WhyDoPeopleGive?

TestingPureandImpureAltruism*

MarkOttoni‐Wilhelm,IUPUILiseVesterlund,UniversityofPittsburghandNBER

HuanXie,ConcordiaUniversity

September2,2014

Abstract: The extant experimental design to investigate warm glow and altruism elicits asinglemeasure of crowd‐out.Not recognizing that impure altruismpredicts crowd‐out is afunctionofgiving‐by‐others,thisdesign'spowertorejectpurealtruismvarieswiththelevelof giving‐by‐others, and it cannot identify the strength of warm glow and altruismpreferences.Theselimitationsareaddressedwithanewdesignthatelicitscrowd‐outatalowandatahigh levelofgiving‐by‐others. Consistentwith impurealtruismwe finddecreasingcrowd‐outasgiving‐by‐othersincreases.Howeverwarmglowisweakinourexperimentandaltruismlargelyexplainswhypeoplegive. *WethankKongWahLai,MichaelMenietti,andLinneaWarrenwhohelpedconducttheexperiments.WethankSandi Wraith and the American Red Cross of South Western Pennsylvania for their help in facilitating ourresearch.We are grateful to BoHonoré for extending his Stata code for the two‐sided fixed‐effects censoredestimatortomodelswithvariablecensoringlevels.SeminarparticipantsatDuke,NYU,IUPUI,andStanfordarethankedforhelpfulcomments.Finally,wearegratefulforgenerousfinancialsupportfromtheResearchFundoftheIndianaUniversityLillyFamilySchoolofPhilanthropy.

1.Introduction

Earlyeconomictheoryofgivingproposedpurealtruismasthemotivationthatexplainswhypeople give to charity (Becker 1974). A donor gets utility from the charity’s output, forexample fromhelping children inneed.Donationsaremodeledas contributions toapublicgood because the donor gets utility from the charity’s increased output even if giving‐by‐others causes the increase. While a priori compelling, the pure altruism model generatesstrongpredictionsthathavebeencontradictedbyfieldevidence.Forexample,becausepurealtruism implies that a donor’s contribution and giving‐by‐others are perfect substitutes, aone dollar lump‐sum tax on a donor used to increase the public good by one dollar ispredictedtocausethedonortocontributeonedollarlesstothepublicgood(Warr1982).Incontrasttothiscompletecrowd‐outprediction, thefieldevidenceisthatcrowd‐out ismuchless‐than‐complete.1 To reconcile the theory–evidence incongruity, Andreoni (1989)proposed impure altruism: in addition to an altruistic/public good utility component, animpurely altruistic donor also gets “warm glow” utility that comes from the amount sheherself gives to the charity.Warm glow is a private good because only the donor gets thisadditional benefit from her contribution. Because impure altruism implies that a donor’scontributionandgiving‐by‐othersarenotperfectsubstitutes,anassumptionthatwarmglowisperceivedasanormalgooddeliverstheless‐than‐completecrowd‐outpredictionneededtoreconciletheorywiththefieldevidence.

Much recentwork on the relative strengths of altruism andwarm glowmotives forgivingusescrowd‐outmeasuredinlaboratorysettings.Labexperimentseliminatefundraisingresponsestogiving‐by‐others(AndreoniandPayne,2011),andofferthepotentialtocontrolthe informationeachdonorhas about the level of giving‐by‐others (Vesterlund, 2006).Therecent experimentalwork has produced awide range of crowd‐out estimates from zero tocomplete, though themajorityof experiments find less than complete crowd‐out and rejectpurealtruism(Andreoni1993;BoltonandKatok1998;Chan,Godby,Mestelman,andMuller2002; Sutter andWeck‐Hannemann 2004; Eckel, Grossman, and Johnston 2005; Gronberg,Luccasen,Turocy,andVanHuyck2012).Rejectingpurealtruism, impurealtruismhasbeenacceptedasthestandardmodelofcharitablegiving.

However, we argue that the experimental approach in this literature has twofundamental limitations. First, previous experiments measure crowd‐out around one, andonly one, exogenous level of giving‐by‐others. However, theoretical analysis of the impurealtruismmodel indicates that the degree of crowd‐out depends on the level at which it ismeasured.Inthelimitasgiving‐by‐othersmovesfromalowleveltoasufficientlyhighlevel,motivesatthemarginshiftfromimpurealtruismtowardpurewarmglow.Equivalently,inthelimit crowd‐out decreases toward zero (Ribar and Wilhelm 2002; Yildirim 2014). Hence,

1 For reviews of the literature on crowd-out measures see Steinberg (1991), Khanna, Posnett, and Sandler (1995), Kingma (1989), Okten and Weisbrod (2000), Payne (1998), Ribar and Wilhelm (2002), Vesterlund (2006, 2014). Andreoni (1988), Bergstrom, Blume, and Varian (1986), and Warr (1983) provide additional examples of the discrepancies between the theoretical predictions of the pure altruism model and field evidence.

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whetherornotacrowd‐outtestrejectspurealtruismdependsonthelevelofgiving‐by‐othersatwhichthetestisconducted.Furthermore,althoughthewarmglowpreferencecomponentis the source of incomplete crowd‐out, a single measure of the magnitude of incompletecrowd‐outcannotidentifythestrengthofwarmglowpreferences.Itisnecessarytomeasurecrowd‐outaroundmorethanonelevelofgiving‐by‐otherstoidentifywarmglowandaltruismpreferences. Second,becauseimpurealtruismwasintentionallydesignedtogeneratethepredictionof incomplete crowd‐out, and thereby reconcile theory with the pre‐existing evidence ofincomplete crowd‐out, it is not convincing to produce additional evidence of incompletecrowd‐out and conclude that the additional evidence establishes impure altruism as the“correct”model.Inshort,impurealtruismhasbeenacceptedasthestandardmodelofgivingbecause itpredicts the comparative static itwasdesigned topredict.With impurealtruismbeingtheacceptedmodelofcharitablegivingitisessentialthatitbesubjectedtoatestthatatleastinprincipleitcanfail.

In this paperwe address both limitations.We introduce a newexperimental design,useittoestimatecrowd‐outatalowandatahighlevelofgiving‐by‐others,anddemonstratethatthepowertorejectpurealtruismdependsonthelevelofgiving‐by‐othersatwhichthehypothesis is tested.We also develop a set of conditions onpreferences sufficient to implythat as giving‐by‐others increases, crowd‐outdecreasesmonotonically, not just in the limit.Under these conditions the impure altruism model generates a testable prediction, apredictionthat itwasnot intentionallydesignedtohave.Usingourtwomeasuresofcrowd‐outwecandirectlytestthedecreasingcrowd‐outpredictionoftheimpurealtruismmodel.

The innovation in thenewexperimentaldesign is to carefully control theexogenouslevelofgiving‐by‐others,astheorysuggestsisnecessarytoidentifyaltruismandwarmglowpreferences.Wedothisbycreatinganindividualizedcharity:eachparticipantispairedwithachild between 1 and 12 years old whose house has suffered extensive fire damage. Theparticipant can give through the experiment to the American Red Cross of SouthwesternPennsylvaniawhichwillusethedonationtobuybooksforthechild.Thebookswillbeusedbyvolunteersatthesceneofthefireasabridgetobeginhelpingthechildcopewiththedisaster.Weastheexperimentersaretheonlyexogenoussourceofgiving‐by‐otherstoprovidebooksforthechild.Bycarefullycontrollingthelevelofthepublicgoodexogenouslygiven‐by‐otherswhileatthesametimeexaminingcontributionstoanactualcharity,theindividualizedcharitydesigncloselycapturesthetheoreticalframeworkofimpurealtruism.

Finally, we use the crowd‐out measurements at the two levels of giving‐by‐others,alongwithincomeeffectsmeasuredatthetwolevelsandanadditionalmeasureofunfundedcrowd‐out, to estimate a structural model of impure altruism. The structural model yieldsestimatesofpreferenceparameters,oneforaltruismandoneforwarmglow,andweusethepreferenceparameterstoassesstherelativestrengthsofaltruismandwarmglowonaveragefor the participants in the experiment. Furthermore, we estimate the structural model foreachindividualtodescribetheheterogeneityinmotivesacrosstheparticipants.

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There are four results from the experiment. First, the experiment provides the firstevidence that crowd‐out depends on the level of giving‐by‐others at which crowd‐out ismeasured. At the low level of exogenous giving‐by‐others to provide books for the childcrowd‐outis97percent,essentiallycomplete,butatthehighlevelofgivingbyotherscrowd‐out is82percent.Hadwe followedtheprevious literatureandmeasuredcrowd‐outonlyatthelowlevelofgiving‐by‐others,wewouldhaveconcludedthatpeoplegivebecauseofpurealtruism.If,however,wehadsetgiving‐by‐othersatthehighlevel,wewouldhaveconcludedthatpeoplegivebecauseofimpurealtruism.2Second,thedecreaseincrowd‐outfrom97to82percentisstatisticallysignificant,andhencetheimpurealtruismmodelpassesthetestbasedon the new comparative static prediction. Third, although impure altruism passes the newtest—specifically, that in addition to the altruism component thewarmglow component ofutilityisnecessarytoexplaintheexperimentaldata—thestructuralmodelindicatesthatthewarmglowmotiveisrelativelyweak:onaveragethewarmglowparameterislessthanone‐twentieth the size of the altruism parameter. Fourth, the individual‐specific preferenceparametersindicatethatninepercentoftheparticipantsweremotivatedonlybypurewarmglow,whiletheremainingparticipantswereroughlyequallysplitbetweenpureandimpurealtruists. Among most of the impure altruists, altruism is stronger than warm glow.Consequently,altruismaccountsforthelargemajorityofcontributionsintheexperiment.

The findings are significant for four reasons. First, although there likely are severalreasonswhypreviousexperimentshavegeneratedarangeofdifferentcrowd‐outestimates,our results provide an experimental validation of a theoretically‐grounded reason for thedifferences. More importantly,because theresultsdemonstrate thatcrowd‐outdependsonthe level of giving‐by‐others, experiments using crowd‐out measurements to identify therelativestrengthsofaltruismandwarmglowpreferencesneedtomeasurecrowd‐outaroundmore than one level of giving‐by‐others. Second, the results enable the first test of thestandardeconomictheoryofcharitablegivingbasedonapredictionthatwasnotintentionallydesignedintothemodeltobeginwith.Third,theresultsarethefirstdescribingheterogeneityacrossindividualsintheirdualaltruismandwarmglowmotivestogive.Finally,theevidenceindicatingthestrengthofaltruismisimportantnotonlybecausetheexistenceofaltruismisafundamental question about humanbehavior, but also because results from somepreviousexperiments have been taken to imply that warm glow is the predominant motivation ofgiving(e.g.,Eckel,GrossmanandJohnston2005;CrumplerandGrossman2008).Tobesure,wedonotinterpretourfindingstosuggestthataltruismmotivatesgivingtoalltypesofnon‐profit organizations, but rather as a demonstration that there are charitable givingenvironmentswherealtruismisthepredominantexplanationofwhypeoplegive.

2Orbecauseofpurewarmglow,aswewillexplaininthenextsection.

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2.TheoryandBackgroundWe follow Becker (1974), Bergstrom, Blume, and Varian (1986), and Andreoni (1990) inderivingdemandcurvesofgivingfromthepureandimpurealtruismmodels.Understandinghowthetwomodelsworkisfacilitatedbyfocusingontheirincomeeffects.Foreachmodelthedemand curve contains two income effects, onewith respect to own income and onewithrespect to giving‐by‐others. The central prediction of pure altruism is that the two incomeeffects are equal, which implies that balanced‐budget crowd‐out is complete. Impurealtruism’swarmglowcomponentcreatesadifferencebetweenthetwoincomeeffects,whichimpliesthatbalanced‐budgetcrowd‐outisincomplete.

This section makes three points. First, previous experiments test pure altruism’scentralpredictionthatbalanced‐budgetcrowd‐outiscompletebymeasuringbalanced‐budgetcrowd‐outaroundasinglelevelofgiving‐by‐others.Althoughasinglemeasureofcrowd‐outissufficient to test pure altruism, we will show that the power to reject pure altruism willdependonthelevelofgiving‐by‐othersatwhichthetestisconducted.Furthermore,asinglemeasure of crowd‐out cannot identify the relative strengths of altruism and warm glowpreferences. Second, experimental findings of incomplete crowd‐out are akin to theincomplete crowd‐out evidence from field studies thatmotivated the design of the impurealtruism model. As such, previous experiments do not provide qualitatively new evidencesupporting impure altruism, other than evidence of the comparative static impure altruismwasdesignedtohave.Third,usinginsightsfromimpurealtruism’sasymptoticproperties,wederiveanewtestoftheimpurealtruismmodel.Thetestisdirect—meaningthatitpositionsimpurealtruismasthenull,ratherthanasthealternative—andisbasedonapredictionthatimpurealtruismwasnotintentionallydesignedtohave.

In the pure altruism model individual i derives utility , from privateconsumptionxi,andfromthecharity’soutputG,apublicgood(Becker1974). ∑ isthe sumof the charitable giftsbyall individuals. Settingprices toone, individual i’s budgetconstraintis ,wheregiishergifttothecharityandwiisherownincome.Giving‐

by‐others to the public good, ∑ , added to both sides of the budget constraint

yields: . The term on the right‐hand side of the budget constraint, ownincome plus giving‐by‐others, is i’s social income: Zi ≡ wi + G‐i. Assuming that ∙,∙ iscontinuousandstrictlyquasi‐concave,andthat i’soptimalgiftgi*>0, results in thebindingfirst‐ordercondition: , , 0.i’spreferredprovisionofthepublicgoodisgivenbythefollowingcontinuousdemandfunction:

G*=q(wi+G‐i) (1)

Thedemandfunctionq(.)istheEngelcurveforthepublicgood,andisafunctionofonlyoneargument (social income) implying that i’s own income and giving‐by‐others are perfect

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substitutes. The two income effects with respect to own income and giving‐by‐others arethereforeequal:dG*/dwi=dG*/dG‐i≜q1.3

Pure altruism’s dG*/dwi = dG*/dG‐i prediction has been subjected to extensiveexperimentaltesting.Testinghastypicallybeenconductedintermsoftheindividual’sgiving:

gi*=−G‐i+G*=−G‐i+q(wi+G‐i) (2)

whichimplies:

dgi*=−dG‐i+q1[dwi+dG‐i]. (3)A one dollar decrease in own income accompanied by a one dollar increase in giving‐by‐others, dwi= −dG‐i, is balanced‐budget from i’s perspective because social income isunchanged.Withnochange insocial incomethere isnochange in i’spreferredprovisionofthepublicgood(G*),butbecausegiving‐by‐othershasincreasedbyonedollar,i’soptimalgiftto decrease by exactly one dollar. In otherwords, balanced‐budget crowd‐out is complete:

| ≜∗

| 1,adirectimplicationofpurealtruism’spredictionthatthe

twoincomeeffectsareequal.Thefirstcrowd‐outtestswerenotexperimental,butrathereconometricfieldstudies

thatestimatedhowmuchgivingbyindividualstocharitiesdecreasesinresponsetochangesingovernmentspendingtargetedtowardsthesamepurposeasthecharityoutput.Extensiveeconometric evidence of what may be seen as a measure of unfunded crowd‐out—

| ≜∗

| 1 — was so much less than complete that no reasonable

magnitudeof theown incomeeffectq1 could reconcile theeconometric evidencewithpurealtruism(seetheworkcitedintheIntroduction).

The econometric field studies’ rejection of pure altruism led Andreoni (1989) toproposetheimpurealtruismmodel,specificallytoproduceamodelthatwouldbe“consistentwith empirical observations” (also see Corners and Sandler, 1984 and Steinberg, 1987).Impurely altruistic utility is , , , where now gi affects utility both from increasingprovisionofthepublicgoodG,andfromgeneratingaprivatewarmglowbenefitforthedonor.Thewarm glow component produces a secondmarginal‐benefit‐of‐giving term in the first‐ordercondition(andusing ):

, , , , , , 0. (4)

TheEngelcurveforthepublicgoodderivedfromthefirst‐orderconditionisnowafunctionoftwoarguments,socialincomeandgiving‐by‐others: 3 This statement holds as long as i’s gift is strictly positive, as we assume to be the case. Bergstrom, Blume, and Varian (1986) derive the comparative statics when some individuals are at corner solutions gi

* = 0.

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∗ , (5)IntheimpurealtruismmodelthetwoincomeeffectswithrespecttoownincomedG*/dwi≜q1andgiving‐by‐othersdG*/dG‐i≜q1+q2 arenotequal. q2 is thedifferencebetween the twoincomeeffects=dG*/dG‐i−dG*/dwi.

In terms of the individual’s giving, predictions of crowd‐out in the impure altruismmodelarechangedaccordingly.Equation(5)implies:

gi*=−G‐i+q(wi+G‐i,G‐i) (6)

and

dgi*=−dG‐i+q1[dwi+dG‐i] +q2dG‐i (7)Thebalanced‐budgetcrowd‐outtestwheredwi=−dG‐istillneutralizestheown‐incomeeffect,q1,butdoesnotneutralize thedifferencebetween the two incomeeffectsq2: |

1 . Aonedollardecrease inownincomeaccompaniedbyaonedollar increase inthegiving‐by‐otherschangesi’spreferredprovisionlevelofthepublicgoodbytheamountq2.Tosecure thepredictionof incompletecrowd‐outseen inthe fieldstudies,q2 isassumedtobepositive. If q1 > 0, q2 > 0 and q1 + q2 < 1, then at themargin both altruism andwarm glowinfluencegiving(Andreoni1989).Themodelreducestothepurealtruismmodelifq1>0andq2=0.Themodelreducestoapurewarmglowmodelifi’spreferredlevelofthepublicgoodincreasesdollar‐for‐dollarwiththeunfundedamountprovidedbyothers:dG*/dG‐i q1+q2=1;hence,ifindividualsaremotivatedatthemarginbywarmglowonly(noaltruism),crowd‐outinresponsetoanunfundedincreaseinG‐iis | 1 0.

Previousexperimentstestpurealtruism’spredictionthatbalanced‐budgetcrowd‐outiscomplete(H0: | =1 ⇔H0:q2=0).Asarepresentativeexample, inadictator

gamewherebothdecisionmakerandrecipientarelaboratoryparticipants,BoltonandKatok(1998) use two treatments to measure balanced‐budget crowd‐out: (1) the initialexperimentalendowmentis$18forthedecisionmakerand$2fortherecipient,and(2)theendowment is $15 for thedecisionmaker and$5 for the recipient.Hence, balanced‐budgetcrowd‐out isbeingmeasuredatG‐i = $2.The results are thatbalanced‐budget crowd‐out isincomplete ( | = .737), and Bolton and Katok conclude that the participants in

theirstudyareimpurealtruists.Otherexperimentshavealsomeasuredcrowd‐outatasinglelevel of giving‐by‐others and have produced a wide range of balanced‐budget crowd‐outestimates.Most,thoughnotall,rejectpurealtruism.4

4 Andreoni(1993)finds.715balanced‐budgetcrowd‐out,andrejectspurealtruism.Gronberg,Luccasen,Turocy,andVanHuyckobtainalargermagnitudecrowd‐out(.90),butstillrejectpurealtruism.Chan,Godby,Mestelman,andMuller (2002)obtain .96 crowd‐outor .67 crowd‐outdependingon the sizeof the lump‐sum taxused tomeasure crowd‐out. Eckel, Grossman and Johnston (2005) obtain zero crowd‐out or complete crowd‐out

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Our first point is that the power to reject pure altruism, under an impure altruismalternativehypothesis, dependson the levelof giving‐by‐others aroundwhich crowd‐out ismeasured. Furthermore, because previous experiments have measured crowd‐out aroundone, and only one, level of giving‐by‐others, their crowd‐out measures cannot be used toidentify the relative strengths of altruism andwarm glow preferences. Understandingwhybegins with the asymptotic comparative statics of impure altruism: under fairly weakconditionsonpreferences(concaveutilityandstrictlyoperativewarmglowatalllevelsofG)asgiving‐by‐othersG‐i→∞⇒q1+q2→1;thatis,theimpurealtruismmodelconvergestoamodelwhere,atthemargin,givingismotivedbypurewarmglow(RibarandWilhelm2002).5Animplicationisthatcrowd‐outasymptoticallydecreasesand,obviously,thatcrowd‐outisafunctionofG‐i.ToillustrateconsidertheCobb‐Douglasimpurealtruismutilityfunction: U(xi,G,gi)=(1−α−β)lnxi+αlnG+βlngi. (8)Figure 1 plots q2 (=dG*/dG‐i − dG*/dwi) and balanced‐budget crowd‐out ( |

∗

| as functionsofG‐i forCobb‐Douglas impurealtruismparameterizedsothat

altruismisrelativelystrongcomparedtowarmglow:α=.40andβ=.10.AsFigure1makesclear,asgiving‐by‐othersincreasesthegapbetweenthetwoincomeeffects(q2)increasesandcrowd‐out decreases.Because the crowd‐out effect size depends onG‐i, the power to rejectpurealtruism(H0: | =1⇔H0:q2=0)alsodependsonG‐i.

dependingonhowthelump‐sumtaxationisframedtotheparticipants,andinterprettheirresultsassupportingpure warm glow. Sutter and Weck‐Hannemann (2004) obtain complete crowd‐out and cannot reject purealtruism. Experiments using the linear voluntary contribution mechanism have produced a similar range ofresults(Anderson,GoereeandHolt1998;Goeree,HoltandLaury2002;cf.PalfreyandPrisbrey1996,1997).5 In addition there are several technical conditions: utility is twice continuously differentiable, has strictly positive first derivatives, UG is finite for all gi > 0, the second derivatives of U(.,.,.) with respect to the two private goods xi and gi are finite for all levels of G, and Uxx − 2Uxg + Ugg is bounded away from zero (again, for all levels of G). The assumption that warm glow is operative also is needed to secure that the impure altruism model, in contrast to the pure altruism model, can predict individual giving in a large economy (Andreoni, 1989). As in Andreoni (1989) it is also assumed that the giving-by-others is addressing a need, through the charity, that itself remains constant.

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To see that a single crowd‐out measure cannot identify the relative strengths ofaltruismandwarmglowpreferences,consideranexperimentthattakesasinglemeasureofcrowd‐outaroundonelevelofgiving‐by‐others,sayG‐i=$10,andfindscrowd‐outouttobe | =.80.Thisresultwouldbeconsistentwiththeα=.40,β=.10preferencesthat

generated Figure 1. However, this result is also consistent with infinitely many α, βparameterizations of Cobb‐Douglas impure altruism. Of these infinitely manyparameterizations,Figure2plotsbalanced‐budgetcrowd‐outasafunctionofG‐iforthree:therelativelystrongaltruismfromFigure1(α=.40,β=.10),altruismandwarmglowatroughlythesamestrength(α= .32,β= .40),andrelativelystrongwarmglow(α= .09,β= .70). Allthreehave | =.80atG‐i=$10.Hence,altruismandwarmglowpreferencescannot

beidentifiedfromasinglemeasureofcrowd‐out.Theunderlyingreasonisthatonemeasureof crowd‐out—equivalently, one income effect—is insufficient to identify two preferenceparameters.

= .40 = .10 = .4 = .1

q2

| dG-i = dwi |

0.2

.4.6

.81

q 2, |

d

G-i

= d

wi |

0 20 40 60 80 100Giving by others (G-i)

Difference between the two income effectsBalanced-budget crowd-out

Notes: The Cobb-Douglas parameters are = .40 and = .10. U = log(G) + log(gi) + (1 - - ) log(xi). Income is held constant at wi = $40.

Figure 1. Cobb-Douglas q2 and balanced-budget crowd-outas giving by others (G-i) increases.

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Our second point is that although most of the previous experimental evidencewarrants rejection of the pure altruism null hypothesis, there are two reasons why theevidencedoesnotofferqualitativelynewsupportofimpurealtruism.First,apurewarmglowmodelisalsoconsistentwithincompletecrowd‐out.ContinuingtheexampleinFigure2purewarmglowpreferences(α=0,β=.80)wouldbeconsistentwithevidencethat | =

.80atG‐i=$10.Moregenerally,rejectionofanullhypothesisdoesnotimplyacceptanceofanyspecificalternative.Second,toreconciletheorywithpre‐existingfieldevidenceofincompletecrowd‐outitwasassumedintheimpurealtruismmodelthatq2>0(implying | <

1), hence it is not convincing to produce additional evidence of incomplete crowd‐out andclaimthattheadditionalevidenceisaqualitativelynewtestofthetheory.6 Our third point is that impure altruism’s asymptotically decreasing crowd‐outprediction suggests a qualitatively new test of impure altruism. Going from asymptoticallydecreasingcrowd‐outasG‐i→∞ toa comparativestatic testable inanexperiment requiresconditionsonpreferencessuchthatdecreasingcrowd‐outismonotonic.Underthefollowingconditions impurealtruismpredictsdecreasingcrowd‐outwhen increasingG‐ibetween two

finitelevels and :

6 The evidence of incomplete crowd-out generated by experiments adds to our knowledge by confirming that incomplete crowd-out is an attribute of preferences. Although the evidence of incomplete crowd-out generated by field studies could be attributed, at least in part, to other phenomena (e.g., institutional features, donors’ lack of information, or unobserved influences on giving), the field evidence was deemed sufficiently informative about preferences to lead theorists to propose impure altruism.

= .40, = .10

= .32, = .40

= .09, = .700

.2.4

.6.8

1

Ba

lanc

ed-

bud

get c

row

d-o

ut, |

d

G-i

= d

wi |

0 10 20 40 60 80 100Giving by others (G-i)

Notes: U = log(G) + log(gi) + (1 - - ) log(xi). Income is held constant at wi = $40. From the single measure of crowd-out | dG-i = dwi | = .80 at G-i = $10 it is possible to make multiple inferences about the relative strengths of altruism ( ) and warm glow ( ) preferences. Three such inferences are displayed: altruism strong relative to warm glow ( = .40, = .10), altruism and warm glow at roughly the same strength ( = .32, = .40), and altruism weak relative to warm glow ( = .09, = .70).

Figure 2. A single measure of balanced-budget crowd-out cannotidentify altruism and warm glow preferences.

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PROPOSITION1.Considera concave impurelyaltruisticutility function,withstrictlyoperativewarm glow, and that satisfies the technical conditions described in footnote 5. Further, ifutility is additively separable with positive third derivatives, then q2 is monotonicallyincreasinginG‐i.7Proof:Differentiatingthefirst‐ordercondition(4)withrespecttoG‐iyields:

q2=(UgG+Ugg+Ugx)/(Uxx+Ugg+UGG−2UGx−2Ugx+2UgG) (9)whichforadditivelyseparableutilityfunctionsreducesto: q2=Ugg/(Uxx+Ugg+UGG). (10)DifferentiatingthesecondderivativeswithrespecttoG‐iyields:

∗

1 0 (11)

∗

0 (12)

∗

1 0 (13)

wheretheinequalitiesfollowfromtheassumedpositivethirdderivatives.Nowdifferentiating(10)withrespecttoG‐i:

. (14)

Concavitycombinedwiththesignsin(11)–(13)implythat ispositive.█

Cobb‐Douglas preferences meet the conditions in Proposition 1; therefore the

balanced‐budgetcrowd‐outplotsinFigures1and2aremonotonicallydecreasing.AppendixAshows thatCobb‐Douglaspreferencesalsohavemonotonicallydecreasingunfundedcrowd‐out ( | → 0), and presents a set of conditions on preferences such that decreasing

7 Intheanalysisofrisk,apositivethirdderivativecorrespondstoprudence,whichcanbeinterpretedasthedisutilityofbeingfacedwithaspecifiedriskdecreasingaswealthgetshigher(EeckhoudtandSchlesinger,2006).

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unfunded crowd‐out is monotonic—hence the marginal motive for giving monotonicallymovesfromimpurealtruismtowarmglow( → 1).

Atestofimpurealtruism’sdecreasingcrowd‐outpredictionthatcanbecarriedoutinafinite–G‐i experimentmust be conducted jointly with some restrictions on preferences.Weoffer three perspectives. First, absent placing some restrictions on preferences the impurealtruismmodelisvoidoftestablepredictions,otherthanq2>0,theassumptionbuiltintothemodelsothatitcouldmatchpre‐existingevidenceofincompletecrowd‐out.Second,previousempirical and experimental analyses of the impure altruism model commonly assumeseparability.8Third,beyondsomelevelofG‐i,monotonicallyincreasingq2becomesapplicableto non‐separable impurely altruistic utility functions satisfying the weak preferenceconditions in Ribar and Wilhelm (2002). As G‐i → ∞ these utility functions becomeasymptoticallyseparable(i.e.,UgG→0andUxG→0).

In the next section we introduce a new experimental design that addresses thelimitationsinthepreviousexperimentalworkbycarefullycontrollingthelevelofgiving‐by‐othersandmeasuringbalanced‐budgetcrowd‐outaroundtwolevelsofG‐i:oneatalowleveland one at a higher level of giving‐by‐others. We use the two balanced‐budget crowd‐outmeasures todemonstrate that rejectionofpurealtruismdependson the level of giving‐by‐othersatwhichthehypothesisistested,andtotestimpurealtruism’sdecreasingcrowd‐outprediction.Werepeatthetestofimpurealtruismusingunfundedcrowd‐outbecausetestingforincreasingq1+q2allowsustodetermineifthemarginalmotiveforgivingisshiftingfromimpure altruism to pure warm glow. Additional caution is required when interpreting theresults from a test of decreasing unfunded crowd‐out because a pure altruismmodel alsopredicts decreasing unfunded crowd‐out if q1 increases a lot; therefore before consideringunfundedcrowd‐outwemustfirstexamineownincomeeffectsq1inisolation.Finally,weusethe two measures of balanced‐budget crowd‐out, combined with own income effectsmeasured at the two levels of G‐i plus an additional measure of unfunded crowd‐out, toidentifytherelativestrengthsofaltruismandwarmglowpreferencestogive.3.ExperimentalDesignToconductthecrowd‐outtestsandidentifytherelativestrengthsofaltruismandwarmglowin motivating charitable giving we wanted to create an experimental environment thatmirroredascloselyaspossiblethetheoreticalanalysisof impurealtruism. Itwasthereforeessentialthatwecontrolthelevelofgiving‐by‐otherstothecharity,andthattheparticipant’sgiftsecuredthefinalandtotalcharityoutput.Wealsowantedtoworkwithanactualcharitysothattheexperimentalresultsremainedrelevanttoactualcharitablegiving.Unfortunately,onecannotsimplyhavetheparticipantgivetoanexistingcharitybecausepeopleoutsidethe 8 Andreoni (1990) notes the need to make a functional form assumption to assess the relative strength of altruism, and uses Cobb-Douglas preferences. The voluntary contribution mechanism experiments use separable utility functions to financially‐inducepublicgoods (Andreoni 1993; Chan, Godby, Mestelman, and Muller 2002; Gronberg, Luccasen, Turocy, and Van Huyck 2012; Sutter and Weck-Hannemann 2004).

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experimentwouldbegivingtothatsamecharity,andtherebywewouldlosecontroloverthelevelofgiving‐by‐others. Tocontrolthelevelofgiving‐by‐otherswhileatthesametimeworkingwithanactualcharitywejoinedwiththeSouthwesternPennsylvaniachapteroftheAmericanRedCrosstocreateanindividualizedcharityforeachofourparticipants:theopportunitytohelpachildinneed inawaynootherdonorsoutside theexperimentweredoing. In theeventofa fire inSouthwestern Pennsylvania the chapter helps the affected families find temporary shelter,providesthemwithclothingandameal,andgivesthemessentialtoiletries.However,priortoourstudynoitemsweregiventothechildrenaffectedbythefire.Wejoinedwiththechaptertocollectfundstobuybooksfortheaffectedchildren.

Eachparticipant in the studywaspairedwith a child (1‐12yearsold)whose familyhome had suffered extensive fire damage. Each participant was given an endowment andasked to allocate it between him/herself and the child. The participants were told that inaddition the research foundation funding the studywoulddonate a fixedamountofmoneytowardsthechild independentoftheparticipant’sallocation.Therefore, thetotalamounttobespentonbooksforthechildwouldbethesumoftheirallocationandthefoundation’sfixeddonation. The books purchased with the total amount would be given to the child by theAmerican Red Cross immediately after the child had been affected by a severe fire.Participantswereinformedthat“Eachparticipantinthisstudyispairedwithadifferentchild.. .Onlyyouhavetheopportunitytoallocateadditionalfunds[additionaltothefoundation’sfixeddonation] to the child.Neither theAmericanRedCrossnor anyotherdonorsprovidebookstothechild.”

InexplainingwhytheAmericanRedCrosswasseekingtheparticipant’scontributionfor books, participants were informed that the chapter’s Emergency PreparednessCoordinator Sandi Wraith had made the following statement: “Children’s’ needs are oftenoverlookedintheimmediateaftermathofadisasterbecauseeveryoneisconcernedprimarilywithputtingthefireout,reachingsafety,andfindingshelter,foodandclothing...justthebasicsoflife.Somanytimes,I'veseenchildrenjustsittingonthecurbwithnoonetotalktoaboutwhat's happening...for this reason I've found trauma recovery experts in the community toworkwith us to train our volunteer responders in how to address children's needs at thesceneofadisaster.......beingabletogivethechildrenfun,distractingbookswillprovideagreatbridge for our volunteers to connect with kids and get them talking about what they'veexperienced.”

Atotalof85undergraduatesattheUniversityofPittsburghparticipatedinoneofsixsessions. There were between 13 and 20 participants in each session. Participants wereseated ina largeclassroom. Theyweregivena folderwithasetof instructions,aquiz,anenvelope, a calculator, and a pen. The instructions were then read out loud, and theparticipantswere given abrief quiz tomake sure that they could calculate thepayoffs of asample decision. After they received answers to the quiz, participants proceeded to thedecisiontask.

13

To identify individual heterogeneity in altruism and warm glow the study used awithin–subject design. Each participant made six decisions. For each decision there was abudget that indicatedtheparticipant’sendowmentandthe foundation’s fixeddonation.Theendowmentandfixeddonationvariedacrossthesixbudgets.Foreachbudgettheparticipantwastoldthatsheorhewas freetoallocateanyportionof theendowmenttothechild.Thechildwould receivebookspurchasedwith the sumof the fixeddonationand theallocationmadebytheparticipant.

Thestudywasdouble‐blind:eachdecisionsheetwasidentifiedonlybyaClaimChecknumber, and this number was used for the participant’s anonymous payment. However,participants had the option of relinquishing their anonymity if they wanted to receive anacknowledgement directly from the Red Cross. Once the decision task was completed theparticipant placed the decision sheet in the envelope, and from that point onward thedecisions were identified only by a Claim Check number (with the exception of theparticipants who requested acknowledgement forms). While one set of experimenterspreparedtheparticipants’paymentsinsealedenvelopes,anotherexperimenterwhodidnotoverseethepaymentwasinchargeofdistributingtheenvelopesbyClaimChecknumber.

To assure participants that the experimental procedures were followed we used averificationproceduresimilartothat inEckeletal.(2005).Duringtheinstructionphasewerandomly selectedoneparticipant tobe themonitor. Themonitor’s jobwas to oversee theproceduresoftheexperiment.Themonitorfollowedtheexperimentersthroughoutthestudy,oversawthatthepaymentprocedureswereasdescribedintheinstructionsandthatforeachchildacheckwasissuedtotheAmericanRedCrossfortheamountdeterminedbysumoftheparticipant’s allocation and the relevant fixed donation. At the end of the experiment themonitormadeastatementindicatingwhethertheexperimentershadfollowedtheproceduresdescribed in the instructions. Participants were then shown the acknowledgements andchecks thatwere tobe sent to theAmericanRedCross.Thesewere shown fromadistancewherenodetailscouldbedetermined.Oncetheparticipantshadreceivedtheirpaymentandleftthestudy,themonitorwalkedwiththeexperimentertothenearestmailbox,anddroppedtheenvelopeswith thechecks into themail.Themonitor thensignedastatement tocertifythat all procedures had been followed, and the statement was subsequently posted in theEconomicsDepartmentattheUniversityofPittsburgh.FinallytheAmericanRedCrosssentareceipttoanyparticipantwhorequestedit,andareceiptforthetotalamountreceived.Thelatter receipt was also posted in the Department. At the request of the Red Cross, theexperimentershandledthepurchaseof85setsofbooks,eachcostingtheamountsgeneratedbytheexperiment.

During thedecision taskparticipantswerepresentedwith the six budgets shown inTable1. Forexample,forBudget1theparticipantwasinformedthatthefoundationpayingfor the study had donated $4 toward books for the child, and that the participant had anendowment of $40 which she could allocate between herself and the child. Any amountallocatedtothechildwouldbeaddedtothe$4fixeddonationandthesumusedtobuybooks.

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Table1 showshow the fixeddonationand theendowmentvariedacross thebudgets.Eachparticipant received the six budgets in one of six randomized orders. At the end of thedecisiontaskthemonitorrandomlyselectedanumberbetween1and6,andthedecisionfortheselectedbudgetwascarriedout.

Table1:Experimentalbudgets.

BudgetFoundation’sfixeddonation

(G‐i)

Participant’sendowment

(wi)1 4 402 10 403 28 404 34 405 4 466 28 46

The six budgets in Table 1 allow us to examine the participant’s demand for giving

bookstothechildandthealtruismandwarmglowmotivesforsuchgiving.Atthelowlevelofgiving‐by‐others(G‐I=4)Budgets5and2effecta$6balanced‐budget increaseingiving‐by‐others funded through a $6 lump‐sum tax. At the high level of giving‐by‐others (G‐i = 28)Budgets6and4effectthesame$6balanced‐budgetincreaseingiving‐by‐others.Henceatalow and at a high level of giving‐by‐others we can measure balanced‐budget crowd‐out(| | | |1 |). Likewise, Budgets 1 and 5 and Budgets 3 and 6 allowmeasurement of own income effects (q1) at a low and at a high level of giving‐by‐others,respectively.Unfundedcrowd‐out( | |1 | canbemeasuredwithBudgets

1and2andBudgets3and4.4.Results Thissectionbeginswithadescriptiveanalysisoftheparticipants’givingtobuybooksforthechild.Thenwepresentestimatesofaveragebalanced‐budgetcrowd‐out,ownincomeeffects,andunfundedcrowd‐out,andcomparetheestimatesfromwhengiving‐by‐othersislowtotheestimates fromwhengiving‐by‐others ishigh.Allof theseestimatesarereduced‐form.Nextweestimatethealtruismandwarmglowpreferenceparametersinastructural,Cobb‐Douglasmodel of impure altruism. We estimate the structural model assuming first that theparticipants’ motives can be represented by a single set of preferences, and then thatpreferences are heterogeneous. We use the structural estimates to assess the relativestrengthsofaltruismandwarmglow.

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4.1.DescriptivestatisticsOur individualized charity design was successful in creating an environment in whichparticipantsgive,asseenintheper‐participantaveragegivinghistograminFigure3.Onlyoneof theparticipantsstuck toacontributionofzero foreachof thesixbudgets,another threehadaveragegivingof$2.50orless.Attheuppercornertherewerefiveparticipantswhogavetheir entire endowment for each of the six budgets, and another two participants who onaveragegave$37.50ormore. Averagegivingacrossthesixbudgets(6x85decisions)was$20.82andthestandarddeviationwas$12.11.Hencetherewasalargeamountofvariationacrossparticipants.

4.2.Crowd‐outandincomeeffectsWe begin by examining the extent to which balanced‐budget crowd‐out is complete andwhetheritdecreasesasgiving‐by‐othersincreases.Wethenshowthattheownincomeeffectchangeslittleasgiving‐by‐othersincreases.Finally,weexaminechangesinunfundedcrowd‐out.4.2.1Balanced‐budgetcrowd‐outThebalanced‐budgetcrowd‐outtestpositionspurealtruismasthenull.Table2presentstheresults. Column1presentsthecrowd‐outestimateatthelowlevelofgiving‐by‐others($4),andcolumn2presentsthecrowd‐outestimateatthehighlevel($28). Columns1and2arelinear regressionswith individual fixed‐effects.Theseestimates arenot adjusted for cornerdecisions.Evenifpurealtruismisthecorrectmodel,decisionsatcornerswouldbelessthan

05

10

15

20

Pe

rcen

t

0 5 10 15 20 25 30 35 40Giving

Note: Includes one person who gave $0 in all six decisions, and five people who gave the maximum in every decision. N = 85.

Figure 3. Average giving per-participant.

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dollar‐for‐dollar responsive to a lump sum tax and transfer. Hence, by not taking cornerdecisions into account the results in columns 1 and 2—like those from previousexperiments—are biased against pure altruism. Therefore columns 3 and 4 re‐estimatecrowd‐out appropriately taking into account the cornerdecisionsusing the two‐sided fixedeffectscensoredestimatorofAlan,Honoré,HuandLeth‐Petersen(2014).Table2.Changeinbalanced‐budgetcrowd‐outbetweenalowandahighlevelofgiving‐by‐others.

Linearmodel Accountforcornerdecisions Giving‐by‐others Giving‐by‐others Low

(1)High(2)

Low(3)

High(4)

Low/High(5)

Giving‐by‐others(G‐i) ‐.94a ‐.77b ‐.97c ‐.82d ‐.99e (.09) (.08) (.09) (.09) (.09) Giving‐by‐othersinteractedwithadummyindicatorthatgiving‐by‐othersishigh

‐ ‐ ‐ ‐.18f

(.12)

Budgets 2,5 4,6 2,5 4,6 2,5,4,6Notes:ThedependentvariableisthenumberofdollarsaparticipantcontributestotheRedCrosstobuybooksforthechild.Theestimatesincolumns1and2arefromlinearregressionswithindividualfixedeffects.Theestimatesincolumns3–5aremarginaleffectsfromthetwo‐sideestimatorbyAlan,Honoré,HuandLeth‐Petersen(2014)thataccountsforthecornersolutionsat$0and$40or$46withindividualfixedeffects.Forcolumn5,therow2coefficient(giving‐by‐othersinteractedwithadummyindicatorthatgiving‐by‐othersishigh)estimatesthechangeincrowd‐outbetweenthelowandhighlevelsofgiving‐by‐others,andindicatesthatatthehighlevelofgiving‐by‐otherscrowd‐outisasmallernegativenumber.Standarderrorsareinparentheses.Standarderrorsincolumns3–5arebootstrapped.N=85participants.Testsofcompletecrowd‐out(H0:│κ|dG‐i=−dwi│≥1)havep‐values:ap=.255.bp=.002.cp=.390.dp=.034.ep=.477.fTestofnodecreaseinbalanced‐budgetcrowd‐outhasp=.07.

Column1indicatesthateverydollarincreaseingiving‐by‐othersfrom$4to$10,whileat the same time own income decreases from $46 to $40, causes a $0.94 reduction inparticipants’giving—94percentcrowd‐out.ComparingBudget5($4,$46)toBudget2($10,$40), the$6balanced‐budget increase ingiving‐by‐otherscausesparticipantsonaverage todecreasegivingby.94x$6.00=$5.64.Crowd‐outisveryclosetocomplete,soclosethatwecannotrejectcompletecrowd‐outatanyreasonablelevelofsignificance(H0:│κ|dG‐i=−dwi│≥1hasp= .255).Hadwe followed theproceduresofpreviousexperimentsandexaminedonly

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onecrowd‐outmeasure,thisresultwouldhaveledustoconcludethatonaverageparticipantsaremotivatedtogivebypurealtruism.

Column2leadstoadifferentconclusion.Atthehigherlevelofgiving‐by‐otherscrowd‐out is77percent,andwecanrejectcompletecrowd‐out(p= .002). Inotherwords,hadwemeasuredcrowd‐outatonlyonelevelofgiving‐by‐others,andthatlevelhadbeenthehigherlevel,wewouldhavereachedtheconclusionthatparticipantsareimpurealtruistsmotivatedbybothaltruismandwarmglow.Clearly,thepowertorejectapurealtruismnulldependsonthelevelofgiving‐by‐othersatwhichthehypothesisistested. The measures of crowd‐out in columns 1 and 2 do not take into account that 12.6percent of the decisions (out of 6 x 85 = 510 decisions)were at a lower or upper corner.Columns3and4takecornerdecisionsintoaccount,andindicatethatcrowd‐outissomewhatlarger in magnitude. Estimated at a low level of giving‐by‐others, crowd‐out is nearlycomplete: 97 percent. Although crowd‐out at a higher level of giving‐by‐others increases(relative to column 2) to 82 percent, we still reject complete crowd‐out (p = .034). Asexpected, by not taking corner decisions into account the results in columns 1 and 2 arebiasedagainstpurealtruism,butcolumns3and4indicatethatcorrectingthebiasdoesnotshiftourqualitativeconclusions.

Theestimatesmovingfromcolumn3tocolumn4suggestthatcrowd‐outisdecreasing.Column 5 directly examines the decrease in balanced‐budget crowd‐out by combining thedatafromthe$6balanced‐budgetincreasesingiving‐by‐othersatthelowandhighlevelsofgiving‐by‐others, and including an interaction term to indicate that the data are from thebudgetswheregiving‐by‐others ishigh.The .18(SE= .12)pointestimateonthe interactiontermmeansthatthemagnitudeofcrowd‐outis18percentagepointssmalleratthehighlevelof giving‐by‐others. Obviously because crowd‐out decreased, impure altruism’s predictionthatbalanced‐budget crowd‐outdecreasesasgiving‐by‐others increasescannotbe rejected.To assess the strength of the evidence in support of impure altruism,we test the oppositehypothesis—that the magnitude of crowd‐out did not decrease: that hypothesis can berejectedatp=.07.Thisevidenceoffersqualitativelynew,andstatisticallysignificant,supportfortheimpurealtruismmodel.9

Random effects Tobit is an alternative estimation approach that can account for thecornerdecisions, under the additional assumption that the errors arenormallydistributed.Random effects Tobit estimates of themodels in columns 3‐5 are similar to the two‐sidedfixed effects censored estimates presented in the table. For instance, randomeffects Tobitestimationof themodel in column5 indicates that crowd‐out at the low level of giving‐by‐othersis−.95(SE=.09),themagnitudeofcrowd‐outis.19(SE=.11)smalleratthehighlevel

9 Comparing the estimates of balanced-budget crowd-out implied by column 5 with the estimates from columns 3 and 4 indicates slight differences that are due to the nonlinear estimation method: the nonlinear method applied to two separate samples (columns 3 and 4) generates slightly different estimates than the nonlinear method applied to the two samples combined into a single model with an interaction term (column 5). Estimates from the linear model are, of course, identical whether generated using separate samples or one combined sample in an empirical model with an interaction term.

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ofgiving‐by‐others,andthehypothesisthatthemagnitudeofcrowd‐outdidnotdecreasecanbe rejected at p = .044. Hence, the random effects Tobit estimates offer slightly strongersupport for the impure altruismmodel. The similarity of the random effects Tobit and thetwo‐sidedfixedeffectscensoredestimatesimpliesthattheerrorsareapproximatelynormal.10

4.2.2OwnincomeeffectsThis section provides evidence that, on average, giving to the individualized charity is anormalgood,andthattheownincomeeffectq1isessentiallyconstantwhenmovingfromthelow to thehigh levelofgiving‐by‐others.Normality is important toestablishbecause it isamaintained assumptionof thepredictionsderived fromboth thepure and impure altruismmodels. Constant q1 implies that the pure and impure altruism models have differentpredictions for unfunded crowd‐out ( | 1 will be estimated in the next

section). With constant q1, pure altruism predicts no change in unfunded crowd‐out. TheevidencefromSection4.2.1thatq2isincreasingimpliesthatifq1isconstant(orincreasing)thenimpurealtruismpredictsthatunfundedcrowd‐outwilldecrease.

Table3column1showsthattheownincomeeffectatthelowlevelofgiving‐by‐othersis.40:withanadditional$6incomeparticipantsonaverageincreasegivingby$2.40.Column2 shows that the incomeeffect is virtually the sameat thehigher level of giving‐by‐others.Column 3 takes the corner decisions into account, and indicates slightly smaller incomeeffects: .32 at the low level of giving‐by‐others, and .36 at the high. Each of the estimatedincomeeffectsissignificantlylargerthanzeroandlessthanone(ps<.001),establishingthatonaveragebothgivingandownconsumptionarenormalgoods.

Table3.Ownincomeeffects.

Linearmodel Accountforcornerdecisions Giving‐by‐others Giving‐by‐others Low

(1)High(2)

Low/High(3)

Income(wi) .40 .41 .32(.06) (.07) (.06)

Incomeinteractedwithadummyindicatorthatgiving‐by‐othersishigh

‐ ‐ .04a(.08)

Budgets 1,5 3,6 1,5,3,6Notes:SeethenotestoTable2.Testsofeachincomeeffectbeingzero(orless)havep<.001.Likewise,testsof

10 A histogram of the within-participant variation (available upon request) also suggests that the data are approximately normal.

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eachincomeeffectbeingone(ormore)havep<.001.aTestofnochangeintheincomeeffecthasp=.583.

The .32and .36estimatesof the incomeeffect in column3 indicateatmostaminor

increasewhenmovingfromthelowtothehighlevelofgiving‐by‐others;thehypothesisthatthetwoincomeeffectsarethesamecannotberejected(p=.583).Hence,theresultsindicatethatq1remainsconstantasgiving‐by‐othersincreases.4.2.3Unfundedcrowd‐outAccounting for the evidence of constant own income effects generates the followingpredictionsforthechangeinunfundedcrowd‐outwhenmovingfromthelowtothehighlevelof giving‐by‐others: (a) decrease under impure altruism and (b) stay constant under purealtruism.Regardless of the own income effect, unfunded crowd‐out is predicted to (c) stayconstant at zero under purewarm glow. Table 4 presents the unfunded crowd‐out results.Ownincomeisheldconstantat$40andgiving‐by‐othersisincreasedfrom$4to$10(column1) and then again from $28 to $34 (column 2). Unfunded crowd‐out is 55 and 36 percent,respectively.Thesemeasuresenableatestofthehypothesisthatonaverageparticipantsaremotivatedbypurewarmglow( | 0).Atboththelowandthehighlevelofgiving‐by‐

others,thezerocrowd‐outpredictionofpurewarmglowcanberejected(ps<.001).Knowing that q1 stays constant between the low and high levels, the 19 percentage

point (SE = 9 percentage points) decrease in unfunded crowd‐out from 55 to 36 percentprovides additional support for the impure altruism model. The hypothesis that themagnitudeofcrowd‐outdidnotdecreasecanberejected(p=.016).Takingcornerdecisionsintoaccount,andcontinuing to include individual fixedeffects, incolumn3, thedecrease incrowd‐out isestimated tobeslightly larger,22percentagepoints,and thehypothesisofnodecreaseincrowd‐outislikewiserejected(p=.013).

Tofurtherchecktheconclusionthatthedecreasingunfundedcrowd‐outsupportstheimpure altruismmodel, rather than being consistentwith pure altruismplus an increasingownincomeeffect,were‐estimatethechangeinunfundedcrowd‐outsettingasidetheN=15participantswhosemotivesarepurealtruism,orpossiblypurealtruism,andwhose incomeeffect increases as giving‐by‐others increases.11 As seen in column 4, the result is that thechangeinunfundedcrowd‐outissmallerfortherestrictedsample,12percentagepoints,butstill statistically significant (p = .062). In short, pure altruistswho have an increasing ownincomeeffectdocontributeviatheirincreasingq1totheTable4column3resultthatq1+q2is

11 We excluded participants (1a) who behaved as pure altruists at both low and high margins (i.e., at both the low and high level of giving-by-others) or (1b) who behaved as a pure altruist at the low margin but whose motives at the high margin cannot be determined (or vice versa) and (2) whose change in the own income effect either was an increase or cannot be determined. See the notes to Table 4 for additional detail. For some participants motives at a margin cannot be determined either because the participant makes corner decisions or because her/his income effect at the margin is so large that it masks motives at that margin. In some cases a participant’s income effect at a margin could not be determined because of corner decisions.

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increasing, but even without them q1 + q2 still increases. This indicates that relativelyspeakingthemarginalmotiveforgivingisshiftingfromimpurealtruismtopurewarmglow.

Table4.Changeinunfundedcrowd‐outbetweenalowandahighlevelofgiving‐by‐others.

Linearmodel Accountforcornerdecisions Giving‐by‐others Giving‐by‐others Low

(1)

High

(2)

Low/High(fullsample)

(3)

Low/High(restrictedsample)c

(4)Giving‐by‐others(G‐i) ‐.55a ‐.36a

(.07) ‐.64 ‐.53

(.07) (.08) (.07) Giving‐by‐othersinteractedwithadummyindicatorthatgiving‐by‐othersishigh

‒ ‒

0.22b

(.09)0.12d

(.08)

Budgets 1,2 3,4 1,2,3,4 1,2,3,4N 85 85 85 70Notes:SeethenotestoTable2.aTestofpurewarmglowH0:κ≥0vs.Ha:κ<0hasp<.001.bTestofnodecreaseincrowd‐outhasp=.013.cExcludedare(i)N=4participantswhobehavedaspurealtruistsatbothlowandhighgiving‐by‐others,andwhohadanincreasingincomeeffect,(ii)N=6participantswhomayhavebehavedaspurealtruistsatbothlowandhighgiving‐by‐others,andwhohadanincreasingincomeeffect(e.g.,behavedasapurealtruistatlowgiving‐by‐othersbutmotivescouldnotbedeterminedathighgiving‐by‐others),(iii)N=1participantwhobehavedasapurealtruistatbothlowandhighgiving‐by‐others,butwhosechangeinincomeeffectcouldnotbedetermined,and(iv)N=4participantswhomayhavebehavedaspurealtruistsatbothlowandhighgiving‐by‐others,andwhosechangeinincomeeffectcouldnotbedeterminedbecauseofcornerdecisions.dTestofnodecreaseincrowd‐outhasp=.062.

4.2.4SummaryThe reduced‐form results—that balanced‐budget crowd‐out is not complete (q2 > 0)whengiving‐by‐othersishigh,thatbalanced‐budgetcrowd‐outdecreases(q2↑)asgiving‐by‐othersincreases, and that unfunded crowd‐out decreases (q1 + q2 → 1) as giving‐by‐othersincreases—suggestthatonaveragetheparticipantsaremotivatedbyimpurealtruism.Atthesame time, when giving‐by‐others is low complete balanced‐budget crowd‐out cannot berejected(q2≈0),andevenwhengiving‐by‐othersishigh,q2=.18‐to‐.19(asimpliedbyTable2,columns4and5)appearstobesmallrelativetotheownincomeeffectq1= .36(Table3,column 3). Hence, even though impure altruism cannot be rejected, the warm glowcomponentofthemodelappearssmall.

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4.3.Astructuralmodelofpreferences:Cobb‐DouglasimpurealtruismTomorerigorously investigatetherelativestrengthofwarmglowandaltruismthissectionestimatestheparametersoftheCobb‐Douglasimpurealtruismutilityfunctionfromequation(8).Theoptimalgiftgib*derivedfromthisutilityfunctionis:gib*=−G‐i,b+

½[(1−β)G‐i,b+(α+β)Zib+{[(1−β)G‐i,b+(α+β)Zib]2−4αG‐i,bZib}½] (15)+ei+uib

wherei=1,...,85indexestheparticipants,b=1,...,6indexesthesixdecisionseachparticipantfaceswithcorrespondingbudgetsofgiving‐by‐othersandownincome,Zib≡wib+G‐i,b,eiisanindividual‐specificrandomeffect,anduibistherandomnessineachparticipant’sgivingthatisnotcorrelatedacrossher/hisdecisions.Usingthedatafromall85participantstoestimatethetwoparametersαandβin(15)isarepresentativeagentapproachtoestimation. Estimation of (15) presents three econometric problems: non‐linearity in theparametersα andβ, thewithin‐participantcorrelation inrandomdeparturesofgiving fromtheCobb‐Douglasspecification(therandomeffectei),andthecornerdecisionsthatcanoccurat$0andattwodifferentupperamounts,$40and$46.Handlingeachproblemoneatatimeis straightforward, but handling all three at the same time is non‐trivial. Therefore, weconstruct a non‐linear random effects Tobit estimator permitting both lower and uppercornersolutions,anduseittoestimate(15).12

Table5reportstheestimates.The .021estimateonthewarmglowcomponent(β) issignificantlygreater thanzero, implying rejectionof thepurealtruismmodel.However, thewarmglowcomponentisrelativelysmall.At.594theestimateonthealtruismcomponent(α)isaboutthirtytimeslarger.

Table5.Non‐linearrandomeffectsTobitestimatesofa

Cobb‐Douglasimpurealtruismutilityfunction.

Coefficient Standard

errorp‐value

α .594 .025 .000β .021 .009 .022ρ .902 .016 .000

Notes:αandβaretheCobb‐Douglasparametersinequation(8). ρisthecorrelationcoefficientoftheerrortermacross

decisionswithin‐individuals.Thelog‐likelihoodis–1466.9.N=85participants,sixdecisionsperparticipants.

12 We calculate the estimates of α and β using maximum likelihood, assuming that uib and ei are normally distributed. To calculate the multivariate normal probabilities when gib = 0 and when gib = wib we use STATA’s maximum simulated likelihood routines (Cappellari and Jenkins 2006), adapting Barslund’s (2007) multivariate Tobit program.

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Anotherwaytoassessthestrengthofwarmglowistoexaminepredictedgivingata

particular budget and determine what share of giving is accounted for by the warm glowcomponent.ConsiderforexampleBudget5($4,$46).Predictedgivingatthisbudgetis$26.81.Howeverifatthisbudgetαwerezero,thenapurewarmglowgiverwithβ=.021wouldgiveonly$0.97.ThususingaCobb‐Douglasspecification,at thisbudgetwarmglowaccounts for3.6percentofpredictedgiving.

The .902 estimate of the correlation coefficient ρ indicates that there is substantialheterogeneityinparticipants’randomdeviationsfromtheCobb‐Douglasmodel.Hence,thereislikelysubstantialheterogeneityacrossparticipantsintheirαandβparametervalues.4.4.HeterogeneouspreferencesIn this section we investigate the heterogeneity in altruistic and warm glow preferencesacross the participants. Themain point to bemade is that, even though the evidence fromSections4.2and4.3revealsbehaviorthatis,onaverage,consistentwithimpurealtruismbutwithweakwarmglow,behindtheaveragebehaviorisconsiderableheterogeneityofmotives.

WeinvestigatepreferenceheterogeneitybyestimatingtheCobb‐Douglasspecificationofimpurealtruismseparatelyforeachindividualparticipant.Specifically,foreachindividualwe estimate the altruism and warm glow parameters in equation (15) using constrainedmaximumlikelihoodTobit,withtheparameterestimatesconstrainedsuchthatαi,βi,∈[0,1].Bindingconstraintsindicatepurealtruism(0<αi<1,βi=0)orpurewarmglow(αi=0,0<βi<1).

Figure4isascatterdiagrampresentingthedistributionofthealtruismandwarmglowpreferenceparameters.Themagnitudeofaltruism is shownalong thevertical axis, and themagnitude of warm glow along the horizontal. Points on the vertical axis representparticipantsmotivatedtogivebypurealtruism,pointsintheinterioroftheplotrepresenttheimpurealtruists,andpointsonthehorizontalaxisrepresentparticipantsmotivatedtogivebypurewarmglow.Themajority of theparticipantsweremotivated to givebypure altruism(43.5percent;N=37)orimpurealtruism(38.8percent;N=33).Onlyninepercent(N=8)weremotivatedbypurewarmglow.Amongthosemotivatedbyimpurealtruism,mostattachagreaterweighttoaltruismthantowarmglow:thereareonlytwoparticipantswithαi,≈βi,andonlythreewithαi<βi.13 The sum αi + βi in Figure 4 is a measure of participant i’s generosity. It is notuncommonfortheterm“altruistic”tobeusedinterchangeablywiththeterm“generous,”butitisnotthecaseinFigure4thatparticipantsmotivatedsolelybywarmglowarelessgenerousthanthosewhoaremotivatedbyaltruism.Lookingalongthehorizontalaxisweseethatallbut two of the purewarm glowparticipants give very large amounts. The average amount

13 Estimates of αi and βi cannot be obtained for the six participants who chose corner solutions for all six of their decisions, and for a seventh participant who chose the upper corner for four decisions and was close to the upper corner for his other two decisions.

23

given among the pure warm glow participants was $21.54, and among the pure altruists$20.43.

4.5.RelativestrengthofwarmglowWeassess the strength ofwarm glow relative to theα +βmeasure of generosity using anindexofwarmglowdefinedas:

≡ . (16)

Thewarmglowindexin(16)isastructuralanalogytoAndreoni’s(1990)marginalindex.14γranges from zero (pure altruism) to one (pure warm glow). Based on the representativepreferencemodelinTable5,thewarmglowindexforthesampleisγ=.034. FromFigure4itisclearthatthedistributionofγiisheavilyskewedtowardlowvalues.The skewed distribution of the strength of warm glow has an important implication forcalculatingtheshareofgivingaccountedforbywarmglow.Therearetwoapproachestothe

14 Andreoni’s (1990) index

is the ratio of the own income effect to the giving-by-others income effect, and

measures the relative strength of altruism at the particular margin (i.e., level of giving-by-others) at which it is evaluated. The warm glow index γ in (16) is a structural analogy to 1

. γ is inframarginal.

i = i

0.2

.4.6

.81

Altr

uism

( i

)

0 .2 .4 .6 .8 1Warm glow (i)

Notes: Points on the y-axis are pure altruism participants. Points on the x-axis are pure warm glow participants. N = 78.

Figure 4: Cobb-Douglas Altruismand Warm Glow Parameters

24

calculation:therepresentativepreferenceapproachusedinSection4.3,andaheterogeneouspreferences approachbasedon thedistributionofαi andβi in Figure4.The representativepreference calculation is based on first combining the individual data during estimation,estimatingtherepresentativeαandβ,andthenimplementingthecounterfactualα=0.Thiswilldifferfromfirstestimatingtheheterogeneousαiandβiandthencombiningtheindividualcounterfactuals αi = 0, because the estimation is non‐linear and the distribution of thestrengthofwarmglowisheavilyskewed.Table6reportstheshareofgivingaccountedforbywarmglowusingeachapproach.

Rows1and2inTable6presenttherepresentativepreferenceapproach.Row1usesallN=85participantsandα=.594andβ=.021fromTable5.Thewarmglowindexγ=.034.Usingtheseαandβestimates,thepredictedgivingforBudgets1–4beginsat$23.12andfallsto$12.99asgiving‐by‐othersincreasesfrom$4to$40.TheactualaveragegivingatBudgets1–4=$24.84,$21.56,$17.01,and$14.84(notshowninthetable).Settingα=0,apurewarmglow giverwithβ = .021would give $0.84 regardless of the level of giving‐by‐others. As ashare of predicted giving, the $0.84 increases from 3.6 to 6.5 percent of predicted giving,movingfromBudgets1to4.

TosetupthecomparisontotheheterogeneouspreferencesapproachinRow3,Row2repeatstherepresentativepreferenceapproachfortheN=78participantsforwhomαiandβicouldbeestimatedinSection4.4.EstimatingtherepresentativepreferencemodelfortheseN=78participantsyieldsα=.569andβ=.026.AlthoughwarmglowisalittlestrongerthaninTable5,andaltruismalittleweaker,thechangeinestimatesisverysmall.Consequently,thecounterfactualpurewarmglowgiverwouldgive$1.04,justalittlemorethaninRow1.AsashareofpredictedgivinginBudgets1to4,the$1.04fromwarmglowincreasesfrom4.7to8.6percent15

Row 3 presents the heterogeneous preferences approach to calculating the share ofgivingaccountedforbywarmglow.TheαiandβiarefromFigure4.Becauseoftheskewnessoftheγi,themedianγi(.026,andnotmuchdifferentthantherepresentativepreferenceγs)ismuchsmallerthantheaverageγi,.211.SettingtheN=70non‐zeroαisfromFigure4tozero,andleavingtheN=41non‐zeroβisattheirvaluesfromFigure4,counterfactualpurewarmglow givingwould be $4.70. In Budgets 1 to 4 this increases from 21.6 to 32.8 percent ofpredictedgiving,againinlinewiththeasymptoticcomparativestaticsofimpurealtruism.

15 For the N = 78, actual average giving at Budgets 1–4 = $23.99, $20.42, $15.46, and $13.16.

25

Table6.Shareofpredictedgivingaccountedforbywarmglow.

γPredictedgivingatBudget(G‐i,wi)

WarmglowamountandshareatBudget(G‐i,wi)

1 2 3 4 1 2 3 4 (4,40) (10,40) (28,40) (34,40) (4,40) (10,40) (28,40) (34,40)

Representativeα,β

N=85 .034 23.12 20.94 14.82 12.99$0.843.6%

$0.844.0%

$0.845.7%

$0.846.5%

N=78 .044 22.26 20.01 13.84 12.07$1.044.7%

$1.045.2%

$1.047.5%

$1.048.6%

Heterogeneousαi,βi

N=78Medianγi .026

.21121.76 19.95 15.49 14.34

$4.7021.6%

$4.7023.5%

$4.7023.5%

$4.7032.8%Averageγi

Althoughbothapproachesindicatethatalargemajorityofgivingintheexperimentis

motivated by altruism, the relative strength attributed to warm glow is larger in theheterogeneous approach than in the representative approach. Not surprisingly, theheterogeneousapproachprovidesmoreaccurate individual–levelpredictions.Andnotethatthe range from 21.6 to 32.8 percent of predicted giving accounted for by warm glow isqualitativelysimilartothe17percentofindividualswhohavelargewarmglow(e.g.,γi≥.80).However,therepresentativeapproachprovidesamoreaccuratepredictionofthecrowd‐outseen at the level of each of the six budgets: the root‐mean square errors of the crowd‐outpredictionsderivedfromthepredictionsinTable6are$1.17inRow2and$1.56inRow3.Includingthetwomeasuresofbalanced‐budgetcrowd‐out, theroot‐meansquareerrorsare$0.78 from the representativeapproachand$0.99 from theheterogeneousapproach. If theobjectiveistopredicttheresponsetopolicychanges—suchas,“Howmuchwilltheaverageresponsebetoachangeingovernmentfunding(giving‐by‐others)?”—thentherepresentativeapproach is more accurate. Although the results support impure altruism, from theperspective of the better prediction of response to policy, warm glow accounts for onlyaroundfivepercentofgiving.5.Conclusion

Impurealtruismwasdevelopedinthe1980stodeliverthepredictionthatpurealtruismcouldnot:incompletecrowd‐out.Sincethentheextantexperimentalapproachhasbeentopositionpurealtruismasthenullhypothesis,anddirectlytestitspredictionofzerobalanced‐budgetcrowd‐out.Most,thoughnotall,balanced‐budgetcrowd‐outexperimentsrejectpurealtruism.Thealternativehypothesisofimpurealtruismhasnot,untilnow,beendirectlytested.

Thepresentresearchleadstofourconclusionsabouttestingpureandimpurealtruism.First,thepoweroftheextantexperimentalapproachtorejectpurealtruismdependsonthe

26

levelofgiving‐by‐othersatwhichpurealtruismistested.Thisfollowstheoreticallyfromtheasymptotic comparative statics of impure altruism, and empirically from our experimentalresults:onlyatthehigherlevelofgiving‐by‐othersdoesthebalanced‐budgetcrowd‐outtesthavepower to rejectpurealtruism.Second,even if thebalanced‐budget crowd‐out testhasenough power to reject pure altruism, its single measure of balanced‐budget crowd‐outcannot identify the strength of warm glow preferences. Third, impure altruism can bepositioned as the null hypothesis, and its prediction that balanced‐budget crowd‐outdecreases as giving‐by‐others increases directly tested. Doing so, our results providestatisticallysignificantsupportfortheimpurealtruismmodel.Fourth,despitetherejectionofpurealtruismandstatisticallysignificantsupport for impurealtruism,estimatesofaltruismandwarmglowpreferenceparameters froma structuralmodel indicate thatwarmglow isweak relative to altruism. Our representative preference approach to estimating thestructuralmodelyieldsanaltruismparameterthatisaboutthirtytimeslargerthanthewarmglowparameter.Ourheterogeneouspreferencesapproachindicatesthataltruismisstrongerthanwarm glow for 83 percent of the participants. Although the precise amount of givingaccountedforbywarmglow—fivepercenttoaroundone‐quarter—dependsontheapproachtaken to estimate the structural preference parameters, regardless of approach altruismaccountsforthelargemajorityofgivingobservedintheexperiment.

Thestrengthofaltruismfoundinthisexperimentisanimportantfinding,butcautionis warranted, as it would be with any empirical result, when thinking about whether thefinding can be extended to other domains. Although, it is reasonable to conjecture thatpreferences for humanitarian public goods—similar to the type we examine in ourexperiment—may be strongly altruistic, it would not be safe to casually extend thepreferencesestimatedheretoalltypesofcharity,suchasnon‐humanitarianpublicgoodslikegivingtoone’salmamater.

Thatsaid,thepresentresearchprovidesevidencethatthereareinstancesofcharitablegiving in which not only does altruism exist, but it is strong. In the charitable givingenvironmentweestablishedinthelab,altruismisthepredominantexplanationofwhypeoplegive.

27

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AppendixA:Monotonicallydecreasingunfundedcrowd‐out.Inthisappendixwederivetworesults.First,weshowthattheCobb‐Douglas impure

altruismutilityfunctionhasmonotonicallydecreasingunfundedcrowd‐outforα+β<1,α>0,and β > 0. Second, we present necessary and sufficient conditions for separable impurealtruismutilityfunctionstohavemonotonicallydecreasingunfundedcrowd‐out.

FortheCobb‐Douglasresult,beginbydifferentiating(15)inthetextwithrespecttoG‐itogetunfundedcrowd‐out | =−1+q1+q2,yielding:

1 (A.1)

where: ≡ 1 (A.2) ≡ 1 2 . (A.3)

Differentiating(A.1)withrespecttoG‐iindicatesthat:

(A.4)

Notingthat 1 and 2 ,theterminsquarebracketsontheright‐handside

of(A.4)reducesto 1 ,and(A.2)and(A.3)usedtoshow: 1 1

(A.5)4 1

If (and only if)α +β < 1,α > 0, andβ > 0, the right‐hand side of (A.5) is strictly positive,

implying ispositiveand | monotonicallydecreasesasG‐iincreases.█

PROPOSITION2.Considera concave impurelyaltruisticutility function,withstrictlyoperativewarm glow, that satisfies the technical conditions described in footnote 5, and further is

additivelyseparable.q1+q2ismonotonicallyincreasinginG‐iifandonlyif

.

Proof: In fashion parallel to obtaining equation (9) in the text, partially differentiating thefirst‐ordercondition(4)withrespecttosocialincomeZiyields:

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q1=(Uxx−UxG−Uxg)/(Uxx+Ugg+UGG−2UGx−2Ugx+2UgG) (A.6)whichforadditivelyseparableutilityfunctionsreducesto: q1=Uxx/(Uxx+Ugg+UGG), (A.7)whichaddingto(10):

q1+q2=(Uxx+Ugg)/(Uxx+Ugg+UGG), (A.8)Differentiating(A.8)withrespecttoG‐i:

. (A.9)

Usingequations(11)–(13),thenumeratoroftheright‐handsidereducesto:

1

(A.10)

.

The(A.10)right‐handsideterminsquarebracketsisnegative,andhence positive,if

andonlyif

.█

Remark:Positivethirdderivativesand wouldsatisfytheconditioninProposition

2 and therefore lead to q1 + q2 monotonically increasing in G‐i. Positive third derivativesensure that the (negative) second derivatives monotonically move toward zero as G‐iincreases,andtheconditionand ensuresthatthesecondderivativewithrespect

to giving moves toward zero faster than does the second derivative with respect to ownconsumption.

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AppendixB:Instructions

ClaimCheck____________Welcome Thankyouforagreeingtoparticipateinourstudyondecisionmaking.Therearetwopartsofthestudytoday.Inthefirstpartyouareaskedtomakesixdecisionsandinthesecondpartyouareaskedtofilloutasurvey.Whenyouhavecompletedyourdecisionswewillrandomlyselectoneofyoursixdecisionsforpayment.Yourtotalpaymentfromthestudywillbethesumofthepaymentthatresultsfromyourdecisionand$5forshowinguptothestudy.Theentirestudyshouldtakeaboutanhour,andattheendyouwillbepaidprivatelyandincash.Aresearchfoundationhasprovidedthefundsforthisstudy.Weaskthatyoudonotspeaktoeachotherormakecomments,excepttoaskquestionsabouttheproceduresofthestudy.Wealsoaskthatyoudonotdiscusstheproceduresofthestudywithothersoutsidethisroom.YourIdentityYouridentityissecret.Youwillneverbeaskedtorevealittoanyoneduringthecourseofthestudy.Yournamewillneverbeassociatedwithyourdecisionsorwithyouranswersonthesurvey.Neithertheassistantsnortheotherparticipantswillbeabletolinkyoutoanyofthedecisionsyoumake.Inordertokeepyourdecisionsprivate,pleasedonotrevealyourchoicestoanyotherparticipant.ClaimCheckAttachedtothetopofthispageisayellowpieceofpaperwithanumberonit.ThisisyourClaimCheck.Eachparticipanthasadifferentnumber.Weuseclaimcheckstomaintainsecrecyaboutyourdecisions,payment,andidentity.YouwillpresentyourClaimChecktoanassistantattheendofthestudytoreceiveyourcashpayment.Pleaseremoveyourclaimchecknow,andputitinasafeplace.DecisionTasksFor the decision tasks you will be paired with a child in Southwestern Pennsylvania(Allegheny,Washington,Greene,andFayetteCounties).Thechildisbetween1and12yearsold,andthechild’sfamilyhomehassufferedextensivefiredamage.Mostorallofthefamily’spossessionshavebeenlost.Foreachofyourdecisionsyouwillbegivenanamountofmoneywhich you will be asked to allocate between the child and yourself. The money allocatedtowards the childwill be spent on children’s books. These bookswill be distributed to thechildby theAmericanRedCrossofSouthwesternPennsylvania, immediatelyafter thechildhasbeenaffectedbyaseverefire.

33

As soon as a fire is reported in Southwestern Pennsylvania, the American Red Cross iscontacted and volunteers are dispatched to the site. They help the affected families findtemporary shelter, provide themwith clothing, a meal, and give them a comfort bag withessential toiletries. Each day an average of one family in Southwestern Pennsylvaniaexperiencesa severe fire.These familiesdependon theAmericanRedCross foremergencyhelptocopewiththesuddenlossoftheirhomeandbelongings.UnfortunatelytheAmericanRedCrossonlyhasfundstoprovidethesefamilieswiththebareessentials,andtheydonotprovideany“comfort”itemsforthechildrenoftheaffectedfamilies.For the study todaywe have joined theAmericanRedCross of Southwestern PA to collectfundstobuybooksfortheaffectedchildren.Ineachofthesixdecisionsyouwillbegivenanamountofmoneywhichyouareaskedtoallocatebetweenthechildyouarepairedwithandyourself. Inaddition the foundationhasagreedtodonatea fixedamountofmoneytowardsthechildindependentofyourallocation.Thusthetotalamounttobespentonthechildisthesumofthefoundation’sfixeddonationandtheallocationyoumaketothechild.Theamountofmoney thatyoucanallocatebetween thechildandyou,aswell as the foundation’s fixeddonationtothechild,willvaryacrossthesixdecisions.The American Red Cross will use the funds collected from your allocation and that of thefoundation to purchase the child books. Each participant in this study is paired with adifferentchild.Ifyouchoosenottoallocateanyfundstothechild,thenthemoneytobespenton the childwill be limited to the research foundation’s fixed donation. Only you have theopportunitytoallocateadditionalfundstothechild.NeithertheAmericanRedCrossnoranyotherdonorsprovidebooks to the child.Yourdecisionalonedetermineshowmuchwillbespentonthechild.In explaining why the American Red Cross is seeking funds for books, their EmergencyPreparednessCoordinatorSandiWraithstates“Children'sneedsareoftenoverlookedintheimmediateaftermathofadisasterbecauseeveryoneisconcernedprimarilywithputtingthefireout,reachingsafety,andfindingshelter,foodandclothing...justthebasicsoflife.Somanytimes, I've seen children just sitting on the curb with no one to talk to about what'shappening...forthisreasonI'vefoundtraumarecoveryexpertsinthecommunitytoworkwithus to train our volunteer responders in how to address children's needs at the scene of adisaster.......being able to give the children fun and distracting books will provide a greatbridge for our volunteers to connect with kids and get them talking about what they'veexperienced.”Once we are ready to proceed to the decisions, you will be given a decision folder and acalculator.The foldercontainsadecision taskwithsixdecisionson it,andanenvelope.Foreachdecisionyouwillhavetoenteryourpreferredallocation.Ifyouwishtoreceiveareceiptfrom the American Red Cross for your allocation to the child, youwill need to fill out theacknowledgmentform.Notehoweverthatbydoingsoyouwillrelinquishyouranonymity.Ifyou wish to remain anonymous, leave the acknowledgment form blank. When you havecompletedthedecisionformpleaseplaceit intheenvelopealongwiththeacknowledgmentform,instructionsandthecalculator.

34

When we have collected all the envelopes we will draw a number between 1 and 6 todeterminewhich one of the decisions counts for payment. Since one decision is randomlyselectedforpayment,youshouldbemakingyourdecisionasifeverydecisioncounts.SampleDecisionsHere isanexampleofthetypeofdecisionyouwillhavetomake.This is justanexampletodemonstratehoweverythingiscalculated.Theexampleisnotmeanttoguideyourdecisioninanyway.Ontheactualdecisionsheetswewantyoutoselecttheallocationthatyoulikebest.Example:Youhavebeengiven$20 toallocatebetween thechildandyourself.Theresearchfoundation’s fixed donation towards the child is $5. Youmust choose howmuchmoney toallocatetowardsthechildandyourself.You may choose to allocate nothing towards the child’s books and $20 to yourself. If thisdecisionisselectedforpaymentthefoundation’sfixeddonationof$5isspentonthechildandyourpaymentfromthedecisionwillbe$20.Alternativelyyoumaychoosetoallocate$20towardsthechildandnothingtoyourself.Themoney to be spent on the child’s bookswill be $20+$5= $25, and your payment from thedecisionis$0.Finally, you may choose to allocate any amount between $0 and $20 to the child and theremainder to yourself. Suppose you choose to allocate $8 towards the child and $12 toyourself.IfselectedforpaymenttheAmericanRedCrosswillreceive$8+$5=$13tospendonthechild’sbooksandyourpaymentforthedecisionwillbe$12.

35

MonitorRoleToverifythatalltheproceduresofthisstudyarefollowedwewillselectaparticipanttobethe monitor of the study. If your Claim Check number is 8 you will be the monitor. Themonitorwill follow theassistantsaround to see thateverything takesplaceasexplained intheseinstructions.Themonitorwillreceiveafixedpaymentforhisorhertime.Oncealldecisionformshavebeencollectedallparticipantswillbegivenasurvey.Whileyouare completing the survey themonitorwillwalkwith twoassistants to a separate room tooverseethatthecalculationofthefundsforthechildandyouareperformedasdescribedinthe instructions. Your paymentwill be placed alongwith a receipt in an envelope that hasyourclaimchecknumberonthefaceofit.TheassistantwillmakeoutachecktotheAmericanRed Cross of Southwestern PA for the amount corresponding to the funds for the childdeterminedbyyourallocation.Onecheckwillbemadeoutforeachchild.Thischeckaswellasanyrelevantacknowledgmentformwillbeplacedinanaddressedandstampedenvelopeto theAmericanRedCross.Onceall the calculationshavebeen completed an assistantwillwalkthemonitorbacktothisroom.Aboxofenvelopeswithyourpaymentswillbegiventoanassistantwhohasnotseenyourdecisionsheets.Themonitorwillthenmakeastatementtoyouon the extent towhich the instructionswere followedasdescribed in the instructions.Onceyouhavecompletedyoursurveyyoumaycometothefronttocollectyourpaymentbyshowingyourclaimcheck. Anassistantwhohasnotseenyourdecisionformwillhandyouthesealedenvelopewithyourpayment.Afterthestudyiscompletedthemonitorandanassistantwillwalktothenearestmailbox(onForbesnexttotheHillmanLibrary)wherethemonitorwilldroptheenvelopeinthemailbox.Toprovethatallproceduresarefollowedthemonitorwillbeaskedtosignacertificatetothateffect.Thiscertificatewillbepostedoutside4916PosvarHall.Upon receipt of the check and acknowledgment form the American Red Cross will send aletter affirming that the check has been used to buy books for the child according to thedescriptionabove.Thisletterwillbepostedoutside4916PosvarHall.Ifyouarethemonitorofthisstudypleaseidentifyyourselfbycomingtothefrontoftheroomnow.Ifyouhaveanyquestionsabouttheprocedures,pleaseraiseyourhandnowandoneofuswillcometoyourseattoansweryourquestion.Beforeweproceedtothedecisiontaskwewantyoutocompleteabriefquiz,tomakesureyouknowhoweverythingwillbecalculated.