How Do Voters Respond to InformationEvidence from a Randomized CampaignIZA DP No 7340Chad KendallTommaso NanniciniFrancesco Trebbi How Do Voters Respond to Information Evidence from a Randomized Ca ID: 416405
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Forschungsinstitut zur Zukunft der ArbeitInstitute for the Study of Labor How Do Voters Respond to Information?Evidence from a Randomized CampaignIZA DP No. 7340Chad KendallTommaso NanniciniFrancesco Trebbi How Do Voters Respond to Information? Evidence from a Randomized CampaignChad KendallUniversity of British ColumbiaTommaso Nannicini IZA Discussion Paper No. April BSTRACTHow DoVoters Respond to Information?Evidence from a Randomized CampaigRational voters update their subjective beliefs about candidates attributes with the arrival of information, and subsequently base their votes on these beliefs. Information accrual is, however, endogenous to voters types and difficult to identify in observational studies. In a large scale randomized trial conducted during an actual mayoral campaign in Italy, we expose different areas of the polity to controlled informational treatments about the valence and ideology of the incumbent through verifiableinformative messages sent by the incumbent reelection campaign. Our treatments affect both actual vote shares at the precinct level and vote declarations at the individual level. We explicitly investigate the process of belief updating by comparing the elicited priors and posteriors of voters, finding heterogeneous responses to information. Based on the elicited beliefs, we are able to structurally assess the relative weights voters place upon a candidates valence and ideology. We find that both valence and ideological messages affect the first and second moments of the belief distribution, but only campaigning on valence brings more votes to the incumbent. With respect to ideology, crosslearning occurs, as voters who receive information about the incumbent also update their beliefs about the opponent. Finally, we illustrate how to perform counterfactual campaigns based upon the structural model.JEL Classification:D72, D83Keywordsvoting, information, beliefs elicitation, randomized controlled trialCorresponding author:Tommaso NanniciniDepartment of EconomicsBocconi UniversityVia Roentgen 120136 MilanItalymail: tommaso.nannicini@unibocconi.it We would like to thank Matilde Bombardini, David Green, Andrea Mattozzi, Jim Snyder, and seminar participants at Alicante, Bank of Italy, Bocconi, Carlo Alberto Turin, EIEF Rome, Harvard, LSE, MILLS workshop, MIT, Petralia workshop, Rotterdam, SciencesPo Paris, UBC, UK Leuven, and Warwick for useful comments. Federico Cilauro, Francesco Maria Esposito, Jonathan Graves, Nicola Pierri, and Teresa Talò provided outstanding research assistance. A large number of people were instrumental in implementing our experimental design: the mayor of Arezzo, Giuseppe Fanfani, and his 2011 reelection campaign, in particular Claudio Repek, were extremely cooperative throughout the entire process; Massimo Di Filippo, Fabrizio Monaci, and the team of IPR Feedback showed tremendous expertise in conducting the surveys. Nannicini acknowledges financial support from the European Research Council (under grant No. 230088). Remaining errors are ours and follow a random walk. alsoshowthat,althoughonlyvalencetreatmentswereeectiveinchangingvotes,ourinformationaltreatmentsalongboththevalenceandideologicaldimensionhadlargeeectsonvoters'beliefs,mov-ingbothrstandsecondmomentsofthebeliefdistributionsforthetwomaincandidates.Indeed,campaigninformationaectednotonlyvoters'beliefsaboutthecandidateoriginatingthemessage,butalsotheirbeliefsabouttheopponent.Intuitively,inBayesiansignalinggames,receivingnomessageisvaluableinformationandourevidenceoncross-learningappearsfullyconsistentwithupdatinginthecontextofaBayesianpoliticalsignalinggame.Thefullcharacterizationoftheindividualbeliefdistributionsweproposeisthecombinationofacarefuldesignofoursurveysandstructuralestimationofarandomutilityvotingmodel.Thelattercomponentofourmethodologydeliverspreciseestimatesofutilityweightsinvoters'preferencesforacandidate'svalenceandideology.Wereportautilityweightonvalenceroughlyequaltothatonideologicallossesawayfromavoter'sblisspoint.Interestingly,wealsoshowthatthepreferenceweightsareheterogeneousinthepopulationanddependonthepoliticalstanceofthevoter,withvotersontherightplacinglessemphasisonthevalencedimension.Finally,weshowthattheideologicallossfunctionawayfromthevoter'sblisspointisconcaveindistance,notconvex(e.g.,quadraticlosses)ascommonlyassumedintheliterature.TherandomutilitymodelweusefollowsthemethodoutlinedinthetheoreticalpaperofRamalhoandSmith(2012)toaccountfornon-randomnessinvoters'willingnesstodisclosetheirvotes.Whilenon-responseinsurveydataisoftenassumedtoberandom,wedemonstratetheimportanceofaccountingforitsendogeneityandsuggestthatthismethodshouldbemoreoftenutilizedinempiricalstudiesinwhichsurveyresponsesarereliedupon.Weconcludeouranalysisbysimulatingcounterfactualelectoralcampaignstoassesstheeectsofspecicblanketortargetedelectoralcampaignsonvoteoutcomes.Wendablanketcampaignofvalencemessagestobethemostvaluableinpersuadingvoters,whichisconsistentwithvoterslackingpriorinformationonthequalityofcandidates.Thispaperisrelatedtoseveralstrandsoftheliterature.Theeectivenessofelectoralcampaignsinmaturedemocraciesisthesubjectofalargeliterature,includingAnsolabehereetal.(1994),AnsolabehereandIyengar(1995),GerberandGreen(2000),GreenandGerber(2004),Gerber,Green,andShachar(2003),Nickerson(2008),andDewan,Humphreys,andRubenson(2010).Typicallythefocusofthesepapersiseitheronself-declaredoutcomesforvotechoicesoronactualoutcomesforturnout.Methodologically,thesepapersrelyoneithersmall-scaleexperimentsforpartisanadsoronrandomizednon-partisancampaignsforturnout.Ourpapercomplementsthisliteraturebyfocusingonactualelectoraloutcomesinalargescaleeldexperiment.Wemustclarify2 thatourpaperisnottherstinstanceofalargescalerandomizedpartisancampaign.Gerberetal.(2011)lookatrandomizationoverintensityofTVads(withnocontroloverthemessagecontent)onself-declaredchoicesduringthe2006RepublicanprimaryfortheTexasgubernatorialelection.Theyndlarge,butshort-lived,eectsofsuchTVads,inconsistentwithBayesianupdating.Unliketheirapproach,werandomizethecontentofpartisanadsandalsoevaluatetheirimpactonactualvoteshares.Ourpaperalsocomplementsthisliteraturefromamethodologicalstandpointbyaugmentingthereducedformapproachwithstructuralestimation.Albeitinthecontextoflessmaturedemocracies,theliteratureindevelopmenteconomicshasalsoexperimentedwithinformationalcampaigning.RelevantcontributionsincludeWantchekon(2003)andFujiwaraandWantchekon(2013),exploringpoliticalclientelisminBenin,Vicente(2013),andBanerjee,Green,andPande(2012).Banerjeeetal.(2011)focusonnon-partisaninformationalcampaignsinIndiaandshowthatinformationaboutthequalicationsofcandidatesmattersforturnout,voteshares,andtheincidenceofvotebuying.Thispaperisrelatedtoavastliteratureoncandidate'svalence,initiatedbyStokes(1963)andincludingEnelowandHinich(1982),AnsolabehereandSnyder(2000),Groseclose(2001),Schoeld(2003),AragonesandPalfrey(2002)amongothers.Morerecently,AshworthandBuenodeMesquita(2009),KartikandMcAfee(2007),andBernhardt,Camara,andSquintani(2011)provideinter-estingtheoreticalstudiesofstrategicelectoralcompetitionwithcandidatesdierentiatedalongboth(ideological)policyplatformandvalencedimensions.GalassoandNannicini(2011)studytheinterplaybetweencandidates'valenceandthecontestabilityofelectoraldistricts.Finally,thispapercontributestothegrowingliteraturefocusedontheelicitationandquan-ticationofsubjectivebeliefs.ElicitationofpriorsisthesubjectofDominitzandManski(1996),Manski(2004),Blass,Lach,andManski(2010),GillandWalker(2005),andDuyandTavits(2008)amongothers.Tothesecontributions,whichmostlyfocusontheelicitationofexpectationsofeconomicoutcomes,ourworkprovidesausefuladditioninthecontextoftheelicitationofmul-tivariatebeliefs.Inparticular,weshowhowtodecoupleinformationaboutmarginalbeliefsandtheirdependenceusingacopulafunctionapproach.Webelievethisapproachmaybeofuseoutsidethepolitico-economicapplicationinourstudy.Therestofthepaperisorganizedasfollows.Section2presentstheempiricalmodel.Section3describestheexperimentalsetting.Section4discussesthereducedformresultsonvotechoices.Section5focusesonthestructuralestimatesofthemodelandSection6ontheexperimentaleectsonvoters'beliefs.Section7presentsourcounterfactualsanddiscussestheimplicationsoftheheterogeneousresponsetoinformationonthepartofvoters.Section8concludes.3 2EmpiricalModel2.1VotersandCandidatesConsideranelectoralracebetweentwocandidates,A,theincumbent,andB,thechallenger.LetthesetofvotersbeN,withjNj=N.Avoteriischaracterizedbyanidealpolicypointdistributedoveraniteanddiscretepolicyspace,,whichiscommonacrossallvoters,withpoliciesP2.Thediscretenessassumptionismeanttocaptureanempiricalfeatureofthesurveydataemployedinthesubsequentanalysis.Votersareheterogeneous,withblisspointsq2,andreceivedisutilityfromapolicychoiceawayfromtheirblisspoint.TheyalsoreceiveutilityfromthelevelofvalenceoftheelectedcandidateV2,wherethesetisniteanddiscrete.Whenpolicypisimplementedbycandidatejofvalencev,theutilityforvoterioftypeqisassumedtobe:U(v;p;q)= vu(qp)u(qp)v+"i;jwheretheutilityfunctionincludesadeterministicportionandacandidate-specicrandomutilitycomponent"i;j,independentofVandP.Theparameter indicatestherelativepreferenceweightofvalenceversusthepolicystance.Weassumeu(0)=0,u0(x)0forx0,andu0(x)0forx0.Forexample,aquadraticlossawayfromvoteri'sblisspoint,(qip)2,tsthissetofassumptions.1However,weassumethemoregeneralformu(x)=jxjwith0.Thepolicystanceofthepolitician,p;aectsvotersheterogeneouslydependingupontheirownidealposition,q,butcandidatesofhigherqualityvarefavoredbyallvoters.Wealsoallowforinteractionsbetweenvalenceandpolicypositionsthataregovernedby.Therandomutilitycomponent"i;jofvoteri'spreferencesforcandidatejcapturesthepersonalappealofjtoi.ItisnotimportantforourpurposestospecifywhetherthetwocandidatesAandBimplementtheirrespectiveidealpolicypositionPonceinoce(seeAnsolabehere,Snyder,andStewart,2001;Lee,Moretti,andButler,2004)orstrategicallycatertheirpolicytovoters(e.g.,asinastandardDownsiansetting).Weareinterestedinthevoters'utilitiesatthetimetheyplacetheirvote,whichonlydependupontheirbeliefsabouteachcandidate'sposition,andnotonhowthepolicypositioncameaboutorwhetherornotitisactuallyimplemented.Ingeneral,ourapproachisrobusttothedetailsoftheelectoralcompetitionstructure.Allvotersparticipateintheelection(votingiscompulsoryinourempiricalsetting).VoteriisassumedtohaveajointpriordistributionfunctionoverVandP,fi;jV;P(v;p),forj=A;B,evaluatedatpoint(v;p)anddenedoverthesupport.WedonotprecludeVfrombeingpotentiallycorrelatedwithPandweallowpriorstodierbaseduponi'scharacteristicsoridealpointq. 1Quadraticlossfunctionsarestandardintheliterature(e.g.,seeAnsolabehereandSnyder,2000).4 Ourexperimentaltreatmentsinducearandomizedchangeintheinformationsetsofvoters,whichwedescribeindetailinSection3.Thediscretenessoftheexperimentalstrategyinducesanitesetofinformationaltypesofvoters.Type1:ReceivingamessageaboutV;butnotP;ofA:Type2:ReceivingamessageaboutP;butnotofV;ofA:Type3:ReceivingamessageaboutbothVandPofA:Type4:ReceivingnomessageaboutVorPofA:Forsimplicity,a\message"indicateshaving(randomly)receivedacampaigninformationtreat-ment,H2f1;:::;4g.LetusindicateasT(h)thesetofvoterstreatedwithinformationtypeH=handletfi;AV;P(v;pjH=h)indicatesthesubjectiveposteriorprobabilitythatvoteri,treatedbymessageh,assignstotheeventthatcandidateAhasvalenceV=vandpositionP=p.Theprocessofupdatingbeliefstypicallyre ectsthecharacteristicsofthegameplayedbetweenvotersandpoliticalcandidates(e.g.,asignalinggame).Ourapproachallowstoleavethenatureofsuchstrategicinteractionunspecied.TheexpectedutilityfromtheelectionofAforvoteri,treatedbyhandwithidealpointq,is:EUiA(h;qi)=XpXvfi;AV;P(v;pjH=h)U(v;p;qi)+"i;A.If,instead,Biselected,theexpectedutilityforvoteroftype(h;qi)is:EUiB(h;qi)=XpXvfi;BV;P(v;pjH=h)U(v;p;qi)+"i;B.Theprobabilitythatioftype(h;q)supportscandidateAisgivenby:PrEUiA(h;qi)EUiB(h;qi).(1)GiventheprobabilitythatavotersupportscandidateA,wecanconsiderastandard,conditionallogitmodel,assuming"ijtobei.i.d.acrossvotersanddistributedwithaTypeIextreme-valuedistributionwithcumulativedistributionfunctionF("ij)=exp(e"ij).Providedinformationonthechoiceofitovoteforj,Yi=j,weobtaintheloglikelihood:lnL()=NXi=1XjdijlnPr(Yi=j)=NXi=1XjdijlneEUij(h;qi) PleEUil(h;qi)wheredijis1ifivotesforj,and0otherwise.Notethatthevectorofparametersofinterest,,includesbothpreferenceparameters[ ;;]andtheparametersofthejointbeliefsfi;jV;P(:),whichwedeneinthefollowingsubsection.5 Onepotentialproblemwiththestandardlogitmodelinasettingemployingvotedeclarationsasopposedtoactualvotesisthatvoters,whensurveyed,mayprefernottodisclosetheirvote.Ifthesampleofvoterswhodonotdisclosetheirvoteiscompletelyrandom,onecanapplythelogitmodeltothesubsampleofresponders.Thisistheapproachtypicallyfollowedintheliterature,oftenwithoutdiagnosticsinsupportofthecrucial\missingcompletelyatrandom"assumption,requiredforanunbiasedestimate.WeprovideevidenceinSection5thatindicatesthatthesubsampleofvotersthatchoosenottodisclosetheirvotesispredictable,soestimationofthestandardlogitmodelwouldleadtobiasedestimatesinoursetting.Wethereforeapplyanovelchoice-basedapproachsuggestedbyRamalhoandSmith(2012)thatallowsfornon-randomnon-responseunderweakassumptions.Themodelassumesthat,conditionalonthevoter'sactualvote,theprobabilitywithwhichavoterchoosestorespondtothesurveyisconstant,butthatthisprobabilitycandependontheirvote.Underthisassumption,wecandenetheloglikelihoodas:lnL()=NXi=10@oiXjdijlnjeEUij(h;qi) PleEUil(h;qi)+(1oi)ln0@1XjjeEUij(h;qi) PleEUil(h;qi)1A1Awhereoiis1ifidisclosesthevote,and0otherwise.Theadditionaljparametersaretheprobabil-itieswithwhichavoterdisclosesthevoteforj.Thersttermoftheloglikelihoodistheprobabilitythatavotervotesforjanddisclosesthevote.Thesecondtermre ectstheprobabilitythatthevotervotesforoneofthecandidates,butchoosesnottodisclosethevote.Notethatwhenj=1forallj,suchthatthevoteisalwaysobserved,weobtainthestandardlogitmodelasaspecialcase.OurresultsinSection5rejectj=1forallj,meaningthatwearejustiedinaccountingforthepossibilityofnon-randomnon-response.2.2Voters'SubjectiveUpdatingHere,wespecifytheprocessbywhichvoters'subjectivebeliefsareupdatedinthepresenceofcampaignadvertising.Forillustrativepurposes,considerthefollowingtimeline. 6 Ourrstassumptionisthatvotersconsiderthecampaigninformationtobetruthful.SucientfreedomofthepressintheItalianelectoralcontextguaranteesthatsuchanassumptionmaybevalidinthecaseoffactualadvertising,asweemployinourexperimentalsetup.Allmessagesarefactualandcanbeindependentlyvalidated.Secondly,weassumerationalBayesianvoters.2Werefrainfromimposingdistributionalas-sumptionsonpriors,posteriors,andonthedistributionofsignals.Instead,weadopttheoptionofelicitingsubjectivepriorsandposteriorsfromspecicallydesignedsurveys.Thisisanimportantstepfortwomainreasons.First,elicitationallowsustoassessquantitativelyhowthemessagingstrategyweemployedexperimentallyoperatesintheeld.Indeed,votersarenotawareoftheran-domizationprocessandupdatetheirbeliefs\asif"themessagesweredirectlysentbythecandidate.Thisisnotanassumption,butpartoftheexperimentaldesign.UndertheassumptionofBayesianvoters,beliefupdatingaboutcandidateAimplies:fi;AV;P(v;pjH=h)=Pri;A(H=hjV=v;P=p) Pri;A(H=h)fi;AV;P(v;p)forh=1;2;3,wherethesubjectiveupdatingtermPri;A(H=hjV=v;P=p) Pri;A(H=h)canberecovereddirectlyfromthedataafterelicitationoffi;AV;P(v;pjH=h)andfi;AV;P(v;p).Second,ourapproachallowsforgeneralstrategicelectoralcommunicationbetweencandidatesandvotersinthebackground.WearenotrequiredtomodelorrestrictthevotinggameplayedamongN,A,andB.AnystrategicsignalingiscapturedbytheupdatingtermPri;A(H=hjV=v;P=p) Pri;A(H=h),whichweestimate,notmodel.3Bayesianupdatingincasethevoterreceivesnomessagefromthecandidaterequiresfurtherdiscussion.ConsiderthecaseofafullyrationalBayesianvoterthatreceivesnocampaignadvertisingfromacandidate,butknowsthatsuchactionwasavailable.Insuchacase,asChappell(1994)states,\absenceofamessageprovidesinformationwhichshouldbeusedinBayesianupdating"withtheresultthatsubjectiveposteriorsprobabilitiesaredierentfrompriorsevenabsentanymessagehavingreachedthevoter.InthecaseofposteriorsaboutcandidateB,forinstance,thisrequiresthatvoteriupdatespriorsbasedonabsenceofanHmessagefromB.Formally:fi;BV;P(v;pjH=h)6=fi;BV;P(v;p)forh=1;2;3,(2)whichisjustiedfromvoterihavingobservedatleastoneextracampaignmessagefromAwithoutanycorrespondingcounter-messagefromB. 2Notethat,whileweneedvoterstoberationalandvotesincerely,theassumptionofBayesianupdatingissimplyconvenientfortheexposition,asourempiricalframeworkallowsustoidentifybeliefupdatinginmoregeneralterms.3Adynamicrepeatedelectionmodelwithbothideologicalandvalenceconsiderationsthatwouldtourproblemis,forinstance,proposedinBernhardt,Camara,andSquintani(2011).7 Thedegreeofrationalityembeddedincondition(2)cannotbeextended,however,totheexper-imentalcontrolgroupH=4,whichdoesnotreceiveanytypeofinformationaltreatmentbyeitherAorBandhencehasnopossibilityofknowingthatsuchspecicmessageswouldbeavailablebutwerenotemployed.ThefundamentalassumptionofourexperimentaldesignmirrorsaStableUnitTreatmentValueAssumption(SUTVA,seeCox,1958;Rubin,1978),asitrequiresthepotentialoutcomeofacontrolunittobeunaectedbythetreatmentassignmentoftheotherunits.Absentcommonshocks,weshouldassumeforH=4thattheposteriordistributionisidenticaltothepriordistribution,thatis,foreveryi2T(4),fi;jV;P(v;pjH=4)=fi;jV;P(v;p)forj=A;B.Moregenerally,weconsideraprocessofBayesianupdatingwhichaccommodatescommonshocksacrossvoters,underthe(testable)assumptionthatthesubjectiveprobabilitiesonsuchshocksareidenticalacrossalli2NandindependentofH.Consider,forinstance,thecaseofposteriorselicitedafteracommoninformationalshock,W,whichcanbethoughtofasthegeneralcampaigncarriedoutbythecandidatesbesidestheinformationalmessagesfromAthatwerandomizeatthemargin.Withrespecttocandidatej,voteriwillbecharacterizedbythefollowingposteriors.Assumption1(SUTVA):fi;jV;P(v;pjH=h;W)=Pri;j(H=hjV=v;P=p) Pri;j(H=h)Prj(WjV=v;P=p) Prj(W)fi;jV;P(v;p)forh=1;2;3;j=A;Bandfi;jV;P(v;pjH=4;W)=Prj(WjV=v;P=p) Prj(W)fi;jV;P(v;p)forj=A;B.ThecredibilityofAssumption1cruciallyrestsontheexperimentaldesigndescribedinSection3andisempiricallyvalidatedinSection4.Finally,theelicitationofmultivariatebeliefs,evenonexpertsubjects,isnotanobviousexercise(KadaneandWolfson,1998;Garthwaiteetal.,2005)andistheobjectofavastliteratureborderingstatisticsandpsychology(datingatleastasbackasSavage,1971).Weoutlineourapproachnext.2.3ElicitationofMultivariateBeliefsElicitationofbeliefsandpriorsisincreasinglycommonineconomicsandpoliticalscience,andisstandardinpsychologyandstatistics.4Wedescribeatransparentprotocolofelicitationwedesignedtoberobusttothebehavioralandtechnologicalconstraintsweface.Specically,wesampledalargenumberofvotersandneedtoelicitmultivariatebeliefsfromeach. 4Forrecentexamplesineconomics,seeDominitzandManski(1996);Manski(2004);Blassetal.(2010);andZafar(2009).SeeGillandWalker(2005)andDuyandTavits(2008)forapplicationsinpoliticalscience.8 Foreachmaincandidatej=A;Bandeachvoteri,jointvalenceandideologysubjectivepriorsfi;jV;P(v;p)andposteriorsfi;jV;P(v;pjH=h)aredenedover.Intheremainderofthissubsection,letusfocusforbrevityontheelicitationofsubjectivepriors,withtheunderstandingthatthesameprocessappliestoposteriors.Intheempiricalanalysiswewillxthecardinalityofbothandtosmallintegergures,basedonMiller(1956),andalargebodyofcognitivepsychologysuggestingthatindividualscanbequitepreciseinevaluatingchoicesonrelativelycoarseunidimensionalsupports,butdisplayhardlyanyprecisiononnersupports.Specically,forreasonsexplainedbelow,weassumethecardinalityoftobeequalto5andthecardinalityoftobeequalto10.Itisevident,however,thatevenforjj=5andjj=10,\bruteforce"elicitationforbothcandidateswouldrequireeachrespondertoanswer5102=100dierentquestionsonthesubjectivelikelihoodofeachspecic(v;p)realization,aneortwhichwouldlikelyfrustratepoliticalexperts,letaloneregularvoters.Garthwaite,Kadane,andO'Hagan(2005)presentaninsightfuldiscussiononthedicultyofelicitationformultivariatepriors.Tothisissue,thereaderversedinelicitationmayaddtheproblemofeectivelytrainingtelephoneinterviewersintheconsistentelicitationofjointprobabilities.5Therefore,wefollowanalternativeroute.2.3.1MarginalBeliefDistributionsWerstfocusoninformationmoreeasilyelicitablefromvoters:theunivariatemarginalsfi;jV(v)andfi;jP(p).Eveninthiscase,fullelicitationofmarginalswouldrequirealargesetof(jj+jj)2=30questions.Westreamlinetheprocessinordertomaintainfeasibilitywithoutexcessivesacriceofaccuracy.Westartbyimposingasimpleregularityassumptiononthedistributionofbeliefs.Assumption2:Subjectivebeliefdistributionsareunimodal.Althoughrestrictive,thisassumptionmakestheinterpretationoftheelicitedprobabilitiesmoredirect.Allofourremainingdistributionalassumptionscanbeillustratedusingthequestionsinoursurveysbywayofexample.WefocusonlyonAforbrevityandconsiderrsthisideologicalpositionP.Weenquireaboutthecentraltendencyofthemarginalprioronideologyasfollows.Q1:HowwouldyoumostlikelydenecandidateA'spoliticalposition?Left(1);Center-Left(2);Center(3);Center-Right(4);Right(5);Don'tKnow(999). 5Whiletheuseoftelephoneinterviewsisnotgenerallynecessary,inourcontextitiswasrequiredtoensuretimelyelicitationofalargesampleofthevotingpopulationascloseaspossibletoelectionday.9 Areasonableinterpretationoftheanswer,withminimalconfusionfortherespondent,isthatthemodeiselicited.Inparticular,weallowthemode,^p;tobeonlyoneofthesevecategories.Assumption3:=f1;:::;5g:Ananswerof\Don'tKnow/Don'tKnowA"implies atpriors,orfi;AP(p)=1=jj=0:2foreveryp.Ourchoiceofthesetfollowstheestablishedresultincognitivepsychologythatindividualsarewellversedinchoicesoverdiscretesetsoflimiteddimensionality(jj10),butthatthiscapacitydeterioratessharplywhenthenumberofoptionsrisesabovesmallintegers(Miller,1956).Suchanassumption,however,hascosts,asemphasizedinManskiandMolinari(2010).Conditionalonnon- atpriors,wefurtherenquireaboutthedispersionaroundthemode.6Q2:HowlargeisyourmarginofuncertaintyaroundcandidateA'spoliticalposition?Certain(1);Ratheruncertain,leaningleft(2);Veryuncertain,leaningleft(3);Ratheruncertain,leaningright(4);Veryuncertain,leaningright(5).Weindicatethelevelofincreasingtightnessofthepriorswiths2=f1;:::;4g,wheres=1ismaximaldispersion,i.e.,thecaseof atpriors;s=2indicatessubstantialuncertainty(answers3or5toQ2);s=3indicatesintermediateuncertainty(answers2or4toQ2);ands=4ismaximaltightness,whichcoincideswithadegeneratepriorspikingat^p(answer1toQ2).Q2alsoelicitsinformationabouttheskewofthebeliefs.Whilewedonotallowexplicitlyforananswerofsymmetricdispersionfors=2;3,nottooverloadtheresponder,theestimationbelowallowsforsymmetricbeliefdistributions.7Letusindicatewithz2f1;1ganegative(i.e.,totheleft/lowervalues)orpositive(i.e.,totheright/highervalues)asymmetryinQ2.LetusdenethemodalprobabilitymasswithP=fi;AP(p=^p).Intuitively,weassumetheprobabilitymassatthemodefi;AP(p=^p)islowerthehigherthelevelofuncertainty.WeallowPtovarywithsandestimateP;s,fromthedatafors=2;3,imposingthebounds:Assumption4:1=jjP;2P;31:Wefurtherassumetheo-modemass,1P;s,tobeallocatedasymmetricallyaroundthemodedependingontheindicatedasymmetry,z.Weassumetheo-modemassdecaysproportionally 6Interviewersweretrainedduringpilotinterviewstoexplaintovotersthatthisquestionentaileduncertaintyaboutsubjectiveevaluationsonthecandidates,andshouldnotbeinterpretedasaright-or-wrongquestion.7Inoursurveys,weactuallyincludedapossibleanswer\uncertain"toassesstheshareofrespondentsindicatingsymmetricdispersionaroundthemode.Theshareofrespondentsinthatcategorywassolowforideology(andactuallynoneforvalence)thatweomititfromexposition.10 tothedistancejp^pjfromthemodeataconstantrate,asdictatedbyafunctiong(x1;x2):f1;:::;jj1g[0;1]![0;1]withgx1(x1;x2)0andgx2(x1;x2)0.Insynthesis,weimpose:Assumption4':fi;AP(p6=^p)=8:1=jjg(P;s;z(p^p))0fors=1fors=2;3fors=4:Concerningg(:),weallocateP(1P;s)massinthedirectionoftheasymmetryimposingthatP2[1=2;1],andallocate(1P)(1P;s)intheoppositedirection,assumingalineardecayoftheo-modemassinbothdirections.Thisspecicationofgallowsforavery exible,butparametricallyparsimoniousmarginaldistribution.ConcerningthevalencedimensionV,weagainenquireaboutthemodalbelief.Q3:Settingasidehis/herpoliticalposition,howwouldyoumostlikelygradecandidateA?From1(minimumcompetence)to10(maximumcompetence)orDon'tKnow(999).Thesetisthenassumedtobeasfollows:Assumption5:=f1;:::;10g.ThisparticularformatofQ3wasdrivenbythefamiliarityofItalianvoterswithprimaryandsecondaryeducationgradescoringrules,with10indicatingthebestpossiblemarkinaschoolassignmentandfailinggradesbeingbelow6.ThedispersionaroundthevalencemodeandtheskewnessofvalencebeliefsaremodeledsimilarlytoAssumptions4and4'withreplacingintheconstructionoffi;AV(v).Weomittheirdescriptionforbrevity.Forillustrativepurposes,Figure1providesanexampleofthemodeledpriorbeliefsaboutthevalenceofAforoneparticularvoter.Thedistributioninthegureisbaseduponthevoter'sreportedmode(^p=7)anduncertainty(s=2)andtheestimatesweobtainfortheparametersgoverningthedistribution.Finally,wemustemphasizethatweonlyelicitthebeliefsaboutvalenceandideologyfortheincumbentcandidate,A,andhismainchallenger,B,duetotheinfeasibilityofelicitingbeliefsaboutallminor,third-partycandidatesparticipatingintheelection.InourestimationinSection5,weassumethatthebeliefsofallnon-incumbentcandidatesarethesameasthoseelicitedforthemainchallenger,B.Whilethisisastarkassumption,wejustifyitbythefactthatthemainnon-incumbentcandidateswereideologicallysimilarandtheirqualitieswererelativelyunknown( atbeliefsalongthevalencedimensionarequitecommonfornon-incumbentcandidates).8 8Themainthird-partychallengerwasalsoaright-wingcandidate,likeB,butwassidelinedbytheirpartyduetopendinglegallitigationrelatedtohispreviousstintinoce.SeeSection3formoreinstitutionaldetails.11 2.3.2JointBeliefDistributions:ACopula-BasedApproachHavingderivedtheunivariatemarginals,wenowderivethejointdistributionsforallvoters.Givenanytwo(univariate)marginals,itispossibletoconstructajoint(bivariate)distributionininniteways.Copulas,introducedbySklar(1959),areusefuldevicesforprovidingarepresentationofamultivariatedistributionfunctionintermsofitsunivariatemarginaldistributions.Droppingthesuperscripts,givencumulativemarginals,FV(v)=Pr(Vv)andFP(p)=Pr(Pp),acopulafunctionCsatisesFV;P(v;p)=C(FV(v);FP(p))whereFV;P(v;p)=Pr(Vv;Pp)isthejointcumulativedistributionfunction.Cisuniqueforcontinuousdensities.Fordis-cretedensities,asinoursetting,typicallythesamejointdistributioncanberepresentedbydierentcopulas,butaspeciccopulauniquelyidentiesajointdistribution.Themarginaldistributionscarryalloftheinformationrelatedtothescalingandshapeofthejointdistributionfunction,whilethecopulafunctionincorporatestheinformationconcerningthedependencerelationshipamongtherandomvariables.Forparsimony,wewillfocusoncopulafamiliescharacterizedbyonedepen-denceparameter.Notice,however,thatthedependenceparameterdoesnotcoincidewithalinearcorrelationparameter;nonlineardependenceisaccommodatedaswell.Weinvestigatethreepopulartypesofcopulas,allowingfordierentdegreesofassociationbetweenVandP.First,independencebetweenVandPproducestheintuitivecopulaFV;P(v;p)=FV(v)FP(p).Second,weallowforcommondependenceacrosssurveyedvoters,givenbyassociationparameter11,employingtheFarlie-Gumbel-Morgensen(1960)familycopula,FV;P(v;p)=FP(p)FV(v)(1+(1FP(p))(1FV(v))),where0impliespositivedependenceand0negativedependence.Potentially,couldbemadevoter-typedependent(e.g.,allowingforadierentforleftandright-wingvoters),butnotvoter-specic.TheFGMfamilyis exible,butallowsonlysmalldeparturesfromindependence.ThethirdtypeofcopulafamilyweconsideristheFrankfamily,FV;P(v;p)=1=log(1+D()),withD()=(eFP(p)1)(eFV(v)1)=(e1)and=.TheFrankfamilyallowslargerdeparturesfromindependenceandrequires6=0.Indeed,theFrankcopulaiswellsuitedtomodeloutcomeswithstrongpositiveornegativedependence.Thedependenceparameterisnotelicitedfromthesurvey,butcanbeestimatedfromthedata.Recallthatweobservevotedecisionsandsuchdecisionsarefunctionofthevoters'posteriors.Givenacopulafamily,wecanestimateadependenceparameteraspartofthevectorofparameters,,bymaximizingthelikelihoodofobservingthosevotesasinequation(1).Onecanfurtheremploystandardgeneralizedlikelihoodratioteststoassesstherelativequalityoftheassumptionsonthecopulafamilyandselectthepreferredfamily.Wefollowthisapproach.12 Tosummarize,oursetofparametersofinterestis=[A;B; ;;;0]withbeliefparameters0=[P;2;V;2;P;3;V;3;P;V;A;B],whereweallowtheassociationparametertobedierentforAandB.Estimating0fromvotedecisionsisonlyfeasiblefortheposteriorjointdistribution.Thepriorjointdistributioncanbefullycharacterizedunderanadditionalassumption.Assumption6:Subjectivebeliefdistributionshaveconstant0.Inparticular,whileweallowmarginalstobeaectedbyourinformationaltreatment,weassumethatthedependencebetweenideologyandvalenceofthecandidateisconstant.Forexample,assumingthatamoderatepolicystanceispositivelycorrelatedwithsmartercandidates,informationthatmovessubjectivepriorstowardhigherlevelsofvalenceVisallowedtohaveanimpactonthepolicystanceP,pushingittowardamoremoderatestance,butitisnotallowedtochangetheassociationbetweenPandV.9Figure2andFigure3provideanexampleofthejointdistributionsforaparticularvoter'sbeliefsaboutcandidateApriortotheelectioncampaignandafterreceivingthevalencemessagetreatment.Eachjointdistributionisdeterminedassumingindependenceofthemarginalsandbasedontheestimatesoftheparametersgoverningthemarginaldistributions.Forthisparticularvoter,receivingthevalencemessageincreasedhisbeliefaboutthevalenceofAandalsoreducedtheuncertaintyalongbothdimensions.InSection6,wewillseethatsuchchangesinbeliefsarerepresentativeofvotersreceivingthevalencemessagetreatment.3ExperimentalDesignInMay2011,incollaborationwiththereelectioncampaignoftheincumbentmayorintheItaliancityofArezzo,weimplementedtheexperimentalstrategyembeddedintheaboveempiricalmodelduringthemayor'sactualelectoralcampaign.Specically,wedividedthecityintofourareas,randomizingattheprecinctlevel,andtheincumbentsentdierentcampaignmessagesbothbymailandbyphonecalltovotersintheseareas.Inthissection,wedescribetheinstitutionalsetting,aswellasthenatureofthe(randomized)campaignmessagesandtools.3.1InstitutionalSettingInItaly,mayorsofcitieswithmorethan15,000inhabitantsaredirectlyelectedunderapluralitysystemwithruno,thatis,intherstroundthecandidatewhoobtainsmorethan50percentofthe 9AsanalternativetoAssumption6,onecouldcalibratejforthepriordistributionatspecicvaluesandobservethesensitivityoftheresults.Anaturalrangeofvaluescouldbethecondenceintervalofthedependenceparameterfortheposteriors.Wedonotpursuethisavenuehere.13 votesiselected,otherwisethetwocandidatesreceivingthemostvotescompeteinasecondroundwhichtakesplacetwoweekslater.Mayoralcandidatesaresupportedbyoneormorepartylists,butvoterscancastseparatevotesforacandidateandapartylistsupportinganothercandidate.Theycanalsovoteonlyforamayoralcandidate,withoutexpressinganypreferenceforpartylists,buttheoppositeisnotallowed,becausevalidvotesforapartylistareautomaticallyattributedtothecandidateformayorsupportedbythatparty.Electedmayorsserveave-yeartermandaresubjecttoatwo-termlimit.Italianmunicipalitiesareinchargeofawiderangeofservices,fromwatersupplytowastemanagement,frommunicipalpolicetocertaininfrastructures,andfromhousingtowelfarepolicies.Mayorsarethekeypoliticalplayersatthelocallevel,astheycanalsoappointtheexecutiveocersanddismissthematwill.Thecitycouncil,whichactsasthelegislativebody,canforcethemayortoresignwithanocondencevote,butinthiscasethecouncilisalsodissolved.Becauseofthisinstitutionalsetting,municipalelectionshavehighsalienceandturnoutisusuallyveryhigh.ArezzoisaprovincialcapitalcityinthecenterofItaly,locatedintheprovinceofthesamename.In2011,ithad100,455inhabitantsand77,386eligiblevoters.Forelectoralpurposes,thecityisdividedinto95precincts(thesmallestelectoralunitwhichusuallycoincideswithaclusterofstreets),whichvotein42pollingplaces(e.g.,schools,publicbuildings).Fromapoliticalpointofview,thecitywascontestable.GiuseppeFanfani,theincumbentmayorelectedin2006whoacceptedrandomizationofapartofhisreelectioncampaign,belongedtothecenter-leftcoalition,butbeforehisrstelectionthecenter-rightcoalitionwonfortwotermsinarow.In2011,hismainchallengerwastheocialcandidateofthecenter-rightcoalition,GraziaSestini,aformerviceministeratthenationallevel.Sixother(minor)third-partycandidateswerealsopresentintheballot.Themainthird-partycandidatewasaformermayorofthecenter-rightcoalition,LuigiLucherini,sidelinedbyhispartyduetopendinglegaltrouble.10LocalpoliticalcampaignsarenotverysophisticatedinItaly,andtheymostlyrelyonpublicrallies,directmailing,andTVappearances(butnoads).Phonebanksarerarelyused,anddoor-to-doorcanvassingalmostneveroccurs. 10Themayoracceptedourproposaltorandomizehiscampaignbecauseofthepossibilityofreceivingpotentiallyusefulinformation.Asthecenter-rightcoalitionwassplitbetweenamainchallenger(Sestini)andalesscompetitiveone(Lucherini),heexpectedeithertowinintherstroundortogototheruno.Therefore,ourrandomizedtrialcouldprovidehimwithaneectivestrategyforcampaigninginthetwoweeksbetweentherstandsecondround.14 3.2RandomizedCampaignTooperationalizeourinformationaltreatments,westudiedthecampaignmaterialsoftheincumbentandassembledrelevantinformationsoastoisolateslogansbasedoneitherhiscompetenceascitymanager(valencemessage)orhispoliticalstance(ideologymessage).Becausewewantedtostayawayfromthestrategicgamebetweenhim,theothercandidates,andthevoters(thatis,wewantedtorandomizehisactualcampaign),weactuallydevisedtwodierentideologicalmessages:oneleaningtowardtheleftandoneleaningtowardthecenterofthepoliticalspectrum.Wethenallowedhimtochoosebetweenthetwoandheselectedtheleftistmessage.Furthermore,althoughourtreatmentofinterestcoincideswithpartisancampaignmessagesdeliveredbyoneofthecandidates,asopposedtonon-partisaninformation,wewantedourinforma-tionaltreatmentstobefactualandnon-emotional,astypicalforcheaporcostlysignalinggames.11Forthisreason,wematchedthemainsloganswithbulletpointsbasedonveriableinformationabouttheincumbent'sperformanceandpolicychoicesduringhisrstterminoce.Futureresearchshouldextendtoemotionalmessagesaswell,butwedidnotexplorethisavenuehere.AppendixFiguresA1andA2showthemail yerscontainingthetwomessages.12Thevalence yerisbuiltaroundtwokeywords:competenceandeort.Theimplicitmessageisthatvotersshouldreelecttheincumbentbecausehewascompetentandeectiveascitymanager.ThefactualinformationprovidedreferstothefactthatArezzodevelopedanurbandevelopmentplanthatwasrankedrstbytheregionalgovernmentandreceivedextrafundingbecauseofitsquality.Theextrafundingwasusedtorebuildmonuments,roads,andparkingslotsinthecitycenter.Theideology yerisbuiltaroundtwokeywords:awarenessandsolidarity.TheimplicitmessageisthatvotersshouldreelecttheincumbentbecausehesharesvaluesthatarecommonlyassociatedwiththeItalianleft.Thebulletpointsfurtherreinforcetheleftisttoneastheypointto\public"services,suchaschildcareandfoodfacilitiesforthepoor,thatwereexpandedduringhisrstterminoce.13Noticethatthetwomail yersareidenticalinsize,layout,colors,fonts,numberofwords,andphotoofthecandidate;onlythecontentofthecampaignmessagediers. 11Themarketingandadvertisingliterature(seeLiuandStout,1987)hasexploredsubjectiveresponsestofactualversusemotionalornonfactualmessages,indicatingsystematicdierences.Asaninterestingcounter,Gerberetal.(2011)presentarandomizedtrialinvolvingnonfactualcampaignmessages.12IntheAppendix,wealsoreporttheEnglishtranslationofthetextofthetwo yers.Additionalmaterialsrelatedtoourrandomizedcampaigncanbefoundonthewebsite:www.igier.unibocconi.it/randomized-campaign.13Tovalidateouroperationalizationofthetwoinformationaltreatmentsexante,werandomlyassignedthetwo yersto50universitystudentsatBocconiUniversity(inMilan)whodidnotknowthemayorofArezzo.Wethenaskedthemtogivetheirsubjectiveassessmentofthepolitician'svalenceandideologyusingthesamequestionsdescribedinSection2.Forthe25studentswhoreceivedtherstmessage,theaveragevalenceevaluationwas6.650(s.d.0.963)andtheaverageideologyevaluationwas3.100(s.d.0.700).Forthe25studentswhoreceivedthesecondmessage,thesevalueswere5.450(s.d.0.973)and2.050(s.d.0.669),respectively.15 Thetwocampaignmessages|valenceandideology|weresuppliedtovotersintwoways,throughdirectmailingandphonecalls.Therandomizationdesignwasimplementedasfollows.Weran-domlydividedthe95precinctsintofourgroups:(i)24precinctsreceivedthevalencemessage;(ii)24precinctsreceivedtheideologymessage;(iii)24precinctsreceivedbothmessages;(iv)23precinctsreceivednomessage(controlgroup).Furthermore,werandomlysplittherstthreegroupsintotwosubgroups:intherst,thetreatmentwasadministeredbybothdirectmailandphonecalls(12precincts);inthesecond,bydirectmailonly(12precincts).14AppendixTableA1reportstheex-antebalancetestsofpredeterminedvariablesattheprecinctlevel.Theavailablevariablesincludethenumberofeligiblevotersenlistedineachprecinct,thecity-wideneighborhoodeachprecinctbelongsto,andpastelectoraloutcomesofnational,regional,European,andmunicipalelections.Asprecinctswerereshuedinthelastdecade,someoutcomesarenotavailableforall95precincts.Allofthepredeterminedvariablesarebalancedacrosstreat-mentgroups.Onlythenumberofeligiblevotersdisplaysacoecientsignicantatthe10percentlevel,becauseofthepresenceofafewsmallprecinctsinthecountrysidethatcouldnotbespreadacrossallgroups.Removingtheseprecinctsfromtheanalysis,however,doesnotaltertheresults.Inordertoincreasetheeectivenessofthecampaignmessages,wedrewusefulinsightsfromtheU.S.experimentalevidencesummarizedbyGreenandGerber(2004).First,weactedintheweekbeforeelectionday,soastoensurethemessagesticksinvoters'minds.Second,wehadourmail yersdesignedbyprofessionalsanddirectlysenttoindividualswiththeirnameandaddressontheenvelope.15Third,wedidnotuseautomatedrobocalls.Weinsteadtrainedvolunteerstomakethecampaignphonecalls.Specically,fromthecandidate'sheadquarters,volunteerscalledallselectedhouseholdswiththefollowingprotocol:rst,theywereinstructedtotalkwiththevotersandaskfortheiropinionforabouttwominutes.Then,theywouldaskthevotertolistentoarecordedmessagefromthecandidate.Attheendofthecall,therecordedvoiceofthecandidatereada30-secondscriptwiththeabovevalenceandideologymessages(oracombinationofthetwo).16Ourrandomizedcampaignusedtheabovetools|mailersandphonecalls|onalargescale.Allhouseholdsinthecityreceivedanenvelopefromtheincumbentcampaign.Theenvelopecontainedtheocialplatformofthepoliticalpartiessupportingthecandidateplusoneofour yers(orbothofthem)accordingtotheassignedtreatmentgroup.Votersinthecontrolgroupreceivedjustthe 14Aswewerealreadypushingtheboundariesintermsofsamplesize,wedecidedthattheaccuracylosscouldnotjustifyanadditionalsubgrouptreatedbyphonecallsonly.15Toavoidsendingmultipleenvelopestothesamehousehold,werandomizedthenameofthereceiverwithineachhousehold,becausewedidnotwanttotargetonlyhouseholdheads.16IntheAppendix,wereporttheEnglishtranslationofthetextofthethreerecordedmessages.Originalaudiolesareavailableonthewebsite:www.igier.unibocconi.it/randomized-campaign.16 platform,butnotthe yerwithourinformationaltreatment.Thisprocedureallowedustokeepthecandidateunawareoftherandomizationoutcome.Ofcourse,thecandidateapprovedallmessagesandpaidforthecostsofthecampaign,butwegavehimclosedenvelopessothathecouldnotinferwhichprecinctswerereceivingone yerasopposedtotheother.Insummary,allhouseholdswithatleastonememberenlistedasaneligiblevoterreceivedourmailers.Ontopofthis,about25percentofthehouseholdsinthetreatmentgroupsalsoreceivedacampaignphonecall.173.3DataToelicitbeliefsaboutthevalenceandideologyofthetwomaincandidatesalongthelinesdescribedinSection2,werantwosurveysof2,042eligiblevotersdistributedacrossalltreatmentgroups.Werantherstsurveytendaysbeforetheelectionand,mostimportantly,beforevotersreceivedtheinformationaltreatments,soastomeasurepriorsanddemographiccharacteristics.Thesecondsurveywasconductedthedayaftertheelectionandwasmeanttomeasureposteriorsand(self-declared)votechoices.Toimplementoursurveys,wecontractedacompanyfromanotherItalianregion,soastohaveinterviewerswithdierentaccentsfromthecampaignvolunteersandtoremoveanylinkbetweenthecampaignandthesurveyphonecalls.About71percentoftherespondentsintherstsurveyalsorepliedtothequestionaboutwhethertheyvotedornotinthesecondsurvey.Therefore,oursampleismadeupof1,455voters,1,306ofwhomactuallyvotedforoneofthecandidates.However,231ofthe1,306votersdidnotspecifyforwhichcandidatetheyvotedandforthisreasonweaccommodateforpotentiallynon-randomnon-responsesinthemodelestimation.Tofurthervalidateourrandomizationdesignexpost,wecheckedforbalancingofthecharac-teristicsofvotersacrosstreatmentgroups.Surveyvariablesincludedemographiccharacteristics,educationalattainment,politicalorientation,homeownership,andhowoftenvotersreadnewspa-persorwatchTV.TheresultsarereportedinAppendixTableA2.Noneofthese(self-declared)individualcharacteristicsisstatisticallydierentacrosstreatmentgroups.18Table1summarizeselectionresultsattheprecinctlevel.Theincumbentmayorwonhisbidforreelectionwithavoteshare51.3percent,enoughtoavoidaruno.Table2showsthe(self- 17Becauseofbudgetandtimeconstraints,wecouldnotreachallhouseholdsbyphone.18Asanadditionalex-postvalidationoftherandomizationdesign,webuiltproxiesofCensuscharacteristicsattheprecinctlevel.Thisexercisehastwolimitations,however.First,datafromthelastavailableCensusreferto2001.Second,precinctsarenoteasilymatchablewithCensuscells.Toovercomethesecondlimitation,weimplementedthefollowinggeocodingprocedure:1)foreachstreet(i.e.,line)belongingtoaprecinctwecalculatedtheweightedaverageofthecharacteristicsoftheCensuscells(i.e.,polygons)overlappingwiththatstreet(withweightsequaltotheoverlappingsegments);2)foreachprecinct,wecalculatedtheweightedaverageofthecharacteristicsoftheassociatedstreets(withweightsequaltothepopulationlivingineachstreet).AppendixTableA3reportsthebalancingtestsoftheseCensuscharacteristicsacrosstreatmentgroups.Althoughtheestimatesarelikelytosuerfromattenuationbiasduetomeasurementerror,noneofthemisstatisticallydierentfromzero.17 declared)votechoicesofsurveyedindividuals.Asoftenhappensinpost-electoralpolls,thereisaslightbandwagoneectinvotedeclarationsfavoringthewinningcandidate(57.1percent).Thebandwagonisnotaconcernforestimationunderthe(plausible)assumptionthatthiseectisorthogonaltoourtreatmentgroups.Inanycase,recallthatastrengthofourapproachisthatwecancross-validatetheconsistencyoftreatmenteectsinthesurveydata(attheindividuallevel)withthoseintheaggregateactualvotingdata(attheprecinctlevel).4EvidenceonChoicesInthissection,weevaluatewhetherourinformationaltreatmentshadanyeectonvotingchoicesatboththeprecinctandindividuallevel.Basedontheexperimentaldesigndescribedintheprevioussection,the(reduced-form)causaleectsofcampaigningonvalenceversusideologycanbeestimatedthroughtheOLSmodel:Yi=6Xk=1 kDki+i(3)whereYiistheelectoraloutcomeofinterest,Dkiarebinaryindicatorscapturingtreatmentgroupstatus,andiistheerrorterm.19Thesixtreatmentgroups,Dk;include:valencemessagebyphone(andmail);valencemessagebymailonly;ideologymessagebyphone(andmail);ideologymessagebymailonly;doublemessagebyphone(andmail);anddoublemessagebymailonly.Observationsreceivingnoinformationaltreatmentaretheexcludedreferencegroup.Table3summarizestheresultsintheaggregatesample,whoseunitsofobservationarethe95electoralprecincts.Atthemargin,partisanadshavenoimpactonturnout.Thereisevidence,however,thatcampaigningonvalencebringsmorevotestotheincumbentwhenphonecallsareusedasacampaigntool.Phonecallsdeliveringthevalencemessageincreasetheincumbent'svoteshareby4.1percentagepoints(i.e.,byabout8.4percentwithrespecttotheaverageshareinthecontrolgroup).Thisestimatedeectissizable,becauseitmustbeinterpretedasanintention-to-treateect:infact,only25percentofthehouseholdsinthetreatedprecinctsreceivedacampaignphonecallandnotallofthemacceptedourinvitationtolistentothemessagerecordedbythecandidate.Becauseofthesmallsamplesize,however,coecientsarenotpreciselyestimatedandwecannotrejectthenullhypothesisthattheyarestatisticallyequaltoeachother. 19Toaccountforpotentialintra-classcorrelationbetweenneighboringprecinctsweclusterstandarderrorsatthepollingplacelevel,whiletoaccountforcorrelatedtimeshocksinsurveydataweincludexedeectsfortheinterviewdate;resultsarenotsensitivetothesemodelingchoices.Empiricalresultsarequalitativelysimilarwhenweincludepredeterminedvariablesasadditionalcovariates,althoughthespecicationbecomesdemandingintermsofdegreesoffreedomintheaggregatedata(resultsavailableuponrequest).18 Whatwecanrejectintheaggregatedataisthenullthatthetwocampaigntools|mailersversusphonebanks|areequallyeective.Ifwemergetogetherallgroupsthatreceivedaninformationaltreatmentwiththesamecampaigntool,wendthat|withrespecttothecontrolgroup|phonecallsincreasetheincumbentvoteshareby2.7percentagepoints(p-value:0.019),while,statistically,theeectofmailersisbothdierentfrom2.7andnotdierentfromzero.ThisresultisinlinewithU.S.experimentalevidenceshowingthatmailersareusuallyineectiveinpoliticalcampaigns(seeGreenandGerber,2004).Inourcase,however,mailersarealsoadministeredtovoterswhoreceiveaphonecall.Therefore,wecannotruleoutthepossibilitythatmailersaloneareineective,buttheybecomeeectivewheninteractedwithothercampaigntoolsdeliveringthesamemessage.Basedontheaboveevidenceontheineectivenessofmailersalone,Table4estimatesequation(3)imposingthisrestriction:includingboth\mail"and\nomessage"inthecontrolgroup.Stan-darderrorsareslightlylower,andthepointestimatesandthestatisticalsignicanceoftheincludedregressorsarealmostidenticalwithrespecttothefullmodel.Inordertovalidatetheaggregateevidenceandtogainstatisticalaccuracy,weestimateequation(3)usingtheindividual-levelsurveydata,wheresamplesizeislessofanissue.Theunitsofobservationarethe1,455eligiblevotersforturnoutorthe1,306actualvotersforthevoteshares.Asalloutcomesarebinary,estimationisbyprobit.Thepricewepayisthathereoutcomesareself-reported,thatis,basedonvotedeclarationsandnotonactualchoices.Theunderlyingassumptionisthatself-reportingbiasisthesameacrosstreatmentgroups.20Table5reportstheestimatesforalltreatmentgroups.Resultsareconsistentwiththeaggregateevidence.Phonecallsdeliveringthevalencemessageincreasetheincumbent'svoteshareby9.5percentagepoints(i.e.,byabout16percentwithrespecttothecontrolgroup).Thiseectislargerthanintheaggregatedata,buttreatmentintensityisalsohigherinthiscontext,becauseallsurveyedhouseholdsreceivedthecampaignphonecall,asopposedtoonly25percentintheaggregatedata.Phonecallsarestillthemoreeectivecampaigntool,withadierencesignicantatthe1percentlevel.Moreimportantly,conditionaloncampaigntool,thevalencemessageisnowstatisticallymoreeectivethantheideologymessageatthe10percentlevel.21Table6furtheremphasizesthispointby 20Aswedocumentinthenextsection,non-responseinvotedeclarationsislikelytobenon-random,i.e.,tobeassociatedwithindividualcharacteristicssuchasideologyorpriorbeliefs.Thisdoesnotimply,however,that(non-random)non-responseshouldnotbeorthogonalto(random)treatmentassignment.21Althoughourexperimentaldesign|basedonrandomizationattheprecinctlevel|didnotallowforstraticationonindividualcharacteristics,wenonethelessinvestigatedpotentiallyheterogeneousresponsesbyrepeatingthebaselineestimationinsplitsamplesalongmanyobservabledimensions.Thepositiveimpactofvalencephonecallsontheincumbent'svoteshareturnsouttobestatisticallylargerforfemales,individualsolderthan65years,individualswithoutacollegedegree,andless-informedvoters.Instead,thereisnosignicantheterogeneityalongpreviouspoliticalorientation,homeownership,ortypeofoccupation(resultsavailableuponrequest).19 focusingoninformationaltreatmentsadministeredbyphone:campaigningonvalencebringsmorevotestotheincumbentandtothepartyliststhatsupporthim,andthesepointestimatesarestatisticallylargerthanthoseofcampaigningonideologyalone.Finally,inAppendixTableA4,weevaluatethepotentialimpactofspilloversacrossneighboringprecincts.AsacounterparttoTable5,weestimatetheeectsonvotingchoicesoftheaveragetreatmentintensityforindividualsvotinginthesamepollingplace,althoughtheymaybelongtodierentprecinctsandthereforetreatmentgroups.IfAssumption1(SUTVA)ismet,weexpectthesemeasurestohavenoimpactonchoicesfortreatmentsdetectedasineectiveinTable5,andtohavealesssignicantimpactfortreatmentsdetectedaseectiveinTable5.Itisthusreassuringthatnoneofthesespilloverestimatesisstatisticallydierentfromzero.225ModelEstimationWenowreporttheresultsfromthemaximumlikelihood(ML)estimationofourvotingmodel.Theestimationprocedureisstraightforwardandreliesonttingindividualvotedeclarations,which|inSection4|wehaveshowntocloselymatchactualvoteoutcomes.23Thespecicationselectionwarrantssomediscussion,however.Section2discussednon-responseparameters[A;B],preferenceparameters[ ;;],beliefpa-rameters[P;2;V;2;P;3;V;3;P;V;A;B],andthechoiceofacopulafamily[Independent;Frank;FGM].Concerningthepreferenceparameters,alargeliteratureinpoliticaleconomicsandpoliticalsciencehasemphasizedpreferenceheterogeneity,forinstanceinthecaseofdistasteforspecicpolicyoutcomes,suchasin ationorunemployment.24Wecaneasilyaccommodatethisfeaturebyallowingadierent[ ;;]vectorforleft-wing(L),centrist(C),andright-wing(R)vot-ers.Wecanaswellaccommodateheterogeneityinthedependencestructureofthebeliefs[A;B]byallowingthemtodierforL,C,andRvoters.Concerningtheskewnessofthemarginalbeliefs,onecanexperimentwithrelaxingthesimple[P;V]toamore exible[P;2;V;2;P;3;V;3],thus 22NoticethatpointestimatesarenotdirectlycomparablewiththoseinTable5becausetheregressorsarenolongerdummiesbutshares.Comparedtotheaveragevaluesandstandarddeviationsofthespillovershares,however,pointestimatesaregenerallysmall,and|asexpected|theyarelargerfortheadministrationofthevalencemessagebyphone,becauseinthosecasesthesharesalsoincludetreatedvotersforwhomthereexistsanon-zeroeect.23TheidenticationofthemodelisassessedthroughseveralroundsofMonteCarlosimulations.Forgivenparametervalueswesimulatedindividualvotesandensuredthattheestimationbasedonthesimulateddataconvergedtotheoriginalstructuralvalues.Ourlikelihoodfunctiondependsonarelativelysmallnumberofparameters.Thisallowsforafairlyextensivesearchforglobaloptimaovertheparametricspace.WeusethepatternsearchalgorithmofMatlabwithdieringinitialvalues.Repeatingtheoptimizationprocedureconsistentlydeliversidenticalglobaloptima.Wealsoemployedageneticalgorithm(GA)globaloptimizerwithalargeinitialpopulationof10;000valuesfollowedbyasimplexsearchmethodusingtheGAvaluesasinitialvaluesforthelocaloptimizer.Bothmethodsresultedinthesameestimatesbutthepatternsearchalgorithmconvergesfasterinourenvironment.24Amongothers,seeDiTella,MacCulloch,andOswald(2001);GerberandLewis(2004).20 allowingtheextentoftheskewtochangewiththevariance.Allthesearetestableparametricconstraintsthatcanbeassessedbasedonlikelihoodratiotests.Ontheotherhand,thechoiceofthecopulafamilyrequiresageneralizedlikelihoodratiotestapproach,asthecopulafamiliesweconsiderarenon-nested.TheVuong(1989)modelselectiontestisappropriateforthispurpose.InAppendixTablesA5andA6wereportthefullsetofmodelestimatesforalltherelevantcombinationsofparametricandcopulaassumptions,whicharepairwisetestedinAppendixTablesA7,A8,andA9throughlikelihoodratiotestsandVuongtests(forthecopula).Accordingtothetests,thepreferredspecicationallowsforheterogeneityinpreferenceparametersalongthevoter'sself-declaredideologicalstance,forindependencebetweentheideologicalandvalencedimensionsofbothcandidates,andforcommon[P;V].Thus,thepreferredmodelspecicationestimates=[A;B;f z;z;zgz=L;C;R;P;2;V;2;P;3;V;3;P;V].WereporttheMLestimatesforthismodelinTable7.Werstnotethattheestimatesoftheprobabilityofresponse(i.e.,theprobabilityofdisclosingone'svote)are0:76and0:99forpredictedvotesforA(A)andB(B),respectively,andareverypreciselyestimated.WhilewecannotrejectthenullthattheprobabilityofresponseisoneforvotersthatvotedforB,wecanstronglyrejectthenullforvotersthatvotedforA;whichjustiesourchoiceofmodelingnon-randomnon-response.25Interestingly,voterswhoarepredictedtohavevotedBaremorelikelytodisclosetheirvote,contrarytothepossiblehypothesisthatthosewhovotedforthewinner(A)shouldbemorewillingtodisclosetheirpreferenceforthewinner.ThisresultsquareswiththeintuitionofconservativevotersinTuscanybeingparticularlyassertive.Generally,thepreferenceparametersareestimatedwithprecision.Theparametergoverningtheinteractionbetweenvalenceandideologyvaluesforthevoter,,isestimatedtobeafairlyprecisezero.Imposing=0clariestheinterpretationof astherelativeweightinpreferencesofvalence(x0)totheweightofideology(1x0).Hence, =x0 1x0=1impliesequalweightsalongbothdimensionsandthisiswhatwendforLandCvoters.TheweightonvalenceforRvotersis,however,muchlower,around27percent,versusa73percentweightonideology.Concerningthecurvatureoftheideologicallossfunctionu(:),surprisingly,wend1forallthreetypesofvoters,indicatingincreasinglossesbutatdiminishingratesfrompoliciesfurtherawayfromthevoter'sblisspoint.Thisisincontrastwiththestandardassumptionof=2,quadratic 25Asfurtherevidenceinsupportoftheprobabilityofdisclosingone'svotebeingnon-random,weranaprobitregressionofadummyindicatingwhetherornotavotewasdisclosedontheelicitedposteriorbeliefsandvoter'sideology.AnFteststronglyrejectsthenullhypothesisofnoexplanatorypowerandhencerandomnon-response(p-value=0.000).Interestingly,thestrongervoters'beliefsaboutthevalenceofeithercandidate,themorelikelyvotersaretodisclosetheirvote.21 losses,forexample.Forcentristvoters,isactuallyestimatedtobezero,althoughtheestimateisratherimprecise.With=0,thelossduetodeviationsfromthevoter'sblisspointisconstantandindependentofthecandidate'spolicy.Thebeliefparametersarealsopreciselyestimatedforthemostpart.Interestingly,thespeci-cationfeedsbackinformationwhichallowsustoassesscertainfeaturesofthesurveydesign.Themodelclearlycapturesanintermediatelevelofuncertaintybetween at(s=1)anddegeneratepri-ors(s=4)forbothvalenceandideology.Theon-the-modeprobabilitymass,V;3;isestimatedataround0:40forvalenceandthecorrespondingparameterforideology,P;3;isestimatedataround0:58.Hence,votersanswering2to5toQ2aremorecertainthanhaving atpriors,butdenitelynotsureaboutthecandidatebeingatthemode(i.e.,answer1toQ2).Alongthevalencedimen-sion,votersdonotperceivethedistinctionbetween\veryuncertain"(s=2)and\ratheruncertain"(s=3)giventhat,attheestimatedvalues,V;3=V;2.However,alongtheideologydimension,\ratheruncertain"doesresultinlessdispersioninthemarginaldistribution.Inaddition,thean-swersgiventotheskewnessdimensionseemtobeimportantonlyalongtheideologicaldimension,whereP1=2,butnotonthevalencedimensionwhereVisnotsignicantlydierentfrom1=2,indicatingasymmetricpartitioningoftheo-modeprobabilitymass.Finally,concerningthechoiceofthecopulaandtheestimatesofthedependenceparameters,wenotethat,althoughboththeFGMandFrankcopulamodelshavetypicallyhigherlikelihoodvaluesthanunderindependence,thelossofparsimonyofthemodeldoesnotjustifytheadditionalparametersaccordingtotheVuongtests(seeAppendixTableA9).Thisresultoccursbecausewecanonlyestimate[A;B]veryimprecisely,whichcanbeeasilyrationalized.Theparameters[A;B]areessentiallyidentiedbyvotersthatare:i)closetoachangeintheirvotechoicebetweenAandB;andii)characterizedbynon-degenerateandnon- atbeliefsalongboththeideologyandvalencedimensions.Thesejointrestrictionssubstantiallyreducethenumberofobservationsprovidingusefulidentifyingvariationforestimating[A;B].Notwithstandingthelackofprecision,lookingatthesignsoftheestimateddependenceparametersinAppendixTablesA5andA6isintriguing.WegenerallyndevidenceofapositiveassociationbetweenleftpositionandvalenceperceptionsforAdrivenbyleft-wingvoters,andapositiveassociationbetweenrightpositionandvalenceperceptionsforBdrivenbyright-wingvoters.Moreextremepositionsappeartobecorrelatedwithhighervalence,inaccordancewiththetheoreticalresultsinBernhardtetal.(2011).TheFrankcopulaispreferredovertheFGMcopula,althoughwecannotrejectthenullofequalt.Thestructuralestimationhasallowedustofullyrecoveralloftheparametersnecessarytocharacterizetheindividualbeliefdistributions.Weproceedtotheanalysisofvoters'beliefsnext.22 6EvidenceonBeliefsTheeectofpartisanadsonbeliefsisinterestingperse,anditcanshedlightontherobustnessoftheimpactofthesameadsonvotingchoices,basedontheirmutualconsistency.Toincreaseaccuracy,werestrictourattentiontoinformationaltreatmentsdeliveredbyphone,thatis,bymeansoftheeectivecampaigntool.InTables8and10,theoutcomesaretheaverageandthestandarddeviationoftheindividualbeliefdistributions|frommodelestimation|ofbothvalenceandideologyoftheincumbentandoftheopponent,respectively.InTables9and11,welookatthesamemomentsoftheindividualbeliefdistributions,butweinsteadusesurveyresponsesasopposedtoestimatesfromthestructuralmodel.Specically,theoutcomesarethe(self-reported)modeandabinarymeasureof\uncertainty"(namely,adummycapturing atpriorsinsurveyresponses).EstimationisbyOLSformultivaluedorcontinuousoutcomesandbyprobitforbinaryoutcomes.26Fortheincumbent,boththevalenceandideologymessageshavetheexpecteddirecteects.Informationonvalenceincreasesperceivedcompetencebyabout5percentwithrespecttotheaverageperception.Thesameholdsforinformationonideology,asperceivedideologydecreases(i.e.,movestotheleft)byabout5percent.Interestingly,secondmomentsarealsoaectedbythetwotreatments:uncertaintyabouttheincumbent'svalenceorideologyisreducedbyadditionalcampaigninformationalongthecorrespondingdimension.Decreaseduncertaintyisarelevantchanneloftheeectofcampaigninformationonchoices.Asamatteroffact,thepositiveeectofvalencephonecallsontheincumbent'svoteshareisstrongerinthesubsampleofvoterswhosepriorsare at.Inthetreatedgroup,weobserveasharptighteningofthebeliefdistribution,whichcontributestotheoveralleect.Thenegativeimpactofideologymessagephonecallsonthecandidate'sideologydoesnottrans-lateintomore(orless)votesforA.Notwithstandingthelargeutilityweightvotersplaceonthisdimension,theshiftinthebeliefdistributionscausedbytheideologyphonecallsisnotstrongenoughtoaectvotingchoices.27Withrespecttoideology,informationontheincumbent'spositionhasinterestingcross-eectsontheperceptionoftheopponent'sposition.VoterswhoreceivedtheideologyphonecallfromtheincumbentcampaignmovetheirsubjectiveevaluationoftheopponentBtotherightby3percent.Thetreatmentalsoreducesuncertaintyalongthisdimension.Thismightbeduetotheincreased 26Forthesakeofintuition,weuseOLSalsofortheideologymode,whichcanonlytakeve(ordinal)values.ResultsfromorderedProbitarequalitativelyidentical(availableuponrequest).27Analternativeexplanationmightbethattheideologymessageaectsright-wingandleft-wingintheoppositeway,butthisisnotwhatwendinoursample.Ideologyphonecallshadnegligibleeectsonvotingbehaviorforbothtypesofvoters,whiletheirimpactonbeliefswasalmostequivalent.23 salienceoftheleft/rightdistinctionortoitsrelativenature,anditiscausalevidenceofcross-learningbetweenpoliticalcampaigns.Thisndingisconsistentwithasophisticatedsubjectiveupdatingbehavioronthepartofthevoters.Forexample,thistypeofevidencewouldbeconsistent(albeitnotproofof)Bayesianupdatinginatwo-candidatesignalinggame.7ModelFitandCounterfactualElectoralCampaignsToconcludeouranalysiswediscussmodeltresultsandcounterfactualelectoralsimulationsbasedonourstructuralestimates.Overall,thestructuralmodelunderthebaselinespecicationpredictstheactualvotecorrectly88:7percentofthetime.Inparticular,wepredictcorrectly95:9percentofthevotesforcandidateAand70:7percentofthevotesforB.Here,thesampleunderconsiderationisrestrictedtothevoterswhodisclosedtheirvoteonly,sincewedonotknowtheactualvoteofthosewhochosenottodiscloseit.Turningtocounterfactuals,nostandardprotocolexistsintheliteratureforrunningthesetypesofexercises,sowehavedevisedone.SupposeonewishestoassesswhatwouldhavehappenedtotheaggregatevoteshareofAifeverybodyinthecityhadreceivedthevalencemessage(i.e.,hadgottentreatmentH=1).Wesimulatethiscounterfactualcampaignusingavestepprocedure.UnderourstabilityAssumption6,foreachvoteri;itispossibletogeneratepriorbeliefdis-tributionsaboutAandBbasedupontheirpriorsurveyanswersand0,thestructuralparametervectorestimatedfromvotesandposteriorbeliefs.Thisistherststep.Secondly,foreachvoteri2T(h)withh6=1(i.e.,nottreatedwiththevalencemessagetobeginwith),itisalwayspossibletondthenearestneighbortreatedmatchinthegrouph=1,i02T(1),basedontheMahalanobisdistancemetricderivedfromcovariates(suchasage,gender,maritalstatus,education,priors,andideology).Voteri0istheclosestmatchtovoteriforwhichthecausaleectofvalenceonbeliefsisactuallyobserved.Essentially,thisisthesameintuitiononewouldfollowinpropensityscoreestimation.Oncetheclosestmatchi0hasbeenidentied,asthirdstepwecomputethedierencebetweeni0'smarginalposteriorandpriorbeliefsateverypointofthesupportofeachofthevalenceandideologydimensions.Fourth,weapplyi0'spointwisechangesinbeliefstoi'spriorstocalculatethecounterfactualposteriormarginalbeliefsofi,undertheassumptionthat,hadigottenthesametreatmentasi0,shewouldhaveupdatedherbeliefsinthesamewayasi0.Fifth,wecomputejointposteriorbeliefsusingtheappropriatecopulafamilyandtheestimated's.Giventheposteriorsforeachvoteri,weobtainasimulatedelectoraloutcome,bycalculatingtheexpectedutilityofeachcandidateforiandthenpredictingtheirvoteforthecandidatewiththehighestexpectedutility.24 Importantly,thissimulationproceduredoesnotrequirethesimulatedelectoralcampaigntoonlyfocusonasingletreatment,butitcanbetweakedtotargetingspecicsubgroupswithdierenttreatments.Forinstance,wecansimulateacampaigninwhichvalencemessagesaresenttoknowncentristandright-wingvoterswhileideologicalmessagesaresenttoleft-wingvoters.Thisisofparticularrelevanceatapointintimewhenpoliticalcampaigns,especiallyintheUS,haveincreasinglyturnedtospecializedcompanies,suchasAristotle,formicrodataacquisitionandselectivecampaignadvertising,atrendwellunderwayalsoincommercialandonlinemarketing.WeexploresomeofthepossibleelectoralcounterfactualsinTable12.Foreachcounterfactual,weincludeallvoters,eventhosewhodidnotdisclosetheiractualvote.Table12reportscounterfactualelectoraloutcomesforvetypesofcampaignsbyA:(1)ablanketvalencecampaign;(2)ablanketideologicalcampaign;(3)ablanketdoublevalence-ideologycampaign;(4)atargetedcampaignofvalencemessagestocenterandright-wingvotersanddoublemessagestoleft-wingvoters;(5)atargetedcampaignofideologicalmessagestocenterandright-wingvotersanddoublemessagestoleft-wingvoters.Allresultsarebenchmarkedtothesimulatedelectoraloutcomethatwouldhaverealizedintheabsenceofanycampaignmessageonourpart.Thecounterfactualsarealsoassessedintheirprecisionbyconstructing95percentasymptoticcondenceintervalsbasedonbootstrappingfromtheasymptoticdistributionoftheparameters.Allourcounterfactualestimatesappearstatisticallyprecise.Themosteectivepossiblecampaignistheelectoralcampaigninwhichvalencemessagesalonearesenttoallvoters.AblanketvalencecampaignincreasesthevoteshareofAby2:2percentagepointsrelativetonocampaign,whichismorethanenoughtomakethedierenceinaclosely-contestedelection.Interestingly,ablanketcampaignofideologymessagesactuallyreducesthevoteshareofAsubstantially,infactbythesame2:2percentagepointsthatablanketvalencecampaignwouldinsteadbringtoA.Infact,the95percentcondenceintervalsforthetwosimulatedcampaignsdonotoverlap,sowecanbereasonablycertainthatablanketvalencecampaignwouldhaveoutperformedablanketideologycampaign.Tounderstandwhytheideologycampaignreducesvoteshares,recallthattheideologicalmessageinourexperimenthasaleftistbent,reducingtheexpectedutilityfromAforR,CandpossiblythemostmoderateoftheLvoters.Overall,thelossofsupportfromCandRinoursampleturnsouttomorethansucienttoosetthegaininLvoters.Forthesamereason,adoublecampaignofbothideologyandvalencemessagesincreasesthevoteshareofAby0:5percentagepoints,which,whileeective,isnotaseectiveastheblanketvalence-onlycampaign.Finally,themixedcampaigninwhichLvotersgetbothtypesofmessageswhileCandRvotersgetvalencemessagesonlyisalmostaseectiveasthevalencecampaign,25 whilethecampaigninwhichLvotersgetbothtypesofmessageswhileCandRvotersgetideologymessagessubstantiallydecreasesA'svoteshare.Insummary,consistentlywithouroverallresults,campaigningonvalenceappearedthemosteectivetooltopersuadevoters.8ConclusionThispaperpresentsnovelevidenceontheeectsofcampaigninformationonvoters'decisionsinalarge-scaleeldexperiment.Importantly,oureectsareobservedbothinvotedeclarationsofsurveyedvotersandinactualvoteoutcomesattheprecinctlevel.Tothebestofourknowledge,thisistherstempiricalrandomizationexerciseintheliteraturethatoperatesatthescaleofanentireelectionandcoverstheentirevotingpopulationinamaturedemocracy.Bothourreduced-formandstructuralestimationresultsuncoverlargeelectoralgainsfromvalence-basedinformationalcampaigning,possiblyduetotherelativelyhigherlackofpriorinformationaboutthecandidatesalongthisdimension.Anadditionalcontributionofourpaperistopresentabeliefelicitationprotocolthatallowsus,whencombinedwithinformationontheelectoralchoicesofvoters,tocompletelycharacterizevoters'beliefsaboutcandidatesalongboththeideologicalandvalencedimensions.Ourmethodologyallowsusto exiblyincorporatemultivariatebeliefdistributionswithinastructuralrandomutilityvotingmodel.Wethenemploythisempiricalmodeltostructurallyestimatebothbeliefdistributionsandvoters'preferenceparameters.Fromamethodologicalviewpoint,weincorporateageneralstructureofbeliefsupdatingthatgoeswellbeyondwhatnormallyachievablewithstandardassumptionsinthepoliticalandcom-mercialadvertisingliterature.Forinstance,letusconsiderconjugatepriorsoftheGaussianfamily.Withnormalbeliefsnewsignalscannotreducetheprecisionofthesubjectivedistributions,theyalwaysreducethevarianceofthesedistributions.Butrelyingonsuchbeliefsisveryrestrictive.Toseethisconsideranotherintuitivebeliefdistribution:abinomial.Whentherearetwo(ormoregenerallynite)states,theprobabilityofthe\good"statecangoupordowndependingonthesignalvalue.Asaresult,thevarianceofthebeliefscanactuallyincreaseordecreaseafterreceivingadditionalinformation.Hence,theimportanceofleavingthebeliefsfamilyunrestrictediscrucialinnotforcingerroneousassumptionsontothedata.Ourestimatesshowthattheutilityweightplacedbyvotersonacandidate'spolicypositionisofapproximatelyequalmagnitudetothatplacedonacandidate'svalenceandthatthecommonassumptionofconvexityofthelossesfromideologicaldistanceisnotsupportedbythedata.We26 alsoshowhowtheinformationaltreatmentswedesignedsystematicallyin uenceboththerstandsecondmomentsofvoters'marginalbeliefsaboutbothcandidatesintheelectoralrace,notonlythebeliefsaboutthecandidateoriginatingthemessage.Webelievethiscausalevidenceofcross-campaignlearningcanproveusefulforunderstandingthelevelofsophisticationinsubjectiveupdatingbyvoters.Potentialapplicationsofourelicitationmethodologyandestimationappeartobequitewide,in-cluding,inadditiontopoliticalcampaigning,commercialadvertisingandmarketing.Ourapproachcouldbeofusefortheassessmentofanytypeofinformationaltreatmentforrandomizedcontrolledtrials,mostofthemcurrentlyperformedindevelopingcountries.Finally,ourincorporationoftheprobabilityofnon-responsemaybeappliedinmanyothercontextsinwhichnon-randomnon-responsetosurveyquestionsseemsplausible(e.g.,reportsofincomeorotherlabor-relatedquestionsforwhichthosesurveyedmaybeuncomfortabledisclosinginformation).27 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Turnout0.7080.7140.0500.3890.78895Incumbentshareovervalidvotes0.5130.5080.0610.3540.66795Incumbentpartiesovervalidvotes0.5410.5420.0650.3580.67995 Notes.Descriptivestatisticsattheprecinctlevelofthevariablesspeciedintherstcolumn.\In-cumbentparties"refertothevotesharesofthepartylistssupportingtheincumbent.Table2{VoteDeclarationsattheIndividualLevel MeanMedianS.d.MinMaxObs. Declaredturnout0.8981.0000.3030.0001.0001,455Declaredvotefortheincumbent0.5711.0000.4950.0001.0001,306Declaredvoteforincumbentparties0.4930.0000.5000.0001.0001,306 Notes.Descriptivestatisticsattheindividuallevelofthevariablesspeciedintherstcolumn.\Incumbentparties"refertothe(self-declared)voteinfavorofthepartylistssupportingtheincumbent.31 Table3{Reduced-FormAggregateEstimates,AllGroups Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Turnout-0.011-0.0000.0130.010-0.006-0.006[0.031][0.015][0.011][0.013][0.009][0.013]Incumbent0.041**0.0040.0130.0210.027*-0.023share[0.019][0.025][0.016][0.025][0.015][0.015]Incumbent0.032*0.0180.0150.0290.021-0.015parties[0.018][0.023][0.016][0.026][0.014][0.015] Notes.Observations:95precincts.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table4{Reduced-FormAggregateEstimates,PhoneCalls Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Turnout-0.0120.012-0.006[0.030][0.011][0.010]Incumbent0.040**0.0120.026*share[0.019][0.015][0.013]Incumbent0.0260.0080.014parties[0.020][0.016][0.012] Notes.Observations:95precincts.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.32 Table5{Reduced-FormIndividualEstimates,AllGroups Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Turnout-0.024-0.0190.0060.033-0.019-0.003[0.027][0.034][0.026][0.022][0.028][0.029]Incumbent0.095**-0.0610.018-0.0280.0350.004share[0.039][0.049][0.049][0.043][0.050][0.050]Incumbent0.109***-0.007-0.008-0.0440.009-0.014parties[0.040][0.060][0.061][0.046][0.051][0.049] Notes.Observations:1,455eligiblevoters(turnout);1,306actualvoters(voteshares).Probitmarginaleectsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table6{Reduced-FormIndividualEstimates,PhoneCalls Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Turnout-0.0260.005-0.021[0.023][0.023][0.023]Incumbent0.110***0.0350.051share[0.033][0.043][0.045]Incumbent0.123***0.0050.022parties[0.032][0.053][0.044] Notes.Observations:1,455eligiblevoters(turnout);1,306actualvoters(voteshares).Probitmarginaleectsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.33 Table7{ModelEstimates,BaselineSpecication Model'sEstimateparameters[s.e.] A=Pr(responsejA)0.76[0.01]B=Pr(responsejB)0.99[0.01] L1.08[0.21] C1.10[0.14] R0.37[0.13]L0.34[0.21]C0.00[0.49]R0.98[0.32]L0.18[0.14]C0.02[0.09]R-0.03[0.05]V;30.40[0.15]V;20.40[0.28]V0.56[0.05]P;30.58[0.16]P;20.38[0.19]P0.71[0.19] Loglikelihood-1,043.60Observations1,306 Notes.Asymptoticstandarderrorsinbrackets.Theselectedspeci-cationassumesindependenceofmarginals,heterogeneouspreferenceparameters,andforcessameskewofmarginaldistributionofbeliefsfordierentstatedlevelsofuncertainty.34 Table8{BeliefsaboutIncumbentfromModelEstimates Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Average0.310**-0.022-0.100valence[0.148][0.142][0.098]Valence0.0050.0630.025std.dev.[0.082][0.095][0.093]Average0.015-0.121**-0.102*ideology[0.063][0.056][0.055]Ideology-0.036-0.090**-0.127***std.dev.[0.060][0.039][0.044] Notes.Observations:1,306actualvoters.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table9{BeliefsaboutIncumbentfromSurveyResponses Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Valence0.326**-0.039-0.092mode[0.157][0.144][0.096]Valence-0.052***0.002-0.003uncertainty[0.013][0.018][0.018]Ideology-0.049-0.104**-0.052mode[0.052][0.052][0.059]Ideology-0.052*-0.046**-0.032uncertainty[0.023][0.019][0.019] Notes.Observations:1,455eligiblevoters.OLScoecients(mode)orProbitmarginaleects(uncertainty)reported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.35 Table10{BeliefsaboutOpponentfromModelEstimates Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Average-0.127-0.045-0.071valence[0.081][0.133][0.094]Valence-0.077-0.096-0.048std.dev.[0.110][0.107][0.132]Average-0.0750.189**-0.032ideology[0.067][0.075][0.070]Ideology0.041-0.177***-0.091std.dev.[0.075][0.064][0.057] Notes.Observations:1,306actualvoters.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.Table11{BeliefsaboutOpponentfromSurveyResponses Referencegroup:mailornomessage ValenceIdeologyDoublebyphonebyphonebyphone Valence-0.094-0.043-0.051mode[0.106][0.133][0.088]Valence-0.028-0.0290.008uncertainty[0.047][0.045][0.054]Ideology0.0230.141**-0.016mode[0.048][0.062][0.063]Ideology-0.044-0.089***0.001uncertainty[0.028][0.030][0.032] Notes.Observations:1,455eligiblevoters.OLScoecients(mode)orProbitmarginaleects(uncertainty)reported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.36 Table12{PredictedVoteDierencesunderCounterfactualElectoralCampaigns CounterfactualtreatmentPredictedvotedierenceinpercentagepoints Blanketvalence2.2treatment[0.77,3.33]Blanketideology-2.2treatment[-3.37,-0.27]Blanketvalence&ideology0.5treatment[-0.73,1.84]Valencetreatmenttocenter&right1.3valence&ideologytoleftvoters[-0.19,2.37]Ideologytreatmenttocenter&right-2.4valence&ideologytoleftvoters[-3.87,-0.92]Actualelectoral1.8campaigneect[1.23,3.14] Notes.Counterfactualadditionalvotes(inpercentagepoints)thatcandidateAwouldhaveobtainedwiththesimulatedcampaignsdescribedintherstcolumnrelativetonoelectoraltreatmentbeingadministered.Bootstrapped95percentcondenceintervalsinbrackets.Condenceintervalsarebasedon1,000drawsfromtheasymptoticdistributionoftheMLparametervectors.37 Figure1{PriorValenceMarginalDistributionforVoter#371 Figure2{PriorJointProbabilityDistributionforVoter#369 38 Figure3{PosteriorJointProbabilityDistributionforVoter#369 39 AppendixForallmaterialsrelatedtothedesignofourrandomizedcontrolledtrial(includingsurveyquestion-naires;coloredtreatment yers;audiolesofthetreatmentphonecalls;andmapsofthetreatmentgroups)pleaserefertothewebsite:www.igier.unibocconi.it/randomized-campaign.Inthenexttwosubsections,wereporttheEnglishtranslationsofthetextofthemail yers(whicharethenshowedinFigureA1andFigureA2)andofthetextofthecandidate'srecordedmessagesforthecampaignphonecalls.Inthesubsectiondevotedtotablesandgures,wereport:balancingtestsofprecinctcharacteristicsacrosstreatmentgroups(TableA1);balancingtestsofindividualcharacteristicsacrosstreatmentgroups(TableA2);balancingtestsof2001Censuscharacteristicsacrosstreatmentgroups(TableA3);estimatesofpotentialspillovereects(TableA4);completesummaryofthestructuralmodelestimations(TablesA5andA6);LRandVoungtestsofmodelselection(TablesA7,A8,andA9); yersforboththevalenceandideologymessage(FiguresA1andA2).A1MailFlyers:EnglishTranslationsValence yer.COMPETENCEANDEFFORT.100millionworthofinvestments:SpentinpartontheFortress,squares,streets,andparkinglots.PIUSS,theintegratedplanforthedevelopmentofthecity:ThecityofArezzowasrankedrstinTuscany;thisisanimportantaccomplishment.Inno-vation:Thedigitalcenter,thehydrogenpipeline,andtheenergyhouse.FANFANIFORMAYOR.Ideology yer.AWARENESSANDSOLIDARITY.Children:Createdanintegratedsystemtocatertheneedsofall,opened3newpublicnurseryschools.Elderly:In-homeassistance,newpublicservicestohelpfamilies.Anetworkofsolidarityfortheneediest:Housing,mealcenters,workintegrationservices.FANFANIFORMAYOR.A2PhoneCallRecordedMessages:EnglishTranslationsValencemessage.DearVoter,the15thand16thofMay,thecitizensofArezzowillvotetoelectthemayorandcitycouncilmen.WeallthereforehavetheopportunitytomakeaninformedchoiceforthefutureofArezzo.Overthelastyears,myadministrationinvested100millionEurostodevelopandimproveourcity.ResultsareundertheeyesofeveryoneandcanbeobservedbysimplylookingattheFortress,thesquares,thestreets,andtheparkinglots.Thankstothequalityofour40 work,thePIUSS|theplanforthedevelopmentofthecityofArezzo|wasrankedrstamongthoseinTuscany.Thiswasanimportantaccomplishmentthatalsoenabledustogainaccesstoimportantnancialresourcestoimprovetheprominenceofourcity.However,wedidmuchmorethanthis,westrivedtoboostinnovationwiththedigitalcenter,thehydrogenpipeline,andtheenergyhouse.Givenalsoallthesereasons,Itakethelibertytoaskforyourvoteintheelectionofthe15thand16thofMay.RewardourCOMPETENCEandourEFFORT.BestregardsfromGiuseppeFanfani.Ideologymessage.DearVoter,the15thand16thofMay,thecitizensofArezzowillvotetoelectthemayorandcitycouncilmen.WeallwillhavetheopportunitytomakeaninformedchoiceforthefutureofArezzo.Forus,futurestandsforSOLIDARITY.Intheseveyearsofcitygovernment,wedealtwithissuesregardingchildhoodcreatinganintegratedsystemofservicesabletoprovideanswerstoallfamiliesandopeningthreenewpublicnurseryschools.Wealsotookcareofourelderlypeople,providingnewservicestohelpfamiliesassistthemandincreasingin-homeassistance.Atthesametime,wedenitelydidnotforgetaboutthosethatfoundthemselveslivingindicultcircumstancesalsobecausetheywereaectedbytheinternationalcrisisthatseverelystruckourregion.Infact,weincreasedhousing,mealcenters,andprofessionalintegrationservicesforallthoseinneed.Givenalsoallthesereasons,Itakethelibertytoaskforyourvoteintheelectionofthe15thand16thofMay.MakeSOLIDARITYwin!Foran\Arezzo"carefulandopentothehardshipsofthoseinneed.BestregardsfromGiuseppeFanfani.Valenceplusideologymessage.DearVoter,the15thand16thofMay,thecitizensofArezzowillvotetoelectthemayorandcitycouncilmen.WeallthereforehavetheopportunitytomakeaninformedchoiceforthefutureofArezzo.Overthelastyears,myadministrationinvested100millionEurostodevelopandimproveourcity.ResultsareundertheeyesofeveryoneandcanobservedbysimplylookingattheFortress,thesquares,thestreets,andtheparkinglots.Thankstothequalityofourwork,thePIUSS|theplanforthedevelopmentofthecityofArezzo|wasrankedrstamongthoseinTuscany.Atthesametime,wedenitelydidnotforgetaboutthosethatfoundthemselveslivingindicultcircumstancesalsobecausetheywereaectedbytheinternationalcrisisthatseverelystruckourregion.Infact,weincreasedhousing,mealcenters,andprofessionalintegrationservicesforallthoseinneed.Givenalsoallthesereasons,Itakethelibertytoaskforyourvoteintheelectionofthe15thand16thofMay.RewardourCOMPETENCEandourEFFORT.MakeSOLIDARITYwin!ForanArezzocarefulandopentothehardshipsofthoseinneed.BestregardsfromGiuseppeFanfani.41 AppendixTablesandFiguresTableA1{Ex-AnteBalancingTestsatthePrecinctLevel Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Eligiblevoters-66.083-101.58319.250-63.667*-65.500-6.083[96.591][70.235][57.771][36.922][66.886][56.033]Firstneighborhood0.0360.0360.203-0.0470.203-0.047[0.136][0.112][0.178][0.112][0.123][0.109]Secondneighborhood0.116-0.051-0.051-0.051-0.0510.033[0.188][0.140][0.151][0.154][0.086][0.128]Thirdneighborhood-0.0140.236-0.0980.152-0.014-0.098[0.190][0.172][0.134][0.199][0.169][0.134]Fourthneighborhood-0.138-0.221-0.054-0.054-0.1380.112[0.149][0.141][0.146][0.164][0.139][0.129]Regional'10turnout-0.005-0.0030.0160.0120.000-0.002[0.025][0.016][0.010][0.010][0.010][0.014]Regional'10left0.0110.0130.0130.0120.004-0.021[0.015][0.019][0.013][0.017][0.013][0.013]Regional'10right-0.015-0.0170.0110.007-0.0060.019[0.015][0.014][0.012][0.018][0.011][0.018]European'09turnout-0.0040.0080.0190.0130.0020.007[0.026][0.012][0.012][0.013][0.011][0.012]European'09left-0.0120.015-0.016-0.0140.018-0.028[0.030][0.026][0.016][0.025][0.019][0.021]European'09right0.009-0.0150.0180.009-0.0140.026[0.022][0.021][0.015][0.024][0.020][0.020]National'08turnout-0.0140.0120.0020.0020.0050.000[0.025][0.008][0.006][0.007][0.007][0.009]National'08left0.0160.026-0.015-0.0040.020-0.019[0.019][0.019][0.019][0.028][0.020][0.017]National'08right-0.018-0.0230.0130.004-0.0240.023[0.020][0.017][0.017][0.028][0.021][0.018]City'06turnout-0.0020.0080.0120.0090.011-0.006[0.020][0.011][0.009][0.013][0.011][0.013]City'06left0.0160.035-0.029-0.0170.009-0.029[0.029][0.024][0.023][0.034][0.021][0.022]City'06right-0.014-0.0370.0280.014-0.0080.022[0.029][0.024][0.022][0.033][0.021][0.024] Notes.Observations:95precincts,86(European),84(National),83(City).OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Eligiblevotersisthenumberofeligiblevotersintheprecinct(average820.168).Theneighborhooddummiescapturethecity-wideneighborhoodtheprecinctbelongsto.Theothervariablesaretheelectoraloutcomesinpastelectionsandareexpressedasvoteshares.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.42 TableA2{Ex-PostBalancingTestsattheIndividualLevel Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Male0.0080.0140.0340.0040.0060.042[0.039][0.050][0.038][0.038][0.047][0.039]Over65-0.0350.004-0.0120.086-0.0460.056[0.053][0.048][0.048][0.053][0.042][0.048]College-0.004-0.0270.0100.0080.035-0.016graduate[0.035][0.041][0.041][0.047][0.045][0.040]Outof-0.0190.010-0.0370.048-0.0410.050laborforce[0.052][0.054][0.058][0.059][0.050][0.053]White0.029-0.0050.032-0.0130.008-0.013collar[0.045][0.043][0.038][0.041][0.039][0.038]Other-0.010-0.0050.006-0.0350.033-0.037occupation[0.049][0.041][0.040][0.039][0.042][0.051]Center-left0.0450.058-0.009-0.033-0.0590.014[0.044][0.055][0.048][0.040][0.042][0.059]Homeowner-0.017-0.007-0.0450.0270.007-0.037[0.040][0.030][0.039][0.036][0.033][0.028]Read0.037-0.0070.025-0.0240.0320.048thepress[0.036][0.038][0.042][0.052][0.049][0.047]WatchTV0.034-0.0160.0380.068-0.0330.055[0.042][0.055][0.039][0.046][0.042][0.038] Notes.Observations:1,455eligiblevoters.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Allvariablesaredummies.ReadthepressandWatchTVcapturewhetherthevoterdeclarestodothis\veryoften"or\often."Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.43 TableA3{Ex-PostBalancingTestsof2001CensusCharacteristics Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymail Males-5.112-1.318-8.103-1.957-2.5871.187[7.450][6.922][6.353][7.245][5.220][8.773]Marriedpeople-5.780-1.608-8.986-2.040-2.8631.256[8.041][7.496][6.905][7.955][5.697][9.541]Collegegraduates-0.5070.093-0.7120.473-0.1770.748[0.661][0.568][0.492][0.725][0.499][1.058]Foreigners-0.400-0.178-0.311-0.255-0.395-0.129[0.339][0.339][0.330][0.339][0.310][0.395]Employmentrate0.002-0.003-0.000-0.0020.005-0.001[0.006][0.006][0.005][0.004][0.005][0.004]Unemploymentrate-0.0010.0040.0010.000-0.0010.003[0.005][0.004][0.004][0.004][0.005][0.004]Homeownership0.011-0.028-0.012-0.023-0.012-0.003[0.025][0.038][0.030][0.025][0.027][0.025] Notes.Observations:95precincts.OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Allvariablesareimputedattheprecinctlevelfrominformationonthe2001Censuscells.Males,Marriedpeople,Collegegraduates,andForeignerscapturetheaveragenumberofindividualswiththatattributeattheprecinctlevel.Employmentrate,Unemploymentrate,andHomeownershipareexpressedasshares.Inparticular,homeownershipistheshareofhousesoccupiedbytheowner.Robuststandarderrorsclusteredatthepollingplacelevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.44 TableA4{EvaluatingPotentialSpillovers,AllGroups Referencegroup:nomessage ValenceValenceIdeologyIdeologyDoubleDoublebyphonebymailbyphonebymailbyphonebymailspilloversspilloversspilloversspilloversspilloversspillovers Turnout0.032-0.0340.0100.0470.0030.028[0.048][0.055][0.044][0.060][0.042][0.054]Incumbent0.099-0.1130.064-0.0200.1240.005share[0.077][0.082][0.080][0.100][0.076][0.099]Incumbent0.081-0.147-0.035-0.1180.0380.006parties[0.079][0.098][0.096][0.104][0.089][0.115] Notes.Observations:1,455eligiblevoters(turnout);1,306actualvoters(voteshares).OLScoecientsreported;dependentvariablesinrowheadingsandtreatmentgroupsincolumnheadings.Eachspilloversvariablecapturestheshareofobservationswhoreceivedthecorrespondingtreatmentinthesamepollingplaceofeveryobservation.Averagevaluesare:0.135(valencebyphone);0.099(valencebymail);0.151(ideologybyphone);0.106(ideologybymail);0.135(doublebyphone);0.113(doublebymail).Fixedeectsforsurveydateincluded.Robuststandarderrorsclusteredattheprecinctlevelinbrackets.Signicanceatthe10%levelisrepresentedby*,atthe5%levelby**,andatthe1%levelby***.45 TableA5{ModelEstimateswithHeterogeneousPreferenceParameters ModeldescriptionCopulafamily:FGMFrankIndpFGMFGMFGMFrankFrankFrankIndpSamealpha:NoNoNoYesYesYesYesYesYesYesRhospecication:StandardStandard-StandardHeteroRestrictedStandardHeteroRestricted-Parameter A=Pr(responsejA)0.760.760.760.760.760.760.760.760.760.76(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)B=Pr(responsejB)0.990.990.990.990.990.990.990.990.990.99(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01) = L1.081.081.071.091.091.091.101.101.081.08(0.23)(0.23)(0.21)(0.23)(0.23)(0.22)(0.23)(0.23)(0.22)(0.21) C1.111.111.111.101.111.111.101.121.111.10(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.15)(0.15)(0.14) R0.360.370.360.360.350.350.350.330.370.37(0.13)(0.13)(0.13)(0.13)(0.13)(0.13)(0.13)(0.14)(0.13)(0.13)=L0.340.340.340.340.340.340.330.330.340.34(0.22)(0.22)(0.21)(0.22)(0.22)(0.22)(0.21)(0.21)(0.22)(0.21)C0.000.000.000.000.000.000.000.000.000.00(0.49)(0.49)(0.48)(0.48)(0.47)(0.47)(0.49)(0.45)(0.45)(0.49)R1.031.031.001.021.041.021.031.100.980.98(0.33)(0.32)(0.32)(0.32)(0.33)(0.32)(0.32)(0.33)(0.31)(0.32)=L0.180.180.180.190.190.180.190.200.190.18(0.15)(0.15)(0.14)(0.15)(0.15)(0.15)(0.15)(0.15)(0.15)(0.14)C0.020.020.020.030.030.030.020.040.040.02(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.10)(0.09)(0.09)R-0.04-0.04-0.04-0.04-0.04-0.04-0.04-0.05-0.03-0.03(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.04)(0.04)(0.05)(0.05)V;30.380.370.400.370.370.360.360.360.400.40(0.15)(0.15)(0.15)(0.15)(0.16)(0.16)(0.15)(0.16)(0.16)(0.15)V;20.380.370.400.370.370.360.360.360.400.40(0.32)(0.32)(0.31)(0.29)(0.30)(0.29)(0.28)(0.28)(0.30)(0.28)V=V;30.590.580.590.560.560.560.560.560.560.56(0.06)(0.06)(0.07)(0.05)(0.05)(0.05)(0.05)(0.05)(0.06)(0.05)V;20.510.510.51-------(0.10)(0.10)(0.10)-------P;30.580.580.590.570.570.570.570.550.560.58(0.17)(0.16)(0.16)(0.16)(0.16)(0.16)(0.16)(0.15)(0.15)(0.16)P;20.380.380.380.370.360.370.370.330.370.38(0.20)(0.20)(0.20)(0.20)(0.20)(0.20)(0.19)(0.19)(0.19)(0.19)P=P;30.710.710.720.700.690.700.690.680.700.71(0.23)(0.23)(0.24)(0.18)(0.18)(0.18)(0.18)(0.17)(0.18)(0.19)P;20.690.690.69-------(0.30)(0.30)(0.30)-------A=LA-1.00-13.67--1.00-1.00-1.00-8.24-30.00-30.00-(10.62)(261.31)-(10.37)(11.69)(11.58)(90.46)(1703.1)(1717.1)-CA----1.001.00-14.1713.22-----(134.16)(136.54)-(4054.00)(4003.60)-RA----1.00--30.00------(15.42)--(786.89)--B=LB-1.00-30.00--1.00-1.00-1.00-30.00-30.00-29.99-(18.42)(2035.20)-(17.90)(18.95)(13.53)(1952.30)(1969.40)(1796.20)-CB----1.001.00-8.438.23-----(190.48)(195.53)-(2618.30)(3160.70)-RB-----1.00---30.00------(42.58)--(5325.70)--Loglikelihood-1043.20-1042.90-1043.30-1043.40-1043.30-1043.40-1043.10-1042.60-1043.10-1043.60Observations1,3061,3061,3061,3061,3061,3061,3061,3061,3061,306 Notes.Asymptoticstandarderrorsinbrackets.Preferenceparametersareallowedtovarywithvoter'sideology(L,C,R);basedonLRtests,ourpreferredspecicationiswithindependentcopulaandsamealpha.Copulafamily:\FGM"standsforFarlie-Gumbel-Morgensen;\Frank"standsforFrankfamily;\Indp"for.Samealpha:\yes"forcesskewofmarginalstobethesameforeachlevelofstateduncertainty;\no"allowstheskewtodier.Rhospecication:\standard"meansbaselineAandB;\hetero"allowsAandBtovarywithvoter'sideology;\restricted"forcesLA=RBandRA=LB. TableA6{ModelEstimateswithoutHeterogeneousPreferenceParameters ModeldescriptionCopulafamily:FGMFrankIndpFGMFGMFGMFrankFrankFrankIndpSamealpha:NoNoNoYesYesYesYesYesYesYesRhospecication:StandardStandard-StandardHeteroRestrictedStandardHeteroRestricted-Parameter A=Pr(responsejA)0.770.770.770.770.770.770.770.770.770.77(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)B=Pr(responsejB)0.980.980.980.980.980.980.980.980.980.98(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01) = L0.890.910.900.880.880.900.910.910.910.89(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09)(0.09) C-------------------- R--------------------=L0.650.680.690.690.680.650.660.660.68(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)(0.14)C--------------------R--------------------=L0.050.060.050.040.040.050.060.060.060.05(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)(0.05)C--------------------R--------------------V;30.400.350.350.340.400.340.340.340.340.34(0.17)(0.16)(0.15)(0.15)(0.17)(0.17)(0.16)(0.16)(0.16)(0.16)V;20.400.350.350.340.400.340.340.340.340.34(0.30)(0.29)(0.29)(0.24)(0.30)(0.25)(0.28)(0.29)(0.29)(0.28)V=V;30.540.540.540.510.520.520.520.520.520.52(0.07)(0.06)(0.06)(0.05)(0.06)(0.05)(0.05)(0.05)(0.05)(0.05)V;20.500.500.50-------(0.11)(0.10)(0.10)-------P;30.600.580.610.650.650.600.610.580.620.65(0.17)(0.15)(0.15)(0.17)(0.17)(0.15)(0.16)(0.15)(0.15)(0.15)P;20.600.550.610.650.650.600.610.580.610.65(0.33)(0.32)(0.32)(0.27)(0.28)(0.26)(0.26)(0.27)(0.26)(0.26)P=P;30.800.770.810.810.820.770.770.740.770.81(0.26)(0.23)(0.27)(0.28)(0.28)(0.22)(0.23)(0.20)(0.23)(0.27)P;20.690.650.70-------(0.42)(0.35)(0.44)-------A=LA-1.00-30.00--1.00-1.001.00-30.00-30.0029.99-(18.09)(1993.00)-(22.79)(38.48)(24.90)(2120.70)(3038.50)(2786.20)-CA----1.001.00-30.0029.60-----(53.29)(41.32)-(1849.70)(7268.40)-RA-----1.00---30.00------(41.50)--(2997.90)--B=LB1.0029.99-1.00-1.00-1.0029.99-30.00-30.00-(29.21)(1633.70)-(37.36)(51.93)(22.23)(3674.60)(4066.60)(2467.70)-CB----1.001.00-22.4227.94-----(86.81)(63.35)-(6915.90)(11627.00)-RB-----1.00---30.00------(81.43)--(7895.00)--Loglikelihood-1057.70-1057.40-1057.70-1057.90-1057.94-1057.70-1057.50-1057.50-1057.40-1057.90Observations1,3061,3061,3061,3061,3061,3061,3061,3061,3061,306 Notes.Asymptoticstandarderrorsinbrackets.UnlikeTableA3,preferenceparametersarenotallowedtovarywithvoter'sideology(L,C,R);basedonLRtests,thesearenotourpreferredspecicationsbutwereportthemforcompleteness.Copulafamily:\FGM"standsforFarlie-Gumbel-Morgensen;\Frank"standsforFrankfamily;\Indp"for.Samealpha:\yes"forcesskewofmarginalstobethesameforeachlevelofstateduncertainty;\no"allowstheskewtodier.Rhospecication:\standard"meansbaselineAandB;\hetero"allowsAandBtovarywithvoter'sideology;\restricted"forcesLA=RBandRA=LB. TableA7{LRTests:RestrictionofPreferenceParametersToBetheSameacrossVoter'sIdeology CopulaTeststatisticP-value FGM28.940.00Frank28.860.00Independent28.620.00 Notes.Skewrestrictedtobethesameacrosslevelsofstateduncertainty.Standardspecication.TableA8{LRTests:RestrictionofSkewToBetheSameacrossLevelsofUncertainty PreferencesCopulaTeststatisticP-value HomogeneousFGM0.290.86HomogeneousFrank0.370.83HomogeneousIndp0.380.83HeterogeneousFGM0.490.78HeterogeneousFrank0.390.82HeterogeneousIndp0.540.76 Notes.Standardspecication.TableA9{VuongTests:CopulaComparisons PreferencesCopulaRhoTestP-valuePreferredcomparisonspecicationstatisticcopula HomogeneousFrankvs.FGMStandard0.760.45FrankHomogeneousIndependentvs.FGMStandard39.480.00IndependentHomogeneousIndependentvs.FrankStandard17.930.00IndependentHeterogeneousFrankvs.FGMStandard1.050.29FrankHeterogeneousIndependentvs.FGMStandard22.670.00IndependentHeterogeneousIndependentvs.FrankStandard12.610.00IndependentHeterogeneousIndependentvs.FGMHeterogeneous52.080.00IndependentHeterogeneousIndependentvs.FrankHeterogeneous26.590.00IndependentHomogeneousIndependentvs.FGMHeterogeneous12.90.00IndependentHomogeneousIndependentvs.FrankHeterogeneous35.930.00IndependentHeterogeneousIndependentvs.FGMRestricted37.190.00IndependentHeterogeneousIndependentvs.FrankRestricted30.780.00IndependentHomogeneousIndependentvs.FGMRestricted40.570.00IndependentHomogeneousIndependentvs.FrankRestricted34.770.00Independent Notes.Skewrestrictedtobethesameacrosslevelofstateduncertainty.48 FigureA1{CampaignFlyerwiththeValenceMessage FigureA2{CampaignFlyerwiththeIdeologyMessage 49