Do markets reveal preferences or shape them?

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ContentslistsavailableatScienceDirect

Journal

of

Economic

Behavior

&

Organization

jo u r n al ho me p ag e :ww w . e l s e v i e r . c o m / l o c a t e / j e b o

Do

markets

reveal

preferences

or

shape

them?

夽

Andrea

Isoni

a,∗

_,

_Peter

_Brooks

b

_,

_Graham

_Loomes

a

_,

_Robert

_Sugden

c

a_Behavioural_Science_Group,_Warwick_Business_School,_Coventry_CV4_7AL,_UK b_Barclays_Wealth,_Singapore

c_School_of_Economics_and_Centre_for_Behavioural_and_Experimental_Social_Science,_University_of_East_Anglia,_Norwich_NR4_7TJ_UK

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received9June2014

Receivedinrevisedform28October2015 Accepted17November2015

Availableonline27November2015

JELclassiﬁcation: C81 C91 D44 Keywords: Shapingeffects Marketdiscipline Repeatedmarkets Pricesensitivity Preferenceimprecision

a

b

s

t

r

a

c

t

Wecontrastthepropositionthatmarketsrevealindependentlyexistingpreferenceswith thealternativepossibilitythattheymayhelptoshapethem.Usingdemand-revealing experimentalmarketinstitutions,weseparatetheshapingeffectsofpricecuesfromthe effectsofmarketdiscipline.Weﬁndthatindividualvaluationsandprevailingpricesare systematicallyaffectedbybothexogenousmanipulationsofpriceexpectationsand endoge-nousbutdivergentpricefeedback.Theseeffectspersisttovaryingdegrees,inspiteoffurther marketexperience.Insomecircumstances,marketexperiencemayactuallyconsolidate them.Wediscusspossibleexplanationsfortheseeffectsofuninformativepricecueson revealedpreferences.

1. Introduction

Thereisnowabundantevidencethat,contrarytothestandardassumptionsofeconomicmodels,thepreferencesof economicagentsareoftenaffectedbysalientbutinformationallyirrelevantcues,speciﬁctotheparticularcontextsinwhich thosepreferencesarerevealed(SlovicandLichtenstein,1968;Bohmetal.,1997;Arielyetal.,2003;Mazaretal.,2013; Sugdenetal.,2013;Maniadisetal.,2014).

Inthispaper,wefocusonaspeciﬁcformofcontext-dependence:thesystematiceffectthatobservationsof,orexpectations about,actualmarketpricesexertonthevaluationsofeconomicagents,evenwhenthosepriceshavenousefulinformational contentfortheformationofprivatevalues(seeKnetschetal.,2001;Loomesetal.,2003;Tufano,2009).Thiseffectposes achallengetothelong-standingviewineconomicsthatmarketsareinstitutionsthatsimplyalloweconomicagentsto revealtheirpre-existingandmarket-independentpreferences:itsuggestsbycontrastthatmarketsmay,toaconsiderable extent,shapepreferences.Inthetraditionalview,themarketisliabletopenalisetraderswhomisreporttheirpreferences

夽 ThisresearchwascarriedoutaspartoftheProgrammeinEnvironmentalDecisionMaking,organisedthroughtheCentreforSocialandEconomic ResearchontheGlobalEnvironmentattheUniversityofEastAnglia,andsupportedbytheEconomicandSocialResearchCounciloftheUK(awardnos. M-535-25-5117andRES-051-27-0146).

∗ Correspondingauthor.Tel.:+4402476150370.

E-mail addresses: [email protected] (A. Isoni), [email protected] (P. Brooks), [email protected] (G. Loomes), [email protected](R.Sugden).

http://dx.doi.org/10.1016/j.jebo.2015.11.006

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andtherebyencouragesthemtocorrecttheirbehaviour(e.g.Binmore,1999;List,2003,2004).Suchmarketdiscipline,itis argued,helpstoreﬁnetherevelationofone’sunderlyingpreferenceswhenthesearenotimmediatelyaccessiblebutemerge astheresultofaprocessof‘discovery’(Plott,1996).

Shapingandmarketdisciplinearebothmechanismsbywhichpricesgeneratedinonetradingperiodcanaffectbehaviour insubsequentperiods,andtheeffectsofbothcanbecumulative.However,whilemarketdisciplineissupposedtopull revealedpreferences towardstheirunderlyingmarket-independent value,shaping mayarbitrarilypull them towards irrelevantcues.Inthenormaloperationofmarkets,discriminatingbetweentheseopposingforcesmayproveextremely challenging,astheycanresultinobservationallyequivalentbehaviour.Takingupthischallengeisthemaincontributionof ourpaper.Wepresentanexperimentwhichusestwomanipulationsaimedatidentifyingtheextentofshapingeffectsin theabsenceofmarketdiscipline,andthepowerofmarketdisciplinetoerodetheeffectsofshaping.

Inourexperimentalsetup,pricecuesaredevoidofanyrelevantinformationalcontent:peopletradeprivatelyowned andindividuallyconsumedgoods,forwhichvaluationscannotbeobjectivelyafﬁliated(e.g.ListandShogren,1999).Since thesegoodsonlyexistinourexperimentandareconsumedinsidethelab,pricecuescannotconveyanyinformationabout alternativetradingopportunities(Harrisonetal.,2004).

Weuseanexogenousandnon-informativemanipulationtoinfluencestatedpriceexpectations,whichactascuesfor valuations.Noticethattheseareexpectationsaboutactualmarketprices,buthavenotbeeninfluencedbyanyprevious marketbehaviour.Soapureshapingeffect–thatis,aneffectthatcannotbeattributedtomarketdiscipline–canbeobserved, ifitoccurs,inthefirstroundoftrading.Then,subsequentroundsallowustoobservetheeffectsofmarketdiscipline.

Wealsouseamoreinnovativemanipulationthatallowsusto‘switchoff’marketdisciplineforidentiﬁablesubsetsof traders:traderswhorepeatedlytradeatpricesthatareclearlyveryadvantageous,andtraderswhorepeatedlydonottrade becausetheyfaceverydisadvantageousprices.Byrepeatingthemarketintheabsenceofmarketdiscipline,wecanobserve thecumulativeshapingeffectsofendogenouspricefeedback.Byswitchingmarketdisciplinebackonforthesametraders, wecanobserveitspowertoerodetheseshapingeffectswhich,giventheircumulativenature,couldbequitelarge.

Topreviewourresultsweﬁndthat,intheabsenceofmarketdiscipline,bothmanipulationsinduceextensiveshaping effects.Whentheseshapingeffectsareexposedtothefullforcesofmarketdiscipline,theyaresometimesweakened,but arenoteliminated.

Ultimately,shapingmayariseforanumberofreasons.Oneextremepossibilityisthatagentsdonothavepreferences whentheygettothemarket,andconstructthemusingarbitrarycuesasanchors(e.g.Slovic,1995;LichtensteinandSlovic, 2006;Arielyetal.,2006;Stewartetal.,2006).Ortheymayreacttopriceinformationbecausetheyusepricesasreference points(e.g.Thaler,1985;Putler,1992;Isoni,2011;WeaverandFrederick,2012;Bordaloetal.,2012).Ourresultssuggestthat thepropositionthatpreferencesarecompletelymalleableistooextreme.Rather,theyarecompatiblewiththeexistenceof underlyingpreferencesofsomeform,butsuggestthatthesearesusceptibletoextraneousinﬂuencesthatmayhavesome longtermresidualeffect,inspiteofthediscipliningforcesoperatinginmarkets.

Thepaperisorganisedasfollows.InSection2,wedescribeourmarketinstitution–amedianpricesellingauction– andderivetheinstitution-specifichypothesesaboutshapingandmarketdisciplinewhichourexperimentswillexamine.In Section3,wedescribeourbroadexperimentaldesign.InSection4,wepresentourfirstmanipulation,designedtotestfor shapingeffectsobtainedthroughexogenouslyinfluencedpriceexpectations.Section5focusesonoursecondmanipulation, inwhichwestudytheroleofendogenouspricefeedback.SomeissuesraisedbyourresultsarediscussedinSection6.In Section7weoffersomeconcludingremarks.

2. Shapingandmarketdisciplineinrepeatedsellingauctions

Allofourtreatmentsemployrepeatedmedian-pricesellingauctionsformonetarylotteries.Ineachauctionround,each traderisendowedwithalotteryandisaskedtoconsiderasetofdiscreteamountsofmoneyspanningagivenrangeandto say,foreachamount,whetherornottheywouldacceptitinexchangeforthelottery.Theelicitationprocedure(described indetailinSection3)isconstrainedtoimposeconsistency:anyonewhoreportswillingness(unwillingness)toacceptsome amountxmustalsoreportwillingness(unwillingness)toacceptanyhigher(lower)amount.Thesmallestamountofmoney thetraderwouldacceptistheirwillingness-to-acceptvaluation(WTA);thelargestamountofmoneytheywouldnotacceptis theirnot-willing-to-acceptvaluation(NWTA).(Implicitly,thetraderisreportingthattheyvaluethelotteryatleastasmuch asNWTAbutnolessthanWTA.)ThemedianNWTAisidentiﬁedandannouncedasthemarketpriceforthatround.Traders whoseNWTAsarestrictlylessthantheannouncedprice(i.e.whohavereportedwillingnesstoacceptthatprice)selltheir lotteriesbacktotheexperimenteratthatprice;andifthisroundoftradingisrandomlyselectedattheendoftheexperiment tobethebasisofpayment,theyarethenpaidthatamount.Theothertraderskeeptheirlotteries:ifthisroundisselected, theyplayoutthelotteryandarepaidaccordingly.Sinceweareinterestedintheshapingeffectofpricecues,thereisno resolutionoflotteriesuntilafterthelastroundandthereisnoinformationaboutothertraders’responsesexceptintheform ofthemedianNWTAwhichconstitutesthemarketprice.

Attheendofeachauctionround,tradersaretoldthemarketpriceforthatroundandhencewhethertheyhavesoldor not.Accordingtotheshapinghypothesis,tradersareliabletorevisetheirNWTAsforthenextroundinthedirectionofthe observedprices.ThiscreatesatendencyforNWTAstobepulledinthedirectionofpricecues,otherthingsbeingequal.

Thistendencyisconceptuallydifferentfromvalueaffiliation.Affiliatedvaluesreflectapositivecorrelationbetween non-observedobjectivepropertiesofagood(e.g.theworthofacommon-valueresource),whileshapingreflectsacorrelation

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betweensubjectiveattitudes(e.g.eachindividual’svaluationofaprivategood)originatingfromapublicsignal.Fora con-trolledtestoftheshapinghypothesis,weneedadesignthatisabletoscreenoutobjectiveafﬁliation,whileallowingfor subjectivevaluestobecorrelated.Whetherornotshapingcanbereconciledwithstandardrationalityassumptionsisa legitimatequestion,butnotthefocusofourinvestigation,whichcentresonwhetherthephenomenonexistsornot,and howstrongitis.

Ourcontrolledtestmakesuseofseveralconvenientpropertiesofmonetarylotteries.Becauseattitudestoriskcanvary acrossindividuals,agivenlotteryislikelytohavedifferentprivatevaluesfordifferentindividuals.Sothemarketpricefor alotteryshouldprovidenoobjectiveinformationthatisrelevantforanindividual’sjudgementofitsprivatevaluetothem, eventhoughitreﬂectsotherpeople’sjudgementsaboutitsworth.Inaddition,sincethelotteriesweusehavenoimmediate substitutesoutsidethelabandare‘consumed’insidethelab(inthesensethatlotteryoutcomesareresolvedattheendof theexperiment),thevalueofalotterytoaparticipantcannotberationallyaffectedbyinferencesaboutexternaltrading opportunities.Afurtherfeatureoflotteries,whichweshallexploit,isthattheirmaximumandminimumprivatevaluesare givenbythehighestandlowestoutcomes.

Controllingforobjectivelyafﬁliatedvaluesandoutsidetradingopportunitiesisnottheonlychallengeonefaceswhen testingforshapingeffects.Asweexplainbelow,ifotherfactorssuchasmarketdisciplinearenotcontrolledfor,observing thatvaluationsmovetowardspreviouslyobservedpricesisnotnecessarilyevidencethatpreferencesaremarket-dependent. Theﬁrstgoalofourexperimentistoseeifshapingeffectsoccurwhenmarketdisciplineisswitchedoff.

Themarketdisciplinehypothesispositsthatagentspossesspreferencesofsomeform,whichareindependentofthemarket. Forexpositionalconvenience,herewemaketheconventionalassumptionthateachtraderhasauniquetrueprivatevalue forthetradedobject.1

OurmarketinstitutionisavariantoftheVickreyauction(Vickrey,1961).Soiftradershavetruemarket-independent privatevalues,itisaweaklydominantstrategyforeachtradertoreportanNWTAconsistentwiththeirprivatevalue(Milgrom andWeber,1982).Ifthesetruevalueswerereadilyaccessibleandthedominantstrategywereeasilycomprehended,then traderswouldbehaveoptimallyeachtimetheytookpartintheauction,andrepetitionwouldhavenoeffectwhatsoever. However,evenifunderlyingpreferencessatisfystandardassumptions,truevaluesmaynotbereadilyaccessible,orthebest strategymaynotbeimmediatelyobvious,sothattheremaybecircumstancesinwhichtradersdeviatefromthisstrategy inonewayoranother.Suchdeviationsmayprovecostly,inwhichcasemarketdisciplinecancomeintoplay.

Toseethis,consideramedian-priceauctionwithntraders(wherenisanoddnumber),indexedbyi=1,...,n.Assumeeach traderhasatruevalue

v

i.Ifthetraderrespondsoptimallytotheelicitationprocedure,theirreportedWTAwillbegreaterthan

orequalto

v

i,andtheirreportedNWTA,whichwedenoteai,willbelessthanorequalto

v

i.However,theiractualresponse

maybedifferentbecauseofsome‘error’(whichmayberandom,ormayreﬂectsomesystematicbehaviouralanomaly). MarketdisciplineoperatesbyexposingthecasesinwhichdeviatingfromtheoptimalstrategyofreportingWTA≥

v

i≥ai

resultsinanundesiredoutcome.Thishappenswheneverai≥p>vior

v

i>p>ai.Intheﬁrstcase,thetraderover-asksandfails

tosellatp,whichismorethantheirtruevaluation,thusforegoingapotentialgain.Inthesecondcase,theyunder-askand sellatp,whichislessthantheirtruevaluation,makingthemworseoff.Inbothofthesesituations,giventherealisedprice, theywouldhaveexperiencedabetteroutcomehadtheyfollowedtheoptimalstrategy.Toavoidincurringthesameloss again,theyshouldrevisetheiraiinthedirectionof

v

iinsubsequentrounds.2Noticethat,iftheydoso,theyalsoreviseaiin

thedirectionofthemarketprice.Thatis,marketdisciplineproducesanempiricaltendencyanalogoustoashapingeffect, whichiswhy,whenmarketdisciplineisinoperation,itisdifﬁculttoisolateshapingeffects.

However,thisdiscipliningeffectdoesnotnecessarilycometobearoneverytraderwhodoesnotbehaveoptimally.There aresituationsinwhichtradersover-askorunder-askbuttheauctionstillhasthesameimplicationsforthemasiftheyhad followedtheoptimalstrategy.Thishappenswheneverp>ai>viorelse

v

i>ai≥p.

Sincemarketdisciplineworksonlyontradersforwhomai≥p>vior

v

i>p>ai,thetraderswhoaresubjecttodiscipline

arelikelytohavetruevaluesthatarerelativelyclosetothemarketprice.Ifthemarketisrepeated,changesinbehaviour willcontinuetobeinducedamongsuchmarginaltradersuntiltheyarenolongervulnerabletomarketdiscipline.Thisisthe caseifandonlyifp>

v

iholdsforalltradersiwhosell,and

v

j≥pholdsforalltradersjwhodonotsell.Onthesimplifying

assumptionthatthemedianNWTAisreportedbyonlyonetrader,the(n−1)/2traderswiththelowestNWTAssell,andthe (n+1)/2traderswiththehighestNWTAsdonotsell.Thus,whennotraderissubjecttomarketdiscipline,themarketprice liesbetweenthe[(n−1)/2]thhighestandthe[(n+1)/2]thhighesttruevalues–justasconventionalmicroeconomictheory wouldpredictforamedian-pricemarket.Inotherwords,ifonedeﬁnesthetruemarketpriceasthepricethatwouldprevail ifalltradersfollowedtheoptimalstrategy,marketdisciplineproducesatendencyforthemarketpricetoconvergetoitstrue value.Thisistheimplicationofthemarketdisciplinehypothesisthatwewilltest.

1_As_we_will_explain_in_Section₆_,_market_discipline_does_not_require_that_preferences_are_{characterised}_by_such_a_degree_of_precision,_but_can_operate_in

ananalogouswayonimprecisepreferences,aslongastheseareindependentofthemarket.

2_Here,_we_make_no_further_assumption_about_the_speed_with_which_true_values_(or_the_optimal_strategy_for_reporting_these)_are_discovered._On_an_extreme

interpretation,onecouldthinkthatasinglecostlyerrorwouldbesufﬁcientforaparticipanttodiscovertheirtruevalue.Alternatively,convergencecould beagradualprocess,inwhichNWTAsareslowlyupdatedinthedirectionsuggestedbytheerrortheparticipantmade(i.e.bydecreasingone’sNWTAin caseofover-askingandincreasingitintheoppositecase).

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However,asnotedearlier,theremaybetraderswhosetruevaluesarefarenoughawayfromthepricesgeneratedby repeatedmarketsthattheirNWTAsneverfallbetweentheirtruevaluesandtherealisedprice.Suchtradersneverexperience thecoststhatgiverisetomarketdiscipline.Nevertheless,theyareexposedtotheshapingeffectsofpricefeedback.Iftraders withthesecharacteristicscanbeidentiﬁed,itispossibletotestfortheexistenceandstrengthofshapingeffectswhile screeningouttheeffectsofmarketdiscipline.Oneofourmanipulationsallowsustoswitchoffmarketdisciplineandexpose traderstoendogenouspricefeedbackcueswhich,ifshapingoccurs,willtendtopulltheirNWTAsawayfromtheirtrue valuesinaparticulardirection.Then,bysettinguprepeatedmarketsinwhichallparticipants’NWTAshavepreviouslybeen shapedinthesameway,wecanswitchmarketdisciplineonandtestwhetherpricesinthesemarketsconvergetowardsa hypothesisedtruemarketprice.

Inourexperiment,wewilltestthefollowinggeneralimplicationsofshapingandmarketdiscipline:

Hypothesis1(Pureshaping). Absentmarketdiscipline,NWTAsarepulledinthedirectionofuninformativepricecues.

Hypothesis2(Marketdiscipline). Withrepetition,pricesconvergetovaluesindependentofuninformativepricecues.

3. Experimentalprocedures

Theexperimentwasconductedin18sessionsattheUniversityofEastAngliaandwasimplementedusingtheZurich ToolboxforReadymadeEconomicExperiments(Fischbacher,2007).The204participantswererecruitedviaemailshots fromthegeneralstudentpopulation.

Ineachsessionparticipantstookpartinthreeauctions,eachrepeatedeighttimes,foratotalof24auctionperiods. Ineachsession,therewereeithertenortwelveparticipants,whowereassignedtotwotradinggroupsofeitherﬁveor sevenparticipants(oursecondmanipulationrequiredustohaveauctiongroupsoftwodifferentsizes).Participantswere re-matchedtoformdifferenttradinggroupsbeforethestartofeachauction,butthecompositionoftradinggroupswaskept constantduringtheeightroundsofanauction.

OneoftheauctionsimplementedourEXPmanipulation(shapingthroughpriceexpectations;seeSection4fordetails). Whetherthisauctioncameﬁrstorlastwascounterbalancedacrosssessions.Theremainingtwoauctionsimplementedour FBKmanipulation(shapingthroughpricefeedback),andwerealwaysruninsequence(seeSection5).3

Ineachroundofeachauction,eachparticipantsawalotterydisplayedontheirscreen.Lotteriesalwayshadexactlytwo possibleoutcomes;thesewerepositiveamountsofmoneyorprizes.Participantsweretoldtheyownedthelotterydisplayed ontheirscreenandhadtheopportunitytosellit.Theywerepresentedwithalistofpricesandaskedtostatewhetheror nottheywouldbewillingtoselltheirlotteryateachprice.Theprices(in

£

)alwaysrangedfromz+0.01toy,whereyand z,y>z,werethetwoprizes.4_The_0.01_was_added_to_the_lower_prize_to_ensure_that_NWTA_was_deﬁned_for_participants_who

acceptedeveryprice,inwhichcasetheirNWTAwassetequaltoz.Forparticipantswhorejectedeveryprice,NWTAwasset equaltoy.Itwasexplainedtoparticipantswhyitwouldbeinconsistenttovaluethelotteryaboveyorbelowz.5_Participants

weretoldthatiftheyagreedtosellfor

£

x,theyshouldalsobewillingtosellforanyamountgreaterthan

£

x(i.e.theywere notallowedtoswitchbackandforthinthemultiple-pricelist).Onceentered,responsescouldbechangedbyrestartingthe wholeprocess,butthiswasonlypossibleonce.Attheendoftheprocess,thecomputerrecordedeachparticipant’sNWTA. AfteranNWTAwasrecordedforeachtraderinagroup,thecomputerdeterminedthemarketpricebyselectingthemedian oftheseamounts.Theinstructionsexplainedhowthemarketpricewasobtained,andthepossibletradingimplications. Beforethebeginningoftheﬁrstauction,therewasapracticeroundforparticipantstofamiliarisethemselveswiththe elicitationprocedures.Theirunderstandingofthebasicruleswastestedbymeansofacomputerisedquestionnaire.

Attheendofeachsessionthecomputerrandomlyselectedoneoftheauctionroundsthathadbeencompletedbythe participant.6_If_the_participant_had_sold_their_lottery_in_that_round,_they_received_the_market_price._If_they_had_kept_the_lottery,

theyplayeditoutandreceiveditsoutcome.Lotterieswereresolvedbydrawingoneofahundrednumbereddiscsfroma bag.Theoutcomeassociatedwitheachnumberwasclearlyindicatedbythelotterydisplay(seeonlineAppendixforan example).Iftheselectedauctionroundwasfromtheﬁrstmanipulation,participantswerealsorewardedfortheiraccuracy inpredictingthemarketpriceintheothergroup(seeSection4.1).Sessionslastedanhourandﬁveminutesonaverage,and theaverageearningwas

£

7.50.

3 _The_full_list_of_sessions,_outlining_our_{manipulations}_and_{counterbalancing,}_can_be_found_in_the_Appendix,_Table_A.2.1.

4 _In_order_to_avoid_having_to_present_participants_with_very_long_lists_of_prices,_the_elicitation_procedure_had_a_number_of_steps._In_the_ﬁrst_step,_the

pricesonofferstartedfrom£(z+0.01)andwentto£ycoveringallmultiplesof£1(foroneofourlotteries,wehadanextrastepatthebeginning,inwhich allpricesexceptthelowestweremultiplesof£10).Inthelaststep,the£1rangebetweenthelowestpricethattheindividualacceptedandthehighest pricesherejectedinthepreviousstepwasbrokendownin£0.10intervals,toarriveatanNWTAexpressedasamultipleof£0.10.Forsomeparticipants priceswentupfrom£(z+0.01)to£y,forotherstheywentdownfrom£yto£(z+0.01).Somescreenshotsofthiselicitationprocedurecanbefoundinthe Appendix.

5 _As_we_explain_in_Section_5.1_,_this_aspect_of_the_elicitation_procedure_was_crucial_for_our_second_{manipulation.}_Gneezy_et_al.₍₂₀₀₆₎_report_evidence_that

someparticipantsvaluelotterieslessthantheirworstpossibleoutcome,aﬁndingthattheylabeltheuncertaintyeffect.However,oneoftheconditions forthiseffecttooccuristhattheprizesofthelotterytobevaluedarenotdirectlyexpressedinmonetaryterms(ibid.p.1290),whichisnottrueinour experiment.

6 _Since_our_second_manipulation_required_that_some_participants_did_not_take_part_in_one_of_the_auctions,_some_participants_completed₂₄_rounds_and

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Table1

RangesforpriceexpectationcuesinEXPmanipulation.

HighCue LowCue

£20ormore £1.00–£2.00

£19.90–£15.00 £2.10–£3.00

£14.90–£10.00 £3.10–£4.00

£9.90–£5.00 £4.10–£5.00

£4.90–£1.00 £5.10ormore

InR1andR8,participantsstatedtheirpricepredictionfortheothergroupin theirsessionbyselectingoneoftherelevantﬁverangesandthenenteringa valuefallingwithinthatrange.

4. EXPmanipulation:shapingthroughpriceexpectations

4.1. Design

Our ﬁrstmanipulationwasdesigned toinvestigatewhetherNWTAscanbeshapedbydivergentpriceexpectations

(Hypothesis1),andwhetheranyresultingshapingeffectsareremovedbymarketdiscipline(Hypothesis2).Thesetreatments involvedarepeatedauction,inwhicheverytraderwasendowedwiththesamelottery.Inordertoallowroomforsizeable shapingeffects,wechosealotterywithafairlyhighvariance.LetK=(

£

z,p;

£

y,1−p)denoteagenericbinarylotteryoffering

£

zwithprobabilityp,and

£

ywithprobability1−p.Thelotteryusedinthispartoftheexperimentwas: E=(

£

1,0.95;

£

50,0.05).

Werandomlydividedparticipantsintotwogroups,whichwelabeltheHighCueandLowCuemarkets.Eachmarket consistedofeightauctionroundsconductedasexplainedinSection3.Wetoldparticipantsthatthereweretwotrading groupsintheroom,andthateveryonehadthesamelottery.Beforetheﬁrstauctionround,weaskedthemtopredictwhat thepricewouldbeintheothertradinggroup,byselectingarangefromalistandthenreportingapointestimatewithinthe chosenrange.Ifoneoftheseauctionroundswasselectedtobepaidattheendoftheexperiment,theywererewardedfor theaccuracyoftheirpredictions,usinganabsolutelossfunctionwithmaximumrewardof

£

2.(Becausepredictionswere madeabouttheothergroup,therewasnoincentiveforparticipantstomisreportvaluationsinanattempttomaketheir predictionscometrue.)Thesameprocedurewasrepeatedbeforethelastauctionroundtoseeifparticipants’expectations adjustedtothepricefeedbacktheyreceived.

TheHighandLowCuegroupsdifferedintermsoftherangesofpricestheywerepresentedwith.Theseareshownin Table1.

BothlistsinTable1coverthewholerangeofvaluesbetweenthetwoprizesoflotteryE,buttheydifferintwoimportant respects.First,themiddlerangecontainsmuchhighervaluesfortheHighCuemarketthanfortheLowCuemarket.Second, theHighCuerangesarepresentedindecreasingorder,whiletheLowCuerangesarepresentedinincreasingorder.We expectedbothoftheseaspectstoinducehigherpriceestimatesintheHighCueconditionthanintheLowCuecondition,on thegroundsthattheﬁrstandthemiddlerangesaremoresalientthantheothers(theseeffectsareknowninthepsychology literatureas‘rangefrequencyeffects’;seeParducci,1965;ParducciandWeddell,1986).7

Ifparticipantshavewell-formedtruevalues,suchmanipulationsshouldhavenoeffect;butiftheyarepronetoshaping effects,thefirst-roundNWTAsintheHighCuemarketscouldbesubstantiallylargerthanthefirst-roundNWTAsintheLow Cuemarket.Sincenofeedbackisprovideduntiltheendofthefirstround,theinitialNWTAsmaybesubjecttoshaping,but cannothavebeenaffectedbymarketdiscipline.Inthissetting,Hypothesis1impliesthatNWTAswillbehigherintheHigh CuegroupthanintheLowCuegroup.

Astheauctionisrepeatedwithfeedback,marketdisciplineisswitchedonandwecaninvestigateitseffects.Because tradershavebeenrandomisedbetweenthetwotreatments,anyunderlyingtruevalues–includingthetruevalueofthe marketprice–shouldhavesimilardistributionsinthetwosubsamples.Therefore,astheauctionisrepeated,Hypothesis2 impliesthatmarketdisciplineshouldinduceconvergenceofthepricesprevailinginthetwomarkets.

4.2. Results

Table2reportsthedataoftheHighCueandLowCuemarketsofourEXPmanipulation.Forbothtreatments,thetable reportsthenumberofobservations,mean,medianandstandarddeviationofthepredictedmarketprices,theactualNWTAs andtheactualmarketpricesinrounds1(R1)through8(R8).

WewilldiscussthedatawithreferencetoFig.1,whichusesthefollowingconventions.Solidmarkersjoinedbysolid linesrefertotheHighCuegroup,whileemptymarkersjoinedbydashedlinesrefertotheLowCuegroup.MeanNWTAsare

7_This_manipulation_bears_some_similarity_to_anchoring_{manipulations}_(e.g._Ariely_et_al.,₂₀₀₃_),_but_the_ﬁnal_price_prediction_is,_effectively,_a_{self-generated}

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Table2

ResultsofEXPmanipulation:shapingthroughpriceexpectations.NWTAvaluationsandmarketpricesforlotteryE=(£1,0.95;£50,0.05).

NWTA Marketprices

Obs. Mean Median St.dev. Obs. Mean Median St.dev.

ELowCuepredictionsR1 102 6.72 4.05 7.23

ELowCuepredictionsR8 102 4.94 4.35 3.18

ELowCueR1 102 10.21 5.40 10.46 18 6.90 6.30 3.26 ELowCueR2 102 8.56 5.35 8.54 18 7.37 5.10 5.68 ELowCueR3 102 7.61 4.90 7.21 18 6.43 4.65 3.95 ELowCueR4 102 8.61 4.80 10.50 18 6.42 4.70 4.65 ELowCueR5 102 7.64 4.40 9.62 18 5.03 4.45 2.08 ELowCueR6 102 6.85 4.30 7.62 18 4.74 4.25 2.07 ELowCueR7 102 7.20 4.20 9.47 18 4.61 4.30 1.92 ELowCueR8 102 6.73 4.20 7.92 18 4.38 4.20 1.98

EHighCuepredictionsR1 102 12.11 12.25 7.99

EHighCuepredictionsR8 102 7.51 6.05 4.82

EHighCueR1 102 12.11 10.05 9.97 18 10.19 10.00 4.17 EHighCueR2 102 9.64 8.90 6.95 18 8.37 7.90 3.10 EHighCueR3 102 9.36 7.40 8.28 18 8.68 8.00 3.91 EHighCueR4 102 8.04 7.30 5.04 18 8.19 7.40 3.61 EHighCueR5 102 8.13 6.40 5.99 18 7.48 7.10 3.14 EHighCueR6 102 8.28 6.20 7.57 18 6.77 6.50 2.86 EHighCueR7 102 8.29 5.40 8.64 18 6.06 5.20 2.51 EHighCueR8 102 8.08 5.15 8.96 18 6.33 5.70 2.71

102participants(18groupsof5or7)wereassignedtotheLowCuetreatment,102(18groupsof5or7)totheHighCuetreatment.Eachgrouptradedfor8 rounds,withfeedbackaboutmarketpriceandtradingoutcomeaftereachround.PricepredictionswereelicitedbeforeR1andbeforeR8usingeitherLow orHighcues. 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 0 1 2 3 4 5 6 7 8 V al ues (£ ) Auction Round Exp. High Ask High Price High Exp. Low Ask Low Price Low NWTA High NWTA Low

Fig.1. ResultsoftheEXPmanipulation.EvolutionofNWTAsandpricesintheHighCueandLowCuemarkets.Note:HighCuedenotedbysolidmarkers joinedbysolidlines.LowCuedenotedbyemptymarkersjoinedbydashedlines;squaresaremeanNWTAs;trianglesaremeanactualmarketprices;solid (empty)diamondsaremeanpricepredictionsforHigh(Low)Cue.

presentedbysquares,whilemeanactualmarketpricesareshownbytriangles.Themeanpricepredictionsarerepresented

bythediamonds.

Theﬁrstissueistoestablishwhetherourmanipulationhasaffectedpriceexpectations.Thisisaprerequisitefortesting

theimplicationsofHypothesis1.InR1,themean(median)expectationis

£

12.11(

£

12.25)intheHighCuemarketand

£

6.72

(

£

4.05)intheLowCuemarket;thisdifferenceisstronglysigniﬁcantinaone-tailMann–Whitneytest(Z=−6.44,p<0.001). Giventhatwehavebeensuccessfulatmanipulatingparticipants’priceexpectations,wecantesttheimplicationsof Hypothesis1bycomparingNWTAsinR1betweenthetwogroups,whenmarketdisciplinecannot operate.Themean (median)NWTAinR1is

£

12.11(

£

10.05)intheHighCuemarketand

£

10.21(

£

5.40)intheLowCuemarket.8_The_two_NWTA

8 _Some_readers_may_ﬁnd_it_surprising_that_our_{participants’}_NWTAs_for_a_lottery_whose_expected_value_is_just_£_3.45_were_so_high._However,_lottery_E_has

thecharacteristicsofa‘$-bet’(i.e.alotteryofferingsmallchanceofwinningalargeprize).Thepreferencereversalliteratureprovidesrobustevidencethat suchlotteriesareoftenovervaluedrelativetotheirexpectedvalues(seeSeidl,2002).

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Table3

EvolutionofNWTAvaluationsinLowCueandHighCuemarketsforsellersandnon-sellers.

Auctionround t NWTAtifsoldatt−1 NWTAtifnotsoldatt−1

<0 0 >0 Mean <0 0 >0 Mean LowCue R1 1 – – – – – – R2 2 3 7 31 2.85 48 7 6 −4.66 R3 3 7 11 24 1.03 38 13 9 −2.34 R4 4 6 12 21 2.42 43 9 11 0.12 R5 5 11 16 13 1.23 37 11 14 −2.38 R6 6 10 16 13 0.41 46 9 8 −1.55 R7 7 12 16 11 1.18 31 22 10 −0.16 R8 8 15 14 12 1.14 28 22 11 −1.55 HighCue R1 1 – – – – – – R2 2 3 11 26 3.29 53 3 6 −6.20 R3 3 5 11 23 3.97 48 6 9 −2.91 R4 4 5 14 23 1.40 42 9 9 −3.22 R5 5 6 17 18 1.42 44 8 9 −0.80 R6 6 9 20 9 0.77 43 13 8 −0.22 R7 7 11 14 17 1.63 40 12 8 −1.11 R8 8 7 12 20 1.12 33 16 14 −1.03

ChangeinNWTAfromroundtoround,NWTAt=NWTAt−NWTAt−1,forparticipantswhosoldandparticipantswhodidnotsellinthepreviousround.For

eachroundoftheauction,thenumbersofsellersandnon-sellerswhodecreased,keptconstantandincreasedtheirNWTAvaluationisreportedtogether withthemeanNWTAt.

distributionsdiffersigniﬁcantlyinaone-tailMann–Whitneytest(Z=−2.17,p<0.05).Theseﬁndingsprovidesupportforthe

implicationsofHypothesis1,andconstituteourResult1a.

Result1a–Shapingthroughpriceexpectations.Intheabsenceofmarketdiscipline,NWTAsarepulledinthedirection ofuninformativepriceexpectationcues.

Wecannowaskhowfartheshapingeffectsofpriceexpectationcuespersistinthefaceofmarketdiscipline.According toHypothesis2,marketdisciplineshouldleadmarketpricestoconvergetovaluesthatareindependentofuninformative pricecues.Sinceparticipantswererandomlyallocatedtothetwotreatments,thismeansthat,withrepetition,market pricesshouldconvergetothesamevalueintheHighandLowCuegroups.Forthistesttobemeaningful,weneedour EXPmanipulationtohaveproducedadifferenceinmarketprices.InR1,themean(median)marketpriceis

£

10.19(

£

10) intheHighCuegroupand

£

6.90(

£

6.30)intheLowCuegroup,adifferencethatisstatisticallysigniﬁcantinaone-tail Mann–Whitneytest(Z=−2.36,p<0.05).

InordertotesttheimplicationsofHypothesis2,wecomparemarketpricesinthelastroundoftheauction,whenmarket disciplinehashadthebestopportunitytoexertitseffects.InR8,themean(median)priceis

£

6.33(

£

5.70)intheHigh Cuegroupand

£

4.38(

£

4.20)intheLowCuegroup.Althoughtheabsolutedifferencebetweenthemean(median)prices observedinthetwogroupsissmallerinR8thaninR1,thedistributionsofmarketpricesstilldiffersigniﬁcantlybetween thetwogroupsinaone-tailMann–Whitneytest(Z=−2.66,p<0.01).9_Therefore,_we_do_not_ﬁnd_support_for_the_implications

ofHypothesis2.10_This_constitutes_our_Result_2a.

Result2a–Persistenceofshapingthroughpriceexpectations.Aftereightauctionrounds,pricesthathavebeenshaped byuninformativepriceexpectationcuesarestillsigniﬁcantlyaffectedbythosecues.

TheevolutionofNWTAvaluationsovertheeightauctionroundsissummarisedinTable3.Forrounds2through8ofthe LowCueandHighCuemarkets,thetablereportsthenumbersofparticipantswhodecreased,keptunalteredorincreased theirNWTA,dependingonwhethertheysoldorkepttheirlotteryinthepreviousround.Forbothsellersandnon-sellers, thetablealsoshowsthemeanchangeinNWTA,NWTAt=NWTAt−NWTAt−1,fromroundtoround.

9_{Participants’}_price_{expectations,}_which_we_elicited_again_before_R8,_are_consistent_with_this_persistent_difference._The_mean_(median)_R8_prediction_is

£7.51(£6.05)intheHighCuegroupand£4.94(£4.35)intheLowCuegroup.Whilethetrendsinthedistributionsofmarketpricesareclearlyvisiblein Fig.1,itispossiblethattheelicitationofpriceexpectationsbeforeR8hadanamplifyingeffectonNWTA(andprice)differences.Ifwetesttheimplications ofHypothesis2usingtheR7pricesinstead,westillﬁndsigniﬁcantdifferences(Z=–2.06,p<0.05inaone-tailMann–Whitneytest).

10_The_theoretical_analysis_of_Section₂_,_which_forms_the_basis_for_Hypothesis_2,_presupposes_that_costly_errors_are_entirely_removed._This_raises_the_question

ofwhethereightauctionroundsaresufﬁcientforpricestohavestabilised,aquestionthatwehavetriedtoanswerbyestimatingasimpleasymptotic functionforthemarketprice:pt=p*+(1/t)bwhereptisthemarketpriceinroundt,p*istheasymptoticvalueofthemarketprice,andbisaparameter

relatedtothespeedofconvergence.Apartfromitseaseofinterpretation,anadvantageofthismodelisthatitcanbeeasilyestimatedwithOLS.Thekey parameterisp*.BycomparingitsvalueintheHighCueandtheLowCuetreatments,wecancheckwhetherpricesaretendingtowardsdifferentvalues.The estimatedvaluesofp*are£6.35intheHighCuegroupand£4.75intheLowCuegroup.Thesevaluesaresigniﬁcantlydifferentfromeachother(p<0.1), indicatingthatpricesappeartobetendingtowardsdifferentvaluesinthetwogroups.SeeTableA.3.1intheAppendixfordetails.

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Table3revealsastrikingregularity.InboththeHighandLowCuegroups,participantshaveaprevalenttendencyto increasetheirNWTAiftheysoldinthepreviousroundandanoppositetendencytodecreasetheirNWTAiftheydidnot sell.11_The_effect_weakens_over_time,_as_more_participants_keep_their_NWTAs_unaltered._This_constitutes_our_ﬁrst_observation.

Observation1–NWTAupdatinginHighandLowCuemarkets.InHighandLowCuemarkets,sellerstendtoincrease theirNWTAandnon-sellerstendtodecreasetheirNWTA.

Observation1showsthatbothsellersandnon-sellersrevisetheirNWTAsinthedirectionofthemarketprice.Butbecause wehavenoinformationabouttheirtruevalues,wecannottellwhetherthisisaneffectofshaping,marketdisciplineorboth. Thisclearlyillustrateswhy,ifoneisinterestedinthecumulativeeffectofshaping,itisusefultoshutoffmarketdiscipline. ThisistheobjectiveofourFBKmanipulation.

5. FBKmanipulation:shapingthroughpricefeedback

5.1. Design

OursecondmanipulationisdesignedtostudytheeffectofpricefeedbackcuesonNWTAs.Unlikethepriceexpectation cuesthatweemployedinourEXPmanipulation,thesecuesareendogenous,astheyaregeneratedbythenormaloperation ofthemarket.

Werandomlydividedparticipantsbetweentwotreatments,thecontroltreatmentandtheshapingtreatment.Thecontrol treatmentwasruninsessionswithtenparticipants.Eachparticipanttookpartintwoseriesofrepeatedauctionsbelonging totheFBKmanipulation,oneforeachoftwodifferentlotteries,alow-valuelotteryLandahigh-valuelotteryH(seebelow forthespecificsoftheselotteries).Ineachrepeatedauction,therewereeightrounds.Theorderofthetwolotterieswas counterbalancedbetweensessions.Inthistreatment,alltraderstakingpartinthesameauctionwereendowedwiththe samelottery,sothatthepricefeedbackreflectedthemedianNWTAforthatlotteryintherelevantround.Eachofthese marketshadexactlyfivetraders.

Bycontrast,theshapingtreatmentwasruninsessionswithtwelveparticipants.Asinthecontroltreatment,therewere twoseriesofrepeatedauctionsinvolvingeightroundsperseries.Theﬁrstseriesineachsessionwasdesignedtocreate conditionsunderwhichthecumulativeeffectsofshapingcouldbeobservedintheabsenceofmarketdiscipline,hence allowingustotesttheimplicationsofHypothesis1.Thesecondseriesofeightroundswasdesignedtoexaminetheimpact ofmarketdisciplineonanysucheffects,asatestofHypothesis2.

Ineachsessionoftheshapingtreatment,theﬁrstseriesconsistedofmixedmarkets,inwhichdifferenttraderswere endowedwithdifferentlotteries.Therewasonemarketwithseventraders–threeendowedwithL,threewithH,andone withamedium-valuelotteryM–andanothermarketwithﬁvetraders–twoendowedwithL,twowithH,andonewithM. ThisarrangementallowedustodropthetwotraderswhohadbeenendowedwithMfromthesecondseries12_,_and_reassign

thetenparticipantswhohadpreviouslybeenendowedwithLorHtotwohomogenousmarkets.Thatis,thefivetraders inasessionwhohadbeenendowedwithLinthefirstseriescontinuedtotradeL,butnowaspartofonemarketwhere allfivetraderswereendowedwithL,whiletheothermarketconsistedofthefivetraderswhohadbeen,andcontinuedto be,endowedwithH.Sincebothhomogeneousandcontrolmarketsconsistedoftradersendowedwiththesamelottery(L insomemarkets,Hinothers),wecanjudgethepersistenceofshapingeffectsbycomparingthepatternsofpricesinour second-serieshomogeneousmarketswiththoseinthecorrespondingcontrolmarkets.

ThekeyinnovationoftheFBKmanipulationistheabilitytoshapeNWTAsthroughtheﬁrst-seriesmixedmarkets.We nowexplainthismanipulationinmoredetail.Weusedthefollowingbinarylotteries:

L=(

£

2,0.8;

£

9,0.2), M=(

£

7,0.5;

£

9,0.5), H=(

£

7,0.2;

£

14,0.8).

Sinceeachtrader’sNWTAwasconstrainedtobenogreaterthanthehigherlotteryprizeandnolessthanthelower(see Section3),thedistributionofendowmentsinthemixedmarketsensuredthatthemarketpriceinthesemarketswasbound tolieinthe(

£

7,

£

9)interval.13

Inthesemarkets,tradersweregivennoinformationaboutthelotteriesownedbyothertraders.Whenweexplainedhow participantsshouldrespondtoquestionsabouttheirwillingnesstoacceptstatedprices,westressedthattheseresponses

11 _In_both_groups,_being_a_seller_in_the_previous_round_has_a_highly_signiﬁcant_positive_effect_on_NWTA

tinarandom-effectspanelregression.SeeTable

A.3.2intheAppendixfordetails.

12 _These_{participants,}_whose_presence_was_required_for_our_manipulation_of_the_price_feedback_(see_below),_were_instead_asked_to_complete_an_unrelated

questionnaire.

13 _Because_of_the_constraint_on_individual_NWTAs,_only_L_traders_could_report_NWTAs_below_£_7,_and_only_H_traders_could_report_NWTAs_above_£_9._The

presenceofoneMtraderineachgroupensuredthatfewerthanhalfofthetradersinthemarketwereendowedwithL,andfewerthanhalfwithH,sothe medianaskwasboundtobeinthe(£7,£9)interval,therangeofadmissibleasksforMtraders.

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werestrictlypersonalandshouldsimplyreﬂecttheirownevaluationofthelotterytheywereendowedwith.Underthese circumstances,fromaconventionalpointofview,itshouldbeirrelevantwhatotherpeopledoandwhattheactualmarket priceturnsouttobe.14

Akeyfeatureofourmixedmarketdesignisthat,sinceNWTAsinthe(

£

7,

£

9)intervalwereadmissibleforalllotteries, thepricefeedbackwascredibleforalltraders.However,theexpectedvalueofL(

£

3.40)wasmuchlowerthanthelowest possibleprice(

£

7),whiletheexpectedvalueofH(

£

12.60)wasmuchlargerthanthehighestpossibleprice(

£

9).Thismakes thepricefeedbackfairlyhighforLtraders,andfairlylowforHtraders,creatingthepotentialforsizeableshapingeffects.

BecausetheexpectedvaluesofLandHliewelloutsidetherangeofpossibleprices,mostLandHtraderswereunlikelyto besubjecttomarketdiscipline,eveniftherewerestrongshapingeffects.ConsiderLtradersundertheassumptionthattrue valuesexistandareunique(thecaseofHtradersisamirrorimage).SincethesetraderswerereportingNWTAsforlotteries thatwerefarinferiortothoseheldbythemajorityoftradersinthemarket,itisnaturaltoexpectthatintheﬁrstauction roundthepricewouldbemuchhigherthanthetruevaluesandNWTAsofalmostallLtraders.Ifthiswasthecase,Ltraders wouldsellatsuchanadvantageouspricethatmarketdisciplinewouldnotbite.Nevertheless,thehighpricewouldstillhave thepotentialtoexertanupwardshapingeffectontheirNWTAs.Becauseofitscumulativenature,oversuccessiveauction roundsthisshapingeffectcouldbequitestrongandyetstillnotraiseNWTAstoalevelatwhichanyLtraderswouldfail tosell(andhencebecomesubjecttomarketdiscipline).Thisfeatureofourdesignallowsus,ineffect,toswitchoffmarket disciplineandtestwhethervaluationscanbeshapedbyendogenouspricecues.15_Therefore,_Hypothesis₁_implies_that,_after

repeatedexposuretomarketpricefeedbackcues,NWTAsforeachoflotteryLandHshoulddifferbetweenmixedmarkets andthecorrespondingcontrolmarkets.

Marketdisciplinewasswitchedonwhentraderswerereassignedtohomogeneousmarkets.SupposethatﬁveLtraders whoseNWTAshaveallbeenshapedupwardsinmixedmarketsnowtakepartinthesamehomogeneousmarket,andthat eachoftheminitiallyreportsthesameNWTAasinthelastroundofthemixedmarket.Then,thetradersreportingthe highestoftheseNWTAswillnolongersell.Forthesetraders,ai≥p>vi:theyover-askandfailtosellatanadvantageous

price.Accordingtothemarketdisciplinehypothesis,theyshouldreactbyreducingtheirNWTAsinthenextround.This tendstoproduceafallinthepriceinthenextround.Again,thetraderswhonowstatethehighestNWTAsfailtosell; ifthesetradersarestillover-asking,marketdisciplineleadsthemtolowertheirNWTAsinthefollowinground,andthe pricefallsagain;andsoon,untilanyover-askingiseliminatedinthemarginaltraders.Amirror-imageargumentappliesto homogeneousHmarkets.

AsexplainedinSection2,ifagentshadpreciseandmarket-independenttruevalues,thisprocessofadjustmentwould cometoanendwhenthepricereacheditstruevalue,whichisfullydeterminedbythedistributionoftraders’truevalues. Sinceparticipantswererandomisedbetweenhomogeneousandcontrolmarkets,thedistributionsoftraders’truevalues shouldnotdiffersystematicallybetweenthesemarkets.Thus,Hypothesis2impliesthat,withrepetition,pricesin homo-geneousmarketsshouldconvergetovaluesthatarenotsigniﬁcantlydifferentfromthoseobservedinthecorresponding controlmarkets.

5.2. Results

Table4reportsthedatawegatheredinthemixed,homogeneousandcontrolmarketsfortheLlottery(inthetoppanel) andtheHlottery(inthebottompanel).Eachrowreportsthenumberofobservations,mean,medianandstandarddeviation ofboththeNWTAsandmarketpricesforeithertheHorLlottery.

ThekeyresultswillbepresentedwiththeaidofFig.2,whichshowstheevolutionofNWTAsandpricesinmixedand controlmarkets(panelsaandb)andinhomogeneousandcontrolmarkets(panelscandd).Ineachpanel,squaresdenote meanNWTAandtrianglesdenotemeanmarketpricesintherelevantmarket.Dataformixedandhomogeneousmarkets areshownusingsolidlines(rememberthatthesameparticipantstookpartinmixedmarketsfollowedbyhomogeneous markets),whiledashedlinesrefertocontrolmarkets.

Westartbylookingatmixedmarkets.Oneofourobjectiveswiththesemarketswastoprovidepricefeedbackwithout thepotentialforthisfeedbacktotriggermarketdiscipline.Inordertohaveasenseofwhetherweachievedthis,wecan lookatthefrequencieswithwhichLtraders(whowereexpectedtotrade)andHtraders(whowereexpectedtokeeptheir lotteries)didactuallysell.Overtheﬁrstsevenroundsofthemixedmarkets(wedonotconsiderthelastroundbecause feedbackreceivedinthatroundcouldhavenoeffectonobservedNWTAsorprices),68%oftheLtraderssoldineveryround, and93%soldatleastsixtimes.88%oftheHtradersneversold,and97%soldatmostonce.16_Thus,_although_a_small_number

ofexceptionallyhighLNWTAsandanevensmallernumberofexceptionallylowHNWTAsprobablyweresubjecttomarket

14_We_have_no_way_to_tell_whether_or_not_participants_thought_other_traders_in_their_group_were_trading_the_same_lottery._Each_{individual’s}_decision_was

framedasadecisionastowhetherornottheywantedtoselltheirlotteryatanygivenprice,andincentivisedaccordingly.Thisisallweneedforourtestsof theshapinghypothesis.Ourassignmentoflotteriestoparticipantsisanalogoustotheinducedvaluetechniqueadoptedinexperimentaleconomicssince Chamberlin(1948)andSmith(1962)tostudymarketbehaviour.Weuselotteriesinsteadoftokenstomakelargeshapingeffectspossible,andemploya median-priceinsteadofadouble-oralauction,butparticipantsonlytradeifthepriceisacceptabletothem.

15_The_auxiliary_hypothesis_that_L_and_H_traders_are_rarely_subject_to_market_discipline_can_be_veriﬁed_by_considering_the_frequencies_with_which_L_traders

failtosellandHtraderssell(seeSection5.2below).

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Table4

ResultsofFBKmanipulation:shapingthroughpriceexpectations.

NWTA Marketprices

NWTAvaluationsandmarketpricesforlotteryL=(£2,0.8;£9,0.2)a

LcontrolR1 60 4.25 4.00 1.10 12 4.15 3.95 0.72 LcontrolR2 60 4.20 4.00 1.16 12 4.04 4.00 0.45 LcontrolR3 60 4.21 3.90 1.38 12 3.85 3.80 0.44 LcontrolR4 60 4.09 3.70 1.37 12 3.78 3.55 0.58 LcontrolR5 60 3.94 3.80 1.15 12 3.78 3.80 0.53 LcontrolR6 60 3.99 3.80 1.14 12 3.80 3.85 0.54 LcontrolR7 60 3.96 3.70 1.20 12 3.73 3.65 0.56 LcontrolR8 60 3.83 3.70 0.93 12 3.68 3.55 0.55 LmixedR1 60 4.64 4.40 1.62 24 7.93 7.90 0.55 LmixedR2 60 4.93 4.70 1.54 24 7.74 7.70 0.53 LmixedR3 60 5.04 4.95 1.51 24 7.60 7.50 0.59 LmixedR4 60 5.53 5.45 1.64 24 7.65 7.60 0.62 LmixedR5 60 5.46 5.45 1.52 24 7.61 7.80 0.55 LmixedR6 60 5.67 5.80 1.64 24 7.64 7.70 0.55 LmixedR7 60 5.72 5.90 1.71 24 7.67 7.65 0.58 LmixedR8 60 5.67 6.45 1.82 24 7.57 7.50 0.50 LhomogeneousR1 60 5.35 5.40 1.49 12 5.53 5.40 0.88 LhomogeneousR2 60 4.94 4.85 1.50 12 4.93 4.85 0.92 LhomogeneousR3 60 4.52 4.40 1.48 12 4.38 4.20 0.87 LhomogeneousR4 60 4.81 4.40 1.75 12 4.87 4.75 1.18 LhomogeneousR5 60 4.65 4.40 1.59 12 4.62 4.35 1.19 LhomogeneousR6 60 4.57 4.40 1.56 12 4.43 4.00 1.13 LhomogeneousR7 60 4.40 4.10 1.47 12 4.23 4.00 0.98 LhomogeneousR8 60 4.60 4.25 1.72 12 4.42 4.20 1.15

NWTA Marketprices

NWTAvaluationsandmarketpricesforlotteryH=(£7,0.2;£14,0.8)b

HcontrolR1 60 11.17 11.45 1.66 12 11.46 11.45 0.71 HcontrolR2 60 11.09 11.35 1.36 12 10.97 10.90 0.88 HcontrolR3 60 11.10 10.95 1.34 12 10.93 11.05 1.00 HcontrolR4 60 11.08 11.40 1.39 12 10.93 11.50 1.18 HcontrolR5 60 11.21 11.50 1.45 12 11.02 11.45 1.26 HcontrolR6 60 11.19 11.40 1.41 12 10.98 11.30 1.09 HcontrolR7 60 11.14 11.30 1.34 12 10.98 11.10 1.13 HcontrolR8 60 10.97 11.20 1.32 12 10.93 11.30 1.11 HmixedR1 60 10.91 11.10 1.66 24 7.93 7.90 0.55 HmixedR2 60 10.91 11.25 1.66 24 7.74 7.70 0.53 HmixedR3 60 10.26 10.45 1.97 24 7.60 7.50 0.59 HmixedR4 60 9.95 10.10 1.99 24 7.65 7.60 0.62 HmixedR5 60 9.93 10.15 2.07 24 7.61 7.80 0.55 HmixedR6 60 10.05 10.40 2.07 24 7.64 7.70 0.55 HmixedR7 60 9.86 9.95 2.00 24 7.67 7.65 0.58 HmixedR8 60 10.09 10.50 2.06 24 7.57 7.50 0.50 HhomogeneousR1 60 10.26 10.40 1.81 12 10.55 10.35 1.05 HhomogeneousR2 60 10.55 10.50 1.54 12 10.51 10.50 0.90 HhomogeneousR3 60 10.51 10.50 1.42 12 10.41 10.50 0.98 HhomogeneousR4 60 10.60 10.70 1.47 12 10.60 10.70 1.02 HhomogeneousR5 60 10.61 10.55 1.37 12 10.55 10.60 0.97 HhomogeneousR6 60 10.48 10.50 1.47 12 10.48 10.45 1.01 HhomogeneousR7 60 10.47 10.50 1.51 12 10.40 10.40 0.95 HhomogeneousR8 60 10.56 10.55 1.28 12 10.33 10.45 0.94

a₆₀_participants₍₁₂_groups_of₅₎_were_assigned_to_a_control_treatment_in_which_each_trader_submitted_an_NWTA_to_sell_the_same_lottery_(L)._Each_group

tradedfor8rounds,withfeedbackaboutmarketpriceandtradingoutcomeaftereachround.60participantsweregiventheLlotteryandtradedinmixed groups(of5or7)inwhichsometradershaddifferentlotteries.Eachgrouptradedfor8rounds,withfeedbackaboutmarketprice(constrainedbetween£7 and£9)andtradingoutcomeaftereachround.Thesameparticipantswerethenre-assignedtotradeinhomogeneousgroupsof5withotherparticipants endowedwiththesamelottery.

b ₆₀_participants₍₁₂_groups_of₅₎_were_assigned_to_a_control_treatment_in_which_each_trader_submitted_an_NWTA_to_sell_the_same_lottery_(H)._Each_group

tradedfor8rounds,withfeedbackaboutmarketpriceandtradingoutcomeaftereachround.60participantsweregiventheHlotteryandtradedinmixed groups(of5or7)inwhichsometradershaddifferentlotteries.Eachgrouptradedfor8rounds,withfeedbackaboutmarketprice(constrainedbetween£7 and£9)andtradingoutcomeaftereachround.Thesameparticipantswerethenre-assignedtotradeinhomogeneousgroupsof5withotherparticipants endowedwiththesamelottery.

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a) L lottery: mixed vs. control c) L lottery: homogeneous vs. control

b) H lottery: mixed vs. control d) H lottery: homogeneous vs. control

2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 1 2 3 4 5 6 7 8 Price MIX L MIX L CTRL Price L CTRL 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 1 2 3 4 5 6 7 8 Price L HOM L HOM L CTRL Price L CTRL 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 1 2 3 4 5 6 7 8

Price MIX H MIX

H CTRL Price H CTRL 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 1 2 3 4 5 6 7 8

Price H HOM H HOM

H CTRL Price H CTRL

Fig.2. ResultsoftheFBKmanipulation.EvolutionofNWTAsandpricesinthemixed,homogeneousandcontrolmarkets.Note:Ineachpanel,dashedlines depicttherelevantcontrolmarket,andsolidlineseitherthecorrespondingmixed(panelsaandb)orhomogeneousmarket(panelscandd).Trianglesare meanpricesandsquaresaremeanNWTAs.

discipline,itseemsclearthatmarketdisciplinecouldhavehadverylittleeffectonanygeneraltrendsintheNWTAsreported byHandLtradersinmixedmarkets.Suchtrendscansafelybetreatedasisolatingtheeffectsofshaping.

Byconstruction,theaveragemarketpriceisconstrainedtobebetween

£

7and

£

9,asindicatedbythehorizontallinesin panelsaandbofFig.2.Throughouttheeightroundsthemean(median)pricefellslightlyfrom

£

7.93(

£

7.90)inR1to

£

7.57 (

£

7.50)inR8.AspricesforL,theseﬁguresarequitehigh;aspricesforH,theyareratherlow.Didthispricefeedbackhave anyeffectonNWTAs?Theanswerisaclearyes.

InthetoppanelofTable4andpanelaofFig.2,wecanseethatthemean(median)NWTAfortheLlotteryrosefrom

£

4.64 (

£

4.40)inR1to

£

5.67(

£

6.45)inR8.17_The_strength_of_these_shaping_effects_is_conﬁrmed_by_the_totally_different_pattern

observedincontrolmarkets,inwhichNWTAsdeclinedoverrepetitions.Asexpected,becauseparticipantswererandomly assignedtotheshapingandcontroltreatments,inR1NWTAvaluesinmixedmarketsdonotdiffersigniﬁcantlyfromthose inthecontrolmarkets(two-tailMann–Whitneytest:Z=−1.32,p=0.1871).However,thedifferencebetweenthetwogroups isstronglysigniﬁcantinR8(one-tailMann–Whitneytest:Z=−5.39,p<0.001).

Markedshapingeffects,althoughnotasstrongasforL,alsoshowupforlotteryH.Themean(median)NWTAwas

£

10.91(

£

11.10)intheinitialround,droppingto

£

9.91(

£

10.45)inR8.18_In_the_{corresponding}_control_market,_NWTAs_varied

verylittleoverthecourseoftheeightrounds,startingat

£

11.17(

£

11.45)andendingat

£

10.97(

£

11.20).The between-subjectcomparisonswiththecontrolmarketconﬁrmthattheseshapingeffectsweresizeable.NWTAswerenotsigniﬁcantly

17_In_fact,_a_signiﬁcant_increase_in_NWTAs_is_already_detectable_in_R2_{(Mann–Whitney}_test:_Z₌_−3.11,_p_<_0.001). 18_This_decrease_was_already_signiﬁcant_in_R2_{(Mann–Whitney}_test:_Z₌_2.26,_p_<_0.05).

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Table5

EvolutionofNWTAvaluationsinmixedmarketsforsellersandnon-sellers.

<0 0 >0 Mean <0 0 >0 Mean L=(£2,0.8;£9,0.2) R1 1 – – – – – – – – R2 2 8 13 35 0.49 3 1 0 −2.43 R3 3 10 18 28 0.22 4 0 0 −1.43 R4 4 10 18 30 0.51 2 0 0 −0.10 R5 5 11 17 24 0.11 5 1 2 −1.26 R6 6 11 22 24 0.23 3 0 0 −0.13 R7 7 14 22 18 0.15 4 0 2 −0.83 R8 8 11 22 20 0.11 7 0 0 −1.30 H=(£7,0.2;£14,0.8) R1 1 – – – – – – R2 2 0 1 2 0.20 35 15 7 −0.69 R3 3 0 1 1 0.20 31 13 14 −0.32 R4 4 0 0 1 0.30 23 23 13 −0.03 R5 5 0 0 0 (n/a) 14 30 16 0.12 R6 6 1 0 0 −0.20 17 31 11 −0.18 R7 7 0 0 2 2.35 17 28 13 0.16 R8 8 0 2 1 0.27 19 27 11 −0.21

differentinR1(two-tailMann–Whitneytest:Z=0.87,p=0.3846),butdifferedstronglyaftereightauctionrounds(one-tail

Mann–Whitneytest:Z=2.78,p<0.01).19

Takentogether,theseﬁndingsprovidestrongsupportfortheimplicationsofHypothesis1.Wecansummarisethemas Result1b:

Result1b–Shapingthroughpricefeedback.Intheabsenceofmarketdiscipline,NWTAsarepulledinthedirectionof uninformativepricefeedbackcues.

Ourdataseemtoindicatethatshapingeffectsarestrongerwhenfeedbackisrelativelyhigh(forlotteryL)thanwhenit islow(forlotteryH).Thisformsoursecondobservation.

Observation2–Asymmetryin thestrength ofshaping.Whenshapingisgenerated throughuninformativeprice

feedbackcues,itseffectsarestrongerwhenthefeedbackisrelativelyhighthanwhenitisrelativelylow.

BeforeturningtotheimplicationsofHypothesis2,itisinterestingtoasktowhatextentthisaggregatepicturereﬂects generaltendenciesratherthanbeingdrivenbyasmallnumberofparticularlymalleableindividualvaluations.Table5reports informationontheround-by-roundevolutionofNWTAsinmixedmarketsforLandH,separatelyforparticipantswhosold inthepreviousroundandparticipantswhokepttheirlotteries.Thestructureofthetableisentirelyanalogoustothatof Table3.20

Aswediscussedabove,becauseofourmanipulationofthepricefeedback,thereareveryfewLtraderswhodonotsell andveryfewHtraderswhodo.AmongsttheLsellers,thegreatmajorityrespondsbyincreasingtheirNWTAs,whileH non-sellershaveapreponderantpropensitytodecreasetheirs.21_As_in_Table₃_,_these_effects_slow_down_slightly_over_time.

Thisformsourthirdobservation.

Observation3–Shapingattheindividuallevel.UninformativepricefeedbackcuesaffecttheNWTAsofthemajority ofparticipantsinthedirectionofobservedprices.

WenowturntothehomogeneousmarketsandourtestsoftheimplicationsofHypothesis2.TheevolutionofNWTAs andpricesinthehomogeneousandcontrolmarketsisdisplayedontheright-handsideofFig.2.Inhomogeneousmarkets, theshapingeffectsgeneratedthroughpricefeedbackcuesareexposedtotheeffectofmarketdiscipline.

Theﬁrstimportantaspecthighlightedbytheright-handsideofFig.2isthatforbothlotteriesthereisare-starteffect thatpartlyoffsetstheshapingeffectsgeneratedinmixedmarkets.NWTAsforlotteryLdropfromtheirR8levelinmixed markets,whileNWTAsforHincrease.Thatis,Ltraders(whoexperiencedconsistentlyhighpricesinamixedtradinggroup andrespondedbygraduallyincreasingtheirNWTAs)loweredtheirNWTAsonjoininganewtradinggroup,priortoanyprice feedback;thereisamirror-imageeffectforHtraders.Theseeffectsaresuggestiveofsomeformofunderlyingtruevalues.

19 _As_explained_in_Section₃_,_in_some_sessions_mixed_markets_came_ﬁrst,_while_in_others_they_followed_the_market_involving_lottery_E,_in_which_all_traders

tradedthesamelottery.Itisreasonabletoaskwhethershapingeffectsarestrongerinthelattercase.Wefoundnoordereffectsofthiskind.Forboth lotteriesandinbothR1andR8,thedistributionsofNWTAswhenmixedmarketsprecededthemarketforlotteryEarenotstatisticallydifferentfromthe distributionswhentheyfollowedit.

20 _The_{corresponding}_information_for_control_markets_is_reported_in_the_Appendix,_Table_A.3.4.

21 _For_both_lotteries,_being_a_seller_in_the_previous_round_has_a_signiﬁcant_positive_effect_(at_the_1%_level_for_L_and_10%_level_for_H)_on_NWTA

tina

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Table6

EvolutionofNWTAvaluationsinhomogeneousmarketsforsellersandnon-sellers.

<0 0 >0 Mean <0 0 >0 Mean L=(£2,0.8;£9,0.2) R1 1 – – – – – – – – R2 2 3 8 13 0.40 29 3 4 −0.94 R3 3 8 5 11 0.15 25 5 6 −0.81 R4 4 7 7 7 0.60 20 7 12 0.13 R5 5 3 7 14 0.52 21 7 8 −0.63 R6 6 4 5 13 0.54 20 14 4 −0.43 R7 7 1 11 10 0.26 17 14 7 −0.43 R8 8 5 10 9 0.57 13 14 9 −0.04 H=(£7,0.2;£14,0.8) R1 1 – – – – – – R2 2 0 4 17 0.99 17 10 12 −0.08 R3 3 1 5 17 0.51 16 15 6 −0.39 R4 4 3 9 11 0.18 12 14 11 0.04 R5 5 3 7 13 0.34 16 17 4 −0.20 R6 6 4 7 13 0.17 17 17 2 −0.34 R7 7 2 13 7 0.26 14 20 4 −0.16 R8 8 2 11 9 0.45 11 21 6 −0.13

TotesttheimplicationsofHypothesis2,welookatmarketprices.ForbothLandH,theR1pricesinhomogeneousmarkets

weresignificantlydifferentfromthoseofthecorrespondingcontrolmarkets(one-tailMann–Whitneytests:forL,Z=−4.85, p<0.001;forH,Z=4.61,p<0.001),showingthecontinuingeffectsofthepricefeedbackcuesthattradersreceivedinthe mixedmarkets,despitethere-starteffect.Overtheeightroundsofthehomogeneousmarkets,thepricesforLdecreased, whilethoseforHremainedmoreorlessstationary.Butattheendofthelastauctionround,priceswerestillsignificantly higherthaninthecontrolgroupforL(one-tailMann–Whitneytest:Z=−1.70,p<0.05),andstillsignificantlylowerfor H(one-tailMann–Whitneytest:Z=1.68,p<0.05),indicatingthepersistenceofshapingeffectsonprices.AsforourEXP manipulation,wedonotfindsupportfortheimplicationsofHypothesis2.22_Our_findings_are_summarised_in_Result_2b.

Result2b–Persistenceofshapingthroughpricefeedback.Aftereightauctionrounds,pricesthathavebeenshaped byuninformativepricefeedbackcuesarestillsigniﬁcantlyaffectedbythosecues.

Table6summarisestheevolutionofNWTAsovertheeightauctionroundsofthehomogeneousmarketsfortheLandH lotteries.ItsstructureisanalogoustothatofTables3and5.Soaretheresults.Forbothlotteries,thereisaprevalenttendency forthosewhohavesoldinroundttoincreasetheirNWTAinroundt+1,andanoppositetendencyforthosewhohavenot soldtoreducetheirstatedvaluations,withthenumberofparticipantswhokepttheirNWTAunalteredslowlyincreasing overtheeightauctionrounds.23_This_forms_the_basis_for_our_fourth_observation.

Observation4–NWTAupdatinginhomogeneousmarkets.Inthehomogeneousmarkets,sellerstendtoincreasetheir NWTAandnon-sellerstendtodecreasetheirNWTA.

ThebehaviourofLsellersandHnon-sellersisofparticularinterestbecauseitisconsistentwithshapingbuthardto reconcilewithmarketdiscipline.Rememberthatallparticipantsenteredhomogeneousmarketsafterbeingexposedtothe mixedmarketsshapingmanipulation,whichpulledtheirNWTAsawayfromtheir(unobservable)truevalues.Giventhe magnitudeoftheseshapingeffects,itisreasonabletoinferthat,intheﬁnalroundsofthemixedmarkets,mostLtraders wereover-askingandsellingatveryadvantageousprices,i.e.

v

i<ai<p.However,whenthesetradersweresubsequently

assignedtohomogeneousmarkets,themedianpricerulemeantthat(approximately)three-ﬁfthsofthemwouldnolonger sell.Accordingtomarketdiscipline,thesetraders,forwhomnow

v

i<p<ai,shoulddecreasetheirNWTAs,whichiswhatwe

seeinTable6.ButeventhoseLtraderswhocontinuedtosellwerelikelytobeover-asking.Forthem,

v

i<ai<p,somarket

disciplinewouldnotbiteandtheyshouldnothavechangedtheirbehaviourinanysystematicway.Yet,aswealsoseein Table6,theyactuallyincreasedtheirNWTAsmorethantwiceasoftenastheyreducedthem–apatternthatsuggeststhey werecontinuingtobeinﬂuencedbymarketpricefeedback.

ThebehaviourofHnon-sellersshowsamirrorimageofthispattern.Intheﬁnalroundsofthemixedmarkets,mostH traderswerepresumablyfacingdisadvantageousprices,under-asking,butnotsellingandthereforenotsubjecttomarket

22_Since_in_both_the_homogeneous_and_control_treatments_valuations_and_prices_vary_little_for_the_H_lottery,_we_do_not_need_to_worry_about_price_convergence

inrelationtothatlottery.ForL,wehaveestimatedasymptoticfunctionsofthesameformasforE(seefootnote12).Theresultingestimatesofp*inthe homogeneousmarket(£4.23)andinthecontrolmarket(£3.67)aresigniﬁcantlydifferentfromeachother(p<0.1).SeetheAppendixfordetails.

23_For_both_lotteries,_being_a_seller_in_the_previous_round_has_a_{signiﬁcantly}_positive_effect_(at_the_1%_level)_on_NWTA

tinarandom-effectspanelregression.

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discipline(i.e.p≤ai<vi).Whentheywereassignedtohomogeneousmarkets,(approximately)two-ﬁfthsofthemwouldsell

theirlotteries;marketdisciplinewouldthenleadthesetraderstoraisetheirNWTAs.Butmarketdisciplinewouldnotbite forthosewithp<ai<vi,whowouldcontinuenottosell.Andyet,asweseeinTable6,thesetraderssubsequentlyreduced

theirasksmorethantwiceasoftenastheyincreasedthem,onceagainsuggestingthatthemarketpricecontinuedtohave someshapinginﬂuence.

Observations1,3and4highlightapervasivetendencyforNWTAstomoveinthedirectionofthemarketprice.This tendencyiscompatiblewithanotherregularityinourdata:thatthevarianceofNWTAswithinauctiongroupsdecreases overrepeatedrounds,whileNWTAdifferencesbetweengroupsincreases.24

6. Discussion

Inthissection,wediscusssomeissuesraisedbyourresults.

Theﬁrstissueconcernstheexplanationofshapingeffects.Ourdatashowaninterestingasymmetrywhich,wereittobe replicated,mightthrowsomelightonthemechanism(s)thatliebehindshaping:shapingeffectsseemtobestrongerwhen NWTAsarebeingpulledupbyhighpricesthanwhentheyarebeingpulleddownbylowprices(seeobservation2).

Thisregularityisconsistentwiththetheoryof‘baddealaversion’(Isoni,2011;WeaverandFrederick,2012;forrelated ideas,seeThaler,1985;Putler,1992).Inthistheory,preferencesarereference-dependentinawaythatmakesindividuals’ valuationsofgoodsdependdirectlyonpriceexpectations.Speciﬁcally,individualsderiveutilityfrommaking‘gooddeals’ (buyingatpricesthatarelowerthanexpected,sellingatpricesthatarehigherthanexpected)anddisutilityfrommaking ‘baddeals’(theopposite).Inthecontextofasellingauction,atraderforwhomtheexpectedpriceishigherthantheir reference-independentvaluationofthegoodwillreportanNWTAhigherthanthatvaluationinordertoavoidparticularly baddeals;conversely,atraderforwhomtheexpectedpriceislowerthantheirreference-independentvaluationwillstate anNWTAlowerthanthatvaluationinordertoenjoyparticularlygooddeals.If,otherthingsbeingequal,thepainofbad dealsisstrongerthanthepleasureofgoodones,thetendencyforNWTAstobepulledupbyhighpriceexpectationswillbe strongerthanthetendencyforthemtobepulleddownbylowexpectations.

Analternativeexplanationofthisapparentasymmetryisthefollowing.WhenNWTAsarebeingpulledupbyahigh marketprice,thetraderswhosepreferencesarebeingshapedaretradingat,andbeneﬁtingfrom,thatprice.Thesefeatures ofthepricemaycontributetoitspsychologicalsalienceandmayencouragefurtherover-asking,inthebeliefthatthiscould prolongaparticularlyfavourablestateofaffairs.Conversely,whenNWTAsarebeingpulleddownbyalowprice,thetraders whosepreferencesarebeingshapedarenottradingatthatprice,andthelowlevelofthepriceisasourceofdisbeneﬁtto them.25

Amorefundamentalissueraisedbyourresultsisthatofexplainingwhyshapingeffectsarepartiallybutnotwhollyeroded bymarketdiscipline.Hadwefoundthatshapingeffectswerecompletelyresistanttomarketdiscipline,thatwouldhave beenconsistentwiththehypothesis,advocatedbysomepsychologists,thatpreferencesdonotexistpriortoelicitation,and areconstructedbyindividualsasandwhentheyareneeded(e.g.Payneetal.,1993,1999;Slovic,1995;Stewartetal.,2006). Butthatisnotwhatwefound.

Alternatively,supposewehadfoundthat,whenmarketdisciplinewasswitchedon,marketpricesconvergedtowards valuesthatwereindependentofourshapingmanipulations.Thatwouldhavebeenconsistentwithaninterpretationof Plott’s(1996)discoveredpreferencehypothesisinwhichthediscoverymechanismismarketdiscipline(Loomesetal.,2003). Accordingtothisaccount,psychologicalfactorsmaycauseirrelevantcuestohavesigniﬁcantimpactsonmarketbehaviour, solongasthatbehaviourdoesnotleadindividualstomakelosses;butwhenbehaviourissubjecttomarketdiscipline,true preferencesaregraduallydiscovered.Butagain,thatisnotwhatwefound.

Inbroad-brushterms,whatweseemtohavefoundisthefollowing.Whenourshapingmanipulationsinducelarge changesinNWTAs(asinthemixedmarketforlotteryL),theinitialeffectofintroducingmarketdisciplineisthatNWTAs moveinthedirectionthatoffsetsthisshaping(NWTAsforLdecreaseintheearlyroundsofthehomogeneousmarket). Indeed,adetectablemoveinthisdirectionisinducedmerelybytellingparticipantsthattheyhavejoinedanewtrading group(NWTAsforLarealreadylowerinR1ofthehomogeneousmarketthantheyareinR8ofthemixedmarket).These effectsmightindicatethatparticipantshavesomevaguesensethattheirshaping-inducedNWTAsdonotaltogetherreﬂect theirunderlyingpreferences.However,theeffectsofshapingarenoteliminated.Aftereightauctionroundsinwhichmarket disciplinehasbeenswitchedon,marketpricesstilldonotconvergetovaluesindependentoftheshapingmanipulation.The implicationisthatparticipantsarenotdiscoveringpreciseunderlyingvaluations.

24 _Table_A.3.5_in_the_Appendix_reports_the_within-_and_{between-group}_variances_of_NWTAs_for_all_or_our_treatments_in_R1_and_R8._In_ﬁve_out_of_six_cases,

thewithin-groupvariancefallsbetweenR1andR8.NWTAdistributionsarenotdifferentacrossauctiongroupsinmatchedtreatmentsinR1,asonewould expectgiventhatparticipantshavebeenassignedtotreatmentsatrandom.ButthenullhypothesesthatNWTAsarethesameacrossgroupscanberejected inﬁveoutofsixcasesinR8.AsimilarresultisfoundbyTufano(2009).

25 _This_idea_was_suggested_to_us_by_Ben_McQuillin._Note_that,_while_evidence_suggests_that_participants_in_auctions_may_derive_utility_from_the_fact_that

theyare‘winning’theauction(e.g.Dechenauxetal.,2014),joyofwinningseemsincompatiblewiththeasymmetrythatweﬁnd(aswellasthegeneral trendsinvaluationupdatingshowninTables3,5and6)because,inasellingauctionlikeours,Ltradersshould,ifanything,decreasetheirNWTAsinstead ofincreasingthemastheyclearlydo.