importance of projectionbias, in SectionsIV and Vweformallyanalyze twoeconomic environments.Section IV exploresthe implications of projection bias in alife-cycleconsumption model with habit formation. Whenconsumption is habit-forming,a personshould rationally pursuean increasingconsumption pro le,so that sheis always consumingmore than sheis accustomedto. Projection bias leads apersonto underappreciate the impact ofcurrent consumption onfuture utility, and henceto consume too much early in life and toolittle late in life relativeto what would beoptimal. More interesting,as timepasses and theperson habituates tohigher consumptionlevels, she may decide to consume more than she had earlierplanned; henceprojection bias cancause saving tofall shortof intentions. Finally, as theperson gets accustomed to higherconsumption levels, she also values income more highly, and hencemight decide to work more (or retire later) than she had earlierplanned. In SectionV weshow how projection bias cancause misguided purchasesof durable goods.The satisfaction that aperson derivesfrom a durable goodoften uctuatesfrom day today, and projectionbias leads apersonto underappreciate how much her futurevaluations maydiffer fromher current valuation. As a result,people will overvaluethe good on high-value days and undervalueit onlow-value days. Apersonmaking a one-time buying decisionis thereforeequally likelyto buy whenshe should notor not to buy whenshe should. However, if theperson has multipleopportunities to buy, and (as is typically thecase) un- buying is moredif cultthan buying,projection bias will lead on averageto overpurchasing of durable goods. Webelieve that projectionbias is importantfor many eco- nomicapplications, and that it can providean intuitiveand parsimoniousaccount for many phenomena that areotherwise 1212 QUARTERLY JOURNALOF ECONOMICS difcultto explain. In SectionVI weextrapolate from our formal analysis in SectionsIV and Vand discuss someof these addi- tionalimplications. We conclude in SectionVII.

II. EVIDENCE OF PROJECTION BIAS In this sectionwe review evidence from a varietyof domains supporting theexistence of projection bias. 1 Acommontype of tastechange is adaptation: peoplehave a remarkableability to adapt tomajor changes in theirlife circumstances,such as ac- quiring seriousmedical conditions, moving to different climates, and changingoccupations (see Helson [1964] and Frederickand Loewenstein[1999] fora recentreview). 2 Moreover,there is a greatdeal ofevidence that peopleunderappreciate the extent of suchadaptation. Speci cally,by comparinga “control” group’s predictionsfor how some major change would affect theirlives to theself-reports of people who have actually experiencedthat change,a numberof studies suggestthat peopleoverestimate the impact ofmajor changes on their long-run level of happiness. In themedical domain, cross-sectional studies haveconsis- tentlyfound that nonpatients ’ predictionsof the quality oflife associatedwith seriousmedical conditions are lower than actual patients’ self-reportedquality oflife. For instance, Sackett and Torrance[1978] ndthat nonpatientspredict that chronicdialysis would yield aquality oflife of0.39,whereas dialysis patients reporta quality oflife of0.56 (ona 0to1 scaleon which0 means as bad as death and 1meansperfect health). Boyd etal. [1990] nd analogouscross-sectional results with regardto colostomies. Thesame pattern alsoshows up in longitudinal studies.Jepson, Loewenstein,and Ubel[2001] askedpeople waiting fora kidney transplant topredict what theirquality oflife would beone year laterif theydid ordid notreceive a transplant, and thenasked

1.See Loewenstein and Schkade [1999]for a summaryof much of the evi- dencepresented in this section, as well as for a discussionof the psychological mechanismsthat underlie projection bias. Also see Loewenstein, O ’Donoghue,and Rabin[2002] for a moreextensive discussion of thisevidence. 2.There are some exceptions to this rule. First, there are a varietyof factors thatimpede adaptation, such as uncertainty about whether a situationis perma- nentand repeated reminders of theoriginal situation. Second, some studies have foundthat people do not seem to adapt to noise; indeed, if anything,they seem to becomeincreasingly irritated by it (foran overview, see Weinstein [1982]). More- over,noise is the one example we know ofthat might contradict ourassertion that peopleunderstand the direction in which tastes change, because people seem to predict thatthey will adapt when in fact theytend to become more irritated. PROJECTION BIAS 1213 thosesame people one year later to report their quality oflife. Patientswho received transplants predicted ahigherquality of life than theyended up reporting,and thosewho did notpredicted alowerquality oflife than theyended up reporting.Sieff, Dawes, and Loewenstein[1999] nd similarlongitudinal resultsfor people testingfor HIV. Outside themedical domain, Gilbert et al. [1998] compared (amongother things) assistant professors ’ predictionsof the impact ofgettingor beingdenied tenureto the self-reports of former assistant professors,and Loewensteinand Frederick[1997] compared thepredictions by surveyrespondents of how various events(e.g., a declinein sport shing and an increasein the numberof coffee shops) would affect theirwell-being over the nextdecade to the self-reports of other respondents about how actual eventsin thepast decadehad affected theirwell-being. A clearpattern emergedin bothstudies: those making prospective predictionsexpected future changes to affect theirwell-being morethan thosemaking retrospective evaluations reported that matchedchanges in thepast had affected theirwell-being. Whilethere are alternative explanations forthe results above,other research suggests that theyare driven in largepart by underappreciationof adaptation. First,in themedical domain, recentresearch by Ubel,Loewenstein, and Jepson[2003] shows that it issometimespossible to “debias” people—tobring nonpatients’ predictionscloser to patients ’ self-reports —by inducing themto think more carefully about adaptation, whichsuggests that underappreciationof adaptation plays asigni cant role in thediscrepancy. Second, a numberof ongoingstudies areruling outother explanations. For instance, a commonlymentioned alternativeis “responsenorming ”—chronicdialysis patients,for instance,might interpret a 0.8 ona 0-to-1 scaledifferently from nonpatients —but Baronet al. [forthcoming] found that making thescales more precise only increases the discrepancy. 3 Finally, andperhaps moreimportantly, analogous results are found in experi- mentson shorter term changes in tastes,for which these alter- nativeexplanations do nothold; we turn to such evidence next.

3.The other main explanation that has been offered is a “focusingillusion ”— thatpeople exaggerate the impact of anything their attention is focused on, includingdisabilities [Schkade andKahneman 1998; Wilson et al. 2000]. How- ever,Ubel, Loewenstein, and Jepson [2003] also found that a widerange of “defocusing” interventionsactually decreased rather than increased nonpatients ’ estimatesof patients ’ qualityof life. 1214 QUARTERLY JOURNALOF ECONOMICS

Aprevalentexperimental nding is the endowmenteffect: peopletend tovalue an object(such as acoffeemug) more highly if theypossess it than if theydo not. 4 Theusual explanation is that peopleadapt toowning or not owning the object, and that thereis morepain uponparting with theobject than thereis joy uponobtaining theobject. An underappreciationof this adapta- tionimplies that unendowedsubjects should underestimate by howmuch becoming endowed will increasetheir valuation, and that endowedsubjects should underestimate by howmuch be- comingunendowed will decreasetheir valuation. Van Boven, Dunning,and Loewenstein[2000] ndcross-sectionalevidence of bothpredictions. In oneexperiment the usual endowmenteffect was replicated by elicitingselling prices from subjects endowed with coffeemugs and buying pricesfrom subjects not endowed (averageselling price 5 $6.37; averagebuying price 5 $1.85). Sellerswere then asked to estimate how much buyers would pay, and buyerswere asked to estimate how much sellers would charge,with subjectsrewarded for accurate predictions. Consis- tentwith projectionbias, theaverage estimate of sellers ($3.93) was lessthan theirown average selling price but morethan the averagebuying price,and theaverage estimate of buyers($4.39) was morethan theirown average buying pricebut lessthan the averageselling price. Loewenstein and Adler [1995] providelon- gitudinal evidenceof theformer prediction. In onestudy, subjects wereshown a coffeemug, told toimagine that theyhad been givenone but had theopportunity to exchange it forcash, and then lled outa formthat elicitedtheir predicted reservation values.After adelay,they were actually giventhe mug, and then askedto complete an identical formthat elicitedtheir actual reservationvalues. Again consistentwith projectionbias, the predicted sellingprices were signi cantly lowerthan theactual sellingprices. Thereis alsoconsiderable evidence on underappreciation of theeffects of hunger. This evidence is particularly valuable becauseit demonstratesthat thesame basic pattern ofmispredic- tion— understanding thedirection of tastechanges but underap- preciatingthe magnitude of the changes —showsup forother types oftaste changes besides adaptation, and it canshow up

4.The endowment effect was rst discussedby Thaler [1980]; see Kahneman, Knetsch,and Thaler [1991] for a review. PROJECTION BIAS 1215

TABLE I PERCENTAGEOF SUBJECTS CHOOSING UNHEALTHY SNACK (FROM READ AND VAN LEEUWEN [1998])

Futurehunger

Hungry Satiated

Current Hungry 78% 42% Hunger Satiated 56% 26%

evenfor taste changes with whichpeople have ample experience and henceought to understand well. Severalstudies lend support tothe folk wisdom that shop- ping onan emptystomach leads peopleto buy toomuch [Nisbett and Kanouse1968; Gilbert,Gill, and Wilson2002]. Thisphe- nomenoncan be interpreted as amanifestationof projectionbias: peoplewho are hungry act as if theirfuture taste for food will reectsuch hunger. Read and van Leeuwen[1998] provideeven sharperevidence of projectionbias with respectto hunger. Of ce workerswere asked to choose between healthy snacks and un- healthysnacks that theywould receivein oneweek, either at a timewhen they should expectto be hungry(late in theafternoon) orsatiated (immediatelyafter lunch). 5 Subjectswere approached tomake the choice either when they were hungry (late in the afternoon)or satiated (immediatelyafter lunch). As depicted in TableI, peoplewho expected to be hungry the next week were morelikely to opt forunhealthy snacks, presumably re ecting an increasedtaste for unhealthy snacks in thehungry state, but in addition, peoplewho were hungry whenthey made the choice were morelikely to opt forunhealthy snacks, suggesting that people wereprojecting their current tastes onto their future tastes. Indeed,if weinterpret the main diagonal —thehungry-hun- gryand satiated-satiated conditions —as reectingtrue preferences,the data texactlythe pattern ofprojectionbias. Forthose subjectswho are currently hungry but expectto be satiated, they understand thedirection in whichtheir tastes will changeas they becomesatiated —fewerchoose the unhealthy snack than in the hungry-hungrycondition — but theyunderestimate the magni-

5.The healthy snacks were apples and bananas; the unhealthy snacks were crisps,borrelnoten, Mars Bars, and Snickers Bars.We adopt the terminology healthyand unhealthy from the experimenters, but none of the snacks were thuslylabeled to the subjects. 1216 QUARTERLY JOURNALOF ECONOMICS tude ofthis change —morechoose the unhealthy snack than inthe satiated-satiated condition.An analogousconclusion holds for subjectswho are currently satiated and expectto be hungry. Whilewe have limited our detailed discussionto a few realms,there is considerablefurther evidence that projectionbias operatesacross a broad array ofdomains. Indeed, virtually all evidencethat weare aware of is consistentwith projectionbias (exceptpossibly noise,as discussed in footnote2). 6 Ourgoal in the remainderof this paper is todemonstrate its potentialimpor- tancefor economics.

III. THE MODEL In this sectionwe build aformalmodel of projectionbias. To describechanges in tastes,we use the apparatus ofstate-dependent utility.Suppose that aperson ’sinstantaneousutility in period t,whichcaptures her tastes, is givenby u(ct,st), where ct is herperiod t consumption.The variable st , her “state,” parameterizesher tastes. The state might re ectpast behavior,as when past consumptionof agooddetermines current addiction tothat good,or exogenous factors, as when uctuationsin serotonin levelsaffect moodor whenpeer pressure affects thebene ts and costsof current behavior. 7 Nextconsider a personcurrently with state s9 who is at- temptingto predict herfutureinstantaneous utility fromconsum- ing c in state s;that is,she is tryingto predict u(c,s). Let u˜ (c,sus9) denoteher prediction. If shewere accurate, her predicted utility would equal trueutility, or u˜ (c,sus9) 5 u(c,s).But theevidence in SectionII suggeststhat, while people understand thequalitative

6.Other domainsfor which there is evidence consistent with projection bias includesexual arousal [Loewenstein, Nagin, and Paternoster 1997], pain [Read andLoewenstein 1999], thirst [Van Boven and Loewenstein 2003], fear [Van Bovenet al. 2003], and heroin craving [Giordanoet al. 2001]. See also Loewen- stein’s[1996,1999] discussion of hot/coldempathy gaps wherein individuals who arein cold visceral states underappreciate the impact of hot visceral states on theirown behavior. 7. By “consumption, ” wemean any current physicalexperience that is rele- vantfor current well-being —inaddition to literal consumption of goods, this mightinclude experiencing a healthoutcome, being exposed to noise, or owning an object.Just as the utility from consuming goods might change over time, the utilityfrom these other types of experiences might change over time, and we capturesuch effects with the “state” variable.For instance, the utility (quality of life)from being a chronic-dialysispatient might depend on how accustomed the personis tobeing a chronic-dialysispatient; in thiscase, consumption is beinga chronic-dialysispatient, and the state re ectshow accustomed the person is to beinga chronic-dialysispatient. PROJECTION BIAS 1217 natureof changesin theirtastes, they underestimate the magnitude ofthese changes. Roughly speaking, this projectionbias meansthat aperson ’spredicted utility u˜ (c,sus9) lies “in between” hertrue future utility u(c,s)and herutility givenher current state u(c,s9).8 In this paper weconsider a particularly simple formof projectionbias.

DEFINITION 1.Predicted utility exhibits simple projectionbias if thereexists a [ [0,1] suchthat forall c, s, and s9, u˜ (c,sus9) 5 (1 2 a)u(c,s) 1 au(c,s9).

Withthis formulation,if a 5 0,the person has noprojection bias: shepredicts herfuture instantaneous utility correctly.If a . 0,the person has projectionbias; thebigger is a,thestronger is thebias. When a 5 1,the person perceives that herfuture tasteswill beidentical toher current tastes. 9 Ourmodel says nothingabout how tastes change; rather, it makespredictions as afunctionof how tastes change. Hence, it mightbe that aperson ’shappiness tends tomean-revert over timedue to adaptation, in whichcase projection bias would lead herto expect some but notenough mean reversion. It couldbe that apersondevelops a tastefor certain types ofconsumption — e.g.,her enjoyment of coffeemight grow over time —in whichcase projectionbias would lead herto underappreciate how much her enjoymentwill grow.Or it couldbe that aperson ’s tastes uctu- atefrom day today, inwhichcase projection bias would lead her tounderappreciate the magnitudes of these uctuations.Our formulationpermits us to analyze theimplications of projection bias— ofunderstanding thedirection of taste changes but under-

8.Our formalassumption is that people correctly anticipatechanges in statesbut underappreciate how these changes map into changes in utility. But sincestates are merely a meansof parameterizing utility functions, it would make littledifference if we assumed instead that people fully appreciate how changes in statesmap into changes in utility but underappreciate the degree to which the stateswill change. 9.While simple projection bias is suf cientfor our analysis in thispaper, it istoo restrictive for use as ageneralde nition.One problem is that, when there aremultiple states, it requires that the magnitude of the bias be identical for differenttypes of states; e.g., that a personwho is currently notthirsty and currently unaddictedto cocaine be just as bad at predicting her preferences when sheis thirsty asshe is atpredicting her preferences when addicted to cocaine. A secondproblem is that the magnitude of the bias cannot depend on the current state;e.g., it doesnot permit that a satiatedperson can predict wellher prefer- enceswhen hungry whereasa hungry personcannot predict wellher preferences whensatiated. See Appendix A inLoewenstein, O ’Donoghue,and Rabin [2002] for amoregeneral formulation of projection bias. 1218 QUARTERLY JOURNALOF ECONOMICS estimatingmagnitudes —forthese and otherpossible types of tastechanges. 10 Mosteconomic decisions involve more than merelypredicting futuretastes; they involve making choices with intertemporal consequences.We next embed our framework above within an intertemporal-choiceenvironment. Suppose that apersonmust choosea path ofconsumption( ct, . . . , cT )whenher (true) intertemporalpreferences are given by

T t 5 t U ~ct, . . . , cT! O d u~ct,st!, t5t where d # 1is herdiscount factor. Standard economicmodels of state-dependentpreferences typically assumethat peopleare “rational” in thesense that theycorrectly anticipate howtheir behavior inuencesthe evolution of states. Formally, for any period t and initial state st,arationalperson chooses a path ofconsumption (ct, . . . , cT),correctly anticipating theassociated path ofstates t (st, . . . , sT),to maximize true intertemporal utility U . Apersonwith projectionbias attempts tomaximize her intertemporalutility, but mayfail todo so because she mispredicts herfuture instantaneous utilities. More precisely, if aperson exhibitsprojection bias and herstate in period t is st, then she perceivesher period t intertemporalpreferences to be

T ˜ t 5 t U ~ct, . . . , cT ust! O d u˜ ~ct,stust!. t5t

Weassume that forany period t and initial state st apersonwith projectionbias choosesa path ofconsumption ( ct, . . . , cT ), cor- rectlyanticipating theassociated path ofstates ( st, . . . , sT ), to maximizeher perceived intertemporal utility U˜ t.Thatis, she behavesexactly as arationalperson would exceptthat (possibly) U˜ t Þ Ut. Toincorporateuncertainty over future consumption or future states,we make the standard assumptionthat apersonmaxi- mizesher expected discounted utility. For instance, suppose that in period t theperson expects her period t consumption-state combinationto be ( c9,s9)with probability p and (c0,s0) with prob-

10.For a discussionof many different types of taste changes, see Loewen- steinand Angner [2003]. PROJECTION BIAS 1219 ability 1 2 p.Just as trueperiod t expectedutility is Et[u(ct,st)] 5 pu(c9,s9) 1 (1 2 p)u(c0,s0),a personwith projectionbias predicts period t expectedutility tobe Et[u˜ (ct,stust)] 5 pu˜ (c9,s9ust) 1 (1 2 p)u˜ (c0,s0ust).Similarly,true expected intertemporal utility is t T t Et[U (ct, . . . , cT )] 5 Et[St5 t d u(ct,st)], and apersonwith projectionbias perceivesher expected intertemporal utility tobe ˜ t T t 11 Et[U (ct, . . . , cT ust)] 5 Et[St5 t d u˜ (ct,st ust)]. Whilethe person ’strueintertemporal preferences Ut are time-consistent,because she incorrectly predicts howher tastes changeover time, her perceived intertemporal preferences U˜ t can betime-inconsistent. Because this timeinconsistency derives solelyfrom misprediction of future utilities, it would makelittle senseto assumethat theperson is fully awareof it. 12 We assume throughoutthe paper that theperson is completelyunaware of thetime inconsistency —that atall timesthe person perceives her preferencesto be time-consistent, and thereforeat all timesshe plans tofollow the consumption path that maximizesher current perceivedintertemporal preferences. As aresult,projection bias can lead to dynamicinconsistency :apersonmay plan tobehave a certainway in thefuture, but later,in theabsence of new infor- mation,revise this plan. 13 Givenany particular setof state-dependent preferencesand particular economicenvironment, our model of projection bias makes specicpredictionsabout how actual behaviordiffers from rationalbehavior. To demonstratethis point,and tohighlight the

11.Research has, of course, documented a numberof inadequacies of expected-utilitytheory (for an overview see Starmer [2000]). To the extent that one feelsthe need to modify expected-utility theory for rational types, one could use thesame modi cationsfor people with projection bias. 12.Another psychological phenomenon that has received increasing atten- tionin research on intertemporal choice is hyperbolic discounting (see in particular,Laibson [1994, 1997] and O ’Donoghueand Rabin [1999a]). Under hyperbolicdiscounting, true preferences are time-inconsistent, and hence a person couldbe fullyaware of thisfact, asmuchof the literature has assumed. 13.Given the logic of our model, it is inherent that a personis unawareof her current misprediction.But onecould imagine a variantof the model where the personis awareof her future propensityto mispredict. She could, for instance, be awareof her general propensity to overshop when hungry, whilestill committing theerror ona case-by-casebasis. The coexistence of day-to-day mispredictions with a “meta-awareness ” ofthese mispredictions is similar to the discussion in O’Donoghueand Rabin [1999b] of how people can simultaneously be aware of theirgeneral tendency to procrastinate and yet still procrastinate on a case-by- casebasis. A modelof “sophisticatedprojection bias ” couldplausibly better de- scribebehavior in some circumstances, such as when sophisticated shoppers know thatthey should not shop on an empty stomach, but we choose our current formulationas a simpleand realistic starting point. 1220 QUARTERLY JOURNALOF ECONOMICS potentialimportance of projectionbias foreconomics, Sections IV and Vformallyanalyze twoeconomic environments.

IV. PROJECTION BIAS AND HABIT FORMATION Forhalf acentury,though most intensively recently, econo- mistshave explored life-cycle consumption models with habit formation.Habit formation —whereinincreases in currentcon- sumptionincrease future marginal utility —was discussed by Duesenberry[1949], and laterformalized by Pollak[1970] and Ryder and Heal[1973]. In recentyears, habit-formation models havebeen used in speci capplications: seeBecker and Murphy [1988], Constantinides [1990], Abel [1990], Campbell and Coch- rane[1999], Jermann[1998], Boldrin,Christiano, and Fisher [2001], Carroll,Overland, and Weil[2000], and Fuhrer[2000]. All ofthese recent researchers have examined habit formationwithin therational-choice framework. 14 In this sectionwe formally analyze theimplications of projectionbias overhabit formationin asimple “eat-the-cake ” model. Suppose that apersonhas income Y toallocate over consumption in periods1, . .., T,whichwe denote by c1 , . . . , cT . For simplicity, weassume that thereis nodiscounting, and that the personcan borrowand saveat 0percentinterest; neither of these assumptionsis importantfor our qualitative conclusions.The person’strueinstantaneous utility in period t is u(ct,st), where the state st canbe thought of as her “habit stock. ” The person’s initial habit stock, s1 is exogenous,and herhabit stockevolves accordingto st 5 (1 2 g)st2 1 1 gct2 1 for some g [ (0,1]. Hence, themore the person consumes in agivenperiod, the higher is her subsequenthabit stock.The parameter g representshow quickly theperson develops (and eliminates)her habit. Weassume that instantaneousutility takesa particularly simplefunctional form:

14.The early literature on habitformation distinguishes between two polar cases: “rationalhabits ” whereinconsumers fully account for how current consumptionaffects future well-being, and “myopichabits ” whereinconsumers do not accountat allfor how current consumptionaffects future well-being. Of thepapers citedin the text, all assume rational habits except for Pollak [1970], which (implicitly)assumes myopic habits. Our modelis equivalent to rational habits when a 5 0andto myopic habits when a 5 1.Muellbauer [1988] provides an excellentoverview of the two extremes,and concludes that the empirical evidence seemsto favor myopic habits. We return tothis and other empirical evidence in Section VI. PROJECTION BIAS 1221

u~ct,st! 5 v~ct 2 st!, where v9 . 0 and v0 , 0. Thisformulation is potentially restrictive,but it capturesthe key featureof habit formationand is commonin theliterature. 15 Thereare actually twokey features that play arolein ourresults below.First, the marginal utility fromconsumption is increasing in thehabit stock( ][]u/]c]/]s . 0),whichimplies habit formation—an increasein currentconsumption increases the future habit stockand thereforeincreases the marginal utility from futureconsumption. Second, the level of utility is decliningin the habit stock( ]u/]s , 0), whichimplies that an increasein current consumptionreduces the utility fromfuture consumption. Al- thoughthis negative “internality ” [Herrnsteinet al. 1993] is not an inherentpart ofhabit formation,it is presentin mostformal analyses,and real-worldinstances, of habit formation. In period1 theperson faces the following choice problem, where s1 is exogenous:

T max U˜ 1~c , . . . , c us ! 5 @~1 2 a!v~c 2 s ! 1 av~c 2 s !# ~c1, . . . ,cT! 1 T 1 O t t t 1 t51 such that

T 5 2 1 # st ~1 g!st21 gct21 for t [ $2, . . . , T% and O ct Y. t51

Forease of presentation, let ( c*1, . . . , c*T)denoterational behavior, A A whichsolves this maximizationwhen a 5 0, and let (c 1 , . . . , c T) denoteplanned behaviorfrom the period 1 perspectivefor a person with a . 0,with thevalue of a suppressed in thenotation. Our analysis throughoutassumes interior solutions for both rational and actual behavior. Apattern typically emphasized in modelsof habit formation is that peoplechoose an increasingconsumption pro le—that is, c1 , . . . , cT —sothat theyare always consumingmore than

15.This formulation is equivalentto that used by Pollak [1970], Constantin- ides[1990], Jermann [1998], Campbell and Cochrane [1999], and Boldrin, Christiano,and Fisher [2001]; indeed, all these papers except Pollak further assume that v takesa CRRA speci cation.Another formulation, proposed by Abel [1990]and used by Fuhrer [2000] and Carroll, Overland, and Weil [2000], g 1 2 s is u(ct,st) 5 (ct/st ) /(1 2 s).Yeta third formulation,suggested by Kahneman and Tversky’s[1979]prospect theory, is to assume that v0( x) , 0 for x . 0 but v0( x) . 0 for x , 0;Bowman, Minehart, and Rabin [1999] use a variantof this approach. 1222 QUARTERLY JOURNALOF ECONOMICS theyare accustomed to. This conclusion holds, however, only if the person’sinitial habit stock s1 is nottoo large. Otherwise, it mightbe optimal to break the initial habit, and theoptimal way todo somight involve a decliningconsumption path that lowers thehabit stockgradually overtime. 16 But sincebreaking a habit is bothleast painful and mostbene cial whendone early in life, beforethe habit has beenfurther developed and whenthe bene- ts will bespread overa largenumber of years,a rationalperson will breaka habit onlyat thebeginning of life.Lemma 1 formally establishesthis conclusionby demonstratingthat oncea person starts furtherdeveloping her habit —byconsumingmore than her habit stock—shewill followan increasingconsumption pro le fromthat periodonward.

LEMMA 1. If c*t $ s*t for some t , T, then c*t , c*t1 1 , . . . , c*T . Wefocuson theimplications of projection bias forsituations in whichrational behavior does not involve early-life habit-breaking episodes:our results below only apply toparameter values suchthat arationalperson would choosean increasingconsumption prole.Lemma 1 impliesthat asuf cientcondition for a rationalperson to choose an increasingconsumption pro le is s1 5 0;more generally, this outcomewill occuras longas the initial habit stock s1 is smallenough. Projectionbias createstwo types ofdistortions in this environment,because the person underappreciates both the negative internalityand thehabit formation.The implication of projection bias overthe negative internality is straightforward. Becauseit impliesthat earlyconsumption decreases utility in all laterperi- ods,the negative internality motivates a personto delay consumption.Hence, an underappreciationof the negative internality makesthe person prone to consume too much early in life and toolittle late in life relativeto rational behavior. The implication ofprojection bias overhabit formationis in principle morecomplicated becausethe basic effectof habit formationis complicated. But forthe case in whichrational behavior does not involve a habit-breaking episode,and thereforeinvolves an increasingcon- sumptionpro le,the person ’shabit stockwill beincreasingover time,and thereforehabit formationmakes her marginal utility

16.Indeed, for s1 . Y/T the person must havea habit-breakingepisode, and thisepisode might last her entire life; that is, she might have c*1 . c*2 . . . . . c*T . PROJECTION BIAS 1223 increaseover time. As aresult,habit formationalso motivates the personto delay consumption.Hence, an underappreciationof habit formation,like an underappreciationof thenegative internality,makes the person prone to consume too much early in life and toolittle late in life relativeto rational behavior. Proposition 1 reectsthis intuition,establishing that wheneverrational be- haviordoes not involve a habit-breaking episode,projection bias leads apersonto (plan to)consume too much early in life and too littlelate in life relativeto what would beoptimal. t A t PROPOSITION 1. If c*1 $ s1,thenfor any a . 0, St5 1 ct . St5 1 c*t for all t , T. Hence,projectio nbias causesa personto plan aconsump- tion prolethat consumesher income too quickly. Perhaps the cleanestillustrati onisintheextreme case where a 5 1, where theperson will plan toconsumethe same amount in all periods ratherthan increaseconsumpt ionover time as would be optimal.17 Moreinteresting is what happens as timepasses and the person’stasteschange in ways shedid notpredict. To study such effects,we examine how a person ’splans changein period2. In period2 theperson reoptimizes given her new perceived preferences;that is,she faces the following choice problem, where s1 A and c1 areexogenous:

T max U˜ 2~c , . . . , c us ! 5 @~1 2 a!v~c 2 s ! 1 av~c 2 s !# ~c2, . . . ,cT! 2 T 2 O t t t 2 t52 such that

A s2 5 ~1 2 g!s1 1 gc1

st 5 ~1 2 g!st21 1 gct21 for t [ $3, . . . , T%

T # 2 A and O ct Y c1 . t52

17.While the assumption that rational behavior does not involve a habit- breakingepisode is suf cientfor overconsumption, it isnot necessary. Proposition 1mightfail because, during ahabit-breakingepisode, habit formation and a declininghabit stock meanthe person ’smarginalutility declines over time, which inturn meansthat habit formation motivates the person to accelerate consumption,and so projectionbias over habit formation leads the person to consume her incometoo slowly. But Proposition1 neednot fail, because projection bias over the negativeinternality still motivates the person to consume her income too quickly. 1224 QUARTERLY JOURNALOF ECONOMICS

Rational behavior,of course, does not change over time, and hencethe solution to this problemfor a 5 0 is (c*2 , . . . , c*T ). For apersonwith projectionbias, thesolution for this problem,which A A A A wedenote by ( c2 , . . . . , cT ),maydiffer fromher period 1 A A plans (c2 , . . . , cT ).Proposition2 characterizesthis revisionof plans in thecase where she is developinga habit and T 5 3. A PROPOSITION 2.Suppose that T 5 3 and c1 . s1 . Then v- . 0 A A A A A A impliesthat c2 . c2 , v- , 0impliesthat c2 , c2 , and A A A v- 5 0impliesthat c2 5 c2 . As theperson ’shabit stockchanges over time, her (perceived) marginalutilities from consumption in eachperiod also change. Whenthe person is developinga habit, thesemarginal utilities all increase.18 Hence,the relative magnitudes of these changes in marginalutility determinethe revision of plans. If v- 5 0, the increasein marginalutility is thesame for all periods,which impliesthat theperson ’smarginaltrade-offs havenot changed, and henceshe does not revise her consumption plan. If v- . 0, theincrease in marginalutility is largerfor period 2 than period 3,and as aresultshe revises her period 2 consumptionupward. If v- , 0,theincrease in marginalutility is smallerfor period 2, and sherevises her period 2 consumptiondownward. 19 Any utility functionthat satis esnonincreasing absolute riskaversion, which includes the CARA and CRRA families,must have v- . 0.Because this seemsa plausible restrictionon the instantaneousutility function,Proposition 2 suggeststhat projectionbias leads peopleto repeatedly readjust their immediate consumptionupwards relativeto their most recent plans. Hence, if peopleexperience habit formationin consumption,projection bias representsa possiblesource for actual saving beingsmaller than planned saving.Laibson, Repetto, and Tobacman[1998]

18.Formally, from a period t perspective,the (perceived) marginal utility fromperiod 2 consumptionis (1 2 a)v9(c2 2 s2 ) 1 av9(c2 2 st) 1 (1 2 a)gv9(c3 2 s3 ); and since s2 . s1 impliesthat v9(c2 2 s2 ) . v9(c2 2 s1 ), thismarginal utility is larger from a period2 perspective.Similarly, from a period t perspective,the (perceived) marginal utility from period 3 consumption is (1 2 a)v9(c3 2 s3 ) 1 av9(c3 2 st); and since s2 . s1 impliesthat v9(c3 2 s2 ) . v9(c3 2 s1),thismarginal utility is also larger from a period2 perspective. 19.We conjecture,but have not proved, that this conclusion holds for T . 3. Theresult that v- 5 0yieldsdynamic consistency is quitegeneral. For the case v- . 0,itis straightforward toshow that marginal utility increases most for period2 andleast for period T,andso, perhaps subject to additional regularity conditions,after reoptimization we should expect period 2 consumptionto in- creaseand period T consumptionto decrease. Analogous conclusions hold for the v- , 0 case. PROJECTION BIAS 1225 reviewconsiderable evidence that theactual saving ofmany householdsfalls shortof their plans. Theauthors posit self- controlproblems and naiveteabout those self-control problems as primarysources of this shortfall.Our analysis suggeststhat projectionbias, in theform of underappreciation of how increasing consumptionin thepresent will raiseone ’sconsumptionstan- dard in thefuture, might also contribute to such mispredictions. Whileour analysis assumesthat aperson ’slifetimeincome is exogenous,our model suggests implications for how projection bias mightin uencedecisions about how hard towork to increase income.Speci cally, let lA bethe marginal utility oflifetime incomeas perceivedfrom period 1, and let lA A bethe marginal utility oflifetime income as perceivedfrom period 2. Again lim- iting ourselvesto the case when a personis developinga habit and thehorizon is T 5 3,Proposition 3 establishesthat the marginalutility oflifetimeincome increases over time. A A A A PROPOSITION 3.Suppose that T 5 3 and c1 . s1 . Then l . l . Proposition3 re ectsa simpleintuition: as timepasses, and the person’srealand perceivedmarginal utilities from consump- tionincrease, income becomes more valuable. Extrapolating be- yondour formal framework, this resultsuggests that projection bias overhabit formationmight lead peopleto pursue higher incomethan planned as timepasses. Projection bias might,for instance,create a forcetoward choosinga laterand laterplanned retirementdate as timepasses, using theproceeds to increase consumption. 20 Similarly,with endogenousper-period labor-lei- suredecisions, projection bias mightcreate a tendencyto repeatedly increaselabor and decreaseleisure relative to earlier plans. Weare wary ofpushing this intuitiontoo far withoutfurther theoreticaland empiricalanalysis, however,because the logic of theargument assumes that thereis noreference dependence in leisure.But wedo note that this intuitionparallels theargu- mentsof many previous researchers, such as Scitovsky[1976] and Frank[1999], whohave argued that peoplespend toomuch timeand energygenerating wealth and toolittle time on leisure activities,and that peopleenjoy increases in theirmaterial con- sumptionless than theythink they will.

20.There is someevidence, however, that people are somewhat accurate at predictingtheir retirement dates (see Bernheim [1989]), although this may in part bedue to the existence of focalretirement ages. 1226 QUARTERLY JOURNALOF ECONOMICS

V. PROJECTION BIAS AND DURABLE GOODS Formost durable goods —suchas atent,a golf-swing trainer, ora JohnnyDepp video —peopleexperience day-to-day uctuationsin theirvaluations. For rational consumers, such uctua- tionsare virtually irrelevant,because they will purchasedurable goodsbased almostexclusively on theirexpected daily valuations forthe goods, and virtually ignoretheir valuations onthe day theyhappen tobe in thestore. But forpeople with projectionbias, buying decisionsare oversensitive to the momentary feelings they experiencewhen they happen tobe in thestore, and thusthe natureof day-to-day uctuationsbecomes important. In this sectionwe present a stylized modelthat identi essomeimplications ofsuch effects. Suppose that aperson ’svaluation ofa durable goodin period t is givenby arandomvariable mt, where mt is distributed iden- tically and independently acrossperiods, and has nite mean m# .

Theperson learns the realization of mt atthestart ofperiod t. For simplicity,we further assume that thedurable goodlasts for exactly D days, and that theperson cannot consume the good on theday shepurchases it. 21 Consider rsta consumerwho has justone opportunity, on day 1,to purchase the item; if shedoes not purchase it onday 1, shecannot purchase it at all. Wenormalize the person ’s intertemporalutility tobe zero when she does not buy theproduct. If shebuys theproduct at price P,shewill enjoythe bene ts of ownership,but mustforgo the consumption of other goods that shecould have nancedwith wealth P.22 Weassume that the person’sutility fromthe durable goodis additively separable from herutility forother goods, and that theprice P representsthe totalutility valueof the other goods forgone by purchasing the durable good.The person ’sstatein period t is hercurrent valuation, or st 5 mt.Finally,we assumethat thereis nodiscounting, or d 5 1;none of our conclusions depend onthis assumption. If theperson buys thedurable goodin period1, then, given

21.While it is often unrealistic to assume that the person cannot consume thegood on theday shepurchases it, none of our qualitative conclusions depend onthis assumption, and it vastly simpli esour analysis. 22.We take the price P tobe exogenous. In Loewenstein, O ’Donoghue,and Rabin[2000] we formulate a morecomplicated model that derives a monopolist ’s pricing andvaluation-changing sales-hype policies in the face of projectionbias by consumers. PROJECTION BIAS 1227 theinformation available, hertrue expected intertemporal utility is

D 1 5 2 5 2 E1@U # E1 O m11k P Dm# P. F k51 G

Apersonexhibiting simple projection bias perceivesher expected intertemporalutility tobe

D ˜ 1 5 2 1 2 E1@U # E1 O @~1 a!m11k am1# P F k51 G

5 Dm# 1 aD~m1 2 m# ! 2 P.

˜ 1 1 m1 . m# impliesthat E1 [U ] . E1 [U ], and m1 , m# impliesthat ˜ 1 1 E1 [U ] , E1 [U ].Hence,an underappreciationof day-to-day uctuationscan lead variouslyto underbuying or overbuying. If herday 1valuation is largerthan average,and sheprojects this above-averagevaluation ontothe future, the person is proneto overvaluethe durable good.If, in contrast,her day 1valuation is smallerthan average,and sheprojects this below-averagevalua- tiononto the future, she is proneto undervalue the durable good. In otherwords, a personwith projectionbias is toosensitive to hervaluation at purchasetime. 23 Whileprojection bias has ambiguouseffects in one-shotbuy- ing decisions,things changedramatically in themore realistic casewhere the person has multipleopportunities to buy adura- blegood. To make this point in aparticularly starkway, we supposethat theconsumer will purchasethe good at mostonce, and canbuy thegood in any period t [ {1,2,. ..}.In this situationa rationalperson either will buy thedurable goodim- mediatelyin period1 orneverbuy thedurable good,and shebuys thedurable goodif and onlyif Dm# 2 P $ 0.Intuitively,given our assumptionthat theperson cannot consume the good on theday shepurchases it, the net expected value of the durable goodis

23.If we allowed immediate consumption, a rationaltype wouldalso be sensitiveto her day 1valuation.But aprojector wouldstill be oversensitiveto her day 1valuation:indeed, the conclusion generalizes that an underappreciationof day-to-day uctuationsleads a personto overvalue the good when m1 . m# and undervalueit when m1 , m# . 1228 QUARTERLY JOURNALOF ECONOMICS independentof the valuation onthe date purchased.Hence, the goodis eitherworth purchasing immediatelyor not at all. 24 Apersonwith projectionbias, likea rationalperson, always perceives that thegood is eitherworth purchasing immediatelyor notat all. But herperception of whether it is worthpurchasing immediatelyis in uencedby hercurrent valuation. As aresult, sheends up purchasing thegood in the rstperiod that Dm# 1 aD(mt 2 m# ) 2 P $ 0. If we let mH denotethe largest value that mt mightpossibly takeon, then there will eventuallybe some periodin whichthe person perceives the good to be worth purchasing if and onlyif Dm# 1 aD(mH 2 m# ) 2 P . 0. Because mH . m# ,apersonwith projectionbias is unambiguouslymore prone to buy thedurable goodthan is arationalperson: she will always buy whenshe should buy,and sometimeswhen she should not. Theintuition behind this conclusionis aninherentasymme- tryin purchasesof durable goods.A decisionnot to buy is revers- ible,so if theperson does not buy today whenshe should, she can still buy in thefuture. But adecisionto buy is irreversible,so if shebuys today whenshe should not, she cannot unbuy in the future.With multiple buying opportunities,a personis pronenot tobuy whenshe should onlyin theunlikely event that shehas a particularly lowvaluation on every buying opportunity,whereas sheis proneto buy whenshe should notin thequite likely event that shehas aparticularly high valuation onat leastone buying opportunity.Hence, projection bias representsa sourceof “impulse purchases ” whereinpeople overbuy durable goodsin re- sponseto transitory desire for that good.Many priortheoretical treatmentsof impulsepurchases have attributed thephenomena tohyperbolic discounting. But fordurable goods,projection bias is morerelevant than hyperbolicdiscounting. Hyperbolic discounting providesa compellingexplanation foroverconsumption on cumulativesmall-scale consumption decisions, such as purchases ofpotato chips, where the net effects of repeatedpurchases can be vast overconsumptionof potatochips. The purchase of a durable good,however, is by its verynature a long-term-consumption decision.As such,self-control problems are less likelyto be implicated in thepurchase of durable than nondurablegoods, whereasprojection bias is morelikely to be implicated.

24.Formally, we assume that when indifferent between buying now versus buyingin the future, people choose to buy now (which would be optimal if we replace d 5 1 with d , 1butvery closeto 1). PROJECTION BIAS 1229

Ouranalysis suggeststhat certaintypes ofsales tactics mightbe understoodas attemptsby businessesto exploitprojec- tionbias. If consumersoverestimate the longevity of theircurrent feelings,sellers will havean incentiveto induce high valuations whenpeople are making buying decisions,via saleshype, enticing displays, ormood-inducingmusic. Sellers will alsohave an incentiveto pressure people to make purchase decisions when hot, and tofacilitate rapid purchasesby consumerswho are in ahotstate that is unlikelyto last, suchas one-clickshopping ontheinternet. Finally,projection bias mightmotivate rmsto turn nondurable goodsinto durable goodsvia “intertemporalbundling, ” e.g., selling membershipsin healthclubs, golf clubs, vacation time shares, orseason ski passes. Consider, for instance, a personwho be- comesenthusiastic about exercise and makesa visit toa health club.Rather than makinga pro tsolelyon that onevisit, the healthclub mayexploit the consumer ’stendencyto project her currententhusiasm into the future by offeringa moreexpensive “club membership ” that entitlesthe person to additional free(or low-cost)visits in thefuture. Indeed, Della Vigna and Mal- mendier[2002] empiricallydocument that peopleoverpay for healthclub memberships.Using a panel data setthat tracks membersof three New England healthclubs, they nd that memberswho chose a contractwith a at monthlyfee paid aprice pervisit of$17, and memberswho chose a contractwith a at yearlyfee paid apriceper visit of$15, eventhough a $10-per-visit contractwas alsoavailable. Della Vigna and Malmendierat- tributethese ndings topartially naiveself-control problems: peoplesign up in an attemptto “commit” themselvesto future exercise,but thendo not have enough self-control to carry out theseplans. Ourmodel suggests an additional possibleexplana- tion:people plan toattend frequentlybecause they project their currententhusiasm into the future, but thendecide not to attend in thefuture when their enthusiasm has waned. 25 In addition tohelping toexplain salestactics, our analysis mayalso shed light onlaws designed tocounteract them. Cooling- off laws enactedat boththe state and federallevel allow consum- ersto rescindcertain types ofpurchaseswithin afewdays ofthe

25.We suspectthat another contributory factor isthat people dislike paying onthe margin for consumption [Prelec and Loewenstein 1998]. Neither this nor projectionbias is likely to explain Della Vigna and Malmendier ’sevidenceof procrastinationin canceling memberships, which is more consistent with naive self-controlproblems. 1230 QUARTERLY JOURNALOF ECONOMICS transaction. 26 Suchlaws canbe viewed as devicesfor combatting theeffects of projection bias. Cooling-off periodsthat forcecon- sumers to reecton theirdecisions for several days candecrease thelikelihood that theyend up owningproducts that theyshould not.Cooling-off laws mayalso have the bene tofreducingsales- persons’ incentivesto hype. If consumerscan return products oncethey cool down and ifsuchreturns are costly for the seller, sellerswill havean incentiveto put buyersin along-runaverage moodrather than an overenthusiasticstate. Althoughour analysis focusessolely on random uctuations in tastes,more generally durable goodsmight involve other types oftaste changes. Projection bias oversuch changes could yield furtherinteresting conclusions. For some durable goods,a person’svaluation systematicallydeclines over time as the “novelty” wearsoff. Projection bias oversuch taste changes would createa tendencyto overbuy,and hence rmsmight engage in attemptsto createincreased feelings of novelty. Alternatively, for other du- rablegoods, a person ’svaluation increasesover time as theper- sondevelops a tastefor the good (or becomes attached tothe good).Projection bias overthese taste changes would createa tendencyto underbuy. In suchcases rmsmight, in fact, engage in behaviorsdesigned toovercome projection bias, suchas offering afree-trialperiod.

VI. OTHER APPLICATIONS SectionsIV and Vderivethe implications of projectionbias in two speciceconomicenvironments. These implications highlight twotypes oferrors to which projection bias cangive rise. First, thefailure topredict futuretaste changes can lead tomisguided choicesfor current consumption, e.g., overconsumption due to underappreciationof habit formation,and oversensitivityto cur- rentvaluations as aresultof exaggerating the longevity of day- to-day uctuationsin tastes.Second, as perceivedtastes change overtime in ways that peopledo not predict, people make plans that theymay end up notcarrying out; e.g., people may consume more(and saveless) than earlierplanned. Webelieve that projectionbias is importantfor many economic applications, and that it canprovide an intuitiveand parsimoniousaccount for manyphenomena that areotherwise dif cultto explain. In this

26.For a detaileddiscussion of such laws, see Camerer et al.[2003]. PROJECTION BIAS 1231 sectionwe extrapolate from our formal analysis in SectionsIV and Vtodiscuss additional implicationsof projection bias. Thereare many implications of projection bias forrecent modelsof habit formationbeyond the formal analysis in Section IV. In recentyears economists have often invoked habit formation in consumptionas an explanation forempirical phenomena that arehard tounderstand within astationary-utility framework.As wediscuss in SectionIV, forinstance, habit formationis some- timesinvoked as an explanation forwhy peoplechoose consumption prolesthat increaseover time. In addition, Constantinides [1990] arguesthat habit formationcan providean explanation for theequity-premium puzzle, becauseit leads peopleto expect to maintain highlevels of risk aversion even with risinglevels of consumptionand wealth(see also Abel [1990] and Campbell and Cochrane[1999]). Fuhrer[2000] showsthat habit formation mightexplain the “excesssmoothness ” ofconsumption (docu- mentedby Campbell and Deaton[1989]) and Carroll,Overland, and Weil[2000] demonstratethat habit formationcan explain recentempirical evidence that periodsof high aggregateincome growthseem to cause periods of high aggregate saving. These explanations derivefrom the fact that,because people expect to adapt totheir changing consumption levels, they adjust slowlyto shocksto their permanent income. Habit formationis acompellingexplanation forthese phenomena,because it accordswell with introspectionand common wisdom,and is consistentwith psychologicalevidence on adaptation.Even so, it has beenhard to nd directevidence of habit formationin time-seriesconsumption data. Dynan [2000] reviews themixed results from tests using aggregateconsumption data, and describeshow such tests might be prone to overstate the degreeof habit formation.Dynan thentests for habit formation using householddata onfoodconsumption, and nds noevidence ofhabit formation.Our model suggests an explanation:even if peopleare characterized by habit formation,projection bias may lead peopleto not react to that habit formationas stronglyas the rationalmodel suggests. Indeed, in oursimple eat-the-cake model,we saw exactlythis point:whereas introducing habit formationwould lead rationalconsumers to switch fromsmooth consumptionto an increasingconsumption pro le,projection bias underminesthis effect.In fact, fora personwith completepro- jectionbias, or a 5 1,the introduction of habit formationdoes not changeher behavior at all.Muellbauer [1988] makesa similar 1232 QUARTERLY JOURNALOF ECONOMICS point whenhe compares rational versus myopic habits —which is equivalentto a 5 0 and a 5 1in ourmodel. Speci cally,he points outthat habit formationwould showup in cross-sectionalevi- denceunder either assumption, but it would showup in time- seriesevidence only under the assumption of rational habits. Giventhat itis hard to ndevidenceof habit formationin time- seriesevidence, Muellbauer concludes that theevidence supports myopichabits. Hence,perhaps abetterhypothesis is that peopleare char- acterizedby acombinationof habit formationand projectionbias. If so,our model suggests where to look for additional evidence. Specically,it predicts speci cpatterns ofdynamic inconsistency. Wealready describedone such prediction in SectionIV: people with projectionbias overhabit formationwill plan tosave more in thefuture than theyactually endup saving (under theplausible assumptionof nonincreasingabsolute risk aversion). Extrapolat- ing fromour model, an additional areaon which there might be dynamic inconsistencyis charitablegiving. Charitable giving depends onatrade-off betweenthe bene ts ofgiving and thecost of forgonepersonal consumption. While the marginal utility ofcon- sumptionmay decline with wealth,habit formationreduces the magnitudeof this change.As aresult,people with projectionbias mayplan toincrease their charitable giving as theirwealth increasesby morethan theyactually endup doing. 27 An obviousapplication ofprojection bias is addiction. Ratio- nal-choicemodels of addiction provideplausible explanations for manydifferent patterns associatedwith addiction, but oftenhave difcultyaccounting for the most central problem: why dopeople becomeaddicted in the rstplace? Because habit formationis a natural way toformalize “addictiveness ”—indeed mostmodels of addiction usethis formulation —ouranalysis in SectionIV sug- geststwo reasons why peoplewith projectionbias mightbe over- proneto develop harmful addictions. First,projection bias may lead peopleto underappreciate the degree to which current con- sumptionhas negativeconsequences for their future health, em- ployment,and personallives; that is,they may underappreciate

27. A difculty withidentifying projection bias via dynamic inconsistency is thatthere are other sources of dynamic inconsistency, such as naive hyperbolic discounting.Here, saving less than planned and giving less than planned also seemconsistent with naive hyperbolic discounting; but in fact onecan distinguish thetwo sources because of the asymmetry in the predictions. Projection bias predictssaving less than planned and giving less than planned when wealth is increasing,but the opposite effects when wealth is declining. PROJECTION BIAS 1233 thenegative internality associated with addictive products.Sec- ond,and perhaps moreimportant, projection bias maylead people tounderappreciate the degree to which current consumption changestheir future desire for addictive products;that is,they mayunderappreciate the habit formationassociated with addic- tiveproducts. This second error is particularly perniciousbecause it canlead peopleto consumeaddictive products intheshort run, planning notto continue in thelong run, but thenend up becoming addicted. 28 Ouranalysis in SectionV ofday-to-day uctuationsin tastes is alsorelevant for addiction. In particular, it suggeststhat people mightoverreact to transitory changes in thecraving for ad- dictiveproducts. When a person ’scravingis particularly high, projectionbias will lead herto overestimate her future craving for thedrug, and thereforemay discourage her from any effortsto quit.Analogously, when her craving is particularly low,projectionbias will lead herto underestimate her future craving for the drug,and thereforemay cause her to make repeated painful effortsto quit onlyto fail in theseendeavors when her craving returnsto average or high levels.There is, in fact, empirical support foraddicts believingthat theirfuture craving will be similarto their current craving. Giordano et al. [2001] studied heroinaddicts whocame to a clinicfor a maintenancedose of Buprenorphine(similar tomethadone). These addicts wereasked tochoose between extra BUP orextracash onavisit scheduledfor vedays later,where half weregiven the choice right before receivingthe BUP and half weregiven the choice right after. Thosemaking the choice before receiving the BUP valued the futureBUP doseby almosttwice as muchas thosewho made the choiceafter receiving the BUP.

28.There is, in fact, evidencethat unaddicted cigarette smokers signi cantly underappreciatetheir own risk ofbecoming addicted. For instance, only 15 percentof highschool students who were occasional smokers (less than one cigarette perday) predictedthat they might be smoking in veyears, when in fact 42 percentwere still smoking veyears later, and 28 percent were daily smokers. But thereis also evidence that addicted cigarettesmokers underappreciate their risk ofstayingaddicted. For instance, 68 percentof highschool students who were heavysmokers (more than one pack perday) predictedthat they would still be smoking in veyears, while 80 percent were still smoking at least half a pack per day veyears later [U. S.DHHS1994].The mispredictions of occasional smokers arearguably larger than those for heavy smokers, and even the mispredictions of heavysmokers could be due to projection bias if theymade predictions while in a nicotine-satedstate. Even so, the average mispredictions of heavy smokers suggeststhat the mispredictions of eventhe occasional smokers might in part bedue tooveroptimism about self-control or other factors rather than projection bias. 1234 QUARTERLY JOURNALOF ECONOMICS

Projectionbias overthe endowment effect has furtherimplications(beyond thosein SectionII). Theusual explanation forthe endowmenteffect is that peopleadapt toowning or not owning objects,and that thereis morepain uponparting with objects than thereis joyupon obtaining objects.Projection bias overthis adaptation has severalinteresting implications. First, because projectionbias leads toexaggerated feelings of loss aversion, it magniesthesize of theendowment effect. In otherwords, while theendowment effect may be caused by valid expectationsthat losseswill hurtmore than gains will help,the endowment effect that weobservein experimentsmay be an exaggeratedresponse tothese real preferences. 29 Perhapsmore important is that people mayfail topredict theendowment effect. At apurelyindivid- ual level,this failurecan lead individuals tomake purchases with afalse senseof their reversibility, and undoubtedly lowersthe costto retailers of offering money-back guarantees and freere- turns.In bilateral economictransactions, it cancause distortions orbreak down in bargaining, becausebuyers will tendto under- estimateowners ’ reservationprices, and ownerswill tendto overestimatebuyers ’ reservationprices. Indeed, Van Boven,Dun- ning,and Loewenstein[2000] experimentallydemonstrate bargaining inef ciencydue to “buyers’ agents” underestimatingsell- ers’ reservationvalues. 30 As highlighted by ouranalysis in SectionV, projectionbias predicts suboptimal patterns ofbehavior when people make de- cisionswith long-termconsequences but experiencehighly variable day-to-day feelings.While our formal analysis concerned durable goods,more important life decisionssuch as marriage, divorce,and especiallyfertility all display sucha pattern.For suchlong-term decisions, momentary uctuationsin feelings should bevirtually irrelevant,but projectionbias will causepeo- ple toexaggerate their longevity and thereforeto give them too

29.Kahneman [1991, p. 143] and Tversky andKahneman [1991] argue that theendowment effect is a “bias” becausepeople ’sactualpain when losing an object isnot commensurate with their unwillingness to part withthat object. Evidence fromStrahilevitz and Loewenstein [1998] supports this interpretation. Loewen- stein, O’Donoghue,and Rabin [2002] present a detailedanalysis of the role of projectionbias in theendowment effect. 30.Also see Genesove and Mayer [2001], who ndevidence of nancialloss aversionin housing markets —ofpeopleexperiencing “pain” whenthey realize a nominalloss on theirhome. In particular, they ndthatsellers subject to nominal lossesset higher asking prices and exhibit a lowerhazard rate of sale.Projection biassuggests that the magnitudes of theseeffects may be largerthan justi ed by anytrue feelings of pain that people experience if and when they do sell their residenceat a loss. PROJECTION BIAS 1235 muchweight in theirdecisions. Hence, projection bias mightlead peopleto get married — ormake proposals ofmarriage that are costlyto rescind —in thethralls oflove,say things theylater wish theyhad notin a tofrage, and fail touse birth controlor to followsafe sexpractices in theheat of passion.There are, in fact, policiesthat seekto circumvent such tendencies: for example, in manystates there are mandatory time delays between ling for marriageor divorce and actual changesin status.And there seemsto be a demand formethods of birth controlthat allowone tocontrol fertility withoutmaking decisions in theheat of passion,such as Norplantand the “morningafter ” pill. Whereasmarriage, divorce, and fertility decisionsare dif - cultto reverse, suicide is totallyirreversible. Yet much suicidal behaviorseems to occur on impulse, or after only a relatively shortperiod of misery.Projection bias maywell contribute to this phenomenon.The literature on depressiondocuments a tendency forpeople who are depressed to project their depressed feelings notonly on thefuture, but alsoon the past. As Solomon[1998, p. 49] expressesit, “Whenyou are depressed, the past and the futureare absorbed entirely by thepresent. . ..Youcan neither rememberfeeling better nor imagine that youwill feelbetter. ” Otherresearch documents that thewill tolive varies dramati- cally overtime. In astudy of168 cancerpatients admitted toa hospital forend-of-life care,the patients ’ will tolive, as measured ona 100-point scale, uctuated an averageof 30 percentover a 12-hour periodand morethan 60 percentover a 30-day period [Chochinovet al. 1999]. Thecombination of such uctuationsand projectionbias also has importantrami cationsfor end-of-life care,in particular for theuse of mechanismssuch as “advanced directives ” and “living wills” that permitpeople to make decisions that will apply when theyare in ahealthstate that rendersthem unable to make decisionsfor themselves. The premise of suchtools is that healthy peoplecan make decisions that will re ecttheir own preferences whensick, but thepresence of projection bias would challengethe validity ofthis assumption(see Coppola etal.[1999] and Druley etal. [1993]). Indeed,in onestudy [Slevin etal. 1988], respondents wereasked whether they would accepta gruelingcourse of chemotherapyif it would extendtheir lives by threemonths. Whileonly 10 percentof healthy people said that theywould acceptthe chemotherapy, 42 percentof current cancer patients say theywould. A natural interpretationis that thevalue of aday 1236 QUARTERLY JOURNALOF ECONOMICS oflife is largerwhen the prospect of death is closeat hand, but projectionbias leads peopleto underappreciate this change. Projectionbias alsohas furtherimplications in themundane worldof consumer theory. Although economists usually capture satiation with astatic modelthat assumesdiminishing marginal utility,we usually havein mind adynamic notionthat theutility ofcurrent consumption depends onrecentconsumption. The satisfaction fromeating a pint oficecream is smallerif onehas just consumedanother pint oficecream. The satisfaction fromeating salmonis smallerif onehas already consumedsalmon for several eveningsin arow.Projection bias oversuch effects has diverse consequences.Most straightforwardly, it leads tooverconsump- tion,or at leastoverordering of appetite-dependent goods.More generally,people may be prone to overpurchase activities that theycurrently do not engage in. People may plan overlylong vacations,believing the ninth day lying onthe beach will be nearlyas enjoyableas the rst;and professionalswho have little timefor reading ortraveling may falsely anticipate theblissful- nessof spending theirretirement years with nonstopreading and traveling.Firms may, of course, take advantage ofsuch mispredictions,by sellinglarge quantities in advance;restaurants may takeadvantage ofprojection bias by offeringall-you-can-eat mealsto hungry diners who underestimate how quickly they will becomesatiated. Weconcludewith perhaps thebroadest implication of projectionbias: muchas in theopening quotation from Adam Smith, projectionbias will lead toa general “over-ratingthe difference betweenone permanent situation and another. ” Projectionbias overhabit formation,for instance, can lead peopleto overrate the differencesbetween “povertyand riches. ” In simpleterms, poor peoplewill overestimatehow good it would beto become rich, and richpeople will overestimatehow bad it would beto becomepoor. Perhapsmore important, because projection bias makespeople mispredicthow they themselves would behavein othersitua- tions,it canlead tomisunderstandings betweenthese two groups ofpeople. For instance, projection bias canlead low-wealthindi- viduals to ndthebehavior of wealthyindividuals reprehensible becausethey expect the rich to engage in morecharitable giving than theyactually do. Althoughon a smallerscale, there is experimentalevidence ofsuch misunderstandings betweengroups. As mentionedabove with regardto projection bias overthe endowment effect, Van PROJECTION BIAS 1237

Boven,Dunning, and Loewenstein[2000] experimentallydemon- stratebargaining inef ciencydue to “buyers’ agents” underesti- matingsellers ’ reservationvalues. They further show that when the buyers’ agentswere asked to explain thehigh pricesof the sellers,they rejected explanations that resembledthe endowment effectin favorof explanations that hingedon greedon thepart of thesellers. Much in thesame way that therich might seem greedyto the poor, projection bias overthe endowment effect can lead tonegative judgments of other people ’scharacters.To the extentthat suchnegative judgments might make people willing toincur losses to hurt others [Gibbons and Van Boven2001; Loewenstein,Thompson, and Bazerman1989], projectionbias mighthave both direct and indirectconsequences in everyday economicbehavior. Smithalso suggests that peopleare likely to exaggerate the importancebetween “private and public station, ” i.e.,social status.In recentyears, social-comparison theory, which studies the ways apersoncares about her status relativeto comparison groups,has receivedincreasing attention from economists. When peoplemake decisions that causetheir comparison groups to change—suchas switching jobsor buying ahousein anew neighborhood —projectionbias predicts that peoplewill underappreciatethe effects of achangein comparisongroups and hence, consistentwith Smith ’sassertion,overestimate the long-term satisfaction that would accompanysuch a change.As aresult, peoplemay be too prone to make reference-group-changing deci- sionsthat givethem a sensationof status relativeto theircurrent referencegroup. If apersonbuys asmallhouse in awealthy neighborhoodin part becauseit has acertainstatus valuein her apartmentbuilding, shemay not fully appreciate that herframe ofreference may quickly become the larger houses and bigger carsthat hernew neighbors have.

VII. DISCUSSION AND CONCLUSION Ourgoal in this paper has beento introduce a formalmodel that canimprove the realism of the economic analysis ofinter- temporaldecision-making by incorporatinga commonform of mispredictionof future preferences. The psychological evidence presentedin SectionII providessupport forthe existence of projectionbias, and ouranalysis and discussionin SectionsIV, V, and VIdemonstratethe potential importance of projection bias 1238 QUARTERLY JOURNALOF ECONOMICS foreconomics. We conclude by putting projectionbias in broader economiccontext, and discussing someshortcomings and potential extensionsof our model. Howmight one empirically identify projectionbias in eco- nomicdata? Accordingto our model, while people may be wrong in theirpredicted utility,they still obeythe axioms of “rational” choicein one-shotdecisions: they have well-de nedpredicted preferencesand makedecisions to maximizethose preferences. 31 Hence,if all weobserve is asingledecision by eachperson, projectionbias maybe dif cultto identify, exceptinsofar as we can nd eld-data analoguesof Read and van Leeuwen ’s [1998] experiments —instancesin whichpeople ’scurrentstate plays “too large” arolein theirdecisions. However, if weobserve multiple observationsfor each decision-maker, researchers can identify projectionbias throughdynamic inconsistency.We might com- paredirectly people ’splans and theirlater behavior, as in the Loewensteinand Adler [1995] experiments.Or we might indi- rectlyinfer dynamic inconsistencyfrom intertemporal behavior, as in thehealth-club evidencefrom Della Vigna and Malmendier [2002].32 Ourreview of evidenceand ouranalysis in this paper leavea numberof open questions. One is theextent to which projection bias diminisheswith experience.That projection bias operateson states,such as hunger,with whichpeople should haveample experiencesuggests that it doesnot disappear with experience. Moreover,an explicit testof the effect of repeated experience failed toproduce any appreciable learning[Van Boven,Loewen- stein,and Dunning 2003]. In this study, “buyers’ agents”—with incentivesto facilitate exchangebut at thelowest possible price — madetake-it-or-leave-it offers for an objectto sellers. There were verounds of possible trade, with feedbackafter each round aboutwhether the bids weretoo high ortoolow. Bids, whichwere initially toolow due to buyers ’ agents’ underappreciationof sellers’ attachmentsto objects, increased over the verounds, and convergedtoward thepro t-maximizing level.However, when a

31.Kahneman [1994] distinguishes between “experiencedutility, ” which re- ects one’swelfare,and “decisionutility, ” which reectsthe attractiveness of optionsas inferredfrom one ’sdecisions;projection bias represents a reasonwhy decisionutility may deviate from experienced utility. 32.When we observe dynamic inconsistency, the question arises whether the sourceis projectionbias or someother error, such as naivehyperbolic discounting. But aswe discuss in footnote 27, it is often possible to ndsituations where differentbehavioral errors predict differenttypes of dynamicinconsistency. PROJECTION BIAS 1239 newobject of similarvalue was substituted forthe original object, thesame pattern occurred.Subjects learned to adjust theirbids upward, but theydid notlearn to anticipate theendowment effect. Arelatedsecond open question is howaware are people of the bias. Theexistence of advice suchas “countto ten before you respond” or “nevershop on an emptystomach ” suggeststhat peopleare aware of projection bias ona meta-level.In addition, wesuspect that manyrules people develop are designed todeal with moment-by-momentprojection bias. Forinstance, in the contextof our durable-good model,people might develop rules suchas neverbuy acaron a rstvisit toa dealer.The need for suchrules provides further evidence that peoplesuffer from projectionbias, but alsoimplies that its damaging effectsmay be mitigated in manycircumstances. Athird openquestion concerns our treatment of projection bias as apureerror. We believethat perhaps themost important reasonto incorporate projection bias intoeconomics is toimprove welfareanalysis (ratherthan solelyto improve behavioral predictions)—tostudy, forinstance, whether addicts aremaking an optimal lifetimedecision to become addicts. As such,we have emphasized theways in whichpeople behave suboptimally. There may,however, be reasons to be more cautious about treating all changesin behavioras suboptimal. 33 As modelsthat re ectthe reality of bothshort-term uctuationsand long-termchanges in preferencesbecome more wide- spread in economics,economists must seriously address theques- tionof whether people accurately predict howtheir preferences will change.We hope our analysis and examplesillustrate the potentialbene ts forboth behavioral and welfareeconomics of incorporatingmispredictions of utilitiesin general,and projection bias in particular, intoformal economic analysis.

33.Projection bias might, for instance, serve the interests of the human race tothe detriment of the individual; e.g., the failure to appreciate adaptation to paraplegiaor blindness may help to limit the number of disabled people in the population.A fullnormative analysis should, as always, take into account such externalities,and it is possible that projection bias mitigates them. Similarly, at theindividual level it is possible that projection bias serves to mitigate other errors;e.g., to work againstfactors such as self-controlproblems or underappreciationof risks that might cause people to exert too little effort at avoiding paraplegia.But wesee no reason to expect projection bias to more often mitigate externalitiesand other errors as opposedto exacerbate them, and we believe that inany event full articulation of all errors and externalities, including projection bias,is the appropriate way toconduct welfareanalysis. 1240 QUARTERLY JOURNALOF ECONOMICS

APPENDIX: PROOFS

Proofof Lemma1. Toeaseour notation, we use v*t [ v9(c*t 2 b s*t) for all t.Also,for any function g(i), we say Si5 a g(i) 5 0 when a . b.

Given a 5 0, the rst-orderconditions are v*t 2 X*t 5 l* for all t, where l*is themultiplier on the income constraint, and T t2 (t1 1 ) X*t [ g St5 t1 1 (1 2 g) v*t .Hence,for all t, v*t2 1 2 X*t2 1 5 v*t 2 X*t or v*t2 1 2 v*t 5 X*t2 1 2 X*t. Because X*t2 1 2 X*t 5 g(v*t 2 X*t),and because v*t 2 X*t 5 v*T ,it followsthat forall t, v*t2 1 2 v*t 5 gv*T . 0,which in turnimplies v*t 5 (1 1 (T 2 t)g)v*T . Hence, v*1 . . . . . v*T,whichgiven v0 , 0 implies c*1 2 s*1 , . . . , c*T 2 s*T . For any t, c*t $ s*t impliesthat c*t $ s*t11 $ s*t;combiningthese conditionswith c*t11 2 s*t11 . c*t 2 s*t impliesthat c*t11 . c*t $ s*t11. Hence, if c*t $ s*t for some t , T, then c*t11 . c*t $ s*t11, which in turnimplies that c*t12 . c*t11 $ s*t12,and soforth. The result follows.

Proofof Proposition 1. We use v*t as in theproof of Lemma 1, and notethat c*1 $ s1 implies c*1 , . . . , c*T and also c*t 2 s*t . A A A A 0 for all t . 1.We also use vt [ v9(ct 2 st ) and vˆ t [ v9(ct 2 A A s1 ),and notethat vˆ t . vˆ s if and onlyif ct , cs . The rst-order A A A A conditionsare vt 2 Xt 1 a/(1 2 a)vˆ t 5 l /(1 2 a), where l is A T themultiplier on theincome constraint, and Xt [ g St5 t1 1 (1 2 t2 (t1 1 ) A A A A A g) vt .Hence,for all t, vt2 1 2 vt 5 Xt2 1 2 Xt 1 a/(1 2 A A A A a)[vˆ t 2 vˆ t2 1 ]. Because Xt2 1 2 Xt 5 g(vt 2 Xt ),and because A A A A vt 2 Xt 5 vT 1 a/(1 2 a)[vˆT 2 vˆt],it followsthat forall t, vt21 2 A A vt 5 gvT 1 a/(1 2 a)[gvˆ T 2 (vˆ t2 1 2 (1 2 g)vˆ t)].By starting with thecondition for t 5 T and iteratingbackwards, wecan derivethat forall t,

A A vt 5 ~1 1 ~T 2 t!g!vT

a T 1 @~1 1 ~T 2 t!g!vˆ 2 ~vˆ 1 g vˆ !#. S 1 2 aD T t O i i5t11

A It is usefulto rewrite this conditionas vt /(1 1 (T 2 t)g) 1 A a/(1 2 a) Rt /(1 1 (T 2 t)g) 5 vT 1 a/(1 2 a)vˆT, where Rt 5 T (vˆ t 1 g Si5t11 vˆ i).Also notethat forall t and s, PROJECTION BIAS 1241

A vt 2 v*t a Rt (1) 1 ~1 1 ~T 2 t!g! 1 2 a ~1 1 ~T 2 t!g! A vs 2 v*s a Rs 5 1 . ~1 1 ~T 2 s!g! 1 2 a ~1 1 ~T 2 s!g! Wenext establish twoclaims. A A Claim 1.There exist t and s such that vt , v*t and vs . v*s. Proof. Suppose otherwise.First, consider the case in which A A vt 5 v*t for all t,whichimplies that ct 5 c*t for all t. Applying A equation(1), vt 5 v*t for all t impliesthat Rt/(1 1 (T 2 t)g) 5 Rs/(1 1 (T 2 s)g) for all t and s;but this requiresthat vˆ t 5 vˆ s A A and therefore ct 5 cs for all t and s,whichcontradicts A c*1 , . . . , c*T .Nextconsider the case in which vt # v*t and A A therefore ct 2 st $ c*t 2 s*t for all t,wherethe inequalities are A A A strictfor some t. For any t, if st $ s*t, then ct 2 st $ c*t 2 s*t A A A impliesthat ct $ c*t and therefore st1 1 $ s*t1 1 ,whereeither st . A A A A s*t or ct 2 st . c*t 2 s*t impliesthat ct . c*t and st1 1 . s*t1 1 . In A A A addition, c1 2 s1 $ c*1 2 s*1 impliesthat c1 $ c*1 and therefore A A A A A s2 $ s*2 , where c1 2 s1 . c*1 2 s*1 impliesthat c1 . c*1 and s2 . A A s*2 .It followsthat ct $ c*t for all t and ct . c*t for some t, which T A T contradictsthat St5 1 ct 5 St5 1 c*t 5 Y.Finally,an analogous A A logicrules out the case in which vt $ v*t for all t and vt . v*t for some t. A Claim 2.There exists t# [ {1, . . . , T 2 1} such that vt # v*t A for t [ {1, . . . , t#} and vt . v*t for t [ {t# 1 1, . . . , T}. A Proof. Suppose otherwise.Let x [ max {tuvt # v*t}, which A existsgiven Claim 1,and let z [ max{t , xuvt . v*t},whichmust A existif theClaim 2is nottrue. Applying equation(1), vz . v*z and A vz1 1 # v*z1 1 togetherimply that Rz/(1 1 (T 2 z)g) , Rz1 1 /(1 1 T (T 2 z 2 1)g),whichmeans [ vˆ z 1 gvˆ z1 1 1 g Si5 z1 2 vˆ i]/(1 1 T (T 2 z)g) , [vˆ z1 1 1 g Si5 z1 2 vˆ i]/(1 1 (T 2 z 2 1)g) or

(2) @1 1 ~T 2 z 2 1!g#vˆ z 2 @1 1 ~T 2 z 2 1!g~1 2 g!#vˆ z11

T , 2 g O vˆ i. i5z12

Weprove that inequality (2) cannothold, from which Claim 2 follows. A A We rstestablish that ct . cz and therefore vˆ t , vˆ z for all 1242 QUARTERLY JOURNALOF ECONOMICS t [ { z 1 1, . . . , x}. Because v*t . v*t1 1 for all t,it followsthat A A A vz . v*z . v*t $ vt for all t [ { z 1 1, . . . , x}. Since vt # v*t A A A A impliesthat ct 2 st $ c*t 2 s*t, c*t 2 s*t . 0impliesthat ct . st A A A A and therefore st1 1 . st , and so st . sz1 1 for all t [ { z 1 2, . . . , A A A A A A A x}. If cz , sz , then sz1 1 . cz ,and therefore ct . st $ sz1 1 . A A A A A A A cz . If instead cz $ sz , then sz1 1 $ sz , and since vz . vt implies A A A A A A A A A that cz 2 sz , ct 2 st , st $ sz1 1 $ sz impliesthat ct . cz . If x 5 T, then vˆ t , vˆ z for all t [ { z 1 2, . . . , T}, and 2 T 2 therefore g Si5 z1 2 vˆ i , g (T 2 z 2 1)vˆ z. But then vˆ z . vˆ z1 1 2 impliesthat g (T 2 z 2 1)vˆ z , [1 1 (T 2 z 2 1)g]vˆ z 2 [1 1 (T 2 z 2 1)g(1 2 g)]vˆ z1 1 ,whichcontradicts inequality (2). A Considerinstead x , T. Given (vt 2 v*t) 1 a/(1 2 a) Rt 5 A (1 2 (T 2 t)g)[vT 2 v*T 1 a/(1 2 a)vˆ T ],it followsthat forall t A A and s, 1/(s 2 t)[(vt 2 v*t) 2 (vs 2 v*s ) 1 a/(1 2 a)(Rt 2 A A A Rs)] 5 2g[vT 2 v*T 1 a/(1 2 a)vˆT]. Hence, (vz 2 v*z) 2 (vz1 1 2 A A v*z1 1 ) 1 a/(1 2 a)(Rz 2 Rz1 1 ) 5 1/n[(vx 2 v*x) 2 (vx 1 n 2 A A v*x1 n) 1 a/(1 2 a)(Rx 2 Rx1 n )]. Given vz . v*z, vz1 1 # v*z1 1 , A A vx # v*x , and vx1 n . v*x1 n,it followsthat ( Rx 2 Rx1 n ) 2 n(Rz 2 n 2 1 Rz1 1 ) . 0. Because Rx 2 Rx1 n 5 vˆ x 1 g Si5 1 vˆ x1 i 2 (1 2 g)vˆ x 1 n and Rz 2 Rz1 1 5 vˆ z 2 (1 2 g)vˆ z1 1 ,this condition becomes (Rx 2 Rx1 n ) 2 n(Rz 2 Rz1 1 ) 5 (1 2 g)(vˆ z1 1 2 vˆ x1 n ) 1 n 2 1 [vˆ x 1 (n 2 1)vˆ z1 1 2 nvˆ z] 1 g Si5 1 (vˆ x1 i 2 vˆ z1 1 ) . 0. Since vˆ x , vˆ z and vˆ z1 1 , vˆ z,applying this conditionfor n 5 1 yields vˆ z1 1 . vˆ x1 1 ,and thenapplying it for n 5 2 yields vˆ z1 1 . vˆ x1 2 , and so forth.It followsthat vˆ x1 n , vˆ z1 1 , vˆ z for all n [ {1, . . . , T 2 2 x},and therefore vˆ t , vˆ z for all t [ { z 1 1, . . . , T}. But then g T 2 Si5 z1 2 vˆ i , g (T 2 z 2 1)vˆ z , [1 1 (T 2 z 2 1)g]vˆ z 2 [1 1 (T 2 z 2 1)g(1 2 g)]vˆ z1 1 ,whichcontradicts inequality (2). Claim 2follows. Finally,we provethe main result. Posit otherwise, and de ne t A t w [ min{tuSi5 1 ci # Si5 1 c*i}.Claims 1and 2togetherimply A A A that v1 , v*1 ,and therefore c1 . c*1 . Hence, w . 1, and cw , c*w . A Note that if w # t# (where t# denedas inClaim 2) then v1 , v*1 , A A and vt # v*t for all t [ {2, . . . , w 2 1},whichimplies that sw . s*w (using logicidentical tothat in proofof Claim 1). But then A A cw , c*w impliesthat vw . v*w ,whichcontradicts that w # t#. It A followsthat w . t# and therefore vw . v*w . A Dene y [ min {t . wuct $ c*t}; such a y mustexist. We can writethe state st as PROJECTION BIAS 1243

2 st 5 gct21 1 ~1 2 g!gct22 1 ~1 2 g! gct23 1 . . .

t22 t21 1 ~1 2 g! gc1 1 ~1 2 g! s1

t21 t22 t212j 5 2 2 2 j21 1 2 t21 g O ci g O ~1 g! O ci ~1 g! s1. i51 j51 F i51 G w w A t t A Then Si5 1 c*i $ Si5 1 c i and Si5 1 c*i , Si5 1 c i for all t , w togetherimply that

w w * 2 A 5 *2 A s w11 sw11 g O c i O ci S i51 i51 D

w21 w2j w2j 2 2 2 j21 *2 A . g O ~1 g! O c i O ci 0. j51 F S i51 i51 DG A A Moreover,when y . w 1 1, s*w 1 1 . s w 1 1 combinedwith c*t . c t A for all t [ {w 1 1, . . . , y 2 1}impliesthat s*y . s y . Since, by A A A the denition of y, c y $ c*y ,it followsthat c y 2 s y . c*y 2 s*y and A A therefore vy , v*y . But given vw . v*w ,this contradictsClaim 2. Theresult follows.

A Proofof Proposition2. As apreliminarystep, we prove c 1 , A A A c 3 and c 2 , c 3 .Positotherwise, and supposethat z [ arg A A A A A maxt[{1 ,2 } c t . Hence, c z $ c z1 1 and c z $ c T ,whichimplies that A A A vˆ z # vˆ z1 1 and vˆ z # vˆ T .Recall that vz 2 vz2 1 5 gvT 1 a/(1 2 a)[gvˆ T 2 (vˆ z 2 (1 2 g)vˆ z1 1 )]. Because gvˆ T 2 (vˆ z 2 (1 2 A A g)vˆ z 1 1 ) 5 (1 2 g)(vˆ z1 1 2 vˆ z) 1 g(vˆ T 2 vˆ z) $ 0, vz 2 vz1 1 . 0. A A A A Given v0 , 0,this impliesthat c z 2 s z , c z1 1 2 s z1 1 , and given A A A A c z $ c z1 1 ,this holds onlyif s z . s z1 1 ,whichin turnholds only A A A if c z , s z . But if z 5 1,this contradicts c 1 . s1 , and if z 5 2, A A A A A A this contradicts c 2 . c 1 . s 2 (c 1 . s1 impliesthat c 1 . s 2 ). 1 3 In period1, true utility is U (c1 ,c2 ,c3 ) 5 St5 1 v(ct 2 st), and perceivedutility is

3 ˜ 1 5 2 2 1 2 U ~c1,c2,c3us1! O @~1 a!v~ct st! av~ct s1!# t51

3 5 2 1 1 2 ~1 a!U ~c1,c2,c3! a O v~ct s1!. t51 1244 QUARTERLY JOURNALOF ECONOMICS

A A A ˜ 1 A A A Period1 behavior( c 1 ,c 2 ,c 3 )mustsatisfy ]U (c 1 ,c 2 ,c 3 us1 )/]c1 5 ˜ 1 A A A ˜ 1 A A A ˜ 1 ]U (c1 ,c2 ,c3 us1)/]c2 5 ]U (c1 ,c2 ,c3 us1)/]c3. Because ]U (c1,c2,c3us1)/]ct 5 1 ˜ 1 A A A (1 2 a)]U (c1,c2,c3)/]ct 1 av9(ct 2 s1) for t [ {1,2,3}, ]U (c1 ,c2 ,c3 us1)/ ˜ 1 A A A 1 A A A ]c2 5 ]U (c1 ,c2 ,c3 us1)/]c3 impliesthat (1 2 a)[]U (c1 ,c2 ,c3 )/]c2 2 1 A A A A A ]U (c1 ,c2 ,c3 )/]c3] 5 a[v9(c3 2 s1) 2 v9(c2 2 s1)]. A A After choosing c 1 . s1 ,in period2, the state is s 2 5 (1 2 A 2 A 3 g)s1 1 gc 1 ,trueutility is U (c2 ,c3 us 2 ) 5 St5 2 v(ct 2 st ), and ˜ 2 A 3 perceivedutility is U (c2 , c3 us 2 ) 5 St5 2 [(1 2 a)v(ct 2 st ) 1 A 2 A 3 A av(ct 2 s 2 )] 5 (1 2 a)U (c2, c3 us 2 ) 1 a St 5 2 v(ct 2 s 2 ). Period A A A A ˜ 2 A A A A A 2 behavior (c 2 ,c 3 )mustsatisfy ]U (c 2 ,c 3 us 2 )/]c2 5 ˜ 2 A A A A A 1 ]U (c 2 ,c 3 us 2 )/]c3 .Notethat for t [ {2,3}, ]U (c1 ,c2 ,c3 )/]ct 5 2 A ˜ 2 A ]U (c2 , c3 us 2 )/]ct for all c2 and c3 .Hence,because ]U (c2 , c3 us 2 )/ 1 A A ]ct 5 (1 2 a)]U (c 1 ,c2 ,c3 )/]ct 1 av9(ct 2 s 2 ) for t [ {2,3}, ˜ 2 A A A ˜ 2 A A A A A ]U (c 2 , c 3 us 2 )/]c2 2 ]U (c 2 , c3 us 2 )/]c3 5 a[v9(c 3 2 s1) 2 v9(c 2 2 A A A A s1)] 1 a[v9(c 2 2 s 2 ) 2 v9(c 3 2 s 2 )]. A A A A v- . 0, s 2 . s1 (which followsfrom c 1 . s1 ), and c 2 , c 3 A A A A A A togetherimply v9(c 2 2 s 2 ) 2 v9(c 2 2 s1) . v9(c 3 2 s 2 ) 2 v9(c3 2 s1), ˜ 2 A A ˜ 2 A A whichin turnimplies that ]U (c 2 , c 3 us2 )/]c2 . ]U (c 2 , c 3 us2 )/ ˜ 2 AA A AA A ]c3 .Giventhe concavity of U ,wemust have c 2 . c 2 and c 3 , c 3 . An analogousargument holds for v- , 0. A A A A v- 5 0impliesthat v9(c 2 2 s 2 ) 2 v9(c 2 2 s1 ) 5 v9(c 3 2 A A s 2 ) 2 v9(c 3 2 s1) 5 k(s2 2 s1 )forsome constant k (i.e., v- 5 0 impliesthat v9 is linearand decreasing,so 2k is theslope of v9), ˜ 2 A A ˜ 2 A A and so ]U (c 2 ,c 3 us2 )/]c2 5 ]U (c 2 ,c 3 us2)/]c3 .It followsthat A A A A A A (c 2 ,c 3 ) 5 (c 2 ,c 3 ).(Theconclusion that v- 5 0yields dynamic A consistencywould hold forany T and for any c 1 .)

Proofof Proposition 3. Usingthe notation from the proof of Proposition2,

1 A A A ]U˜ ~c1 ,c2,c3 us1! lA 5 ]c1 1 A A A ]U˜ ~c1 ,c2 ,c3 us1! 5 ]c2 1 A A A ]U˜ ~c1 ,c2 ,c3 us1! 5 , ]c3 ˜ 2 AA AA A ]U ~c2 , c3 us2 ! and lAA 5 ]c2 ˜ 2 AA AA A ]U ~c2 , c3 us2 ! 5 . ]c3 PROJECTION BIAS 1245

˜ 2 A A ˜ 2 A A A Theconcavity of U impliesthat l $ min {]U (c 2 , c 3 us 2 )/]c2 , ˜ 2 A A A ˜ 2 A A A ]U (c 2 , c 3 us 2 )/]c3 }. For t [ {2,3}wehave ]U (c 2 , c 3 us 2 )/]ct 5 ˜ 1 A A A A A A A ]U (c 1 ,c 2 ,c 3 us1 )/]ct 1 a[v9(c t 2 s 2 ) 2 v9(c t 2 s1 )]. Then s 2 . A s1 (which followsfrom c 1 . s1 )combinedwith v0 , 0 implies A A A ˜ 2 A that v9(c t 2 s 2 ) . v9(c t 2 s1 ).Hence,for t [ {2,3}, ]U (c 2 , A 2 ˜ 1 A A A A c 3 us 2 )/]ct . ]U (c 1 ,c 2 ,c 3 us1 )/]ct 5 l .Theresult follows.

CARNEGIE MELLON UNIVERSITY CORNELL UNIVERSITY UNIVERSITY OF CALIFORNIA, BERKELEY

REFERENCES Abel,Andrew, “AssetPrices under Habit Formation and Catching up with the Jones,” American EconomicReview, LXXX(1990), 38 – 42. Baron,Jonathan, David A. Asch,Angela Fagerlin, Christopher Jepson, George Loewenstein,Jason Riis, Margaret G. Stineman,and Peter A. Ubel, “Effect of AssessmentMethod on the Discrepancy betweenJudgments of Health Dis- ordersPeople Have and Do Not Have: A WebStudy, ” Medical Decision Making, forthcoming. Becker, Gary, andKevin Murphy, “ATheoryof Rational Addiction, ” Journal of Political Economy, XCVI(1988), 675 –700. Bernheim,B. Douglas, “TheTiming of Retirement: A Comparisonof Expectations andRealizations, ” inDavidA. Wise,ed., The Economicsof Aging (Chicago,IL: Universityof Chicago Press, 1989). Boldrin,Michele, Lawrence Christiano, and Jonas Fisher, “HabitPersistence, AssetReturns, and the Business Cycle, ” American EconomicReview, XCI (2001), 149–166. Bowman,David, Deborah Minehart, and Matthew Rabin, “LossAversion in a Consumption-SavingsModel, ” Journalof EconomicBehavior andOrganiza- tion, XXXVIII(1999), 155 –178. Boyd,Norman, Heather J. Sutherland,Karen Z. Heasman,David L. Tritcher,and BernardCummings, “WhoseUtilities for Decision Analysis? ” Medical Deci- sionMaking, X (1990), 58– 67. Camerer,Colin, Samuel Issacharoff, George Loewenstein, Ted O ’Donoghue,and MatthewRabin, “Regulationfor Conservatives: Behavioral Economics and the Case for ‘AsymmetricPaternalism, ’ ” University ofPennsylvania Law Review, CLI(2003),1211 –1254. Campbell,John, and John Cochrane, “By Forceof Habit:A Consumption-Based Explanationof Aggregate Stock MarketBehavior, ” Journalof Political Econ- omy, CVII(1999), 205 –251. Campbell,John, and Angus Deaton, “WhyIs ConsumptionSo Smooth? ” Review of EconomicStudies, LVI(1989),357 –374. Carroll,Christopher, Jody Overland, and David Weil, “Savingand Growth with HabitFormation, ” American EconomicReview, XC(2000),341 –355. Chochinov,Harvey M., Douglas Tataryn, Jennifer J. Clinch,and Deborah Dud- geon, “Willto Live in the Terminally Ill, ” The Lancet, CCCLIV (1999,Issue 9181,September 4), 816 – 819. Constantinides,George, “HabitFormation: A Resolutionof theEquity Premium Puzzle,” Journalof Political Economy, XCVIII(1990), 519 –543. Coppola,Kristen M., JamilaBookwala, Peter H. Ditto,Lisa K. Lockhart, Joseph H.Danks,and William D. Smucker, “ElderlyAdults ’ Preferencesfor Life- SustainingTreatments: The Role of Impairment,Prognosis, and Pain, ” Death Studies, XXIII(1999), 617 – 634. DellaVigna, Stefano, and Ulrike Malmendier, “OverestimatingSelf-Control: Evi- dencefrom the Health Club Industry, ” WorkingPaper, University of Califor- niaat Berkeley and Stanford University, 2002. 1246 QUARTERLY JOURNALOF ECONOMICS

Druley,Jennifer A., PeterH. Ditto,Kathleen A. Moore,Joseph H. Danks,A. Townsend,and William D. Smucker, “Physicians’ Predictionsof Elderly Out- patients’ Preferencesfor Life-Sustaining Treatment, ” Journalof Family Practice, XXXVII(1993), 469 –475. Duesenberry,James, Income,Saving, and the Theoryof Consumer Behavior (Cambridge,MA: HarvardUniversity Press, 1949). Dynan,Karen, “HabitFormation in ConsumerPreferences: Evidence from Panel Data,” American EconomicReview, XC(2000),391 –406. Frank, Robert, LuxuryFever (NewYork, NY: FreePress, 1999). Frederick,Shane, and George Loewenstein, “HedonicAdaptation, ” in Daniel Kahneman,Edward Diener,and Norbert Schwarz, eds., Well-Being: The Foundationsof Hedonic Psychology (NewYork, NY: Russell Sage Foundation Press,1999). Fuhrer,Jeffrey, “HabitFormation in Consumptionand Its Implications for Mone- tary-PolicyModels, ” American EconomicReview, XC(2000),367 –390. Genesove,David, and Christopher Mayer, “LossAversion and Seller Behavior: Evidencefrom the Housing Market, ” Quarterly Journalof Economics, CXVI (2001),1233 –1260. Gibbons,Robert, and Leaf Van Boven, “ContingentSocial Utility in thePrisoners ’ Dilemma,” Journalof Economic Behavior andOrganization, XLV (2001), 1–17. Gilbert,Daniel T., MichaelJ. Gill,and Timothy D. Wilson, “TheFuture Is Now: TemporalCorrection in AffectiveForecasting, ” Organizational Behavior and HumanDecision Processes, LXXXVIII(2002), 430 –444. Gilbert,Daniel T., Elizabeth C. Pinel,Timothy D. Wilson,Stephen J. Blumberg, andThalia P. Wheatley, “ImmuneNeglect: A Sourceof Durability Bias in AffectiveForecasting, ” Journalof Personality andSocial Psychology, LXXV (1998), 617–638. Giordano,Louis A., WarrenK. Bickel,George Loewenstein, Eric A.Jacobs,Gary J.Badger,and Lisa A. Marsch, “MildOpioid Deprivation and Delay to ConsequencesAffects How Opioid-Dependent Outpatients Value an Extra MaintenanceDose of Buprenorphine, ” WorkingPaper, Substance Abuse TreatmentCenter, Psychiatry Department,University of Vermont,Burling- ton, 2001. Helson,Harry, Adaptation-Level Theory:An Experimental andSystematic Ap- proach toBehavior (NewYork, NY: Harperand Row, 1964). Herrnstein,Richard, George Loewenstein, Drazen Prelec, and William Vaughan, Jr., “UtilityMaximization and Melioration: Internalities in Individual Choice,” Journalof Behavioral Decision Making, VI(1993),149 –185. Jepson,Christopher, George Loewenstein, and Peter Ubel, “Actualversus Esti- matedDifferences in Quality of Life before and after Renal Transplant, ” WorkingPaper, Department of Socialand Decision Sciences, Carnegie Mellon University,2001. Jermann,Urban, “AssetPricing inProduction Economies, ” Journalof Monetary Economics, XLI(1998),257 –275. Kahneman,Daniel, “Judgementand Decision-Making: A PersonalView, ” Psycho- logical Science, II(1991),142 –145. ——, “NewChallenges to the Rationality Assumption, ” Journalof Institutional and Theoretical Economics, CL (1994),18 –36. Kahneman,Daniel, and Amos Tversky, “ProspectTheory: An Analysisof Decision under Risk,” Econometrica, XLVII(1979), 263 –291. Kahneman,Daniel, Jack L.Knetsch,and Richard H.Thaler, “Anomalies:The EndowmentEffect, LossAversion, and Status Quo Bias, ” Journalof Eco- nomicPerspectives, V(1991Winter), 193 –206. Laibson,David, “Essayson Hyperbolic Discounting, ” Ph.D.thesis, Department of Economics,Massachusetts Institute of Technology,1994. ——, “GoldenEggs andHyperbolic Discounting, ” Quarterly Journalof Economics, CXII(1997), 443 – 477. Laibson,David, Andrea Repetto, and Jeremy Tobacman, “Self-Controland Saving forRetirement, ” BrookingsPapers onEconomic Activity, 1 (1998), 91–196. Loewenstein,George, “Out ofControl:Visceral In uenceson Behavior, ” Organi- zationalBehavior andHuman Decision Processes, LXV(1996),272 –292. PROJECTION BIAS 1247

——, “AVisceralAccount ofAddiction, ” inJon Elster and Ole-J ørgenSkog, eds., Getting Hooked:Rationality and Addiction (Cambridge,UK: CambridgeUni- versityPress, 1999). Loewenstein,George, and Daniel Adler, “ABiasin the Prediction of Tastes, ” EconomicJournal, CV(1995),929 –937. Loewenstein,George, and Erik Angner, “Predictingand Indulging Changing Preferences, ” inGeorge Loewenstein, Daniel Read, and Roy Baumeister, eds., Time andDecision: Economicand Psychological Perspectives onIntertempo- ral Choice (NewYork, NY: RussellSage Foundation Press, 2003). Loewenstein,George, and Shane Frederick, “PredictingReactions to Environmen- tal Change,” inMaxBazerman, David Messinck, Ann Tenbrunsel, and Kim- berlyWade-Benzoni, eds., Environment,Ethics, andBehavior (SanFrancisco, CA: NewLexington Press, 1997). Loewenstein,George, and David Schkade, “Wouldn’tItBe Nice? Predicting Fu- tureFeelings, ” inDanielKahneman, Edward Diener,and Norbert Schwarz, eds., Well-Being: The Foundationsof Hedonic Psychology (NewYork, NY: RussellSage Foundation Press, 1999). Loewenstein,George, Daniel Nagin, and Raymond Paternoster, “TheEffect of SexualArousal on Predictionsof Sexual Forcefulness, ” Journalof Crime and Delinquency, XXXIV(1997), 443 –473. Loewenstein,George, Ted O ’Donoghue,and Matthew Rabin, “ProjectionBias in PredictingFuture Utility, ” Departmentof Economics Working Paper E00- 284,University of Californiaat Berkeley,2000. Loewenstein,George, Ted O ’Donoghue,and Matthew Rabin, “ProjectionBias in PredictingFuture Utility, ” Centerfor Analytic Economics Working Paper 02-11,Cornell University, 2002. Loewenstein,George, Leigh Thompson, and Max Bazerman, “SocialUtility and DecisionMaking in Interpersonal Contexts, ” Journalof Personality and SocialPsychology, LVII(1989), 426 – 441. Muellbauer,John, “Habits,Rationality and Myopia in the Life Cycle Consumption Function,” Annales d’Economieet de Statistique, IX(1988),47 –70. Nisbett,Richard E.,andDavid E. Kanouse, “Obesity,Hunger, and Supermarket ShoppingBehavior, ” Proceedings ofthe AnnualConvention of the American PsychologicalAssociation, III(1968),683 –684. O’Donoghue,Ted, and Matthew Rabin, “DoingIt Now or Later, ” American Eco- nomicReview, LXXXIX(1999a), 103 –124. O’Donoghue,Ted, and Matthew Rabin, “Incentivesfor Procrastinators, ” Quarterly Journalof Economics, CXIV(1999b), 769 – 816. Pollak,Robert A., “HabitFormation and Dynamic Demand Functions, ” Journal of Political Economy, LXXVIII(1970), 745 –763. Prelec,Drazen, and George Loewenstein, “TheRed and the Black: MentalAc- countingof Savingsand Debt, ” Marketing Science, XVII(1998), 4 –28. Read,Daniel, and George Loewenstein, “Enduring Painfor Money: Decisions Basedon thePerception of Memoryof Pain, ” Journalof Behavioral Decision Making, XII(1999),1 –17. Read,Daniel, and Barbara van Leeuwen, “PredictingHunger: The Effects of Appetiteand Delay on Choice, ” Organizational Behavior andHuman Deci- sionProcesses, LXXVI(1998), 189 –205. Ryder, Harl,and Geoffrey Heal, “OptimalGrowth withIntertemporally Depen- dentPreferences, ” Review ofEconomic Studies, XL (1973), 1–33. Sackett, DavidL., andGeorge W. Torrance, “TheUtility of Different Health States asPerceived by the General Public, ” Journalof Chronic Diseases, XXXI (1978), 697–704. Schkade,David, and Daniel Kahneman, “DoesLiving in California Make People Happy?A FocusingIllusion in Judgments of LifeSatisfaction, ” Psychological Science, IX(1998),340 –346. Scitovsky, Tibor, The JoylessEconomy: An Inquiryinto Human Satisfaction and Consumer Dissatisfaction (Oxford, UK: Oxford UniversityPress, 1976). Sieff,Elaine, Robyn Dawes, and George Loewenstein, “Anticipatedversus Actual Responsesto HIV TestResults, ” American Journalof Psychology, CXII (1999), 297–311. Slevin,Maurice L., H. Plant,D. Lynch, J.Drinkwater, andW. M.Gregory, “Who 1248 QUARTERLY JOURNALOF ECONOMICS

ShouldMeasure Quality of Life,the Doctor orthePatient? ” British Journal of Cancer, LVII(1988), 109 –112. Smith,Adam, The Theoryof Moral Sentiments, Knud Haakonssen,ed. (Cam- bridge:Cambridge University Press, 2002). Solomon,Andrew, “APersonalHistory: Anatomy of Melancholy, ” New Yorker, LXXIII(January 12, 1998), 46 – 61. Starmer,Chris, “Developmentsin Non-Expected Utility Theory: The Hunt for a DescriptiveTheory of Choice under Risk, ” Journalof Economic Literature, XXXVIII(2000), 332 –382. Strahilevitz,Michal, and George Loewenstein, “TheEffect ofOwnershipHistory onthe Valuation of Objects, ” Journalof Consumer Research, XXV (1998), 276–289. Thaler,Richard, “Towarda PositiveTheory of Consumer Choice, ” Journal of EconomicBehavior andOrganization, I (1980), 39– 60. Tversky, Amos,and Daniel Kahneman, “LossAversion in Riskless Choice: A Reference-DependentModel, ” Quarterly Journalof Economics, CVI (1991), 1039–1061. Ubel,Peter, George Loewenstein, and Christopher Jepson, “Disabilityand Sun- shine:Can Predictions Be Improved by Drawing Attentionto Focusing Illu- sionsor Emotional Adaptation? ” WorkingPaper, University of Michigan MedicalCenter, 2003. U.S.Departmentof Health and Human Services (U. S. DHHS), Preventing TobaccoUse AmongYoung People: AReport ofthe Surgeon General (Wash- ington,DC: U.S.GovernmentPrinting Of ce, 1994). VanBoven, Leaf, and George Loewenstein, “Projectionof TransientDrive States, ” Personality andSocial Psychology Bulletin, XXIX(2003), 1159 –1168. VanBoven, Leaf, David Dunning, and George Loewenstein, “Egocentric Empathy Gapsbetween Owners andBuyers: Misperceptions of theEndowment Effect, ” Journalof Personality andSocial Psychology, LXXIX(2000), 66 –76. VanBoven, Leaf, George Loewenstein, and David Dunning, “Mispredictingthe EndowmentEffect: Underestimationof Owners ’ SellingPrices by Buyer ’s Agents,” Journalof Economic Behavior andOrganization, LI(2003),351 – 365. VanBoven, Leaf, George Loewenstein, Ned Welch, and David Dunning, “The Illusionof Courage: Underestimating Social-Risk Aversion in Self and Oth- ers,” WorkingPaper, University of Colorado,Boulder, 2003. Weinstein,Neil, “CommunityNoise Problems: Evidence against Adaptation, ” Journalof EnvironmentalPsychology, II(1982),87 –97. Wilson,Timothy D., Thalia P. Wheatley,Jonathan M. Meyers,Daniel T. Gilbert, andDanny Axsom, “Focalism:A Sourceof DurabilityBias in Affective Fore- casting,” Journalof Personality andSocial Psychology, LXXVIII(2000), 821–836.