From Pigou to extended liability - on the optimal taxation of externalities under imperfect

forthcoming,ReviewofEconomicStudies

FromPigoutoExtendedLiability:

OntheOptimalTaxationofExternalitiesunder

ImperfectFinancialMarkets.?

JeanTirole

?

March3,2009

Abstract

Pigoviantaxationofexternalitieshaslimitedappealifthetortfeaserhasinsuf-?cientresourcestopaythedamagewhenitoccurs.TodefendPigoviantaxationinthepresenceofjudgment-proofagents,itsproponentspointatthemanyinstitutionsextendingliabilitytothirdparties.YetlittleisknownaboutthevalidityofPigou’sanalysisinthiscontext.

Thepaperanalyzesthecostsandbene?tsofextendedliabilityandinvestigateswhetherfullinternalizationiscalledforinthepresenceofagencycostsbetweenpotentialtortfeasersandprovidersofguarantees.Itscontributionistwo-fold.It?rstshowsthatthebetterthe?rms’corporategovernanceandthestrongertheirbalancesheet,themorecloselytaxesshouldtrackthecorrespondingexternality.Itthendevelopsthe?rstanalysisofextendedliabilitywhenguarantorsthemselvesmaybejudgment-proofandtheextensionofliabilitymaygiverisetofurtherexternalities.Relatedly,itderivesthecurvatureoftheoptimaltaxationofexternalitiesinamulti-plant?rm.

Keywords:Pigoviantaxation,externalities,?nancialconstraints,extendedlia-bility,snowballe?ects.

JELnumbers:D62,D82,H23,J65,Q58

1Introduction

Animportantcontributionofeconomicstopublicpolicyrestsonthepreceptthatpricesignalsshouldforceproducersofexternalitiestointernalizethewelfareofothereconomicagents.Pigou(1920)’scelebratedinsightonthetaxationofexternalitiesprovidesanintellectualfoundationforavarietyofpoliciesfrompollutiontaxes/permitstoexperiencerating;italsounderliestheexpectationdamagesremedyforbreachincommerciallaw.Fromapolicyperspective,though,Pigou’sinternalizationprinciple—therequirementthatthepolluterpaythedamagein?ictedonthepollutee—raisestheconcernthatthepolluterhaveinsu?cientresourcestopaythedamageswhenitoccurs.Inlegalterms,thepollutermaybe“judgment-proof”.ShallowpocketsmaysubstantiallyreducethepolicyappealofPigoviantaxation.Andindeed,manyenvironmental,personalor?nancialobligationsareevadedthroughbankruptcyandabandonmentofoperations.1

ProponentsofPigoviantaxationretortthat,inthepresenceofsolvencyconcerns,potentialpollutersshouldbeforcedtocontractwithothercorporateentitiesor?nancialintermediarieswhowillstepinandguaranteepaymentsincaseofdamage.Suchextendedliabilitypreventspollutersfromescapingtheirduties.

Insupportofthisview,manyvehiclesforextendingliabilitiestoathirdpartyhavedeveloped,eitherspontaneouslyorthroughregulation,2overtheyears.Mandatorycarinsurancecoversdamagesin?ictedonthirdparties.Banksandgovernmentsguarantee?rms’paymentstosuppliers(throughlettersofcredit)orworkers(throughunemploymentinsurancefunds).Depositinsurancefundsandcapitaladequacyrequirementsprotectdepositorsagainstpoorriskmanagementby?nancialinstitutions.Insomepaymentsystems,bankscanincreasetheiroverdraftfacilitybysecuringsomeguaranteefromotherbanks.Manufacturingunitsoftenbene?tfromanexplicitorimplicitbackingofexternalclaimsbyaparentcompany.Extendedliabilityisalsoubiquitousforenvironmentaldamages.3

ThispaperrevisitsPigovianthinkingbyconsidering?nanciallyconstrainedagentsmonitoredby?nancialintermediaries,businesspartners,orparentcompanies.Theframe-workisotherwiseastandardoneinwhichtheagent,a?rm,mayimposeanegativeex-ternalityonathirdparty,aworker,theenvironmentorthetaxpayer.The?rm,runbyanentrepreneur,haslimited?nancialresources.Thestatecandemandextendedliability,thatisasktheintermediarytopaypartoforthefullpenaltywhenthe?rmisjudgment-proof.Extendingliabilityhowevercanimprovewelfareonlyiftheintermediaryhasmoreinformationthanthestate.Inthetraditionofcorporate?nance,thepaperthusassumesthattheintermediaryactsasadelegatedmonitor.Asusualinthat?eld,theincomethatispledgeableto?nancialintermediariesis

notthe?rm’stotalsurplus,astheentrepreneurenjoysarent.

Severalquestionscanberaisedinthiscontext.First,whatarethecostsofextendedliability?Should?rmsandtheirguarantorsbeheldaccountableforthefullexternality,asPigousuggested,or,tothecontrary,shouldsomeofthesocialcostbesocialized?Second,cantheextensionofliabilitytootherindustrialcompaniesjeopardizeotherwisehealthyactivities?

Thepaperobtainstwosetsofinsights:

(1)Well-diversi?edguarantors.We?rstassumethattheguarantorisneverjudgmentproofhimself.Onemayhaveinmindawell-diversi?ed?nancialintermediary.Anaturalbenchmarkprincipleisthenthe“delegationprinciple”:Becausetheguarantorisbetterinformedaboutthepotentialtortfeasorthanthestate,thecostoftheexternalityshouldbepassedthroughtotheguarantor,whothenwritesanoptimalsecond-bestcontractwiththe?rm.ThisdelegationprincipleextendsthevalidityofPigovianreasoningto?rmswithlimitedfundsbutpotentialguarantors.4

Wederiveconditionsunderwhichthisdelegationprincipleholds,andunveiltwoexcep-tions.The?rstdeparturefromthedelegationprincipleoccurswhenthecontractbetweenthe?rmandtheintermediaryisnotsecondbestduetoexpostrenegotiation.We?ndthatapartialextensionofliability,bystrengtheningtheintermediary’sbargainingpo-sition,helpsthe?rmobtain?nancingandraisessocialwelfare.Werelatetheextensionofliabilitytothe?rm’sstrengthofbalancesheetandtothequalityofmonitoring.Inparticular,liabilityisextendedmore,thestrongerthe?rm’sbalancesheet.

Thesecondexceptionoccurswhen?rmsareheterogenous.Apartialextensionof

liabilitythenfavors?nanciallyweak?rms,whoaremorelikelytocausethedamage,tothedetrimentofstrongerones.Limitedextendedliabilityallowsthestatetokeepthe?nanciallyweak?rms“onboard”whilekeepingexternalitiesatareasonablelevel.(2)Snowballe?ectsandjudgment-proofguarantors.Parentcompanies,customers,sup-pliers,orotherindustrialcompaniesmaybebestplacedtomonitorthepotentialtort-feasor.Anextensionofliabilitytothemmayjeopardizetheirownactivities.Thatis,judgmentproofnessmaypropagatethroughtheguaranteeingchain.Similarly,banksmayfacehardshipwhentheborrowerstheyguaranteefail,andre-insurersmaynotbeabletocovertheinsurancecompanies’losses.Worsestill,theextensionofliabilitymayleadtotheextensionofexternalities.Forexample,amonitorwhoisaskedtocoverthecostoflayo?sbythemonitoreemaybeforcedtolayworkerso?himself.

Suchsnowballe?ectsareinvestigatedinatractable“nestedinformationstructure”modelofindependentinterest.Tore?ectthepossibilitythatguarantorsthemselvesbejudgment-proof,weconsideramodelwithnexantesymmetric?rmswithlimitedfundsandmutuallymonitoringeachother.Each?rmfacesuncertainty;forexample,inthelay-o?interpretation,each?rmmayfaceaproductivityshockthatmakescontinuedemploy-mentlessattractive.Usingtheemploymentinterpretationasanillustration,therealiza-tionofuncertaintyunfoldsinthefollowingway:First,arandomnumberm∈{0,···,n}of?rmsareunviable,leadingtoasmanyclosures.Second,thecommonproductivityyofthen?mremainingandpotentiallyviable?rmsisdrawnfromacontinuousdistributionGn?m(y).Thenumbermiscalledthe“breadth”oftheshock,whilethedistributionsGn?m(·)areorderedthroughthestandardhazard-ratecomparison,givingrisetoanotionof“depth”oftheshock.Thestateknowsneitherthebreadthnorthedepthoftheshock.Itisshownthatitisoptimalto(partially)extendliabilityifbreadthanddeptharenegativelycorrelated.Intuitively,iftheshockonpotentiallyviable?rmsislikelytobesmall(inastochasticsense)whenother?rmsshutdown,thenrecoveringthecostoftheexternalitythroughextendedliabilitycreatesonlylimitedsnowballe?ects.

Bycontrast,liabilityisnotextended(despitemutualmonitoring)whenshocksareindependent.Andliabilityis“negativelyextended”(virtuous?rmsreceivesupportwhenotherscreateexternalities)ifbreadthanddeptharepositivelycorrelated.Theoverarchingprincipleisthustheuseoftheinformationconveyedbytheexistenceofexternalitiesabouttheabilityofotherstobearextendedliability.Theotherkeylessonisthatsnowballe?ectssubstantiallymitigatethebene?tsofextendedliability.

Thisn-?rmsnowballe?ectadmitsare-interpretationintermsofasingle,?nanciallyconstrained?rmwithndi?erentactivities.Theresultsthenimplythattheper-layo?taxscheduleisdecreasing(respectivelyconstant,increasing)withthenumberoflayo?s

3

ifthebreadthandthedepthoftheshockarenegatively(respectivelynot,positively)correlated.

Thepaperisorganizedasfollows:Section2setsupthebasicmodel,andshowsthatitappliestoavarietyofpolicyenvironments,includingexperiencerating,environmentaltaxationandprudentialregulation.Section3derivestheoptimallevelofextendedliabilitywhen?rmsareexantehomogenousandshowshowpolicyshouldaccountforthe?rms’balancesheetstrengthandforcapitalmarketimperfections.Itthenextendstheanalysistoexante?rmheterogeneity.Section4investigatestheextensionofliabilitytootherindustrialcompaniesandanalyzessnowballe?ects.Finally,section5concludeswithpotentialalleysforresearch.

Relationshiptotheliterature:Thereisbynowalargeliteratureonthee?ectsofextendedliabilityonthelevelofenvironmentalcare,whichIwillnottrytoreviewexhaustively(ausefulcollectionofstate-of-the-artcontributionscanbefoundinBoyeretal2007).Thispaperdi?ersfromthisliteratureinseveralimportantrespects.First,unlikeanumberofpapersitallowsafullrangeofinstrumentsforthegovernment.Namely,thelattercansetupafund(forexample,adepositorunemploymentinsurancefund)collectingmoneyfrom?rmsregardlessofwhethertheyexertexternalities.Theabsenceofafundcreatesaroleforthirdpartiesasconduitsforthestate;withfullinstrumentrangebycontrast,the?nancialintermediaryorbusinesspartnerisnotneededforlevyingthecontributiontothefundandextendedliabilitymakessenseonlyifthe?nancialintermediaryorbusinesspartnermonitorsthetortfeasor.Weaccordinglycasttheargumentina(rathergeneral)corporate?nanceframework.

Second,itfocusesondi?erente?ects;inparticular,startingfromthedelegationprin-cipleasaPigovianbenchmark,itunveilsthreefactors,therenegotiationof?nancialcontracts,theheterogeneityof?rms,andsnowballe?ectsthatcallforlimitstoextendedliability.Italsocontainsthe?rstanalysisofextendedliabilitywith?nanciallyconstrainedguarantors.

Pitchford(1995)makestheimportantpointsthatthetortfeasor’sincentivestoexertcareneedtobepreserved,andthatanincreaseinlenderliability,becauseitmustbeo?setbyapaymenttothelenderintheabsenceofaccident,reducesthetortfeasor’sincentives.Thusinsuchan“e?ciencywageframework”inwhichmanagerialincentivesaretradedo?againstrents,fullextendedliabilityisingeneraldominatedbypartiallenderliability.Thelenderinthemodelisaconduitforgovernmentpolicy,collectingincomefromthe?rmonthegovernment’sbehalfasthegovernmentcannotlevycontributionstoafundintheabsenceofaccident;the(partial)extensionofliabilityisonewayofimplementing

4

3.4generalizestheanalysistoanendogenouschoiceofmonitoringintensitybythein-termediary.Onemayforthemomenthaveinmindthattheinvestorsspendascreeningcostm(otherwise,theyareexposedtoliabilityonothertypesof“bad?rms”),that,asabyproduct,makesthemknowledgeableabouttheentrepreneur’sactivityandwritethe?nancialcontractsaspositedabove.15?Valueandrents.

Asusual,itisusefultostartwiththerealallocation(characterizedbythecuto?

y)≡

????

+∞

+∞

y)≡y)dG(y)

denotethenetsocialproductivityandtheentrepreneur’sexpectedrentforcut-o?

d??y=

y

TheexpectednetproductivityN(

??

??

+∞

ydG(y)<0.

????

y=b.

Assumption3(singlepeakednessofinvestorrevenue)ThefunctionN(

y)issingle-peakedinthecut-o?y?>b.

??

Forexample,whentherentdependsonlyontherealizedincomeR(y,y??r(

Relaxingthisassumptionwouldleadustoaddtheconstraintthattheentrepreneurnotsigncontractswithnon-monitoringinvestors.Itisimmediatetocheckthattheextraconstraintisnon-bindinginthe“exantecontracting”casebelow.Withexpostcontracting,onecan?ndconditionsunderwhichnon-monitoringcontractsarenotviable.

15

10

Givenpublicpolicy{τ,f,μ},thenetvalueforthecoalitionisgivenby:16

VE?(I+m)≡?G(

(y?w?τ)dG(y)?(I+m).(3)

y

Becausetheinvestorsbreakeven,theentiresurplusgoestotheentrepreneur,whothere-forereceivesnetutility:17

VE?(I+m).

Toproduce,theentrepreneurmustsecure?nancingfromtheinvestors.Giventhepres-enceofnon-pledgeableincome,themaximumamountthattheentrepreneurcanpledgeisgivenby:

VI≡?G(

(y?w?τ?R(y,

y

y+denotethevaluethatmaximizespledgeableincome.18Forexample,whenR(y,

y+?r(

y)wheneverthe?nancingconstraint

(5)isbinding.

Theoptimalcontractbetweentheentrepreneurandtheinvestorsisillustratedgraph-icallyinFigure2:

Ry,

y

??+∞

y)f+

??

y)??

dG(y)?(I+m?A)?t

fortheinvestors,wheret≥0denotetheexpectedextrarentgrantedtotheentrepreneur(equivalently,hebringsonlyA?tupfrontandkeepst).Theinvestorsmustbreakeven(condition(4)below),which,substitutingfort,yields(3).t>0attheoptimalpolicycorrespondstoanon-binding?nancingconstraint.17

Theentrepreneur’sgrossutilityisthenA+(V18

E?I?m).Notethaty?,butforanarbitraryinstitutionalenvironment{w,τ,f},while

I+m?Ay)no?nancingy)?R(bilaterallyef?cientcut-off

yFigure2

ForA≥A1,thebilaterallye?cientcut-o?

y).WhenA

fallstoA2(

y+),though,nomoreconcessionscanraisethepledgeableincome

andtheinvestmentcannolongerbe?nanced.

WhenA

y∈[w+τ?f,

y.

Discussion:natureofexternalityandroleofmonitoring.

Inthismodel,theexternalityexertedbytheinvestors-entrepreneurcoalitionrelatestothechoiceofthelayo?threshold

19

Theexternalityisherelinkedtothechoiceofcontinuation,e.g.,ofhowmuchliquiditytheen-

12

Itisalsoworthcommentingontheroleofmonitoring.Inthisbasicmodel,monitoringbyanintermediaryallowsinvestorstorecoupincomeingoodstatesofnature.Ittherebyharnessesthe?rm’scontributivecapabilityandallowsthe?rmto(indirectly,throughinvestors)payalayo?taxinbadstatesofnature.Thisisobviouslyanimportantaspectofmonitoring.Anotherimportantaspectconsistsforthemonitorinexertinghercontrolrightssoastochangethedistributionofincome;alternativelythemonitormaya?ectwhathappenstotheworkerincaseoflayo?:Byprovidingon-the-jobgeneralisttrainingorbymakingitsemployeesmoreconnectedandvisibletotheoutside,the?rmcanreducethelengthofunemployment(whichisequivalenttoincreasingbinthismodel).20Monitorsthuscanexercisetheircontrolrightstoeitherreducetheprobabilityofbankruptcy/layo?ortoimprovethesakeoflaid-o?workers.AsSection3.4howeverwillshow,ouranalysisfullycarriesovertothisotherdimensionofmonitoring,showingthatthereisnosub-stantivedi?erencebetweenthe“contributive-capability-enhancement”andthe“ex-anteintervention”viewsofmonitoring.

2.2Examples

Example1(stealingorincentivepayment):Supposethattheentrepreneurcanstealafractionβofrealizedincome.Equivalently,βycouldbeassociatedwithanincentivepaymentaimedatpreventingtheentrepreneurfromtaking(output-contingent)privatebene?ts.Then

R(y,

entrepreneurfromstealingtheentireoutput.21

Example2(perksandprestigefromo?ce):Supposethattheentrepreneurenjoysnon-monetaryprivatebene?tBfrombeingino?ce.22Then

R(y,

y}.y}.

Themonitoringcostcaninthisexamplebeviewedasacostrequiredtopreventthe

Inamilderversion,theentrepreneur’sprivatebene?twoulddependonthe?rm’sscaleorlaborforce,bringingExample2closertoExample1.Examples1and2canmore

generallybecombinedas

R(y,

y},

with0≤r(y2)?r(y1)y1(less-than-unitaryincrements).InExamples1and2,N?Ristriviallysingle-peaked,with

y?)=b,

thatis:

1?β

(Example1)and

?

y?w?τ+f)g(

?

y?w?τ+f?r(y).

y+?r(

Aratherdi?erentanalysisofexpostbargainingisconductedinBlanchardandTirole(2008).There,underexpostwagebargaining(?rmsandworkersbargainoverwagesafterinvestmentshavebeensunk),anincreaseinthelayo?taxmakesiteasierforworkerstocapturesomeoftheupsidepro?t.Giventhe?rms’breakevencondition,theseupsidegainsareo?setbylowerwagesorlowerunemploymentbene?tswhenthe?rmislessproductive,destroyinginsuranceoverall.Expostwagebargainingthuscallsforless-than-fullexperiencerating.Notethatbargainingoccursbetweenthe?rmandtheworkersandthatthelatterareriskaverse.Riskaversioniskeytotheextentthatexpostwagebargainingdestroysinsurance.Herethe?rmandits?nanciersarebothriskneutral.

23

14

Needlesstosay,thispaperdoesnotexhaustthetopic.Anotherreasonwhytheprivatesector’sexposuremightoptimallybelimitedisthatthegovernment,throughitspolicies,a?ectstheprobabilityofcreationofexternalities:intheunemploymentapplication,?rmproductivityandunemploymentlengthdependonpublicpolicy;similarly,authoritiesimpacttheenvironmentalandindustrialaccidentexternalities,orthelevelofabankruptbank’sliabilities.Then,thestatemayhavetobeheldaccountable.Finally,thestochasticenvironmentinouranalysisofsnowballe?ects(withina?rmoracoalitionof?rmsunderextendedliability)generatedatwo-dimensionaladverseselectionproblem.Moregener-ally,thePigoviananalysisshoulddevelopmultidimensionaladverseselectionmodelinginordertoanalyzetheoptimaltaxationofexternalitiesinmulti-activityenvironments.Thesemodelsasourtwo-dimensionalone,willalsoprovemostusefultodeepenourratherimperfectunderstandingoftheroleofgovernmentsinalleviatingtheriskandimpactof?nancialcontagion.

Limitedaccesstocapitalmarketsisanubiquitousfeatureofdevelopedandless-developedeconomies.Thewidespreadpolicyconcernsabouttheimpactoflayo?orenvironmentaltaxeson?nanciallyfragilecompaniesorofstringentprudentialregulationon?nanciallyfragile?nancialinstitutionsdeservemoreattentionfromeconomictheoristsandempiricists.Wehopethatthispaperwillencouragefurtherworkinthisdirection.

40

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42

Because

y

β(y?<0and

?c

?β

??

y?)](

+∞

.

y?)]dG(y)?(I+m)+A

ItcanbecheckedthatthesamecomparativestaticswithrespecttoβandAhold.Proposition3.Underexpostbargaining,shallow-pocket?rmsmustshutdownmoreoften(yˉ≥b)thaniftheyhadsubstantialnetworth(weredeep-pocket?rms).Layo?sareexcessivefroma?rst-bestperspective,butareanecessaryconcessiontoinvestors.TheoptimalpolicyinvolveslessinternalizationthanthatprescribedbyPigou’srule:Thegrossandnetcontributionrates,c≡f/μand??c≡(f?τ)/μ,arelowerthan1.Thesecontributionratesincreasewiththestrengthofthe?rm’sbalancesheet(A)andwiththequalityoftheirgovernance(1?β).

Remark:Propositions2and3showthatthekeydi?erencebetweenExample3andExamples1and2isthatthecontractbetweenentrepreneursand?nanciersinExample3isathird-bestcontract,whosedistancetothesecond-bestoneisin?uencedbypublicpolicy,andnotthefactthattherentfunctionisafunctionofyonlyinExamples1and2.28

y;thentheentrepreneurincursprivatecostcinordertocreateprivatebene?tB(c)ifheisretained;?nallyyisrealizedand??thecontractisimplemented(commitmentcase).Theentrepreneurchoosescsoastomaximize?c+1?G(

y)11{y≥

y)≡B(c(

specifyingalow

y,Proposition2applies.

y:anentrenchedentrepreneur(i.e.,withacontract

25

3.3Heterogeneityandcross-subsidies

Supposenowthatthereare“strong”and“weak”?rms,inproportions(ρ,1?ρ).TheproductivitydistributionsforthesetwotypesareGH(y)andGL(y),respectively,whereGHdominatesGLinthesenseof?rst-orderstochasticdominance(the?rmsdi?eronlyinthisdistribution).While?nancialintermediariescantellthetwotypesapart,thegovernmentcannot;thebestthegovernmentcandoistoo?eranincentivecompatible

????

menu{fH,τH},{fL,τL}inwhich?rmsselfselect.Bycontrast,itisstillsociallyoptimaltoo?erundi?erentiatedunemploymentinsuranceμandtherebyinduceauniformwagewintheeconomy.Withobviousnotation,thepolicymustsatisfythegovernment’sbudgetconstraint:

??ρGH(

??

??

??

yH)]τH+(1?ρ)GL(yL)]τL

≡ρ?H+(1?ρ)?L≥0.

Asusual,welfare(μ)isequaltosocialsurplus,

??+∞ρ(y?b)dGL(y)?(I+m)

yL

minustherentsenjoyedbythe?rmscomparedtotheabsenceofinvestment.

Tocomputethestrong?rms’rent,whichisdeterminedbythepayo?theygetbymim-ickingtheweaktypes,letusassumeforsimplicitythattheirproductivityissu?cientlyhighthattheyfacenocreditconstraintwhenmimickingtheweaktype;andsotheircuto?isw+τL?fL.[Thereasoninggeneralizestothecaseinwhichmimickingthelowtypemakesthehightypecredit-constrained.]Thehightypes’rentisthen????+∞??ρ[y?(w+τL)]dGH(y)?GH(w+τL?fL)fL

w+τL?fL

????

=ρ

+∞

??w?fL

where

??[y?w+fL]dGH(y)?[1?GL(

??fL=fL?τL

??

yL)μ??L,

isthenetlayo?taxfortheweaktypes.Furthermore,

Notethat,foragiven

yL)]

??

??isstrictlypositive,andsoitisoptimaltochoosefLassmallaspossible,thatissuchthat29

??yL=w?fL

andusing?rst-orderstochasticdominance(GH(yL))yields:

y,m)thatdependsontheintensityofmonitoringm,whichwe

??yL,fLandμaregivenbythisequality.

27

nowtaketobevariableinsteadof?xed.30Ex-anteinterventionconsistsinmonitoringinordertoexercisecontrolrights.ThisexerciseshiftsthedistributionofincomeG(y,m)(advising),possiblybyconstrainingtheentrepreneur’srentR(y,

+∞

y,m)≡

??

y,m)≡

AsinSection3.1,onecanobtainan??

+∞

y,m)dG(y,m).

upperboundforsocial(worker)welfarebynotingthatfullinsurance(w=b(m)+μ)isstilloptimalandbysolvingProgramI’:32

max{w,

y,m)?(I+m)

(13)w≤N(

y,m)?(I+m)+A.

(14)

AsinSection3.2.1,letusimplementthecorrespondingupperboundinthecom-mitmentcasethroughPigoviantaxation.Fromnowon,wedenoteby{

y,m??}anarbitrarychoicebythe

coalition.Pigoviantaxationrequiresanex-postassessmentoftheexternality:33

f(m??)≡μ+[b(m)?b(m??)].

(15)

Thesociallyoptimalvalue,m,andthechosenlevel,m??,willbeequalundertheimple-mentingscheme,andsoτ=0.

Letusassumeforexamplethatconstraints(13)and(14)arebothbindingandletθdenotetheratioofthetwomultipliers.FromProgramI’,thesociallyoptimalvalues{

y,m?????m???

θ

y,m????

.

AndbecausePigoviantaxationeliminatesexternalitiesonthirdparties(heretheworkers),(

1+θ=

N????1+θ

R????

1+θ

A??

??

.

(16)Thus,iftheentrepreneurandtheinvestorscancontracton??

y=y)but

notonthemonitoringintensity,themonitormustbeincentivizedtochoosem??=mifentrepreneurialwelfareistobemaximizedgiventhestate’spolicy.Themonitorproperlyinternalizesthetaxfaslongassheismadeaccountableforit.Butthemonitor’sincentivetomonitormustfurtherbealignedwiththatofthecoalition(givenby(16))withrespecttotheimpactofm??onGandR.Indeed,PaganoandRoell(1998)showthatdiscipliningmonitorshaveexcessiveincentivestomonitoriftheyreceivetheentirepledgeableincome,astheydonotinternalizetheentrepreneurialrent.35Conversely,onemayintuitthatthepledgeableincomemay,forthesamereason,provideanadvisorwithinsu?cientincentives.Thissuggeststhatthecoalitionwillsetsomeincentiveschemez(y)forthemonitor,thatdi?ersfrompledgeableincome.Indeed,lettingthemonitorpaythelayo?tax,themonitorsolves:

??

+∞

y,m??)f(m??)?m.??(17)

Suppose,?rst,thatmonitoringmaychangethedistributionofincome(advising)andtheworker’sopportunitycost,butnottheentrepreneur’srent.Then,for(16)and(17)todeliverthesamesolutionandthereforeform??tobeequaltom,thecoalitioncanchoose:

z(y)=y?[b(m)+μ]?

θ

y).

y????μ+b(m)?b(m??)??

+

??

+∞

??

Finally,ifbreadthanddeptharepositively(negatively)correlated,

yk,when

kissmall.

Fullinternalization.Fullinternalizationoccurswhen

f≥

???

f≡Σkpkk

Deep-pocketcoalitions(asde?nedby(24))fullyinternalizethecostoftheirlayo?s.Less-than-fullinternalization.Forshallow-pocketcoalitions

f?≤

f(where

?

??

+∞

(y?b)dGk(y).(25)

b

?????

f,λ>0andso

d

f<

pricingequations”:

ymkgk

f?isgivenby

??ymk

??

ykaregivenbythe“monopoly

??

nI+

ym

??

y?

????1?Gkyk?b

??=λ

ykyk

35

.

(i)Thecuto?sareincreasing(

y2≤···≤

(f),while0<λ<1for

?

yk=bforallkasλ=0)occurswhenbalancesheetsarestrong

f<

f≤

yk=b).Letusthereforeturntothemoreinterestingcaseofshallow-pocket?rms.Aswenotedearlier,?rmscareonlyaboutthetotalpaymentT?when?activitiesremaininoperation.Thus,andquitegenerally,wecannotidentifyalayo?taxschedulewithoutmakinganassumptiononthepayrolltaxschedule.Weaccordingly(andreasonably)assumethatthepayrolltaxscheduleislinear:

τ?=τ

Let

Fm≡mfm

denotethetotallayo?taxformlayo?s.

Webeginwiththecaseofindependentdistributions,andthengeneralizetheanalysis.Independentdistributions.

SupposethatGk(y)=G(y)forallk.Theoptimalpolicycanthenbeimplementedbylinearpayrollandlayo?taxes:

τk=τandfk=f=

forall?.

y=(w+τ)?f.(27)

f∈

?????

f,inequilibrium,

??????????

y)τ=Σkpkn?1?G(

??y?

f??

y

36

Negativecorrelationbetweendepthandbreadth.

Letuschoosethelayo?taxschedule{Fm}andtheper-workerpayrolltaxτsothatwithkviableactivities,thecuto?

yk?w?τ?Fn?k=?Fn.

??

(28)

Tocheckforincentivecompatibility,wemustverifythatall“downwardincentivecon-

straints”(DIC)aresatis?ed:42

k??

yk?w?τ?Fn??Thisamountsto

??

?Fn≥?

whichisindeedsatis?edif

??y???

?Fn,k

=?

??yk?w?τ???Fn?k=(k?1)

??

yk?(w+τ)=???Fn?k+1?Fn?k??

.

y

??y?b??dG(y)??

?nI.

When

f?,then

ymand

μ≡Σkpkk??1?G

??

ym?b??+n

42

Notethatif(DIC)issatis?edfor

37

forall?

fandτ.yk.

(DIC)

(DAIC)

Letusshowthatifthecuto?sareincreasingink(positivecorrelation),then(DAIC)impliesmoregenerallythatthe(DIC)constraintsaresatis?ed:

k??

yk?1?w?τ?Fn?k+1+(k?1)

=(k?2)

????

??

??

yk?1

??

yk???

≥(k?2)

yk≥

????

yk?w?τ?Fn?k+2+

yk?1

ykisincreasingink(positivecorrelation),

theallocationisincentivecompatible.

Furthermore,themarginallayo?tax,Fn?k+1?Fn?k,isdecreasingink,thatisin-creasinginthenumberoflayo?s:thelayo?taxscheduleisconvex.

Extendedliability.Recallthatthemodeladmitstwointerpretations:onewithasingle,multi-activity?rm,andanotherwithnsingle-activity?rms.Thelatterallowsustodiscussextendedliability.Note?rstthatinthecaseofindependentdistributions,itisoptimaltotreatthe?rmsseparatelyandlevyper-layo?tax

fandletusnormalizethelayo?taxscheduleinanaturalway:44

Fn=n

f

Weassumethatfinthediscussionofextendedliability.Otherwise,fullinternalizationatthe?rmlevelobtainsandthereisnoextendedliability.??n??44

Whenthe(DAIC)constraintsarebinding(convextaxschedule),Fn?F0=?u=1

??

yn?w?τ,sosetτsuchthat

yn?(w+τ).

43

?

38

Whenthelayo?taxscheduleisconvexbycontrast,the?rmsthatretaintheirworkersreceiveabreak.Thiscanbeinterpretedasareductioninthepayrolltaxwhenother?rmslaytheirworkerso?.

Proposition7.Extendingliabilitytootherindustrialcompaniesraisesthepossibilityof“snowballe?ects”.Underthenesteduncertaintystructure,when

f,thestatemay

?

notapplyfullexperienceratingevenwhenfeasible(i.e.,incaseofpartiallayo?s).(i)Withindependentdistributions,theoptimalallocationcanbeimplementedthroughalinearlayo?-tax-cum-payroll-taxscheme.

(ii)Theper-layo?taxdecreaseswiththenumberoflayo?s(thelayo?taxscheduleiscon-vex)ifthedepthandbreadthoftheproductivityshockarenegatively(positively)correlated.(iii)Inthemulti-?rminterpretationofthemodel,liabilityisextendedifandonlyifthedepthandbreadthoftheproductivityshockarenegativelycorrelated.

5Summaryandconclusion

Should?rmsandtheirguarantorsbemadeaccountableforthefullexternality,asPigousuggested?Theargumentinfavorofthis“generalizedPigouprinciple”isthatthegov-ernmentshoulddelegatethemonitoringtoaprivatepartywho,ifmadefullyaccountable,willwritee?cientsecond-bestcontractswiththe?rm.Wevalidatedthis“delegationprin-ciple”,butunveiledtwolimitations:First,itnolongerholdsifcontractsbetween?nancialintermediariesand?rmsarenotsecond-beste?cient,asweillustratedthroughthecaseofexpostrenegotiation.ThepublicpolicythenplaysadualroleofpromotingPigovianinternalizationandoffacilitatingthe?rm’saccesstoamonitor.Thecontributionrateshouldthenbelessthanunitary.Second,when?rmsareheterogenous,alimitedtaxationofexternalities(again,acontributionratebelowone)cross-subsidizestheweaker?rmsandlimitstherentsofstrongerones.

Second,tappingpro?tsinanother(monitoring)industrialcompanyhasitslimits,asextendingliabilitymayextendexternalities.Snowballe?ectswerestudiedinatractablenested-information-structuremodelofindependentinterest,showingthattheliabilityshouldnotbeextendedwhenthepartners’failureconveysbadornonewsabouttheguarantors’ownactivities.Overall,thecaseforextendedliabilityismuchweakerwhentheguarantorhimselfhasaweakbalancesheetandthestructureofshocksmakespropagationlikely.

Itwasfurthershownthatforasingle,multi-activity?rm,theper-layo?taxshoulddecrease(beconstant,increase)withthenumberoflayo?sifthebreadthanddepthofproductivityshocksarenegatively(not,positively)correlated.

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