experiment on interdependent time preferences Social motives vs social inﬂuence:An Games and Economic Behavior

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Games and Economic Behavior 105 (2017) 177–194

Contents lists available atScienceDirect

Games and Economic Behavior

www.elsevier.com/locate/geb

Social motives vs social inﬂuence:

An experiment on interdependent time preferences ^✩

Ismael Rodriguez-Lara

^a

, Giovanni Ponti

^b^,^c^,^d^,∗

aMiddlesexUniversity,London,UnitedKingdom bUniversidaddeAlicante,Spain

cTheUniversityofChicago,UnitedStates dLUISSGuidoCarli,Roma,Italy

a r t i c l e i n f o a b s t r a c t

Articlehistory:

Received14May2014 Availableonline26July2017

JELclassiﬁcation:

C91 D70 D81 D91

Keywords:

Socialpreferences Riskandtimepreferences Socialinﬂuence Beliefelicitation

We design an intertemporal Dictator Game to test whether Dictators modify their discounting behavior whentheir owndecision isimposed ontheirmatched Recipients.

Werunfourdifferenttreatmentstoidentifytheeffectofpayoffsexternalitiesfromthose relatedtoinformationandbeliefs.OurdescriptivestatisticsshowthatDictatorsdisplaya markedpropensitytoaccountfortheintertemporalpreferencesofRecipients,bothinthe presenceofexternalities(socialmotives)and/orwhentheyknowabout thedecisionsof theirmatchedpartners(socialinfluence).Wealsoperformastructuralestimationexercise to control for heterogeneityin risk attitudes. As for individual behavior, our estimates confirmpreviousstudiesinthathighriskaversionisassociatedwithlowdiscounting.As forsocialbehavior,wefindthatsocialmotivesoutweighsocialinfluence,especiallywhen werestrictoursampletopairsofDictatorsandRecipientswhosatisfyminimalconsistency conditions.

©²⁰¹⁷^TheÂuthor(s).^Published^byÊlsevierÎnc.^Thisîsânôpenâccessârticleûnder^the CCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

“Attheﬁrsttimeofsexualunionthepassionofthemaleisintense,andhistimeisshort[...]

Withthefemale,however,itisthecontrary,forattheﬁrsttimeherpassionisweak,andthenhertimelong[...]

Ifamalebealong-timed,thefemaleloveshimthemore,butifhebeshort-timed,sheisdissatisﬁedwithhim.”

[“TheKamaSutraofVatsyayana”–Burtonetal. (2009)]

✩ WethankDanielMüller,VincentCrawfordandtwoanonymousrefereesfortheirusefulcommentsandsuggestions,whichimprovedthequalityofthe manuscriptsigniﬁcantly.WealsothankseminarparticipantsattheEuropeanUniversityInstitute,the2013IMEBEMeeting(Madrid),SEET(Tenerife),the PETMeeting13(Lisbon),theAlhambraMeetsColosseoAEWMeeting(Rome),theILondonExperimentalWorkshop,andtheFUR2014Meeting(Rotterdam).

ThispaperhasbeenrevisedwhileGiovanniPontiwasvisitingtheCenterforExperimentalSocialScience(CESS)atNewYorkUniversity.Hewouldlike tothankAlbertoBisin,GuillaumeFréchette,AlessandroLizzeri,CarolineMadden,AndrewSchotterandallpeopleatCESSandEconNYUfortheirkind hospitality.Finally,aspecialthankgoestoDanielaDiCagno,whohasbeeninvolvedintheearlierdevelopmentsofthisproject.Theusualdisclaimers apply.FinancialsupportfromtheSpanishMinistryofEconomyandCompetitiveness(ECO2014-58297-RandECO2015-65820-P),GeneralitatValenciana (ResearchProjectsGrupos3/086)andInstitutoValencianodeInvestigacionesEconómicas(IVIE)isgratefullyacknowledged.

*

Correspondingauthorat:DepartamentodeFundamentosdelAnálisisEconómico,UniversidaddeAlicante,03071Alicante,Spain.

E-mailaddress:giuba@ua.es(G. Ponti).

http://dx.doi.org/10.1016/j.geb.2017.06.007

0899-8256/©²⁰¹⁷^TheÂuthor(s).^Published^byÊlsevierÎnc.^Thisîsânôpenâccessârticleûnder^the^CC^BY-NC-ND^license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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1. Introduction

We oftenshow concerns for others by changing the timing of a speciﬁc course ofaction. This happens routinely in household key decisions such as selling a house, investing in a pension plan or even getting divorced. The empirical literature on health economics hasextensively studied the relationship betweentime preferences forone’s own private health and for others’ health (see Lazaro et al., 2001, 2002 or Robberstad, 2005 for earlier contributions on this area andMahboub-Ahari etal., 2014fora recentmeta-analysis).Itis alsowell documented(see, e.g., Abdellaouietal., 2013;

Browning,2000;Mazzocco,2004, 2007,amongothers)thatmulti-personhouseholdsavingandconsumptionpatternsmay strongly differfrom thoseof single-personhouseholds, evenafter controllingforindividual characteristics (e.g.,own risk aversion, ordiscounting) ofeach household component. As all theseexamples illustrate,social (i.e., interdependent)concerns mayaffect the timing of choices: decisionmakers may try to accommodate others’intertemporal concerns, when decisionsaffectthelatter’sprospectsandwelfare.

Thispaperaimsatprovidingevidenceontheeffectsofsocialpreferencesonintertemporaldecisions.Moreindetail,weare interestedinbetterunderstandinghowmuch–andinwhichdirection–individuals’preferencesforanticipatingordelaying anactioncanbeaffectedbythepresenceofpayoffexternalities.Clearly,ourmotivatingexamplesleadtoabroaderconcept ofsocialpreferences,comparedwithitscurrentusageintheﬂourishing–mainlyexperimental–literatureonthesematters, where socialpreferencesareusually restrictedtopeople’s intereston“thefairnessoftheirownmaterialpayoffrelativetothe payoffofothers...”(FehrandSchmidt,1999,p.819). Incontrastwiththisliterature, inthispaperconcernsforothersmay notonlyinvolveothers’materialconsequences (e.g.,monetaryoutcomes,consumptionbundles),butalsoothers’concernsand inclinations, such asrisk aversion or discounting.This,inturn,calls formodeling social preferencesasmappeddirectlyon others’individualutilities (Harrisonetal.,2014).

Thismodeling approachbasically framessubjects’behaviorasmaximizing asocialwelfare function,whichrequiresan operational solutionofthe delicateissue ofinterpersonalcomparisonofutilities (which is,probably,the reasonwhythe mainstream literature has always preferred to restrict the domain of social preferences to the physical outcome space).

By contrast,theempiricalliterature we justcited– take,e.g. Mazzocco, 2007,eq. (3) –positsthat householdsmaximize a convex linearcombination ofthe individual (“selﬁsh”) utilities oftheir members, which are assumedto be derived as differentparametrizations–dependingonindividualcharacteristics–ofthesamefunctional,withweightsbeinginterpreted asproxiesofeachmember’sbargainingpowerwithinthehousehold.Thisisgoingtobethemodelingapproachweusein thispaper.

Ourempiricalevidencecomesfromamulti-stagelaboratoryexperimentwhereweinvestigateonthelinkbetweentime andsocial preferencesbywayofMultiplePrice Lists(MPLs, HoltandLaury,2002, 2005).Since timeandrisk preferences are interwined,wefollowAndersenetal. (2008)by eliciting(own)risk andtimepreferencesby wayofseparate tasksin the ﬁrsttwostagesoftheexperiment(see alsoAndersenetal.,2014b;Harrisonetal., 2013a, 2005orSutter etal.,2013 forapplicationsofsimilarmethods).Thus,we useMPLstoelicitriskpreferencesandcontrol forthecurvatureofsubjects’

utility functionwhenestimatingtimepreferencesby wayofanothersequenceoftenMPLsinwhichsubjectsareaskedto choose betweenanimmediatesmallerreward andan increasingly largerlater reward.Thenovelty ofourapproachrelies on incorporatinga socialdimension tothis protocol. Thus, once subjects have completed the ﬁrst two stages, we match them inpairs andassign therolesofDictators andRecipients. Then,Dictatorsgo through,onceagain, the samesequence ofintertemporaldecisionsknowingthat–thistime–their choicesmayalsobeimplementedfortheir assignedRecipient.

Subjects’ information on others’ risk and time decisions and the presence of payoff externalities deﬁnes our treatment conditions:

1. inthebaseline treatment(T₀,INFO-SOCIAL),Dictatorsmaketheir intertemporalchoicesafterbeinginformedofwhat theirassignedRecipienthadchosenintheﬁrsttwostagesoftheexperiment;

2. intheBELIEF-SOCIALtreatment(T1),beforedecidingforthepair,Dictatorsgothroughanadditionalstageinwhichwe elicittheirbeliefsonriskandtimeconcernsoftheirassignedRecipient;

3. intheINFO-PRIVATE treatment(T2), subjectsreceive (exactly asin thebaseline) informationon risk/timeindividual choicesoftheirgroupmate,butnopayoffexternalitiesareimposedonothers;

4. intheNOINFO-SOCIALtreatment(T₃),Dictatorsmaketheirintertemporaldecisionsforthepairwithoutpriorknowl- edge(orelicitedbelief)oftheRecipient’srisk/timedecisions.

Ourdesignstrategyallows toteaseapartsocialmotives from socialinﬂuence.ThecomparisonbetweentheINFO-SOCIAL and the INFO-PRIVATE treatments allows us to determine whetherinformed Dictators change their decisionmore often when theyact onbehalfofthepair(socialmotives)comparedwiththesituationinwhich–whateverthereason–they canjustmimicthebehavioroftheirassignedRecipient(socialinﬂuence),withoutimposinganypayoffconsequenceonthe latter.¹ Alongsimilar lines,we can alsocompare thebehavior ofuninformed Dictatorsin theBELIEF-SOCIAL andtheNO

1 TheroleofsocialinfluencewasfirststudiedinPsychologybySherif (1937)andAsch (1955).Theeconomicliteratureonthistopicincludespapers oninformationalinfluence,thatis,herdingorobservationalcascades(see,e.g.,Banerjee,1992; Bikhchandanietal.,1992orFerietal.,2011)andnormative influence,thatis,imitationbasedonmoraljudgment (see,e.g.,HungandPlott,2001orMorenoandRamos-Sosa,2017).Theinterestedreaderonthe comparisonbetweenthesetwobehavioralphenomenacanconsultGoereeandYariv (2015)andthereferencestherein.

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I. Rodriguez-Lara, G. Ponti / Games and Economic Behavior 105 (2017) 177–194 179

INFO-SOCIALtreatmentssoastomeasuretheimpactofbeliefelicitationintheemergenceofsocial(time)preferences.This is what Krupkaand Weber (2009)labelas theeffect offocusing on social preferences: guessingand thinking aboutthe actionsofothersleads–instandardDictatorgames–tofocusmoreonthesocialnormand,asaresult,moregenerosityis observed.

FollowingRodriguez-Lara (2010),ourexperimentaldesignisbuiltaroundthestructuralestimationexerciseofSection4.2, inwhichsubjects’behaviorisframedbywayofaconvexlinearcombinationbetweenthe(“selfish”)utilitiesofDictatorand Recipient. By contrast withthe literature cited earlier, here weights reflect the Dictator’sconcerns about the Recipient’s risk aversion anddiscounting. In this respect, our identification strategy crucially relies on the experimental design by manipulatingsubjects’incentivesandinformationinthevariousstagesoftheexperiment.

The remainder ofthepaperis arrangedasfollows.Section 2 reviewstherelevant literatureon thesematters. InSec- tion3welayoutourexperimentaldesign,whereasSection4reportsourresults.First,Section4.1reportssomedescriptive statisticsonsubjects’behaviorinthevariousstagesoftheexperiment.Hereweshowthati)Dictators’choicessigniﬁcantly moveinthedirectionoftheirmatchedRecipientsinourbaseline treatment;ii)socialinﬂuenceisanotherimportantfactor inexplainingchoices,inthatDictatorstendtomoveinthedirectionofRecipientsalsointheINFO-PRIVATEtreatmentand iii)KrupkaandWeber’s2009focusing effectisalsorelevantintheabsenceofinformationinthatelicitingbeliefsseemsto triggersocialpreferencesintheBELIEF-SOCIAL,comparedwiththeNOINFO-SOCIALtreatment.

Section 4.2teststhe robustnessofourpreliminary ﬁndingsby wayofastructuralmodelinwhichwe frame subjects’

choiceswithin therealmof arandom utilitymaximization problem, by whichwe cancontrol forsubjects’heterogeneity in risk preferences.We lookboth at subjects’i) individualdecisions (and elicitedbeliefs) in Stages1to 3,as well asii) Dictators’ intertemporal choices in Stage 4. As for the former, our evidence is consistent with previous ﬁndings in that our subjects exhibit, on average, (Constant Relative) Risk Aversion (CRRA, Hey and Orme, 1994; Holt and Laury, 2002;

Harrison and Rutström, 2008) and non-exponential discounting (Coller et al., 2012; Benhabib et al., 2010; Andersen et al., 2008). In addition, we also find (consistently withSutter etal., 2013 andDean andOrtoleva, 2012), that individual (own)risk andtime preferencesare stronglycorrelated,inthatrisk aversesubjectsare alsomorepatient.Finally,wesee that –oncewe control forrisk aversionin ourstructuralestimation–social motives outweighboth socialinfluenceand focusing, inthat the estimatedweight ofthe Recipient’sutility is positive andhighly significant only when externalities andinformationareboth present(i.e.,inourbaselinetreatment).Bycontrast,the“socialinfluence”conjecture(proxiedby theestimated weightforthe INFO-PRIVATEtreatment)isonly partiallyvalidated, since theestimatedcoefficient remains positive,butisonlysignificant at10%confidence,andonly whenwedonot restrictour sampletopairs ofDictatorsand Recipients who satisfy minimal consistency conditions(see Section 4.1.3). Alsoforthe focusing hypothesis, the estimated weightintheBELIEF-SOCIALtreatmentispositive,butnotsignificant.

Finally,Section 5 concludes,followed by Appendicescontaining informationon the identiﬁcationstrategy, the experi- mentalinstructions,thedebrieﬁngquestionnaireandsupplementaryexperimentalevidence.

2. Relatedliterature

Notwithstandingour“socialtwist”,thispapersitssquarelyintheemergingliteraturethatappliesexperimentalmethods tostudythelinkbetweenindividual riskandtimepreferences(see, amongothers,AndreoniandSprenger,2012a, 2012b;

Halevy,2008; Laury etal.,2012).Inthisrespect,we borrowthe methodologyputforwardby Andersenetal. (2008) and controlforthecurvatureoftheutilityfunctionwhenelicitingdiscountrates.Tothisaim,adoubleMPLisemployedtoelicit riskandtimepreferencesindependently,thatis,withtwoseparatetasks:oneMPLoverlotteriespaidoffatthetimeofthe experiment(Stage1),anotherintertemporal MPLofcertainmonetary payoffspaidoffatdifferenttimes(Stage2).Similar methodshavebeenemployedbyAndersenetal. (2006, 2014b),Harrisonetal. (2005),Cheung (2015),Sutter etal. (2013) orFredericketal. (2002),amongothers.

AndreoniandSprenger (2012b),instead,applyanidentiﬁcationstrategybetweenriskandtimepreferencesinwhichsub- jectsallocateabudgetoftokensbetweenriskyprospectsthatrewardatdifferentpointsintime(seealsoMiaoandZhong, 2015).Withthisdesign,thenullhypothesisofriskneutralityisalsorejected.Othermethodstoelicittimepreferencesare thoseofBenhabibetal. (2010),wheresubjectsare askedtoelicitintertemporalequivalents,i.e., theamountofmoneythat receivedtoday(inthefuture)that wouldmakethemindifferenttosomeamountpaidinthefuture(today)orLauryetal.

(2012),wheretheelicitationofriskpreferencesdoesnotrequireanyassumptionontheformoftheutilityfunction.² Along similar lines, we here mention an emerging literature that, by wayof joint elicitation of risk and social preferences,claims that the empiricalcontent ofthe lattermaybe severelyreduced by thepresence ofsome –strategic, or environmental–uncertainty(Winter,2004; Winteretal.,2008; Cabralesetal.,2008; FrignaniandPonti,2012).³

Tothebestofourknowledge,thisistheﬁrstpaperthatelicitsdiscountratesinamodelofsocialpreferences.Theonly relatedprecedents weare aware ofare the papersof PhelphsandPollak (1968)and Kovarik (2009). PhelphsandPollak (1968) propose an intergenerational modelin whicheach generation cares abouttheconsumption of futuregenerations,

2 SeealsoAndreonietal. (2015)orHarrisonetal. (2013a)foradiscussiononthedifferentelicitationmethods.

3 Anderssonetal. (2016),Chakravartyetal. (2011)andHarrisonetal. (2013b)arefurtherexamplesoftheinvestigationofsocialpreferencesintherisk dimension.

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which is discounted in a non-linear manner. Kovarik (2009)collects evidence on therelationship between altruism and discounting, showing thatdonations ina DictatorGame decreaseasthe momentforreceiving paymentsis delayed.This contradictsstandardtheoriesoftimepreferences,includingexponentialandhyperbolicdiscounting.

Last,butnot least, giventhat ourestimation strategyinvolves thejointelicitation ofrisk, time andsocialpreferences by wayofseparate experimental tasks,our findingsare to becompared withthoseofsome recent papersthat establish empirical correlations among these behavioral traits. In this respect, our finding are consistent withthose of Sutter et al. (2013), in that subjectswithacomparativelylowerdegreeofriskaversiondiscountthefuturesignificantlymore (see also Burks etal.,2009andDeanandOrtoleva,2012).Becauseourdebriefingquestionnairecollects awidevarietyofindividual characteristics,wecanalsoestablishapositivecorrelationbetweenthewillingnesstoacceptthedelayedpaymentandthe scoreinthecognitiveskills,alsoreportedbyAndersonetal. (2011)orBurksetal. (2009).⁴

3. Experimentaldesign 3.1. Sessions

Thirteen experimental sessions were run at the Laboratory for Research in Experimental Economics (LINEEX), at the Universidad de Valencia. A total of 624 subjects (48 per session) were recruited within the undergraduate population of the University. The experimental sessions were computerized. Instructions were read aloud and we let subjects ask aboutanydoubttheymayhavehad.Allsessionsendedwithadebrieﬁngquestionnairetodistillsubjects’individualsocio- demographicsandsocialattitudes.⁵ Eachsessionlasted,onaverage,1hourand40minutes.

3.2. Stages

Eachsubjectparticipatestooneofthefourtreatmentconditions(T0 to T3).Stages1and2(commontoalltreatments) are usedtoelicitindividual(own)risk andtime preferences,respectively. AfterStage2,participantsarematchedinpairs.

Inoneofthetreatments(T1,labeledasBELIEF-SOCIAL),subjectsfaceanadditionalstage(Stage3)inwhichweelicittheir beliefs on(own)risk andtimepreferencesoftheir assignedgroupmate.Then, inStage4(common toall treatments),we assign subjects the role of Dictator and Recipient, and all subjects go again through the same sequence of decisions of Stage 2. Ourtreatment conditions(Section 3.6) determine whetherthe Dictators’ decision in Stage 4 is binding for the Recipient,andtheinformationDictatorsreceive(ifany)abouttheRecipients’decisionsinStages1and 2.

3.3. Stage1.Ownriskpreferenceelicitation

We elicit subjects’ individual risk preferences by way of a MPL in which subjects face the ordered array of binary lotteries ofFig. 1.As Fig. 1shows, subjectsface asequenceof11 binarylotteries, oneforeach row.The entiresequence is characterized by the fact that the “risky” option (B) is increasingly more proﬁtable, as the probability of the highest prize(e^190,ⁱⁿ^ourparametrization)growsinprobability,andsoisfallingtheexpectedpayoffdifferencebetweenoptions A and B. In decision1 (11) lotteries are degenerate,giving probability 1 tothe lower (larger) prize forlottery Aand B, respectively.Arisk-neutralsubjectshouldbeswitchingfromoptionAtoBindecision 6,whentheexpectedpayoffdifference betweenoptionAandoptionBgoesnegative.Thehighertheswitchingpoint,themoreriskaversethesubject is.

3.4. Stage2.Individualtimepreferenceelicitation

MPLs are also used to elicit time preferences. In Stage 2 subjects go through 10 decision rounds, each of which is characterized byaspeciﬁc timedelay,

τ

,rangingfrom1to180days.Foreach MPL,

τ

,subjectsface20binarychoices,k, andchoosebetweenreceivinge ¹⁰⁰ⁱⁿ^the^dayôf^theêxperiment^(hereafter^“today”) ânde ¹⁰⁰

(1+₃₆₅ⁱ^k )^τ

in

τ

days, wherethesequenceofAnnualInterestRates(AIR),ik,constantacrossrounds,

τ

,variesfrom2%to300%.Delayscorrespond to

τ

=¹,3,5,7,15,30,60,90,120 and180 days.Fig. 2reportsthe userinterfaceofthe MPLcorrespondingto adelay of 100 days,thesame usedin theexperimental instructions.⁶ Contraryto other studies (e.g.,Andersen etal., 2008, 2014b;

Coller andWilliams, 1999; Coller etal., 2012) the AIRis not showntosubjects inthe userinterface. Anotherimportant differencewithrespecttothesepapersisthatsubjectsdonotmakeauniqueintertemporaldecision(withdifferentdelays distributedbetweensubjects).Instead,all subjectsgothroughall intertemporalMPLs.⁷

4 SeeAppendixD2.

5 Theexperimentwasprogrammedandconductedwiththesoftwarez-tree (Fischbacher,2007).Translatedversionsoftheinstructionsandthedebrieﬁng questionnairecanbefoundinAppendixB.

6 TheinterestedreadercanseethefullsetofMPLsofStage2inAppendixC(TableC1).

7 Thiswithin-subjectdesignhasbeenalsousedbyTanakaetal. (2010),Cheung (2015)andSutteretal. (2013).

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Fig. 1. Stage 1 user interface.

Fig. 2. Stage 2 user interface.

ContrarytowhathappensinStage1,subjectsmakeonlyonedecisionforMPL,inthattheyaresimplyaskedtoindicate their “switching point” (if any)fromoption A (e ¹⁰⁰ ^“today”) ^to ^option^B ⁽e ¹⁰⁰

(1+^yk)³⁶⁵^τ

in

τ

days). Thus, “time consistency”(seeSection4.1.3)withineachMPL–butnotacrossMPLs–isartiﬁciallyimposed.

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3.5. Stage3.Beliefelicitation(onlyforT1)

Asweexplainedearlier,attheendofStage2subjectsarematchedinpairs.Inoneofourtreatments,(T₁,BELIEF-SOCIAL) subjectsareaskedtopredicttheirmatchedpartner’sdecisionsinStages1and2.Predictionsareincentivized,asdetailedin Section3.8.

3.6. Stage4.Socialtimepreferenceelicitation

InStage4,foreachmatchedpair,subjectsareassignedtheroleofDictatororRecipient(withtheexceptionofT₂,where allsubjectscanbeconsideredas“Dictators”oftheirownfate).AllsubjectsareremindedabouttheirownchoicesinStages 1and2.Then,bothDictatorsandRecipientsgothrough–onceagain–thesamesequenceofMPLsasinStage2.⁸Subjects’

informationonothers’riskandtimepreferences–togetherwiththepresenceofpayoffexternalities–deﬁneourtreatment conditions,asfollows:

•^In ^our ^baseline ^treatment ^(T0, INFO-SOCIAL: 6 sessions, 288 subjects), Dictators are informed about their partner’s choicesinStages1and2beforemakingtheirdecisionforthepair.

•^In ^the BELIEF-SOCIAL treatment (T₁: 2sessions, 96 subjects) Dictators are remindedabout their own predictions of Stage3beforemakingtheirdecisionforthepair.AsinT0,theDictator’sdecisionhaspayoffconsequencesforthepair inthattheDictator’schoiceimposesapayoffexternalityontheRecipient.

•^In ^the INFO-PRIVATEtreatment (T₂: 3 sessions, 144subjects), all subjects receive informationabout thedecision of their matched partner inStages1 and2 exactlyasin T0,butno payoff externalities are imposed.Thus, all subjects chooseagainacrossall10decisionrounds,

τ

,thepayofftheywouldliketoreceiveforthemselves(asinStage2).

•^In^theNO-INFO-SOCIALtreatment(T₃:2sessions,96subjects),neitherDictatorsreceiveinformationabouttheRecip- ients’previous decisions,nor weelicit theDictators’beliefs aboutRecipients’behavior inStages1and2.By analogy withtreatments T0 andT1,Dictators’decisionshavepayoffconsequencesfortheirmatchedRecipients.

Fig. 3 reportsthe Stage 4 userinterface for ourbaseline treatment (INFO-SOCIAL). As Fig. 3 shows, the top (bottom) screen provides information about the lottery (intertemporal) choices of Stage 1 and 2, for both the deciding subject (Player A)andherassignedpartner(PlayerB),wheretheinformationaboutthelatterreferstotheRecipient’sactualchoice (or theDictator’selicitedbelief) dependingon thetreatmentcondition. IntheNOINFO-SOCIAL(T3) treatmentthePlayer B columnishidden,inthatDictatorsmakeadecisionforthepairwithoutanyinformationontheRecipients’decisionsin Stages1and2.

3.7. Matching

Alongthedevelopmentofthisresearchproject,threearethematchingprotocolsthathavebeenused.⁹

1. RandomMatching(RM).Inthiscase,DictatorsandRecipientsarerandomlymatched,withnofurtherrestriction.

2. DissortativeMatching(DM).Inthiscase,we usedatafromStage2tocompute theaverageswitchingpointpersubject acrossall10decisionrounds,

τ

,whereaverageswitchingpointistakenasaproxyofindividualdiscounting(thehigher the switching point, the lower the discounting). We then matchthe mostpatient Dictator withthe most impatient Recipient, thesecond mostpatient Dictator withthesecond mostimpatientRecipient,andsoon.Thisdesign feature makes thatDictatorsarethemostpatientsubjectsinhalfofthecouples,toprovidesuﬃcientdispersion/variabilityin thedataminimizethepossibilityofmatchingsbetweensubjectswithverysimilartimepreferences,thusmakingsocial preferencesverydiﬃculttoidentify.

3. EﬃcientRandomMatching(ERM).Inthiscase,weimposethatconsistentDictatorsarerandomlymatchedwithconsistent Recipientswheneverpossible.Thisdesignenhanceseﬃciencyofourstructuralestimationexercise(seeSection4.1.3).

Table 1summarizesourtreatmentlayout,includinginformationonthenumberofsessions(bymatchingprotocol)and thenumberofsubjects(Dictators)ineachofthetreatments.

3.8. Financialrewards

Allsubjectsreceivee10justtoshowup.ForthepaymentofStages1and2,weselectatrandomonesubjectandone decisionpersessionforpayoff.Byanalogy,inStage3werandomlypickonesubjectandoneStage1or Stage2prediction.

Aprizeofe ¹⁰⁰îs^paidⁱⁿ^caseôfâ^correct^guess.¹⁰Âs^for^Stage^4,^we ^follow^the^same^payment^protocolâsⁱⁿ^Stage ^2:

8 AlsoRecipientsgothroughthesamesequenceofdecisions,althoughitismadeclearintheinstructionsthatRecipients’decisionshavenomonetary consequencesoneitherparty.

9 Wearegratefultotwoanonymousrefereesforexpandingthescopeofthepaperandconsideringalternativematchingprotocols.

10 This,inturn,impliesthatourbeliefelicitationprotocolisneutraltosubjects’degreeofriskaversion(seeAndersenetal.,2014a).

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Fig. 3. Stage 4 user interface (T0to T2).

Table 1

Treatmentconditions.

Cod. Treat. Info Pay. ext. #Sessions (RM/DM/ERM) #Subj. (dict.)

T0 INFO-SOCIAL Yes Yes 6 (1/2/3) 288(144)

T1 BELIEF-SOCIAL Beliefs Yes 2 (2/0/0) 96(48)

T2 INFO-PRIVATE Yes No 3 (1/1/1) 144(144)

T3 NO INFO-SOCIAL No Yes 2 (2/0/0) 96(48)

Total 13 (6/3/4) 624(384)

one matchedpairandonedecisionisselected atrandomandboth,theDictator andtheRecipient, arepaidaccordingto theDictator’schoice.

All choicesarepaid atthe endofthe experiment, whenwe randomly select2subjects perstage for thepaymentof a randomlyselecteddecision.¹¹ Theshow-up fee andthedecisions forStages1and3are paidincash on thesameday of the experiment. By contrast, we take extreme care with the payment of Stages 2 and 4, as we are concerned with the transaction costs associated with receiving delayed payments (including physical costs and payment risk). To make all choicesequivalentexceptforthe timingdimension, allpayments aremadeby wayofabank transfertothe subjects’

account.Thisistominimize transactioncostsandequalizethemacrossperiods,includingpaymentsforsubjectswho opt forthepayment“today”.¹²Thedatesofalldelayedpaymentsweresettoavoidpublicholidaysandweekends.

11 Althoughthismethodyieldsacompoundlotteryoverthevariousstagedecisions,thereexistssubstantialevidenceshowingthatthisdoesnotcreatea responsebias(see,amongothers,StarmerandSugden,1991; Cubittetal.,1998andHeyandLee,2005).

12 Werunallsessionsat10a.m.toensurethatsubjectswouldreceivethebanktransferthesamedayoftheexperimentifthiswasselectedforpayment.

Tocontrolforcredibilityinthepaymentmethod,weaddaformallegalcontractbetweenthelegalrepresentativeofthe laboratory(LINEEX)andthe subjectswhowereselectedfor payment.Thiscontractisprivatelyreceivedbythesubjectsinanenvelopandincludesaformalstatementona20%

compensationifpaymentsdonottakeplaceatthestateddate.

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Fig. 4. Aggregate behavior in the lottery tasks.

3.9. Debrieﬁng

Allsessionsendwitha(computerized)debrieﬁngquestionnaireincluding,amongothers,

1. standardsocio-demographics, such as gender, that we code usingthe dummyvariable Female that takes value 1 for females(it is 0otherwise);the rooms/householdsize ratio, RSR, astandard proxyofthehousehold wealth,together withtheself-reportedweeklybudget, WB;

2. proxiesofcognitiveability,suchasFrederick’s(2005)CognitiveReﬂectionTest(CRT),a3-itemtaskofquantitativenature designedtomeasurethe tendencyto overrideanintuitive andspontaneousresponsealternativethat isincorrectand toengageinfurtherreﬂectionthatleadstothecorrectresponse;

3. proxiesofsocialcapital drawnfromtheWorldValuesSurvey,such asself-reportedmeasures ofindividual happyness,or personalinclinationstoward trust (seeGlaeseretal.,2000)and inequality.

4. Results

Section 4.1providessummarystatisticsofourbehavioraldata,stagebystage,whileinSection4.2we performastruc- tural estimation exercise, where subjects’risk, time andsocial preferencesare framed within the realm ofa parametric welfare function consisting in a convex linear combination between the Dictator’sand the Recipient’s “selﬁsh” utilities.

Section4.1.3includesadiscussionontheconsistencyofchoicesandhowitaffectsourstructuralestimations.

4.1. Descriptivestatistics

4.1.1. Stages1and3:riskpreferences

Fig. 4 plots the relative frequencies of subjects selecting the “safe” option (A) across all 11 lotteries in Stage 1 (all treatments) andStage3 (treatmentBELIEF-SOCIAL).Fig. 4 alsoreportsoptimalchoicesunderRisk Neutrality(RN),which correspondtothelotterywiththehighestexpectedvalue(i.e.,OptionAintheﬁrst5decisionsandOptionBthereafter).¹³

AsFig. 4shows,subjectsdisplayaggregateriskaversion,inthatswitchingtoOptionBoccursataslowerpace,compared withthe RNbenchmark(p<0.001) (e.g.,HoltandLaury, 2002; HarrisonandRutström,2008).¹⁴ Asexpected, wedo not detectanysigniﬁcanttreatmentconditionsusingtheKrusall–Wallistest(p=⁰.148).¹⁵

4.1.2. Stages2and3:individualtimepreferences

Rememberthat,foreachofthe10delays,

τ

,subjectsmustidentifytheminimumamountofmoney(ifany)theywould needtoreceiveinthefutureagainsttheimmediatebanktransferofe ^100.^{Fig. 5}^summarizes^subjects’^behaviorⁱⁿ^stages

13 FigureD1inAppendixDreportsthesameinformationbymatchingprotocol.

14 Unlessotherwisestated,allreportedp-valuesarederivedfroma(two-tail)Wilcoxon–MannWhitneytestbetween-subjectandaWilcoxonsigned-rank testwithin-subject.

15 SeeEckelandGrossman (2008).

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Fig. 5. Aggregate behavior in the intertemporal task.

2(alltreatments)and3(treatmentT1),withtheverticalaxisrepresentingthe distributionof“averageswitchingpoints”, thatis,theﬁrstdecision(outofasequenceof20)forwhichsubjectsexpresstheirpreferenceforthedelayedpayment.¹⁶

AsFig. 5 shows,averageswitchingpoints decreasewithdelay (i.e.,forincreasingdelays, subjects’indifferenceinterest rategoesdown).Thisevidencecontradicts(isconsistentwith)exponential(hyperbolic)discounting,respectively.

4.1.3. Inconsistentbehavior

Tothe extent to which,in the structuralestimations ofSection 4.2, we frame subjects’behavior within the realm of speciﬁcparametricmodels(alongwithalltheimplicitauxiliaryassumptionsthatcomewiththem),weareinterestedina priorcheckonwhetherobservedbehaviorsatisﬁesbasicconsistency conditionscompatiblewithourpostulatedtheoretical setup.

IntheMPLofStage1,standardbehavioralrestrictions(namely,monotonicity,ﬁrst-orderstochasticdominanceandtran- sitivity)requirethatsubjectswhofacetheMPLofStage1satisfythefollowing

Condition1.AsubjectshouldchooseoptionAintheﬁrstrow,optionBinthelastrow,andswitchfromoptionAtoBonce –andonceonly–alongthesequence.

WealsolookalongsimilarlinesattheintertemporaldecisionsofStage2.Rememberthatweforcesubjectstoswitchat mostoncewithineach MPL,i.e.,consistencyisartiﬁciallyimposedwithin delays,

τ

,bythesameexperimental design.No furtherrestrictionisimposedby theexperimental protocolwhencomparingchoicesacross MPLs.Inthisrespect,anatural requirementiscontainedinthefollowing

Condition2.Ifa subjectpreferse ¹⁰⁰^todayâgainst âny^higherâmounte ^{x at} ^some^point

τ

inthefuture,then,forall

τ

>

τ

,sheshouldneverprefere^x<x againste¹⁰⁰^today.¹⁷

Fig. 6reportsan overviewofourdatawithregard toinconsistentbehavior, asdeﬁnedbybothconditions1and2.We consider four different categories, depending on whether subjects are in/consistent in the risk (Condition 1) and/or the time preference (Condition 2) task.As Fig. 6 shows, roughly 60% of ourpool (352 subjectsout of 624) passesboth our consistencytests,andwecannotrejectthenullthatthedistributionofin/consistentsubjectsisthesameacrosstreatments (Krusall–Wallistest,two-tail: p=⁰.98).

MotivatedbytheevidenceofFig. 6,weareinterestedincharacterizingsubjects’inconsistencybywayoftheobservable heterogeneitythat canbe inferredby thedebrieﬁngquestionnaire. Tothisaim,we ﬁrstpartitionoursubjectpoolinfour groups,dependingontheirrisk(intertemporal)in/consistency,respectively.Sinceourtwoproxiesofconsistencyarestrongly correlated (Spearman Beta=⁰.17, p<0.01), Table 2 reportsthe estimates of i) the probability of beinginconsistent in eithertaskbywayofabivariateprobitregression,wherethesetofcovariatesincludesproxiesfromthequestionnaireand

16 Ifasubjectalwayspreferstheimmediatepayment,weassignthischoicewith“option21”,whichisalsoaveragedoutinFig. 5.AppendixD2reports therelativefrequencyofchoicesinfavoroftheimmediatepaymentforeachpossibledelay.

17 Condition2isakintowhatTanakaetal. (2010)deﬁneas“time-inconsistentbehavior”.

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Fig. 6. In/consistent behavior in Stages 1 and 2.

ii) theprobability offailingatleastoneofourconsistencytests(incDUMMY)againstthesamesetofcovariatesby wayof astandardlogitregression.¹⁸Asitturnsout,bothgenderandcognitivereﬂectionplayakeyroleinourestimations.Thisis whyweincludeintheregressionsaninteractionterm,andalsoreportourestimationsbymalesandfemales.

Ourfindings suggest apositive (negative) significanteffectof Female (CRT) onthe likelihoodofinconsistentbehavior in anyofthetwo stages,asboth marginaleffectsare highly significant.Whenwe conditionour estimateson gender,we observethat CRT has asignificant(negative)effect,butonlyforfemales. Bycontrast,socio-demographicsorsocial capital proxies haveonlyamarginalimpactinall regressions.Thisisconsistentwithpreviousresultsintheliterature (take,e.g., Frederick,2005andCuevaetal.,2016).¹⁹

Oncewe haveacquiredabetter grasponthemain determinantsofinconsistentbehavior,the next–ratherdelicate – questioniswhattodowiththosesubjectswhodonotpassourconsistencytests.Thisisbecauseourbehavioralparadigm– withspeciﬁcreferencetothestructuralestimationsofSection4.2–imposesmuchstrongerconsistencyconditions,whose violationmayaffectournumericalexerciseinunexpected directions,whoseinterpretationgoeswellbeyondthescope of thispaper.Inthisrespect,ouranalysisofindividualbehaviorinStages1to3(sections4.1.4and4.2.1)followstheapproach in Dean andOrtoleva (2012) orSutter et al. (2013) in that we discard all observations frominconsistent subjects. This reduces ourdatabaseto 352subjectsout of624(56%). Asforthe analysisofDictators’choicesinStage 4(sections 4.1.4 and4.2.2),we focustheanalysisonthoseconsistent Dictatorswhosatisfy Conditions1and2.Thisreducesourdatabase to210subjectsoutof384(53%).AssomeoftheseconsistentDictatorsmighthavereceivedinformationaboutinconsistent Recipients in the INFO-SOCIAL and the INFO-PRIVATE treatments, we control for the inconsistency of Recipients in the regressionsofTable 6.Alongsimilarlines,inourstructuralestimationswealsocheckwhetherDictators’beliefsintreatment T1 satisfythesameconsistencyconditions.Table 3 summarizesthenumberofin/consistentpairsineach treatment.This includes informationaboutconsistent beliefsintreatment T₁ andconsistentDictatorsin theNO INFO-SOCIALtreatment, whereDictatorsreceivednoinformationabouttheirmatchedRecipient.

As Table 3 shows,not onlythe majorityofthepairs (210out of384,55%)is characterizedby aconsistent Dictator – somethingwealreadyknowfromFig. 6–butalsothatpairswithbothconsistentDictatorsand Recipientsarethemajority within thissubgroup (139 pairs out of 210: 66%). In treatments T0 and T2 this is partially dueto the use of our ERM matchingprotocolinsomeofthesessions(seeTable 1).

4.1.4. Socialmotivesvs.socialinﬂuence.Somepreliminaryevidence

We beginourdescriptiveanalysisofStage4bylookingatthedifferencebetweentheintertemporalchoicesinStage 2 and4, tobe interpreted asanecessary condition fortheexistence ofsocial motives/inﬂuence.Panel (a)ofFig. 7 reports the relative frequency ofrounds where thedecisions of consistentDictators inStages 4differ fromthose in Stage2. To assesstherelativeimportanceofsocialmotives/inﬂuence, Panel(b)displays,foreachtimedelay,therelativefrequencyof informed Dictators who change their choices in T0 (INFO-SOCIAL) vs. T2 (INFO-PRIVATE). Panel (c)looks directly at the focusing effectbyshowingthebehaviorintreatmentswithpayoffexternalitiesandnoinformation(T1:BELIEF-SOCIALvs.

18 ThereportedmarginaleffectsfollowtheapproachputforwardbyAiandNorton (2003)andKaraca-Mandicetal. (2012)intheestimationofmarginal effectsinnonlinearmodelsthatincludeinteractionterms.Wealsorunaprobitregression(notreportedhere)withqualitativelysimilarresults.

19 Theinterestedreaderontheeffectsofcognitivereﬂectionandgenderinintertemporalpreferencescanlook,amongothers,atBenjaminetal. (2013) andCollerandWilliams (1999).PontiandRodriguez-Lara (2015)andCuevaetal. (2016)investigateonthelinkbetweenCRTandsocialpreferences.

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I.Rodriguez-Lara,G.Ponti/GamesandEconomicBehavior105(2017)177–194187 Table 2

In/consistentbehavior:regressionresults.

Inconsistent (pooled data) Inconsistent (males) Inconsistent (females)

Stage 1 Stage 2 incDUMMY Stage 1 Stage 2 incDUMMY Stage 1 Stage 2 incDUMMY

Logit estimates

Female 0.602^∗∗∗ 0.313^∗∗ 0.905^∗∗∗

(0.137) (0.148) (0.215)

Cognitive reﬂection (CRT) −^1.022^∗∗∗ −^0.033 −^0.901^∗ −^1.015^∗∗∗ ^0.009 −^0.903^∗ −^1.719^∗∗∗ −^1.509^∗∗∗ −^3.043^∗∗∗

(0.343) (0.322) (0.486) (0.341) (0.316) (0.488) (0.358) (0.407) (0.594)

Interaction (Gender×^CRT) −^0.654 −^1.430^∗∗∗ −^2.134^∗∗∗

(0.490) (0.522) (0.767)

Weekly budget 0.002^∗ 0.002^∗ 0.004^∗∗ 0.002 −0.001 0.004 0.002 0.005^∗∗∗ 0.004

(0.001) (0.001) (0.002) (0.002) (0.002) (0.003) (0.002) (0.002) (0.003)

Room size ratio 0.158 0.175^∗ 0.288* 0.102 0.151 0.322 0.194 0.226^∗ 0.247

(0.098) (0.093) (0.171) (0.148) (0.145) (0.264) (0.139) (0.122) (0.222)

Happiness −^0.834^∗∗∗ −^0.159 −^1.013^∗∗∗ −^0.640^∗∗ −^0.407 −^0.907^∗ −^0.964^∗∗∗ ^0.015 −^1.088^∗∗

(0.218) (0.216) (0.339) (0.323) (0.329) (0.486) (0.293) (0.294) (0.478)

Trust (general social survey) −^0.494^∗∗ ^0.047 −^0.339 −^0.176 ^0.325 −^0.069 −^0.696^∗∗ −^0.065 −^0.555

(0.236) (0.274) (0.375) (0.368) (0.438) (0.567) (0.309) (0.361) (0.507)

Inequality loving −0.861^∗∗ −0.041 −0.844 −0.318 0.410 −0.262 −1.198^∗∗ −0.240 −1.288

(0.415) (0.484) (0.663) (0.663) (0.815) (1.051) (0.537) (0.607) (0.873)

Constant 0.410 −^1.174^∗∗ ^0.263 −^0.141 −^1.261^∗ −^0.317 ^1.367^∗∗∗ −^0.964 ^1.637^∗∗

(0.388) (0.475) (0.636) (0.580) (0.761) (0.951) (0.509) (0.590) (0.833)

Marginal effects

Female 0.392^∗∗∗ 0.184^∗∗∗ 0.470^∗∗∗

(0.028) (0.024) (0.029)

Cognitive reﬂection (CRT) −0.466^∗∗∗ −0.241^∗∗∗ −0.495^∗∗∗

(0.079) (0.083) (0.077)

Obs. 624 624 624 277 277 277 347 347 347

Notes.Standarderrorsinparentheses:^∗∗∗p<0.01,^∗∗ p<0.05,^∗p<0.1.

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Table 3

Numberofin/consistentpairsineachtreatment.

T0 T1 T2 T3

INFO-SOCIAL BELIEF-SOCIAL INFO-PRIVATE NO INFO-SOCIAL POOL DATA

Consistent Dictators 80 (0.55) 30 (0.62) 79 (0.54) 21 (0.43) 210 (0.55)

Consistent pairs (Dictators and Recipients) 58 (0.40) 27 (0.56) 54 (0.37) . .

Consistent Dictators, inconsistent Recipients 22 (0.15) 3 (0.06) 25 (0.17) . .

Inconsistent Dictators (or Both Inconsistent) 64 (0.45) 18 (0.37) 65 (0.45) 27 (0.56) 174 (0.45)

Number of Dictators 144 48 144 48 384

Note.ThereisnoinformationabouttheRecipientinT1(BELIEF-SOCIAL)andT3(NO-INFO-SOCIAL),butwereportinthetablethenumberofpairsinwhich consistentDictatorshaveaconsistent/inconsistentbeliefintheformertreatment.

Fig. 7. Dictators’ decisions in Stage 4.

T₃: NO INFO-SOCIAL). Further evidenceon the effect of elicitingbeliefs is presented in Panel (d),where we show how consistentDictatorsmovetheirswitchingpointintothedirectionoftheirbeliefsinStages2to4oftreatment T1.

As Panel(a)shows,whenDictatorsareprovided withinformationabouttheRecipients’decisions,changesinbehavior are morelikelyinthepresenceofpayoffexternalities (INFO-SOCIAL:50.6%vs INFO-PRIVATE:37.1%) while,intheabsence ofinformation,Dictatorstendtochangetheir behaviormorefrequentlyifbeliefsareelicited(BELIEF-SOCIAL:44.7%vs NO INFO-SOCIAL:31.4%).²⁰Panels(b)and(c)conﬁrmthispreliminaryevidencedisaggregatingourobservationsbytimedelay.

As Panel(b)shows, informedDictatorsare morelikely tochangetheir decisionwhenthe latterhaspayoffconsequences for the Recipients. Therefore socialmotives seemstronger than socialinﬂuence (p<0.004). Onthe other hand,Panel (c)

20 TableD3inAppendixDreportstheestimatedcoeﬃcientsofaprobitregressiononthelikelihoodofchangingthedecisioninStage4controllingfor Dictactors’individualcharacteristics.

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Table 4

ChoicesofDictatorsinStage4comparedwiththoseofRecipientsinStage2.

T0 T1 T2 T3

INFO-SOCIAL BELIEF-SOCIAL INFO-PRIVATE NO INFO-SOCIAL POOL DATA (a) Frequency of Recipients’ choices matched by Dictators who moved their choices in Stage 4

Choices move towards the Recipients’ choices 0.67 0.56 0.56 0.29 0.29

Recipients’ choices are perfectly matched 0.15 0.09 0.14 0.06 0.06

Choices move against the Recipients’ choices 0.18 0.36 0.30 0.65 0.65

(b) Tobit regression on the switching point in Stage 4:ϕ^τ_{P 4}= (1−α)ϕ^τ_{P 2}+α ϕ^τ_{P 3}

Estimates of alpha 0.262^∗∗∗ 0.481^∗∗∗ 0.116^∗∗∗ 0.050 0.186^∗∗∗

(0.049) (0.146) (0.027) (0.041) (0.028)

Notes.IntheTobitregression,ϕ^τ_{P k} correspondstotheswitchingpointofDictatorsinStagek= {²,4}^when^the^future^payment^is^delayedτ days.The valueofϕ^τP 3denotestheswitchingofthematchedRecipientortheDictator’selicitedbelief.Robuststandarderrors(clusteredattheindividuallevel)in parentheses:^∗∗∗p<0.01,^∗∗p<0.05,^∗p<0.1.

shows that, without information,eliciting beliefsseem to trigger social preferences, in that Dictators are more likely to changetheirchoicesintheBELIEF-SOCIALcomparedwiththeNO-INFO-SOCIALtreatment(p<0.096).²¹Thislatterevidence is in line with the idea of “focusing” put forward by Krupka and Weber (2009), where belief elicitation has a positive effectonpro-socialbehavior. Finally,Panel(d)showsthat Dictatorsbelieve thatRecipientsare moreimpatientthan they are. Interestingly, Dictatorsin the BELIEF-SOCIAL treatment seem to weight their own preferences andbeliefs aboutthe Recipients’preferencesandchooseaswitchingpointinStage4thatisroughlybetweenthetwo.Thisevidenceisperfectly inlinewithourtreatmentofsocialtimepreferences.

Inourpaper,wearenotonlyinterestedindetectingachangeofbehaviorbetweenstages2and4,butalsothedirection of such changes. One question to be addressed is then under which treatment the behavior of the Recipients is better matchedbytheirassignedDictator.InPanel(a)ofTable 4wedisaggregatetheevidenceofFig. 7(a)bylooking,bytreatment, attherelativefrequencyofDictators’choicesthat i)movetoward,ii)perfectlymatchoriii)move againsttheRecipients’

choices(belief)ofStage2(3),respectively.AsTable 4shows,withtheexceptionofT₃,aclearmajorityofchoicesinStage 4 haschangedwithrespecttoStage2inthedirectionoftheRecipients’preferences.²²

Panel(b) ofTable 4 providesa quantitative assessmenton thestatisticalsigniﬁcanceof suchchanges by estimatinga doublecensoredtobitmodel(clusteredforsubjects)bywhichtheswitchingpointofDictatorsinStage4,

ϕ

^τ_S4∈ {¹, ...,21}^, is calculatedasa convex linearcombinationbetween ownchoices inStage 2 (

ϕ

^τ_S2) andthe informationreceived orthe Dictator’selicitedbeliefs,(

ϕ

^τ_S3):

ϕ

^τ_S4

_{= (}

1

− α ) ϕ

^τ_S2

₊ αϕ

^τ_S3

₊ ε

_τ

.

AsPanel(b)shows,

α

ispositiveandhighlysignificantinalltreatmentswiththeexceptionofT₃ (NOINFO-SOCIAL),this confirming thatDictators’thresholdsmove inthedirectionofthoseoftheir groupmates,once theyknow(or theyreflect upon)theothers’timeconcerns.²³ Thiseffectseemsstrongerinthepresenceofpayoffexternalities (wheresocialmotives apply),butdoesnotvanish withoutthem,asafurther signoftheempiricalcontent ofsocialinfluence, too.Consistently with our finding in Fig. 7, the estimated

α

is the highest(lowest) in the BELIEF-SOCIAL (NO INFO-SOCIAL) treatments, respectively.Inthisrespect,framingthedecisionoftheDictatorasanexplicitchoicebetweentwoselves –whetheractual or simplyﬁctitious–seemstoworkasanecessaryconditionforadetectablechangeinbehaviorinthedirectionoftheother’s decision.WhenwelookattheintertemporalchoicesofStage4,weindeedﬁndthatDictatorsaremorelikelytofollowtheir ownchoicesofStage2intheINFO-PRIVATEcomparedwiththeINFO-SOCIAL(p=⁰.019)treatment.Similarly,Dictatorsare morelikely tofollowtheir own choicesin theNO-INFO-SOCIALcompared withtheBELIEF-SOCIALtreatment (p<0.037) (seeAppendixD3).

4.2. Structuralestimations

The estimates ofTable 4 show a signiﬁcant shift in the directionof the Recipient’sdecision, conditional upon i)the provision of some explicit information (or belief) about the latter’s decision, and/or ii) a modiﬁcation of the incentive structuretoexperimentallyinducepayoffexternalities.Theseconsiderationsnotwithstanding,theestimatesofTable 4look at our behavioral evidence on intertemporal decisions only, disregarding the information on individual risk preferences collectedinStage1.AswealreadydiscussedinSection2,thismayintroduceaconfound–namely,Dictators’heterogeneity in own risk concerns – that our own experimental design can, indeed, control for. This is the reason why we test the

21 Whendoingpairwisecomparisons,wecompute,foreachDictator,thefrequencyofroundsinwhichthedecisionwaschangedandtreateachDictator asanindependentobservation.AllourﬁndingsarerobustifwerestrictoursampletoconsistentpairsinsteadofconsistentDictators.

22 SeeFigureD3inAppendixDforthesameevidencedisaggregatedbytimedelays.

23 Theestimatedcoeﬃcientforthe NOINFO-SOCIAL treatmentmakessenseonlywithin therealmofsome “rationalexpectation”hypothesis,since DictatorsareneverinformedabouttheirmatchedRecipient’sdecision.Nevertheless,wereporttheT3estimatedcoeﬃcientforthesakeofcompleteness, andalsoforadirectcomparisonwiththatofT1,wherealsoDictatorsarenotinformed,buttheirbeliefsabouttheRecipients’decisionsareelicited.