1996 the resolution of uncertainty_an experimental study

7/28/2019 1996 the Resolution of Uncertainty_An Experimental Study

http://slidepdf.com/reader/full/1996-the-resolution-of-uncertaintyan-experimental-study 1/16

The Resolution of Uncertainty: An Experimental StudyAuthor(s): Martin Ahlbrecht and Martin WeberReviewed work(s):Source: Journal of Institutional and Theoretical Economics (JITE) / Zeitschrift für die gesamte Staatswissenschaft, Vol. 152, No. 4 (December 1996), pp. 593-607

Published by: Mohr Siebeck GmbH & Co. KGStable URL: http://www.jstor.org/stable/40751933 .

Accessed: 13/03/2013 21:00

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

Mohr Siebeck GmbH & Co. KG is collaborating with JSTOR to digitize, preserve and extend access to Journal

of Institutional and Theoretical Economics (JITE) / Zeitschrift für die gesamte Staatswissenschaft.

http://www.jstor.org

This content downloaded on Wed, 13 Mar 2013 21:00:01 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=siebeck

http://www.jstor.org/stable/40751933?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp





http://www.jstor.org/stable/40751933?origin=JSTOR-pdf

http://www.jstor.org/action/showPublisher?publisherCode=siebeck



TheResolution fUncertainty:nExperimentaltudy

byMartin Ahlbrecht andMartin Weber

Meaningfulecision roblemsftennvolventertemporalhoices.n the ase ofuncertainty,he resolution f uncertaintys an essential eature f decisionalternatives.arlyresolutionfuncertaintyight ffer lanning enefits,ateresolutionmight e preferredordecisionmakerswho want ohopeas longaspossible or good consequence.Thefocus f thispaper sentirelyescriptive. epresentn experimentaltudyinvestigatingubjects' esolutionreference. e find hat omesubjects referearlynd somepreferateresolutionfuncertainty.e also find hat his refer-encesystematicallyependson the source of utilitynd on theprobabilitiesinvolved.JEL: D 81,D 90)

1. Introduction

Considerhe ollowinghoiceproblem: or ottery,onewillknow ntl now)whethern t2 nextChristmas)ne will receive ither 1= $100 or z2 = $0.Choosing ottery, one willnot knowtheconsequence ntilnextChristmas.Aswe will howbelow, raditionalheories o not discriminateetweenarly(E) and late L) resolution funcertaintynd thuspredictndifferenceetween

thetwo otteries.As nthe xample,most conomic ituationsrecharacterizedy he act hattheuncertaintybouttheoutcome fa riskylternatives - at leastpartially- resolved efore he outcome s to be received. he result f an investmentdecision, or xample, suallybecomesknownbefore ll revenues re to becollected.n ourstudywe will nvestigateeople'spreferencesowards arly rlate resolution funcertainty.

Wewill irstrove hat raditionalheoriesrenot ble topredict preferencefor nyof hose otteriesresentednfigure. Theexpected tilityEU) of heselotteriess

EU(E) = ρ · «($100) + (1 - ρ) ·u($0) = EU(L).

Expected tilityoes notdiscriminateetween esolvingotteries.

Journalf nstitutionalndTheoreticalconomicsJITE),Vol. 52 1996)© 1996J. . B.MohrPaulSiebeck) ISSN 0932-4569







594 Martin hlbrechtndMartinWeber SM'E

. Zl (e.g.$100)

< 1"PΝ"PΝ z2 (e.g. 0)

t, t2

z, (e.g. 100)p ^/^

L <^

z2 (e.g.$ 0)

t, t2Figure

One-Stageotteries andL

Models of ntertemporalhoicebehavior avemostly een nspired ythe

work of Koopmans 1960]who has laid the axiomaticbasis fordiscountedutility.See,e.g.,Lancaster [1963],Koopmans,Diamond and Williamson[1964], ell [1974],Meyer 1976], ndFishburn nd Rubinstein1982].) heexpected iscounted tilityEDU) of the bove lotteriess

EDU(E) = q-1 -ρ -u($ 100)+ q~l · (1 - p) ·«($ 0) = EDU(L),

where is an appropriate iscount actor.Whileexpected iscounted tilityallows forvariationn thetiming fconsequences,t cannot ccountfor heeffectsaryingncertaintyesolutionmayhave on people'spreferences.

Individualsmaybe concerned bout thetiming funcertaintyesolutionfor wo reasons. irst,f ntermediateecisions avetobemade, arly esolu-tionmight ffer lanning enefits.See Markowitz [1959],Mossin [1969],







152/4 1996) TheResolutionfUncertainty:nExperimentaltudy 595

Machina [1984],ndSpence nd Zeckhauser 1972] or discussion.)econd,individualsmightbe averse to not knowingor to knowing) bout futureconsequences orpurely sychologicaleasons uch as hopeor fear.

The mostmportantpproach hat anmodel esolutionreferenceas beenproposed yKreps and Porteus[1978], 1979] henceforthP). Wepresenthismodelwhich s based on a solid axiomatic oundationnthefollowing.hereare somefirst conomicmodels whichhave used the KP modelto deriveeconomic heories. hew and Epstein 1989]have ntegratedon-EU axiomsinto heKP model.Epstein nd Zin [1991]haveextendedt to an infiniteimehorizon ndapplied ttoeconometrictudies fconsumptions-savingsehav-

ior n macroeconomics.See also Weil [1990].)Pope 1995] eveloped model hatncorporatedope nd fear. heassumed

thatutilitys derivednotonlyfrom he realizations f the outcomes n thepost-outcomeeriod, ut lso from hefearnd thehopedueto the tate fnotknowing uringhepre-outcomeeriod. he overall tilityf n alternativesthe um f heutiles verbothpre-outcomendpost-outcomeeriod. elayingthetime funcertaintyesolution,.g.,prolongs hepre-outcomeeriod ndshortenshepost-outcomeeriod, hereforehangingheoverallutilityfanalternative. únera andDe Neufville [1983, 51]argue hat he ubstitutionprincipleendersxpected tilityoo nflexiblen theface f equential ecision

problems, hereuncertaintybout the stateof nature s only gradually e-solved.

Whethereopledo takethe time f resolution funcertaintyntoaccountwhenmakingnintertemporalhoice s anempiricaluestion.n this aperwewill xperimentallynvestigatentertemporalhoicebehaviorwhen heresolu-tionofuncertaintyaries.Wewilltest,f- peopledo have a preferenceor arly r late resolutionfuncertainty,- such a preferenceepends n theprobabilitiesr theconsequences f the

lotteries,

- preferencesor esolution reaffectedytheframingf thedecision.Insection wepresenthemodel fKrepsand Porteus [1978], 1979]which

is able tomodelpreferenceor esolution funcertainty.Althoughmore han15years ld,theirpproach emains heonly xiomatizedmodel ntheface fdelayed ncertaintyesolutionnd thereforeeeds o be contrastedgainst heexperimentalvidence ecollect hroughouthis aper.Thehypothesesnd thedesign f our studies re presentedn section and section . Therewe alsodiscuss hefindingsftworecentmpiricaltudiesChewand Ho [1994] and

1 Thepresentationf theKreps and Porteus[1978]modelfollowshepresentationin Ahlbrecht andWeber 1995].2 Thestudy f Chew and Ho [1994]wasdone ndependentlyf ourstudy.







596 MartinAhlbrechtnd MartinWeber JJDTTIE

Wu [1992])that nvestigatereferencesor resolution f uncertainty.3heresults four studies redescribedn section . The paperconcludeswithdiscussion ftheresults nd thediscussion f some economicmplications.

2. A Theoretical odelof PreferencesorResolutionf Uncertainty

Krepsand Porteus [1978],1979]have ntroduced model of ntertemporalchoice hat llowsfornon-indifferenceo the imingfuncertaintyesolution.Ithas become hebasis for urther ork nmodellingttitudesowards ncer-

tainty esolution.For the ake ofsimplicityf theexposition, eonly onsider otteries ithfiniteupport nR in a two-periodetting. lso, inceourobjectives not toanalyze ow onsequencesn the woperiods reevaluatedgainst neanother,we considernly onsequencesnperiod ,as in the xamples resentedbove.Period1 serves nly o resolve heuncertaintyboutperiod consequences.

The outcome fperiod resolutions a lotteryverpossible onsequencesnperiod . For a metricpace 2, etD{Q) denote he etofprobability easureson Ω. Thenthe et ofpossible utcomes fperiod resolutionsD(R) and weconsider he outcome paceD(D(R)). KP haveformulatedxiomsforprefer-enceson theoutcome pace4 (D(R)). Like KP, we will call elements f theoutcome pacetemporalotteries. hree fKP' s axioms reclosely elated othevonNeumann-Morgensternxioms f ompleteness,ontinuitynd substi-tution.n addition, P introduce temporal onsistencyxiom. upposethat,inperiod ,an individual refers to z',where and z' denote otteries verconsequencesnperiod . Then, nperiod ,he stillprefers to z'.

Letzfie {1 /})denote hepossibleotteriesver onsequencesnperiodthat the decisionmakermaybe facedwith fter eriod uncertaintyeso-lution. etPidenote heprobability ithwhich ,occurs fter eriod resolu-tion.Finally,etEU(z^) denote heexpected tilityf otteryf ubject o autilityunctionwhich hedecisionmakerwill mploynperiod inorder oevaluate ,.

KP prove hat heir xioms re necessarynd sufficientor here oexistcontinuous,ealvalued, trictlyncreasingunctionuch hatf ,d' retemporal

3 Quite numberf tudiesnvestigatentertemporalecision-makingithoutonsid-ering ncertaintyesolution. orthe aseof ertaintyee, .g.,Loewenstein ndPrelec[1992],Benzion,Rapoport and Yagil [1989],and Thaler [1981].For the case ofuncertaintyeeStevenson1990]whofoundubjects' iscount ates obe ower or iskyprospectshanfor ertain nes. AhlbrechtandWeber 1996] ttributedhis ffecto

subjects aving ifficultiesnevaluatingisk nd time imultaneously.helley [1994]analyzed ain-losssymmetriesn ndividualiscount ates nd relatedhem oframingeffects.

4 KP consider larger utcome paceallowing onsequencesnevery eriod.Theiroutcome pacecontains (D (R)) as a subset.








lotteries,decisionmaker refers^ d' if ndonly fKP(d) > KP(d'). Here,theKP utility P(d) of thetemporalottery is defined s

(I) KP(d)= íPixh{EO{z$.i=l

In I),ft lays heroleof utilityunction,ince emporalotteriesre evaluatedbythe xpectationfft. ontraryo theutilityunctionwhich aptures nlythedecisionmaker's isk referencesnperiod ,ft lso models he ndividual's

attitude owardsuncertaintyesolution. or illustration,econsiderigure.Letu(zmax) 1,u(zmin) 0 andft(x) x2. nsertingnto I),we see thatKP(L)is equal to p2.In contrast,n £, ft s appliedto u{zmax) 1 and u(zmin) 0,yielding P(E) = p.Thus for < ρ < 1 we haveXP(£) = ρ > ρ2 = KP(L' apreferenceor arly esolution.

We see thatKP model an allow for preferenceor arly r ate resolutionofuncertainty.or thegeneral ase,KP show hat t s convexconcave, inear)if nd only ffor ll p,zmaxnd zmin,he decisionmakerwillalwayspreferoverL (L overE, be indifferentetween hetwo).

3. Hypotheses

3.Í ResolutionreferenceorDifferentources f Utility

Considerhe ransformationunctiontwhichncodes referenceor ncertain-ty esolution.tsargumentsreutiles f he ntertemporaltilityunction,notthe ctualconsequences.t could beargued hat n individual's referenceor

uncertaintyesolutionhould hereforeot

dependn the

ypef

onsequences,e.g., n whetherheyremonetaryr health onsequences.n otherwords, heKP model anbeinterpreteds assuming referenceor ncertaintyesolutionto be fixed or achindividual,onstant ver ll sorts fdecision roblems.tmaybeperfectlylausible or decisionmaker, owever,opreferarly esolu-tion ormonetaryonsequences hile tthe ame ime ot otest gainst fatalhereditaryiseaseforwhich heresnocure.Every conomic genthas earnedto deal andcopewithmonetary ains ndlosses, utwho wouldnotbe afraidto learnwhen ne willeventuallyie?

To derive ypotheses,ne needs o ook atexistingxperimentalesults.Wu

[1992] nvestigatedreferencesor ne decision

ontext,here

ubjectshould

considerhemselveseing consultantssigned o an interestingboring) ro-jectorremainingn the ameproject fteroming ack from olidays.n thiscontext, e found hat77% of thesubjectswanted o have theuncertaintyresolvednthe ase ofan interestingroject. he number ropped o 55%, if







598 MartinAhlbrechtndMartinWeber ΛΙΠΠΕ

the newprojectcould be boring.5Chew and Ho [1994] testedbehaviortowardsresolution of uncertaintyn different ontexts: the disclosure of one's exam

grades and the context of a tax refund. n the tax refund ontext, heyfoundmorepeople to prefer arlyresolutionofuncertaintyndependent f the conse-

quences than in the exam context. Here quite a number of subjects (39%)preferred arly late) resolution ftheywereexpectinga good (bad) grade.

Based on the iterature nd based on our intuition,we do not see anyreason

why preference or arlyor late resolutionofuncertaintyhould not varyoverdifferentources of utility, .g.,differ etweenmonetary nd health lotteries.

HypothesisThe

preferenceor resolutionof

uncertainyaries over different

sources ofutility.

3.2 TypeX Behavior

It has been argued (Chew and Ho [1994]) thatpreference or ate resolution sassociated with small probabilitiesof arge gains. Chew and Ho [1994] extendthe KP model to allow what we term"Type X" behavior, i.e., the resolution

preference ariesdependingon whether he outcome is more or less probableand on whether t is a gain or a loss. If the probabilityofwinning s small,

resolutionwill most likelybe a disappointment,destroyingthe individual's

hope ofwinning.n order to sustainhope, subjects preferate resolution.Chewand Ho [1994]establishhope in an experimental tudyreferringo possible taxrefunds nd grade reports. n figure ,this would correspondto a smallp, say,ρ = 0.05, and u(zl)= 1, u(z2) = 0. Contrary, fthe probabilityof winning s

high, say ρ = 0.95, resolutionofuncertainywillmost likelydo away withthesmallprobability f notwinning. his will ead people topreferarlyresolution.We call this witching reference oruncertaintyesolution TypeX" behavior.For losses,TypeX behavior will be opposite to the resolutionpreferences or

gains.

The KP model can accomodate TypeX behavior using an S-shapedtransformation unctionh, i.e. concave for small utilities and convex for

large ones. Using fc(0, ) = (*- 0.5)3, one gets KP(E) = (2 ρ - l)(0.5)3 and

KP(L) = (p- 0.5)3 for«(zj = 1 and u(z2) = 0. For thiscase, late (early)reso-lutionis preferred orρ < (>) 0.5. Note, however,that theconcavityof h forutiles ess than0.5 forcespreference or ate resolution mong all lotterieswithlow expectedutilities. or instance, or = 0.5,u(z^ = 0.5 and u(z2) = 0, a KP

utilitymaximizerwiththe h ofour example would preferate resolution.

TypeX behaviorcan be definedmoreor less restrictively.s a less restrictive

definition, subject'spreferences called "weak TypeX" forgains, if t is not

constant,and, as theprobabilityofwinning ncreases,thepreference hangestowardsearlyresolution respectively,heopposite for osses). For instance,

5 Theprobabilitieso remain n the ameassignmentere /3, heprobabilitiesorchanging/3.







152/41996) TheResolutionfUncertainty:nExperimentaltudy 599

subjectmaypreferateresolution orprobabilitiesessthan5% andbe indif-ferento resolutionime orarger robabilities. subject's references called"strong ypeX," if n addition o beingweakTypeX, forthesmallest ndhighest robabilitiesskedthe ubject tates strict reference.orinstance,subjectmaypreferate resolution or robabilitiesess than5%, be indifferentto resolutionimeforprobabilities etween % and 95%, and preferarlyresolutionorprobabilitiesreaterhan95%.

Ofcourse, hehypothesis ill not be that themajority fsubjects howsTypeX behavior,incemany ubjects' referencesaybewhollynsensitiveochangesn theprobabilities.ne may, ornstance, erywelldecidethatone

preferso know s early s possiblenany aseor that nesimply oes not areaboutresolutionime t all.Rather,urhypothesissthat f subject's refer-ences are at all sensitive o probabilities, is responsepatternwill not bearbitraryut be ofTypeX.

Hypothesis: Among ubjectswhosepreferencesor esolution funcertainydepends nprobabilities,ypeX behavior xplainsmore han tschancepro-portion.

3.3 Framing ffects

Consider pregnant omanwhohas decided hat, uring regnancy,hedoesnot want o know bouther hild's ex. Shehas thus xpressed referenceorlate resolutionfuncertainty.ponhernextmedical xamination,erdoctortellsherthatheknownswhethert willbe a girl r a boyand asksher f hewantshim o tellher.Knowing hat heuncertaintyboutherchild's ex hasalreadybeen resolvedthough otyetbeen revealed o her)mightmake herchangehermind.

This woman'spreferenceannotbe described nlybythe time hegetstoknow hefuture,ut talsodepends nwhetherthers ottoknowbefore er,

respectivelyhetherhe

uncertaintys resolved ut

merelyot known oher.

An event ree tructures in theKP model an only onsider he nformationprocessfor he decisionmaker. t cannotcapture he differenceetween neventnot resolved nd an event esolved utsimply ot known.

From ntuition ethink hat eopledo not ikeothers o knowf hey o notknow hemselves.his eads tohypothesis.

Hypothesis: Subjects referarly s well s lateresolution funcertaintyverthe ituationhat heoutcome f the venthas beenrevealed o someone lsebutnot to them.

4. Subjects ndQuestionnaireWeconductedwo tudies.Wesegregatedheframingffectart nto n extrastudyn ordernotto havesubjects ransferrames o the tudy or ncertaintyresolution.







600 MartinAhlbrechtndMartinWeber ΛΠΤΓΙΕ

Subjectswere raduatetudents rommanagementourses t theUniversityofMannheim nd Cologne.Therewere267 participantsn study and 337participantsn study . Subjectswerenotpaid forparticipationince mple-mentingn incentiveompatible aymentcheme or elayed ncertaintyeso-lution eemedmpossible. he most mportantifficultyouldprobably avebeen o nstall mechanismo ensure hat articipantshohandled ossespaidus a given mount ndue timenthefuture.

In bothstudies, ubjectswere nstructedo thoroughly orkthroughquestionnairehat sked hem o choosebetweenhoice airs£,L) of emporallotteries. onsequenceswere osses or gains expressedn Deutsche Marks

(DM). For each choicepair, ubjects ould state preferenceor ne of he woalternativesr ndifferenceetween he wo.Theintroductoryheet xplainedthat therewere no right r wrong nswers, ut that we were nvestigatingpeople'spreferences.ach temporal ottery as bothverbally escribednddepicteds an event ree as infigure).The resolutionrocesswas describedas a fair oin,or,where robabilities erenot50%, as thedrawing f a ballfrom n urn.The resolutionntxwas to takeplaceon the amedaywhile heone on t2was to takeplacetwo months ntothefuture.6

4.1 DesignStudyWe had fourypes f uestionnairesA,B, C,andD), see table1. Eachquestion-nairewas answered yone fourth f thesubjects.A and Β dealt withgains,

Table1

Design

Questionnaire

AB CD

monetaryutcomesnDM (0 ± 1000)

Zl z2 ρ τγ z2 ρ zx z2 ρ Zj z2 ρ

1000 0 0.01 1000 0 0.05 1000 0 0.01 1000 0 0.051000 0 0.5 1000 0 0.5 1000 0 0.5 1000 0 0.51000 0 0.99 1000 0 0.95 1000 0 0.99 1000 0 0.95

extrememonetarynd health utcomes

Zl z2 ρ Zl z2 ρ Zl z2 ρ ζ, z2 ρ

1 mio 0 0.01 disease no disease 0.01 lose assets no loss 0.01 disease no disease 0.051 mio 0 0.5 disease no disease 0.5 lose assets no loss 0.5 disease no disease 0.5

6 Thequestionnaireontained omefurtherhoicequestionswhichwe used to testsomehypothesesngradual esolutionfuncertainty;ee Ahlbrecht andWeber 1995]for descriptionfthehypothesesnd theresults.








C andD are the quivalentsfA andB,butdealtwithosses.Theorder fthequestions aschangedwithinachtype f uestionnarieccordingo a randomprocess.

To test or he ffectfdifferentources futilityhypothesis), ubjectsweregivenwo hoices vs.L (seefigure)with γ DM 1 millionndz2 = DM 0,and with = 0.01 andρ = 0.5 questionnaire).For losses, 2 andρ were hesame as forgainswhile 1 describedhe oss of all of thesubjects' ssets C).Extremeon-monetaryutcomesweremodelled s a pchance fhavingnher-ited severe enetic iseasethatwould ead to deathat theage of about50.Subjectswerepresented ith ither = 0.01 andρ = 0.5 (Β),orρ = 0.05 and

ρ = 0.5 (D). Wedid not ask subjects o evaluate otteries ith = 0.95 andρ = 0.99forwe felt hiswould be bothunrealisticnddemotivating.

To testhypothesisonTypeX behavior, epresentedubjectshe hoiceΕvs.L (seefigure)with γ= DM 1000, 2 = DM 0 andthree ifferentrobabil-ities ; subjectswere resented ith ither = 0.01, = 0.5 andρ = 0.99 ques-tionnaire andC),orρ = 0.05, = 0.5andρ = 0.95 questionnaire andD).

4.2 DesignStudy

The fact hat omeone lseknowsbuta subject oes not knowwas modelledby notary ublicwhowassupervisinghe ossof he oin andwho wasgoingto informhe ubject ithermmediatelyfter hetoss or later.This situationmaybe differentrom hepregnantwomanexample n thatthedoctorwasopenlywillingoreveal he rue tate f heworldwhile henotary ublic snot.To the xtent,owever,hat oth xamplesead to thefact hat heuncertaintyis resolved o someone thedoctor r thenotary ublic), hey resimilar.

The toss of thecoin couldtakeplaceeithernίλorf2.There re then hree ossibilities:

(a)toss and informationn

tl;(b) toss ntl9 nformationni2;(c) toss and informationn i2.

Ofcourse, henotary ublic annotgiveyouthe nformationeforehetoss,whichwouldbe thetheoreticalourthossibility.ere, a) and c) correspondto Ε and Lof figure, and (b) correspondso delayed nformationorthedecisionmaker.Wehypothesizedhatboth a) and(c) arepreferredo (b).

Allprobabilities ere ixed t 50% and we hadzx= DM 100, 2 = DM 40.The choicepairs o test or urhypothesisndelayednformationonsisted fone-stage esolutionotteries

(1): (a) vs. b) and(2): (c) vs. b).

Through1),wetestwhetherubjects refero know arlierwhen omeone lsealready nows,hrough2)we testwhetherubjects referthers o know ater







602 MartinAhlbrechtnd MartinWeber «ΒΠΤΠΕ

when heyhemselveso notyetknow.Both 1) and 2) separatelyesthypoth-esis 3.Halfofthe ubjectsweregiven hoicepairs oncerningnlygainswhile he

other alfwasgiven hoice airs oncerningnlyosses.Eachsubjectwasgivenone ofthetwo choicepairs 1) and (2).

5. Results

5.1 Study

Twosubjectswere xcluded romnalysis ince hey id not answer ll ques-tions.The analysis resented ererefers o 265 subjects. able 2 summarizespreferenceor arly nd late resolutionotteriess statedbythe ubjects.

Consider irstesponses ornormalmonetaryutcomes. he largest roupfor ll four uestionnâmess constant referenceor arlyresolution, hichaccounts or43% ofthesubjects,onstant ndifferences thesecond argestgroup,which ccounts or 5%. Constant referenceor ate resolutions thesmallestmong he onstantreferenceroupswith %. Combininghese hreegroups,4% of he ubjectstated onstant references,ndtwo hirds f hemhad a (constant) referenceor arly r late resolution.

Table

Responses orResolution fUncertaintyin %)

Questionnaire

A B C D sum

monetaryutcomes p to DM 1000

constantarly 40 38 49 43 43constantndifferent 33 24 22 19 25constantate 3 11 5 9 7strong ypeX 13 5 14 4 9weakTypeX* 6 3 6 9 6other 4 20 5 15 11sum 100 100 100 100 100

extrememonetarynd health utcomes

outcome: win1mio. disease lose assets disease

constantarly 46 50 54 55 51constantndifferent 19 8 26 4 14constantate 4 27 12 19 16nonconstant 30 15 8 21 18sum 100 100 100 100 100

* Which re not also strong ypeX.








Hypothesis Sources fUtility.We nvestigatedfpreferenceor arly esolu-tion funcertaintysstrongeror xtreme onetaryutcomeshan ornormalmonetaryutcomes. or gains, onstant referenceorearlyresolutionc-counts or 1/67 ubjectswhen onsequencesreextreme,nd 27/67 ubjectswhen onsequencesre normalquestionnaire).This s not tatisticallyignif-icant Z = 0.70,ρ < 0.25).The same result olds for osses questionnaire),where orrespondingroportionsre35/65 nd 32/65 Z = 0.53,ρ < 0.30).

Contraryohypothesis,we see thatpreferenceor arlyresolutions notsignificantlyifferentor xtrememonetarynd health osses 35/65n C vs.70/133n Β and D, Ζ = 0.16,ρ < 0.44).However, ignificantlyore ubjects

preferateresolutionor xtreme ealth osses han or xtreme onetaryosses(31/133nΒ andD vs.8/65nC, Ζ = 1.79, < 0.04).This effectecomes venmore ignificantomparingxtreme ealth ossesto normalmonetaryosses(31/133n Β andD vs.9/132nC andD, Ζ = 3.75, < 0.01).This shows hatthe ource futilityoes nfluenceubjects' esolutionreference,.e.theresultscomfirmypothesis. t also indicates hat referenceor arly esolutionoesnotonlyreflectotential lanning enefits.f thiswasthecase,preferenceorearly esolutionhould ise s the takes ecomemore xtreme,ut t doesnot.On thecontrary,referenceor ate resolutionisesforhealth onsequences.

We did not find ny significantifferencefpreferencesorresolution f

uncertaintyhen onsequencesregainsvs. losses.Therewere lightly orepeople ndifferentogains han o osses, ndslightly orepeoplepreferredoknowearlyrather han ate for osses thanforgains.These results o notsupport hefindingsf Wu [1992].Recall that n his specificontextmorepeopleprefero knowearlierwhen hepotential utcome s a loss.

Hypothesis: TypeX Behavior.hishypothesiss confirmednquestionnairesA,C andD, but s notconfirmednquestionnaire. InA,19% of he ubjects(B: 8%, C: 20%, D: 13%) showed trongr weakTypeXpreferences.mongallpatterns,his s a lessthan hanceproportionn all questionnaires.7his s

simply ecausethe resolution referencef themajority fsubjects s notsensitiveo probabilityhanges.Hypothesis, however,estrictsttention o the 24 non-constantatterns.

The chanceproportion fTypeX amongthese s 29.2%.8 Thisneeds to becompared o the observedproportionsfTypeX amongthenon-constantpatterns.heseare82.6% inA,29% inB,80% inC, and46% in D.9 Except

7 Therewere questionswith possible nswersach, hus 3= 27possible esponsepatterns.fthese, are constant. etting IL standfor hepatternearly,ndifferent,late," he patternsEI, EEL, Eil, EIL, ELL, IIL, ILL are ofTypeX. TypeX's chanceproportionmong ll patternsherefores 7/27 25.9%.

* Of the24non-constantatterns, areofTypeX, 7/24 29.2%.* E.g., nquestionnaire,among he 3% ( = 13% + 6% 4-4%) non-constantat-

terns,he19% TypeX patterns epresentproportionf19/23 82.6%.







604 MartinAhlbrechtnd MartinWeber «DUTTE

for uestionnaire,this s significantlyore p < 0.01 forA,C, as well s D)than hechanceproportionf 29.2%.10Ourresults stablish hat here resubjectswhose resolutionreferences

sensitiveochangesntheprobabilitiesnd that here xists ver-proportional-lymoreTypeX behavior mong hese ubjectsnquestionnaires,C and D.Wehavenoexplanation,owever, hy uestionnairegives differenticture.The observed ypeX effects clearestn A andC,where ypeX patterns otonly xceed he hanceproportionf29.2%,but lso representhemajorityfobserved atterns.hismay suggest hatTypeX behavior s stronger hereprobabilitiesre as extremes 1% or 99% (as in A andC).

5.2 Study

Hypothesis: Framing ffects. ne subjectwas excludedfrom heanalysisbecausehegavemore han ne answer erquestion. hefollowingable um-marizes ubjects' hoicebetween hoicepairs 1) and(2) instudy . The num-bers 5/20/5 ean hat 5% of he ubjectstated referenceora) (or c)), 0%were ndifferentnd 5% preferredb).

The overwhelming ajorityfsubjectswas averse o delayed nformationabout theresolved ncertainty.eloweachentryregiven heΖ statisticsnd

the correspondingignificanceevels.11Our hypothesesre confirmed tρ < 0.01 evel oth or ains nd osses.There s no differenceetweenains ndlosses.

Table

Subjects'Responsesin %) forChoicePairs 1) and (2)

gains losses sum

(1): (a) vs. b) 75/20/5 79/15/6Ν = 84 Ν = 85 Ν = 169

Ζ = 6.44,ρ = 0.00 Ζ = 6.72,ρ = 0.00(2): (c) vs. b) 44/46/10 42/46/12

Ν = 82 Ν = 84 Ν = 166Ζ = 3.09,ρ = 0.00 Ζ = 2.72,ρ < 0.01

sum Ν = 166 Ν = 169 Ν = 335

10Thisneeds o be tested y binomial est. heprobabilityor ach ofnon-constantresponses o be ofTypeX is 29.2%. The number fthe observed ypeX responsesthereforesbinomiallyistributed.heparametersf theunderlyinginomial istribu-

tion reρ = 0.292 and thenumber fthe bserved on-constantatteras. ue to smallsample izes, his istributionannot ccuratelyeapproximatedy henormal istribu-tion, husZ-values annotbegiven.11For theuppereft ntry,.g.,63 ( = 75%) subjects referreda), while ( = SVo)preferredb), suchthatΖ = (63-4)/841/2 6.44.







152/4 1996) The Resolutionf Uncertainty:nExperimentaltudy 605

6. Discussionnd mplications

Thispaperhasexploredndividualhoicebehavior orntertemporalotterieswhich iffernthe resolution funcertainty.

Our firstmportantindings that ubjectswerenot ndifferentetweenarlyand late resolutionfuncertainty,oth nlotteriesoncerning onetaryut-comes s well s the ndividual's ealth tatus. hispreferenceor esolutionfuncertaintyandepend n the ource futilitynvolved.Wehave lso dentifieda certainhanging esponse atternTypeX behavior). hisbehavior ouldbemotivatedy general referenceor arly esolutionairedwith ear ndhopeif heprobabilitiesre extreme.referenceor arly esolutionsnot,however,a functionfplanning enefitshat ouldbe associatedwith arlier nowledge.Psychologicalffectslayan importantolewhen tcomesto informationnone'sfutureealth tatus.Notknowingne'sfate s better hanknowing hereinformationasnegativealue.Adescriptiveheoryhould hereforeotdefineresolutionreferencenly s a functionftheutilityffuture utcomes utallowresolutionreferenceo differor ifferentources futility. e were bleto establish ne potential ramingffectn thisfield. irst, eopleare averseagainstreceivingnformationaterthan resolution as actually akenplace.Thus, or escriptiveurposes,heresolution funcertaintyannotbe reducedto the nformationlow owards hedecisionmaker.

We think hatpreferencesorresolutionfuncertaintyan helpto under-stand mportantealworld roblems. ake, .g.,thequestionwhynotenoughpeople akemedical heck-ups. ur resultsuggesthatwith lowprobabilityofsomethingad happening uitea number fsubjects refero delaytheresolution funcertaintyregardlessfthemedical dvantage fhaving akenthecheck-up arly).

In future ork necould imto furthernderstandreferencesor esolutionofuncertainty.twillbeinterestingoconsider radual esolution funcertain-

ty,s mostrealworld

uncertaintys not resolved t once.12 n addition twill

be worthwhileo empiricallyest hestrengthf the resolution referencendifferentconomic ettings. tthispoint, nly ndividual ecisionmaking asbeen nvestigated.t willbe interestingo see howstrong referencesowardsresolutionfuncertaintyre for roups nd howthese referencesave mpacton a market evel.

References

Ahlbrecht,M. andWeber,M. [1995],Gradual ResolutionfUncertainty," orkingPaperNo. 95-13,Lehrstühleür inanzwirtschaft,niversität annheim.

12See Ahlbrecht and Weber 1995]fora firstxperimentaltudy o investigategradual esolutionfuncertainty.







606 Martin Ahlbrecht nd Martin Weber JJOTTIE

- -and

- -[1996],AnEmpirical tudy f ntertemporalecisionMakingntheCaseofRisk,"Managementcience, orthcoming.

Bell, D.E. [1974], "EvaluatingTime Streams of Income," Omega, 2, 691-699.

Benzion,U., Rapoport,A. andYagil, J. 1989], DiscountRates nferredromDeci-sions: An Exoerimentaltudv Managementcience. 5. 270-284.

Chew, S. H. and Epstein,L. G. [1989], The Structure f Preferencesnd AttitudesTowards heTiming f theResolution fUncertainty,"nternationalconomicReview,0,103-117.

- and Ho, J. . [1994], Hope: An Empirical tudy f Attitude owardTiming fResolution," ournalfRisk ndUncertainty,, 267-288.

bPSTEiN,. u. and zin, s. b. [l^ij, Substitution,iskAversion,nd me lemporai

Behavior of Consumptionand Asset Returns:An Empirical Analysis," JournalofPolitical conomy,9,263-286.Fishburn, P. C. and Rubinstein, A. [1982],"Time Preference,"nternational conomic

Review, 23, 677-694.Koopmans, T. C. [1960], "StationaryOrdinal Utility nd Impatience,"Econométrica, 8,

287-309.-- , Diamond, P.A. and Williamson, R. E. [1964], "Stationary Utilityand Time

Perspective,"Econométrica,32, 82-100.ICreps, D. M. and Porteus, E. L. 11978J, Temporal Resolution ot Uncertainty nd

Dynamic Choice Theory," Econométrica, 6, 185-200.-- and -- [1979J, Temporalvon Neumann-Morgensternnd Induced Preferences,

Journal f Economic Theory, 0, 81-109.

Lancaster,K.

[1963],An Axiomatic

Theoryof Consumer Time

Preference,Interna-

tional EconomicReview, 4, 221-231.Loewenstein, G. [1987], "Anticipation and the Valuation of Delayed Consumption,"

EconomicJournal, 7, 666-684.-- and Prelec, D. [1992], "Anomalies in IntertemporalChoice: Evidence and an

Interpretation," p. 119-145 in: G. Loewenstein and J. Elster eds.), Choice OverTime,Russell Sage Foundation: New York.

Machina, M. J. 1984],"Temporal Risk and the Nature of nduced Preferences," ournalofEconomic Theory,33, 199-231.

Markowitz, H. M. [1959], PortfolioSelection,Wiley: New York.Meyer, R. Κ 11976J, Preterenes Over lime," pP· 473-514 in: K. L. Reeney and

H. Raiffa eds.), Decision WithMultipleObjectives: Preferencesnd ValueTradeoffs,

Wiley:New York.

Mossin, J. 1969], "A Note on Uncertainty nd Preferences n a Temporal Context,"AmericanEconomicReview, 59, 172-173.

Munera, H. A. and De Neufville, R. [1983], "A Decision Analysis Model Whenthe SubstitutionPrinciple is not Acceptable," pp. 247-262 in: B. Stigum andF. Wenstop eds.), Foundations f Utilitynd Risk TheoryWithApplications,Reidel:Dordrecht,The Netherlands.

Pope, R. [1995], Towards a More Precise Decision Framework; A Separation of theNegativeUtilityof Chance From Diminishing Marginal Utility nd the PreferenceforSafety," Theory nd Decision, 39, 241-265.

bHELLEY,M. [1994J, Uain/Loss Asymmetryn Risky Intertemporal hoice, Organiza-tional ehavior nd HumanDecision rocesses, 9,124-159.

Spence, M. and Zeckhauser, R. J. 1972], "The Effect f theTimingof ConsumptionDecisions and the Resolutionof Lotteries n the Choice ofLotteries,"Econométrica,40,401-403.

Stevenson, M. K. [1990], "The Impact of Temporal Context and Risk on the JudgedValue ofFutureOutcomes," OrganizationalBehavior nd Human DecisionProcesses,52,455-491.








Thaler, R. [1981], Some Empirical vidence n DynamicConsistency,"conomicsLetters, , 201-207.Weil,P. [1990], Nonexpected tilitynMacroeconomics,"uarterlyournalfEco-

nomics, 0,29-42.Wu, G. [1992], TemporalRisk and ProbabilityWeights:Rank-,Sign-, nd Timing

Dependent tility,"Working aper,HarvardBusiness chool,Cambridge,MA.

Dr.MartinAhlbrechtProfessor artinWeberLehrstuhlürAllgemeineWL,Finanzwirtschaft,nsbes. ankbetriebslehre

Universität annheim6813Î MannheimGermany

1996 the resolution of uncertainty_an experimental study

Documents