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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.
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.
Table2
Experimentaldesign:payoffsstructurefortreatmentsinPart2.
Game Payofftoproposer Payofftoreceiver
NR 100−x x
OR 100−x 100withp=100x
0withp=100−x100
SR 100withp=100−x100 x
0withp=100x
NOR 100−x1−x2 x1+(100−x1)withp=100−xx21
x1withp=(100−x100−x1)−x12
NSR 100−x1withp=(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+(1−p)x1,thusimplying p=x2/(100−x1).
5 Thechoiceofawithinsubjectsdesignisnotcompletelyinnocentgivenourinterestinriskaversionforprosocialbehavior.Subjectsmayplayameta- gameand–forexample–increasegivinginonetreatmentandreduceitinanothertreatmentwithoutaffectingtheexpectedpayofftothemselvesor anotherplayeracrossallgames.Thesameissuewould,however,resultifallperiodsarepaid.Theonlyworkaroundwouldbetohaveone-shotdecisions.
WedecidedtofollowthedesignbyBrocketal.(2013)toallowforwithinsubjectscomparisons.Givingadditionalfeedbacktothereceiveronthechoicesin alltreatmentscanbeexpectedtonotonlyclosethemoralwiggleroom,butalsotoreducethelikelihoodthatsubjectsviewthefullgameasameta-game.
Moreover,theorderofthetreatmentsisrandomized.Ifameta-gameisplayed,wewouldthereforeexpectordereffectstobepresentwhenconsidering theindividualdata.Wedonotfindanyindicationthatsuchordereffectsexist.
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(100−x)/100theproposergets100−xmorethanthe receiver.Assuch,inequalityaversionwithrespecttofinalpayoffshasthesameimpactongivinginORandSR.However,theriskinessofownpayoffinSR shouldtypicallyleadtolowergivingrelativetoORforplayerswhoarerisk-aversewithrespecttotheirownpayoff.
8KrawczykandLeLec(2016)discusstheimportanceofefficiencyorientation.Weconcentrateonpreferencesoverownandothercertaintyequivalents, insteadofalsoconsideringefficiencyaswehavenomeasuretodistinguishbetweenownorotherriskaversionandriskaversionwithrespecttoefficiency.
9Duetoacodingerror,wemiss17observationsfortherisktaskfortheotherplayer’spayoff,thusafullcharacterizationispossiblefor124outof141 subjects.
10Thedistributionofrisk-attitudesissimilarforthosewhoendedupbeingreceivers.Inparticular,intheinformationtreatment,58receiversareRAown and12areNRAownwhichcorrespondtoRApartnerandNRApartnerbywhichwecodetheinformationaboutriskattitudesofrecipientsgiventodictators intheinformationtreatment.
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.
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.
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.
References
Agranov,M.,Bisin,A.,Schotter,A.,2014.Anexperimentalstudyoftheimpactofcompetitionforotherpeople’smoney:theportfoliomanagermarket?
Exp.Econ.17(4),564–585.
Bolton,G.E.,Brandts,J.,Ockenfels,A.,2005.Fairprocedures:evidencefromgamesinvolvinglotteries.Econ.J.115,1054–1076.
Brock,J.M.,Lange,A.,Ozbay,E.Y.,2013.Dictatingtherisk–experimentalevidenceongivinginriskyenvironments?Am.Econ.Rev.103(1),415–437.
Brock,J.M.,Lange,A.,Ozbay,E.Y.,2016.Dictatingtherisk:experimentalevidenceongivinginriskyenvironments:reply?Am.Econ.Rev.106(3),840–842.
Chakravarty,S.,Harrison,G.W.,Haruvy,E.E.,Rutstroem,E.E.,2011.Areyouriskaverseoverotherpeople’smoney?South.Econ.J.77(4),901–913.
Dana,J.,Weber,R.A.,Kuang,J.X.,2007.Exploitingmoralwiggleroom:experimentsdemonstratinganillusorypreferenceforfairness?Econ.Theory33(1), 67–80.
Dave,C.,Eckel,C.C.,Johnson,C.A.,Rojas,C.,2010.Elicitingriskpreferences:whenissimplebetter?J.RiskUncertain.41(3),219–243.
Eckel,C.C.,Grossman,P.J.,2008.Forecastingriskattitudes:anexperimentalstudyusingactualandforecastgamblechoices?J.Econ.Behav.Organ.68(1), 1–17.
Faro,D.,Rottenstreich,Y.,2006.Affect,empathy,andregressivemispredictionsofothers’preferencesunderrisk.Manag.Sci.52(4),529–541.
Fehr,E.,Schmidt,K.M.,1999.Atheoryoffairness,competition,andcooperation.Q.J.Econ.114(3),817–868.
Fischbacher,U.,2007.z-tree:Zurichtoolboxforready-madeeconomicexperiments?Exp.Econ.10(2),171–178.
Frignani,N.,Ponti,G.,2012.Riskversussocialpreferencesundertheveilofignorance?Econ.Lett.116(2),143–146.
Fudenberg,D.,Levine,D.K.,2012.Fairness,riskpreferencesandindependence:Impossibilitytheorems.J.Econ.Behav.Organ.81,606–612.
Güth,W.,Levati,M.V.,Ploner,M.,2008.Onthesocialdimensionoftimeandriskpreferences:anexperimentalstudy?Econ.Inquiry46(2),261–272.
Krawczyk,M.,LeLec,F.,2010.‘Givemeachance!’anexperimentinsocialdecisionunderrisk.Exp.Econ.13,500–511.
Krawczyk,M.,LeLec,F.,2016.Dictatingtherisk:experimentalevidenceongivinginriskyenvironments:comment?Am.Econ.Rev.106(3),836–839.
Pahlke,J.,Strasser,S.,Vieider,F.M.,2015.Responsibilityeffectsindecisionmakingunderrisk.J.RiskUncertain.51,125–146.
Rabin,M.,1993.Incorporatingfairnessintogametheoryandeconomics.Am.Econ.Rev.,1281–1302.
Rohde,I.M.,Rohde,K.I.,2011.Riskattitudesinasocialcontext.J.RiskUncertain.43,205–225.
Saito,K.,2013.Socialpreferencesunderrisk:equalityofopportunityversusequalityofoutcome?Am.Econ.Rev.103(7),3084–3101.
Schildberg-Hörisch,H.,2010.Istheveilofignoranceonlyaconceptaboutrisk?anexperiment.J.PublicEcon.94,1062–1066.