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Contents lists available atScienceDirect

Journal of Economic Behavior & Organization

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / j e b o

On the determinants of giving under risk

Jana Freundt

, Andreas Lange

DepartmentofEconomics,UniversityofHamburg,VonMellePark5,20146Hamburg,Germany

a r t i c l e i n f o

Articlehistory:

Received22September2016 Receivedinrevisedform10July2017 Accepted14July2017

Availableonline21July2017

JELclassification:

C91 D03 D63 D64 D81 Keywords:

Riskpreferences Prosocialbehavior Proceduralfairness Empathy

a b s t r a c t

Bymeansofalaboratoryexperimentweinvestigatetheroleofriskpreferencesforprosocial behavior.Modifyingthewaythedecision-makerortherecipientareexposedtorisk,our designallowstoidentifyhowriskpreferencesimpactgiving-decisions.Bymeasuringthe decision-makers’riskpreferencesregardingboththeirownaswellastherecipients’payoff, wegeneratenewinsightsintohowsocialpreferencetheoriesmayextendtoriskysituations.

©2017ElsevierB.V.Allrightsreserved.

1. Introduction

Theroleofriskanduncertaintyforpro-socialbehaviorhasreceivedsubstantialinterestintherecentliterature.Motivating examplesrangefromcharitablegivingwithuncertainimpacts,climatepoliciesdemandingcurrentgenerationstobear abatementcoststoincreasethechanceoflimitingfutureclimateimpacts,toeverydayinteractionslikeeducatingand raisingchildrentoimpacttheirfuturewell-being.Withinthebehavioraleconomicliterature,aparticularfocushasbeen setondiscussingtheroleofcomparisonsofpayoffchancesversuscomparisonsoffinalpayoffswhenexanteevaluatingthe fairnessofallocationsinthepresenceofrisk.1

Asopposedtoacomparisonofexpostpayoffs,exanteproceduralfairnessdenotesequalityofchancestowinagiven prize,irrespectiveofwhofinallyreceivesthatprizeexpost.Whenextendingsocialpreferencestoriskysituations,the proceduralfairnessofanallocationistypicallyevaluatedbyacomparisonofexpectedvaluesoflotteries(Fudenbergand Levine,2012;Brocketal.,2013;Saito,2013).Whiletheimplicitassumptionofrisk-neutralitysimplifiestheexpositionof thesemodels,italsoleavesopendifferentwaysofextendingthesemodelstocaptureriskaversion.Riskaversionmay,in fact,cruciallyimpactpro-socialbehavior.ThisargumenthasbeenpickedupinacommentbyKrawczykandLeLec(2016) andthesubsequentreplybyBrocketal.(2016).KrawczykandLeLec(2016)suggestthatgivingtoothersmaydeclineunder

Correspondingauthor.

E-mailaddresses:Jana.Freundt@wiso.uni-hamburg.de(J.Freundt),Andreas.Lange@wiso.uni-hamburg.de(A.Lange).

1 Experimentalevidencesuggeststhatbothfairnessviewsareimportanttounderstandgivingdecisionsunderrisk,seeforexampleBoltonetal.(2005), KrawczykandLeLec(2010),RohdeandRohde(2011),Brocketal.(2013).

http://dx.doi.org/10.1016/j.jebo.2017.07.017 0167-2681/©2017ElsevierB.V.Allrightsreserved.

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Table1

Experimentaldesign:lotterychoicesinPart1.

Outcomes

A B EV Std.dev.

1 52 52 52 0

2 44 68 56 12

3 36 84 60 24

4 28 100 64 36

5 20 116 68 48

6 0 136 68 68

riskaversion:intuitively,therewardofgivingdecreasesbecausethecertaintyequivalentofarisk-averserecipientissmaller underrisk.Incontrast,Brocketal.(2016)pointoutthatthissmallercertaintyequivalentmayleadtolargergivingifthe decision-makerisconcernedwithinequalityinthesenseofFehrandSchmidt(1999).Thus,thedirectionoftheimpactof riskaversionongivingcruciallydependsonhowanindividual’ssocialpreferenceinteractswithriskaversion.Theexistent literatureisinconclusiveonthisquestionanditultimatelyremainsanempiricalquestionhowriskaversionaffectsprosocial behavior.

Inthispaper,weprovideexperimentalevidencefromvariantsofdictatorgamestoclarifytheroleofriskandriskaversion forprosocialpreferences.Importantly,wegenerateseparatemeasuresofadecisionmaker’sriskaversionoverownpayoff andanotherperson’spayoffaswellastheotherperson’sownriskpreference.Arelatedliteraturehasalreadyshownthat decisionsmaydifferwhenmakingchoicesoverlotteriesforoneselfvs.onbehalfofanagent.2Havingseparatemeasuresof riskaversionallowsustoidentifytowhatextenteitherriskattitudematterswhendistributingpayoffchancesinvariants ofthedictatorgame.Inaddition,weexaminetheroleofsocialinformation.

Weshowthatbothmeasuresofriskattitudesareinformativeofprosocialbehaviorunderrisk.Whilerisk-aversedictators reducegivingwhentheirownpayoffbecomesrisky,amorenuancedpictureevolveswhenthepayoffoftherecipientbecomes risky.Wedonotfindevidencethatbelievedoractualriskaversionoftherecipientleadsthedictatortogiveless.Onthe contrary,givingparticularlydeclineswhendictatorsknoworbelievetherecipienttobenon-risk-averse.Weidentifystrong heterogeneitiesinindividualreactionstoriskingivingsituations.Byshowingtheimportanceofdifferentiatingbetweenrisk typesinsteadofconcentratingonaveragetreatmenteffectsmeasuresofaggregatebehavior,ourfindingsindicateamore complexwayhowprosocialpreferencesextendtosituationsunderrisk.

2. Experimentaldesign

Theexperimentconsistsoftwoparts:Part1elicitssubjects’riskpreferences,whilePart2confrontssubjectswithfive variantsofthedictatorgame.

InPart1,weusethesimpleriskelicitationtaskbyDaveetal.(2010)andEckelandGrossman(2008)togenerateseparate measuresofriskattitudesregardingthepayoffofthedecisionmakerhimselfaswellasthepayoffofanotherplayer.For this,subjectsmaketwodecisionsinrandomorder:oneonalotterythatdeterminestheirownpayoff,andanotherdecision onalotterythatdeterminesthepayoffofanothersubject.Forbothdecisions,subjectschoseoneoutofsix50/50-lotteries aspresentedinthefirsttwocolumnsofTable1.Lotteriesareconstructedsuchthatahigherexpectedvaluecorresponds toalargervariance(seethirdandfourthcolumnofTable1).WerefertothelotterychoicesasLownforchoicesoverown payoffsandasLotherforchoicesovertheotherone’spayoffs.Individualsareexpectedtochooselottery5or6iftheyare risk-neutralwithrespecttotheirownortheothersubject’spayoff(Lown>4orLother>4,respectively),respectively.Risk- seekingindividualsmaychooselottery6andrisk-averseindividualsmaychooselotteries1to4.3Correspondingly,wecode subjectswhochoose1through4asRAownandthosewithchoices5or6asNRAown(fornon-risk-averse)whenthelottery determinestheirownpayoff.Thosewhomaderisk-averse(non-risk-averse)choicesfortheirrandomlymatchedplayer aredefinedasRAother(NRAother).Inaddition,weaskparticipantstostatetheirbeliefaboutthemodechoiceforown payoff(referredtoasLbelief)(asinChakravartyetal.(2011)).Thistaskisconductedafterallchoiceshavebeenmadeandis incentivizedwith50centsforacorrectguess.

Part2consistsoffivedictatorgames,playedinrandomorder,summarizedinTable2.Participantsstayinthepairsfrom Part1.Beforedecisionsaretaken,arandomdrawdetermineswhoisassignedtheroleofproposerandreceiver.Playersare toldthatallgivingdecisionsarerevealedtothereceiversattheendoftheexperimentinordertoclosethe‘moralwiggle- room’(Danaetal.,2007)andthatonedecisionwillberandomlyselectedforpayment.Beforebeginningwithpart2,dictators seeasummaryoftheirownlotterychoices.Inabetweentreatmentdesign,weexploretheroleofsocialinformation:half ofthedictatorsadditionallyreceiveinformationofthe(own)lotterychoiceofthereceiver.

2Chakravartyetal.(2011)andFaroandRottenstreich(2006)findmoreriskneutralityinchoicesonbehalfofanagent,whilePahlkeetal.(2015),Agranov etal.(2014)orEckelandGrossman(2008)findtheopposite.

3Withthisinterpretationofindividuals’choiceswefollow,amongothers,Daveetal.(2010).Note,however,thatsubjectswithaverylowdegreeofrisk aversionmightalsochooselottery5.

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Table2

Experimentaldesign:payoffsstructurefortreatmentsinPart2.

Game Payofftoproposer Payofftoreceiver

NR 100x x

OR 100x 100withp=100x

0withp=100−x100

SR 100withp=100−x100 x

0withp=100x

NOR 100x1x2 x1+(100x1)withp=100−xx21

x1withp=(100−x100−x1)−x12

NSR 100x1withp=(100−x100−x1)−x12 x1+x2

0withp=100−xx2

1

InalltasksinPart2,theproposer’sendowmentequals100unitsoftheexperimentalcurrencyunit‘Taler’,whilethe receiverhasnoendowment.ThepayoffstructureofthetasksissummarizedinTable2.TaskNoRisk(NR)isastandard dictatorgame,inwhichthedictatorreceives100−xtokenswhengivingxtokenstotherecipient.IntaskOtherRisk(OR), therecipientfacesagamblebetweenwinning100or0tokenswithaprobabilityofwinninggivenbyx/100,whilethe dictatorreceives100−xtokensforsure.TaskSelfRisk(SR)mirrorsORasitgivesacertainpayoffxtotherecipient,while thedictatorreceives100or0,withthechanceofwinningbeing(100−x)/100.Whilealltreatmentscoincideinexpected valueofgiving,ORandSRintroduceriskinessintothegivingdecisionwiththeriskborneitherbytherecipient(OR)orthe dictator(SR).Asrobustnesschecks,weaddtwocomplementarytaskswhichallowforbothriskyandnon-riskygiving,i.e.

wheretheproposercanchooseherpreferredgivingchannel.TaskNORcombinesNRandORwiththedictatorreceiving 100−x1−x2,whiletherecipientreceivesatleastx1,butmayget100tokenswithprobabilityx2/(100−x1).4Analogously, taskNSRcombinesgameNRandSRbygivingtherecipientapayoffofx1+x2whilethedictatorgivesupx1forsure,but mayloseallpayoffwithprobabilityx2/(100−x1).Thatis,forachoiceofx2=0bothNORandNSRcoincidewithNR,while forx1=0thepayoffstructuresareidenticaltoORandSR,respectively.Adecision-makerthushasawiderrangeofgiving options,consistingofgivingsafetokensvs.givingchancestowininNOR,andgivingwhichdecreasesownpayoffforsure vs.givingwhichmakesownpayoffriskyinNSR.Assuch,thetypeofriskpreferencesmaynotonlydeterminehowmucha playergives,butalsothechannelthatisprimarilybeingused.

Weemployawithin-subjectdesignwhereparticipantsstaywiththesamerandomlymatchedpartnerforthewhole experiment.Aftertheparticipantscompletetheexperiment,feedbackisgivenabouttheoutcomesofthelotteriesandthe decisionsoftheproposer.Onetaskisrandomlychosenforpayment.5

Whileweareprimarilyinterestedinthedecisionsoftheproposers,weadditionallyaskreceiverstostatetheirexpec- tationsabouttheamountgiventothemineachgameand,afterallchoiceshavebeenmade,tojudgethefairnessofthe allocationtheirdictatorchoseforthem(onascale:1(veryfair)through5(unfair)).

TheexperimenthasbeenconductedattheExperimentalLaboratoryoftheSchoolforBusiness,EconomicsandSocial SciencesattheUniversityofHamburgin2013and2015.Itwasprogrammedinz-tree(Fischbacher,2007).282students oftheUniversityofHamburgparticipated in10sessionsofapproximately45minutes.Theaveragepayoffwas10.14D, instructionscanbefoundinadownloadablesupplementtothepaper.

3. Predictions

Thetreatmentsaredesignedtoinvestigatetherolethatriskaversionplayswithinprosocialpreferences.Alltreatments allowforidenticalallocationsofexpectedpayoffssuchthatexantefairnesspreferencesbasedoncomparisonsofexpected values(Brocketal.,2013)predictthesametotalgivinginalltreatments.Inotherwords,forrisk-neutralplayersweshould observenotreatmentdifferences.

4 Thispayoffstructurewasconstructedto(i)correspondtogivingx1+x2tokensinexpectation,and(ii)forthereceivertohaveasafeminimumpayoffof x1,whilewewantedtokeepthemaximumpayoffat100.Thus,theprobabilityofgetting100necessarilyisgivenbyx1+x2=p100+(1p)x1,thusimplying p=x2/(100x1).

5 Thechoiceofawithinsubjectsdesignisnotcompletelyinnocentgivenourinterestinriskaversionforprosocialbehavior.Subjectsmayplayameta- gameandforexampleincreasegivinginonetreatmentandreduceitinanothertreatmentwithoutaffectingtheexpectedpayofftothemselvesor anotherplayeracrossallgames.Thesameissuewould,however,resultifallperiodsarepaid.Theonlyworkaroundwouldbetohaveone-shotdecisions.

WedecidedtofollowthedesignbyBrocketal.(2013)toallowforwithinsubjectscomparisons.Givingadditionalfeedbacktothereceiveronthechoicesin alltreatmentscanbeexpectedtonotonlyclosethemoralwiggleroom,butalsotoreducethelikelihoodthatsubjectsviewthefullgameasameta-game.

Moreover,theorderofthetreatmentsisrandomized.Ifameta-gameisplayed,wewouldthereforeexpectordereffectstobepresentwhenconsidering theindividualdata.Wedonotfindanyindicationthatsuchordereffectsexist.

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Table3

SummaryofchoicesforlotteriesinPart1.Lown,LotherrefertothechoicesofthelotteriesinTable1whenmakingthechoiceoverownpayofforoverthe otherone’spayoff,respectively.Lbeliefstatesthesubjects’beliefsaboutthemodeinLown.

1 2 3 4 5 6 Mean

Proposers

Lown 41 27 30 13 18 12 2.9

Lother 35 28 24 9 15 13 2.84

Lbelief 53 42 30 5 7 4 2.19

All

Lown 69 55 64 29 35 29 3.01

Lother 68 55 45 19 35 26 2.9

Lbelief 101 82 55 17 18 8 2.3

Table4

SummaryofswitchingbehaviorbetweenLownandLotherinPart1.

Lown

1 2 3 4 5 6

Lother

1 36 9 2 4 4

2 11 22 9 2 3 1

3 7 21 19 7 5 3

4 4 1 11 5 2 2

5 5 1 3 3 17 2

6 5 1 1 2 3 14

BasedonaversionofthemodelbyFehrandSchmidt(1999)thatincorporatesaversiontoexpostpayoffinequality,6 Brocketal.(2013)showthatgivinginORwillbesmallerthaninNR.Forsuchpreferences,givinginSRcanbeexpectedto beevensmallerforrisk-averseplayers.7

Inpresenceofexantecomparisonsforasituationwheretherecipient’spayoffisrisky(OR),Brocketal.(2013,2016) indicatethatgivingtoarisk-averserecipientmayincreaseifthedictatorwantstoequalizecertaintyequivalents.Krawczyk andLeLec(2016)pointoutthereverseeffectthatgivingtoarisk-averserecipientmaydeclinebecauseitbecomesmore costlyforthedictatortoconvertoneunitofhiswealthintothecertaintyequivalentoftheotherplayer.8Assuch,exante preferencesbasedoncomparisonsofcertaintyequivalentsmaytheoreticallyleadtoincreasesordecreasesofgivingforrisk- aversetypes.Oppositereasoningappliesforrisk-lovingtypes.ThedifferenceingivingbetweenNRandORthusremainsan empiricalquestion.Whenthedictator’spayoffbecomesrisky(SR),boththepriceeffectaswellasanattempttoequalize certaintyequivalentswouldleadtoreducedgiving.

Wehypothesizethatourmeasureofownriskaversionhasparticularexplanatorypowerwhenconsideringthechange fromNRtoSR.Thebeliefabouttheriskaversionoftheotherplayer,however,isexpectedtomatterinORwhennoinformation isgiven,whiletherevealedrisk-attitudeoftherecipientisexpectedtodrivethetreatmentdifferencewheninformationis given.

4. Results

Thetwochoicesoverlotteriesshowonaveragemoderateriskaversion,seeTable3.Thelotterychoicesallowusto categorize141proposersasRAown(111)vs.NRAown(30).Outof124proposers,9wecode96playersasRAotherand28as NRAother.10Weusetheseclassificationstostudytheimpactongivingdecisionsintherespectivetasks.Theresultsarenot significantlyalteredwhenusingdifferentcategorizations.

6Naturally,alternativewaysofspecifyingexpostpreferencescouldleadtomodifiedresults.

7Infact,ORandSRbothleadtoexactlythesamedifferencesinpayoffswiththesameprobabilities,hencetothesameexpostinequalityforgivenx:

withprobabilityx/100thereceivergetsxtokensmorethantheproposer,whilewithprobability(100x)/100theproposergets100xmorethanthe receiver.Assuch,inequalityaversionwithrespecttofinalpayoffshasthesameimpactongivinginORandSR.However,theriskinessofownpayoffinSR shouldtypicallyleadtolowergivingrelativetoORforplayerswhoarerisk-aversewithrespecttotheirownpayoff.

8KrawczykandLeLec(2016)discusstheimportanceofefficiencyorientation.Weconcentrateonpreferencesoverownandothercertaintyequivalents, insteadofalsoconsideringefficiencyaswehavenomeasuretodistinguishbetweenownorotherriskaversionandriskaversionwithrespecttoefficiency.

9Duetoacodingerror,wemiss17observationsfortherisktaskfortheotherplayer’spayoff,thusafullcharacterizationispossiblefor124outof141 subjects.

10Thedistributionofrisk-attitudesissimilarforthosewhoendedupbeingreceivers.Inparticular,intheinformationtreatment,58receiversareRAown and12areNRAownwhichcorrespondtoRApartnerandNRApartnerbywhichwecodetheinformationaboutriskattitudesofrecipientsgiventodictators intheinformationtreatment.

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Table5

Summaryofgivingbehavior(mean(std.))andfractionofsubjectswithpositivegivinginPart2.

n All RAown NRAown RAother NRAother

141 111 30 96 28

NR x 22.46 24.79 13.83 23.72 19.29

(21.32) (21.37) (19.06) (20.05) (25.92)

x>0 71.6% 79.3% 43.3% 76% 53.6%

OR x 19.60 21.18 13.77 20.93 13.39

(22.13) (22.58) (19.67) (22.54) (21.82)

x>0 73.8% 80.2% 50% 79.2% 50%

SR x 15.11 15.15 14.93 12.85 19.79

(22.89) (20.54) (30.47) (18.07) (32.04)

x>0 56% 61.3% 36.7% 58.3% 42.9%

NOR x1+x2 24.04 25.82 17.47 24.48 20.86

(25.67) (25.95) (23.88) (24.94) (28.43)

x1+x2>0 75.2% 81.1% 53.3% 80.2% 53.6%

NOR sure x1 13.84 15.23 8.70 14.17 10.50

(17.72) (16.86) (20.07) (16.22) (16.58)

x1>0 64.5% 72.1% 36.7% 69.8% 39.3%

NOR risky x2 10.20 10.59 8.77 10.31 10.36

(15.36) (15.77) (13.89) (15.5) (17.46)

x2>0 56% 57.7% 50% 58.3% 46.4%

NSR x1+x2 24.26 25.68 19.00 22.94 23.43

(26.61) (26.33) (27.41) (22.51) (33.97)

x1+x2>0 72.3% 76.6% 56.7% 78.1% 50%

NSR sure x1 16.00 17.42 10.73 16.65 12.00

(19.21) (18.52) (21.09) (18.66) (16.88)

x1>0 65.3% 70.3% 46.7% 68.8% 46.4%

NSR risky x2 8.26 8.25 8.27 6.29 11.43

(16.2) (15.33) (19.37) (12.16) (24.6)

x2>0 39.7% 40.5% 36.7% 39.6% 28.6%

Wenotethatlotterychoicesoverownandother’spayoffaresignificantlycorrelatedasreportedinTable4.However, 54%oftheparticipantsswitchedbetweenthetwochoicesand106outof247chosethelotteryfortheotherplayerthatthey believedtobethemodechoice.11

ThesummarystatisticsfordecisionsinthedictatorgamesinPart2arepresentedinTable5.Wereportaveragegiving acrossallplayersaswellasdecisionsseparatedbyrisktypes.ComparedtothestandarddictatorgameNR,wefindthat averagegivingdecreasesfrom22.5to19.6tokensinOR,i.e.whenthepayofftotherecipientisrisky(p<0.01,Wilcoxon signed-ranktestonequalityofdistributions).Eventhoughsignificant,theeffectsizeissmallerthaninBrocketal.(2013) whichhintsattheimportanceofhavingclosedthe‘moralwiggleroom’asinKrawczykandLeLec(2010)andinlinewiththe discussioninKrawczykandLeLec(2016)andBrocketal.(2016).Riskinessofownpayoffleadstoasignificantlylargerdecline to15.1tokens(SR<NR,p<0.01;SR<OR,p<0.01).ReintroducingasafetransferoptioninNOR(24.0tokens)andNSR(24.3 tokens)stabilizestotalgivingatthelevelofthestandarddictatorgame,albeitboththesafeandtheriskytransferoptionsare used.12Itisnoteworthythatthepercentagesofplayersgivingpositiveamountsareverysimilaracrosstreatments(varying between71.6and75.2%),exceptforSR(56.0%).Thus,thedecisiontogiveornottogiveseemslargelyunaffectedbythe introductionofriskforalltypesofplayersaslongasgivingdoesnotintroduceriskonownincome.Incontrast,theshare ofsubjectswhogiveapositiveamountdecreasessubstantiallywhengivingnecessarilygeneratesrisktoownpayoff.13 Consistentwithpreviousliterature,thesetreatmentdifferencesshowthatexantepreferencesbasedoncomparisonsof expectedvaluesalonecannotexplainthedata.Conversely,thedeclineofgivingfromNRtobothORandSRisconsistent withexpostcomparisons,whileexpostpayoffinequalityàlaFehrandSchmidt(1999)asmodeledinBrocketal.(2013) cannotexplainthesignificantuseoftheriskytransferoptioninNORwhichmaytriggerdisadvantageousinequality.

Aswearemainlyinterestedinclarifyinghowriskpreferencesaffectprosocialdecisions,wenowseparatetreatment effectsdependingonriskattitudes.Interestingly,riskaversiongenerallycorrelateswithprosocialbehaviorinthestandard

11 Lbeliefdoesnothaveexplanatorypowerbeyondthedecisionsactuallytakenforothers(Lother)orforoneself(Lown)andthereforeisnotusedintheanalysis reportedbelow.

12 Interestingly,theaveragetreatmenteffectsarequiteaccuratelyanticipatedbythereceiversintherisktreatmentsasreportedinTable6.Furthermore, recipientsappeartotaketheriskintoaccountwhenevaluatingthefairnessofadictator’sallocationdecision:forexample,recipientsviewthesignificantly reducedgivinginSRrelativetoNRasonlymarginallylessfair.

13 Usingbootstrappedt-teststhattakethecardinalinformationinthedataintoaccount,wearriveatthesameconclusionsonthesignificanceoftreatment differences,exceptforthechangefromNRtoOR,whichisnolongershowntobesignificant.

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Table6

Summary(mean(std.))ofexpectations,giving,andfairnessjudgments(scale:1(veryfair)5(unfair))ofreceiversinPart2.

Treatment Expectation Giving Fairnessjudgment

(byreceiver) (byproposer) (byreceiver)

NR 17.72 22.46 3.23

(20.36) (21.32) (1.77)

OR 17.25 19.60 3.33

(22) (22.13) (1.66)

SR 14.79 15.11 3.55

(23.78) (22.89) (1.57)

NOR 22.14 24.04 3.52

(27.11) (25.67) (1.58)

NORsure 14.15 13.84

(19.87) (17.72)

NORrisky 7.99 10.20

(13.09) (15.36)

NSR 23.8 24.26 3.48

(29.46) (26.61) (1.63)

NSRsure 15.82 16

(19.14) (19.21)

NSRrisky 7.99 8.26

(16.98) (16.20)

dictatorgame:RAownplayersgive24.8tokenswhileNRAownplayersonlygive13.8(p<0.01,MW-Utest).Thatis,players whoarerisk-aversewithrespecttotheirownpayoffgivemoretootherplayersintheabsenceofrisk.Adesiretoreduce differencesofownpayoffsacrossdifferentstatesoftheworldisthereforecorrelatedwithadesiretoreducedifferences betweenpayoffsofdifferentplayers.Thisfindingisconsistentwithriskaversionbeingcorrelatedwithinequalityaversion, inlinewithfindingsonbehaviorunderaveilofignorance(e.g.,Schildberg-Hörisch,2010;FrignaniandPonti,2012).

Weidentifysubstantialheterogeneitiesintreatmenteffects.Theaveragetreatmentdifferencesareparticularlydriven byrisk-averseplayers:givingofRAownproposersdeclinesfromNRtoORandmorestronglyfromNRtoSR(NR>OR,NR>SR, OR>SR,allp<0.01,Wilcoxon).Inotherwords,notonlyriskforoneself,butalsorisktotheotherplayerresultsinreduced givingbyrisk-averseplayers.Thisfindingrelatestoa‘crowdingout’effectofsocialpreferencesifthoseareinconflictwith riskpreferencesasproposedbyGüthetal.(2008).WhenasafegivingoptionisreintroducedinNORandNSR,totalgiving stabilizesforrisk-aversetypes(RAownandRAother).Againinlinewithourhypothesesontheimpactofriskaversion, risk-averseplayersinthesetreatmentsparticularlyusethesafegivingoption(x1>x2,p<0.01,Wilcoxon).

Itisintuitivethatnon-risk-averseplayers(NRAown)arenotveryresponsivetotheintroductionofrisksinORandSR.

NRAownplayersalsouseboththeriskyandsafegivingchannelsinNORandNSRtoasimilarextent.Importantly,however, givingbyNRAotherproposersinORissubstantiallysmallerthaninNR(13.39vs.19.29tokens,p<0.1,Wilcoxon).14In contrast,givingbyRAotherproposersonlydecreasesbyasmall(insignificant)amount.Inlinewiththisobservation,the levelofgivingdiffersbetweenRAotherandNRAothertypesonlyinORandforthesurechannelinNOR,i.e.NORsure.15Risk aversionw.r.t.theotherplayer’spayoffthusupholdsgivingwhentheotherplayer’spayoffbecomesrisky.Thisfindingis consistentwiththequalitativepredictionsbasedoncomparisonofcertaintyequivalentsassuggestedbyBrocketal.(2016) whichappeartodominatethepriceofgivingeffectsuggestedbyKrawczykandLeLec(2016).

Thenon-parametricresultsalreadyindicatethatriskattitudes(asmeasuredbyourtask)areimportantdriversofprosocial actionsunderrisk.InordertoprovidefurtherevidenceonhowchangesingivingfromNRtoORandNRtoSRaredrivenby riskattitudes,werelyonlinearregressionswhicharereportedinTable7.Theseallowustoadditionallyconsidertherole thatsocialinformationabouttherecipients’riskattitudesplaysforgivingdecisions.WeuseOLSestimationswithrobust standarderrorstoexplaindifferencesingivingbetweenORandNR(GivingOR-GivingNR)inmodels(1)–(5).Ourcovariates ofinterestareriskpreferencesoverothers’payoff(RAother)andtheactualriskattitudesofthepartner(RApartner)inthe informationtreatment.Regression(6)explainsthedifferenceingivinginSRvs.NR(GivingSR-GivingNR)bytheproposers’

ownriskattitudes(RAown).

Thenegativeandsignificantconstantincolumn(1)and(2)isconsistentwiththenon-parametricresultthatNRAother participantssignificantlyreducegivingfromNRtoOR.Thiseffectisnolongervisiblein(3),indicatingthatNRAotherloses itsimpactwhenproposersadditionallygetinformationaboutthereceiver’sactualchoice.Whensocialinformationisgiven (3–5),theactualriskattitudeofthematchedpartner(RApartner)hasmoreexplanatorypower:again,thosematchedwith anon-risk-aversepartnerreducegivingsignificantly(seecolumn(5)).Importantly,andinlinewiththenonparametric results,dictatorswhobelievetheotherplayertoberisk-averse(column(2)),orknowtobematchedwitharisk-averse partner(column(5))showamuchsmallerreductionofgivingthanthanthosegivingtoanon-risk-averserecipient,even

14ThelimitedsignificancemaybepartlyduetothesmallernumberofNRAotherplayers.

15Bootstrappedt-testsagainshowverysimilarsignificancelevelsindifferencesbetweentypesandbetweentreatmentsasidentifiedbythenonparametric tests.ThedifferencebetweenNRandORisnotsignificantforRAotherandthelevelofgivinginNORsureisnotsignificantlydifferentcomparingRAother andNRAother.

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Table7

LinearregressionsofdifferencesingivingbetweenNRandOR(1–5)andNRandSR(6).

(1) (2) (3) (4) (5) (6)

Info-treatment All NoInfo Info Info Info All

Dep.Var. OR-NR OR-NR OR-NR OR-NR OR-NR SR-NR

RApartner 6.56 6.46

(1.42) (1.47)

RAother 3.10 7.83 −1.63 −1.85

(0.80) (1.34) (−0.34) (−0.40)

RAown −10.74*

(−1.76)

Constant −5.89* −10.64** −1.14 −6.28 −7.67** 1.10

(−1.84) (−2.04) (−0.34) (−1.24) (−2.48) (0.19)

Observations 124 61 63 62 70 141

R-squared 0.00 0.03 0.00 0.01 0.01 0.04

Note:Robustt-statisticsinparentheses.***p<0.01,**p<0.05,*p<0.1.Inthenoinformationtreatment,47proposersareRAotherwhile14areNRAother (column(2)).Intheinformationtreatment49proposersareRAotherwhile14areNRAother(column(3)),58receiversareRAownand12areNRAown whichcorrespondtoRApartnerandNRApartner(column(5)).

thoughinbothcases,(2)and(5),thedifferencesof7.83and6.46tokensarenotstatisticallysignificant(p=0.18andp=0.15, respectively).16Whensocialinformationisgiven,thisseemstobetakenintoaccountbyatleastafractionofsubjectsandto haveacomparableeffectastheempatheticpreferencesonbehalfoftheotherperson.Whenriskforthedictator’spayoffis introduced,column(6)ofTable7showsthatthisdoesnotchangebehaviorfornon-risk-averseplayers,whilesignificantly differentbehaviorresultsforrisk-aversedictatorswhoreducetheirgiving.

5. Conclusions

Thecomparisonofgivingdecisionsacrossourtreatmentscontributesseveralinsightsintotherolethatriskpreferences playforprosocialbehavior.Risk-averseandnotrisk-averseproposersgiveverydifferentamountsinthebaseline,indicating animportantcorrelationbetweenriskattitudesandprosocialpreferences.Whenthepayoffofthedictatorhimselfbecomes risky,thosewhoarerisk-aversereducegiving,whilenon-risk-aversedictatorsdonot.Whenthepayoffoftherecipient issubjecttorisk,dictatorswhoknoworbelievetherecipienttobenon-risk-aversereducegiving,whileamuchsmaller reductionoccurswhentherecipientisorisbelievedtoberisk-averse.

Inotherwords,wedonotfindevidencethatbelievedoractualriskaversionoftherecipientleadsthedictatortogive less.Instead,givingdeclinesinparticulartorecipientswhoarebelievedtobeoractuallyarenon-risk-averse.Whilethe observationsforriskinproposers’ownpayoffareinlinewiththeexpectationbyKrawczykandLeLec(2016)thatagents maygiveless“simplybecausekeepingthetokensismoreefficient”(p.837),theformerfindingleadsustoquestionthis reasonasthesoleexplanation.Instead,thedifferentialtreatmenteffectforORwouldbeinlinewiththeideasformulated inBrocketal.(2016)thatriskaversionoftherecipientmayleadto(relatively)highergivingifdictatorsdesiretogive aparticularcertaintyequivalenttotherecipient.However,anexclusiverelianceoncertaintyequivalentsasenteringex antepreferencesfallsshortofexplainingthedeclineingivingtonon-risk-averseagentsinORcomparedtocertainty.As such,behaviorappearstobeconsistentwithinequalityaversionw.r.t.certaintyequivalentsincombinationwithother motiveslikeefficiencyconcernsoraversiontodisadvantageousinequity.Givenourdata,wemightspeculateaboutanother interpretationforthelatterobservation:wefindthatrisk-averseagentsgivemoreinastandarddictatorgame.Ifsubjects anticipatethiscorrelationoftypes,theymaybeledtobelievethatanon-risk-averserecipientwouldnotgivethemmuch iftheroleswereswitched.Assuch,thelevelofriskaversionoftheotherplayermayserveasasignalofkindness(Rabin, 1993),therebyresultinginreducedgivingtonon-risk-aversesubjects.

Overall,theresultsindicateimportantheterogeneitiesinwhichplayersadjustprosocialbehaviorwhengivingisrisky.

Theheterogeneoustreatmenteffectsweobserveleadustoconcludethatatype-basedanalysisisofmajorimportanceinthis sortofsituations.Ourstudyprovidesevidenceontheimpactofdifferentdimensionsofriskaversiononprosocialbehavior underrisk,howeverriskpreferencesasmeasuredinourstudycannotserveasasoleexplanationfortheobservedgiving pattern.Afurtherexplorationoftheinteractionbetweenriskaversionandprosocialbehaviorappearsafruitfulavenuefor furtherresearch.

AppendixA. Supplementarydata

Supplementarydata associated with this article can be found, in theonline version, at http://dx.doi.org/10.1016/

j.jebo.2017.07.017.

16 RAownandNRAownhavenopredictivepowertoexplainthedifferencebetweenORandNR,thereforetheresultsareleftoutinTable7.

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