WHIC IS TH FAI SEX GENDE DIFFERENCE IN ALTRUISM AMES N - PDF document

WHICHISTHEFAIRSEX?GENDERDIFFERENCESINALTRUISM*JAMESANDREONIANDLISEVESTERLUNDWestudygenderdifferencesinaltruismbyexaminingamodiŽeddictatorgamewithvaryingincomesandprices.Ourresultsindicatethatthequestion“whichisthefairsex?”hasacomplicatedanswer—whenaltruismisexpensive,womenarekinder,butwhenitischeap,menaremorealtruistic.Thatis,weŽndthatthemaleandfemale“demandcurvesforaltruism”cross,andthatmenaremoreresponsivetopricechanges.Furthermore,menaremorelikelytobeeitherperfectlyselŽshorperfectlyseless,whereaswomentendtobe“equalitarians”whoprefertoshareevenly.I.IArewomenmorealtruisticthanmen?Isonesexmorefairthantheother?Iftherearesystematicdifferencesinaltruismbysex,theneconomictheoristswillseenewpredictionsfrommodelson,forinstance,charitablegiving,bargaining,andhouseholddecisionmaking.Forempiricalresearchers,suchsexdifferencesmayinuenceviewsonthecharitablededuction,intergenera-tionaltransfers,ortheallocationsamongspousesresultingfromhouseholdbargaining.Whiletheimplicationsofsexdifferencesinaltruismhavegonelargelyunexploredbyeconomists,therearesomepreliminaryindicationsthatsuchdifferencesmaybeim-portant.Duringthepastdecade,forinstance,researchershavenoticedthatmalesandfemaleshavedifferentpatternsofchari-tablegiving,witheachsexfavoringdifferenttypesofcharitiesandinuencedbydifferentfactors.1Inaddition,fundraisersforcharityhavecometorealizethesubstantialgivingpotentialoffemaledonorsandaredesigningsex-speciŽcsolicitationstrate-gies.2Policymakers,too,havenotedgrosssexdifferencesinphilanthropy,withwomenapparentlymoreresponsivetothe*WearegratefultoYannisBilias,GaryBolton,GaryCharness,MichaelConlin,RachelCroson,StevenDurlauf,CatherineEckel,ElizabethHoffman,CatherineKling,MichaelLynn,andBradleyRufeforhelpfulcommentsandconversations.WethankIsaacRischallforexpertresearchassistance.Inaddi-tion,weacknowledgetheNationalScienceFoundationforŽnancialsupport.1.Eller[1997]discussesestategiving,andAndreoni,Brown,andRischall[1999]discussannualgiving.Bothstudies,whichwillbediscussedmorelater,showsigniŽcantdifferencesinmaleandfemalegiving.2.Ithasevenbeenclaimedthat“Womeninphilanthropyisthehottesttopicinfundraisingtoday”[Panas1994].FordiscussionsoffemaledonorsseeVonSchlegellandFisher[1993],OstranderandFisher[1995],andOstrower[1995].©2001bythePresidentandFellowsofHarvardCollegeandtheMassachusettsInstituteofTheQuarterlyJournalofEconomics,February2001293 needforcharitablegiving.3Suchsystematicdifferencescouldaffecteconomists’models,dataanalyses,andresearchmethodol-ogieswheneveraltrusimmaybeafactorindecisions.Anaturalplacetolookforsexdifferencesisincontrolledlaboratoryexperiments.Whileeconomicexperimentshavefoundgreatvariationinaltruismamongindividuals,noconsensushasemergedongenderasanexplanatoryvariable.4Inpublicgoodsgames,forexample,somehavefoundall-malegroupstobemorecooperativethanall-femalegroups,andothershavefoundtheopposite.5Inultimatumbargaininggames,menandwomenwerefoundtobenodifferentintheofferstheymake,butwomenaremorewillingtoacceptunfairoffersthanmen.6Inthedictatorgame,therearealsomixedresults,withsomeŽndingnodiffer-encesbysex,whileothersŽndall-femalegroupstobemoregenerousthanall-malegroups.7Wetakeanewlookatgenderandaltruismbyaskinghowmaleandfemale“demandsforaltruism”maydiffer.Tofocusonaltruismapartfromstrategicconcerns,welookatthedictatorgame,andratherthanlookingatasinglechoiceasothershavedone,weobserveindividualgivingdecisionsondifferentbudgetswithdifferent“pricesofaltruism.”Hence,wecanidentifygenderdifferencesbasedonboththelevelsandvariationsinthepriceofgiving.Ourresultsprovideapotentialforexplainingandunifyingthevarietyofresultsinotherstudies.Inparticular,weŽndthatwhenitisrelativelyexpensivetogive,womenaremoregenerousthanmen;however,asthepriceofgivingdecreases,menbegintogivemorethanwomen.Thatis,maleandfemaledemandcurvesforaltruismcross,andmenaremoreresponsivetopricechanges.3.Onesuchinterestinggenderdifferenceoccurredduringarecessionin1991,whenwomenincreasedtheirphilanthropicgivingby2.4percent,whilemendecreasedtheircontributionsbyjustover20percent[Mixer1993].4.Forthevastvariationacrosssubjects,see,forexample,Isaac,Walker,andWilliams[1994],Andreoni[1993,1995],andAndreoniandMiller[1998].Foranexcellentandcomprehensivereviewoftheresultsongenderdifference,seeEckelandGrossman[1998].5.Brown-KruseandHummels[1993]Žndmalegroupstobemorecoopera-tive,whileNowellandTinkler[1994]Žndfemalegroupstobemorecooperative.6.SeeEckelandGrossman[1997a].Also,Solnick[1997]ŽndsnosigniŽcantgenderdifferencesinofferorrejectionrates,butdoesŽndthatsubjectsexpectfemalepartnerstobemorecooperative.7.BoltonandKatok[1995]ŽndnosigniŽcantmale-femaledifferences,whileEckelandGrossman[1997b]Žndall-femalegroupsaremorealtruisticthanall-malegroups.Experimentsbypsychologistsandothersocialscientistshave,likeeconomists,alsofoundvaryingresults,witheithersexsometimesseenasmorealtruistic.SeeEagly[1995]forareviewofpsychologyevidence.294QUARTERLYJOURNALOFECONOMICS Inaddition,menaremorelikelytobeeitherperfectlyselŽshorperfectlyseless,whereaswomentendtobe“equalitarians”whoprefertoshareevenly—aresultthatechoespsychologicalŽnd-ings.Insum,weŽndthatthequestion“whichisthefairsex?”hasacomplicatedanswer—dependingontheprice,eithersexmaybeseenasmorefair.Thenextsectionofthispaperpresentstheexperimentaldesign.Wethenpresenttheresultsinthreeparts.First,welookforevidenceofgenderdifferencesintherawdata.Nextwecharacterizethatdifferenceinaneconomicframework,andpro-videapredictivemodelofbehaviorbysex.Third,wecompareourresultswithpastexperimentalresultsongenderdifferences.ThepaperendswithadiscussionofsomeofthepotentialimplicationsofourŽndings.II.EDESIGNTheexperimentwasconductedattheUniversityofWiscon-sinandatIowaStateUniversity.Thesubjectswerevolunteersfromintermediateandupperleveleconomicscourses.Theex-perimentsatbothuniversitiesconsistedoftwoexperimentalses-sions.AtWisconsinbothsessionsconsistedof35subjects,whilethetwoatIowaStatecontained38and34subjectseach,foratotalof142subjects.Theexperimentlastedlessthananhour,andsubjectsearnedanaverageof$9.60.Weplacednoemphasisongenderwhenrecruitingorrunningtheexperiment.Thisdiffersfromotherswhocomparedall-malewithall-femalegroups.Thiswasdonetoavoidunwantedpsycho-logicalinuences,suchas“in-group”effects,andtogetapictureofthemale-femaledifferencethatwouldnaturallyoccurinanexperimentnotdesignedtotestforsuchdifferences.Asaresult,approximatelytwo-thirdsofoursubjectpoolwasmale.8TheexperimentemployedamodiŽcationofthedictatorgame.9InthisgameasubjectdecideshowtoallocateaŽxedpayoffbetweenhimselfandanothersubject,overaseriesofdifferent“budgets”ofpayoffs,withdifferentrelativepricesofown-payoffandother-payoff.Thisthenallowsustolookatindi-8.AtWisconsin49ofthe70subjectsweremale,andatIowaState46of72weremale.9.AcopyoftheinstructionsusedisgivenintheAppendix.295WHICHISTHEFAIRSEX? vidualdemandcurves,andhencediscussvariationbothwithinandacrosssubjects.Itisimportanttonotethatthisexperimentwasoriginallyconductedtoexaminewhetherpreferencesforaltruismarecon-sistentwiththeaxiomsofrevealedpreference,suchasGARP.Theresults,reportedinAndreoniandMiller[1998],indicatethatindeedasimpleneoclassicalframeworkwithwell-behavedpref-erencesforgivingcanbeusedtodescribethedata.Thispaperextendstheirworktowhetherdemandsdifferbysex.EachsessionoftheexperimentwasconductedbyŽrstassem-blingallthesubjectsinaverylargelecturehall,beingcarefultokeepsubjectsseparated.Thesubjectswerethengivenanenve-lopecontainingtheirinstructions,apencil,anda“claimcheck”withtheiridentiŽcationnumberonit.Thesubjectsusedtheclaimchecktocollecttheir“earningsenvelope”attheendoftheexperiment.Theproceduresguaranteedthatneitherthesubjectsnortheexperimentercouldlinkanyonetotheirchoices.ThesubjectsweretoldthattheirtaskwastoallocateaŽxednumberoftokensbetweenthemselvesandananonymouspersonrandomlychosenfromthegroup.Allsubjectsweregiveneightdifferentallocationproblemsandwereaskedtomakeanalloca-tiondecisionineachofthem.10Theyweretoldthattheexperi-menterwouldchooseoneoftheproblemsatrandomandcarryoutthesubject’sdecisionwithanotherrandomlychosensubjectastherecipient.Eachofthedecisionproblemsdifferedinthenum-beroftokenstobedividedandthenumberofpointsatokenwasworthtoeachsubject.Allsubjectsweregiventhesamesetofdecisionproblems,althoughtheorderoftheproblemswasran-domizedforeachsubject.Tokenswerewortheither1,2,or3pointseach,andtotaltokensavailablewaseither40,60,75,or100.Foreachdecisionproblem,subjectsweretoldtheycouldholdtokensorpassthemtotheotherplayer.SubjectsmadetheirdecisionbyŽllingintheblanksinthestatementslikethefollow-ing:“Divide60tokens:Holdat1pointeach,andPassat 2pointseach.”Finally,subjectsweretoldthateachpointearnedwouldbeworth$0.10inpayoff,hence75pointswouldearn$7.50.EachoftheeightproblemsislistedinTableI.Noticethatthevaluesofthetokenscanbeusedtocalculate10.Whileitisofinteresttosolicitaverylargenumberofdecisions,wewantedtosecurethesubjectsareasonableexpectedreturnfromeachdecision;hencethenumberofallocationproblemswaslimitedtoeight.296QUARTERLYJOURNALOFECONOMICS thesubjects’budgetsintermsofpayoffs.ConsiderBudget1.Inthiscase,transferringatokenraisestheothersubject’spayoffpoby3points,andreducesone’sownpayoffpsby1,implyingthatthepriceoftheopponent’spayoff,po,is0.33andthepriceofps,is1.Inthiswaywecanthinkofthetokenendow-mentasanincomevariable,thepriceofself-payoffastheinverseoftheholdvalue,andthepriceofother-payoffastheinverseofthepassvalue.InordertopoolthedatafromtheUniversityofWisconsinwiththosefromIowaStateUniversity,wemustbesurethatthepotentialresultsareduetogenderdifferencesandnottoinstitu-tionaldifferences.Whencomparingmeangivingforeachsexandbudget,onecannotrejectthehypothesisthatgenerosityisthesameatWisconsinasatIowaState.Thus,thesampleswerepooledforouranalysis,creatingacombinedsampleof47femalesubjectsand95malesubjects.III.RESULTSWewillreporttheresultsintwoparts.First,wewilllookattherawdataforevidenceofmaleandfemaledifferences.Second,wewillcharacterizethatdifferenceinaneconomicallymeaning-fulway,thatis,throughutility,demandcurves,andelasticity.III.A.IsThereaMale-FemaleDifference?Acrosstheeightbudgetsmenonaveragepassed$2.56(s.d.1.18)totheotherplayer,whilewomenpassedanaverageof$2.60TABLEIALLOCATIONCHOICES BudgetTokenendowmentHoldvaluePassvaluepsPricepoPrice140131.000.33260121.000.50375121.000.50460111.001.005100111.001.00660210.501.00775210.501.00840310.331.00 297WHICHISTHEFAIRSEX? (s.d.0.83).ThisdifferenceisnotsigniŽcant(t=0.24),indicatingthatonaveragemalesandfemalesareverysimilar.11Thissimplecomparisonofsamplemeansacrosstheeightbudgets,however,isquitemisleading.InTableIIweshowthechoicesacrosseachofthebudgets.Hereweexpressthebudgetsbychoosingown-payoffpsasthenumeraire,andlettingp=po/psbetherelativepriceofgivingtotheothersubjects,andlettingrealincomembethetokenendow-mentdividedbyps.Whenexaminingthemeangivingacrossindividualbudgets,weseelargedifferencesbetweenmalesandfemales.First,whentherelativepricechangesinfavorofgiving,bothmalesandfemalesincreasethepayoffpassed;however,theydosointwoentirelydifferentmanners.Menonaverageincreasetheproportionoftokensgiven,whereaswomendecreasetheproportion.Theresultingrangeofpayoffpassedisthereforelargerformalesthanforfemales.Second,neithergenderisuniformlymorealtruisticthantheother.Womenappearlessgenerousthanmenwhenthepriceofother-payoff,po,islowerthanthepriceofself-payoff,ps,whiletheoppositeholdswhentherelativepriceofgivingisgreaterthanorequaltoone.ThisdifferenceissigniŽcantwhentherelativepriceofgivingislargerthanone,andismarginallysigniŽcantwhentherelativepriceislessthanone.1211.With8budgetsand142subjects,N=1136.12.Thep-valueofaone-tailedtestis0.026forBudget1,0.07forBudget2,and0.063forBudget3.TABLEIIMEANPAYOFFTOOTHERPARTY BudgetTokenendowmentIncomempo/psAllsubjectsMalesubjectsFemalesubjectst-stat1404.001/33.794.183.011.962606.001/24.024.303.491.483757.501/24.685.004.031.534606.0011.541.361.9122.26510010.0012.522.332.9221.4266012.0021.421.211.8222.0777515.0021.711.422.2922.3584012.0030.890.671.3222.97Average2.572.562.6020.24 298QUARTERLYJOURNALOFECONOMICS FigureIillustratesthisŽndingbyshowingtheamountofincomepassedasafractionofownincome,m.Notethatmistheamountonewouldearnbypassingnothingtotheothersubject.Wecanseethatthiscurve,whichisnotaproperdemandcurve,isatterformalesthanforfemales,andthatthemalecurvecrossesthefemalecurvefrombelow.Thatis,formentheratioofpayoffpassedtoincomeismoresensitivetopricethanitisforwomen.13III.B.AnEconomicStatementoftheDifferenceOnecanconceptualizethesedifferencesbyassumingthatsub-jectshavewell-behavedpreferencesoftheformUs=Us(ps,po)overthebudgetps+ppo=m,wherepdenotestherelativepriceofgiving,po/ps,andmdenotestherealvalue(inunitsofps)ofagiventokenendowment.Thisimpliesthatwecanviewthepayoffpassed,po,asresultingfromademandfunctionpo=po(p,m).Usingthisapproach,thegenderdifferenceinpricerespon-13.Thedataforbudgetswiththesamerelativepricewerepooledforthisanalysis.Anexaminationofpayoffpassedasproportionofincomedemonstratesthatforagivenpricewecannotrejectthehypothesisthattheallocatedincomehasnoeffectontheproportionofpayoffpassed(forfemalesthep-valueis0.60atpo/ps=12,0.56atpo/ps=1,and0.98atpo/ps=2;formalesthep-valueis0.58atpo/ps=12,0.87atpo/ps=1,and0.74atpo/ps=2).FIGUREIPayoffPassedasFractionofIncome299WHICHISTHEFAIRSEX? sivenesscanbeviewedasadifferenceinthepriceelasticityofdemand.Holdingincomeconstantandcomparingtheindividualdemandsattwodifferentpricelevels,wecancalculatethearcpriceelasticityforeachindividual.Therearetwosuchpossiblecomparisons,andforbothoftheseweŽndthattheaverageofthefemalepriceelasticityissmallerthanitisformales.Atanincomeof$12.00andforanincreaseinpricefromp=2top=3,theaveragepriceelasticityformenis21.03,andthatforwomenis20.60.Atanincomeof$6.00andforapriceincreaseofp=12top=1,theresultissimilar;theaveragepriceelasticityformalesis21.12,andforfemalesitis20.70.InbothcasesthedifferenceissigniŽcant.14Whilethemaledemandonaverageiselastic,thatoffemalesisinelastic.Anotherwaytolookatsexdifferencesistoexaminethevariationwithinasubject.Acloserlookatthedata(seeAndreoniandMiller[1998])revealsthattherearethreebehavioralclustersconsistentwithbehaviorunderthreedifferentutilityfunctions.First,somesubjectschosetofree-rideandtopassnotokens;henceitislikelythattheirobjectivefunctionisoftheform,Uf(ps,po)=ps.Second,otherschosetoprovideeachparticipantwithequalpayoffs,implyingbehaviorconsistentwiththatofaLeontiefutilityfunctionUl(ps,po)=min{ps,po}.Finally,agroupofmalesallocatedtheirtokenstothepersonwiththehighestredemptionvalue,implyingthatautilityfunctionofperfectsub-stitutes,Up(ps,po)=ps+po,canrationalizetheirbehavior.Withthesethree“strong”cases,wecanexactlydescribethechoicesof47percentofthemalesubjectsand36percentofthefemales.TheremainingsubjectsdidnoteasilyŽtthesewell-knowncases.Instead,byminimizingtheEuclideandistancebe-tweentheactualbehaviorandthebehaviorpredictedbyoneofthethreeutilityfunctions,thesesubjectscanbeclassiŽedasweaklysimilartooneofthethreeutilityfunctions.TableIIIillustratestheclassiŽcationsformalesandfemales.BycombiningthestrongandweakclassiŽcations,weseeseveraldifferences.First,almosthalfthemenareselŽsh,while14.Asimplet-testrevealsthatthearcpriceelasticityissmallerformalesthanforfemaleswithap-valueof0.089whenthepriceincreasesfrom2to3,andwithap-valueof0.007whenthepriceincreasesfrom12to1.Apracticallyidenticalresultwasfoundfrom10,000independentbootstrapsamples.Forapriceincreasefrom2to3wefoundthatonly8.7percentof10,000meanfemaleelasticitieswerelargerthanthecorrespondingmeanformen.Forapriceincreasefrom12to1,only0.5percentofthemeanelasticitiesforfemalesweregreaterthanformales.300QUARTERLYJOURNALOFECONOMICS only36percentofthewomenareselŽsh.Second,menarefarmorelikelytotreatother-payoffasaperfectsubstitutetotheirownpayoff.Finally,thechoicesof54percentofthewomenresemblebehaviormostconsistentwithaLeontiefutilityfunc-tion,whileonly25percentofthemenappeartohavesuchpreferences.ThesedifferencesareshowninFigureII.Asex-pected,werejectthenullhypothesisthattheutilityfunctionclassiŽcationisindependentofgender(x[2]2=13.39,a0.001).15Inparticular,menaremorelikelytobeeitherperfectlyselŽshortomaximizetotalpayoffsofbothsubjects,whilewomenaremorelikelytoinsistonequality.Notethatwecanuseourresultstounderstandgenderdif-ferencesinotherexperimentsbyestimatingrepresentativede-mandcurvesformalesandfemales.Ratherthanestimatingasingleaggregatedemandcurve,weaggregateourownfunctionbasedontheresultspresentedabove.FromTableIIIweseethatthree“strong”functionalformsofdemandcandescribenearlyhalfofoursubjects.ThesethreeareLeontief(l),perfectsubstitutes(p),andselŽsh(f).Weassumethatpreferencesforthesesubjectsareobservedwithouterror,andforeachcasewesolveforanindividualdemandfunction,poj,j=l,p,f.Fortheestimationweassumethatsubjectsinthe“weak”Žttingcategoryhavedemandsoftheform,pow(p,m)=(12a)g2+am/p2ag1/p.16Inestimatingthisdemandfunction,we15.SimilarresultsholdwhenwelookatthedataaspresentedinTableIII.WhendeterminingwhetherthestrongclassiŽcationisindependentofgenderx[2]2=6.37,andfortheweakclassiŽcationx[2]2=8.44.16.Thatis,theunderlyingpreferencesareoftheLinearExpenditureModel(LEM)form,U(ps,po)=(ps2g1)12a(po2g0)a.ThebeneŽtofusingthisfunctionTABLEIIISUBJECTCLASSIFICATIONBYPUTILITYFUNCTIONa UtilityfunctionMaleFemaleStrongWeakTotalStrongWeakTotalSelŽsh24214571017Leontief131124101525Perfectsubstitutes81826044 a.AfemalesubjectexactlyhalfwaybetweenstrongLeontiefandPerfectsubstitutesisnotincludedinthisanalysis.301WHICHISTHEFAIRSEX? needtoappropriatelyaccountforthecharacteristicsofourdata.First,subjects’choicesarecensoredatbothendsofthebudgetconstraint,andsecond,ourdataconsistofeightdecisionsperindividual.Toappropriatelycontrolforbothofthesefeaturesofthedata,weestimatearandom-effectstwo-limittobitmodel.Finally,theerrortermwasfoundtobehetereoskedasticwhendemandswerespeciŽedinlevels.Hence,toassurehomoskedas-ticity,thedemandswereestimatedasbudgetshares.TheresultsfortheweakcategoryarereportedinTableIV.WhileallthecoefŽcientsofthemaledemandfunctionaresigniŽcant,onlythecoefŽcientonincomeissigniŽcantlydifferentfromzeroforfemales.17ComparingtheloglikelihoodfunctionsrevealsthatthecoefŽcientsformenandwomenintheweakcategoryaresigniŽcantlydifferentfromoneanother(x[5]2=34.81).Wecannowcombinetheindividualdemandcurvestoformaweighteddemandcurve.Letqkbetheproportionofsubjectsineachgroupk.Thentheweightedmaleandfemaledemandfunc-tionsare isthatitallowsustocapturepotentialgenderdifferencesinpriceaswellasincomeelasticities.17.ForallthreeregressionswecanrejectthejointhypothesisthatthecoefŽcientsequalzero:forfemalesx[2]2=6.7,formalesx[2]2=122.7,andforallx[2]2=107.7. FIGUREIIPreferenceDistribution(StrongandWeak)302QUARTERLYJOURNALOFECONOMICS po(p,m)5qwpow(p,m)1qlpol(p,m)1qppop(p,m)1qfpof(p,m).FigureIIIillustratesthetwodemandfunctionsform=100,whichcorrespondstopredicteddemandsinatraditional$10dictatorgame.18Notethatwecanrejectthehypothesisthatthedemandfunctionsarethesameformalesandfemales,withx[8]2=49.54.19Assuggestedabove,themaleandfemale“demandcurvesforaltruism”doindeedcross.Athighpricesofaltruismwomendemandmore;atlowpricesmendemandmore;andatpricesinbetweenmenandwomenareequallyaltruistic.Furthermore,therepresentativemaledemandcurveismoreresponsivetoapricechangethanthefemaledemandcurve.Notethatthereasonthatthemaledemandcurveisnotaone-to-onemappingatp=1isthatcloseto10percentofthemalesviewown-andother-payoffasperfectsubstitutes,henceacontinuumofdemandsisoptimalatp=1.III.C.ComparisontoOtherStudiesAreourŽndingsconsistentwithpriorstudiesondictatorgames?Mostotherstudieshavefoundthatsubjects,onaverage,18.Inmakingthesepredictions,onemustaccountforthecensoringofindi-vidualdemands.19.Thisisatestofthehypothesisthatthesetofparametersthatgeneratethemaledemandcurveequalsthatoffemales.TherelevantparametersaretheŽveestimatedcoefŽcientsfromtheweakdemandcurves—includingsuandse,theparameterestimatesfortheerrortermsresultingfromtherandomeffectstobitestimation—plusthethreeproportionsofsubjectsinstrongpreferencegroups.TABLEIVESTIMATESOFWEAKLEMDEMANDFUNCTIONSa MaleandfemaleFemaleMalepo(p,m)212.0310.28m p19.51 p22.4910.24m p14.90 p218.5310.32m p112.23 p(2.05)(0.05)(1.99)(2.87)(0.07)(2.85)(2.75)(0.07)(2.60)N803050lnL2195.13244.362133.36 a.Numbersinparenthesesarestandarderrorsoftheestimatesdirectlyabovethem.303WHICHISTHEFAIRSEX? giveawayabout25percentofagivenpie.20Inour$10.00dictatorgametheaveragegiftis$2.52(25.2percent),andinthe$6.00gametheaveragegiftis$1.54(25.6percent),whichsuccessfullyreplicatesearlierstudies.Next,canourresultsexplainthemixedevidenceongenderdifferencesfromotherexperiments?Whilewecanmakesomecomparison,therearemanydifferencesacrossexperimentsthatmakedirectcomparisonsdifŽcult.Inparticular,weŽndthemaximumvarianceinthebehaviorofmenwhenthepriceofaltruismisunity.Unfortunately,thisistheprevailingpriceinmanyexperiments.So,forinstance,thefactthatBoltonandKatok[1995]ŽndnosexdifferenceswhenthepriceisoneisnotasurpriseinlightofourŽnding.21NorisitinconceivablethatEckelandGrossman[1997b],comparingall-malewithall-female20.See,forexample,Forsytheetal.[1994],CasonandMui[1997],Bolton,Katok,andZwick[1998],andBohnetandFrey[1999a,1999b].21.Also,BoltonandKatok[1995]donotallowgivingtoexceed50percent,makingcomparisontoourresultsmoredifŽcult.FIGUREIIIAverageLEMDemandCurves(m=100)304QUARTERLYJOURNALOFECONOMICS groupswithapriceofone,ŽndthatwomenaresigniŽcantlymoreFinally,EckelandGrossman[1996],inasequentialgame,Žndthatwomenare,overall,morelikelytopaytopunishself-ishnessthanaremen.Inarelatedstudy,CrosonandBuchan[1999]foundthatwomenaremorelikelytorewardgenerouscontributionsinthetrustgame.ItisdifŽculttocomparedemandsforrewardsandpunishmentwithourestimatesofdemandforaltruism.However,theseŽndingsdoshowthatfemaleshavemoreofaninterestinequalityandjustice,whichisverymuchinsyncwithourŽndingthatwomenweremorelikelytobeIV.DISCUSSIONWhatdotheseresultsmeanforexperimentalresearch?First,theyindicatethattherearesystematicdifferencesbysex,andthatthesecanhaveimportantandinterestingconsequencesforeconomicbehavior.Second,theresultshaveimplicationsforex-perimentalmethodology.Inparticular,experimentersmayneedtotakegreatercareinassuringthattheirstudiesaregenderbalanced,andthatŽndingsareduetoeconomicfactorsandnotthegendercompositionoftheirsamples.Doourresultsapplyoutsideofexperiments?Anaturalplacetolookforsexdifferencesinaltruismisincharitablegiving.Foryears,publiceconomistshavebeenstudyingtheeffectofthecharitabledeductionfortaxpayers,whichactsasasubsidytolowerthepriceofgiving.Ifmenandwomenhavesystematicallydifferentpriceelasticities,thentaxpolicycouldhaveadifferentincidenceonmalesthanfemales,andoncharitieswhosedonorsmayvarybysex.Usingthe1992and1994surveysbytheInde-pendentSector,Andreoni,Brown,andRischall[1999]showthatonecanrejectthehypothesisthatsinglemenandsinglewomenhavethesamedemandfunctionsforannualgiving.InstartlingresemblancetoourresultstheyŽndthatthemaledemandforaltruismismoreelasticthanthatoffemales,andthatthetwodemandcurvescrossinawaythatresemblesFigureIabove.Similarresultsholdwhencomparingmaleandfemale“deciders”inmarriedhouseholds,wherethedecideristhespousewhoisreportedtobeprimarilyresponsibleforthecharitablegivingdecisions.Again,marriedmaledecidersarefarmorepriceelasticthanmarriedfemaledeciders.305WHICHISTHEFAIRSEX? Anotherarenaforaltruismisrestauranttipping.Theloreisthatwomentiplessthanmen.AccordingtorecentworkbyConlin,O’Donoghue,andLynn[1999],thisdependson,amongotherthings,thesizeofthebill.Theseresearchersinterviewedcustomersleavingover40restaurantsinHouston,Texas.Theresultsindicatethatpeopletendtoview15percentofthebillastheappropriatetipforaserverwhoperformswell.Asthebillsizegetslarger,however,meetingthissocialnormbecomesmoreexpensive.WhatConlin,O’Donoghue,andLynn’sdatarevealisthat,infact,thepercent-tipisadecreasingfunctionofthebillsizeforbothmenandwomenandthatmen’spercent-tipismoreresponsivetothebillsizethanwomen’s.22Allelseequal,asthebillsizeincreases,men’spercent-tipsdeclineatafasterratethanthoseofwomen.Forthetypicalmaleandfemalediners,menwilltipbetterthanwomenforsmallbills,uptoabout$27,butafterthatthewomenbecomebettertippers.ThisisperfectlyconsistentwithourŽndingsintheexperiment.V.CONCLUSIONThisstudyŽndsthat,dependingonthepriceofgiving,eithersexcanbefoundtobemorealtruistic.Whenthepriceofgivingislow,menappearmorealtruistic,andwhenthepriceishigh,womenaremoregenerous.Stateddifferently,menaremorelikelytobeeitherperfectlyselŽshorperfectlyseless,whereaswomencaremoreaboutequalizingpayoffs.ThisleadstodemandcurvesforaltruismthatcrossandthoseformenaremoreThereareseveralimportantconsequencesofthisresult.First,thisŽndingcanpotentiallyunifyaliteraturethathasthusfarbeenfracturedbyinconsistentŽndings.Byshowingthatdifferencesinaltruismdependontheprice,wecanbegintoorganizestudiesthatsometimesfoundmentobemorealtruisticandsometimeswomen.Second,thisindicatesaneedformore22.ThisŽndingwascommunicatedtousthroughpersonalcorrespondencefromtheauthors.Wedeeplyappreciatetheirwillingnesstoprovideuswithinformationthatrelatestothehypothesisofthispaper.Theestimatesarebasedonasampleof2141customers.Independentvariablesincludethebill-size,bill-sizesquared,sexofthecustomer,andsexinteractedwiththebill-size,andbill-sizesquared,ageofthecustomer,groupsize,coursesordered,alcoholcon-sumption,ratingsforqualityoffoodandservice,whethertheserverandcustomerarethesamesex,anindicatorofhowoftenthecustomerdinesatthatrestaurant,inadditiontoŽxedeffectsforeachrestaurant.Theslopeoftheestimatedresponsetobill-sizeissteeperformenforallbillsinexcessof$10.26.306QUARTERLYJOURNALOFECONOMICS attentiontosexdifferencesinexperimentaleconomics.Ifdiffer-encesappearwithrespecttoaltruism,theymayappearinotherbehavioraswell.23This,inturn,meansthatresearcherswouldbewisetoassurethattheirexperimentalŽndingsaretheresultofeconomicincentivesandnotofvaryingsexcompositionsoftheircontrolandtreatmentgroups.Therearealsopotentialapplicationsofthisresulttotherealworld.Ifsexdifferencesinaltruismaretrulypresent,assug-gestedbyevidencefromcharitablegivingandfromrestauranttipping,thenthosewhobrokerinaltruism,suchascharitiesandfundraisers,mayŽnditintheirintereststolearnmoreaboutthesedifferencesandtoexploitthemintheirenterprises.Fortaxpolicy,sexdifferenceinaltruismmayalsoindicatethattheinci-denceofthetaxdeductiontocharitymaydifferbysexaswell,withmen—andthecharitiestheyfavor—gettingagreatershareofthesubsidy.Insum,whenobservablecharacteristicsofindividualshavepredictableeffectsonbehavior,itpresentsimportantopportuni-tiesforeconomiststolearnaboutbehavior,aswellasimportantwarningsignsabouthowtocollectandanalyzedata.Thisstudygivesmoreevidencetothepropositionthatgenderdifferencesineconomicexperimentsmaybeonesuchfactorthatresearcherswillhavetoexaminemorecarefullyinthefuture.APPENDIXClaimCheckNumber WelcomeThisisanexperimentaboutdecisionmaking.Youwillbepaidforparticipating,andtheamountofmoneyyouwillearndependsonthedecisionsthatyouandtheotherparticipantsmake.Ifyoumakegooddecisions,youstandtoearnaconsider-ableamountofmoney.23.Evidenceisrisingthattherearesexdifferencesinriskaversionaswell.See,forexample,Levin,Snyder,andChapman[1988],HudgensandFatkin[1985],ZinkhanandKarande[1991],Arch[1993],andKoganandWallach[1964].RecentevidenceintheeconomicsliteraturealsosupportsthisŽnding.SeeEckeletal.[1997],JianakoplosandBernasek[1998],andPowellandAnsic[1998].307WHICHISTHEFAIRSEX? Theentireexperimentshouldbecompletewithinanhour.Attheendoftheexperimentyouwillbepaidprivatelyandincashforyourdecisions.Aresearchfoundationhasprovidedthefundsforthisexperiment.YourIdentityYouwillneverbeaskedtorevealyouridentitytoanyoneduringthecourseoftheexperiment.Yournamewillneverberecordedbyanyone.Neithertheexperimentersnortheothersubjectswillbeabletolinkyoutoanyofyourdecisions.Inordertokeepyourdecisionsprivate,pleasedonotrevealyourchoicestoanyotherparticipant.ClaimCheckAtthetopofthispageisanumberonayellowpieceofpaper.ThisisyourClaimCheck.Eachparticipanthasadifferentnum- ber.YoumaywanttoverifythatthenumberonyourClaimCheckisthesameasthenumberonthetopofpage4.YouwillpresentyourClaimChecktoanassistantattheendoftheexperimenttoreceiveyourcashpayment.Pleaseremoveyourclaimchecknowandputitinasafeplace.THISEXPERIMENTInthisexperimentyouareaskedtomakeaseriesofchoicesabouthowtodivideasetoftokensbetweenyourselfandoneothersubjectintheroom.Youandtheothersubjectwillbepairedrandomly,andyouwillnotbetoldeachother’sidentity. Asyoudividethetokens,youandtheothersubjectwilleachearnpoints.Everypointthatsubjectsearnwillbeworth10cents.Forexample,ifyouearn58pointsyouwillmake$5.80intheEachchoiceyoumakeissimilartothefollowing:Example:Divide50tokens:Hold]1pointeach,andPass]2 pointseach.Inthischoiceyoumustdivide50tokens.Youcankeepallthetokens,keepsomeandpasssome,orpassallthetokens.Inthisexample,youwillreceive1pointforeverytokenyouhold,andtheotherplayerwillreceive2pointsforeverytokenyoupass.Forexample,ifyouhold50andpass0tokens,youwillreceive50308QUARTERLYJOURNALOFECONOMICS points,or503$0.10=$5.00,andtheotherplayerwillreceivenopointsand$0.Ifyouhold0tokensandpass50,youwillreceive$0andtheotherplayerwillreceive5032=100points,or1003$0.10=$10.00.However,youcouldchooseanynumberbetween0and50tohold.Forinstance,youcouldchoosetohold29tokensandpass21.Inthiscaseyouwouldearn29points,or293$0.10=$2.90,andtheothersubjectwouldreceive2132=42points,thatis423$0.10=$4.20.Hereisanotherexample:Example:Divide40tokens:Hold]3pointseach,andPass]1 pointeach.Inthisexampleeverytokenyouholdearnsyou3points,andeverytokenyoupassearnstheothersubject1point.Again,eachpointyouearnisworth$0.10toyou,andeachpointtheothersubjectearnsisworth$0.10totheothersubject.ImportantNote:Inallcasesyoucanchooseanynumberto holdandanynumbertopass,butthenumberoftokensyouholdplusthenumberoftokensyoupassmustequalthetotalnumber oftokenstodivide.Pleasefeelfreetouseyourcalculator,oroneprovidedbytheexperimenter,tocalculatepointsandtoassurethatallofthetokenshavebeenallocated.EARNINGMONEYINTHISEXPERIMENTYouwillbeaskedtomake8allocationdecisionsliketheexampleswejustdiscussed.Wewillcalculateyourpaymentsasfollows:Afterallyourdecisionsformshavebeencollected,wewillshufetheformsandrandomlypairyourformwiththatofanothersubjectinthisexperiment.Usingatableofrandomnumbers,wewillselectoneofyourdecisionstocarryout.Youwill thengetthepointsyouallocatedinthe“hold”portionofyourdecision,andtheothersubjectwillgetthepointsyouallocatedonthe“pass”portionofyourdecision.Youwillthenbepairedagainwithadifferentsubjectintheexperiment.Thistimewewillrandomlychooseoneoftheothersubject’seightdecisionstocarry out.Theothersubjectwillgetthepointsinthe“hold”portionofthedecision,andyouwillgetthepointsinthe“pass”portion.Wewillthentotalthepointsfromthesetwopairingsanddetermineyourmonetaryearnings.Theseearningswillbeplaced309WHICHISTHEFAIRSEX? inyourearningsenvelope.Themonitorchosenatthebeginningoftheexperimentwillverifythattheseproceduresarefollowed.Afterallthecalculationshavebeenmade,anotherexperi-menterwhowasnotinvolvedintheexperimentuntilthistimewillaskyoutobringupyourclaimcheckandwillhandyouyourearningsenvelope.Thiswillagainhelptoguaranteeyourprivacy.Onthefollowingpagearethe8choiceswewouldlikeyoutomake.PleaseŽllouttheform,takingthetimeyouneedtobeaccurate.Whenallsubjectsaredone,wewillcollecttheforms.Thankyouverymuch.Goodluck)ClaimCheckNumber DECISIONSHEETDirections:PleaseŽllinalltheblanksbelow.MakesurethenumberoftokenslistedunderHoldplusthenumberlistedunderPassequalsthetotalnumberoftokensavailable.Remember,allpointsareworth$0.10toallsubjects.1.Divide40tokens:Hold@3pointseach,andPass @1pointeach.2.Divide40tokens:Hold@1pointseach,andPass @3pointeach.3.Divide60tokens:Hold@2pointseach,andPass @1pointeach.4.Divide60tokens:Hold@1pointseach,andPass @2pointeach.5.Divide75tokens:Hold@2pointseach,andPass @1pointeach.6.Divide75tokens:Hold@1pointseach,andPass @2pointeach.7.Divide60tokens:Hold@1pointseach,andPass @1pointeach.8.Divide100tokens:Hold@1pointseach,andPass @1pointeach. 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