Using“Piece‐RateEquivalents”andRelativePayoffsto
ExploreGenderDifferencesintheWillingnesstoCompete
JohnIfcher
SantaClaraUniversity
500ElCaminoReal
SantaClara,CA95053
jifcher@scu.edu
408‐554‐5579
HomaZarghamee
BarnardCollege
ColumbiaUniversity
NewYork,NY10027
hzargham@barnard.edu
212‐854‐8946
Preliminarydraft:November21,2013
Pleasedonotcitewithoutpermissionfromtheauthors.
JELclassificationcodes:C91,J16,J24
Keywords:Competitiveness;GenderDifferences;RelativePayoff;Piece‐Rate
Equivalent
Acknowledgements
MurielNiederleandLiseVesterlundwerekindenoughtosharetheirz‐Tree
programwithus.LaraMoultonandMarianneFaragprovidedexcellentresearch
assistance.FinancialsupportfromtheLeaveySchoolofBusinessatSantaClara
Universityisgratefullyacknowledged.
Abstract
Laboratoryexperimentshavedemonstratedthatmenaresignificantlymorewilling
tocompetethanwomengivenabinarychoicebetweenaPiece‐Rate(PR)and
Winner‐Take‐All(WTA)paymentinstereotypically‐maletasks.Thisdifferenceis
ascribedtovariantoverconfidenceandpreferenceforcompetition,andisbelieved
tohaveaprofoundimpactonthemarketforhighly‐competitivejobs,wherewomen
areunderrepresented.Inthispaper,wedevelopanewinstrumenttomeasurethe
willingnesstocompetebyofferingsubjectsaseriesofPRpaymentsrangingfrom0
to100percentoftheWTApayment,whichenableustoidentifythePRequivalentof
a$2.00WTApayment;thatis,thevalueofthe$2.00WTApayment.Wefindthat
womenvalueWTApaymentssignificantlylessthanmen,about$0.28less;andthat
womenrequireapremium(relativetomen)ofabout40percenttocompete.Our
newinstrumentismoresensitivethanthetraditionalbinary‐choiceinstrument,as
itclassifiesthewillingnesstocompeteinto21categories.Thisenableustoidentify
relationshipsthatarenotidentifiableusingthebinary‐choiceinstrument.For
example,wefindthatsubjectswhoarethemostwillingtocompetealsohavehigh
abilityonaverage;andthatthereisapositiverelationshipbetweenthewillingness
tocompeteandGPAformen(notforwomen),andapositiverelationshipbetween
thewillingnesstocompeteandtakingSTEMcoursesforwomen(notformen).
1.Introduction
Laboratoryexperimentshavedemonstratedthatmenaresignificantlymorewilling
tocompeteinastereotypically‐maletaskthanarewomen(Niederle&Vesterlund
(NV),2011).Thisgenderdifferenceisascribedtovariantbeliefsaboutrelative
performanceandpreferencesforcompetition(bygender).1Thegenderdifferencein
thewillingnesstocompeteisbelievedtohaveaprofoundimpactonthelabor
market,especiallyinthemarketforthemostcompetitiveandlucrativejobs,where
womenareunderrepresented.Forexample,womenheld2.5percentofthefive
highestpaidjobsatU.S.firmsbetween1992and1997(Bertrand&Hallock,2001).
Thisdisparitypersistseveninthefaceoffemaleeducationalgainsandgreater
governmentguaranteesagainstgenderdiscrimination(Goldin,Katz,&Kuziemko,
2006).NV(2011)assertthatthegenderdifferenceinthewillingnesstocompete
impliesthatwomenenter—andconsequentlywin—fewercompetitions,andthus,
mayhelpexplainwomen’sunderwhelmingperformanceinmale‐dominatedfields.
Importantly,thisiscostlynotonlyforwomenwhomaynotadvanceinlucrative,
male‐dominatedfields,butalsoforsocietyasthebestjobcandidatemaynotbe
matchedwithajob.
Twoimportantquestionsfollow(NV,2011).First,whatincentivescouldchangethe
situation?Second,doesnatureornurtureexplainthegenderdifference?
Researchershavebeguntoexaminethefirstquestion.Forexample,Niederle,Segal,
andVesterlund(2013)investigatetheimpactofaffirmativeactionintheNV(2007)
setting.Theyfindthathavingaquotaforwomenincreaseswomen’swillingnessto
compete,especiallyamonghigh‐abilitywomen.BalafoutasandSutter(2010)find
thatprovidingwomenwithahandicapalsogeneratesareductioninthegender
differenceinthewillingnesstocompete(theyalsoreplicateNV’squotafinding).
Competinginteamshasalsobeenshowntoreducethegenderdifferenceinthe
willingnesstocompete(e.g.,Dargnies,2009;Healy&Pate,2011).Finally,Gupta,
PoulsenandVilleval(2013)showthatwomenaremorewillingtocompetein
single‐sexcompetitionsthaninmixed‐sexcompetitions.
Thispaper’sfirstcontributionistoconsideradifferentincentivethatcouldreduce
thegenderdifferenceinthewillingnesstocompete:financialincentives.Specifically,
weattempttoidentifythe“relativepayoff”—WTApaymenttoPRpayment—thatis
1NV(2007)spawnedaseriesoflaboratoryexperimentsthattesttherobustnessandlimitsoftheir
seminalfinding:menaresignificantlymorewillingtocompeteinamathtaskthanarewomen.For
example,researchershaveconductedlaboratoryexperimentsthat(a)manipulatesubjects’beliefsby
providingsubjectswithfeedbackregardingtheirrelativeperformance(e.g.,Cason,Masters,&
Sheremeta,2010;Wozniak,Harbaugh&Mayr,2009)andusingtasksthatarenotstereotypically‐
male(e.g.,Grosse&Riener,2010;Kamas&Preston,2009;Wozniaketal.,2009);(b)explicitlycontrol
forriskpreferences(e.g.,Casonet.al.,2010;Wozniaketal.,2009);and(c)employproportional
winner‐take‐allpayments(e.g.,Casonet.al.,2010).Whilethisbodyofresearchhasillustrated
circumstancesunderwhichNV(2007)doesnothold,themainfinding(thatmenaresignificantly
morewillingtocompeteinstereotypically‐maletasksthanarewomen)hasbeenreplicated
repeatedly(seeNV(2011)forathoroughreviewoftheliterature).
necessaryforasubjecttocompete.Todoso,weoffersubjectsaseriesofchoices
betweenPiece‐Rate(PR)payments—rangingfrom0to100percentoftheWinner‐
Take‐All(WTA)payment—andaWTApayment.Wefindthatwomenrequirea
significantlygreaterrelativepayofftocompete,about40percentmore,thanmenon
average.IntheU.S.,incontrast,womenarebelievedtobepaidless(notmore)than
menforsimilarjobs(Bertrand&Hallock,2001).Thus,itshouldcomeasnosurprise
thatwomenareunderrepresentedinthemostcompetitive,male‐dominatedjobs.
Moreover,ourfindingsuggeststhatifwomenreceivedasalarypremium(relativeto
men)thattheirunder‐representationinsuchjobsmightbereduced.
Thispaper’ssecondcontributionistodevelopaninstrumentthatenablesusto
measurethestrengthofasubject’swillingnesstocompetealongacontinuumand
alsoataseriesofrelativepayoffs.Incontrast,thetraditionalbinary‐choice
instrumentprovidesresearcherswithasingledatapointregardingthesubject’s
willingnesstocompete.Consequently,weareabletodemonstratethatNV(2007)
holdsforallPRpaymentsbetween5and70percentoftheWTApayment.Further,
weareabletoidentifyrelationshipsbetweenthewillingnesstocompeteandother
variablesthatarenotidentifiableusingthetraditionalbinary‐choiceinstrument.
Forexample,wefindthatsubjectswhoarethemostwillingtocompetealsohave
highabilityonaverage.
Thispaper’sthirdcontributionistoexploretherelationshipbetweenthe
willingnesstocompete—usingournewinstrument—andacademicperformance,
enrollmentinScience,Technology,Engineering,andMath(STEM)courses,and
participationinvarsityathletics.Wefindthatthereisapositiverelationship
betweenthewillingnesstocompeteandGPAformen,butnotforwomen;andthat
thereisapositiverelationshipbetweenthewillingnesstocompeteandtakingSTEM
courseforwomen,butnotformen.KamasandPreston(2012)findnogender
differenceinthewillingnesstocompetebetweenmaleandfemaleSTEMmajors.
OurresultsuggestsanexplanationforKamasandPreston’sresult.Wefinda
positiverelationshipforwomen(butnotformen)betweenthenumberofSTEM
coursesawomentakesandherwillingnesstocompete.GiventhatSTEMmajors
takemoreSTEMcoursesthannon‐STEMmajors,femaleSTEMmajorsshouldbe
morewillingtocompetethanfemalenon‐STEMmajors;andthus,femaleSTEM
majorsmaybemoresimilartomenintheirwillingnesstocompetethanfemalenon‐
STEMmajors.Finally,wefindthatfemalevarsitycollegeathletesaremorewillingto
competethanwomenwhoarenotvarsitycollegeathletes.
Theseresultsareimportantforatleasttworeasons.First,ithasbeensuggestedthat
theunderrepresentationofwomeninSTEMfieldsmayhelpexplainwhywomenare
paidlessthanmenonaverage.Ourfindingsuggeststhatwomenwhoareless
willingtocompetearelesslikelytotakeSTEMcourses,andpresumablyenterSTEM
fields.Itisimportanttonote,however,thatouranalysisisunabletodemonstratea
causallink.Thus,thisevidenceismerelysuggestive.Forexample,incontrast,our
resultmightimplythatwomenwhotakemoreSTEMcoursesbecomemorewilling
tocompete.ThisisimportantasitaddressesthesecondofNVquestions:Does
natureornurtureexplainthegenderdifference?Ourresultregardingfemalevarsity
collegeathletesisalsosuggestiveofthesamerelationship:Womenwhoparticipate
incollegevarsityathleticsbecomemorewillingtocompete.Again,wehavenot
demonstratedacausallink,andthus,ourresultcouldimplythatwomenwhoare
morewillingtocompetealsoparticipateincollegevarsityathletics.
Therestofthepaperunfoldsarefollows.Section2describedtheexperimental
design.Sections3and4presentsanddiscusstheresults,respectively.
2.ExperimentalDesign
Inbrief,ourexperimentalprocedurewasasfollows(additionaldetailsareprovided
below).(1)Subjectsreadandsignedtheinformedconsentform.(2)Subjects
completedfourtasksinwhichtheyaddedfivetwo‐digitnumbersforfiveminutes.
EachtaskwasincentivizedwitheitheraPiece‐Rate(PR)orWinner‐Take‐All(WTA)
payment.Intwoofthefourtaskssubjectshadtochoosebetweenthetwopayment
schemes.(3)Subjectscompletedafifthtask,inwhichtheychosebetweenvarious
payment‐schemesforthefirsttaskretrospectively.(4)Subjectsevaluatedtheir
performanceonthefirstfourtasks.(5)Subjectscompletedfiveadditionaltasksthat
arepartofaseparatestudyanddiscussedinIfcherandZarghamee(2013).(6)
Subjectscompletedariskpreferencetask.(7)Subjectsansweredquestions
regardingdemographicandothercharacteristics.(8)Subjectsreceivedtheir
paymentandexitedtheexperimentalsession.Experimentalsessionslasted
approximately90minutes.Subjectsreceivedaminimumpaymentof$18andan
averageof$30fortheirparticipation.Theexperimentwasprogrammedand
conductedwiththesoftwarez‐Tree(Fischbacher2007);NVgraciouslyprovided
theirz‐Treeprogram,whichwemodifiedforthisstudy.Allinstructionswereread
aloudbytheexperimenterandareincludedinAppendixA.2
2.1.Subjects
ThelaboratoryexperimentwasconductedatSantaClaraUniversityinthefallof
2012.One‐hundredandeightundergraduatestudents(58male,50female)were
recruitedfromcoursesthatallundergraduatestudentsarerequiredtotake.These
courseswerechoseninanattempttoensurethatthesamplewasrepresentativeof
theundergraduatestudentbody.Prospectivesubjectsweretoldthatparticipation
inthestudywouldtakeabout90minutesandthattheywouldbepaidfortheir
participation,withanaveragepaymentof$32andaminimumpaymentof$16.
2.2.Tasks1,2,and3
ThisexperimentbuildsuponNV(2007)andthefirstthreetasksreplicatethosein
NV(2007).Subjectshadfiveminutestoperformsummations;eachsummationwas
2Weranthreepilotsessionswith36subjectsinthesummerof2012.Thepilotsessionsdidnot
includethefiveadditionaltasksthataredescribedinitem(5)above.
offiverandomlychosen,two‐digitnumbersdisplayedhorizontallyacrossa
computerscreen.Subjectsweregivenapenandscrappapertouseduringthe
session;subjectswerenotallowedtousecalculators.Immediatelyaftersubjects
submittedananswer,theprograminformedthemiftheiranswerwascorrect,
displayedthenumberofcorrectandincorrectanswerssubmittedbythesubject
duringthetasksofar,andpresentedanewsummationproblem.Afterfiveminutes,
thetaskendedandsubjectscouldnotsubmitadditionalanswers.Subjectsreceived
nofeedbackfromtheprogramorexperimenterregardingtheperformanceofother
subjectsintheirsession.
Thepaymentschemeforthefirstthreetasksvaried.Beforecompletingeachtask,
subjectsreceiveddetailedinstructionsregardingthetaskandpaymentscheme(all
instructionswerereadaloudbytheexperimenter).Thepaymentschemefortask1
wasa$0.50PRpaymentpercorrectanswer.Thepaymentschemefortask2wasa
WTApaymentandthusdependedonperformancerelativetoothergroupmembers.
Thesubjectwhosubmittedthemostcorrectanswerswithineachgroupoffour
subjectsreceived$2.00percorrectanswer;theotherthreegroupmembers
receivednopayment.Tiesweresettledrandomlybythecomputer.
Theinstructionsexplicitlystatedthatasubject’sgroupincludedthosethreeother
subjectssittinginthesame(front‐to‐back)rowasthesubject;thatis,thosesubjects
sittingimmediatelyinfrontofand/orbehindthesubject.Whensubjectsarrivedfor
theirsession,theexperimenterassignedsubjectstoseatsbysimplystating,for
example,“Pleasesitinseat10.”Theorderinwhichseatswereassignedwasnot
systematicexceptthattheexperimenterattemptedtoseattwofemaleandtwomale
subjectsineachrow.Lastly,therewasnoexplicitmentionofthegroups’gender
balance,however,subjectscouldobservetheothersubjectsintheirgroupand
session.Ofthe27groupsintheexperiment,24hadtwomaleandtwofemale
subjects,twohadthreemaleandonefemalesubject,andonehadfourmale
subjects.Allresultsreportedbelowarerobusttodroppingthethreegroupsthat
haveanunequalnumberofmaleandfemalesubjects.
Thepaymentschemefortask3wasdeterminedbythesubject’schoicebetweenthe
$0.50PRandthe$2.00WTApaymentusedintasks1and2,respectively.The
instructionsexplicitlystatedthatifsubjectschoosethe$2.00WTApayment,then
theirperformanceintask3wouldbecomparedtotheirgroup‐mates’performance
intask2.Asintask2,tiesweresettledrandomlybythecomputer.
2.3.Tasks4and5
Task4usedthesamesummationtaskastasks1through3buthadadifferent
paymentscheme.Inanattempttomorefullyunderstandsubjects’preferences
betweenPRandWTApayments,weofferedsubjectsaseriesofchoicesbetween
variousPRpayments,rangingfrom$0.00to$2.00,anda$2.00WTApayment.All
choiceswerepresentedverticallyonasinglescreen.Thefirstchoicewasbetweena
$0.00PRpaymentanda$2.00WTApayment.Thenextchoicewasbetweena$0.10
PRpaymentanda$2.00WTApayment.Thereafter,thePRpaymentincreasedin
$0.10incrementsuntilitreached$2.00(seeFigure1forascreenshotofthisseries
ofchoices).Wewouldexpectsubjectstochoosethe$2.00WTApaymentwhenthe
alternativeisa$0.00PRpayment;conversely,wewouldexpectsubjectstochoose
the$2.00PRpaymentwhenthealternativeisa$2.00WTApayment.
Weattempttoidentifythestrengthofeachsubject’spreferenceforaPRpayment
relativetoaWTApaymentbyobservingherswitchpoint:theminimumPRpayment
thesubjectpreferredtoa$2.00WTApayment.Switchpointsrepresentthe“PR
equivalentofthe$2.00WTApayment”—hereafterdenotedsimply“PR‐equivalent.”
Further,weexaminethedistributionofPR‐equivalentstodeterminethemeanand
medianPR‐equivalentaswellasthePR‐equivalentCDF.
Task5usesthesamepaymentschemeastask4.However,intask5subjectsare
choosingbetweenvariousPRpayments,rangingfrom$0.00to$2.00,anda$2.00
WTApaymentfortheirandtheirgroup‐mate’sperformanceintask1.Subjectswere
remindedhowmanyquestionstheyansweredcorrectlyintask1,butagainreceived
noinformationregardinghowothersubjectsinthesessiondid.AsinNV(2007),
task5isincludedinthisstudyinanattempttoruleoutriskandfeedbackaversion
asanexplanationforgenderdifferencesintherelativepreferenceforPRpayments.
2.4.Beliefsregardingrankintasks1through4
Subjectswereaskedtorankthemselvesrelativetotheirgroup‐matesintermsofthe
numberofquestionstheyansweredcorrectlyintasks1through4:1stbest,2ndbest,
3rdbest,or4thbest(i.e.,worst).Subjectswereinformedthattheywouldbepaidan
additional$1foreachtaskinwhichtheyrankedthemselvescorrectly.Thensubjects
completedfiveadditionaltasks,6through10,whichusedthesamepayment
schemesastasks1through5,respectively,butusedarandomtaskinplaceofthe
summationtask.Tasks6through10arenotconsideredinthestudyandarepartof
aseparatestudydiscussedinIfcherandZarghamee(2013).3
2.5.Task11
Task11wasastandardrisk‐preferencemeasure(Holt&Laury,2002).Subjects
chosebetweenaseriesoffixedpayments,rangingfrom$0.00to$10.00,anda
lotterywitha50%chanceofa$10paymentanda50%chanceofa$0payment.All
choiceswerepresentedverticallyonasinglescreen.Thefirstchoicewasbetweena
$0.00fixedpaymentandthelottery.Thenextchoicewasbetweena$1.00fixed
3InIfcherandZarghamee(2013)wenotonlyexploresubjects’willingnesstocompeteinarandom
taskbutalsoinvestigateordereffects.Thus,100subjectscompletedtasks6through10firstand
tasks1through5second.Asweareprimarilyfocusedonthenewinstrumentinthispaperandthere
isevidenceofsubstantialordereffects,wedonotincludethe100subjectswhocompletedthe
randomtasksfirstandthesummationtaskssecondintheanalysisinthispaper.
paymentandthelottery.Thereafter,thefixedpaymentcontinuedtoincreasein
$1.00incrementsuntilitreached$10.00.
2.6.Questionnaire
Subjectscompletedaquestionnairethatincludedquestionsregardingtheir
demographicandothercharacteristics,forexample,dateofbirth,gender,race,
familybackground,personalitycharacteristics,andsubjectivewell‐being.In
addition,thequestionnaireincludedquestionsregardingtheirpastandcurrent
participationincompetitivesports,whichenabledustoexaminewhethersuch
participationiscorrelatedwiththerelativepreferenceforaPRpayment.Wealso
askedforsubjects’permissiontodownloadtheirtranscriptandincorporatetheir
choiceofmajorsandcoursestaken(aswellastheircoursegrades)intoour
analyticaldatabase;allsubjectsgaveuspermissiontodoso.Thiswasdoneto
examinewhetherthelikelihoodofpursuingSTEM(Science,Technology,
Engineering,andMath)majorsandcoursesiscorrelatedwiththerelative
preferenceforaPRpayment.
2.7.Payments
Subjectsweregivendetailedinstructionsregardingthecalculationoftheir
payment;again,allinstructionswerereadaloudbytheexperimenter.Subject‐
paymentsincluded:a$5.00show‐upfee;$11.00forcompletingtheeleventasks;a
$1.00paymentforcorrectlyindicatingtheirrankintasks1,2,3,or4(andtasks6,7,
8,or9);andapaymentbasedontwooftheelevencompletedtasks.Todetermine
whichtwotaskswouldbepaid,twonumbers,betweenoneandeleven,were
randomlychosen(withoutreplacement)usingabingospinnerafterallsubjectshad
completedthequestionnaire.Iftasks4or5(or9or10)werechosen,thenoneof
the21PRpaymentswasrandomlychosen,againusingthebingospinner.Iftask11
waschosen,thenoneofthe11fixedpaymentswasrandomlychosenandthelottery
wasimplementedusingthebingospinner.Subjectpaymentswerepaidincash.The
paymentwasplacedinanenvelopewithonlythesubjects’identificationnumberon
it,andsubjectsreceivedtheirpaymentenvelopesastheyexitedthesession.
3.Results
3.1.ReplicationofmainNV(2007)findings
WebeginbyreplicatingNV’smainresults.First,thereisnogenderdifferencein
performanceonthesummationtaskinanyofthefourtasks,1through4.For
example,intask1menandwomencorrectlyanswer9.6and8.8questions,
respectively,onaverage(p=0.40);allp‐valuesreportedinthepaperaretwo‐sided.
Onemalesubjectcorrectlyansweredanaverageof49questionspertask;the
secondbestperformingsubjectcorrectlyanswered20questionspertask.Ifthebest
performingsubjectisdroppedfromthecalculation,thenmenandwomencorrectly
answer9.0and8.8questions,respectively,onaverage(p=0.81).4Subjects’
performanceiscorrelatedacrossthetasksforbothgenders(Spearmanrank
correlationsrangefromalowof0.52forwomenbetweentasks1and2toahighof
0.84formenbetweentasks3and4).Finally,performanceimprovessignificantly
betweentasks1and2;marginallybetweentasks2and3;andinsignificantly
betweentasks3and4forbothgenders(men:9.6,10.6,11.4,and11.6;women:8.8,
10.5,11.0,and11.1).
Second,comparedtowomen,menaresignificantlymorelikelytochoosethe$2.00
WTApaymentwhenofferedachoicebetweenitandthe$0.50PRpaymentintask3
(0.57versus0.34,p=0.02).Examiningtherelationshipbetweenthechoiceofthe
WTApaymentintask3andperformanceontasks1and2,onefindsthat,forboth
menandwomen,thosewhochoosetheWTApaymentintask3donotperform
significantlybetterintasks1and2thandothosewhochoosethePRpayment(p≥
0.14forallmeasures)(seeTable1).Formen,theimprovementinperformance
betweentask1and2isnotsignificantlydifferentforthosewhochoosetheWTA
versusPRpaymentintask3(1.2versus1.0,p=0.83).Forwomen,however,those
whochoosetheWTApaymentintask3improvesignificantlymorebetweentasks1
and2thandowomenwhochoosethePRpayment(2.9versus1.0,p=0.03).This
resultdivergesfromNV.Lastly,aprobitestimationshowsthatwomenare
significantlylesslikelythanaremen(marginaleffect=24percentagepoints)to
choosetheWTApayment,controllingfortask‐2performanceandimprovementin
performancebetweentasks1and2.
3.2.MeasuringthewillingnesstocompeteusingPR‐equivalents
Weidentifythestrengthofeachsubject’srelativepreferenceforaPRpaymentby
observingthePR‐paymentequivalentoftheWTApayment(hereafterdenoted“PR‐
equivalent”):theminimumPRpaymentthesubjectchoosesovera$2.00WTA
payment.PRpaymentsincreasein$0.10incrementssoasubjectwhoswitchesat
the$0.60PRpaymentmighthaveswitchedataPRpaymentbetween$0.51and
$0.59aswell.ThegreaterthePR‐equivalent,thegreaterthePRpaymentneedsto
be(relativetothe$2.00WTApayment)forasubjecttochoosethePRpayment,
implyingastrongerrelativepreferenceforWTApayments.Weinterpretrequiringa
greaterPR‐equivalentasindicatingagreaterwillingnesstocompete.Accordingly,
weinterpretthewillingnesstocompeteasincreasinginPR‐equivalent.
Ofthe108subjectsinthestudy,100haveidentifiablePR‐equivalents.Specifically,
96choosetheWTApaymentwhenthePRpaymentis$0.00,continuetochoosethe
WTApaymentuntilauniquePRpaymentatwhichtheychoosethePRpayment,and
4Duringtask2onefemalesubjectraisedherhandandreportedthatshecouldnotenterananswer
toasummationquestionintothecomputer.Theexperimenterwalkedovertohercomputerand
enteredtheanswerforherwithoutaproblem.Afterthatshedidnotreportanyproblemsentering
answersintothecomputer.Theexperimentertoldherthatiftask2wasselectedasthepaymenttask
herpaymentwouldbeadjusted.Task2wasnotselectedasapaymenttaskforthesession.
thereafterchoosethePRpaymentforallremainingvaluesofthePRpayment.Two
subjectsalwayschoosetheWTApaymentforallPRpayments,includingthe$2.00
PRpayment;thesesubjectsarecodedashavinga$2.10PR‐equivalent.Incontrast,
twosubjectsalwayschoosethePRpayment,evenwhenitis$0.00;theyarecoded
ashavinga$0.00PR‐equivalent.Finally,eightsubjects’PR‐equivalentcannotbe
identified,astheirchoicesdonotfollowanyoftheprecedingpatterns.Forexample,
someswitchbetweentheWTAandPRpaymentsmorethanonce.Theseeight
subjectsaredroppedfromallfurtheranalyses.
Figure2illustratesthedistributionoftask‐4PR‐equivalents.ThemeanPR‐
equivalentis$0.81,illustratingthatonaveragesubjectsrequirea$0.81PRpayment
toswitchfromthe$2.00WTApaymenttothePRpayment.ThemedianPR‐
equivalentis$0.60.ThemodalPR‐equivalentis$0.50,with20percentofsubjects
switchingatthisPRpayment.ThesecondmostcommonPR‐equivalentis$1.00;16
percentofsubjectshavethisPR‐equivalent.Sothedistributionisbi‐modaland
subjectsappeartobunchatthe$0.50and$1.00PRpayment.Finally,36percentof
subjectshaveaPR‐equivalentof$1.00orgreater.
Examiningthedistributionoftask‐4PR‐equivalentsbygender,oneobservesaclear
distinctionbetweenthetwodistributions(Fisher’sexacttest:p=0.04)(seeFigure
3).ThemeanandmedianPR‐equivalentsaresignificantlygreaterformenthanfor
women,$0.94versus$0.66(p=0.01),and$0.85versus$0.60,respectively.Further,
onlyninepercentofmenhaveaPR‐equivalentof$0.50orless;incontrast,28
percentofwomenhaveaPR‐equivalentof$0.50orless.Conversely,whileonlynine
percentofwomenhaveaPR‐equivalentof1.50orgreater,thecorrespondingfigure
formenis20percent.Regressingtask‐4PR‐equivalentsongender,onefindsthat
men’sPR‐equivalentsaresignificantlygreaterthanwomen’s(b=$0.28,p=0.01).
Figure4illustratestheCDFofthosewhochoosethePRpaymentovertheWTA
paymentforallPRpaymentsbetween$0.00and$2.00bygender.ThefemaleCDFis
everywheretotheleftofthemaleCDF.Thisindicatesthatagreaterpercentageof
womenchoosethePRpaymentovertheWTApaymentatallPRpayments.Thus,
NV’sseminalfindingisnotdependentontherelativepayoffbeingfour($2.00WTA
paymentto$0.50PApayment).However,theverticaldistancebetweenthemale
andfemaleCDF(thedifferenceinthepercentofmenandwomenthatchoosethePR
paymentatagivenPRpayment)issmalleratPRpaymentsnear$0.00and$2.00.
EstimatingtheverticaldistancebetweenthemaleandfemaleCDF,weregress
subjects’choices(1=WTApaymentand0=PRpayment)forallPRpayments
between$0.00and$2.00ongender;weclustertheobservationsbysubject,as
subjects’21choicesarenotindependent.Womenare13.5percentagepointsless
likelytochoosetheWTApaymentthanaremenacrossallPRpayments(p=0.01);
limitingtheanalysistoPRpaymentsbetween$0.50and$1.50,womenare17.5
percentagepointslesslikelythanarementochoosetheWTApayment(p=0.01).
Onecancomparesubjects’choicesbetweena$0.50PRand$2.00WTApaymentin
task3,wherethechoiceispresentedasinNV(2007),andintask4,whereitis
presentedasthesixthof21choices.Althoughthechoiceitselfisthesame,the
contextchanges.Intheformer,thechoiceispresentedbyitself.Inthelatter,the
choiceispresentedinthecontextofaseriesofbinarychoicesbetweenvariousPR
paymentsanda$2.00WTApayment.Theframingappearstohaveanimpacton
subjects’choices.Intheformersetting,59percentofmenand35percentofwomen
choosetheWTApayment(theseresultsareslightlydifferentthanthosepresented
previously,astheeightsubjectswithunidentifiabletask‐4PR‐equivalentsarenot
included).Inthelattersetting,thepercentofmenwhochoosetheWTApayment
increases10percentagepoints(p=0.17)to69percent;forwomenthepercent
increases19percentagepoints(p=0.01)to54percent.Thatwomen’schoicesare
moreaffectedisperhapsnotsurprisinggiventhatCrosonandGneezy(2009)find
thatwomenaremorecontext‐sensitivethanaremen.Lastly,subjects’task‐3choice
ofpaymentscheme(1=WTApaymentand0=PRpayment)ishighlycorrelated
withtheirtask‐4PR‐equivalent(Spearmanrankcorrelation=0.61,p=0.00),
suggestingthatbothinstrumentsaremeasuringasimilarparameter.
ExaminingeachPRpaymentseparately,womenaresignificantlylesslikelyto
choosetheWTApaymentthanaremenforallPRpaymentsbetween$0.10and
$1.30(p<0.10foreach)exceptthe$0.50PRpayment.Conversely,womenarenot
significantlylesslikelytochoosetheWTApaymentthanaremenfornineof21PR
payments.ThelackofasignificantgenderdifferencewhenthePRpaymentis$0.00
and$2.00isnotsurprising,asonewouldexpectsubjectstochoosetheWTA
paymentintheformerandthePRpaymentinthelatter.Further,thelackofa
significantgenderdifferenceatthe$0.50PRpaymentappearstobeidiosyncraticas
thereisasignificantgenderdifferenceforneighboringPRpayments.However,the
lackofasignificantgenderdifferencewhenthePRpaymentisbetween$1.40and
$1.90suggeststhatmenarenotmorelikelytochoosetheWTApaymentwhenthe
PRpaymentislarge,thatis,whenthePRpaymentisatleast70percentoftheWTA
payment.
3.3.UsingPR‐equivalentstocalculatethe“relativepayoff”ofWTApayments Ithasbeenarguedthatgenderdifferencessuchasthoseobservedinthisandother
papersareimportantastheymayexplainthepaucityofwomeninsomehighly
competitivejobs(NV,2011).Inotherwords,womenshyawayfrompositionsthat
includecompensationschemesthatmimic,insomerespects,WTApayments.PR‐
equivalentsenableustoexaminehowmuchgreateraWTApaymenthastobe
relativetoaPRpaymentsothatasubjectchoosestheWTApayment.Specifically,
the“relativepayoff”atthePR‐equivalentistheWTApaymentdividedbythePR
paymentatthePR‐equivalent.Forexample,ifisasubject’sPR‐equivalentis$0.80,
thentherelativepayoffatherPR‐equivalentis2.5(=$2.00WTApayment÷$0.80
PRpayment).Inotherwords,aslongastherelativepayoffisgreaterthan2.5,the
subjectwillchoosetheWTApayment;otherwiseshewillchoosethePRpayment.
RelativepayoffsatthePR‐equivalentcanrangefromone($2.00PR‐equivalent)to
infinity($0.00PR‐equivalent).ThegreatertherelativepayoffatthePR‐equivalent,
thegreatertheWTApaymentneedstoberelativetothePRpayment,forasubject
tochoosetheWTApayment,implyingaweakerrelativepreferenceforWTA
payments.WeinterpretrequiringagreaterrelativepayoffatthePR‐equivalentas
indicatingalowerwillingnesstocompete.Accordingly,weinterpretthewillingto
competeasdecreasingwiththerelativepayoffatthePR‐equivalent.
Nextwerepeattheanalysisaboveusingsubjects’relativepayoffattask‐4PR‐
equivalents.Women,onaverage,choosetheWTApaymentaslongastherelative
payoffisgreaterthan3.0(=$2.00WTApayment÷$0.66meanPR‐equivalent).In
contrast,men,onaverage,choosetheWTApaymentaslongastherelativepayoffis
greaterthan2.1(=$2.00WTApayment÷$0.94meanPR‐equivalent).Thus,
comparedtomen,womenrequirea43percentrelativepayoff“premium,”on
average,tochoosetheWTApayment.UsingthemedianinsteadofthemeanPR‐
equivalenttheresultissimilar:themajorityofwomenrequirearelativepayoff
greaterthan3.3(=$2.00WTApayment÷$0.60medianPR‐equivalent)tochoose
theWTApayment.Incontrast,menrequirearelativepayoffgreaterthan2.4(=
$2.00WTApayment÷$0.85medianequivalent).Thiscorrespondstowomen
requiringa37.5percentrelativepayoff“premium”tochoosetheWTApayment.
Theseresultssuggestthat,allelseequal,womenrequireasubstantiallylarger
payoff,onaverage,tocompete.
Intheirseminalwork,NVoffersubjectsasingle,carefullychosenrelativepayoffof4
(=$2.00WTApayment÷$0.50PRpayment).NVchoosethisrelativepayoffasit
ensuresthattheexpectedpayoffisthesameforPRandWTApaymentsifasubject’s
chanceofwinningtheWTAtournamentis25percent(therearefoursubjectsin
eachgroup).UsingNV’sinstrument,oneisnotabletodeterminehowlargethe
relativepayoffneedstobesothatasubjectchoosestheWTApayment,thestrength
ofasubject’srelativepreferenceforWTApayments,northerelativepayoff‐
premiumthatisneededsothatwomenareaslikelyasmentochoosetheWTA
payment.
3.4.Responsivenessofchoicestorelativepayoff
Weexaminetheresponsivenessofsubjects’choicestochangesintherelativepayoff
oftheWTApayment.Specifically,weperformaprobitregressionofsubjects’choice
ofpaymentscheme(1=WTApaymentand0=PRpayment)onthelogofrelative
payoffsintask4.Thechoicebetweena$0.00PRand$2.00WTApaymentsis
droppedfromthisanalysisastherelativepayoffwouldbeinfinite(=$2.00÷$0.00).
Theobservationsareclusteredbysubject,asthesubjects’20choicesarenot
independent.Theresultsindicateahighlysignificantpositiverelationshipbetween
thelogoftherelativepayoffandthelikelihoodofchoosingtheWTApayment;that
is,thelikelihoodthatsubjectschoosetheWTApaymentoverthePRpayment
increasesintherelativepayoff.Themarginaleffectsindicatethatdoublingthe
relativepayoffisassociatedwitha45percentincreaseinthelikelihoodofchoosing
theWTApayment(p=0.00).Interestingly,thestrongpositiverelationshipissimilar
formenandwomen.Interactingthelogoftherelativepayoffswithgenderand
addingagenderdummy(1=femaleand0=male)totheregression,wefindthatthe
coefficientontheinteractiontermisnotsignificantlydifferentthanzero(p=0.17).
Themarginaleffectsimplythatdoublingtherelativepayoffisassociatedwitha58
percent(p=0.00)anda35percent(p=0.00)increaseinthelikelihoodofchoosing
theWTApaymentformenandwomen,respectively.Thus,therelationshipbetween
therelativepayoffandthelikelihoodofchoosingtheWTApaymentissimilarfor
menandwomeneventhoughwomenarelesslikelytochoosetheWTApaymenton
average.
3.5.ResponsivenessofPR‐equivalentstoperformance
Regressingtask‐4PR‐equivalentsongenderandtask‐3performance,thecoefficient
onfemaleisnegativeandstatisticallysignificant(b=‐0.27,p=0.01),indicatingthat
aftercontrollingforperformancewomen’smeanPR‐equivalentis$0.27lessthanis
men’smeanPR‐equivalent(seeTable2).Ifonedoesnotcontrolfortask‐3
performance,thecoefficientonfemaleisvirtuallyunchanged,b=‐0.28(p=0.01);
thus,performancedoesnotexplainthegenderdifferenceinthewillingnessto
compete,asmeasuredbyPR‐equivalents.
Interestingly,thecoefficientontask‐3performanceispositiveandstatistically
significant(b=0.03,p=0.00),indicatingthatforeachadditionalsummation
questionasubjectanswerscorrectlyherPR‐equivalentincreasesbyanaverageof
$0.03.Wecontrolfortask‐3performancesincesubjectschoosetheirtask‐4PR‐
equivalentbeforecompletingtask4.Specifically,whilechoosingtheirtask‐4PR‐
equivalentsubjects’beliefscouldnothavebeeninfluencedbytheirtask‐4
performance.Thecoefficientsonfemaleandperformancearesimilarif,insteadof
controllingfortask‐3performance(whensubjectschosebetweenaWTAandPR
payment),wecontrolfortask‐2performance(whenallpaymentswereWTA
payments)ortask‐4performance.Finally,controllingforimprovementsin
performancebetweentasks1and2,and2and3,doesnotaffecttheresults.
TheresultabovedivergesfromNV(2007).NVfindthatsubjects’likelihoodof
choosingtheWTApaymentdoesnotincreasewithperformanceaftercontrollingfor
genderandimprovementinperformance.Thisraisesthequestionofwhetherour
resultsdivergefromNV(2007)becauseourinstrumentisdifferentorbecauseour
sampleisdifferent.Toexaminethisquestionweperformaprobitregressionof
task‐3choiceofpaymentscheme(1=WTApaymentand0=PRpayment)ontask‐2
performanceandimprovementinperformancebetweentasks1and2;recall,task3
mimicstheNVinstrument.Thecoefficientontask‐2performanceispositivebut
insignificant(marginaleffect:b=0.02,p=0.19)(seeColumn4ofTable2).This
replicatestheresultinNV(2007)andindicatesthatthereisnotasignificant
relationshipbetweenperformanceandthelikelihoodofchoosingtheWTApayment
intask3.Thus,ourPR‐equivalentinstrumentappearstobemoresensitivethan
NV’s.Specifically,weareabletoconfirmthatthewillingnesstocompete,as
measuredbyPR‐equivalents,isincreasinginperformance.
Figures5aand5billustratetherelationshipbetweentask‐4PR‐equivalentsand
task‐3andtask‐2performance,respectively.Examiningthefiguresclosely,the
positiverelationshipbetweenPR‐equivalentsandperformanceismostapparentfor
high‐valuePR‐equivalents.Forexample,meantask‐3performanceforsubjectsin
thefirstthroughfifthquintileoftask‐4PR‐equivalentsis10.3,10.5,10.4,11.4,and
14.2,respectively;further,meantask‐3performanceforsubjectsinthetenthdecile
oftask‐4PR‐equivalentsis17.1.Themeantask‐3performanceofsubjectsinthe
fifthquintileandtenthdecileoftask‐4PR‐equivalentsissignificantlygreaterthan
themeantask‐3performanceforsubjectsnotinthosegroups(14.2versus10.6,p=
0.01,and17.1versus10.7,p=0.00,respectively).Theresultsaresimilarifweuse
task‐2performanceinsteadoftask‐3performance,orifweimposeatopcodeof30
onthesubjectwhoanswered51questionscorrectlyintask3.Thisresultisperhaps
notsurprisingastheWTAtournamenthasfourparticipants.Soonlysubjectswho
believetheyarethebestintheirgroupshouldhaveelevatedPR‐equivalents.Using
NV’sinstrument,thisresultisobscuredassubjectsarenotabletoexpressthe
strengthoftheirpreferenceforWTApayments(astheyareabletowithPR‐
equivalents).
Interestingly,forbothmenandwomen,thosewithhigh‐valuetask‐4PR‐
equivalents—11menand4womenhavePR‐equivalentsof$1.50orabove—have
significantlybettertask‐3performancethandothemenandwomenwithPR‐
equivalentsbelow$1.50(men:15.6versus10.6,p=0.02;andwomen:14.8versus
10.7p=0.03).Thesameresultsareobtainedifoneusestask‐2performance.Thus,
somemenandwomenexpressagreaterwillingnesstocompete,asmeasuredby
PR‐equivalents,andtheypresumablybelievetheyhaveahighlikelihoodof
receivingtheWTApayment.Incontrast,comparingthosewhochoosetheWTA
paymenttothosewhochoosethePRpaymentintask3,thedifferenceintask‐2
performanceisnotsignificantlydifferentformennorwomen(men:11.5versus9.9,
p=0.38;andwomen:11.7versus9.9,p=0.12).
Finally,somequalitativeevidenceregardingtherelationshipbetweenthe
willingnesstocompeteandperformancewarrantsmention.Weasksubjectsthe
followinginthequestionnairethatisadministeredafteralltasksarecompletedbut
beforepayment‐revelation:“Whatfactorsdidyouconsiderinmakingyourchoice
betweentheTournamentandPiece‐ratepaymentschemeinTask3?”Thesubject
withthebestperformance,averaging49correctanswerspertask,statesthat
“BecauseIamsuchabeastataddition,Ipickedtournamentscheme.TheleastIgot
was45right.”Healwayschosethe$2.00WTApayment,evenwhenoffereda$2.00
PRpaymentintask4.Thesubjectwiththesecondbestperformance,averaging20
correctanswerspertask,didnotanswertheabovequestion,buthistask‐4PR‐
equivalentis$2.00.SohedoesnotchoosethePRpaymentuntilitisequaltothe
WTApayment.Finally,thesubjectwiththethirdbestperformance,averaging18.5
correctanswerspertask,statesthat,“IconsideredmybeliefinhowwellIcanadd
andhowwellIdidinthepreviousone.AlsoIconsideredmyprejudgementsonthe
otherpeopleinmygroupbasedongender/howfastIheardthemclickinginthe
previousones.”Hertask‐4PR‐equivalentis$1.50.Herresponseindicatesthateven
thoughsubjectsdonotreceiveformalfeedbackabouttheirrelativeperformance
fromtheexperimenter,subjectsmaybeattemptingtodeterminehowwelltheyare
doingrelativetoothersubjectsintheirgroupusingauditoryorother
environmentalcues.Thus,subjectswithhigh‐valuePR‐equivalentsmaybeawareof
theirsuperiorrelativeperformance;andtheirwillingnesstocompete,asmeasured
byPR‐equivalents,mightsimplyreflectthattheyknowtheyareadeptatthetask
andmaynotrepresentageneralizedpreferenceforcompetition.
Insummary,likeNV(2007),wefindevidencethatmenhaveagreaterwillingnessto
competethandowomen:men’smeantask‐4PR‐equivalentissignificantlygreater
thanwomen’s;andmenaresignificantlymorelikelythanwomentochoosethe
$2.00WTApaymentoverthe$0.50PRpaymentintask3.However,unlikeNV
(2007),wefindevidencethatawillingnesstocompeteislinkedtosuperior
performance:task‐4PR‐equivalentsarepositivelyrelatedtotask‐3performance;
andthosewhohaveahigh‐valuetask‐4PR‐equivalentarestrongperformers,on
average.
3.6.ResponsivenessofPR‐equivalentstobeliefsaboutperformanceandrisk
preferences
Malecollegestudentsarebelievedtobemoreoverconfidentthanfemalecollege
students(Croson&Gneezy,2009;Ifcher&Zarghamee2013).Inoursample,men’s
meantask‐3self‐rank(where1=1stbest,2=2ndbest,3=3rdbest,and4=4thbest)
issignificantlyhigherthanwomen’s(1.7versus2.3,p=0.00),eventhoughmen’s
meantask‐3performanceisnotsignificantlybetterthanwomen’s(11.4versus11.0,
p=0.71).Men’sgreaterwillingnesstocompetecouldsimplybetheresultoftheir
greateroverconfidence.Regressingtask‐4PR‐equivalentsongenderandtask‐3self‐
rank,thecoefficientonfemaleisnegativeandsignificant(b=‐0.20,p=0.04),
indicatingthataftercontrollingforoverconfidencemenstillhaveagreater
willingnesstocompete,asmeasuredbyPR‐equivalents,thandowomen(seeTable
3).Thecoefficientontask‐3self‐rankisnegativeandsignificant(b=‐0.14,p=0.02),
indicatingthatthewillingnesstocompeteisincreasingwithself‐rank.Theseresults
mirrorresultsinNV(2007).
Anotherpotentialexplanationfortheobservedgenderdifferenceinthewillingness
tocompeteisvariantriskpreferences.Menarebelievedtobelessriskaversethan
arewomen(Croson&Gneezy,2009).Inourstudy,wemeasureriskpreferences
usingaHolt‐Laurylottery(task11).Weidentifysubjects’task‐11certainty
equivalentusingthesameprocedureasweusetodeterminesubjects’task‐4PR‐
equivalent.Ofthe100subjectswithidentifiabletask‐4PR‐equivalents,99have
identifiabletask‐11certaintyequivalents.Thegreaterthetask‐11certainty
equivalent,thegreaterthefixedpaymentiswhenthesubjectswitchesfromthe
lotterytothefixedpayment,indicatingthesubjectislessriskaverse.Inoursample,
themeantask‐11certaintyequivalentismarginallygreaterformenthanitisfor
women($5.20versus$4.70,p=0.09),suggestingthatmeninourstudyarelessrisk
aversethanarewomen.Regressingtask‐4PR‐equivalentsongenderandtask‐11
certaintyequivalents,thecoefficientonfemaleisnegativeandsignificant(b=‐0.21,
p=0.03),indicatingthataftercontrollingforriskpreferences,asmeasuredbytask‐
11certaintyequivalents,menhaveagreaterwillingnesstocompete,asmeasured
bytask‐4PR‐equivalents,thandowomen(seeColumn4ofTable3).Thecoefficient
ontask‐11certaintyequivalentsispositiveandsignificant(b=0.14,p=0.00),
indicatingthatthewillingnesstocompeteincreasesasriskaversiondecreases.
Further,controllingforallthreecovariatesinthesameregression,task‐3
performance,task‐3self‐rank,andtask‐11certaintyequivalents,thecoefficienton
femaleremainsnegativeandsignificant(b=‐0.18,p=0.04),indicatingthat,after
controllingforperformance,self‐rank,andriskpreferences,menhaveagreater
willingnesstocompete,asmeasuredbyPR‐equivalents,thandowomen.Again,this
mirrorsNV(2007).Importantly,controllingforself‐rankandriskpreferencesdoes
notdiminishtherelationshipbetweenthewillingnesstocompeteandperformance.
Thecoefficientontask‐3performanceispositiveandsignificant(b=0.03,p=0.01),
indicatingthatthepositiverelationshipbetweenperformanceandwillingnessto
competeisnotexplainedbyself‐rankandriskpreferences(seeColumn5ofTable
3).ThisresultagaindivergesfromNV(2007)andraisesthequestionofwhetherthe
divergenceisduetothenewinstrumentoradifferentsample.Toexaminethis
question,weregresstask‐3choices(NV’sinstrument)ontask‐2performance,task‐2
self‐rank,andtask‐11certaintyequivalents.Thecoefficientontask‐2performance
isnotsignificant(b=0.00,p=0.87),indicatingthatwhenusingNV’sinstrumentit
appearsthatthereisnorelationshipbetweenperformanceandthewillingnessto
compete,asmeasuredbythechoicebetweena$0.50PRpaymentanda$2.00WTA
payment(seeTable4).Interestingly,inthisspecification,thecoefficientonfemaleis
negativebutnotsignificant(b=‐0.15,p=0.19).ThisalsodivergesfromNV(2007)
whereasignificantgenderdifferenceinthewillingnesstocompeteisfoundafter
controllingforperformanceandself‐rank.Incontrast,thecoefficientsontask‐2self‐
rankandtask‐11certaintyequivalentaresignificantlyrelatedtothewillingnessto
compete(negativelyandpositively,respectively).
Finally,repeatingtheaboveregressionformenandwomenseparately,wefindthat
therelationshipbetweenthewillingnesstocompeteandperformanceandself‐rank
holdformenbutfornotwomen.Formen,thecoefficientontask‐3performanceand
ontask‐3self‐rankare0.03(p=0.00)and‐0.14(p=0.06),respectively;theyare
0.02(p=0.69)and0.04(p=0.72)forwomen,respectively(seeColumns6and7of
Table3).Incontrast,therelationshipbetweenthewillingnesstocompeteandrisk
preferencesissimilarformenandwomen(men:b=0.11,p=0.00,andwomen:b=
0.13,p=0.01).Usingtask‐2performanceandself‐rankinplaceoftask‐3
performanceandself‐rankintheregression,onefindssimilarresultsexceptthat
therelationshipbetweenthewillingnesstocompeteandtask‐2self‐rankisnow
significantforwomenbutnotmen(men:b=‐0.06,p=0.41,andwomen:b=‐0.30,p
=0.00).
3.7.Impactofchoicesonexpectedpayments
Toexaminetheimpactofsubjects’choicesontheirpayments,wecalculateeach
subject’sexpectedpaymentbasedonherchoicesforeachofthe21offeredPR
paymentsintask4.Forexample,ifasubjectchosethe$0.50PRpaymentoverthe
$2.00WTApayment,thenherexpectedpaymentwouldbetheproductofthe$0.50
PRpaymentandhertask‐4performance.Incontrast,ifasubjectchosethe$2.00
WTApaymentoverthe$0.50PRpayment,thenherexpectedpaymentwouldbethe
productofthe$2.00WTApayment,hertask‐4performance,andtheprobabilityof
winningtheWTAtournament,wheretheprobabilityofwinningisimputedusing
thedistributionofwinners’task‐2performancewhenallpaymentsareWTA
payments.Foreachsubjectwealsocalculatethesubject’smaximumpossible
expectedpaymentforeachofthe21offeredPRpayments.Specifically,wecalculate
asubject’sexpectedpaymentfromchoosingthePRandWTApayment(asdescribed
above),andselectthelargerofthetwo.
Theexpectedpaymentsofsubjects’choicesare,onaverage,88percentoftheir
maximumpossibleexpectedpayments.Asapercentageofthemaximumpossible
expectedpayment,theexpectedpaymentfromsubjects’choicesisgreatestwhen
thePRpaymentis$0.00or$2.00,asalmostallsubjectschosetheWTAandPR
payment,respectively,therebynearlymaximizingexpectedpayments.Table5
presentstheaveragepercentofthemaximumpossibleexpectedpayment
representedbytheexpectedpaymentofsubjects’choices.Asapercentageofthe
maximumpossibleexpectedpayment,theexpectedpaymentfromsubjects’choices
islowest—74percent—atthe$0.50PRpayment.The$0.50PRpaymentisthe
valueatwhichtherelativepayoffofthePRpaymentisthesameasthe
unconditionalchanceofwinningtheWTAtournament:one‐quarter.Interestingly,
theanalogouscalculationfortask3(when$0.50istheonlyPRpaymentoffered)is
69percent,whichisnotsignificantlydifferent(p‐valueofdifference=0.23).
Figures6and7illustratetherelationshipbetweenthepercentofthemaximum
possibleexpectedpaymentsandtask‐3performanceandtask‐4PR‐equivalents,
respectively.Noclearpatternemergesineitherfigure.Tosystematicallyexamine
thisrelationship,weregressthepercentofthemaximumpossibleexpected
paymentongender,task‐3performance,task‐3self‐rank,andtask‐11certainty
equivalent.Noneofthecoefficientsisstatisticallysignificant.However,dividingthe
sampleintolow‐andhigh‐performingsubgroups—subjectswhoperformworse
thanandbetterthanthetask‐3median(11summations),respectively—onefinds
thatthecoefficientonthetask‐11certaintyequivalentisnegativeandsignificant(b
=‐6.45,p=0.04)forthelow‐performingsubgroup,andpositiveandsignificant(b=
2.65,p=0.01)forthehigh‐performingsubgroup(seeTable6).Thisindicatesthat,
forlow‐performing(high‐performing)subjects,thepercentofthemaximum
possibleexpectedpaymentisincreasing(decreasing)withriskaversion.Inother
words,forlow‐performingsubjects,riskaversionispositivelyrelatedtothepercent
ofthemaximumpossibleexpectedpaymentrepresentedbytheexpectedpayment
ofsubjects’choices.Themagnitudeofthecoefficientislarge:requiringanextra
dollartoswitchfromthelotterytothefixedpaymentisassociatedwithalossof
6.45percentagepointsofthemaximumpossibleexpectedpayment.The
relationshipistheoppositeforthehigh‐performingsubjects,butthecoefficientis
smaller.Thisindicatesthatreducedriskaversionispositivelyrelatedtothepercent
ofthemaximumpossibleexpectedpaymentforhigh‐performingsubjects.Itisalso
interestingthatthecoefficientonfemaleisnegativeandmarginallysignificant(b=‐
6.86,p=0.09)forthehigh‐performingsubjectsbutnotforthelow‐performing
subjects,suggestingthathigh‐performingfemalesearnalowerpercentageoftheir
maximumpossibleexpectedpaymentthandotheirmalecounterparts.Thisgender
differenceisnotobservedforthelow‐performingsubjects.Thisresultisinlinewith
theNV(2007)resultthathigh‐performingwomenunder‐compete.
3.8.Relationshipbetweentask‐4PR‐equivalentsandSTEMcoursesandGPA
Ithasbeensuggestedthatgenderdifferencesinthewillingnesstocompetemay
explainthepaucityofwomeninSTEMfields.Toexplorewhetherthisisthecase,we
regresstask‐4PR‐equivalentsonthenumberofSTEMcoursessubjectshavetaken;
wecontrolfortask‐3performance,task‐3self‐rank,andtask‐11certainty
equivalentsineachregressioninthissection.Thecoefficientonthenumberof
STEMcoursesispositivebutinsignificant(b=0.10,p=0.21)(seeTable7).The
resultschangemarkedly,however,whentheanalysisisrepeatedseparatelyformen
andwomen.ThecoefficientonSTEMcoursesispositiveandsignificantforwomen
(b=0.03,p=0.01),andnegativeandinsignificantformen(b=‐0.003,p=0.68).
Thisindicatesthatwomenwhohaveagreaterwillingnesstocompete,asmeasured
bytheirPR‐equivalents,takemoreSTEMcoursesthandowomenwhohavealower
willingnesstocompete.Incontrast,formenthereisnorelationshipbetweenthe
willingnesstocompeteandSTEMcourseenrollment.Ananalogousregressionthat
considerstherelationshipbetweenthewillingnesstocompeteandhavingaSTEM
majorfindsasimilarpattern:apositiverelationshipforwomenbutnotformen;
however,noneoftheresultsaresignificant.
ExaminingtherelationshipbetweenthewillingnesstocompeteandcumulativeGPA
onefindstheoppositeresult:thereisapositiveandsignificantrelationshipbetween
thetwoformen(b=0.27,p=0.01)butnotforwomen(b=0.15,p=0.55).This
indicatesthatmenwhohaveagreaterwilinesstocompetehavehigherGPAsthan
menwhohavealowerwillingnesstocompete(seeTable8);thisrelationshipdoes
notholdforwomen.Asaspecificationcheck,weincludeSTEMcoursesandGPAas
independentvariablesinthesameregression,andtheresultsareunchanged.The
juxtapositionofthesetworesultscanleadtosomeinterestingspeculation.For
example,formen(butnotforwomen)doingwellacademicallyisdrivenbya
willingnesstocompete;andforwomen(butnotmen)takingSTEMcoursesisdriven
byawillingnesstocompete.Moreover,therelationshipbetweenthewillingnessto
competeandtask‐3performanceholdsformen,butnotwomen.So,perhapsitisnot
surprisingthattherelationshipbetweenthewillingnesstocompeteandGPAholds
formen,butnotwomen.However,itmustbenotedthattherelationshipsidentified
abovearesimplycorrelational,andthus,nocausalinferenceshouldbepresumed.
3.9.Relationshipbetweentask‐4PR‐equivalentsandparticipationinvarsitysports
Socialscientistsstudyingthepreferenceforcompetitionhaveponderedwhetherit
canbelearned.Inanattempttoexplorethisquestionweasksubjectsabouttheir
participationinhighschoolandcollegevarsitysports;whilewecannotidentify
causalrelationship,wecanexploretherelationshipbetweenthewillingnessto
competeandparticipationinvarsitysports.Wefirstconsiderparticipationin
collegevarsitysports.Regressingtask‐4PR‐equivalentsonparticipationincollege
varsitysports,wefindthatthecoefficientonparticipationispositiveandsignificant
forwomen(b=0.85,p=0.05)butinsignificantformen(b=0.07,p=0.78).This
appearstoindicatethatforwomenparticipatingincollegevarsitysportsis
positivelyrelatedtoawillingnesstocompete.Themagnitudeoftheeffectis
noteworthy,implyingthatparticipationisassociatedwitha$0.85increaseintask‐4
PR‐equivalent.Cautionmustbeusedwheninterpretingthisresultasitisbasedon
twofemaleandthreemalecollegevarsityathletes.Further,whethermore
competitivewomenparticipateincollegevarsitysportsorwhetherwomenlearnto
bemorecompetitivethroughcollegevarsitysportsisnotidentifiableinthisstudy
andmustbeexaminedinafutureresearchproject.
Examiningtherelationshipbetweenthewillingnesstocompeteandparticipationin
highschoolvarsitysports,weregresstask‐4PR‐equivalentsonparticipationinhigh
schoolvarsitysports.Wefindthattherelationshipisnegativeandinsignificantfor
bothmenandwomen(men:b=‐0.23,p=0.21,andwomen:b=‐0.05,p=0.66).The
negative(thoughinsignificant)coefficientmayatfirstappearcurious.However,65
percentofsubjectsarehighschoolvarsityathletes.Thus,collegevarsityathletesare
ahighlyselectivegroupandhighschoolvarsityathletesarenot.Thatis,thesetwo
subgroupsmaynotbesimilar.Forexample,whilemeantask‐3performancefor
varsitycollegeathletesisbetterthanfornon‐athletes(13.6versus11.2,p=0.33),
meantask‐3performanceforvarsityhighschoolathletesisworsethanfornon‐
athletes(11.0versus12.1,p=0.31).Onepossibleexplanationforthenegative
relationshipbetweenthewillingnesstocompeteandparticipationinhighschool
varsityathleticsmightbethatathletesarelessoverconfidentthannon‐athletes.
Thatis,highschoolvarsityathletesmightlearntobelessoverconfidentthrough
competingandinevitablylosing.Further,wespeculatethatthisshouldbeespecially
trueforlow‐performingmen,sincetheycanbethemostoverconfident.Inour
samplewefindsupportforthisexplanation:highschoolvarsityathletesrank
themselveslowerthannon‐athletes(2.1versus1.8,p=0.15);thereisasimilar
patternforthefivecollegevarsityathletes(2.2versus2.0,p=0.59).Furthermore,
thedifferenceislargerformen(1.9versus1.2,p=0.01)thanforwomen(2.4versus
2.2,p=0.35),andislargestformenwhosetask‐3performanceisworsethanthe
median(2.3versus1.4,p=0.05).Restrictingtheregressiontomenwithtask‐3
performancebelowthemedian,wefindthatthecoefficientonhighschoolvarsity
participationisnegativeandmarginallysignificant(b=‐0.47,p=0.08).Again,the
magnitudeoftheeffectisnoteworthy,suggestingthatparticipationinhighschool
varsityathleticsisassociatedwitha$0.47decreaseintask‐4PR‐equivalentforlow‐
performingmen.
Interestingly,therelationshipsidentifiedbetweenthewillingnesstocompeteand
STEMcourses,GPA,andvarsitysportsparticipationarenotidentifiableusingtask‐3
choices.Specifically,weconducttheanalogousanalysesexceptwithaprobit
regressionusingthetask‐3choiceofpaymentscheme(1=WTApaymentand0=
PRpayment)asthedependentvariableandaddingcontrolsfortask‐2performance
andself‐rank.Allthecoefficientsofinterestareinsignificant.Thus,thetask‐3
measureisnotsensitiveenoughtoidentifytherelationshipsidentifiedabove.
Lastly,thecoefficientsontask‐3performance,task‐3self‐rank,andtask‐11
certaintyequivalentsinthissectionareconsistentwithourpriorresults:
performanceispositivelyrelatedtothewillingnesstocompeteformen,andgreater
riskaversionisinverselyrelatedtothewillingnesstocompeteformenandwomen.
3.10.Task5
SubjectsretrospectivelychosewhethertheywantedtoapplyaPRpaymentora
$2.00WTApaymenttotheirtask‐1performanceforthesame21PRpayments
offeredintask4.InNV(2007),ananalogoustaskisusedtoruleoutpotential
explanationsfortheobservedgenderdifferenceinthewillingnesstocompete.NV
findnosignificantgenderdifferenceinchoicesbetweena$0.50PRanda$2.00WTA
paymentwhentheyregresssubjects’retrospectivechoicesongender,task‐1
performance,andtask‐1self‐rank.Theyarguethatthesalientdifferencebetween
thetworesultsisthatsubjectscompletethetaskaftermakingtheirchoiceonlyin
themainresult.Theyinterpretthisfindingasdemonstratingthattheobserved
genderdifferenceinthemainresultisexplainedbyavariantpreferencefor
competitionandnotbyotherfactors,forexample,overconfidenceandfeedbackand
riskaversion.ReplicatingNV’sexercise,weregresstask‐5PR‐equivalentson
gender,task‐1performance,andtask‐1self‐rank.Thecoefficientonfemaleis
negativeandmarginallysignificant(b=‐0.14,p=0.07).Thus,thereissome
evidencethatthereisagenderdifferencewhenusingretrospectivechoices.
However,thecoefficientbecomesinsignificant(b=0.10,p=0.18)ifoneaddstask‐
11certaintyequivalents(riskaversion)totheregression(seeColumn3ofTable8).
NVdidnotmeasuresubjects’riskpreferencesdirectly,sotheycouldnotconductan
analogousregression.Thus,wefindsupportthatcompletingthetaskafterchoosing
thepaymentschemeisanimportantcontributortosubjects’observedwillingness
tocompete.
4.Discussion
Wedevelopanewinstrumenttomeasurethewillingnesstocompetebyoffering
subjectsaseriesofPRpaymentsrangingfrom0to100percentoftheWTA
payment.TheofferedPRpaymentsimplyrelativepayoffs(WTApaymenttoPR
payment)rangingfrominfinityto1.Weidentifyeachsubject’sPRequivalentofthe
WTApayment.Thatis,thevalueoftheWTApaymenttothesubject.Wefindthat
womenvaluethe$2.00WTApaymentsignificantlylessthandomen,about$0.28
less;andthatwomenrequireapremium(relativetomen)ofabout40percentto
compete.Giventhisresultandthefactthatwomenarepaidlessthanmenforthe
samejobonaverage,itisperhapsnosurprisethatwomenareunderrepresentedin
competitive,male‐dominatedfields.Ourresultalsosuggeststhatifwomenwere
offeredapremium(relativetomen)forcompetingthatthegenderdifferenceinthe
willingnesstocompetemightbeeliminated.
WeusethenewinstrumenttodemonstratethatNV’smainresultholdsforPR
paymentsbetween5and70percentofthe$2.00WTApayment.Thus,NV’sfinding
holdformanyrelativepayoffsandisnotdependentontheratioofthePRpayment
totheWTApaymentbeingequaltotheunconditionalchanceofwinningthe
tournamentinthebinary‐choiceinstrument.Otherresearchershavedemonstrated
thatthereisagenderdifferenceinthewillingnesstocompeteusingproportional
tournamentpaymentaswell(e.g.,Casonet.al.,2010).
Ourinstrumentismoresensitivethanthebinary‐choiceinstrument,asitclassifies
thewillingnesstocompeteinto21categories.Thisenableustoidentify
relationshipsbetweenthewillingnesstocompeteandothervariablesthatarenot
identifiableifoneusesthebinary‐choiceinstrument.Forexample,wefindthat
subjectswhoarethemostwillingtocompetealsohavehighabilityonaverage.This
relationshipisnotidentifiableusingthebinary‐choiceinstrument.Itisimportantas
itimpliesthatatleastpartiallythewillingnesstocompetemaynotbedependent
uponindividual’soverconfidenceandpreferenceforcompetition.Rather,itmaybe
taskspecific.Thatis,individualsmaybemorewillingtocompete,notsurprisingly,
intasksatwhichtheyareabove‐averageorexceptional.Thisinterpretationis
supportedbystudiesthatfindmenarenotmorewillingtocompetethanwomenin
stereotypically‐femaletasks(e.g.,Kamas&Preston,2009).Further,asonesubject
reportedinthequestionnaire,subjectsarereceivingfeedbackontheirrelative
performancebasedonnoisesintheroomandothercues.Outsidethelab,
individualspresumablyusevariouscuestohelpdeterminetheirlikelihoodof
winningcompetitions.Womenmaybemoresensitivetosuchcues;again,Croson
andGneezy(2009)findthatwomenaremorecontext‐sensitivethanmen.Finally,
wefindevidencethatthewillingnesstocompeteisdecreasingwithriskaversion.
Thus,thewillingnesstocompeteappearstoberelatedtobothperformanceandrisk
preferencesinadditiontooverconfidenceandpreferencesforcompetition.
Further,wefindapositiverelationshipbetweenthewillingnesstocompeteand
GPAformen(notforwomen);apositiverelationshipbetweenthewillingnessto
competeandtakingSTEMcoursesforwomen(notformen);andapositive
relationshipbetweenwillingnesstocompeteandparticipationinvarsitycollege
athleticsforwomen(notformen).Thelattertworesultsmaysuggestthat
individualscanlearntoincreasetheirwillingnesstocompete.Thatis,takingSTEM
coursesandparticipatinginvarsitycollegesportmayincreasewomen’swillingto
compete.However,asweemphasizeinthepaper,ourresearchdesigndoesnot
enableustodemonstrateacausalrelationship,andthus,causationcouldruninthe
oppositedirection:STEMcoursesandvarsitycollegeathleticsmayattractwomen
whoarethemostwillingtocompete.Furtherresearchisneededtoidentifythis
potentiallyimportantcausalrelationship,asitwouldhelpexplorewhetherwomen’s
willingnesstocompetecanbeaugmented.
Finally,giventhansubjects’choicebetweena$0.50PRpaymentanda$2.00WTA
paymentareimpactedbythecontextinwhichthechoiceispresented(task3versus
task4)suggeststhatsubjectschoicesintask4mightbeimpactedbyquestion‐order
andoranchoringeffects.Thus,furtherresearchiswarrantedtodeterminewhether
ourfindingsmightbesensitivetotheframingofthequestion.
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Table1:Task‐1andtask‐2performancebygenderandchoiceoftask‐3paymentscheme
Gender
Women
Men
Choice of payment scheme in task 3
PR payment
WTA payment
p‐value (two‐tail)
PR payment
WTA payment
p‐value (two‐tail)
Task 1
8.94 (0.45)
8.65 (0.71)
0.72
Average performance
Task 2
9.94 (0.56)
11.53 (1.00)
0.14
8.56 (0.62)
10.39 (1.25)
0.24
9.68 (0.59)
11.36 (1.34)
0.30
Task 2 ‐ Task 1
1.00 (0.42)
2.88 (0.85)
0.03
1.12 (0.39)
0.97 (0.53)
0.83
Observations
33
17
25
33
Table2:Estimatesfromregressingtask‐4PR‐equivalentsongenderandperformance
Task‐4 Task‐4 Task‐4 Task‐3 choice PR‐equivalent PR‐equivalent PR‐equivalent of WTA payment (1)
(2)
(3)
(4)
Female
‐0.268 (0.097) *** ‐0.276 (0.097) *** ‐0.274 (0.097) *** ‐0.258 (0.098) ***
Task‐3 performance
0.031 (0.008) *** 0.032 (0.009) ***
Task‐2 performance
0.032 (0.008) *** 0.016 (0.012)
Improvement between tasks 1 and 2
0.010 (0.020)
0.000 (0.016)
0.013 (0.022)
Improvement between tasks 2 and 3
‐0.013 (0.021)
100
100
100
Observations
100
Table3:Estimatesfromregressingtask‐4PR‐equivalentsongender,performance,self‐rank,andcertaintyequivalents
Task‐4 Task‐4 Task‐4 Task‐4 Task‐4 Male task‐4 Female task‐4 PR‐equivalent PR‐equivalent PR‐equivalent PR‐equivalent PR‐equivalent PR‐equivalent PR‐equivalent (6)
(1)
(2)
(3)
(4)
(5)
(7)
Female
Task‐3 performance
Task‐3 self‐rank
Task‐11 (lottery) certainty equivalent
Observations
‐0.284 (0.101) *** ‐0.268 (0.097) *** ‐0.197 (0.096) **
0.031 (0.008) ***
‐0.136 (0.059) **
100
100
100
‐0.212 (0.093) **
‐0.183 (0.088) **
0.025 (0.009) *** 0.025 (0.006) ***
‐0.037 (0.060)
‐0.137 (0.071) *
0.136 (0.027) *** 0.123 (0.029) *** 0.107 (0.029) ***
53
99
99
0.015 (0.038)
0.038 (0.106)
0.126 (0.046) ***
46
Table4:Estimatesfromregressingtask‐3choiceofpaymentschemeongender,performance,self‐rank,andcertainty
equivalents
Task‐3 choose WTA payment (1)
Female
Task‐2 performance
Task‐2 self‐rank
Task‐11 (lottery) certainty equivalent
Observations
‐0.250 (0.098) **
0.021 (0.012) *
100
Task‐3 choose WTA payment (2)
Task‐3 choose WTA payment (3)
‐0.177 (0.107)
‐0.154 (0.115)
0.003 (0.010)
0.002 (0.010)
‐0.199 (0.068) *** ‐0.152 (0.069) **
0.139 (0.043) ***
99
100
Table5:Averagepercentofthemaximumpossibleexpectedpaymentrepresentedbytheexpectedpaymentofsubjects’
choicesbyPRpayment
Percent of maximum
$0.00
0.980 (0.141)
0.10
0.783 (0.385)
0.20
0.763 (0.394)
0.30
0.748 (0.402)
0.40
0.762 (0.387)
0.50
0.738 (0.371)
0.60
0.755 (0.344)
0.70
0.741 (0.333)
0.80
0.774 (0.308)
0.90
0.792 (0.294)
1.00
0.809 (0.265)
1.10
0.836 (0.238)
1.20
0.852 (0.226)
1.30
0.868 (0.217)
1.40
0.889 (0.211)
1.50
0.917 (0.174)
1.60
0.942 (0.154)
1.70
0.953 (0.149)
1.80
0.961 (0.147)
1.90
0.968 (0.146)
2.00
0.995 (0.052)
Average
0.881 (0.161)
Standard deviation in parenthesis PR payment
Table6:Estimatesfromregressingpercentofmaximumpossibleexpectedpaymentongender,performance,self‐rank,and
certaintyequivalents
Task‐3 performance Dependent variable: percent of All worse than maximum possible expected payment (1)
median (2)
Female
‐1.806 (2.832)
‐0.539 (5.818)
Task‐3 performance
0.079 (0.322)
1.923 (1.420)
Task‐3 self‐rank
0.613 (2.771)
3.114 (3.982)
Task‐11 (lottery) certainty equivalent ‐1.597 (1.624)
‐6.447 (2.955) **
Observations
99
43
Task‐3 performance better than median (3)
‐6.863 (3.910) *
0.057 (0.336)
1.095 (3.256)
2.648 (0.955) ***
44
Table7:EstimatesfromregressingPR‐equivalentsongender,STEMcourses,performance,self‐rank,andcertaintyequivalents
All (1)
Dependent variable: Task‐4 PR‐equivalent
Female
STEM courses
Task‐3 performance
Task‐3 self‐rank
Task‐11 certainty equivalent
Observations
Men (2) ‐0.168 (0.088) *
0.010 (0.008)
‐0.003 (0.007)
0.026 (0.008) *** 0.025 (0.006) ***
‐0.038 (0.058)
‐0.138 (0.070) *
0.124 (0.029) *** 0.106 (0.031) ***
53
99
Women (3) 0.027 (0.009) ***
0.015 (0.036)
0.021 (0.107)
0.118 (0.044) ***
46
Table8:EstimatesfromregressingPR‐equivalentsongender,GPA,performance,self‐rank,andcertaintyequivalents
All (1)
Dependent variable: Task‐4 PR‐equivalent
Female
Cumulative GPA
Task‐3 performance
Task‐3 self‐rank
Task‐11 certainty equivalent
Observations
‐0.222 (0.088)
0.248 (0.091)
0.022 (0.009)
‐0.027 (0.060)
0.115 (0.029)
99
**
***
**
Men (2)
0.266 (0.094) ***
0.023 (0.007) ***
‐0.113 (0.073)
*** 0.104 (0.027) ***
53
Women (3)
0.147 (0.246)
0.015 (0.039)
0.040 (0.109)
0.119 (0.051) **
46
Figure1:ScreenshotofchoicesbetweenvariousPRpayments,rangingfrom$0.00to$2.00,anda$2.00WTApayment
Figure2:Distributionoftask‐4PR‐equivalents
0
5
Fr eq uen cy
10
15
Figure3:Distributionoftask‐4PR‐equivalentsbygender
0
.5
1
1.5
2
Task-4 PR-equivalents ($)
Female
Male
.8
.6
.4
.2
0
% ch o o s e P R p a y m en t
1
Figure4:CDFbygender
0
5
10
15
20
PR payment ($0.10)
Females
Males
Figure5a:Relationshipbetweentask‐4PR‐equivalentsandtask‐3performance
Figure5B:Relationshipbetweentask‐4PR‐equivalentsandtask‐2performance
Figure6:Relationshipbetweenthepercentofthemaximumpossibleexpectedpaymentsandtask‐3performance
Figure7:Relationshipbetweenthepercentofthemaximumpossibleexpectedpaymentsandtask‐4PR‐equivalents