Tax evasion under behavioral structures

(1)

Availableonlineatwww.sciencedirect.com

ScienceDirect

EconomiA15(2014)30–40

Tax

evasion

under

behavioral

structures

夽

Gabriela

S. Pantoja

a

,

Rodrigo

S. Pe˜naloza

b,∗

a_Ministry_of_Development,_Industry_and_Foreign_Trade_of_Brazil_(MDIC),_Brazil1

b_Department_of_Economics,_University_of_Brasília,_Brazil

Availableonline27March2014

Abstract

Westudythestrategicinteractionsbetweenthefiscalauthorityandthetaxpayerregardingtaxevasionandauditing.Wefitthis interactionintoaBayesiangameandintroducetheconceptofbehavioralconsistency,whichhelpsreducingthenumberofavailable strategiesandmodelsthestylizedfactaccordingtowhichthechoicetoevadeissubjecttobehavioralpatterns.

JELclassiﬁcation: H26;D82;C72

Keywords:Taxevasion;Bayesianequilibrium;Behavioralconsistency

Resumo

Nestetrabalhoestudamosasinterac¸õesentreocontribuinteeofisconoquedizrespeitoàevasãofiscaleàauditoria.Paraisso, construímosumjogobayesianoeintroduzimosahipótesedeconsistênciacomportamental,quereduzoconjuntodeestratégiase modelaofatoestilizadosegundooqualaevasãoounãoevasãoestásujeitaapadrõescomportamentais.

Palavras-chave:Evasãofiscal;EquilíbrioBayesiano;Consistênciacomportamental

1. Introduction

Theevolutionofthegovernment’sroleinmodernsocietiesandthestrengtheningofitsinstitutionshasbroughtto theoreticalattentiononeofthemostseriousproblemsforthefunctioningofthegovernment:thetaxevasion.Indeed, sincethegovernment’sroleineducation,healthandinfrastructurearecostly,theneedforfinancinghasincreased,for whichreasonaudithasbecomeanimportantmechanisminthehandsoffiscalauthorities.Thereis,however,aclear trade-offbetweenthecosttoauditandthebenefitfromrecoveringtaxrevenues.Inaddition,thetaxpayer’sincome

1 _The_content_of_this_paper_does_not_represent_the_opinion_of_the_MDIC.

夽 _We_thank_an_anonymous_referee_for_comments_and_suggestions.

∗_{Corresponding}_author.

E-mailaddress:[email protected](R.S.Pe˜naloza).

PeerreviewunderresponsibilityofNationalAssociationofPostgraduateCentersinEconomics,ANPEC.

(2)

is,tosomeextent,privateinformation, hencethe fiscalauthorityfacesanasymmetricinformationproblem,which amountstoanextracost.

Inthispaperwestudytheproblemoftaxevasionbytakingintoaccountincentiveissues.Ontheonehand,the taxpayerfacesatrade-offbetweenreportingandnotreportinghistrueincome.On theotherhand,thegovernment facesatrade-offbetweenauditingandnotauditing.Theinteractionbetweenthegovernmentandthetaxpayerleadsto avarietyofequilibriadependentonparameterssuchascosts,taxratesandsoon.

Andreonietal.(1998)andAndvigandMoene(1990)showstylizedfactsthatshouldbetakenintoconsideration regardingthismatter.Thetaxpayerbehavesaccordingtomoralprinciplesthatareexternaltothegame.Forinstance, ifhedoesnotevade,itisbecauseitismorallyincorrecttodoso.Inaddition,hisactionisofteninfluencedbythe actionsofothertaxpayers.Forexample,apoortaxpayerevadesbecausetherichoneevades.Theseminalarticlein theliteratureontaxevasionisAllinghanandSandmo(1972)’s,henceforthA–S.Inthatarticle,theybuiltamodelof taxevasioninwhichlaborsupplyandreturnoncapitalaregiven.Theagentdecideshowmuchofhisincometoreport andthereisanendogenousprobabilitythathisnon reportedincomebedetectedbythegovernment,inwhichcase thetaxpayerisforcedtopayafinehigherthantheinitialtaxshare.Thereportedincomeischosensoastomaximize hisexpectedutility.Thischoicedependsontheprobabilityofdetection,onhisriskaversionandonthepenaltyfine. Yitzhaki(1974)pointedoutthatintheirmodelanincreaseinthetaxshareyieldstoanambiguouseffectontaxevasion. Thereisanegativeincome-effectinthesensethatanincreaseonthetaxratemakesthetaxpayerpoorerandhenceless riskaverse,sothatthereportedvalueofincomeincreases.Thereisalsoasubstitution-effect.Sincethefineleviedon thetaxpayerforthesamenon-reportedamountofincomedoesnotvarywhenthereisanincreaseofthetaxshare,there isasmallerdifferencebetweenthetaxshareandthepenaltyfine,whichthencreatesanincentiveforhistoincreasethe non-reportedincome.Yitzhakithensuggestedanewapproach,accordingtowhichthepenaltyfinefornotreporting thetrueincomeisnotproportionaltothereportedincome,buttothenonpaidportionofthetaxrate.Withthis,the ambiguitywouldbepronetodisappear.However,asSandmo(2005)observed,thedisappearanceofthisambiguity doesnotmatchempiricalevidenceandintuition,sincetheagenthasanincentivetoreducehisreportedincomeshould thedifferencebetweenthetaxrateandthepenaltyratedecrease.

Sousaetal.(2008),basedonamodelbyFismanandWei(2004),usecommercedatabetweenBrazilandtheUnited Statesanddataonimporttariffsinordertomeasuretheimpactoftariffsontaxevasion.Theyshowedthathighertariffs implyhigherdegreeof evasion.Inaddition,thisrelationisnotlinear,sotheimpactismeaningfulonlyaftersome levelofimportaliquot.SiqueiraandRamos(2006)extendstheA–Smodelandfindaresultthatpointstotheopposite direction.Theyshowedthatanincreaseofthemarginalaliquotreducestaxevasionand,inaddition,thatanincreaseof theprobabilityofdetectionandofthepenaltyfinealsoleadstoareductionoftaxevasion.Thedifferencesbetweenthese resultsmayreflecttheincomeandsubstitution-effectpointedoutbyYitzhaki(1974).RichterandBoadway(2005) usetheA–SmodelaswellasYitzhaki’sinordertostudytheinteractionbetweentaxevasionandtaxstructure.Under Yitzahki’sframework,theoptimaltaxdesignremainedinvariantwithrespecttotheintroductionofrisksinherentto taxevasion.UnderA–Sframework,ontheotherhand,itshowedatrade-offbetweentaxdistortionandthemagnitude oftaxevasion.Goerke(2003)studieswhathappenswiththeamountoflaborinthemarketasthetaxstructurebecomes moreprogressive.Whenopportunitiestoevadeareintroducedintothemodel,employmentincreasesastaxesbecome moreprogressive.Inparticular,thisresultholdsonlywhenpartofthepenaltyfineisdependentonthenon-reported income,asintheA–Smodel.From thesetwopapers,itispossibletoconcludethat taxevasioninfluencesthetax designanditsimpactontaxpayers.

Mostofthepapersfocusontheindividualdecision-making.SchneiderandKlinglmair(2004)estimatethesizeof theinformallabormarketin110countriesandshowthatthesizevarieswiththecountry.Sandmo(2005)showsthat thesevariationscannotbeexplainedbythemagnitudesofthetaxratesandfinesalone.Cowell(1990)emphasizesthat taxevasionrequiresatheoryofsocialinteraction,sinceitisasocialphenomenon.Therefore,partoftheevasioncould beexplainedbyfactorsrelatedtothesocialinteractionbetweenagents.IntheA–Smodel,the taxpayergetstoan opinionabouttheprobabilityofdetectionalsobyobservingtheotheragentsandtheirprobabilitiesofbeingaudited. Thenthetaxpayer’ssubjectivebeliefofbeingdetecteddependsonhisownevasionandtheevasionofothers.Ifhe perceivesthatthenon-reportedincomebyothersincreases,hissubjectivebeliefofbeingdetectedisreducedandhis non-reportedincomeincreases.Onthetopofthat,thereisadisutilityfromnotreportingthetrueincome,thoughthis couldbelowerincaseheperceivesthatmanyotherdonotreporttruthfully.Intheirstudyoncorruption,Andvigand Moene(1990)alsofindthesamepattern:themorecorrupttheenvironmenttheindividualisin,theharderitisforthe individualtobehonest.

(3)

Adilemmaextensively studiedintheliteratureof taxevasionistheexistence ofpeoplewhodeclare fullytheir incomeiftheexpectedvalueoftheutilitywhenthetaxpayerdonotreportpartofitsincome,ispositive.According toAndreonietal.(1998),therearemoralandsocialfactorsthatinfluencethedecisiontoevade.Amongthesefactors arethefeelingsof guiltandshamethatagentsfeelbynotdeclaringalltheirincome.Thereisadisutilitywhenthe agentfeelshedidsomethingwrong.Furthermore,theperceptionoffairnessinthetaxburdenfromthetaxpayeralso influencestheirdecisions.Ifheperceivesthatitstaxburdenisunfaircomparedwiththetaxburdenofothers,orifit perceivesthatothersdonotfullydeclaretheirincomeandthereforeisatadisadvantage,thereisanincentivetoevade hisincome.AnotherfactorthatinfluencestheamountofreportedincomementionedbyAndreonietal.(1998)isthe satisfactionof thetaxpayerwithrespecttogovernmentpolicies.Themisuseoftaxesbythegovernmentisanother incentivetocircumventthesystemoftaxpayments.Anotherstudythatexplainsevasionasasocialphenomenonis thatofBarthetal.(2005)whoconsiderthecaseoftwopeoplewhoreceivethesameincome,theoneworkinglonger andhavingalowerremunerationandotherworkinglessbutgettingmorefortimeworked,andbothpayingthesame amountoftaxes.Thefirstgroupfeelswrongedandhasanincentivetolieaboutitsincome.Alltheseanalyzesconsider theinteractionsamongtaxpayers,notjustindividualmotivationstoexplaintaxevasion.

Someauthorsusegametheorytoanalyzetaxevasion.Pruzhansky(2004)viewsthehonestyoftaxpayersdifferently. Themodelarisesfromtheideathattherearenocompletelyhonesttaxpayers,thatis,undercertainconditionseveryone canescape.ThemodelisaBayesiangamebetweenthetaxpayerandthegovernmentandthisconceptofhonestyis includedintheequilibriumtheyfind.Thisworkistheclosesttoours.However,inthemodelofPruzhansky(2004), giventwoincomelevels,lowandhigh,theactionsofeachtaxpayeraretodeclaretheirownincomeortheincomeof theother.Thisimpliesthatthelow-incometaxpayermaydecidetodeclarethathisincomeishigh.Inourmodel,as weshallseelater,thedecisionisbetweenevadingandnotevading,andincomelevelissimplyprivateinformation, i.e.,thetypeoftaxpayer.

Anothersubjectofgreatimportanceintheliteratureof taxevasionistherelationoftheprobabilityofdetecting evasionwiththelevelofincomereportedtothegovernment.ReinganumandWilde(1985)wereoneofthefirstto studythisrelationshipandusedforanalysisanauditsystemdifferentfromtheusualrandomaudit.Theyconsidered thatthegovernmenthassomeinformationabouttheincomeofthepopulationsothatitcanestablishathresholdlevel ofincomereported.Givenareportedincome,ifitisbelowthethreshold,itisconsideredtobeaverylowincome,then thetaxpayerwillbeauditedwitha100%probability.Incontrast,ifabove,itwillnotbeconsideredlowandwillnot beaudited.Accordingtotheirfindings,thecostofauditingtothegovernmentishigherwhentheauditsarerandom. Inaddition,theauditwithaestablishedminimumlevelofincomeweaklydominatestherandomauditincasesofa lumpsumtaxandataxproportionaltoincome.

Thispaper addressestheissueof tax evasionfromtheperspective ofthe governmentandthetaxpayer. Itaims toanalyzetherelationsbetweengovernmentandtaxpayerupontheincentivesthatthegovernmenthastoauditand incentivesthatthetaxpayerhastoevade.Forthis,webuildaBayesiangameinwhichthetaxpayermaybeeitherof twotypes,ataxpayerwithhighincomeorlowincome.

Ourcontributionistheadoptionofwhatwecallbehavioralconsistency.Thisconceptfacilitatesthecomputation ofequilibria,sinceitreducesthesetofstrategiesavailable,andisabletomodelthewidelyrecognizedphenomenon wherebytheevasionorthe non-evasionbyataxpayer isaresultofthe evasionor non-evasionthatheobservesin theothertaxpayersor,alternatively,theideathattheactofevadingornotevadingissubjecttobehavioralprinciples externaltothegame.Basically,astrategyisbehaviorallyconsistentiftheactiontakenisinvariantwithrespecttothe outcomeoftherandomvariablethatdeterminesthetypeoftaxpayer.Thus,ifataxpayercanbeoftwotypes,richor poor,andcantakeoneoftwopossibleactions,evadeandnottoevade,andgiventhatapurestrategyinaBayesian gamecouldbe,forexample,evadeifrichandnotevadeifpoor,andanotherpurestrategycouldbenotevadeifrich andnotevadeifpoor,thenthelatterisabehaviorallyconsistentpurestrategyandtheformeristhereforebehaviorally inconsistent.Thus,wehavetwodistinctbehavioralstructures(consistencyandinconsistencyofbehavior)which,as alreadymentioned,inadditiontodescribestylizedfactsalsoserveasacriterionforeliminationofpurestrategies,a propertyusefulforourmodel,asthecriterionforselectionofrationalizablestrategiesseemsunabletoreducethesize ofthenormalformgame.

Wedetermine,moreover,theBayesianequilibriainmixedstrategiesundertheconditionofbehavioralconsistency andalsobehavioralinconsistency,duetothefactthattherearenoequilibriainpurestrategies.Ineachcase,whetherin behavioralconsistencyorinconsistency,weinterpretthemixedstrategiesintermsofthetaxparametersofourmodel, particularlythecostoftaxauditandfinesincaseofevasionandalsointermsofthedistributionoftypes.

(4)

In Section2 we constructthe Bayesian game, whichwe callthe tax evasion game, andintroduce the concept of behavioralconsistency. Wecalculatethe Bayesianequilibria inmixed strategiesbothinthe caseof behavioral consistencyandinconsistency.Thenweanalyzetheequilibriaintermsofthemodelparameters.Section3concludes thepaper.

2. Taxevasiongameunderbehavioralstructures

Inthissection,webuild aBayesiangamebetweenthefiscalauthority(government)andthetaxpayer.Sincethe taxpayer’swealthishisprivateinformation,thefiscalauthorityfacesasymmetricinformation.Inordertotakeinto accounttheexistenceofexternalmoralrulesthatinducethetaxpayertobehaveconsistentlywhateverhiswealth,we introducetheconceptoftaxpayer’sbehavioralconsistencyintothegame,whichisthenoveltyofourpaper.Inaddition, wealsoshowwhathappenswiththeequilibriumofthegameshouldthetaxpayerbehaveinconsistently.

InSection2.1wepresenttheprimitivesofourtaxevasionBayesiangame.InSection2.2wefindthemixedstrategy BayesianequilibriumunderbehavioralconsistencyandinSection2.3theequilibriumunderbehavioralinconsistency. InSection2.4weanalyzetheequilibriaintermsoftherelevantparametersofthegame:thetaxrate,thefeeonevasion, averageincomeandauditingcosts.

2.1. PrimitivesofthetaxevasionBayesiangame

Therearetwoplayers:thegovernment(player1)andthetaxpayer(player2).Weintroduceasymmetricinformation byassumingthatplayer2canbeeitheroftwotypes.LetT2={Y,y}bethesetoftypes:

T2=

_y,

withprobability p Y, withprobability 1−p

where0<y<Yarethelevelsofincome,yislowincomeandYishighincome.Thetaxpayer’stypeisprivateinformation, everythingelseiscommonknowledge.Denotebyπ={p,1−p}theprobabilitydistributionofthetaxpayer’stypes yandY.Henceyoccurswithprobabilityp,Ywithprobability1−p.LetT1= {θ}bethegovernment’ssetoftypes,

whichisasingleton,hencethereisnoasymmetricinformationwithrespecttoitstype,thatis,ithasonlyonetype, whichoccurwithprobability1.

LetC1={A,A}bethepairofpossibleactionsavailabletoplayer1,whereAistoauditandA isnottoaudit.

LetC2={E,E}bethepairofpossibleactionsavailabletoplayer2,whereEistoevadeandE isnottoevade.The

decisiontoevadeisthedecisionnottofulfilltheindividualincometaxform,thatis,thetaxpayerdoesnotdisclosure hisincome.Theincometaxshareisdenotedbytandthepenaltyfeeforevasionisdenotedbyϕ,whereϕ>t.The assumptionϕ>tisprettynatural,sinceitpunishesevasion.Whenthegovernmentaudits,itincursintoacostc>0and identifiesthetaxpayerwhodidnotreporthistruetype.

Thepayoffmatrixconditionalonplayer2beingoftypeyis:

Matrix1. Player2 Player1 A A E y(1−ϕ),ϕy−c y,0 E y(1−t),yt−c y(1−t),yt

Eachcellinmatrix1showsthepayoffofplayers2(thelineplayer)and1(thecolumnplayer).Whenthetaxpayer decidestoevadeandthegovernmentdecidestoaudit,whichcorrespondstocell(E,A),thetaxpayer’spayoffishis income,y,reducedbythefeeleviedonhisincomeduetotheevasion,yϕ,thatis,y−yϕory(1−ϕ).Thegovernment’s payoffistherevenuefromthefee,yϕ,reducedbythecostofauditing,c,that is,ϕy−c.Considernowthe profile (E,A),inwhichthetaxpayerevadesandthegovernmentdoesnotaudit.Thetaxpayer’spayoffishisfullincome,y, andthegovernment’sisobviouslynil.Intheprofile(E, A),thetaxpayerdoesnotevadeandthegovernmentaudits. Thetaxpayer’spayoffishisincomeminusthetaxpaid,thatis,y−tyory(1−t),andthegovernment’sistherevenue

(5)

Matrix2. Player2 Player1 A A E Y(1−ϕ),ϕY−c Y,0 E Y(1−t),Yt−c Y(1−t),Yt

fromtaxminusthecostofauditing,yt−c.Finally,ifthetaxpayerdoesnotevadeandthegovernmentdoesnotaudit, (E, A),thenthetaxpayer’spayoffisalsoy(1−t),andthegovernment’sequalstherevenuefromtax,yt.Anidentical reasoningappliestothepayoffmatrixconditionalonplayer2beingoftypeY:

Bothconditionalmatricescanbesynthesizedinthenormal formofthe Bayesiangame,whosematrixisgiven below: Matrix3. Player2 Player1 A A EE y−ϕy,ϕy−c y,0 EE y−ϕpy−Yt(1−p),ϕpy+Yt(1−p)−c y−tY(1−p),tY(1−p)

EE y−typ−ϕY(1−p),typ+ϕY(1−p)−c y−ytp,ytp

EE y−ty,ty−c y−ty,ty

Thepurestrategiesavailabletoplayer2areEE,EE, EE, EE,andforplayer1A,A.Theentriesinmatrix3are theexpectedpayoffsforeachplayer,wherey=yp+Y(1−p)istheaverageincome.

Notethatthegovernmentauditisrandom,sothatthedecisiontoauditornottoauditistakenbeforeobservingthe realizationofitseffectivepayoff.Indeed,intheBayesiangame,playerschoosesimultaneouslytherandomvariables (mixedstrategies)that theywillannouncetoeachother.Thus,thefactthatthegovernmentknowsthatitgetszero payoffwhenit doesnotauditandtaxpayersevade,aswe saidthisdoesnotmean thatitobservedthispayoffand, therefore,thatitknowsthattaxpayersevaded.Thegovernmentknowsonlythatthezeropayoffisapossiblerealization ofarandomvariable,sinceintheBayesiangame,themixedstrategiesaredecidedexante.

Inthefirstentryofmatrix3,inwhichtheactionsareEE(taxpayer)andA(government),thetaxpayer’spayoffis hisaverageincomeminustheaveragepenaltypaidtothegovernment.Thegovernment’spayoffisthetaxcollected fromthetaxpayerminusthecosttoaudit.Weobserveapatterninallentries.Thepayoffstothetaxpayer(firstand thirdcolumn)aretheaverageincomeminustheamountpaidtothegovernment.Thegovernment’spayoff(second andfourthcolumn)willalwaysbefinecollectedminusthecosttoaudit.Tosimplifymatters,definethefollowing: Γ1=ϕy,Γ2=ϕpy+t(1−p)Y,Γ3=tpy+ϕ(1−p)Y,Γ4=ty,Γ5=0,Γ6=t(1−p)Y,Γ7=tpyandΓ8=ty.

Matrix3canthenberewrittenas:

Matrix4. Player2 Player1 A A EE y−Γ1,Γ1−c y,0 EE y−Γ2,Γ2−c y−Γ6,Γ6 EE y−Γ3,Γ3−c y−Γ7,Γ7 EE y−Γ4,Γ4−c y−Γ8,Γ8

Matrix4describesthenormalformoftheBayesiangame.ThepayoffsU1andU2ofplayers1and2aregivenby

theelementsofthematrixabove.Ineachcell,thepayoffU1istotherightandthepayoffU2istotheleft.Forexample,

(6)

ThevariableΓ5doesnotappearintheabovematrixbecauseitisnull,asthegovernmentdonothaveanygain

whenalltaxpayersdonotpaytheirtaxesandarenotaudited.Arelevantfact isthat thereisnostrictlydominated strategiesinthetaxevasiongame.Indeed,giventheconditionϕ>t,onecaneasilyshowthatthereareonlytwopossible orderingsforthevariablesΓ above.Toauditing,wehaveΓ1>Γ3>Γ2>Γ4andΓ1>Γ2>Γ3>Γ4.Thefirstordering

occurswhenpy<(1−p)Y,thesecondoneoccurswhenpy>(1−p)Y.Tonon-auditing,wehaveΓ5<Γ7<Γ6<Γ8

andΓ5<Γ6<Γ7<Γ8.Withtheseorderings,inanycase,thereisnostrictlydominatedstrategies,thatis,allstrategies

arerationalizable.Therefore,wecannotdeleteanylinesandthereisnoBayesianNashequilibriuminpurestrategies. ABayesiangameisthecollectionJ={N,T1,T2,π,C1,C2,U1,U2},inwhichN={1,2}isthesetofplayers,

Tiisthesetoftypesofplayeri∈N,πiistheprobabilitydistributionoverthetypesofplayeri∈N,Ciisthesetof actionsofplayeri∈NandUiisthepayoffofplayeri∈N.Ourgamewillbecalledthetaxevasiongameandits normalformisgivenbymatrix4above.

Apurestrategyforplayeri∈Nisaprescriptionofactionforeachtype,i.e.,itisafunctionsi:Ti→Ci.Amixed (orrandom)strategyfor playeri∈Nisaprescriptionofprobabilitydistributionforeachtype,i.e.,itisafunction μi:Ti→(Ci),inwhich(Ci) isthesetof probabilitydistributionsover Ci.Defineμi(ti)=σi. Aproﬁle ofpure

strategiesforthegameJisapairs=(s1,s2).AproﬁleofmixedstrategiesforJisapairμ=(μ1,μ2).Withoutloss

ofgenerality,amixedstrategywillbeidentifiedwithitsimageσ=(σ1,σ2)∈(C1)×(C2).Let|Ti|bethe(finite) cardinalityofTi.Define:

C|Ti|

i =Ci×···×Ci

|Ti|times

anddefinethea-traceofC|Ti|

i asthevector(a,...,a)∈C|iTi|,wherea∈Ci.Denotebytr(Ci)thesetofalla-tracesof C|Ti|

i .

Deﬁnition. ABayesianNashequilibriuminpurestrategies(mixed)ofthegameJ={N,T1,T2,π,C1,C2,U1,U2}

isaNashequilibriuminpurestrategies(mixed)ofthegamedescribedbynormalform.

Deﬁnition. Let(σ₁∗,σ₂∗)beaBayesianNashequilibriuminmixedstrategiesofthetaxevasiongameJ.Wesaythat (σ₁∗,σ₂∗)is:

(a) behaviorallyconsistent(orsimplyconsistent)iftheactiontakenbyeachplayerisinvariantwithrespecttoitstype, thatis,ifsupp(σ∗_i)⊂tr(Ci),∀i∈N,inwhichsupp(σ_i∗)isthesupportofσ_i∗.

(b) behaviorallyinconsistent(orsimplyinconsistent)ifitisnotconsistent,thatis,ifsupp(σ_i∗)∩tr(C_i)=∅. Inthetaxevasiongame,thebehaviorallyconsistentactionsavailabletothetaxpayerare(E,E)and(E, E).The behaviorallyinconsistentactionstothetaxpayerare(E,E)and(E, E).Notethatourconceptofbehavioralconsistency isnotexactlytheusualconceptofconsistencyofbeliefs(Myerson,1997,pp.168–177).Theconceptofconsistency ofbeliefshastodowiththebehaviorinstatesthathavezeroprobabilityinequilibrium.Thatisbecausethese proba-bilitiesareendogenous.However,byexogenouslyplacingzeroprobabilityonstrategiesthatcharacterizebehavioral inconsistency,itispossibletofindequilibriathatmatchthestylizedfactsthatwementioned.Therefore,ifontheone hand,theconceptofconsistencybeliefsolvesproblemsofrationalityinstatesofzeroprobability,inotherhand,what westateisthatthereareexogenousconstraints(moral,cultural,whatever)whichaloneplaythisrole.Therefore,the presupposedenvironmentforthegameisfundamentallydifferent,forinstance,fromKrepsandWilson(1982),who dealwithconsistentbeliefsystems.

2.2. Bayesianequilibriumunderbehavioralconsistency

WesaythattheBayesianequilibriumisconsistentiftheactionchosenbytheplayeristhesameregardlessofits type,i.e.,ifthetaxpayerbehaviorisconsistentwithsomebehavioralormoralprincipleexternaltothegame.Thus,a consistentequilibriumindicatesthatthetaxpayereitheralwaysevadesorneverevades.Astrategyinwhichthetaxpayer evadesifheisofatypeanddoesnotevadeifheisofanothertype,isnotpartofaconsistentequilibrium.Ifs2:T2→C2

(7)

respecttothegovernment(player1),therestrictiontoconsistentstrategiesisirrelevant,sincethegovernmenthasonly onetype.

InordertoanalyzetheBayesianequilibriuminmixedstrategies,assumethebeliefofplayer2withrespecttothe probabilitiesassociatedwiththeactionsofplayer1isgivenbythedistributionαand1−αtoauditandnottoaudit, respectively.Similarlythebeliefofplayer1withrespecttotheprobabilitiesassociatedwiththeactionsofplayer2is givenbytheprobabilitiesβ,γ,δandεfortheactionsEE,EE, EE andEE,respectively.

Matrix5. Action A _A˜ Subjectiveprobabilities α 1−α EE β y−Γ1,Γ1−c y,0 EE γ y−Γ2,Γ2−c y−Γ6,Γ6 EE δ y−Γ3,Γ3−c y−Γ7,Γ7 EE ε y−Γ4,Γ4−c y−Γ8,Γ8

Proposition1. Suppose0<c<ϕy.ThenthebehaviorallyconsistentBayesianequilibriuminmixedstrategiesis givenby: Bcons = t ϕ ◦A⊕ 1− t ϕ ◦A, c ϕy ◦EE⊕ ϕy−c ϕy ◦EE

Proof. First, we show that α=t/ϕ, i.e., the value of α is equal to the tax rate divided by the punishment suf-fered by the taxpayer when he does not pay the tax and is audited. Making U2(EE|α◦A⊕(1−α)◦A)=

U2(EE|α◦A⊕(1−α)◦A),2 we have (y−Γ1)α+y(1−α)=(y−Γ4)α+(y−Γ8)(1−α).Solving for α, we

find α1=((Γ8)/(Γ1+Γ8−Γ4)). Making U2(EE|α◦A⊕(1−α)◦A)=U2(EE |α◦A⊕(1−α)◦A), we have

(y−Γ1)α+y(1−α)=(y−Γ3)α+(y−Γ7)(1−α). Solving for α, we find α2=((Γ7)/(Γ1+Γ7−Γ3)).

Mak-ing U2(EE|α◦A⊕(1−α)◦A)=U2(EE|α◦A⊕(1−α)◦A), we have (y−Γ1)α+y(1−α)=(y−Γ2)α+

(y−Γ6)(1−α). Solving for α, we find α3=((Γ6)/(Γ1+Γ6−Γ2)). Substituting the variables Γ in terms

of y, Y, p, t and ϕ, we have α1=α2=α3, a common value that we denote by α. To calculate α, is

sufficient to use α3. Thus, α=((tY(1−p))/(ϕy+tY(1−p)−ϕpy−Yt(1−p)))=((tY(1−p))/(ϕyp+ϕY(1−

p)+tY(1−p)−ϕyp−tY(1−p))), hence α=((tY(1−p))/(ϕY(1−p))), that is, α=((t)/(ϕ)). Secondly, given that the Bayesian equilibrium analyzed is the consistent equilibrium, the subjective probabilities related to the actions (EE ) and (EE), are null. Thus, given that γ=δ=0, we have: β=((c)/(ϕy)) and ε=((ϕy− c)/(ϕy))). Indeed, from U1(A|β◦EE⊕γ◦EE⊕δ◦EE ⊕ε◦EE)=U1(A|β◦EE⊕γ◦EE⊕δ◦EE ⊕ε◦

EE)wegetβ(Γ1−c)+γ(Γ2−c)+δ(Γ3−c)+ε(Γ4−c)=βΓ5+γΓ6+δΓ7+εΓ8.Sinceγ=δ=0andΓ5=0,we

haveβ(Γ1−c)+ε(Γ4−c)=εΓ8.Therefore β(Γ1−c)=ε(Γ8−Γ4+c). Substituting Γ1,Γ4 andΓ8 in terms of

y,t andϕ,we get β(ϕy−c)=ε(ty−ty+c).Thenε=(β(ϕy−c))/(c).Wealsoknowthat β+γ+δ+ε=1.But γ=δ=0, hence β+ε=1. By substituting ε=(β(ϕy−c))/(c) into β+ε=1, we get (β+β(ϕy−c))/(c)=1, in which (β(c+ϕy−c))/(c)=1. Thus, β=(c)/(ϕy). Isolating the term ε we have ε=(1−c)/(ϕy). Therefore, ε=(ϕy−c)/(ϕy).Itremainstoshowthenecessityofthecondition0<c<ϕy.Theprobabilitiesβareεarepositive. Inaddition,ifβ+ε=1,wehavethat0<β<1and0<ε<1.Substitutingthevalueofβintothepreviousinequalitywe get0<((c)/(ϕy))<1.Therefore,0<c<ϕy,asclaimed.

2.3. Bayesianequilibriumunderbehavioralinconsistency

ThebehaviorallyinconsistentBayesianequilibriumoccurswhenthetwotypesoftaxpayerstakecontraryactions. Wethensaythattheequilibriumisinconsistent.Inthiscasethesubjectiveprobabilityofplayer2associatedwiththe

(8)

actionofplayer1remainsαand(1−α)toauditandnon-auditrespectively.Thus,theequalityα=(t/ϕ)stillapplies. Ontheotherhand,subjectiveprobabilitiesofplayer1withrespecttotheactionsofplayer2aredifferent.Weconsider βandεnullwhicharetheoddsrelatedtoactions(EE)and(EE).

Proposition2. SupposeϕY(1−p)<c<ϕypandc<((ϕy)/(2)).ThenthebehaviorallyinconsistentBayesian equi-libriuminmixedstrategiesisgivenby:

Bincons= t ϕ ◦A⊕ 1− t ϕ ◦A, c−ϕY(1−p) ϕyp−ϕY(1−p) ◦EE⊕ ϕyp−c ϕyp−ϕY(1−p) ◦EE

Proof. Consider the subjective probabilities over the actions of player 2 (line player, taxpayer) as described in matrix 5. By definition, β=ε=0. The expected utility of player 1 is denoted by: U1(A|β◦EE⊕γ◦EE⊕δ◦EE ⊕ε◦EE)=U1(A|β◦EE⊕γ◦EE⊕δ◦EE ⊕ε◦EE). From this

it follows that β(Γ1−c)+γ(Γ2−c)+δ(Γ3−c)+ε(Γ4−c)=βΓ5+γΓ6+δΓ7+εΓ8. Since β=ε=0, we

have γ(Γ2−Γ6−c)=δ(Γ7−Γ3+c). Substituting Γ2, Γ3, Γ6 and Γ7 in terms of y, Y, t and ϕ, we

get γ[ϕyp+tY(1−p)−tY(1−p)−c]=δ[typ−typ−ϕY(1−p)+c], in which γ(ϕyp−c)=δ[c−ϕY(1−p)]. Therefore, γ=((δ[c−ϕY(1−p)])/(ϕyp−c)) and δ=((γ(ϕyp−c))/(c−ϕY(1−p))). Also, we know that β+γ+δ+ε=1. But β=ε=0, so that γ+δ=1. Substituting δ=((γ(ϕyp−c))/(c−ϕY(1−p))) into γ+δ=1 we get γ+γ((ϕyp−c)/(c−ϕY(1−p)=1)), hence (1/(γ))=((c−ϕY(1−p)+ϕyp−c)/(c−ϕY(1−p))). Thus, γ=((c−ϕY(1−p))/(ϕyp−ϕY(1−p))). Substituting γ=((δ[c−ϕY(1−p)])/(ϕyp−c)) into γ+δ=1, we get δ+δ((c−ϕY(1−p))/(ϕyp−c))=1, thus (1/δ)=((ϕyp−c+c−ϕY(1−p))/(ϕyp−c). Therefore, δ=((ϕyp−c)/(ϕyp−ϕY(1−p))). The distribution (α, 1−α) of the subjective probability over the government’s actions is obviously the same as in Proposition 1. It remains to show the neces-sity of the conditions ϕY(1−p)<c<ϕyp and c<((ϕy)/2). Since, by necessity, 0<γ<1 and 0<δ<1 and given that γ=((c−ϕY(1−p))/(ϕyp−ϕY(1−p))), then 0<((c−ϕY(1−p))/(ϕyp−ϕY(1−p)))<1, i.e., 0<c−ϕY(1−p)<[ϕyp−ϕY(1−p)], so that ϕY(1−p)<c<[ϕyp−ϕY(1−p)+ϕY(1−p)]. Thus, ϕY(1−p)<c<ϕyp. Since ϕY(1−p)<ϕyp,we can compare the equations γ=((c−ϕY(1−p))/(ϕyp−ϕY(1−p))) and δ=((ϕyp−c)/(ϕyp−ϕY(1−p))). We know that δ>γ. Substituting the values of δ and γ into the previous inequality we get ((ϕyp−c)/(ϕyp−ϕY(1−p)))>((c−ϕY(1−p))/(ϕyp−ϕY(1−p))),i.e., ϕyp−c>c−ϕY(1−p). Hence,ϕyp+ϕY(1−p)>2c,fromwhichwegetϕy>2cand,therefore,c<((ϕy)/2),asclaimed.

2.4. Analysisoftheequilibria

Theequationsfoundinthemodelallowustoanalyzetheincentivesof bothplayersinthetaxevasiongame.In Section2.2,inwhichwefoundtheresultsfortheconsistentBayesianequilibrium,theprobabilitiesα,βandεwere relatedtothevariablest,ϕ,yandc.Furthermore,wefoundthelimittothecostofauditing,c.Thepropositionofthis sectionshowsthatthebeliefofplayer2withrespecttotheactionsofplayer1,{α,1−α},dependsonthemagnitude oftheincometaxrate,t,andonthepunishmentchargedonthetaxpayerwhenhedoesnotreporthisincomeproperly, ϕ.Specifically,α=(t/ϕ).Thus,thetaxpayerbelievesmorestronglythatthegovernmentwillauditwhentheincometax rateincreases,andbelieveslessstronglythatthegovernmentwillauditwhenthepunishmentimposedonthetaxpayer increases.Ontheotherhand,thebeliefofthetaxpayerwithrespecttothegovernmentactionnottoauditisinterpreted intheoppositewaywhenthetaxrateandpunishmentparametersvary.

Proposition1 showsthat thedegrees ofbeliefprescribed bybehaviorallyconsistentBayesianequilibria,β eε, are givenbyβ=(c/(ϕy))andε=((ϕy−c)/(ϕy)).Suchequalitiesdenotethesubjectiveprobabilitiesof player1 withrespecttoEEandEE strategiesofplayer2.The probabilityβ isdirectlyproportionaltothecostof auditing andisinverselyproportionaltothepunishmentandtotheaverageincome.Whenthecostofauditingincreases,the governmenttendstodecreasethe frequencyof audits,the taxpayerinturnhasmoreincentivestoevade,whichis consistentwiththemodel, i.e.,whenthe costof auditingincreasesthegovernmentbelieves thatthe taxpayerwill evade withahigher probability. Thepunishmentis avariablethatdiscouragesthe taxpayer toevade,becausethe greater thepunishment, thegreater hisexpensesifaudited.Thus,agreaterpunishmentdecreasesthe beliefofthe governmentwithregardtotheevasionofthetaxpayer.Anothervariablethatbehavesthesamewayasthepunishment withrespecttoβistheaverageincome.Thehighertheaverageincome,theloweristhebeliefthatplayer1assigns

(9)

totheEEstrategyofplayer2.Theaverageincomedependsonthedifferentincomesofthetaxpayer(yandY)and itsprobabilities(pand1−p).Thehighertheaverageincome,theloweristhebeliefthatplayer1assignstotheEE strategyofplayer2.Theaverageincomedependsonthedifferentincomesofthetaxpayeranditsprobabilities.Ifthe tax-payer’sprobabilitypofhavinglowincomefalls,theaverageincomeincreases,andtherefore,theparameterβdecreases. Thismeansthatthehighertheproportionoflow-incometaxpayers,thegreateristhebeliefofthegovernmentthat taxpayerswillnotevade.Thisisastylizedfactintheliterature,henceourmodelalsocapturesthisfact.See,forinstance, the2010InternationalMonetaryFundreportonfiscalpolicyindevelopedanddevelopingcountries(IMF,2010).3

TheparameterεdenotesthebeliefofthegovernmentwithregardtotheEEstrategyofthetaxpayer.Thisparameter dependsonthesamevariablesas theparameterβ.However,thevariablesinfluencethe parameterdifferently:εis directlyproportionaltothepunishmentandtotheaverageincome,andisinverselyproportionaltothecostofauditing. Averyhighcostisadisincentivetothefrequencyof governmentaudits. Thus,thegovernmentbelievesthatifthe costofauditingincreases,theamountoftaxpayerswhodeclaretheirincomecorrectlydecreases.Inthegovernment’s view,theincreaseinaverageincomeleadstoadecreaseoftaxpayerswhodonotdeclaretheirincomecorrectly,and thesameanalysiscanbemadewithrespecttotheincreaseofpunishment.

AlsoaccordingtoProposition1,itisnecessarythat0<c<ϕy.Thus,thecostofauditingmustnecessarilybe greaterthanzeroandlessthantheamountofpunishmentmultipliedbytheaverageincome.Thevalueofϕyisthe amountthatthegovernmentcollectsfromtaxpayersifallofthemevadeandtheyareallaudited,i.e.,itisthehighest amountthatthegovernmentcanraise.Itisthereforeevidentthatthecostofauditingshouldbelessthanthemaximum governmentgain.Otherwise,thisgainwouldbenegative,i.e.,theactualtaxactivitywouldbesociallyinefficient.

InSection2.3wegotthedegreesofbeliefprescribedbybehaviorallyinconsistentBayesianequilibriumγ andδ withrespecttothevariablest,ϕ,yandc.Ifthepenaltyϕincreases,thenthegovernmentdecreasesthebeliefγthat thelow-incomewillevadeandthatthehigh-incomewillnotevade,sinceγ=((c−ϕY(1−p))/(ϕ[yp−Y(1−p)])).So whenthepunishmentishigh,thegovernmentbelievesmorestronglythatthepoortaxpayerwillnotevadeandthatthe richtaxpayerwillevade,whichiscorroboratedbythevalueofδ=((ϕyp−c)/(ϕ[yp−Y(1−p)])).

ThevalueofδrelatestothestrategyEE andispositivelyrelatedtothepunishment.Therefore,theanalysisofthe impactonδduetoanincreaseofpenaltyisthesameastheonepreviouslydone,inwhichwestudiedtheimpactofa declineinthevalueofthepunishmentγ.

Thecostof auditinghasadirecteffectonthevariableγ.Ifauditingbecomesmoreexpensive,thegovernment believesmorestronglythatthelow-incometaxpayerwillevadeandthehigh-incometaxpayerwillnotevade.Onthe otherhand,thecostofauditinghasareverseeffectonthevariableδ,i.e.,ifthecostincreases,thegovernmentbelieves lessstronglythatthelow-incometaxpayerwillnotevadeandthatthehigh-incometaxpayerwillevade.

Theprobabilitythatthetaxpayerisalow-incomeindividualalsoinfluencesthegovernment’sbeliefonthetaxpayer’s strategies.Whenthisprobabilityincreases,thevariableγ increases,thatis,thegovernmentbelieves morestrongly thatthelow-incometaxpayerwillevadeandthatthehigh-incometaxpayerwillnotevade.Thevariableδ,onitsturn, decreases,whichmeansthatthegovernmentbelieveslessintenselythatthelow-incometaxpayerwillnotevadeand thehigh-incometaxpayerwillevade.

Proposition2alsogivestheconditionsfortheequilibriumvaluesofγandδtoexist,namely,ϕY(1−p)<c<ϕypand c<((ϕy)/2).Theseconditionsestablishlimitsonthecostofauditing.Thecostmustbegreaterthanthepenaltyamount paidbythehigh-incometaxpayerandlessthanthepenaltyamountpaidbythelow-incometaxpayer.Moreover,the secondconditionrequiresthatthecostshouldbesubstantiallylessthanthemaximumthatthegovernmentcancollect fromtaxpayers,ϕy.Ontheotherhand,intheconsistentequilibrium,thecostshouldbelowerthanthemaximumgain ofthegovernment.Onepossibleinterpretationforthesedifferentconditionsintheequilibriaisthat,intheinconsistent equilibrium,thegovernmentissusceptibletovariationsinthebehaviorofthetaxpayer.Thus,theconditionthatthe costmustbesubstantiallylessthanthemaximumgainofthegovernmentwouldguaranteethatitwouldnotincurinto alosswhenauditing.

Theinconsistentequilibriumequationsallowustoidentifythedifferencesintheanalysisofthegovernmentwhen itevaluatestheimpactsofthevariablesonthelow-incometaxpayeroronthehigh-incometaxpayer.Thepunishment isseenbythegovernmentassomethingthatencourageshigh-incometaxpayerstoevade.Ontheotherhand,thecost ofauditingisseenasafactorthatdiscourageshigh-incometaxpayerstoevade.

(10)

Theanalysisofthegovernmentwithrespecttothelow-incometaxpayergoestheotherwayround.Theideathat withtheincreaseofthefine,low-incometaxpayersaremorelikelytoevadeisquiteplausible.However,underthesame conditions,thedecisionofthehigh-incometaxpayersnottoevadeiscounterintuitive.Similarly,givenanincreaseof thecost,withthecorresponding increaseof γ,itisalsoplausiblethatthelow-incometaxpayerwillevade,butthe decisionof the high-incometaxpayer not toevade is,oncemore, counterintuitive.Farfrom thesecounterintuitive resultsassociatedwithinconsistentbehaviorbeingaburdenonthemodel,wecanconcludethefollowing:iftaxpayers’ reactionstochangesinthecostofauditingandchangesinthetaxpenaltiesareconsideredrationallyplausiblereactions, thenitisjustifiedtoclaimthattaxpayersactuallyare behaviorallyconsistent.Thisthesisissupportedbyprevious studiesthatshowsthatmoralfactorsinducetheagenttohaveagoodbehaviororbadbehavioraccordingtothebehavior ofsocietyasawhole,asshownbyAndvigandMoene(1990),Andreonietal.(1998),amongothers.Thebehavioral consistencycaneasilybeinterpretedinaccordancewiththisprinciple.TheEE strategy,whichmeansnottoevade whenthetaxpayer’stypeislowincomeandnottoevadewhenitishighincome,mayrefertheideathatthepoordo notevadebecauseheobservesthattherichdonotevadeeitherandviceversa.Conversely,theEEstrategyrefersto theideathatthepoorevadesbecauseheobservestherichevadingandviceversa.Ourcontributionisthemodelingof thisprinciplethroughtheconceptofbehavioralconsistency.

3. Conclusion

ThearticleanalyzedtheincentivesthattaxpayersandthegovernmenthaveinthetaxevasionBayesiangame.In ourmodel,taxpayershavetwotypes,highincomeandlowincome.ThisisquitedifferentfromPruzhanski(2004)’s model,inwhichtheactionavailabletothetaxpayerishisreportinglowincomeorhighincome.Whywouldataxpayer reportahigherincome?Inourmodel,onthecontrary,thelevelofincomeishisprivateinformationandhisdecisionis whethertoevadeornot,which,inouropinion,ismuchmorereasonable.Westudiedtheequilibriaunderconsistency andinconsistency.Inbothinstances,wealsostudiedtheequilibriumbeliefsintermsoftheparameters.Ourconcept ofconsistentBayesianequilibriumfitquitewellthestylizedfactsthatagentsfollowmoralprincipalsexternaltothe game.

Anextensionofthemodelistodifferentiatethefineandthetaxratebetweenrichandpoor.Indeed,itisnaturalto assumethatthefinesandratesthatwouldbeleviedonthelow-incometaxpayerwouldbelowerthantheoneslevied onthehigh-incometaxpayers.Supposetherateonlow-incomeist1 andthe fineisϕ1.Similarlylett2andϕ2 be,

respectively,the rateandthefine relatedtohigh-incometaxpayers.Onecaneasilyshowinthiscase,amongother things,that theratio(t1/ϕ1)=(t2/ϕ2)mustholdfortheequilibriumtoexist.Aspointedoutintheliteraturereview,

taxevasioninfluencesthetaxdesign.Anextensionusingdifferentratesandfinestotaxpayerswithdifferentincomes wouldbringquiteplausibleexplanationsfortheeffectsoftheinteractionbetweentaxevasionandtaxdesign.

In sum,our model describesthestrategic interaction betweenthe tax authorityandthe taxpayer regardingtax evasionandtaxaudit,takingintoaccount twodistinctbehavioralstructures:behavioralconsistencyandbehavioral inconsistency.TheideaistoincorporateintheBayesiangamethenotionthatthetaxpayer,whateverhistype,may wanttodosoinaccordancewiththesocialbehaviororaccordingtomoralprinciplesexternaltothegame.Ourmodel, bydescribingstylizedfactsasaBayesiangame,hasshownthatbehavioralconsistencyperfectlyagreeswithplausible andintuitiveresults,whichmeanstherelationshipbetweenthetaxpayerandthetaxauthoritiesisindeedcharacterized bythesubmissiontomoralprinciplesorimitationofsocialbehavior.

References

Allingham,M.,Sandmo,E.A.,1972.Incometaxevasion:atheoreticalanalysis.J.PublicEcon.1,323–338.

Andreoni,J.,Erard,B.,Feinstein,E.J.,1998.Taxcompliance.J.Econ.Lit.36,818–860.

Andvig,J.C.,Moene,E.K.,1990.Howcorruptionmaycorrupt.J.Econ.Behav.Org.13,63–76.

Barth,E.,Cappelen,A.,Ognedal,E.T.,2005.FairTaxEvasion.DepartmentofEconomics,UniversityofOslo,Mimeo.

Cowell,F.,1990.CheatingtheGovernment.MITPress,Cambridge,Mass.

Fisman,R.,Wei,S.-J.,2004.Taxratesandtaxevasion:evidencefrommissingimportsinChina.J.Polit.Econ.112,471–500.

Goerke,L.,2003.Taxevasionandtaxprogressivity.PublicFinanc.Rev.31(2),189–203.

InternationalMonetaryFund–IMF,2010.FromStimulustoConsolidation:RevenueandExpenditurePoliciesinAdvancedandEmergingEconomies. FiscalAffairsDepartment,StaffteamledbyBenedictClements,VictoriaPerry,andJuanToro,Washington,DC.

(11)

Myerson,R.,1997.GameTheory:AnalysisofConflict.HarvardUniversityPress,Cambridge,MA.

Pruzhansky,V.,2004.HonestyinaSignalingModelofTaxEvasion,TinbergenInstitute,DiscussionPaper,022/1.

Reinganum,J.,Wilde,E.L.,1985.Incometaxcomplianceinaprincipal-agentframework.J.PublicEcon.26,1–18.

Richter,W.,Boadway,R.,2005.Tradingofftaxdistortionandtaxevasion.J.PublicEcon.Theory7(3),361–381.

Sandmo,A.,2005.Thetheoryoftaxevasion:aretrospectiveview.Natl.TaxJ.58(4),643–663.

Schneider,F.,Klinglmair,E.R.,2004.ShadowEconomiesAroundtheWorld:WhatDoWeKnow?,CESifoWorkingPaper,1167.

Siqueira,M.L.,Ramos,E.F.S.,2006.Evasãofiscaldoimpostosobrearenda:umaanálisedocomportamentodocontribuinteanteosistemaimpositivo brasileiro.Econ.Apl.10(3),399–424.

Sousa,M.S.,Tannuri-Pianto,M.E.,Santos,E.C.A.S.,2008.Impostodeimportac¸ãoeevasãofiscal:umainvestigac¸ãodocasobrasileiro.Rev.Brasil. Econ.62(1),77–93.