1IntroductionPeople'schoicesoftenlooklikethechoicesmadebythosearoundth - PDF document

1IntroductionPeople'schoicesoftenlooklikethechoicesmadebythosearoundthem:wewearwhatisfashionable,we\havewhatthey'rehaving,"andwetryto\keepupwiththeJoneses."Suchpeereectshavebeenanalyzedacrosseldsineconomics.1Motivatedbyconcernsoverherdingandnancialmarketinstability,anespeciallyactiveareaofresearchhasexaminedtheroleofpeersinnancialdecisions.Beyondstudyingwhetherpeersaectnancialdecisions,dierentchannelsthroughwhichpeereectsworkhavegeneratedtheirownliteratureslinkingpeereectstoinvestmentdecisions,andtonancialmarketinstability.Modelsofherdingandasset-pricebubbles,potentiallybasedonverylittleinformation,focusonlearningfrompeers'choices(BikhchandaniandSharma,2000;ChariandKehoe,2004).Modelsinwhichindividuals'relativeincomeorconsumptionconcernsdrivetheirchoiceofassetholdings,andarticiallydriveupsomeassets'prices,focusonpeers'possessionofanasset.2Inthispaper,weuseahigh-stakeseldexperiment,conductedwithanancialbrokerage,toseparatelyidentifythecausaleectsofthesechannelsthroughwhichaperson'snancialdecisionsareaectedbyhispeers'.Identifyingthecausaleectofone'speers'behavioronone'sownisnotoriouslydicult(see,forexample,Manski,1993).Equallydicultisidentifyingwhyone'sconsumptionorinvestmentchoiceshaveasocialcomponent.Broadly,therearetworeasonswhyapeer'sactofpurchasinganasset(orproduct,moregenerally)wouldaectone'sownchoice.First,onemayinferthatassets(orproducts)purchasedbyothersareofhigherquality;werefertothisassociallearning.Second,one'sutilityfrompossessinganasset(orproduct)maydependdirectlyonthepossessionofthatasset(orproduct)byanotherindividual;wecallthissocialutility.Supposeaninvestoriconsiderspurchasinganancialassetunderuncertainty.Incanonicalmodelsofherdingbasedonsociallearning,informationthatapeer,investorj,purchasedtheassetwillprovidefavorableinformationabouttheassettoinvestori:investorj(actinginisolation)wouldonlyhavepurchasedtheassetifheobservedarelativelygoodsignaloftheasset'sreturn.Thefavorableinformationconveyedbyinvestorj'srevealedpreferenceincreasestheprobabilitythatinvestoripurchasestheasset,relativetomakingapurchasedecisioninisolation.3Adirecteectofinvestorj'spossessionofanancialassetoninvestori'sutilitymightarisefor 1SeminaltheoreticalarticlesincludeBanerjee(1992)andBikhchandanietal.(1992).EarlyempiricalresearchincludesCaseandKatz(1991),Katzetal.(2001),Sacerdote(2001),andZimmerman(2003).Durlauf(2004)surveystheliteratureonneighborhoodeects.Peereectshavealsobeenstudiedbypsychologistsandsociologists:in uentialsocialpsychologyresearchincludesAsch(1951)andFestinger(1954);areviewofempiricalresearchonpeereectsinsociologyispresentedinJencksandMayer(1990).2Preferencesoverrelativeconsumptioncanarisefromthe(exogenous)presenceofotherindividuals'consumptiondecisionsinone'sutilityfunction,(e.g.Abel,1990,Gali,1994,CampbellandCochrane,1999)orcanariseendoge-nouslywhenoneconsumesscarceconsumptiongoods,thepricesofwhichdependontheincomes(andconsumptionandinvestmentdecisions)ofotherindividuals(DeMarzoetal.,2004,DeMarzoetal.,2008).Foranoverview,seeHirshleiferandTeoh(2003).3AveryandZemsky(1998)presentamodelinwhichpricesadjustinresponsetoherdingbehavior;however,inoursettingthereisnoassetpriceadjustment(seealsoChariandKehoe,2004).1 assignedinvestor2toreceiveeithernoinformationaboutinvestor1'sinvestmentdecision,ortoreceiveinformationaboutboththeinvestmentdecisionandtheoutcomeofthelotterydeterminingpossession.Thus,amonginvestor1'swhochosetopurchasetheasset,theassociatedinvestor2'swererandomlyassignedtooneofthreeconditions:inconditionA,noinformationaboutinvestor1'sdecisionwasprovided;inconditionB,investor2'sreceivedinformationthatinvestor1madeadecisiontopurchasetheasset,butwasnotabletoconsummatethepurchase(solearningoccurredwithoutpossession);and,inconditionC,investor2'sreceivedinformationthatinvestor1madeadecisiontopurchasetheasset,andwasabletoconsummatethepurchase(solearningoccurred,alongwithpossession).Acomparisonofchoicesmadebyinvestor2'sinconditionsAandBrevealstheeectofsociallearning;acomparisonofconditionsBandCrevealstheimpactofinvestor1'spossessionoftheassetoverandabovetheinformationconveyedbyhispurchase,thatis,socialutility;acomparisonofconditionsAandCrevealsthetotaleectofthesetwochannels.Ourexperimentalevidencesuggeststhatbothchannelsthroughwhichpeereectsworkareeconomicallyandstatisticallysignicant.Amonginvestor2'swhosepeerchosetopurchasetheassetwendthefollowing:inthe\noinformation"conditionA,42%chosetopurchasetheasset;inthe\sociallearningonly"conditionB,thetake-uprateincreasedto71%;nally,inthe\sociallearningplussocialutility"conditionC,therateincreasedto93%.Notonlydoindividualslearnfromtheirpeers,butthereisalsoaneectofpossessionbeyondlearning.Tobetterunderstandinvestors'decisionmakinginthedierentconditions,andtohelpusevaluatealternativeinterpretationsofthetreatmenteectsweobserve,wepartneredwiththebrokeragetoconductafollow-upsurveyoftheinvestorsinthestudy(seeSection2.4fordetails).Werstanalyzethesociallearningchannel,presentingevidenceofpositivebeliefupdatingamonginvestor2'swholearnedabouttheirpeers'purchasedecisions,andofheterogeneoussociallearningeectsconsistentwithamodelinwhichunsophisticatedinvestorslearnmorefromothers'purchases,andsophisticatedinvestors'purchasesaremorein uential.WealsondevidencesuggestiveofsocialutilityconcernsamonginvestorswhochosetopurchasetheassetinconditionC.Theevidencefromthefollow-upsurveyadditionallyhelpsusruleoutseveralalternativeinterpretationsofthetreatmenteectsweobserve,aswellasconfoundingfactors(wediscussalternativehypothesesandlimitationsofourstudyfurtherinSection3).Ourworkcontributesmostdirectlytotheempiricalliteratureonpeereectsininvestmentdecisions,someobservational(e.g.,Hongetal.,2004,Hongetal.,2005,IvkovicandWeisbenner,2007,Brownetal.,2008,Li,2009,andBanerjeeetal.,2011),someexperimental(e.g.,Du oandSaez,2003,Beshearsetal.,2011).Ourpapergoesbeyondtheexistingliteraturebyusingexperimentalvariationtoseparatelyidentifythecausalrolesofdierentchannelsofpeereects.Disentanglingthesechannelsisofmorethanacademicinterest:itcanprovideimportant,policy-relevantevidenceonthesourcesofherdingbehaviorinnancialmarkets.Ourndingsofsignicantsociallearningandsocialutilityeectssuggestthatgreaterinformationprovisionmightmitigate3 2.1DesigningtheAssetTheassetbeingoeredneededtosatisfyseveralrequirements.Mostfundamentally,thereneededtobeapossibilityoflearningfromone'speers'decisions.Inaddition,becausemanyofourcomparisonsofinterestareamonginvestor2'swhoseassociatedinvestor1'schosetopurchasetheasset,theassetneededtobesucientlydesirablethatenoughinvestor1'swouldchoosetopurchaseit.Tosatisfytheserequirements,thebrokeragecreatedanew,riskyassetspecicallyforthisstudy.Theassetisacombinationofanactively-managed,open-endedlong/shortmutualfundandarealestatenote(LetradeCreditoImobiliario,orLCI)foratermofoneyear.Thelong/shortfundseekstooutperformtheinterbankdepositrate(CDI,CerticadodeDepositoInterbancario)byallocatinginvestmentfundstoxed-incomeassets,equitysecurities,andderivatives.TheLCIisalow-riskassetthatisattractivetopersonalinvestorsbecauseitisexemptfrompersonalincometax;itcanbethoughtofasanappealing,high-yieldCD.TheLCIoeredinthisparticularcombinationhadsomewhatbettertermsthantherealestatenotesthatwereusuallyoeredtoclientsofthebrokerage,thusgeneratingsucientdemandtomeettheexperiment'sneeds.First,thereturnoftheLCIoeredintheexperimentwas98%oftheCDI,whilethebestLCIoeredtoclientsoutsideoftheexperimenthadareturnof97%oftheCDI.Inaddition,thebrokeragermusuallyrequiredaminimuminvestmentofR$10,000toinvestinanLCI,whiletheoerintheexperimentreducedtheminimuminvestmentthresholdtoR$1,000(thelong/shortfundalsorequiredaminimuminvestmentofR$1,000).Thebrokeragepilotedthesaleoftheasset(withoutusingalotterytodeterminepossession),toclientsotherthanthoseinthecurrentstudy,inordertoensureapurchaserateofaround50%.Anotherrequirementwasthattherebenosecondarymarketfortheasset,forseveralreasons.First,wehopedtoidentifytheimpactoflearningfrompeers'decisionstopurchasetheasset,ratherthanlearningfrompeersbasedontheirexperiencepossessingtheasset.Investor2mayhavechosennottopurchasetheassetimmediately,inordertotalkwithinvestor1,thenpurchasetheassetfromanotherinvestor.Wewishedtoruleoutthispossibility.Inaddition,wedidnotwantpeerpairstojointlymakedecisionsaboutsellingtheasset.Finally,wedidnotwantinvestor2topurchasetheassetinhopesofsellingittoinvestor1wheninvestor1'sinvestmentchoicewasnotimplementedbythelottery.Inresponsetotheseconcerns,thebrokerageoeredtheassetonlyatthetimeoftheirinitialphonecalltotheclientandstructuredtheassetashavingaxedtermwithnoresale.Analrequirement,givenourdesiretodecouplethepurchasedecisionfrompossession,wasthattheremustbelimitedentryintothefundtojustifythelotterytoimplementpurchasedecisions.Thebrokeragewaswillingtoimplementthelotterydesignrequired,justiedbythesupplyconstraintfortheassettheycreated.Attheindividuallevel,themaximuminvestmentintheLCIcomponentwassetatR$10,000.5 investmentswiththebrokerage,andthusallocatednewresourcesinordertopurchasetheasset).Then,acomputerwouldgeneratearandomnumberfrom1to100(duringthephonecall),andifthenumberwasgreaterthan50,theinvestmentwouldbeauthorized.12Followingthecalltoinvestor1,thesamebrokercalledtheassociatedinvestor2.Thebrokersweretoldthat,foreachpair,bothinvestorshadtobecontactedonthesamedaytoavoidanycommunicationabouttheassetthatmightcontaminatetheexperimentaldesign.Only6outof150investor2'shadcommunicatedwiththeirassociatedinvestor1'sabouttheassetpriortothephonecallfromthebrokerage(droppingthese6observationsdoesnotaectanyofourresults).Ifthebrokerdidnotsucceedinreachinginvestor2onthesamedayastheassociatedinvestor1,thebrokerwouldnotattempttocontacthimagain;thisoutcomeoccurredfor12investor1's,whoarenotincludedinourempiricalanalysis.Thus,brokerscalled162investor1'sinordertoattainoursamplesizeof150pairssuccessfullyreached.Whenthebrokerreachedinvestor2,hebeganthescriptjustashedidforinvestor1:describingtheasset,includingthelotterytodeterminewhetherapurchasedecisionwouldbeimplemented.Next,duringthecall,thebrokerimplementedtheexperimentalrandomizationandattemptedtoselltheassetundertheexperimentally-prescribedconditions(describednext).Ifinvestor2chosetopurchasetheasset,arandomnumberwasgeneratedtodeterminewhetherthepurchasedecisionwouldbeimplemented,justaswasthecaseforinvestor1.2.3RandomizationintoExperimentalConditionsTheexperimentalconditionsweredeterminedasfollows.Amongthegroupofinvestor1'swhochosetopurchasetheasset,theirassociatedinvestor2'swererandomlyassignedtoreceiveinformationaboutinvestor1'schoiceandthelotteryoutcome,ortoreceivenoinformation.Therewasthusa\doublerandomization"{rst,thelotterydeterminingwhetherinvestor1wasabletomaketheinvestment,andsecond,therandomizationdeterminingwhetherinvestor2wouldbeinformedaboutinvestor1'sinvestmentchoiceandtheoutcomeoftherstlottery.Thisprocessassignsinvestor2'swhoseassociatedinvestor1'schosetopurchasetheassetintooneofthreeconditions(refertoFigure1);investorcharacteristicsacrossthethreeexperimentalconditionscanbeseeninTable1(wegenerallypresentmeansofthevariousinvestorcharacteristics,withtheexceptionoftheearningsvariable,themedianofwhichisshowninordertomitigatethein uenceofoutliers).One-thirdwereassignedtothe\noinformation,"control,conditionA.Halfofthesecomefromthepoolofinvestor2'spairedwithinvestor1'swhowantedtheassetbutwerenotauthorizedtomaketheinvestment,andhalffromthosepairedwithinvestor1'swhowanted 12Amonginvestor1'swhowantedtopurchasetheasset,acomparisonofthecharacteristicsofinvestor1'swhosepurchasedecisionwasauthorizedandinvestor1'swhosepurchasedecisionwasnotauthorizedcanbeseeninAppendixTableA.2.Therandomizationresultedinareasonabledegreeofbalanceacrossgroups:5of6testsofequalityofmeancharacteristicsacrossgroupshavep-valuesabove0.10.Onecharacteristic,gender,issignicantlydierentacrossgroups.7 2.4Follow-upSurveyBetweenNovember26,andDecember7,2012,thebrokerageconductedafollow-upsurveywithasubsetoftheclientsfromthemainstudy;investorsweretold(truthfully)thatthebrokeragewishedtolearnaboutitsclientsinordertoprovidethemwithmoreindividualizedservicesandinformation.Thefollow-upsurveywasconductedwithtwoprimarygoalsforthepurposesofourwork:rst,tomeasureinvestors'nancialsophistication;andsecond,tocollectinformationthatcouldbeusedtobetterunderstandthedecisionmakingprocessesbehindthechoicesofinvestor2's(fortheEnglishlanguagesurveyquestionnaires,seeAppendixC).Inouranalysisbelow,weexamineheterogeneityinsociallearningeectsamonginvestor2'sinconditionsAandB,dependingonwhetherinvestor2,ortheassociatedinvestor1,isnanciallysophisticated.Tomeasuretherelevantsetofinvestors'nancialsophistication,thebrokeragecontactedtheinvestor2'sinconditionsAandB,aswellastheirassociatedinvestor1's,andaskedthemtoassesstheirownnancialknowledge;inaddition,thebrokerageaskedtheseinvestorsaseriesofobjectivequestionsmeasuringnancialliteracy.14Forsummarystatisticsonthenancialsophisticationsurveyquestions,seeAppendixTableA.3,PanelA.Wealsocollectedsurveyevidencethatcanhelpusunderstandthedecisionmakingofinvestor2'sacrossexperimentalconditionsA,B,andC.Inparticular,weaskedaboutseveralaspectsofinvestors'decisions:(i)howinvestorsviewedthelotterythatdeterminedwhetherpurchasedecisionswereimplemented(surveyinginvestorsinconditionsA,B,andC);(ii)howinvestorsrespondedtoinformationabouttheirpeer'spurchasedecisionandlotteryresult,aswellaswhethertheinformationprovidedbybrokerswascredible(surveyinginvestorsinconditionsBandC);(iii)whetherinvestors'decisionswerespecicallyaectedbytheirpeer'slostlottery(conditionB);and,(iv)whethersocialutilityconsiderationsaectedinvestors'decisionstopurchasetheasset(investorsinconditionCwhochosetopurchasetheasset).Forsummarystatisticsonthedecisionmakingsurveyquestions,seeAppendixTableA.3,PanelB.Itisimportanttohighlighttwoweaknessesofthefollow-upsurvey.First,investorsmayhaverespondedinwaysthattheythoughtwouldpleasethesurveyor.Itisimportanttonote,however,thatthevastmajority(over90%)ofsurveycallswerenotmadebytheinvestor'susualbroker,butbyanotherbrokerattherm,withwhominvestorsdidnothaveapersonalrelationship.Thismitigatesconcernsaboutsurveyordemandeects(resultsareverysimilarexcludingsurveysinwhichthesurveywasconductedbythebrokerwhomadetheexperimentalsalescall,seeAppendixTableA.4).Inaddition,manyofthequestionsasked,suchasthoseregardingnancialsophisti-cationortheupdatingofbeliefs,didnothaveananswerthatwouldbeviewedmorefavorablyby 14ThespecicquestionscomefromtheNationalFinancialCapabilitySurvey(translatedintoPortuguese),andhavebeenusedinstudiesbothintheUSandinothercountries(LusardiandMitchell,2011a,b).Investor2'sotherthanthoseinconditionsAandB,andinvestor1'sotherthanthoseassociatedwithinvestor2'sinconditionsAandB,werenotaskedthesenancialsophisticationquestionstoreducethebrokerage'stimecommitmenttothefollow-upsurvey.9 \sociallearningplussocialutility"conditionC,thetake-upratewas93%,signicantlylargerthanthetake-uprateinbothconditionsAandB.15Thesedierencesrepresenteconomicallyandstatisticallysignicantoverallpeereectsandindicatethatsociallearningwithoutpossessionaectstheinvestmentdecision,asdoespossessionbeyondsociallearning.Finally,thecoecientontheindicatorforconditionAnegiseconomicallysmall,anditisnotstatisticallysignicant,suggestingthat\selection"eectsaresmallinoursetting.AnaturalquestionaboutTable2iswhetherourstatisticalinferencesaresound,giventherela-tivelysmallnumberofobservationsineachexperimentalcondition.Asanalternativetostandardt-teststodeterminestatisticalsignicance,weranpermutationtestswith10,000repetitionsforpairwisecomparisonsoftake-upratesacrossconditionsA,B,C,andAneg.Torunthepermutationtests,werandomlyassign\placebotreatment"statustoinvestorsintheconditionsofinterest,10,000times,andcalculateadistributionof\placebotreatmenteects."Wethencomparethesizeofthetreatmenteectswendusingtheactualtreatmentassignmenttothedistributionof\placebotreatmenteects."Whilethepermutationtestisnotanexacttest,itcancomplementourinferencesusingt-tests.Forourmaincomparisons,wendp-valuesthataretriviallylargerusingpermutationteststhanusingt-tests,butourinferencesareunchanged,suggestingthatinferencesusingt-testsarevalid(seeAppendixTableA.8,PanelA,column1).Wenextpresentregressionresultsincludingbrokerxedeects(Table2,column2)andin-cludingbothbrokerxedeectsandbaselinecovariates(column3);then,weestimatearegressionincludingthesecontrolsandusingthecombinedsampleofinvestor1'sandinvestor2'sinordertohavemoreprecision(column4).Theoverallpeereect,aswellastheindividualsociallearn-ingandsocialutilitychannels,estimatedusingthesealternativemodelsareverysimilaracrossspecications(consistentwithsuccessfulrandomizationacrossconditions).16Wenowdelvemoredeeplyintoourdata,andanalyzeinvestors'responsestothefollow-upsurvey,inordertobetterunderstandthetreatmenteectsweobserve.Werstpresentadditionalevidenceoneachofthetwochannelsofsocialin uencewestudy.Then,wediscusspotentialconcernswithourexperimentaldesignandtheinterpretationofourresults. 15Thep-valuefromatestofequalitybetweentake-upratesinconditionsAandC{theoverallpeereect{is0.000.Thep-valuefromatestthatconditionBequalsconditionA{sociallearningalone{is0.043.Thep-valuefromatestthatconditionCequalsconditionB{possession'seectabovesociallearning{is0.044.Notethatonemightwishtocomparetake-upratesinconditionsBandCtoabroader\noinformation"controlgroupthanconditionA.Weusedataoninvestors1'stoestimatethetake-uprateofpositively-selectedindividualsusingGMM,imposingtheoveridentifyingrestrictionthatinvestor1'stake-uprateisaweightedaverageofinvestor2'sinconditionsAandAneg.Whilesociallearningeectsaresmaller,ourresultsarequalitativelyunchanged(seeAppendixTableA.7).WepreferusingindividualsinconditionAasthecontrolgroupasitismostinternallyvalid:investor1'scallscameearlierinthedaythancallstoinvestor2's,anddidnotincludetheinformationrandomizationthatwaspartofthecallsmadetothelatter(atestoftheoveridentifyingrestrictionintheGMMmodelalsonearlyrejectsthenull).16Examiningalternativeoutcomes{theamountinvestorschosetoinvestintheasset,oradummyvariablein-dicatingwhethertheinvestmentamountwasgreaterthantheminimumrequired{yieldsverysimilarresults(seeAppendixFigureA.2andTableA.9;forp-valuescalculatedusingpermutationtests,seeTableA.8,PanelA,columns2{3).11 2'sinconditionsAandB),withthetake-uprateastheoutcomevariable,fordierentcategoriesofinvestor2's.InTable3,PanelA,wepresentsociallearningtreatmenteectsestimatedfromregressionswithoutcontrols(i.e.,comparisonsofmeans).Incolumns1{2,weestimateseparatesociallearningeectsfornanciallysophisticatedandnanciallyunsophisticatedinvestor2's,re-spectively.Weregresstheinvestmentdecisiondummyvariableona\nanciallysophisticated"indicator;aninteractionbetweenaconditionBindicatorandthenanciallysophisticatedindi-cator;and,aninteractionbetweenaconditionBindicatoranda\nanciallyunsophisticated"indicator.Incolumns4{5,weestimateseparatesociallearningeectsforinvestor2'sassociatedwithnanciallysophisticatedandnanciallyunsophisticatedinvestor1's,respectively.Weesti-materegressionsanalogoustocolumns1{2,butsubstituteindicatorsoftheassociatedinvestor1'snancialsophisticationfortheindicatorsofinvestor2'snancialsophistication.PanelBpresentsestimatedsociallearningeectsfrommodelsthatincludebaselinecontrolsandbrokerxedeects.TheresultsinTable3matchourpredictions.First,incolumns1{2,weobservesmall,sta-tisticallyinsignicantsociallearningeectsonnanciallysophisticatedinvestor2's,andlarge,signicanteectsonunsophisticatedinvestor2's.17Column3showsthatthedierencebetweenthetreatmenteectsforsophisticatedandunsophisticatedinvestor2'sisalsostatisticallysignif-icant.Next,incolumns4{5,wendlarge,statisticallysignicantsociallearningeectsamonginvestor2'sassociatedwithnanciallysophisticatedinvestor1's,andsmall,insignicanteectsamonginvestor2'sassociatedwithnanciallyunsophisticatedinvestor1's(take-upratesacrosssub-groupsarepresentedinAppendixFiguresA.3.1andA.3.2).Wendresultsthatareverysimilarusingtheobjectivemeasureofnancialknowledge(seeAppendixTableA.10)orusingalternativeoutcomes(amountinvestedoranindicatorofaninvestmentlargerthantheminimum;seeAppendixTablesA.11andA.12).Toaddressconcernsaboutstatisticalinferencesgiventhesmallcellsizes,weranpermutationtestswith10,000repetitionsforeachsubgroup'ssociallearningeect,andourinferencesareunaected(p-valuespresentedinAppendixTableA.8,PanelB).Evidenceofupdatedbeliefs.Webelievethatinvestor2'shighertake-uprateinconditionB,andacomponentoftheirhighertake-uprateinconditionC,resultedfrompositivelyupdatingtheirbeliefsabouttheassetafterhearingthattheirassociatedinvestor1chosetopurchaseit.Whilebrokersdidnotelicitpriororposteriorbeliefsduringtheinitialsalescall,inthefollow-upsurvey,investorsinconditionsBandCweredirectlyaskedwhetherthefactthattheirassociatedinvestor1wantedtopurchasetheassetaectedtheirbeliefsaboutthequalityoftheasset.Wendthat67%ofinvestor2'sinconditionsBandCreportedpositivelyupdatingtheirbeliefsaboutthequalityoftheassetafterlearningthattheirpeerchosetopurchaseit,consistentwithasocial 17Unsophisticatedinvestor2'shavealowertake-uprateinconditionAthandosophisticatedinvestor2's.Thismaybearesultofsamplingvariation(thedierenceintake-upratesisnotstatisticallysignicant)oraresultofdierentpriorbeliefsabouttheassetintheabsenceofanypeereect.Itisimportanttonotethateveniftake-upratesinconditionAwereswitchedacrossgroups,wewouldcontinuetondsignicantsociallearningeectsamongunsophisticatedinvestor2'sandnosignicantsociallearningeectsamongsophisticatedinvestor2's.13 3.5AlternativeHypothesesandConfoundingFactorsInanidealexperiment,conditionBwouldhavedieredfromconditionAonlybecauseofsociallearning;and,conditionCwouldhavedieredfromconditionBonlyintheaddedeectofsocialutility.Inpractice,theremayhavebeenotherdierencesacrossconditions;herewediscusswhethertheywerelikelytohaveplayedanimportantroleingeneratingthetreatmenteectswend.Eectsofthelotterytoauthorizeinvestments.Onemightwonderifthepresenceofthelotterydistorteddecisionsbymakingtheassetappeartobescarceanddesirable.Wedonotbelievethiswasthecase.First,theassetusedinthestudycouldnotbere-soldonthemarketfollowingpurchase,sothelotterydidnotsendasignalaboutexternaldemand.Second,wecancomparethetake-upratesinourexperimenttothoseinapriorpilotstudywithoutalotterytoauthorizeinvestments:thepurchaserateinthepilotstudywas48%{verysimilartowhatweobserveamonginvestorsinourstudyreceivingnoinformationabouttheirpeers.Evidencefromthefollow-upsurveyisalsoinformative:weaskedinvestor2'sinconditionsA,B,andCwhetherthepresenceofthelotterywasasignicantfactorintheirpurchasedecision.Only4.3%ofrespondentsreportedthatitwas(andourresultsarerobusttodroppingthemfromouranalysis).Finally,wendsuggestiveevidenceinthefollow-upsurveythatinvestor2'sinconditionBdidnotupdatetheirviewsabouttheasset'squality(orabouttheirlikelihoodofwinningthelottery)afterlearningabouttheirpeer'sunsuccessfullotteryoutcome.Moregenerally,becauseallconditionsincludedthelottery,itisunlikelythata\leveleect"ofthelotterycouldgeneratethepeereectsweobserve.However,animportantquestioniswhetherthelotteryinteractedwiththeinformationprovidedinconditionBorC.Forexample,investor2'smightfeelguiltpossessinganassetthattheirpeerwaspreventedfromacquiring;or,theymightespeciallydesireanassettheirpeerexplicitlycouldnotacquire{adesireto\getaheadoftheJoneses."However,wearereassuredbyourndingsofheterogeneoustreatmenteects(inTable3):itisdiculttotellastoryinwhichthedesiretogetaheadofone'speerisconcentratedamongthenanciallyunsophisticated,andamonginvestor2'swhoseassociatedinvestor1isnanciallysophisticated.Anotherconcernisthatlearningthatinvestor1possessedtheassetmighthaveenhancedtherevealedpreferencesignalinconditionC,relativetoconditionB.Investor2'sinconditionBmighthavebelievedthattheirassociatedinvestor1'sdidnotreallychoosetopurchasetheasset.However,inthefollow-upsurvey,weaskedinvestor2'sinconditionsBandCiftheybelievedtheinformationprovidedbythebroker,and97%replied\yes."Arelatedpossibilityisthatinvestor2'sinconditionsBandCviewedthelotteryoutcomeasasignalofwhetherinvestor1'schosetofollowthroughwiththeirpurchasedecision.Inthefollow-upsurvey,weaskedinvestor2'sinconditionsA,B,andCiftheythoughttheycouldhavechangedtheirchoiceaftertherealizationofthelottery;94%ofthemanswered\no."Thus,itisunlikelythatinvestor2'sviewedthepurchasedecisionasnon-binding.Ourresultsarerobusttodroppinginvestorsrespondingtoeitherofthesequestions15 2'sinconditionBorCmighthavemadetheirinvestmentdecisionsthinkingaboutthepossibilityoftheirchoicesbeingdiscoveredbytheirpeers.However,allbutveinvestorswereknowntohavelinkswithonlyoneotherclient(theirassociatedinvestor1).Thus,oncetheoerwasmadetoinvestor1,investor2typicallyhadnootherpeerwhomightreceivetheoer(ourresultsarerobusttodroppingthe5investor2'swhowerepartoflargernetworksofclients,availableuponrequest).Inthefollow-upsurvey,weaskedinvestor2'sinconditionsBandCiftheywereconcernedthattheirpurchasedecisionwouldberevealedtootherclients.Only11%oftherespondentsreplied\yes,"andourresultsarerobusttodroppingtheseinvestors(resultsavailableuponrequest).Ifinvestor2'swereconcernedabouttheirassociatedinvestor1'saskingabouttheasset,thelotterytoimplementapurchasedecisionprovidedinvestor2'swithcoverforanon-conformingchoice.Anotherconcernisthatbrokerscouldexertdierentialeorttowardsellingtheassetunderdierentexperimentalconditions.Fortunately,webelievethattheimpactofthesupplysideonourmeasuredtreatmenteectswaslikelylimited.First,becausebrokerswerecompensatedbasedontheassetstheysold,theywereincentivizedtoselltheassetinallconditions,ratherthantoconrmanyparticularhypothesis.Second,ifbrokereortdidvaryacrossconditions,onemighthaveexpectedbrokerstolearnhowtousetheinformationinthevariousconditionsmoreeectivelyastheymademoresalescalls.However,wendthattreatmenteectsdonotsignicantlyvarywithbrokerexperience(seecolumn2ofAppendixTableA.13).Finally,hearingapeermentionedmightincreasetheattentionpaidtothebroker'ssalespitch.However,brokersprovidedtheinformationabouttheasset(inadouble-blindmanner)priortomentioninginvestor1'schoice.Inaddition,ourndingsofheterogeneoustreatmenteectsaresuggestiveofactuallearning:one'searsarelikelytoperkupwhenhearinganypeer'sname;but,oneismorelikelytolearnfromthechoiceofasophisticatedfriend,justaswend.3.6ExternalValidityAnalimportantconcernwithourdesignregardstheexternalvalidityofthendings.Thereareseveralimportantqualicationstothegeneralityofthetreatmenteectsweestimate.First,thetypeofsociallearningonwhichwefocusisthatofclassicmodels,suchasBanerjee(1992)andBikhchandanietal.(1992):learningthatoccursuponobservationoftherevealedpreferencedecisiontopurchasemadebyapeer.Weabstractawayfromtheadditionalinformationonemightacquireafterapeer'spurchase(e.g.,bytalkingtothepeerandlearningaboutthequalityofaproduct,asinKaustiaandKnupfer,2012)andfromanychangeinbehaviorduetoincreasedsalienceofaproductwhenconsumedbyone'speers.Thesechannelsareshutdowninourstudybecauseofthedesignofthenancialasset,butarelikelyimportantaswell.Second,ourtreatmenteectsareestimatedfromthebehaviorofaparticularsampleofinvestors.Thepeerswestudyareveryclose{oftenfriendsorfamily{incontrasttootherworkinthisarea,whichfocusesonco-workers,andndssmallerpeereectsoninvestmentdecisions(e.g.,Du oand17 amongunsophisticatedinvestors.Thismay,insomeinstances,increasewelfare,asuninformedinvestorscanbenetfromtheknowledgeofsophisticatedpeers.Ontheotherhand,inecientherdsandexcessiveassetpricevolatilitymayoccurwhenindividualsignoretheirprivateinformation,orlackinformationaboutthenancialmarketsinwhichtheyareparticipating(Banerjee,1992;Bikhchandanietal.,1992;AveryandZemsky,1998;ChariandKehoe,2004).Inthiscase,onemightwishtoeducateunsophisticatedindividualsorprovidemoreinformationaboutassets'qualitytoincreaseinvestors'relianceontheirprivateinformationandreduceherding.Importantly,ourndingofsignicantsocialutilityeectssuggeststhatinformationprovisionwillnotreduceherdingasmuchasonewouldexpectfromamodelthatincludesonlysociallearningeects:evenifindividualsarenanciallysophisticated,andhaveverypreciseprivatesignalsofassetquality,theymaychoosetofollowtheirpeersforsocialutilityreasons.Ourworkshouldbeextendedinseveraldirections.Mostfundamentally,itisimportanttodeterminetheirexternalvalidity.Onemightbeinterestedinwhetherourndingsextendtoassetswithdierentexpectedreturnsordierentexposurestorisk;or,toinvestmentdecisionsmadefromalargerchoiceset.Onemightalsowishtostudywhetherinformationtransmitteddirectlyamongpeershasadierenteectfrominformationtransmittedthroughbrokers.Theselectionofinformationtransmittedbybrokersandbypeersisendogenous,andstudyingtheprocessdetermin-ingwhichinformationgetstransmitted,andtowhom,isofgreatinterest.Studyinginformationtransmissionthroughalargernetworkofindividualsisimportantaswell.Inadditiontothecontextofnancialdecisionmaking,ourexperimentaldesigncouldbeusedinothersettingstoidentifythechannelsthroughwhichpeereectswork.Inmarketing,varioussocialmediarelyondierentpeereectchannels:Facebook\likes",Grouponsales,andproductgive-awaysallrelyonsomecombinationofthechannelsstudiedhere.Futureworkcancomparetheeectivenessofthesestrategies,andtheirimpactthroughdierentchannels,usingdesignssimilartoours.Onecouldalsoapplyourexperimentaldesigntothestudyoftechnologyadoption:onemightwishtodistinguishbetweenlearningfromapeer'spurchasedecisionandthedesiretoadopttechnologiesusedbyothers.Finally,health-promotingbehavioroftenisaectedbothbylearningfrompeers'purchasesandbypeers'actualuseofhealthcaretechnology(e.g.,vaccinationorsmokingcessation).20Inthesesettingsandothers,separatelyidentifyingtherolesofsociallearningandsocialutilitymightbeofinteresttopolicymakers. 20FosterandRosenzweig(1995),ConleyandUdry(2010)andDupas(forthcoming)identifytheimportantroleplayedbysociallearningintechnologyadoption;KremerandMiguel(2007)studythetransmissionofknowledgeaboutde-wormingmedicationthroughsocialnetworks;and,Sorensen(2006)studiessociallearninginemployees'choicesofhealthplans.Socialutilitymightexistinthesesettingsbecauseusingatechnology(oradoptingabehavior)mightbeeasierorlessexpensivewhenothersnearbyuse(oradopt)it,orbecauseonewishesnottofallbehindthoselivingnearby.19 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Dupas,Pascaline,\Short-RunSubsidiesandLong-RunAdoptionofNewHealthProducts:Evi-dencefromaFieldExperiment,"Econometrica,forthcoming.Durlauf,StevenN.,\NeighborhoodEects,"HandbookofRegionalandUrbanEconomics,2004,4.Festinger,Leon,\ATheoryofSocialComparisonProcesses,"Journal:HumanRelations,1954,7,117{140.Fliessbach,Klaus,BerndWeber,PeterTrautner,ThomasJ.Dohmen,UweSunde,ChristianE.Elger,andArminFalk,\SocialComparisonAectsReward-RelatedBrainActivityintheHumanVentralStriatum,"Science,2007,318(5854),1305{1308.Foster,AndrewD.andMarkR.Rosenzweig,\LearningbyDoingandLearningfromOthers:HumanCapitalandTechnicalChangeinAgriculture,"JournalofPoliticalEconomy,December1995,103(6),1176{1209.Frey,BrunoS.andStephenMeier,\SocialComparisonsandPro-socialBehavior:Testing"ConditionalCooperation"inaFieldExperiment,"AmericanEconomicReview,December2004,94(5),1717{1722.Gali,Jordi,\KeepingUpwiththeJoneses:ConsumptionExternalities,PortfolioChoice,andAssetPrices,"JournalofMoney,CreditandBanking,1994,26(1),1{8.Grinblatt,Mark,MattiKeloharju,andSeppoIkaheimo,\SocialIn 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Manski,CharlesF.,\IdenticationofEndogenousSocialEects:TheRe ectionProblem,"ReviewofEconomicStudies,1993,60(3),531{542.Mas,AlexandreandEnricoMoretti,\PeersatWork,"AmericanEconomicReview,2009,99(1),112{145.Moretti,Enrico,\SocialLearningandPeerEectsinConsumption:EvidencefromMovieSales,"ReviewofEconomicStudies,2011,78(1),356{393.Sacerdote,Bruce,\PeerEectswithRandomAssignment:ResultsforDartmouthRoommates,"QuarterlyJournalofEconomics,May2001,116(2),681{704.Shue,Kelly,\ExecutiveNetworksandFirmPolicies:EvidencefromtheRandomAssignmentofMBAPeers,"April2012.UniversityofChicago,BoothSchoolofBusiness.Sorensen,AlanT.,\SocialLearningandHealthPlanChoice,"RANDJournalofEconomics,Winter2006,37(4),929{945.Taylor,Chris,\TightBudgets,WildMarketsHurtInvestmentClubs,"December2011.Zimmerman,DavidJ.,\PeerEectsinAcademicOutcomes:EvidencefromaNaturalExperi-ment,"ReviewofEconomicsandStatistics,February2003,85(1),9{23.25 Table2:PeerEects,SocialLearning,SocialUtility,andSelection:Take-upRates DependentvariableWantedtopurchasetheasset (1)(2)(3)(4) Learningalone0.285**0.298**0.328**0.278**(ConditionB-ConditionA)(0.136)(0.140)(0.134)(0.127)Learningandpossession0.505***0.540***0.552***0.500***(ConditionC-ConditionA)(0.110)(0.122)(0.123)(0.111)Negativeselection-0.0340.011-0.0050.042(ConditionAneg-ConditionA)(0.114)(0.124)(0.118)(0.117)Investor10.128(0.106) Possessionalone0.220**0.242**0.224*0.222**(ConditionC-ConditionB)(0.106)(0.109)(0.124)(0.108)Mean(noinformation;peerchosetheasset)0.423(ConditionA)(0.099) BrokerxedeectsNoYesYesYesControlsNoNoYesYesN150150150300R20.1860.2280.2830.219 Notes:Column1presentstheresultsofaregressionofadummyvariableequaltooneiftheinvestorwantedtopurchasetheassetonadummyforconditionC,adummyforconditionB,andadummyindicatingwhethertheassociatedinvestor1didnotwanttopurchasetheasset(ConditionAneg).Investor2'sinconditionAistheomittedgroup.Thisregressionusesonlythesampleofinvestor2's.Theregressionpresentedincolumn2includesbrokerxedeects.Theregressionpresentedincolumn3includesthecovariatespresentedinTable1.Wedidnotincludeearningsasthiswouldreduceoursamplesize(resultsincludingearningsaresimilar).Theregressionpresentedincolumn4combinesthesampleofinvestors1and2,andincludesanindicatorvariableforinvestor1.Standarderrorsareclusteredatthepairlevel.Inallcolumns,\Possessionalone"givesthedierencebetweenthecoecienton\Learningandpossession"andthecoecienton\Learningalone."*signicantat10%;**signicantat5%;***signicantat1%.28 ONLINEAPPENDIX(NOTFORPUBLICATION)AppendixA:AppendixFiguresandTablesFigureA.1:Investor2'stake-uprates Note:Thisgurepresentsthemean(and95%condenceinterval)ofthetake-uprateforeachgroupofinvestor2's.InvestorsinconditionsAtoChavepeerswhowantedtheasset.Theseinvestorswererandomlyallocatedtooneofthese3groups.ThoseinconditionAhadnoinformationabouttheirpeers.ThoseinconditionBhadinformationthattheirpeerswantedtopurchasetheassetbuthadthatchoicerejectedbythelottery.ThoseinconditionChadinformationthattheirpeerswantedandreceivedtheasset.InvestorsinconditionAneghavepeerswhodidnotwanttopurchasetheasset(andreceivednoinformationabouttheirpeer).1 TableA.2:CovariatesBalance-OtherRandomizations Assignmenttoinvestor1orinvestor2Lotteryforinvestor1'swhowantedtheasset p-valueofp-valueofInvestor1Investor2testNWonLosttestN(1)=(2)(5)=(6) (1)(2)(3)(4)(5)(6)(7)(8) Age39.1237.180.2230039.4739.710.9478(1.14)(1.12)(2.34)(2.23)Gender(=1Ifmale)0.7470.6130.013000.8610.6900.0778(0.036)(0.040)(0.058)(0.072)Married0.4400.3870.353000.4720.4050.5678(0.041)(0.040)(0.084)(0.077)Single0.5270.5870.303000.5280.5000.8178(0.041)(0.040)(0.084)(0.078)Earnings5,0004,0000.222705,0005,0000.5974(499)(507)(925)(754)Relationshipwith----0.440.600.1978peer(=1iffamily)(0.08)(0.08) Notes:Columns1and2presenttheaveragesofthecorrespondingvariable,respectively,forinvestorsassignedtobeintheroleofinvestor1andforthoseassignedtobeintheroleofinvestor2.Robuststandarderrorsinparentheses.Relationshipwithpeerisnotconsideredinthiscomparisonsincethisvariableisequalforbothgroupsbyconstruction.Column3presentsthep-valueofanF-testthatthemeanofthecorrespondingvariableisthesameforthesetwogroups.Column5presentstheaveragesforinvestor1'swhowantedtheassetandwonthelottery,whilecolumn6presentstheaveragesforinvestor1'swhowantedtheassetbutdidnotwinthelottery.Column7presentsthep-valueofanF-testthatthemeanofthecorrespondingvariableisthesameforthesetwogroups.Forearnings,wepresentthemedianandthep-valueofatestthatthemedianofthisvariableisthesameforthecorrespondinggroups.Thesamplesizefortheearningsvariableissmallerduetomissingvalues.5 TableA.4:Follow-upSurvey-ExcludingInvestorsInterviewedbySameBroker QuestionUniverseSamplesizeResults PanelA:FinancialLiteracySurvey1.Self-assessedInvestor2'sinconditionsA80(outof100)Mean:3:9nancialliteracyandB,andtheirassociatedStandarddeviation:1:7(range:1-7)investor1'sProportion4:61:25%2.InterestrateInvestor2'sinconditionsA80(outof100)Correct:83:75%compoundingquestionandB,andtheirassociatedinvestor1's3.In ationquestionInvestor2'sinconditionsA80(outof100)Correct:85:00%andB,andtheirassociatedinvestor1's4.DiversicationquestionInvestor2'sinconditionsA80(outof100)Correct:67:50%andB,andtheirassociatedinvestor1's5.BondpricesquestionInvestor2'sinconditionsA80(outof100)Correct:16:25%andB,andtheirassociatedinvestor1'sQuestions(2)-(5)0correctanswers:6:25%1correctanswer:6:25%2correctanswers:31:25%3correctanswers:41:25%4correctanswers:15:00% PanelB:QuestionsRegardingtheSalesCall1.EectoflotteryInvestor2'sinconditionsA64(outof78)No:95:31%onpurchasedecisionBandC2.BelievedpurchasedecisionInvestor2'sinconditionsA64(outof78)No:93:75%couldhavebeenchangedBandCafterlottery3.Peer'slotteryresultInvestor2'sinconditions45(outof52)No:100%aectedbeliefsaboutBandCownlottery4.Peer'slotteryresultInvestor2'sinconditions45(outof52)No:97:78%aectedbeliefsaboutBandCqualityoftheasset5.Was(not)wantingsomethingInvestor2'sinconditionB20(outof24)No:100%yourpeercouldnothaveasignicantfactorindecision?6.EectofpeerdecisiononInvestor2'sinconditions46(outof52)Positiveupdate:67:39%beliefsaboutqualityBandCNoupdate:32:61%oftheasset7.WaswantingtohavetheInvestor2'sinconditionC24(outof26)Yes:62:50%samenancialreturnasyourwhowantedtheassetpeerasignicantfactorindecision?8.WaswantingtohavethesameInvestor2'sinconditionC24(outof26)Yes:41:67%assetasyourpeertotalkaboutwhowantedtheassettheassetasignicantfactorindecision?9.DidyouthinkaboutInvestor2'sinconditionC24(outof26)Yes:79:17%whatyourpeercoulddowhowantedtheassetwiththereturn?10.WasthefearofnothavingInvestor2'sinconditionC24(outof26)Yes:33:33%areturnyourpeercouldwhowantedtheassethaveasignicantfactorindecision?11.DidyoubelievetheInvestor2'sinconditions45(outof52)Yes:97:78%informationprovidedBandCbythebroker?12.WereyouconcernedaboutInvestor2'sinconditions45(outof52)No:88:89%yourdecisionbeingrevealedBandCtootherclients? Notes:thistablereplicatesTableA.3excluding11investorswhowereinterviewedbythesamebrokerwhomadethesalescall.7 TableA.6:LogitAverageMarginalEects-PeerEects,SocialLearning,SocialUtility,andSelection:Take-upRates DependentvariableWantedtopurchasetheasset (1)(2)(3)(4) Learningalone0.285**0.295**0.355***0.275**(ConditionB-ConditionA)(0.138)(0.143)(0.124)(0.127)Learningandpossession0.505***0.542***0.556***0.527***(ConditionC-ConditionA)(0.104)(0.112)(0.103)(0.106)Negativeselection-0.0340.018-0.0060.052(ConditionAneg-ConditionA)(0.106)(0.131)(0.107)(0.116)Investor10.132(0.096) Possessionalone0.220**0.247**0.202*0.252**(ConditionC-ConditionB)(0.108)(0.105)(0.104)(0.120)Mean(noinformation;peerchosetheasset)0.423(ConditionA)(0.099) BrokerxedeectsNoYesYesYesControlsNoNoYesYesN150150150300 BrokerxedeectsNoYesYesYesControlsNoNoYesYesN150150150300 Notes:ThistablereplicatestheresultsfromTable2usingLogitmodelsinsteadofordinaryleastsquaresregressions.Thecoecientspresentedareaveragemarginaleects.Standarderrorsarebootstrappedandclusteredatthepairlevelincolumn4.*signicantat10%;**signicantat5%;***signicantat1%.9 TableA.8:PermutationTests(p-values) DependentvariableTake-upratesAmountinvestedInvestedmorethanminimum(1)(2)(3) PanelA:MainresultsLearningalone[0.052]*[0.012]**[0.047]**(ConditionB-ConditionA)Learningandpossession[0.000]***[0.000]***[0.000]***(ConditionC-ConditionA)Possessionalone[0.063]*[0.011]**[0.047]**(ConditionC-ConditionB)Negativeselection[0.812][0.646][0.270](ConditionAneg-ConditionA) PanelB:HeterogeneityLearningby Sophisticated[0.922][0.675][0.324]Non-sophisticated[0.008]***[0.004]***[0.083]*Dierence[0.053]*[0.071]*[0.428]Learningfrom Sophisticated[0.038]**[0.009]***[0.028]**Non-sophisticated[0.801][0.816][1.000]Dierence[0.434][0.155][0.028]** Notes:Thistablepresentstheresultsoftwo-sidedpermutationtestswith10,000replicationsforthemainresultsinthepaper.Foreachpairwisecomparison,werandomlyreassigntheexperimentaltreatmentconditions,drawingtreatmentassignments(withoutreplacement)inthesameratiosastheactualexperimentaltreatmentassignments.Basedonthese\placebo"treatmentassignments,wecalculate\placebotreatmenteects"using10,000independentreassignments.Thedistributionof\placebotreatmenteects"fromthe10,000reassignmentsapproximatesthedistributionofourestimatorunderthenullhypothesisthatthetreatmenteectsarezero.Wecalculatep-valuesfromthepermutationtestsastheproportionof\placebotreatmenteects"thataregreater(inabsolutevalue)thantheestimatedtreatmenteectsusingtheactualexperimentaltreatmentassignments.PanelAreportsp-valuesfrompermutationtestsforpairwisecomparisonsoftheconditionsofinterestusingthreedierentoutcomevariables:take-uprates,amountinvested,andadummyvariableindicatingwhethertheinvestorinvestedmorethantheminimumamount.PanelBreportsp-valuesfrompermutationtestsfortheheterogeneityresultsusingtheself-assessedmeasureofnancialliteracy.*signicantat10%;**signicantat5%;***signicantat1%.11 TableA.10:HeterogeneityofSocialLearningEects-ObjectiveMeasureofFinancialSophistication Investor2isnanciallyAssociatedinvestor1isnanciallysophisticatedsophisticated p-valueofp-valueofYesNotest(1)=(2)YesNotest(4)=(5)(1)(2)(3)(4)(5)(6) PanelA:nocontrolsLearningalone0.1960.394*0.5330.386**0.1000.349(ConditionB-ConditionA)(0.227)(0.218)(0.175)(0.246) PanelB:fullspecicationLearningalone0.0310.892**0.0850.399*-0.1110.291(ConditionB-ConditionA)(0.367)(0.450)(0.210)(0.408) Mean(noinformation;peerchosetheasset)0.4290.3750.8160.4000.4001.000(ConditionA)(0.139)(0.180)(0.132)(0.162) Notes:ThistablereplicatestheresultsfromTable3usinganobjective(insteadofself-assessed)measureofnancialliteracy,basedonfournancialliteracyquestionsconductedinafollow-upsurvey.Investorswhoanswered3ormorequestionscorrectlywereclassiedasnanciallysophisticated.SeeAppendixCforanEnglishversionofthenancialliteracyquestions.*signicantat10%;**signicantat5%;***signicantat1%. 13 TableA.12:HeterogeneityofSocialLearningEects-InvestedMorethanMinimum Investor2isnanciallyAssociatedinvestor1isnanciallysophisticatedsophisticated p-valueofp-valueofYesNotest(1)=(2)YesNotest(4)=(5)(1)(2)(3)(4)(5)(6) PanelA:nocontrolsLearningalone0.1450.333**0.3940.329**0.0000.036(ConditionB-ConditionA)(0.165)(0.143)(0.152)(0.000) PanelB:fullspecicationLearningalone0.1350.2330.6730.235*0.2130.928(ConditionB-ConditionA)(0.148)(0.161)(0.135)(0.172) Mean(noinformation;peerchosetheasset)0.0770.0000.3330.0560.0000.334(ConditionA)(0.078)(0.000)(0.056)(0.000) Notes:ThistablereplicatestheresultsfromTable3usingadummyvariableequaltooneiftheinvestorinvestedmorethantheminimumamountinsteadoftake-uprateasdependentvariable.Thenancialsophisticationvariableisbasedontheself-assessmentquestionconductedinthefollow-upsurveydescribedinthetext.Investorsratedtheirnancialknowledgefrom1(verylow)to7(veryhigh).Investorswhoreported4orhigherwereclassiedasnanciallysophisticated.*signicantat10%;**signicantat5%;***signicantat1%. 15 AppendixB:ASimpleModelofFinancialDecisionsUnderSocialIn uenceOurmodelstudiesaninvestmentdecisionmadebyanindividualunderseveralconditions.First,wepresenttheinvestmentdecisionunderuncertainty,butwithnosocialin uence.Second,wepresenttheinvestmentdecisionwithsociallearningpresent,usingtheingredientsofacanonicalsociallearningmodel:apeermakesaninvestmentactingonaprivatesignal,andthisactioncanbeusedbyanotherinvestortomakeaninformationalinferencebeforetakinghisownaction.Third,weallowtheownershipofanassettoaectasocially-relatedinvestor'sutilityofowningtheasset,asidefromanylearning{thatis,weallowforasocialutilityeect.Apeer'spurchasedecisiontypicallywillproducebothsociallearningandsocialutilityeects;weconsideracaseinwhichbotheectsareactive(thefull\peereect")andacaseinwhichtherevealedpreferencepurchasedecisionisde-coupledfrompossession.Thisde-couplingallowsonetoobserveeachchannelthroughwhichpeereectswork,andmotivatesourexperimentaldesign.InvestmentwithoutPeerEectsConsideraninvestori'sdecisiontoinvestinariskyasset.21Theasset'sreturnisgivenbyx,withprobabilitydensityfunctionf(x),andinvestori'sutilityisui(x)=u(x)foralli.Inoureldexperiment,investorsreceivedcallsfrombrokerswhooeredthemanancialassetforpurchase.Thebrokersattemptedtoconveythesameinformationabouttheassetineverycallusingapre-speciedscript;thus,theinformationtheyprovidedcanbethoughtofasasignal,si,comingfromasingledistribution,withprobabilitydensityfunctiong(si).Importantly,noteveryinvestorwouldhavereceivedexactlythesameinformation:callsevolveindierentways,investorsaskdierentquestionsabouttheasset,etc.,meaningthateachinvestorreceivedadierentsignalrealization,si,fromthecommondistributionofsignals.Forexpositionalsimplicity,assumethattheconditionaldensityf(xjsi)satisesthemonotonelikelihoodratioproperty(MLRP)suchthat,intuitively,highervaluesofsiareindicativeofhighervaluesofx.Undertheseconditions,investoriiswillingtoinvestifandonlyifZu(x)f(xjsi)dxu;(2)whereudenotestheoutsideoptionoftheinvestor.Giventhatf(xjsi)satisesMLRPandgivenmildmonotonicityassumptionsontheutilityfunctionu(
)oftheinvestor,thereexistsauniquethresholds1suchthatforanysis1investoriiswillingtoinvest.Denotethedecisiontobuy 21Notethatweimplicitlyassumethatwheninvestinginisolation,investoridoesnottakeintoconsiderationanyinvestorj(j6=i)atall{heis\unaware."Inthecontextofourexperiment,webelievethatthisassumptionisreasonable,aswediscussinthetext.17 notationofourmodel,aninvestorj'spurchaseofanasset,bj=1,typicallyimpliesboththatinvestoriinfersfavorableinformationabouttheasset,sjs1,andthatinvestorjnowpossessestheasset,pj=1,whichmightaectinvestori'sutilityofowningtheasset(duetoatasteforjointconsumption,\keeping-up-with-the-Joneses"preferences).Wheninvestoriobservesthatinvestorjexpressedanintentiontoinvest,bj=1,andwasallowedtoinvest,pj=1,bothinvestori'sutilityu(xjpj=1)andhisinformationabouttheassetf(xjsi;sjs1)areaected,relativetohischoiceinisolation(thatis,relativetou(x)=u(xjpj=0)andf(xjsi)).24Inthiscase,oneobservesthe\full"peereect,andinvestoriinvestsifandonlyifZu(xjpj=1)f(xjsi;sjs1)dxu:(7)Denotethethresholdforsiabovewhichinvestoriiswillingtoinvestwhenexposedtobothpeereectschannelsbys3.Then,thedecisionruleforinvestoriisgivenbybi=1,sis3:(8)Toseparatetheeectsofsociallearningandsocialutility,weneedtodecouplewillingnesstopurchase(andtheinformativesignalofthepurchasedecision)frompossession.Considerthesituationwhereinvestoriobservesthatinvestorjexpressedarevealedpreferencetoinvest,butwasnotallowedtodoso(perhapsduetocapacityconstraints).Inthiscase,investoriinfersthatsjs1,butalsoknowsthatinvestorjdidnotobtaintheasset,sopj=0.Thisconditionisequivalenttothe\sociallearningalone"problemdiscussedabove:thereisnodirecteectofpossessiononinvestori'sutilityfromtheasset,butthereissociallearning.Thus,investoripurchasestheassetifandonlyif(4)issatised(sinceu(x)=u(xjpj=0))andthisleadstothesamedecisionruleas(6)withthethresholds2.Thefollowingpropositionsummarizesinvestori'spurchasedecisionsacrossconditions.Proposition1.Thethresholdforthesignalsiabovewhichinvestoriiswillingtopurchasetheasset(and,thelikelihoodofapurchaseoftheassetbyinvestori)ishighest(lowest)whentheinvestormakeshisdecisioninisolation,lower(higher)whenheobservesthatinvestorjintendedtopurchasetheassetbutdidnotobtainit,andlowest(highest)wheninvestorjintendedtopurchasetheasset,andobtainedit:s1s2s3(andPr(sis3)Pr(sis2)Pr(sis1)).Proof.Therelationshipbetweens1ands2followsimmediatelyfromcomparingtheinequalities(2)and(4)andthemonotonelikelihoodratiopropertyoff(xjsi;sj).Similarly,comparisonoftheinequalities(4)and(7)andu(x)=u(xjpj=0)u(xjpj=1)establishesthats2s3.Finally,Pr(sis3)Pr(sis2)Pr(sis1)followsfromtherankingofthethresholds. 24Weareassumingherethattheutilityfunctiondiscussedabove,u(x),isthesameasu(xjpj=0)here.Inaddition,weareassumingthatinvestorjmadehisdecisioninisolation.19 HeterogeneousInvestorsInpractice,someinvestorsaremorenanciallysophisticatedthanothers,andonewouldexpectthatthisvariationwillaectthepeereectswestudyhere{especiallytheimpactofsociallearning.Inparticular,anunsophisticatedinvestormayhavemuchmoretolearnaboutanassetfromthepurchasedecisionoftheirpeerthandoesasophisticatedinvestor,asthesophisticatedinvestorlikelyhasaverygoodsenseoftheasset'squalityfromhissignalalone.Dieringnancialsophisticationcanbecapturedinourmodelbyallowingthesignalssiandsjtobedrawnfromdistributionswithdieringprecision.Forsimplicity,wemaketheassumptionthat,incontrasttounsophisticatedinvestors,sophisticatedinvestorsreceiveperfectlyinformativesignals.Thisassumptiongeneratesthefollowingpredictionofheterogeneouseectsofsociallearning.Proposition3.Thethresholdss1ands2forthesignalsiabovewhichinvestoriiswillingtopur-chasetheasset(andhencethelikelihoodofinvestoripurchasingtheasset)areidenticalifinvestoriisnanciallysophisticated(i.e.,signalsiisperfectlyinformative).Ifinvestorjissophisticated,theninvestorifollowsthechoiceofinvestorjwhenobservingthedecisionofinvestorj.Proof.Ifsiisperfectlyinformative(i.e.,investoriissophisticated),thensiisasucientstatisticforx.Asaresult,sj,andhencethepurchasedecisionofinvestorj,hasnoinformationalvalueforsophisticatedinvestorianddoesnotin uencethethresholds1.Hence,s1=s2.Ifsjisperfectlyinformative,theninvestorjknowsthevalueofxandmakesaperfectlyinformedinvestmentdecision.Asaresult,investorifollowsinvestorj'schoice.Proposition3suggeststhatsociallearningwillbelimited(infact,giventhesimplifyingas-sumptionsmade,willbenonexistent)forsophisticatedinvestors.Theseinvestorsaresucientlywell-informedthattheyarenotin uencedbytherevealedpreferenceofanotherinvestor.Thepropositionfurthershowsthatsociallearningwillhaverelativelystrongeectsoninvestmentchoicesiftheinvestorwhosechoiceisobservedissophisticated.26 26Wehaveassumedthatsophisticatedinvestorsreceiveperfectlyinformativesignals.Ourresultscanbeextendedtothecaseinwhichsophisticatedinvestorsreceivemoreinformative,butstillimperfectlyinformative,signals.Whileresultsforgeneraldistributionsofx,siandsjthatsatisfyMLRPdonotexist,itisstraightforwardtoshowthatforbinarysignalstructures,theimpactofsociallearningwillberelativelysmallwhentheobservinginvestorissophisticatedandrelativelylargewhentheobservedinvestorissophisticated.Finally,itisworthnotingthat,anotherinvestor'spossessionoftheassetcouldstillaectnanciallysophisticatedinvestors'choices;similarlyananciallyunsophisticatedinvestor'spurchasedecision{whenaccompaniedbypossession{couldin uenceapeer'schoice.Bothoftheseeectswouldworkthroughthesocialutilitychannel.Thus,weemphasizethatthesepredictionsofheterogeneoustreatmenteectsapplytosociallearningeectsalone,butnotnecessarilytheoverallpeereect.21 c.Donotknowd.Refusetoanswer(5)Ifinterestratesrise,whatwilltypicallyhappentobondprices?a.Theywillriseb.Theywillfallc.Theywillstaythesamed.Thereisnorelationshipbetweenbondpricesandtheinterestratese.Donotknowf.RefusetoanswerQuestionsRegardingtheSalesCall(1)Forinvestor2'sinconditions1,2,and3Whentheassetwasoeredtoyouinthebeginningoftheyear,wehadtousealotterygiventhattheassetwasinlimitedsupply.Atthatmoment,youdecidedtopurchase(notpurchase)theasset.Wasthepresenceofthelotteryasignicantfactorinyourdecision?a.Yesb.No(2)Forinvestor2'sinconditions1,2,and3Beforetheresultofthelottery,youmadeapurchasedecision.Didyoubelieveyoucouldhavechangedyourdecisionafterthelottery?a.Yesb.No(3)Forinvestor2'sinconditions2and3Whentheassetwasoeredtoyou,youwereinformedthat[NAMEOFTHEASSOCIATEDINVESTOR1]wantedtheasset,butthathe/shelostthelottery(andhe/shewonthelottery).Inthelottery,youhad50%chanceofwinningand50%chanceoflosing,independentlyoftheresultfor[NAMEOFTHEASSOCIATEDINVESTOR1].Whenyouwereinformedthat[NAMEOFTHEASSOCIATEDINVESTOR1]lost(won)thelottery,howdidthisaectyourbeliefsaboutthelikelihoodofwinningthelottery?a.Itwouldbemorelikelytowinthelotteryb.Itwouldbelesslikelytowinthelotteryc.Thelikelihoodofwinningthelotterywouldremainunchanged.31 (10)Forinvestor2'sincondition3whodecidedtopurchasetheassetYouwereinformedthat[NAMEOFTHEASSOCIATEDINVESTOR1]hadtheasset.Wasthefearofnothavingareturnhe/shecouldhaveasignicantfactorinyourdecision?a.Yes.b.No.(11)Forinvestor2'sinconditions2and3Thebrokerinformedyouthat[NAMEOFTHEASSOCIATEDINVESTOR1]wantedtopurchasetheasset.Didyoubelieveinthisinformation?a.Yes.b.No.(12)Forinvestor2'sinconditions2and3Yourchoiceswereneverrevealedtootherclients.Still,wereyouconcernedaboutthispossibilitywhenyoudecidedtopurchase(nottopurchase)theasset?a.Yes.b.No.33