幸福经济学论文

www.elsevier.com/locate/econbase

Thereliabilityofsubjectivewell-beingmeasures☆AlanB.Kruegera,⁎,DavidA.SchkadebbPrincetonUniversity,UnitedStates

UniversityofCalifornia,SanDiego,UnitedStates

aReceived19March2007;receivedinrevisedform9October2007;accepted29December2007

Availableonline16January2008

Abstract

Thispaperstudiesthetest–retestreliabilityofastandardself-reportedlifesatisfactionmeasureandofaffectmeasurescollectedfromadiarymethod.Thesampleconsistsof229womenwhowereinterviewedonThursdays,twoweeksapart,inSpring2005.Thecorrelationofnetaffect(i.e.,duration-weightedpositivefeelingslessnegativefeelings)measuredtwoweeksapartis.,whichisslightlyhigherthanthecorrelationoflifesatisfaction(r=.59).Correlationsbetweenincome,netaffectandlifesatisfactionarepresented,andadjustedforattenuationbiasduetomeasurementerror.Lifesatisfactionisfoundtocorrelatemuchmorestronglywithincomethandoesnetaffect.Componentsofaffectthataremoreperson-specificarefoundtohaveahighertest–retestreliabilitythancomponentsofaffectthataremorespecifictotheparticularsituation.Whilereliabilityfiguresforsubjectivewell-beingmeasuresarelowerthanthosetypicallyfoundforeducation,incomeandmanyothermicroeconomicvariables,theyareprobablysufficientlyhightosupportmuchoftheresearchthatiscurrentlybeingundertakenonsubjectivewell-being,particularlyinstudieswheregroupmeansarecompared(e.g.,acrossactivitiesordemographicgroups).©2008ElsevierB.V.Allrightsreserved.

Keywords:Subjectivewell-being;Lifesatisfaction;Netaffect;DayReconstructionMethod(DRM)

1.Introduction

Economistsareincreasinglyanalyzingdataonsubjectivewell-being(SWB).From2000to2006,157papersandnumerousbookshavebeenpublishedintheeconomicsliteratureusingdataonlifesatisfactionorsubjectivewell-being,accordingtoasearchofEconLit.1Dataonlifesatisfactionorhappinesshavebeenusedasoutcomemeasuresinstudiesofthetradeoffbetweeninflationandunemployment,theeffectofcigarettetaxesonwelfare,theeffectofGermanreunificationonwell-being,andtheeffectoflotterywinningsonwell-being.2Inaddition,lifeandwork

TheauthorsthankDanielKahneman,NorbertSchwarz,ArthurStoneandtwoanonymousrefereesforhelpfulcommentsandtheHewlettFoundation,theNationalInstituteonAging,andPrincetonUniversity'sWoodrowWilsonSchoolforfinancialsupport.⁎Correspondingauthor.

E-mailaddress:akrueger@princeton.edu(A.B.Krueger).1ProminentexamplesareLayard(2005),BlanchflowerandOswald(2004a,b),andFreyandStutzer(2002).2See,forexamples,DiTellaetal.(2003),GruberandMullainathan(2002),Frijtersetal.(2004),GardnerandOswald(2001).0047-2727/$-seefrontmatter©2008ElsevierB.V.Allrightsreserved.doi:10.1016/j.jpubeco.2007.12.015

☆1834A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–1845

satisfactionmeasureshaveappearedasexplanatoryvariablesinstudiesoflaborturnover,productivityandhealth.3Ifitcouldbemeasuredaccurately,orevenapproximately,subjectivewell-beingisanaturalvariableforeconomiststomodelandunderstandbecauseutilitymaximizationisacentralideaineconomics,fromeitheranormativeorpositiveperspective.Hereweanalyzethetest–retestreliabilityoftwotypesofmeasuresofsubjectivewell-being:astandardlifesatisfactionquestionandaffectiveexperiencemeasuresderivedfromtheDayReconstructionMethod(Kahnemanetal.,2004).Althougheconomistshavelongstandingreservationsaboutthefeasibilityofinterpersonalcomparisonsofutilitythatwecanonlypartiallyaddresshere,anotherquestionconcernsthepersistenceofsubjectivewell-beingmeasurementsforthesamesetofindividualsovertime.Absentdramaticevents,overalllifesatisfactionshouldnotchangemuchfromweektoweek.Likewise,individualswhohavesimilarroutinesfromweektoweekshouldexperiencesimilarfeelingsovertime.Howpersistentareindividuals'responsestosubjectivewell-beingquestions?Toanticipateourmainfindings,bothmeasuresofsubjectivewell-being(lifesatisfactionandaffectiveexperience)displayaserialcorrelationofabout.60whenassessedtwoweeksapart,whichislowerthanthereliabilityratiostypicallyfoundforeducation,incomeandmanyothercommonmicroeconomicvariables(Boundetal.,2001;AngristandKrueger,1999).Ifmeasurementerrorsarewhitenoise,areliabilityratioof.60impliessubstantialattenuationifthevariableisusedasanexplanatoryvariableinaregression.Measurementerrorwhensubjectivewell-beingisusedasadependentvariablewouldimplyalossofprecisioninresultingestimates.Nonetheless,theestimateddegreeofreliabilityofsubjectivewell-beingdataisprobablyhighenoughtodetecteffectswhentheyarepresentinmostapplications,especiallyifsamplesarelargeandthedataareaggregatedacrosspeopleoractivities.

ThelifesatisfactionquestionthatweexamineisnearlyidenticaltothatusedintheWorldValuesSurvey,andsimilartothatusedinmanyotherwell-beingsurveys.Thereisareasontoexpect,however,thatlifesatisfactionmeasuressuchasthismaynotbeasstablefromweektoweekasmightbeassumed.Rather,thesejudgmentsaretheresultofacomplexthoughtexperiment,whichisoftenpartiallydependentontransientinfluences(e.g.one'smoodatthetime;seeSchwarzandStrack,1999).

FormeasurementsoftheaffectiveexperienceofdailylifethegoldstandardisperhapstheExperienceSamplingMethod(ESM)(alsocalledEcologicalMomentaryAssessment(EMA)),inwhichparticipantsarepromptedatrandomintervalstorecordtheircurrentcircumstancesandfeelings(CsikszentmihalyiandLarson,1987;Stoneetal.,1999).Thismethodofmeasuringaffectminimizestheroleofmemoryandinterpretation,butitisexpensiveanddifficulttoimplementinlargesamples.TheDayReconstructionMethod(DRM)isarecentdevelopmentinthemeasurementofaffectiveexperience,whichreducesthecostofobtainingthisinformation.Consequently,weusetheDRM,inwhichparticipantsarerequestedtothinkabouttheprecedingday,breakitupintoepisodes,anddescribeeachepisodebyselectingfromseveralmenus(Kahnemanetal.,2004).TheDRMinvolvesmemory,butisdesignedtoincreasetheaccuracyofemotionalrecallbyinducingretrievalofthespecificsofsuccessiveepisodes(RobinsonandClore,2002;Belli,1998).Evidencethatthetwomethodscanbeexpectedtoyieldsimilarresultswaspresentedearlierforsubpopulationaverages(Kahnemanetal.,2004).AcriticaladvantageoftheDRMisthatitprovidesdataontimeuse—avaluablesourceofinformationinitsownright,whichhasrarelybeencombinedwiththestudyofsubjectivewell-being.

Inthispaperwereportreliabilitymeasuresforasampleof229employedwomenwhoeachfilledoutaDRMquestionnairefortwoWednesdays,twoweeksapartin2005.Wecomparethesereliabilityestimatestothoseofglobalwell-beingmeasuresmoretypicalintheliterature,andwedecomposethereliabilityofduration-weightednetaffectintoacomponentduetothesimilarityofactivitiesacrossdaysandotherfactors.Wealsoprovideanapplicationusingthereliabilityestimatestocorrectobservedcorrelationsbetweenself-reportedwell-beingandothervariables(e.g.,income)forattenuation.WeconcludewithadiscussionoftheimplicationsofmeasurementerrorforDRMstudiesandforwell-beingresearchmoregenerally.

1.1.Whatisreliabilityandwhyshouldwecare?

Consideranobservedvariable,y,whichisanoisymeasureofthevariableofinterest,y⁎.Wecanwriteyi=yi⁎+eiwhereyiistheobservedvalueforindividuali,yi⁎isthe“correct”value,andeiistheerrorterm.Underthe“classicalmeasurementerror”assumptions,eiisawhitenoisedisturbancethatisuncorrelatedwithyi⁎andhomoskedastic.Classicalmeasurementerrorwillleadcorrelationsbetweenyandothervariablestobeattenuatedtoward0inlargesamples.4Ifwecanmeasureyi34See,forexamples,Freeman(1978),ClarkandGeorgellis(2004),andPattersonetal.(2004).

Ifyisoflimitedrange(e.g.,abinaryvariable)thanewillnecessarilybecorrelatedwithy⁎.Weignorethisissueforthetimebeing.

A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–18451835

attwopointsintime,andifthemeasurementerrorsareindependentandhaveaconstantvarianceovertime,thenthecorrelationbetweenthetwomeasuresprovidesanestimateoftheratioofthevarianceinthesignaltothetotalvarianceiny.Wethusdefinethereliabilityratio,r,asr=corr(yi1,yi2),wherethesuperscriptsindicatethemeasurementtakeninperiods1

ðy⁎Þ

.and2.Undertheassumptionsstated,plimr¼varðvar⁎yÞþvarðeÞInadditiontosummarizingtheextentofrandomnoiseinsubjectivewell-beingreports,thesignal-to-totalvarianceratioisofinterestbecause,inthelimit,itequalstheproportionalbiasthatariseswhenSWBisanexplanatoryvariableinabivariateregression.Furthermore,asweexplainbelow,correlationsbetweenSWBandothervariablesareattenuatedbyrandommeasurementerrorinSWB.AnimportantapplicationofSWBdatainvolvesestimatingthecorrelationsamonglifesatisfaction,affectandothervariablessuchasincome(e.g.,Argyle,1999).Wecanusethereliabilityratiotocorrectthosecorrelationsforattenuation,whichwouldmeanthatmanyreportedrelationshipsarestrongerthanpreviouslythought.

Ofcourse,ifthemeasurementerrorisnotclassical,thetest–retestcorrelationcanunder-orover-statethesignal-to-totalvarianceratio,dependingonthenatureofthedeviationfromclassicalmeasurementerror.Withonlytworeportsofy,andwithoutknowledgeofy⁎,itisnotpossibletoassesstheplausibilityoftheclassicalmeasurementerrorassumptions.Iftheerrorsinmeasurementarepositivelycorrelatedovertime,thenthetest–retestcorrelationwillover-statethereliabilityofthedata.Nevertheless,thetest–retestcorrelationisaconvenientstartingpointforsummarizingthereliabilityofsubjectivewell-beingdata.1.2.Relatedliterature

Thereisavastempiricalliteratureonsubjectivewell-being(seeKahnemanetal.,1999forasurvey).Subjectivewell-beingismostcommonlymeasuredbyaskingpeopleasinglequestion,suchas,“Allthingsconsidered,howsatisfiedareyouwithyourlifeasawholethesedays?”or“Takenalltogether,wouldyousaythatyouareveryhappy,prettyhappy,ornottoohappy?”Suchquestionselicitaglobalevaluationofone'slife.Surveysinmanycountriesconductedoverdecadesindicatethat,onaverage,largeincreasesinpercapitanationalincomehavebeenfoundtohavelittleeffectonreportedglobaljudgmentsoflifesatisfactionorhappinessoverthelastfourdecades.Althoughreportedlifesatisfactionandhouseholdincomearepositivelycorrelatedinacrosssectionofpeopleatagiventime,increasesinincomehavebeenfoundtohavemainlyatransitoryeffectonindividuals'reportedlifesatisfaction(Easterlin,1995).5Moreover,thecorrelationbetweenincomeandsubjectivewell-beingisnotablyweakerwhenameasureofexperiencedhappinessisusedinsteadoflifesatisfaction(Kahnemanetal.,2006).Ofcourse,suchlowcorrelationscouldbepartiallyduetoattenuation,ifmeasurementerrorishigh.

Table1summarizespastestimatesofthereliabilityofSWBmeasures.Single-itemmeasuresofSWBhavebeenfoundtohavemoderatereliabilities,usuallybetween.40and.66,evenwhenaskedtwiceinthesamesession1hourapart(AndrewsandWhithey,1976).KammannandFlett(1983)foundthatsingle-itemwell-beingquestionsundertheinstructionstoconsider“thepastfewweeks”or“thesedays”hadreliabilitiesof.50to.55whenaskedwithinthesameday.Interestingly,theonlystudyweareawareofthatlookedatthereliabilityofanESMmeasureofduration-weightedhappinessfoundacorrelationontheupperendoftherangefoundforsingle-itemglobalwell-beingmeasures(Steptoeetal.,2005).Overall,therehasbeensurprisinglylittleattentionpaidtoreliability,despitethewideuseofthesemeasures.

TheSatisfactionwithLifeScale(SWLS,Dieneretal.,1985)isanothercommonlyusedglobalsatisfactionmeasure.Incontrasttothesinglequestionmeasuresitconsistsoftheaverageoffiverelateditems,eachofwhichisratedona7-pointscalefromStronglyDisagree(1)toStronglyAgree(7).Theitemsare:“Inmostwaysmylifeisclosetomyideal”;“Theconditionsofmylifeareexcellent”;“Iamsatisfiedwithmylife”;“SofarIhavegottentheimportantthingsIwantinlife”;and“IfIcouldlivemylifeover,Iwouldchangealmostnothing”.AkeyreasonthatSWLShasprovenmorereliablethansingle-itemquestions(seeTable1),isthatsinceitisthesumofmultipleitems,itbenefitsfromerrorreductionthroughaggregation.EidandDiener(2004)usedastructuralmodeltoestimatereliabilityforasampleof249students,measuredthreetimeswithfourweeksbetweensuccessivemeasurements.Aftercontrollingfortheinfluenceofsituation-specificfactors,theyestimatedthattheimputedstabilityforlifesatisfactionwasveryhigh,around.90.

SeeDeaton(2007)foracarefulstudyoftherelationshipbetweenaveragesubjectivewell-beingacrosscountriesandthelogarithmGDPpercapita.DeatonfindsapositiveeffectofthelevelofGDP,butGDPgrowthhasanegativeassociationwithSWB.

51836A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–1845

Table1

EstimatesofReliabilityforWell-BeingMeasures

Test–retestcorrelation

Single-itemmeasures

AndrewsandWhithey(1976)KammannandFlett(1983)Multiple-itemmeasuresaAlfonsoandAllison(1992)Pavotetal.(1991)Blaisetal.(19)Dieneretal.(1985)YardleyandRice(1991)Magnusetal.(1992)ESM

Steptoeetal.(2005)

aTemporalinterval1hourSameday

Variable

Lifesatisfaction

Overallhappiness,satisfaction

.40–.66.50–.55

.83.84..82.50.542weeks1month2months2months10weeks4yearsSWLSSWLSSWLSSWLSSWLSSWLS

.65Weekend–weekdayExperiencedhappiness

Note:FromPavotandDiener(1993),Table2.

Onereasonforthemodestreliabilityofsubjectivewell-beingmeasurescomparedwitheducationandincome,whichtypicallyhavereliabilityratiosofaround.90,couldbethesusceptibilityofSWBquestionstotransientmoodeffects.Forexample,researchershavedocumentedmoodchangesduetosuchsubtleeventsasfindingadimebeforefillingoutaquestionnaire,thecurrentweather,orquestionorder,whichinturninfluencereportedlifesatisfaction(e.g.,Schwarz,1987).EidandDiener(2004)usedastructuralmodel,whichattemptedtoseparatesituationalvariabilityfromrandomerrorandbasicstability,andfoundthatanywherefrom4%to25%ofthevarianceinvariousaffectandsatisfactionmeasureswereaccountedforbysituation-specificfactors.Inanearlierstudy,Ferringetal.(1996)estimatedthesizeoftransientfactorsasbetween12%and34%oftotalvariance.SincetheexperiencedaffectmeasureproducedbytheDRMisfocusedonreconstructingaspecificeventandtheaffectactuallyexperiencedduringit,thereisatleastthepossibilitythatsuchmeasureswillbelessvulnerabletocurrentmoodatthetimeoftheinterview.WemightexpectDRMmeasurestobelessreliableovertimethanlifesatisfaction,however,becauseaperson'sactivitieschangefromdaytoday,andaffectisassociatedwithactivities.Atthesametime,DRMmeasuresareaveragesofmultipleresponses,whilegloballifesatisfactionofhappinessisoftenassessedwithjustonequestion.IfESMisanyguide,theDRMmaybeatleastasreliableasreportedoveralllifesatisfaction.2.Method

Weevaluatethetest–retestreliabilityoftheDRMbyhavingthesamerespondentscompleteaDRMquestionnairetwoweeksapartregardingthesamedayoftheweek(Wednesday).Thequestionnaire,whichisavailablefromtheauthorsonrequest,alsocontainedstandardgloballifesatisfactionmeasures.TheresultingdataprovideinformationforthesamesampleabouttherelativestabilityoftheDRMcomparedtothetypesofgloballifesatisfactionquestionsusedinmostwell-beingresearch.

Forcomparabilitywithsomepreviousstudies,therespondents(n=229)wereselectedbyrandomselectionofwomenfromthedriver'slicenselistinTravisCounty,Texasandscreenedforemploymentandagebetween18and60.Respondentswerepaid$50uponcompletingthefirstquestionnaireandanadditional$100uponcompletingthesecondoneforatotalof$150.6TheinterviewdatesweretwoThursdays,March31,2005andApril14,2005.FollowingtheDRMprocedure,participantsreportedonthepreviousday.Completiontimesfortheself-administeredinstrumentrangedfrom45to75min.Theethniccompositionofthesamplewas67%white(non-Hispanic),7%

Atotalof241respondentscompletedthefirstquestionnaire.Ofthese,10didnotshowupforthesecondsessionand2showedupbutfailedtofollowthequestionnaireinstructionssufficiently.Therewasnosignificantdifferencebetweenthe229whocompletedbothquestionnairesandthese12dropoutsonanydemographicvariable,noronlifesatisfactionormoodindatafromthefirstsession(whichtheyallcompleted).Whileitispossiblethatthegreaterpaymentinthesecondsessioncouldhaveinfluencedwell-being,thepaymentcameafterthequestionnaireswerecompleted,andwefoundnosignificantdifferencesinthelevelofsatisfactionoraverageaffectbetweensessions.

6A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–18451837

AfricanAmerican,21%Hispanic,and5%other.Averageagewas42.8years.Medianhouseholdincomecategorywas$40,000–$50,000.Itispossiblethattheofferofapaymentaffectedindividuals'moods,butitisimportanttonotethatcompensationwasnotreceiveduntilaftertheinterviewwascompleted.

TheDRMprotocoldescribedbyKahnemanetal.(2004)wasfollowed.GroupsofparticipantswereinvitedtoacentrallocationforasessiononThursdayevening,wheretheyansweredaseriesofquestionscontainedinfourpackets.Thefirstpacketincludedgeneralsatisfactionanddemographicquestions.Next,therespondentswereaskedtoconstructadiaryofthepreviousday(Wednesday)asaseriesofepisodes,notingthecontentandthebeginningandendtimeofeach.Inthethirdpacket,theywereaskedforadetaileddescriptionofeveryepisodeasexplainedbelow.Thefourthpacketcontainedsomegeneralattitudeanddemographicquestions.Theaveragenumberofepisodesarespondentdescribedforthedaywassomewhathigherinthesecondsession(14.8vs13.2,pb.001,byapairedt-test)althoughthetotaltimecoveredbytheepisodeswasnodifferent(16.8vs16.7h,pN.20,byapairedt-test).Thesefigurescomparetothe14.1episodesand15.4hreportedinKahnemanetal.(2004).

ThefirstfewquestionsinthesurveywereglobalSWBquestions.Firstwastheoveralllifesatisfactionquestion,“Takingallthingstogether,howsatisfiedareyouwithyourlifeasawholethesedays?Areyouverysatisfied,satisfied,notverysatisfied,notatallsatisfied?”Next,similarsatisfactionquestionswereaskedfor“yourlifeathome”and“yourpresentjob”.Twoglobalmoodquestionsfollowed,forhomeandforwork.Thequestionposedwas,“Whenyouareathome,whatpercentageofthetimeareyouinabadmood____%,alittleloworirritable____%,inamildlypleasantmood____%,inaverygoodmood____%”.Thelasttworesponsecategorieswereaddedtogethertoobtainthepercentageoftimeinagoodmood.Netmoodwascomputedbysubtractingthesumofthefirsttworesponsecategoriesfromthesumofthelasttwo.Thesameprocedurewasappliedtotheworkmoodquestion.

Allrespondentsreceivedthepacketsinthesameorder.TheDRMisunlikelytobecontaminatedbythelifesatisfactionquestioncomingfirst,becauseitinvolvesaverydetailedprocedurewhichiscarefullygroundedintheactualexperiencespeoplehad.Ontheotherhand,therecouldbeapotentiallyseriousproblemwithhavingthelifesatisfactionquestionaftertheDRM,sinceitisathoughtexperimentandmoresusceptibletotransientinfluencesandordereffects.Inaddition,theoveralllifesatisfactionquestionusuallycomesbeforedomain-specificquestionsinwell-beingsurveys,sowearematchingtheliteratureonthispointaswell.

TheaffectmeasuresderivedfromtheDRMarecombinationsoftheduration-weightedaffectiveadjectivesthatrespondentsratedforeachepisode.Netaffectwascomputedbysubtractingtheaverageofnegativeemotions(encompassingtense/stressed,depressed/blueandangry/hostile),denotednegativeaffect(NA),fromtheaverageofpositiveemotions(encompassinghappy,affectionate/friendlyandcalm/relaxed),denotedpositiveaffect(PA).7Difmaxistheduration-weightedaverageofhappylessthemaximumoftense/stressed,depressed/blue,angry/hostile.TheU-indexiscloselyrelatedtoDifmax,andequalsonewhenDifmaxb0andequals0otherwise;thatis,attheepisodelevel,theU-indexequalsoneifthemostintensefeelingisanegativeone.Wedurationweighttheepisode-leveldata,sotheperson-levelU-indexmeasurestheproportionoftimethatanindividualspendsinanunpleasantstate.DifmaxandtheU-indexreflecttheintuitionthatanepisodecanbeaversiveifonlyoneofthenegativefeelingsisintense(KahnemanandKrueger,2006).3.Results

Table2presentsthecorrelationsbetweenvariousmeasuresforthesamepersoninthefirstandsecondsessions,aswellas95%confidenceintervals.Wefocusfirstonoverallmeasuresofaffectiveexperience.PerhapsthemostsurprisingfindingisthatthereliabilitiesofNetAffect(r=.)andDifmax(r=.60)areatleastashighasthatforlifesatisfaction(r=.59).Satisfactionwithdomainsoflife(workandhome)ismorereliablethansatisfactionwithlifeoverall.8Thecorrespondinghomeandworkmoodmeasuresarealsomorereliablethanlifesatisfaction.Anothernotablefeatureoftheresultsisthatpositiveaffectappearstobesomewhatmorereliablethannegativeaffect.

Theextenttowhichaperson'sratingofaparticularadjectiveoverdifferentepisodesofthedayrepresentspersonaltraitsorisinfluencedbythevariabilityinsituationsislikelyrelatedtothereliabilityofthatadjective.Ifagivenperson

Frustratedwasexcludedfromnegativeaffectforcomparabilitywithourotherstudies.

SeeKristensenandWestergaard-Nielsen(2006)forastudyofthereliabilityofself-reportedjobsatisfactioninsixEuropeanUnioncountries.Usinga10-pointscalejobsatisfactionquestionthatwasadministeredtwiceinthesamesurvey,theyfindthat80%ofworkersclassifiedthemselvesidenticallyorwithinonepoint,anddifferencesinclassificationsweresymmetricaroundzero.

871838A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–1845

Table2

Correlationsbetweenselectedmeasuresatperiod1andperiod2

Observed

Lower

GlobalmeasuresLifesatisfactionHomesatisfactionWorksatisfactionHomenetmoodWorknetmoodExperiencemeasuresNetaffectDifmaxU-index

PositiveaffectHappy

Affectionate/friendlyCalm/relaxedPA

NegativeaffectTense/stressedDepressed/blueAngry/hostileFrustratedNA

OtheraffectadjectivesImpatientforittoendCompetent/doingwellInterested/focusedTired

DemographicsHouseholdincomeEducation(years)Age

.59.74.68.70.68

.49.68.61.63.61

95%confidenceinterval

Upper.67.80.75.76.75

..60.50.56.51.40.71.68.59

.62.68.56.68.54.61.46.61.70.75..75

.54.60.54.48.60.44.51.44.37.51.62.68.63.57.68

.56..57.65.47.55.47.56.65.71.65.72

.96.981.00.95.981.00.97.991.00

Note:confidenceintervalsforthecorrelationsarenotsymmetricbecausetheyarebasedonthenon-linearFisher'sztransformation(z=.5[ln(1+r)−ln(1−r)]),whichisnormallydistributedandusedforsignificancetesting.

Samplesizesare228or229,exceptforage,whichis223duetomissingdata.

tendstofeelthesamewaymostofthetime(a“happy”personora“depressed”person)regardlessofthesituation,thenthisadjectivemightbeexpectedtohavegreaterreliabilityacrossthetwosessions,sincetheactivitiesthepersonengagesinonthetwodaysvary.Tocrudelygaugetheextenttowhichparticularadjectivesareperson-boundorsituation-bound,foreachadjectivewepooledthetwosessionsandcomputedthevarianceoftheduration-weightedpersonalaveragesacrosspeopleandtheaveragevariancewithineachperson'sdaysacrossepisodes,andthentooktheratioofthebetween-peopletowithin-personvariances.Ahighratiowouldindicatethatanadjectiveisrelativelyconstantforaperson(moreofanindividualdifferencelikeatrait)andalowratiowouldindicatethatanadjectiveisdeterminedmorebythesituationthanwhothepersonis.ResultsareshowninTable3.Quiteplausibly,feelingdepressedappearstobeamoretrait-likedescriptor,whilefeelingtense/stressedorimpatientforanepisodetoendarehighlysituational.Interestingly,wefoundacorrelationof.41betweenthevarianceratioandthereliabilityratiosshowninTable3,whichindicatesmoderatesupportforthehypothesisofgreaterreliabilityfortrait-likeemotions.9WealsocomputedtheseratiosfortheDRMsampleinKahnemanetal.(2004).Thetwosamplesproducedverysimilarsetsofratios—forthe8adjectivesincommonbetweenthetwosamplesthecorrelationoftheratioswas..

9A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–1845

Table3

Aretrait-likefeelingsmorereliable?Adjective

Depressed/blueTired

Angry/hostile

Competent/doingwellAffectionate/friendlyHappy

Calm/relaxedFrustrated

Interested/focusedTense/stressed

Impatientforittoend

2Meanwithin-individual(σw)

2Acrossindividuals(σa)

22Ratio(σa/σw)

1839

Reliability.60

.65.54..68.62.56.48.57.54.56

.701.38.811.021.311.181.311.431.191.501.83.921.39.73.881.10.99.951.02.831.01.961.321.01.90.86.84.84.73.71.70.68.53

3.1.Affectivesimilarityoftimeallocation

Wenextexaminetheaffectivesimilarityofhowindividualsspenttheirtimeonthetwosurveyreferencedays.Wecandecomposethereliabilityratiointoacomponentthatreflectsthehedonicsimilarityofactivitiesinthesurvey

1referencedaysandallotherfactors.LetAijdenotenetaffectforpersoniduringheractivityinepisodejinweek1,and2Aijnetaffectforpersoniduringtheactivityinepisodejinweek2.Iftheindividualengagedinmultipleactivitiesduringanepisode,weusetheonethatwasindicatedasmostimportantatthetime.Usinghijtodenotethefractionofthedaydevotedtoepisodej,Pwewriteaveragenetaffectoverthecourseofthedayinweek1andweek2asyi1andyi2,P11222respectively,definedasy1i¼jhijAjandyi¼jhijAj.Thereliabilityofaveragenetaffectinsuccessiveinterviews,whichwehaveemphasizedsofar,ismeasuredbyρ=cov(yi1,yi2)/σy1σy2.Thereliabilityratioreflectstheaccuracyofreportingofthedataandthepersistenceofaveragenetaffectovertime.Theaffectiveexperiencedatacouldbeaccuratelyreported,butifpeopleengageinactivitiesthatyieldverydifferentaffectiveexperiencesfromweektoweek,thecorrelationwillnonethelessbelow.

Toascertaintheproportionofthereliabilityratiothatresultsfromengaginginactivitiesthatyieldsimilaraffective

¼Ph1A¯¯experiencesovertime,wedefiney1ijijj,whereAjistheaverageaffecttakenoverallpeoplewhiletheyareP2¯ˆ1ˆ2engagedinactivityj.Analogously,wedefiney2i¼jhijAjforthefollow-upinterview.Noticethatyiandyiarepredicted

averagenetaffectbasedentirelyonanindividual'stimeallocationandthesample'soverallratingofactivityj.Anindividual'saffectiveratingdoesnotenterinthesepredictions(exceptthroughthesamplemean).Astraightforward

ˆ1andyˆ2,whichwedenoteasr′.measureofthesimilarityofactivitiesonthereferencedaysisthecorrelationbetweenyiiTheshareofasingleday'ssignalinaveragenetaffectthatisattributablepurelytotheaffectivesimilarityoftheactivitiesengagedintwoweeksapartisgivenby:

󰀂󰀃12covyi;yi

j¼:2covðy1i;yiÞWecanalsodefinethefractionoftheobservedvarianceinaveragenetaffectduetothesimilarityofactivitiesas:

󰀂󰀃12covyi;yi

Á:g¼Àry1;ry2¯WemeasureAjintwoways.First,wesimplyassigntheaveragenetaffectassociatedwithactivityj.Second,we

assigntheconditionalaveragebasedonalinearregressionofnetaffecton22activitydummiesand9interactionpartnerdummies.Table4presentsthesedecompositionsforNetAffect.

Theresultsindicatethatindividualswouldhaveacorrelationofaround.30intheirnetaffectonthereferencedatesiftheyusedthesample-wideaveragenetaffecttoratetheiractivities.Becauseactivitiesandinteractionpartnersonly

ˆ1andofyˆ2isaccountforaround10%ofthevariationinnetaffectattheepisodelevel,however,thevarianceofyii12considerablylowerthanthevarianceofyiandyi.Consequently,theshareofthecovarianceorvarianceofreportednet

1840A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–1845

Table4

Theaffectivesimilarityoftimeuseafortnightapart

2ðy1i;yiÞrV¼covÞðry1;ry2

i

i

¯jPredictionofA

Activity(22)

Activity(22)andinteractionpartner(9)

j¼

covðcovð2y1i;yi

2y1i;yiÞÞcov

Ág¼Àry1ry2

.006.009

󰀂2y1i;yi

󰀃.267

.322.009.014

affectthatisaccountedforbytimeuseisquitesmall,ontheorderofaround1%.Whenwelookatspecificaffectswereachasimilarconclusion.Forexample,timeuseaccountsforonly2%oftheestimatedsignalintense/stress.Thus,therelativelyhighreliabilityoftheDRMdataacrosstwoweekscomesaboutmainlybecauseofindividualdifferencesinaffect,irrespectiveofthesituationsthatpeoplefindthemselvesinonthereferencedays.3.2.Adjustingcorrelationsforattenuation

Oneconsequenceoflessthancompletereliabilityisthatobservedcorrelationbetweentwomeasuredvariablesxandyareattenuatedinproportiontothedegreeoferror.Assumingclassicalmeasurementerror,theasymptoticequationrelatingtheobservedcorrelationtothe“true”correlation(i.e.,correlationofthecorrectlymeasuredvariables)is(Nunnally,1978):

pffiffiffiffiffiffiffiffiffiffiffi

rxy¼qxyrxxryywhererxyρxyrxxryy====

observedcorrelationbetweenxandytruecorrelationbetweenxandyreliabilityofxreliabilityofy.

Thecorrectionforattenuationusesthisrelationtoproduceanasymptoticallyunbiasedestimateofthe“true”correlationbyrearrangingtosolveforρxywehave:

rxy

qxy¼pffiffiffiffiffiffiffiffiffiffiffirxxryy:Attenuationcorrectionsaresomewhatcontroversialbecausetheyareonlyasymptoticallyunbiasedandbecausethedegreeofattenuationmayvaryacrossdatasets.Thus,iftheassumptionsofclassicalmeasurementerroraresatisfied,themagnitudeoftheadjustedcorrelationisbesttakenasaruleofthumbestimateforthetruecorrelation.

Usingtheasymptoticformulaasanapproximation,wecanexaminetheeffectthatmeasurementerrormighthaveonobservedrelationships.Table5showssomeexamples.Perhapsmostimportantly,thefirstrowshowsthatthe

Table5

ExamplesofCorrectionforAttenuationx

NetaffectDifmaxU-index

HouseholdincomeHouseholdincomeHouseholdincomeHouseholdincome

y

LifesatisfactionLifesatisfactionLifesatisfactionLifesatisfactionNetaffectDifmaxU-index

rxy.31.37−.26.21.12.10−.06

ρˆxy.50.62−.48.28.15.13−.09

rxx..60.50.96.96.96.96

ryy.59.59.59.59..60.50

A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–18451841

correlationbetweenlifesatisfactionandnetaffectrisesto.50whenweadjustformeasurementerrorinbothvariables.Althoughthisisasubstantialincrease,theresultingcorrelationnonethelessindicatesthatdailynetaffectandlifesatisfactionaredistinctdescriptorsofindividuals'lives.3.3.Testingforheteroskedasticerrors

Althoughwithonlytwotemporalobservationswecannotdirectlytesttheassumptionsofclassicalmeasurementerror,wecaninvestigatewhetherdiscrepanciesinnetaffectovertimearehomoskedasticerrors.Specifically,weregressnetaffectatperiod2onthesamemeasureatperiod1andtestforhomoskedasticerrors.Withclassicalmeasurementerroreiisassumedtohavethesamedistributionforalli.ToexaminethispropertyweusethemethodofKroenkerandBassett(1982),whichemploysquantileregressions.Fig.1showsascatterdiagramofnetaffectatperiods1and2,with20thand80thquantileregressionlines.Thereisonlyamarginallysignificantdifferencebetweenthe20thand80thquantileregressionlines(t=−1.70,p=.09),whichindicatesthatthereispossiblysomeevidenceofheteroskedasticity.However,adjacentcomparisonsyieldmixedresults—ifweinsteadusethe40thand60thor30thand70thquantilepairingsthetestisnotsignificant,butwiththe25thand75thorthe10thand90thpairingsthetestissignificant(pb.05).UsingadifferenttestforhomoskedasticerrorsduetoWhite(1980),weregressnetaffectatperiod

Fig.1.Scatterplotofnetaffectatperiods1and2withquantileregressionlines.

1842A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–1845

2onperiod1,andthenregresstheresultingsquaredresidualsonperiod1netaffect;n⁎R2fromthissecondregression∼χ2.TheresultingR2is.004andχ2(1)=.916,ns,fromwhichwecannotrejectthehypothesisofhomoskedasticerrors.Itispossiblethattheassumptionofhomoskedasticmeasurementerrorcouldbeviolated,butthedeviationisprobablyslight.

3.4.Reliabilityofaggregateactivityexperienceratings

Thereliabilitieswehavecomputedthusfararedefinedattheleveloftheindividual.Formanyapplications,however,thekeyissueisnotthereliabilityofnetaffectforindividuals,butratherthereliabilityofaveragenetaffectacrossindividualsengagedinvariousactivities.Thequestionofreliabilityinthiscontextiswhetheragivenactivity

¯jforproducesthesameaverageexperienceatdifferenttimes.AsimpletestforthisistocomputethemeanvaluesA

eachactivityforeachtimeperiodandcorrelatethevectorsacrossactivities.Table6presentsthemeannetaffectforeachdaybyactivityandinteractionpartner.ThetwoDRMsproducearemarkablysimilarpatternsofmeannetaffectacrossactivities(r=.96,seeTable6andFig.2)andalsoofrelativefrequency(r=.99,seethirdandsixthcolumnsofTable6).Noteforexample,thatintimaterelations(whichincludesnon-sexintimacy)andplayingareatthetopinbothcases,whilecommutingandworkingarebothatthebottom.Thisisconsistentwithrelatedfindingsintheeconomics

Table6

Netaffectbyactivityorsocialcontext

Period1Mean

ActivitiesPlaying

IntimaterelationsRelaxing

Walking,takingawalkWatchingTVExercisingEatingReading

Preparingfood

Praying/worshipping/meditatingTalking,conversationRest/sleepChildcare

HomecomputerDoinghouseworkGrooming,selfcareShopping,errandsOtheractivitiesListeningtomusic

Listeningtoradio,newsCommuting,travelingWorking

SocialinteractionsFriends/relatives

Spouse/significantotherMychildrenParents

Otherpeople

Customers/studentsCo-workersBoss

4.094.073.683.613.423.373.343.243.193.142.942.852.802.752.732.652.552.472.422.412.192.07

Standarderror.26.33.17.23.13.23.13.19.16.32.12.28.24.26.19.14.26.19.19.20.14.14

N48291035318754210981655421776838012520378148119104211218

Period2Mean4.1.403.913.603.353.423.443.133.203.242.872.812.802.542.862.593.182.472.362.262.222.02

Standarderror.24.27.16.25.14.29.11.20.16.33.13.26.25.27.19.14.18.18.19.21.14.14

N482611959193492161011604322088877112122091148113107218214

3.423.103.103.052.532.252.211.88.18.17.16.41.18.19.14.19126143122401311042071293.193.182.912.552.632.382.402.08.19.17.18.34.20.24.15.1913315012535135206121

A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–18451843

Fig.2.Meannetaffectforactivitiesbysession.

literatureonsex(BlanchflowerandOswald,2004a)andcommuting(StutzerandFrey,2007)whichuseddifferentmethodsthanthoseemployedhere.4.Discussion

Weanalyzedthepersistenceofvarioussubjectivewell-beingquestionsoveratwo-weekperiodforasampleof229workingwomen.WefoundthatbothoveralllifesatisfactionmeasuresandaffectiveexperiencemeasuresderivedfromtheDRMexhibitedtest–retestcorrelationsintherangeof.50–.70.Whilethesefiguresarelowerthanthereliabilityratiostypicallyfoundforeducation,incomeandmanyothercommonmicroeconomicvariables,theyareprobablysufficientlyhightoyieldinformativeestimatesformuchoftheresearchthatiscurrentlybeingundertakenonsubjectivewell-being,particularlyincaseswheregroupmeansarebeingcompared(e.g.richvspoor,employedvsunemployed)andthebenefitsofstatisticalaggregationapply.Inothersituations,reliabilityestimatescanbeusedtoadjustcorrelationsandregressioncoefficientsforattenuationbias.

ItisperhapssurprisingthatmeasuresintendedtoassessthegeneralstateofSWBoveranextendedperiod(suchasoveralllifesatisfaction)shouldbenomorereliablethanmeasuresofaffectiveexperienceondifferentdaystwoweeksapart.One'sgeneralleveloflifesatisfactionwouldbeexpectedtochangeonlyveryslowlyovertime,becausemostoftheknowncorrelates(age,income,maritalstatus,employment)oflifesatisfactionalsochangeslowly.Akeyfactorbehindthisresultisprobablythefactthatansweringalifesatisfactionquestionexplicitlyinvokesanon-systematicreviewofone'slife,whichleavessuchmeasuresvulnerabletotransientinfluencesthatdrawattentiontoarbitraryorincompleteinformation(e.g.one'simmediatemood,theweather).Bycontrast,measuresofaffectiveexperiencefromexperiencesamplingortheDRMdonotrelyonsuchcognitiveappraisals,andhavethebenefitofaggregatingover

1844A.B.Krueger,D.A.Schkade/JournalofPublicEconomics92(2008)1833–1845

severalepisodesandadjectives,Theyalsohavethedisadvantage,however,thatnotwodays(evenifintentionallymatched,asinourstudy)areidentical.

Anotherapplicationofreliabilityestimatesistoassistinthedeterminationofappropriatesamplesizesforthemeasurementofvariousemotionalexperiences.Inclinicaltrials,forexample,ifSWBmeasuresareoneoftheoutcomevariablesofinterest,reliabilitiescanbeusedtohelpdeterminethesamplesizeneededtodetectanexpecteddifferencebetweengroups.Becausethereliabilitiesaremodest,theriskofincorrectlyconcludingthatgroupsdonotdifferisofparticularconcern.Aswesawinourexamplesofcorrectionforattenuation,thetruestrengthofrelationshipscouldeasilybeunder-estimatedinthesmallsamplesthatclinicalstudiessometimesemploy(e.g.withspecialpopulations).Analternatedesignapproachtolargersampleswouldreduceerrorbysamplingthesamepeopleatdifferentpointsintime,orbyselectingadjectivesthatarelesssituationalandmoreperson-specific.References

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