Journal of Financial Stability 8 pps

Most existing studies of thecyclicality of capital regulatory regimes, both theoretical and empirical, are based on indus-trialized countries.3 However, the pervasiveness of financial mar

journal homepage:www.elsevier.com/locate/jfstabil

Pierre-Richard Agénora,b,∗, Luiz A Pereira da Silvac

a r t i c l e i n f o

Available online 11 August 2010

PACS:

E44

H52

G28

Keywords:

a b s t r a c t

Thispaperanalyzesthecyclicaleffectsofbankcapitalrequirementsinasimplemodelwithcreditmarket imperfections.Lendingratesaresetasapremiumoverthecostofborrowingfromthecentralbank,with thepremiumitselfdependingoncollateral.BaselI-andBaselII-typeregulatoryregimesaredefinedand

acapitalchannelisintroducedthroughasignalingeffectofcapitalbuffers.Themacroeconomiceffectsof

anegativesupplyshockareanalyzed,underbothbindingandnonbindingcapitalrequirements.Factors affectingtheprocyclicalityofeachregime(definedintermsofthebehavioroftheriskpremium)arealso identified

© 2010 Published by Elsevier B.V

1 Introduction

The global financial crisis triggered by the collapse of the

subprime mortgage market in the United States has led to a

reassessment of the policies and rules that have allowed the

buildupoffinancialfragilities.Theregulatoryframework,andthe

distortionsinbankbehaviorandthefinancialintermediation

pro-cessthatitmayhaveledto,havecomeunderrenewedscrutiny

Indeed,itisnowwellrecognizedthattheBaselIregulatorycapital

regimethatU.S.banksweresubjecttogavethemstrongincentives

toreducerequiredcapitalbyshiftingloansofftheirbalancesheets.1

Banksturnedtoan“originateanddistribute”model,inwhich

luiz.apereira@bcb.gov.br (L.A Pereira da Silva).

dardizedloans,mostlyhigh-riskmortgages—involvingnomoney down,interestonlyorlessastheinitialpayment,withno documen-tationonborrowers’capacitytopay,andinitial“teaser”interest rates that would adjustupwardeven if marketrates remained constant—couldbebundledandsoldassecurities,therebyleaving theoriginatingbankfreetouseitscapitalelsewhere.Asthehousing marketdeteriorated,anduncertaintyabouttheunderlyingvalue

ofsubprimemortgage-backedsecuritiesmounted,effortsto main-taincapitaladequacyledtomassivedeleveraging,capitalhoarding, liquidityshortages,andcontractionsincreditsupply,withadverse consequencesforthefunctioningofbothrealandfinancialmarkets (seeCalomiris,2009;Kashyapetal.,2009)

Since consultationsontheBasel IIaccordstarted, and since itseventualadoption in2004,therehasbeenabroaderdebate

ontheprocyclicalityeffectofprudentialandregulatoryrulesand practices.2WithBaselII,capitalrequirementsarebasedonasset qualityratherthanonlyonassettype,andbanksmustuse “mark-ingtomarket”topriceassets,ratherthanbookvalue.Astherules makebankcapitalrequirementsmoresensitivetochangesinthe

overthebusinesscycle,therequiredregulatorycapitalvarieswith

thebusinesscycle.Forinstance,whenassetpricesstartdeclining,

banksmaybeforcedtoundertakecontinuouswritedowns

(accom-paniedbyincreasedprovisioning),andthisraisestheirneedfor

capital.Capitalrequirementsmaythereforeincreaseinacyclical

downturn.Ifbanksarehighlyleveraged,tomaintaintheircapital

ratioduringarecession,theymusteitherraisecapital(whichis

dif-ficultand/orcostlyinbadtimes)orcutbacktheirlending,which

inturntendstoamplifythedownturn.Thus,theintroductionof

risk-sensitivecapitalchargesmaynotonlyincreasethevolatility

ofregulatorycapital,itmayalso(bylimitingbanks’abilitytolend)

exacerbateaneconomicdownturn

Most existing studies of thecyclicality of capital regulatory

regimes, both theoretical and empirical, are based on

indus-trialized countries.3 However, the pervasiveness of financial

marketimperfectionsindevelopingcountries,coupledwiththeir

greater vulnerability to shocks, makes a focus onthese

coun-trieswarranted.Formiddle-incomecountries,inparticular,these

imperfections cover a broad spectrum: underdeveloped capital

markets,whichimplylimitedalternatives(suchascorporatebonds

andcommercialpaper)tobankcredit;limitedcompetitionamong

banks; more severe asymmetric information problems, which

makescreeningoutgoodfrombadcreditrisksdifficultandfosters

collateralizedlending;apervasiveroleofgovernmentinbanking,

both directly or indirectly;uncertain publicguarantees;

inade-quatedisclosureandtransparency,coupledwithweaksupervision

andalimitedabilitytoenforceprudentialregulations;weak

prop-ertyrightsandaninefficientlegalsystem,whichmakescontract

enforcementdifficultandalsoencouragescollateralizedlending;

andavolatileeconomicenvironment,which increasesexposure

toadverseshocksandmagnifies(allelseequal)boththe

possibil-ityofdefaultbyborrowersandtheriskofbankruptcyoffinancial

institutions.Oneimplicationisthatalargemajorityofsmalland

medium-sizefirms(operatingmostlyintheinformalsector)are

simplysqueezedoutofthecreditmarket,whereasthosewhodo

haveaccesstoit—well-establishedfirms,oftenbelongingto

mem-bersofthelocalelite—faceanelasticsupplyofloansandborrow

attermsthatdependontheirabilitytopledgecollateral.Credit

rationing—whichresultsfundamentallyfromthefactthat

inade-quatecollateralwouldhaveledtoprohibitiverates—istherefore

largely“exogenous.”Asecondimplicationistheimportanceofthe

costchannel,whichbecomesakeypartofthemonetary

transmis-sionmechanism.4Thegoalofthispaperistoanalyzethecyclical

effects of BaselI- and BaselII-type capital standards in a

sim-plemacroeconomic modelthatcapturessomeofthesefinancial

featuresandimplications.Asitturnsout,akeyvariableinthe

deter-minationofmacroeconomicequilibriumistheriskpremiumthat

bankschargetheircustomers,dependingontheeffectivecollateral

thattheycanpledge

Thepapercontinuesasfollows.Section2presentsthemodel

BaselI-andBaselII-typeregulatorycapitalregimesaredefined,the

latterbylinkingtheriskpremiumonloanstoriskweights.A“bank

Bikker and Metzemakers (2004) , Gordy and Howells (2006) , and Van Roy (2008) For

and Li (2008) , and the literature surveys by Drumond (2008) , and VanHoose (2007)

Pereira da Silva (2009) provides references to the limited literature on

capitalchannel”isaccountedforbyintroducingasignalingeffectof capitalbuffersonbankdepositrates;thisdifferssignificantlyfrom theliteratureonthistopic,whichtendstofocusonthefinancing choicesofbanksinanenvironmentwheretheModigliani–Miller theoremfails(see,forinstance,VandenHeuvel,2007).Section3 focusesonthecasewherecapitalrequirementsarenotbindingand studiestheimpactofanegativesupplyshockonmacroeconomic equilibriumandthedegreeofcyclicalityoflendingandinterest rates.5Thefinalsectionofferssomeconcludingremarks

2 The model

Themodelthatwedevelopbuildsonthestatic,open-economy frameworkwithmonopolisticbankingdevelopedbyAgénorand Montiel(2008a).Inwhatfollowswedescribethebehaviorofthe fourtypesofagentsthatpopulatetheeconomy,firms,households,

asinglecommercialbank,andthecentralbank

2.1 Firms Firmsproducea single,homogeneousgood Tofinancetheir workingcapitalneeds,which consistsolely oflaborcosts,firms mustborrowfromthebank.Totalproductioncostsfacedbythe representativefirmarethusequaltothewagebillplusthe inter-estpaymentsmadeonbankloans.Forsimplicity,wewillassume thatloanscontractedforthepurposeoffinancingworking capi-tal(whichareshort-terminnature),arefullycollateralizedbythe firm’scapitalstock,andarethereforemadeataratethatreflects onlythecostofborrowingfromthecentralbank,iR.Firmsrepay workingcapitalloans,withinterest,attheendoftheperiod,after goodshavebeenproducedandsold.Profitsaretransferredatthe endofeachperiodtothefirms’owners,households

Let W denote the nominal wage, N the quantity of labor employed,andiR theofficialratechargedbythecentralbankto thecommercialbank(ortherefinancerate,forshort);thewagebill (inclusiveofborrowingcosts)isthus(1+iR)WN.Themaximization problemfacedbytherepresentativefirmcanbewrittenas

whereYdenotesoutputandPthepriceofthegood

Theproductionfunctiontakestheform

whereA>0isasupplyorproductivityshock,K0isthe beginning-of-periodstockofphysicalcapital(whichisthereforepredetermined), and˛∈(0,1)

Solvingproblem(1)subjectto(2),takingiR,PandWasgiven, yields

˛APN˛−1K01−˛−(1+iR)W=0

Thisconditionyieldsthedemandforlaboras

Nd=



˛AK01−˛

(1+iR)(W/P)

1/(1 −˛)

whichcanbesubstitutedin(2)togive

(1+iR)(W/P)

˛/(1−˛)

areinverselyrelatedtotheeffectivecostoflabor,(1+iR)(W/P)

Giventheshortrunnatureofthemodel,thenominalwageis

assumedtoberigidat ¯W 6Thisimplies,from(3)and(4),that

Nd=Nd(P;iR,A), Ys=Ys(P;iR,A), (5)

withNd,Ys

P>0,Nd

iR,Ys

iR<0,andNd

A,Ys

A>0.7Anincreasein bor-rowingcostsorareductioninprices(whichraisestherealwage)

exertacontractionaryeffectonoutputandemployment

Realinvestmentisnegativelyrelatedtothereallendingrate:

whereiListhenominallendingrate,atheexpectedrateof

infla-tion,andh<0.8

Using(5)and(6),thetotalamountofloansdemanded(and

allo-catedbythebank)tofinancelaborcostsandcapitalaccumulation,

LF,isthus

2.2 Households

Householdssupplylaborinelastically,consumegoods,andhold

two imperfectlysubstitutable assets:currency (whichbears no

interest),innominalquantityBILL,andbankdeposits,innominal

quantityD.Becausehouseholdsownthebank,theyalsoholdequity

capital,whichisfixedat ¯E.9Householdfinancialwealth,FH,isthus

definedas:

Therelativedemandfor currencyisassumedtobeinversely

relatedtoitsopportunitycost:

BILLH

whereiDistheinterestrateonbankdepositsand<0.Using(8),

thisequationcanberewrittenas

D

wherehD(iD)=1/[1+(iD)]andhD>0.Thus,

BILLH

wherehB=(iD)/[1+(iD)]andhB<0

Realconsumptionexpenditurebyhouseholds,C,depends

neg-ativelyontherealdepositrate(whichcapturesanintertemporal

effect)andpositivelyonlaborincomeandtherealvalueofwealth

atthebeginningoftheperiod:10

C=˛0+˛1

¯

W N

P −˛2(iD−a)+˛3



FH 0

P



where aistheexpectedinflationrate,˛1∈(0,1)themarginal propensitytoconsumeoutofdisposableincome,and˛0,˛2,˛3>0 Thepositiveeffectofcurrentlaborincomeonprivatespendingis consistentwiththeevidenceregardingthepervasivenessof liq-uidity constraintsin middle-incomecountries(see Agénor and Montiel, 2008b)and the(implicit)assumption that households cannotborrowdirectlyfrombankstosmoothconsumption 2.3 Commercialbank

Assetsofthecommercialbankconsistoftotalcreditextended

tofirms,LF,andmandatoryreservesheldatthecentralbank,RR Thebank’sliabilitiesconsistofthebookvalueofequitycapital, ¯E, householddeposits,andborrowingfromthecentralbank,LB.The balancesheetofthebankcanthereforebewrittenas:

Reservesheldatthecentralbankpaynointerestandaresetin proportiontodeposits:

where∈(0,1)

2.3.1 Interestratepricingrules The bank is risk-neutral and sets both deposit and lending rates.11

2.3.1.1 Depositrateandcapitalbuffers Fromthemonopolybank optimizationproblemdescribedinAgénorandMontiel(2008a), thedepositrateisgivenby

iD=



1+ 1

D

−1

whereDistheinterestelasticityofthesupplyofdeposits

We alsoconsidera more generalspecification, inwhich the bank’scapitalpositionaffectsitsfundingcosts,througha “signal-ing”effect.Specifically,weassumethatthebank’scapitalbuffer (asmeasuredbytheratioofactualtorequiredcapital)allowsit

toraisedepositsmorecheaply,becausehouseholdsinternalizethe factthatbankcapitalincreasesitsincentivestoscreenandmonitor itsborrowers.Depositors,therefore,arewillingtoacceptalower, butsafer,return.12

capitalbuffer, measuredasaratio,isthus ¯E/ER.Thealternative

specificationthatweconsideristhus

iD=εD(1−)iRf



¯E

ER



whereεD=(1+1/D)−1,0<f(·)≤1,f<0, and f(1)=1.The

lastconditionimpliesthatif ¯E=ER,bankcapitalhasnoeffecton

thedepositrate,asspecifiedin(15).Thestrengthofthebank

cap-italchannel,asdefinedhere,canthereforebemeasuredbyf

However,from(12),whethertheexistenceofthischannel(which

operatesthroughthedepositrate)mattersdependsonthe

pres-enceofanintertemporalsubstitutioneffectonconsumption

Modelsconsistentwiththisidea(andwithmorerigorousmicro

foundations)aredevelopedinChen(2001),wherebanks,which

actasdelegatedmonitors,mustbewell-capitalizedtoconvince

depositorsthattheyhaveenoughatstakeinfundingriskyprojects,

andwithAllenetal.(2009),whohavearguedthatmarketforces

leadbankstokeepcapitalbuffers,evenwhencapitalisrelatively

costly,asbankcapitalcommitsthebanktomonitorand,without

depositinsurance,allowsthebanktoraisedepositsmorecheaply

Our specificationis alsoconsistentwiththeview,discussed by

CalomirisandWilson(2004),thatdepositorshavealow

prefer-enceforhigh-riskdepositsandmaydemanda“lemonspremium”

(orpenaltyinterestrate)asaresultofaperceivedincreaseinbank

debtrisk.Tolimitthisrisk(andthereforereducedepositrates),

banksmayrespondbyaccumulatingcapital.Thisviewissupported

bytheempiricalresultsofDemirgüc¸-KuntandHuizinga(2004),

whichshowanegativerelationshipbetweendepositsratesand

theratioofbankcapitaltobankassets.Moredirectsupportis

pro-videdbyFonsecaetal.(2010),inastudyofpricingbehaviorby

morethan2300banksin92countriesovertheperiod1990–2007

Theyfoundthatcapitalbuffers(definedas( ¯E−ER)/ER,ratherthan

¯E/ER)arenegativelyandsignificantlyassociatedwithdepositrate

spreads,regardlessoftheregulatoryregime.Moreover,this

asso-ciationappearstobestrongerfordevelopingcountries,compared

toindustrialcountries

Alternatively,thelinkbetweenthecapitalbufferanddeposit

ratescouldreflectthefactthatwell-capitalizedbanksfacelower

expectedbankruptcycosts(thatis,lowerexpostmonitoringcosts

in case ofdefault)and hence lowerfundingcostsexante from

households.Whatevertheinterpretation,thegeneralpointisthat

in a volatile economic environment, where therisk of adverse

shocksishigh,signalsaboutabank’ssolvencycanhavea

signifi-canteffectondepositors’behavior—particularlywhengovernment

depositguarantees(intheformofadepositinsurancesystem,for

instance)donotexistorarenotreliable.13

2.3.1.2 Lendingrateandthe riskpremium Again,fromthebank

optimizationproblemdescribedinAgénorandMontiel(2008a),

thecontractuallendingrate,iL,isgivenby

whereεL=(1+1/L)−1,withLdenoting(theabsolutevalueof)

theinterestelasticityofthedemandforinvestmentloans,andL

therisk premium, which is inversely related totherepayment

(2004) focus on the behavior of New York City banks during the 1920s and 1930s.

probability.Thus, thelendingrateissetasapremiumoverthe centralbankrefinancerate,whichrepresentsthemarginalcostof funds.Withnonbindingcapitalrequirements,weassumethatthe premiumisinverselyrelatedtotheasset-to-liabilityratioofthe borrower,givenbythe“effective”valueofcollateralpledgedby theborrower(thatis,assetsthatcanbeborrowedagainst)divided

byitsliabilities,thatis,borrowingforinvestmentpurposes,I.In turn,the“effective”valueofcollateralconsistsofafraction∈(0, 1)ofthevalueofthefirm’soutput:

L=g

Ys

whereg<0.This specificationis consistentwith theviewthat collateral,byincreasingborrowers’effortandreducingtheir incen-tivestotakeonexcessiverisk,reducesmoralhazardandraisesthe repaymentprobability—inducingthebankthereforetoreducethe premiumonitsloansforinvestmentpurposes.14Thus,anincrease

ingoodsorassetprices,orareductioninborrowing,tendstoraise thefirm’seffectiveasset-to-liabilityratioandtoreducetherisk premiumdemandedbythebank

2.3.2 Capitalrequirements Capitalrequirementsare based onthe bank’srisk-weighted assets.Supposethattheriskweighton“safe”assets(reservesand loansforworkingcapitalneeds)are0,whereastheriskweight

oninvestmentloansis >0,respectively.Risk-weightedassetsare thus PI.Thecapitalrequirementconstraintcanthereforebe writ-tenas

where ∈(0,1)isthecapitaladequacyratio(theso-calledCooke’s ratio).Ifthepenalty(monetaryorreputational)costofholding cap-italbelowtherequiredlevelisprohibitive,wecanexcludethecase where ¯E<ER;theissueisthereforewhether ¯E=ERor ¯E>ER

Weconsidertwoalternativeregimesforthedeterminationof theriskweight Underthefirstregime,whichcorrespondsto BaselI,theriskweightisexogenousat R;thebankkeepsaflat minimumpercentageofcapitalagainstloansprovidedforthe pur-poseofinvestment.Underthesecond,whichcorrespondstoBasel

II,capitalrequirementsarerisk-based;theriskweightis endoge-nousandinverselyrelatedtoloanquality,whichinturnisinversely relatedtotheriskpremiumimposedbythebank,L.Thisis simi-larinspirittolinkingtheriskweighttotheprobabilityofdefault

ofborrowers,asproposedbyHeid(2007).Thus,asallowedunder BaselII,weassumethatthebankusesanIRBapproach,oritsown defaultriskassessment,incalculatingtheappropriateriskweight andby implicationrequired regulatorycapital.Thisassumesin turnthatthestandardsembeddedinthebank’sriskmanagement systemhave beenvalidated by theregulator—the centralbank here—throughanInternal CapitalAdequacyAssessmentProcess (ICAAP).15

Formally,thetworegimescanbedefinedas16 =

R≤1 under Basel I

Montiel (2008a,b) There is therefore no “balance sheet” or “net worth” effect on

effect.

16

inpartial equilibrium,a negativesupply shock(afallin A)

low-erseffectivecollateralandraisestheriskpremiumoninvestment

loans, L; underBasel II,therisk weight associatedwith these

loans, (L),andcapitalrequirementsalsoincreaseandbank

lend-ingfor investmentmust fallifthe capitalconstraint is binding

( ¯E=ER)

Thelinkbetween andLunderBaselIIisconsistentwith

spec-ificationsthatrelateriskweightstotheborrower’sprobabilityof

defaultoverthebusinesscycle,asforinstanceinTanaka(2002)

andHeid(2007).Theseresultscaptureoneofthegeneralconcerns

aboutBaselII:duringarecessionforinstance(say,anegative

sup-plyshock,asdiscussedhere),iflendingtofirmsisconsideredriskier

becausecollateralvaluesfall,thebankwillberequiredtoholdmore

capital—or,failingthat,toreducelending(indirectlyinthepresent

case,byincreasingtheriskpremium).Inturn,thecreditcrunchwill

exacerbatetheeconomicdownturn,makingcapitalrequirements

procyclical

However,inthepresentsettingtherearealsoanumberofother

(endogenous)factorsthatwillaffectthepremium.Thefallin

lend-ingthatmayresultfromabindingcapitalconstraintfollowingan

increaseinrisktendsnotonlytoreduceoutputbutalsothe

col-lateralrequiredbythebank;thisdampenstheinitialincreasein

thepremium.Inaddition,changesinlendingandaggregate

sup-plywillaffectprices,whichwillaffecttheequilibriumvalueofthe

premiumaswell.Withthebankcapitalchannelembeddedinthe

model,changesinthecapitalbufferwillalsoaffectthedepositrate

andconsumption,whichinturnwillaffectaggregatedemandand

prices.Theseinteractionsimplythattheneteffectofshockscanbe

fullyassessedonlythroughageneralequilibriumanalysis

2.3.3 Borrowingfromthecentralbank

Giventhatfirms’demandforcreditdeterminestheactual

sup-ply of loans, and that the required reserve ratio is set by the

monetaryauthority,thebalancesheetcondition(13)canbesolved

residuallyforborrowingfromthecentralbank,LB.Becausethereis

noreasonforthebanktoborrowifitcanfunditsloanoperations

withdeposits,andusing(14),wehaveLB=max[0,LF−(1−)D−

¯E].17

2.4 Centralbank

Thebalancesheetofthecentralbankconsists,ontheassetside,

ofloanstothecommercialbank,LB.Ontheliabilityside,itconsists

onlyofthemonetarybase,MB:

where

Monetarypolicyisoperatedbysettingtherefinancerateatthe

constantrateiR andprovidingliquidity(atthediscretionofthe

commercialbank)throughastandingfacility

Becausecentralbankliquidityisendogenous,themonetarybase

isalsoendogenous;thisimplies,using(14)and(21),thatthesupply

ofcurrencyis

2.5 Market-clearingconditions Therearefivemarketequilibriumconditionstoconsider:four financial(deposits,loans,centralbankcredit,andcash),andonefor thegoodsmarket.Marketsfordepositsandloansadjustthrough quantities,withthebanksettingpricesinbothcases.Thesupplyof centralbankcreditisperfectlyelasticattheofficialrefinancerate

iRandthemarketalsoequilibratesthroughquantityadjustment Theequilibriumconditionofthegoodsmarket,which deter-minesthegoodspriceP,isgivenby:

Thelastequilibriumconditionrelatestothemarketforcash,and (undertheassumptionthatthecounterparttobankloansisheld

byfirmsintheformofcurrency)involves(11)and(23).However, thereisnoneedtowritethisconditionexplicitly,giventhatby Walras’Lawitcanbeeliminated.18

Table1summarizesthelistofvariablesandtheirdefinitions

3 Nonbinding capital requirements

Wefirstconsiderthecasewhereexistingequitycapitalishigher thantherequiredvalue,thatis, ¯E>ER,regardlessofwhether is endogenousornot.Thisisconsistentwiththeevidencesuggesting that,innormaltimes,banksoftenholdmorecapitalthanthe reg-ulatoryminimum—possibly asa resultof marketdiscipline(see Rochet, 2008).However,although bankcapitalis nota binding constraintonthebank’sbehavior,itstillplaysanindirectrole,by affectinghowthebanksetsthedepositrate.19

3.1 Macroeconomicequilibrium ThesolutionofthemodelisdescribedinAppendixA,underthe assumptionsthata==0and ¯W=1.Asshownthere,themodel canbecondensedintotwoequilibriumconditionsintermsofthe riskpremium,L,andthepriceofthedomesticgood,P:

L=g

 Ys(P;iR,A) h[εL(1+L)iR]



Ys(P;iR,A)=˛1

Nd(P;iR,A)

P −˛2εDiRf

¯E

L(1+L)iR]

0 − L F ) + (LB,d1 − L B − L B )

1 − L F

0 , L B =

cash.

Table 1

Households

F H

Firms

Commercial bank

i D , i L Bank interest rates, deposits and investment loans

Central bank

Capital adequacy ratio

Fig 1.Macroeconomic equilibrium with nonbinding capital requirements.



0

P



whereasthesecondisthegoodsmarketequilibriumcondition(24),

aftersubstitutionfrom(5),(6),(12),(16),(17),and(20)

AgraphicalpresentationoftheequilibriumisshowninFig.1.In

thenortheastquadrantofthefigure,thefinancialequilibriumcurve

(25)islabeledFF.AsshowninAppendixA,FFdoesnotdependon theregulatoryregime;itslopeisgivenby

dL dP



NB,FF

I,II

= g

˙



Ys P

h



<0,

whereNBstandsfor“nonbinding”and˙>0isdefinedinAppendix

A.Intuitively,ariseinpricesstimulatesoutputandincreasesthe effectivevalueoffirms’collateralrelativetotheinitialdemandfor loans;theriskpremiummustthereforefall,attheinitiallevelof investment

Thegoodsmarketequilibriumcondition(26)yieldsthecurves labeledG1G1(whichcorrespondstotheBaselIregime)andG2G2

(correspondingtotheBaselIIregime).Theslopesofthesecurves aregivenby,respectively

dL

dP



NB,GG

I

1

YPs+˛1

P2(Nd−PNd)−˛2εDiRf ¯E

R 2h

+˛3



FH 0

P2



where1<0if ˛2 is not toolarge(seeAppendix A)and, with (L)= Rinitially,

dL dP



NB,GG

II

= 

1

2

dL dP



NB,GG

I

where2<0and2>1.Thus,acomparisonof(27)and(28) impliesthatG2G2isflatterthanG1G1.Inspectionoftheseresults alsoshowsthatcurvesG1G1andG2G2haveasteeperslopethanin theabsenceofabankcapitalchannel(f=0),givenby

dL dP



GG= 1

εLiRh

YPs+˛1

P2(Nd−PNd)+˛3



FH 0

P2



, whichistheslopeofcurveGGinFig.1

Intuitively,thenegativeslopeoftheGGcurvescanbeexplained

asfollows.Ariseinpricestendstoloweraggregatedemandthrough

a negativewealth effecton consumption Atthe same time, it increasesthe nominal valueof loans and thus capital require-ments;thefallinthecapitalbufferraisesthedepositrate,which (throughintertemporalsubstitution)lowerscurrentconsumption However,theincreaseinPalsoboostsaggregatesupply,by reduc-ingthereal(effective)wage,andmaystimulateconsumption,as

aresultofhigherlabordemandanddistributedwageincome.20 Becausethe shiftin supply outweighsthewage income effect, andbecausethewealthandcapitalbuffereffectsare unambigu-ouslynegative,anincreaseinpricescreatesexcesssupply.Therisk premiummustthereforefalltostimulateinvestmentandrestore equilibriuminthegoodsmarket.ThisimpliesthattheGGcurves haveanegativeslope,asshowninthefigure

Curves G1G1 and G2G2 are steeper than curve GG (which correspondstof=0)becausethebankcapitalchanneladds addi-tionaldownwardpressureonconsumption—requiringthereforea largerfallinthepremiumtogenerateanoffsettingexpansionin investment.21

Byimplication, theintuitivereason whyG2G2 is flatterthan

G1G1 isbecauseunderBaselIIthereisanadditionaleffect—the

Fig 2. Negative supply shock with nonbinding capital requirements.

fallintheriskpremiumalludedtoearlierlowerstheriskweight

Thismitigatesthereforetheinitialdropinthecapitalbuffer(atthe

initiallevelofinvestment)inducedbytheriseinprices.Inturn,

thisdampenstheincreaseinthedepositrateandthedropin

con-sumption.Giventhataggregatesupplyandwageincomeincreases

inthesameproportioninbothregimes,theriskpremiummust

fallbylessunderBaselIItostimulateinvestmentandreestablish

equilibriumbetweensupplyanddemand

Understandarddynamicassumptions,localstabilityrequires

theGG curvestobesteeperthanFF.22Thepositiverelationship

betweentheriskpremiumandthelendingrateisshowninthe

northwestquadrant,whereasthenegativerelationshipbetween

thelending rate and investment is displayedin the southwest

quadrant.Thesupplyofgoods,whichisanincreasingfunctionof

thepricelevel,isshowninthesoutheastquadrant.Thedifference

betweensupplyandinvestmentinthesouthwestquadrantgives

privatespending,C.Theeconomy’sequilibriumisdeterminedat

pointsE,D,H,andJ.23

3.2 Negativesupplyshock

Considerfirstanegativeshocktooutput,thatis,adropinA.24

TheresultsareillustratedinFig.2;becausethedifferencebetween

thetworegulatoryregimesisonlyintermsoftheslopeofcurveGG,

weconsideronlytheBaselIregime,toavoidclutteringthegraph

(2008a)

unnecessarily.Differencesbetweenthetworegimesarepointed outlater.WealsofocusatfirstonthemovementleadingtopointE Thefirsteffectoftheshockisofcourseadropinoutput;as showninthesoutheastquadrant,thesupplycurveshiftsinward, withoutput(attheinitiallevelofprices)droppingfromHtoM.The dropinoutputlowersthevalueofcollateralattheinitiallevelof investment;thepremiummustthereforeincreasetoaccountfor thefactthatlendinghasnowbecomemorerisky.CurveFFtherefore shiftsupward,andLrisesfirstfromEtoB.Thefallinoutputalso leadstoexcessdemandonthegoodsmarket;atinitialprices,the riskpremiummustthereforeincreasetorestoreequilibrium(by loweringinvestment).CurveG1G1thereforeshiftsalsoupward Thereis,however,“overshooting”inthebehaviorofthe pre-mium; the initialincrease is not sufficient to eliminate excess demandthroughadropininvestmentonly—todosowouldrequire

anincreasefromEtoB,whichisnotfeasible.Accordingly,prices mustincrease,whichtend(throughanegativewealtheffect)to lowerconsumptionaswell.Becausetheincreaseinpricesalso low-ersrealwages,theinitialdropinoutputisdampened;afterfalling fromHtoM,outputrecoversgraduallyfromMtoH.The associ-atedincreaseinthevalueofcollateralallowsthepremiumtofall, fromBtothenewequilibriumpoint,E.Inthenewequilibrium,the lendingrateishigher,investmentlower,andsoisconsumption However,itisalsopossibleforthenewequilibriumtobe char-acterizedbyalowerpremiumandhigherprices;thisisillustrated

bythecurvesintersectingatpointE”’inFig.2.Thiscorrespondsto

acasewherecurveFFshiftsonlyslightly(whichoccursiftherisk premiumdoesnotadjustrapidlytochangesinthecollateral-loan ratio,thatis,gissmall)andG1G1shiftsbyalargeamount(which occursifinvestmentisnotverysensitivetothelendingrate).25 Fol-lowinganupwardjump(fromEtoB),thepremiumundergoesa prolonged“decelerator”effect,eventuallywithasmalleradverse effectoninvestment,butatthecostofhigherprices.26

Howdoesthe“capitalchannel”operateinthissetting?Because investmentfalls,capitalrequirementsalsofall.Thisimpliesthatthe bank’scapitalbufferincreases.Throughthesignalingeffect dis-cussedearlier(f<0),thedepositratefalls;this,inturn,tendsto increaseconsumptiontoday(allelseequal)throughintertemporal substitution.Putdifferently,althoughbankcapitalhasnodirect effectonloans,itdoeshaveindirecteffects,totheextentthatit affectsdepositrates,aggregatedemand,andthusprices—whichin turnaffectoutput,collateral,andtheriskpremium.This transmis-sionchannelissimilarunderbothregulatoryregimes—exceptthat withBaselIItheeffectonpricearemagnifiedandtheeffectonthe riskpremiumismitigated

Moreformally,letusdefineavariablexasbeingisprocyclical (countercyclical)withrespecttoanexogenousshockzifits move-mentinresponsetoz,asmeasuredbythefirstderivativedx/dz,is suchastoamplify(mitigate)themovementinequilibriumoutput

inresponsetothatshock,dY/dz.Inthepresentsetting,wecanfocus

ontheriskpremium,giventhatthesupplyofloansisperfectly elas-tic,andthattherealdemandforcreditforthepurposeoffinancing workingcapitalneedsis(bydefinition)procyclical.Here,wehave dL/dA+0,whichimpliesthattheriskpremiumcanbeeither pro-cyclicalwithrespecttoA—fallingduringboomsandrisingduring

as in Agénor and Montiel (2008a) , in terms of the value of the beginning-of-period

out-put,asperthedefinitionabove—orcountercyclical(dL/dA>0).This

ambiguityexistsregardlessoftheregulatoryregime,becauseitholds

evenintheabsenceofabankcapitalchannel(f=0or˛2=0)—given

thatinthiscaseneitherFF,norGG,dependson

Inthecasewheref>0(and˛2>0),theimpactoftheregulatory

regimeonthedegreeofprocyclicalityoftheriskpremiumcanbe

formallyassessedbycalculatingthederivativeoftheequilibrium

outcomedL/dAwithrespectto␴,thatis,d2L/dAd ,inamanner

similartoHeid(2007).Moreintuitively,thisoutcomecanbegauged

byexamininghow affectstheslopesofFFandGG.Asnotedearlier,

FFdoesnotdependon ;G2G2isflatterthanG1G1;andboth ¯E and

G2G2haveasteeperslopewithf>0thanwithf=0

By implication,withnonbindingcapital requirements, anda

bankcapital channel,bothregulatoryregimesmagnifythe

pro-cyclical effectofa negativesupply shockontheriskpremium;

allelseequal,BaselIIislessprocyclicalthanBaselI.Intuitively,

thereasonwhytheregulatorycapitalregimemagnifiesanupward

movementintheriskpremiumcomparedtothecasewherethe

regimedoesnotmatter(f=0)isbecausetheimprovementinthe

capitalbuffertends(asnotedearlier)tostimulateprivate

consump-tion;consequently,attheinitiallevelofprices,“bringingdown”

aggregatedemandtothelowerlevelofoutputrequiresalarger

dropin investment—andthereforea largerincrease in the

pre-mium.ThismovementisalsomoresignificantintheBaselIregime,

becauseinthecaseofBaselIItheinitialincreaseinthepremium

raisestheriskweight—whichinturnlimitsthedownwardeffecton

capitalrequirementsresultingfromthefallinthelevelof

invest-ment(thatis,ERfallsbylessthanthedropinIbecause rises);

asaresult,theincreaseinthecapitalbufferislesssignificant,the

depositratefallsbyless,andthestimulustoconsumptionis

miti-gated.Theriseintheriskpremiumrequiredtorestoreequilibrium

tothegoodsmarketisthusofalowermagnitude

4 Binding capital requirements

Wenowconsiderthecasewherethecapitalrequirement

con-straint (19) is continuously binding, that is, ¯E= F Because

equityispredetermined,banklendingforinvestmentmustadjust

tosatisfythecapitalrequirement:

regardlessofwhether isendogenousornot.Weassumethat

con-straint(29)iscontinuouslybinding,duepossiblytoheavypenalties

orreputationalcostsassociatedwithdefaultonregulatory

require-ments,asnotedearlier

With(29)determininginvestment,Eq.(6)isnowsolvedforthe

lendingrate:

iL=h−1



¯E 

wherea=0forsimplicity.Theinterestrate-settingcondition(17)

isnowusedtosolvefortheriskpremium:

L= i

L

εLiR −1= 1

εLiR h

−1



¯E 

Collateralthereforeplaysnolongeradirect roleindetermining

theriskpremium;Eq.(18)servesnowtodeterminetheeffective

collateralrequired,thatis,coefficient.Ofcourse,forthesolution

tobefeasiblerequires<1,whichweassumeisalwayssatisfied

Thus,wecontinuetoassumethatcreditrationingdoesnotemerge

Inadditiontothefinancialequilibriumcondition(31),whose

solutionnowdependsontheregulatoryregime,macroeconomic

equilibriumrequiresequalitybetweensupplyanddemandinthe goodsmarket.Using(29),thisconditiontakesnowtheform:

Ys(P;iR,A)=˛1N

d(P;iR,A)

P −˛2εDiR+˛3



FH 0

P



whosesolutiondependsalsoontheregulatoryregime

Withabindingcapitalrequirement,thecapitalbufferisunity, andbecausef(1)=1,thedepositrate-settingconditionis(15).Thus, thebankcapitalchannel,asidentifiedintheprevioussection,does notoperate.However,theadjustmentprocesstoshockscontinues

todependinimportantwaysontheregulatoryregime;forclarity,

weconsiderthemseparately

4.1 Constantriskweights MacroeconomicequilibriumundertheBaselIregimeisnow illustratedinFig.3.Asbefore,thesoutheastquadrantshowsthe positiverelationshipbetweenoutputandprices.From(29),and with constantatFF,investmentandpricesareinverselyrelated,

asshowninthesouthwestquadrant.Eqs.(30)and(31)alsoimply

anegativerelationshipbetweeninvestmentandtheriskpremium,

asdisplayed in the northwest quadrant Because both the risk weightandinvestmentandindependentoftheriskpremium,the goodsmarketequilibriumcondition,shownascurveG3G3inthe northeastquadrant,is vertical.Thefinancial equilibrium condi-tion,shownascurveF3F3,hasnowapositiveslope,givenby(see AppendixA):

dL

dP



B,FF

I

=− 1

εLiR h

−1 

¯E

P2 R



whereBstandsfor“binding.”

Intuitively,thereason whyFFispositivelyslopedisbecause higherprices nowreduce realinvestment(asimplied by(29)), whichinturncanonlyoccurifthepremiumincreases.The equi-libriumobtainsatpointsE,H,J,andD.Graphically,F3F3issteeper

Fig 4. Negative supply shock with binding capital requirements (Basel I regime).

thelarger Ris,sothat∂[dL/dPB,FF

I ]/∂ R>0.Allelseequal,the higher Ris,thelargertheeffectofanyshockthatleadstoashift

inthefinancialequilibriumconditionontheriskpremium,andthe

smallertheeffectonprices

AsshowninFig.4,anegativesupplyshockleadstoaninward

shiftofthesupplycurve(asbefore),butthishasnodirecteffecton

thepremiumattheinitiallevelofprices,incontrasttothecaseof

nonbindingrequirements.Thus,F3F3doesnotshift.Excessdemand

ofgoodsrequiresanincreaseinpricestoclearthemarketandG3G3

shiftstotheright.Theincreaseinpriceslowersinvestment,andthis

mustbeaccompaniedbyanincreaseintheriskpremium.Theprice

hikealsolowersconsumption,throughanegativewealtheffect

Thus,theadjustmenttoanegativesupplyshockentailsbothan

increaseinpricesandareductioninaggregatedemand.Thenew

equilibriumpositionisatpointsE,H,J,andD.Theriskpremium

isthusunambiguouslyprocyclical(dL/dA<0)

Toanalyzetherole ofthecapitalregimeinthetransmission

processofthisshock,recallthatwithabindingrequirementthe

depositrate-setting condition(16)becomesindependentof the

capitalbuffer.However,ascanbeinferredfrom(29),thehigher

therisk weight(andthecapital adequacy ratio), thelargerthe

dropininvestmentandlending;thesmallerthereforethe

adjust-mentinpricesrequiredtoequilibratesupplyanddemand.Thus,

the“capital channel”operates now through investment,rather

thanconsumption.Atthesametime,however,a largerdropin

investmentmustbeaccompaniedbyalargerincreaseintherisk

premium.Formally,itcanbeshownthatthegeneralequilibrium

effectisd2L/dAd R>0

4.2 Endogenousriskweights

UndertheBaselIIregime,theendogeneityof precludesthe

useofafour-quadrantdiagramtoillustratethedeterminationof

equilibrium;itisnowshowninasinglequadrant,inFig.5.The

determinationofthefinancialequilibriumconditionF4F4follows

regime).

thesamelogicasbefore;itthereforehasapositiveslope,given nowby(seeAppendixA):

dL

dP



B,FF

II

=− 1

˙4

1

εLiR h

−1 

¯E

P2 R



where ˙4>0if  isnottoolarge,and˙4<1.A comparison

of(33)and(34)showsthatthisslopeissteeperthanunderBasel

I.Intuitively,thereasonisthatnowthedirect,positiveeffectof

anincreaseinpricesonthepremium(whichvalidatesthefallin realinvestment,asnotedearlier),iscompoundedbyanincrease

intheriskweight.Thus,allelseequal,shockswouldnowtendto havelargereffectsontheriskpremium,andmoremutedeffects

onprices,thanunderthepreviousregime

Thegoodsmarketequilibriumcondition,however,isnolonger vertical;because␴ dependsonL,itcanbedisplayedasanegative relationshipbetweentheriskpremiumandthepricelevel,denoted

G4G4inFig.5,withslope

dL

dP



B,GG

II

4

YPs+˛1

P2(Nd−PNd)+˛3



FH 0

P2



+ ¯E

P2 R

, (35) where4<0

ThereasonwhyGGisdownward-slopingisnowdifferentfrom thenonbindingcase:hereanincrease inthepricelevellowers realinvestment,as impliedbythebindingconstraint(29);this mustbevalidatedbyanincreaseintheriskpremium.However, thepriceincreasealsolowersconsumptionandstimulatesoutput (forreasonsoutlinedearlier);inturn,thisrequiresafallintherisk premiumtostimulateinvestmentandrestoreequilibriumbetween supplyanddemand.Thefigureassumesthatthesecondeffect dom-inatesthefirst(orequivalentlythat isnottoolarge),soG4G4

hasindeedanegativeslope.Thus,thegoodsmarketequilibrium conditionisnowlesssteep;allelseequal,shockswouldtendto havemoremutedeffectsontheriskpremium,andlargereffects

onprices,thanunderBaselI.Becausetheslopesofthetwocurves areaffectedinoppositedirectionbyaswitchfromBaselItoBasel

II,itcannotbeascertainedaprioriwhethershockswouldtendto havelargereffectsontheriskpremium,asunderthenonbinding case—whereonlyGGwasaffectedbyaswitchinregime

Fig 6.Negative supply shock with binding capital requirements (Basel II regime).

Fig.6illustratestheimpactofanegativesupplyshock.Curve

G4G4shiftstotherightandtheequilibriumischaracterizedbya

higherriskpremiumandhigherprices,asinFig.4.Thus,theshock

isprocyclical,asunderBaselI.ButeventhoughonlytheGGcurve

shifts(asisthecaseunderBaselI),theinitialpositionofFFmatters

forthefinaloutcome.Thus,whetherBaselIIismoreprocyclicalor

lessprocyclicalthanBaselIcannotbedeterminedunambiguously

Insum,withbindingcapitalrequirements,anegativesupply

shockisunambiguouslyprocyclicalandunderBaselI.Thehigher

theriskweight Ris,thestrongertheeffectofashockontherisk

premium.TheshockisalsounambiguouslyprocyclicalunderBasel

II;However,whetherasupplyshockentailsmoreprocyclicalitywith

respecttoBaselIinthebehavioroftheriskpremiumcannotbe

ascertainedapriori

5 Concluding remarks

Thepurposeofthispaperhasbeentoanalyzetheprocyclical

effects of BaselI- and BaselII-type capital standards in a

sim-plemodelthatcapturessomeofthemostsalientcredit market

imperfectionsthatcharacterizemiddle-incomecountries.Inour

model,capitalrequirementsareessentiallyaimedatinfluencing

bank decision-makingregarding exposuretoloandefault They

affectboththequantityofbanklendingandthepricingofbank

deposits.Thebankcannotraiseadditionalequitycapital—aquite

reasonableassumptionforashort-termhorizon.Thedepositrate

is sensitivetothesize ofthebuffer, througha signalingeffect

Well-capitalizedbanksfacelowerexpectedbankruptcycostsand

hencelower fundingcostsfromthepublic Wealsoestablisha

linkbetweenregulatoryriskweightsandthebank’sriskpremium

underBaselII;thisisconsistentwiththefactthatinthatregime

theamountofcapitalthatthebankmustholdisdeterminednot

onlybytheinstitutionalnatureofitsborrowers(asinBaselI),but

alsobytheriskinessofeachparticularborrower.Thus,capital

ade-quacyrequirementsaffectnotonlythelevelsofbanklendingrates,

andthusinvestmentandoutput;theyalsoaffectthesensitivityof

theseratestochangesinoutputandprices

Ouranalysisshowedthatdifferenttypesofbankcapital

regula-tionsaffectindifferentwaysthetransmissionprocessofanegative

supplyshocktobankinterestrates,prices,andeconomicactivity

Asdiscussedintheexistingliterature,andregardlessofthe regu-latoryregime,capitalrequirementscanhavesizablerealeffectsif theyarebinding,becauseinordertosatisfythembanksmaycurtail lendingthroughhikesininterestrates.However,wealsoshowed that,evenifcapitalrequirementsarenotbinding,a“bankcapital channel”mayoperatethroughasignalingeffectofcapitalbuffers

ondepositrates.Ifthereissomedegreeofintertemporal substitu-tioninconsumption,thischannelmaygeneratesignificanteffects

ontherealeconomy

Severalpolicylessonscanbedrawnfromouranalysis.First, reg-ulatorsshouldpaycarefulattentiontotheimpactofriskweightson bankportfoliobehaviorwhentheyimplementregulations.Second, capitalbuffersmaynotactuallymitigatethecyclicaleffectsofbank regulation;inourmodel,capitalbuffers,byloweringdepositrates, areactuallyexpansionary.Thus,ifcapitalbuffersareincreased dur-inganexpansion„withtheinitialobjectiveofbeingcountercyclical, theymayactually turn out tobe procyclical.This is an impor-tantconclusion, given theprevailing viewthat counter-cyclical regulatoryrequirementsmaybeawaytoreducethebuildupof systemicrisks:ifthesignalingeffectsofcapitalbuffersare impor-tant,“leaningagainstthewind”maynot reducetheamplitude

of thefinancial-business cycle.27 A more detailed studyof the empiricalimportanceofthesesignalingeffects,buldingperhaps

onFonsecaetal.(2010),isthusapressingtaskformiddle-income countries.Moreover,thepossibility ofasymmetriceffectsshould alsobeexplored;forinstance,ahighcapitalbufferingoodtimes mayleadhouseholds(asownersofbanks)toputpressureonthese bankstogeneratemoreprofits,inordertoguaranteea“minimum” returnonequity;bycontrast,thesignalingeffectalludedtoearlier maybestrengthenedinbadtimes

Ouranalysiscanbeextendedinseveraldirections.Oneavenue couldbe to extend the bank capital channel as modeled here

byassumingthat a largecapital bufferinducesbanksnot only

toreducedepositrates(asdiscussedearlier)butalsotoengage

inmore risky behavior, which maylead themto relaxlending standardsandlowerthecostofborrowinginordertostimulate thedemandforloansandincreaseprofits.However,becausethis wouldleadtoanexpansionaryeffectoninvestment,itwouldgo

inthesamedirectionastheconsumptioneffectalludedtoearlier Thus,ourresultswouldnotbeaffectedqualitatively

Aseconddirectionwouldbetorelaxtheassumptionof port-folioseparation,forinstancebyintroducinga“joint”costfunction fortheproduction/managementofloansanddeposits.Inthatcase, equilibriumconditionsforprofitmaximizationwouldbe interde-pendent;bothbankrateswoulddependonthecapitalbuffer,and thiswouldsubstantiallyaffectthewaythebankcapitalchannel operatesinthemodel.Alternatively, itcouldbeassumed, asin Agénoretal.(2009),thatbankcapitalhasnoeffectonthedeposit ratebutinsteadreducestheprobabilityofdefault(byincreasing incentivesforbankstomonitorborrowers)andthatexcess capi-talgeneratesbenefitsintermsofreducedregulatoryscrutiny.As shownthere,asimilarambiguityinrankingtheprocyclicalityof BaselIandBaselIImayemerge

InAgénoretal.(2009),wehavealsoembeddedthefinancial featuresofthepresentmodelinadynamicoptimizingframework,

inlinewithothercontributionssuchasMarkovic(2006),Aguiar andDrumond(2007),andMehandMoran(2010).Thisallowsus