Capital Requirements and Financial Problems with the ... · Bowornlux K., Capital Requirements and...

Southeast Asian Journal of Economics 4(1), June 2016: 1-27

Capital Requirements and Financial Problems with the Macroeconomy

Bowornlux KaewtunGraduate Student at Faculty of Economics, Thammasat University

Email: [email protected]

Abstract

The 2008 financial crisis has revitalized policymakers to find an appropriatepolicytorespondtorecurringfinancialproblem.Thepurposeofthispaperistoinvestigatetheimpactsofcapitalrequirementsinresponsetoshocksandtofindouthowcapitalrequirementsworkinreducingfinancial problemsandstabilizingbalancesheets.Weconsideramacroeconomicmodelwithabankingsectorthatisallowedtoborrowfundsfromtheinternationalanddomesticmarkets.Theresultsshowthatcapitalrequirementsareefficientin responding to financial problems. It increases the bank’s networth and reducesitsleverageratio.Alessaggressivepolicyproduceslowerlossesandstabilizes the variation of networth and bank leverage.But a high degree of responsiveness is required if authorities aim to accelerate net worth accumulationandovercomeabankingcrisis.However,capitalrequirementsare lesseffective inresponding to technologyshocks.Capital requirementscannotfullystabilizenetworthandbalancesheets.

Keywords: Capital requirements, financial problems, andmacroeconomicmodel

2 • Southeast Asian Journal of Economics 4(1), June 2016

1. Introduction

The 2008 financial crisis has shown that macroeconomic stabilitydoes not guarantee banking sector stabilization. Sometimes the financial problem is not related to the policy interest rate, rather it depends on the banker behavior in making decisions on their balance sheets. A bank maximizesitsprofitbypurchasingtheassetsandfinancesbyborrowingfromfinancialmarkets.However,manybanks failed to internalize their balancesheetsandmadedecisionsbasedontheaggregateassetprices.Thiscontributedthefinancialeffectstothebankingsystemandaccumulatedthesystemicrisk.Afterasubprimecrisis,thedevaluationintheassetshassharplydeterioratedbanks’ balance sheets and net worth contraction. Thus, banks face high external finance premiums and induce to a reduction of investment and output.Theimpactsoffinancialproblembecomemoresevereandleadtoasignificantoutputloss.Moreover,ittakestimeforpolicymakerstoovercomesuchabankingcrisis.

The objective of this paper is to find out whether the regulatory instrument imposed by theBasel committee helps tomitigate the bankingproblem and improves banks’ balance sheets. The capital requirement is introducedtoregulatebanks’behaviorandtolimittheimpactsofthefinancialproblem.To end this question,we use a standard open economywith thebankingsectorfollowingGertlerandKaradi(2011).Inthissetup,itshowsthe capital inflows from the agency problem between domestic financial intermediaries and foreign investors.The leverage ratio canbedeterminedwithin themodel and itwill fluctuate over the cycles.As a sequence, theamount of credit supply that the bank can extend from the external funds dependsonendogenousbankcapital(networth).Inthepresenceofadverseshocks,namelyatechnologyshockandcapitalqualityshock,areductioninthe bank capital leads to a self-enforcingfinancial acceleratormechanism.Thatisbankswillreducetheirdomesticcreditsupplyimmediatelyinordertorestoreacceptablebankcapitallevels,therebydrivingtheassetpricesdownfurther.

Manypapersinvestigatethepotentialbenefitofcapitalrequirementon the financial crisis, such asMeh et al. (2008),Angeloni et al. (2009),

Bowornlux K., Capital Requirements and Financial Problems with the Macroeconomy • 3

Dib(2010),Chistensenetal.(2011),Gertleretal.(2012),andfindthatthepotentialgainsofcapitalrequirementreducetheimpactsofthefinancialcrisis.Meh et al. (2008), uses a standard dynamic stochastic general equilibrium(DSGE) model with the bank to examine the effects of bank capital and balancesheetsontheeconomy.Thepaperfindsthatthebank’scapitalhasanegative relation to the financial shock and helps stabilizing the financial crisis. The bank’s capital shortage generates double impacts during the economydownturnduringcrisis.Angelonietal.(2009),usingaDSGEmodelwithmonetarypolicyreachesthesimilarconclusion.Thekeyfindingisthatastrongcountercyclical capital requirement improveseconomic losseswhentheeconomyishitbythebankingcrisis.Thegainsofcapitalrequirementinrespondingtotechnologyshocksdependontheaggressiveofthemonetarypolicy.Dib (2010) analyzes the role of capital requirement in propagating theeffectsofshocksinrealeconomyunderfinancialfrictionsenvironment by using a DSGE model with an active role of banking sector, financial accelerators, andfinancial frictions in thecapitalmarket.The result showsthatthefinancialfrictionsinthecapitalmarketamplifytheeffectsofshocksontheeconomyandthecapitalrequirementreducesrealimpactsofshocks by stabilizing macroeconomic variables. Chistensen et al. (2011), extends further by investigating the interaction between the monetary policy andcountercyclicalbuffers.Thestudyreveals thatastronginteractionbetweenthecapitalrequirementandmonetarypolicyarebenefit.Thecountercyclicalbank leverage regulation ismore beneficial if bank’s capital shock arises.Gertleretal.(2012)investigatestheimpactsofcapitalrequirementwhetheritdiscourages thebank to issue short-termdebtsandencourages thebank toincreasethenetworth.Thestudyfindsthatthecapitalrequirementcanstabilizethe bank’s balance sheets and the potential benefit is highwhen economyfacesafinancialcrisis.Thispaperdiffersfromthepreviousstudiesintwokeyaspects. First, themodel is analyzed under a neoclassical perspective of asmallopeneconomythatthebankisallowedtoborrowfromaninternationalfinancialmarket.Second,themodeliscalibratedbasedontheThaieconomicparameters.

This paper is organized as follows. Section 2 briefly presents thebaselinemodeldescription.Section3isthequantitativemodelanalysis.Thelastsectionofferssomeconclusionsandremarks.


2. The baseline model

The core framework is a small open economyneoclassicalmodel. Wemodify thismodelwithafinancial sectorbasedonGertlerandKaradi(2011)andSteffen(2011).Afinancialintermediaryisallowedtoborrowfromtwofinancial sources,namelydomesticdepositsand internationalfinancialmarkets.Therearefourtypesofagentsintheeconomy:households,financialintermediaries,non-financialfirmsandcapitalproducers.Thecapitalproducers’productionissubjecttothecapitaladjustmentcosts,otherwisethecapitalcanchangeeasily.Thefinancialintermediariesareownedbydomestichouseholdsandinvestmainlybypurchasingassetsofnon-financialdomesticfirms.Anagency problembetweenfinancial intermediaries and lenders generates anendogenousborrowingconstraintontheleverageratiointhefinancialsectorandintroducesthefinancialacceleratormechanismfollowingBernankeetal.(1999).Wealsoincludeadisturbancetothequantityofcapital.Withafinancialfrictionsprocess,theshockinducesasignificantcapitallossinthebankingsector,whichinturnsincreasesatighteningcreditandasignificantdownturn.Therealactivityoftheeconomydependsonthefinancialcontract,andthebanks’ balance sheets constraint limits domestic production.Next,wewillcharacterizethebasicingredientsofthemodel.

2.1 Households

Assumingthatthereismeasureonecontinuumofidenticalhouseholdsintheeconomy,eachhouseholdengagesinconsumption,savings,andlaborsupply.Ahouseholdsavesbylendingfundstocompetitivefinancialinterme-diaries.

Withineachhousehold, there isafraction(1 - f)ofworkersandafractionfofbankers.Workerssupplylabortonon-financialfirmsandreturnthewagetheyearntothehousehold.Bankersmanagefinancialintermediariesandcontributetothehousehold’sincomebytransferringtheirearningsbackto the household. Within each household, there is perfect consumption insurance.Bankersfaceafinitehorizontoinsurethatovertimetheywillnotaccumulatecapitaluntiltheycanfundallinvestmentprojectsfromtheirowncapital.Inparticular,bankershaveprobability(1 - {)toexitfromthefinancial


sector,which is independent of history.The average survival time for thebankerstoworkinthefinancialsectoris1/(1 - {)andleadstotheamount f(1 - {)ofbankersthatexitthefinancialsectorandbecomeworkersineachperiod.Tokeepaconstantratioofworkersandbankers,asimilaramountofworkersmovestothefinancialsector.Bankerswhoexitfinallytransfertheirretainedearningstotheirhousehold.Thenewentrybankerswillbeprovidedwithsomestart-upfundsfromtheirfamilywhichwillbedescribedlater.

Householdsmaximizeexpectedlifetimeutilityfunctionbychoosingalevelofconsumption(Ct),laborsupply(Ht),andnextperioddepositlevelDtH 1+^ h.Thehouseholdpreferencesaregivenasfollows:

maxEC

vH

1 1t

t

t

t tv

0

1 1

bv|

--

+

3 v

=

- +

; E/ (1)

withb ∈(0,1)denotesthesubjectivediscountfactorandv,v,|>0representthedegreeofriskaversion,theelasticityoflaborsupplyanddisutilityweight,respectively.

Theintermediaries’depositisaoneperioddepositwhichpaysarealgrossreturnRtd fromperiod t - 1to t. Inequilibrium, it isconsideredasa riskless asset. Let DtH 1+ be the total demand for deposits the household acquires,Wtbetherealwage,and∏tbethenetpayoutstothehouseholdfromtheownershipofbothnon-financialfirmsandfinancial intermediaries.Thehouseholdbudgetconstraintisgivenasfollows:

C D WH R Dt tH

t t td

tH

t1 P+ = + ++ (2)

Thehousehold’scorrespondinglyoptimalconditionsforconsumption,laborsupply,andsavingare,respectively,givenby

E CC

,t t tt

t1

1K = v

v

+ -+-

; E (3)

CH

Wt

tv

t|

=v- (4)

E R 1,t t t td

1 1b K =+ +6 @ (5)

whereΛt,t + 1isthemarginalrateofsubstitutionofconsumptionbetweentheperiodtandt + 1.Equation(4)setsthemarginalrateofsubstitutionbetween


consumption and leisure equal to the realwage.The last equationdenotes the optimal savings decision which implies that the household smooths consumptionovertime.

2.2 Financial intermediaries

The financial intermediaries are owned by domestic households.Bankslendfundsobtainedfromhouseholdsandinternationalfinancialmarketsto non-financial firms.Bankers act as specialists that assist in transferringfundsfromsaverstoinvestors.Theyengageinthematuritytransformationbyholdinglongtermassetsandfundtheseassetswithshorttermliabilities.Thefinancialintermediariescapturetheentirebankingsectorincludinginvestmentbanksandcommercialbanks.

The representative financial intermediary j is separated into two subunits,a liabilitiesunitandoperationunit.The liabilityunitobtains twosourcesoffunding,namelydepositorsandforeignlenders,andthensellsthemas liabilities to theoperationunit.Theoperationunitactsasacommercialbankandusesliabilitiestoexpanditsbalancesheetbypurchasingtheassets.

Theliabilityunitobtainsdeposits D jtB

1+^ hwithaninterestrateRtdandforeigndebts B*

jt^ hwithaninterestrateR*t .Thentheysellliabilities(Ljt)toan

operationunitwithaninterestrateRtL.However,toobtaintheforeigndebts,

bank faces a convex adjustment cost, LB

2

*

b

jt

jt2

xj-e o .j is a desire level of

foreigndebttoliabilitiesratio.Itcoststotheliabilityunitifthestructureofdebtoverthedesiredlevel.Thepurposetointroducethisfrictionistowedgebetweenadomesticinterestrateandforeigninterestrate.

Theliabilityunitmaximizationproblemisspecifiedasfollows:

(2( ) )max E R L R D R B LB

,, 1 1

* *

*

2

0D Bt

it t i t

Ljt t

djtB

t jtb

jt

jt

i1 1*

jtB

jt

bx

jK - - - -3

+ + +=+ +

/ (6)

subjecttotheliabilitiesconstraintgivenby

L D B1 1 1

*

jt jtB

jt= ++ + + (7)


Theliabilityunitchoosesoptimaldepositstomaximizetheirprofitasfollows:

R R LB

LB

1 1

1

1

*

1

2

1

*

tL

td

bjt

jt

jt

jtx j- =- -+ +

+

+

+

+^ê

^êh

h ohh o (8)

The liabilityunitchoosesoptimalforeigndebts tomaximize theirprofitasfollows:

R R LB

LD

1 1

*

1

1

*

1

2

1

tL

t bjt

jt

jt

jtB

x j- = -+ ++

+

+

+^ê

êhh o

h o (9)

Dividing equation (8) by equation (9), we get the return to liabilities as follows:

R R LD

R LB

1 1

1

1

1

*

1

1

*

tL

td

jt

jtB

tjt

jt= ++ +

+

+

++

+e eo o (10)

Notethatthereturnonliabilitiesisasumaverageoftheinterestrates.

The operation unitmaximizes the expected terminal values of networth.LetNjtbetheamountofnetworththattheintermediaryjholdsattheendofperiodt,Ljt + 1betheliabilitiescomposingofdomesticdeposits D 1jt

B+^ h

andthenon-contingentdebts B 1

*

jt+^ hthatbanksissuetointernationalfinancialmarkets,Zjt be the quantity of financial claims on non-financial firms thatbankshold,andQtdenotestherelativepriceofeachclaim.Therelationshipbetweenassetsandliabilitiesofbalancesheetoffinancialintermediaryjattimetisgivenby

Q Z N L 1t jt jt jt= + + (11)

The Ljt + 1 can be thought as the intermediary’s debts andNjt as its equity capital.ThebankassetsearnthestochasticreturnR 1t

K+ overthisperiod.Note

thatbothR 1tK+ andR 1t

L+ aredeterminedendogenously.

Over time, the financial intermediary’s net worth evolves as the difference between earnings on the assets and interest repayments on its liabilities,whichisgivenby

N R Q Z R L1 1 1 1jt tK

t jt tL

jt= -+ + + +^ ^h h

R R Q Z R N1 1 1tK

tL

t jt tL

jt= - ++ + +^ h (12)


The growth of networth above the riskless return is increasing in the totalquantityofassets,QtZjt,anddependsonthe interestratepremiumR R1 1tK

tL-+ +^ h.Whenthebankersreceiveapaymentonitsassets,herepaysto

thelenders.

Let ,i

t t 1bK + denotethestochasticdiscountfactorthatthebanker,att,appliestotheearningsatt + i.Inordertosetanincentiveforthefinancialintermediarytoengageinfinancialintermediation,theriskadjustedinterestratepremiummustbepositiveatalltimesandgivenasfollows:

0E R R, 1 1 1t ii

t t i t iK

t iL $bK -+ + + + + + +^ h , 0i $ (13)

The rational bankerwill not fund the assets if a discounted return lessthanthediscountedborrowingcost.Underperfectcapitalmarkets,thisrelationship always holds at equality, the risk adjusted premium is zero. However, with imperfect capital markets, the premium must be positive duetolimitsonthebank’sabilitytoreceivefunds.Aslongastheincentiveconstraintalwaysholds,thebankerskeepbuildingassetsuntiltheyexitfromthefinancialsector.Thefinancialintermediaryusesthehousehold’sdiscountfactor,sinceitisownedbythelatter.Thismotivatesthefinancialintermediary’sobjective tomaximize the terminal values of the net worth which can be carriedovertothehouseholdattheendofitslifetime.

Formally,thebankers’maximizetheexpectedterminalwealth,givenby

1maxV E N0

1, 1 1jt

Zti

i it t i jt i

jt

{ { b K= -3

=

++ + + +^ ^

^h h

h/ (14)

withN R R Q Z R N1 1 1 1jt i t iK

t iL

t i jt i t iL

jt i= - ++ + + + + + + + + + +^ h

Givenapositiveinterestratepremium,E R R, 1 1 1t ii

t t i t iK

t iLbK -+ + + + + + +^ h,

thefinancialintermediarywantstoextenditsassetsindefinitelybyborrowingadditionalfundsfromthefinancialmarkets.Insodoing,wefollowGertlerandKaradi(2011)byadoptingamoralhazardproblembetweeninternationalinvestorsanddomesticbanksmotivates to limit theborrowingbehaviorof the bankers. Specifically, at the beginning of the period the banker has a possibility to divert the fractionmt of available funds from theproject andtransfersthembacktothehouseholdthatheorsheisamember.Thecosttothe banker is that lenders can force the intermediary into bankruptcy and


recovertheremainingfraction(1 - mt)ofassets.However,itistoocostlyforthelenderstorecoverthefractionofassetsthatbankerhaddiverted.

The lender iswilling to supply the funds into thebanking system, ifthefollowingincentiveconstraintholds:

V Q Zjt t t jt$ m (15)

Onlyifthevalueofthebankerontheleftishigherthanthevaluetodivertfundsontheright,thelendersareinsuredthattheywillnotgoingtobedefrauded,andcontinuallylendtheircapitaltothedomesticbanks.Theleftiswhatbankerswouldloseiftheydiverttheassets,whereastherightisthegainindoingso.Withaprofitmaximizationobjective,thebankerswillexpandtheassetsup to thepoint that the incentivecompatibilityconstraint isbinding,andiftheinterestratepremiumisalwayspositive.

The solution of the bank operation maximization problem can be expressedinthefollowingform:

V l Q Z n Njt t t jt t jt= + (16)

with

1l E R R x l, 1 1 1 , 1 , 1 1t t t t tK

tL

t t t t t{ b b {K K= - - ++ + + + + +^ ^h h" ,

1n E R z n, 1 1 , 1 , 1 1t t t t tL

t t t t t{ b b {K K= - ++ + + + +^ ^h h" , (17)

where x Q Z Q Z, 1 1 1t t t jt t jt=+ + + is the gross growth rate of the assets from period t to t + 1, and z N N, 1 1t t jt jt=+ + is thegrossgrowth rateof thenetworth.Theltdenotestheexpectedmarginalgainsofhavingadditionalassetgiventhenetworthbeingconstantandntistheexpectedvalueofthebankofhavingadditionalunitof thenetworthgiven theassetbeingconstant.Thevalueofltisrelatedtothepositiveinterestratepremiumconstraint.Withthefrictionlesscompetitivecapitalmarkets,thebankwillexpandborrowinguptothepointthattherateofreturnwilladjustuntillt iszero.Thus,theagencyproblemthatisintroducedmayputlimitsonthisarbitrage.

Iftheincentiveconstraintisbinding,itcanbeshownthattheinterme-diary’sassetsareconstrainedbyitsnetworth.Theincentiveconstraintcanbeexpressedasfollows:


l Q Z n N Q Zt t jt t jt t t jt$ m+ (18)

Givenabindingconstraint,theassetholdingbyfinancialintermediariescanbeexpressedinthetermofnetworthpositionasfollows:

Q Z ln

Nt jtt t

tjtm

=-

c m (19)

GivennetworthNjt beingconstant, an increase in assetquantityZjtwouldbreak this balance and raises an incentive for the banker to divert funds. Rearranging thepreviousequationyields thebank j’s leverage ratioas therelationoftheassetoverthenetworth,givenby

Q Z Nt jt t jtz= (20)

with

ln

tt t

tz

m=

-

whereztistheratioofassettocapital,whichreferstotheindividualfinancialintermediary’sleverageratio.Thisconstraintlimitsbank’sleverageratiotothepointwherethebankerhasincentivetocheatexactlybalancedbythecost.Hence,theagencyproblemleadstoanendogenousconstrainedbank’sbalancesheets(thenetworth)toacquiremoreassets.

Theassetdivertingprocessisincreasinginthenetworthandassetsgrowths, but decreasing in the leverage ratio.We can think that the bank diverts the fraction of assets for a personal purpose (e.g. payout a large bonus),whichcanbewritteninthefollowingfrom:

n l

tt

t t tm

z

z=

+ (21)

Given 0Njt 2 , the constraint isbindingonly if0 lt t1 1 m . In thisinstance,itisprofitableforthebankertoexpandassetssinceltisgreaterthanzero.Thelarger is lt, thegreater is theopportunitycost to thebankerfrom beingforcedintobankruptcy.Thisisbecauseofanincreaseintheassetgrowthandopportunitytodivertassetstosatisfythebanksmaximizationproblem. Ifltrisesabovemt,theincentiveconstraintdoesnotbind,thepresentvalueofthebankalwaysexceedsthegainfromdivertingfunds.


Thenetworthevolutioncanberearrangedinthefollowingform:

N R R R N1 1 1 1jt tK

tL

t tL

jtz= - ++ + + +^ h6 @ (22)

Regarding to equation (20), the leverage ratio is specified by a non-firm- specificcomponent.Thisallowsustoobtaintheaggregatedemandforassetsand the aggregate net worth of the financial system by summing over all individualsasfollows:

Q Z Nt It t Itz= (23)

withztdenotestheaggregateleverageratiointhebankingsector,ZItistheaggregatedemandforanassetquantity,andNItistheaggregatenetworthofthebankingsystem.

Wecanderiveanequationofmotionforthenetworthofthebankingsystem, byfirst recognizing that it is the sumof the networth of existing bankers(Net)andthenetworthofenteringbankers(Nnt).Itcanbeexpressedasthefollows:

N N Nt et nt= + (24)

Sincethefraction{ofthebankersatperiodt - 1surviveuntilperiodt,thenetworthofexistingbankersisgivenby

N R R R N1 1et tK

tL

t tL

t{ z= - +- -^ h6 @ (25)

It canbe observed that themain source of variation inNetwill be fluctuationsintheexpostreturnontheassetRtK.Inaddition,thenetworth(Net) is increasingintheleverageratio(zt).Theenteringbankersreceiveatransfer from their family as a start up value, which is equal to fraction

1~ {-^ h of value of assets 1 Q Z1 1t t{- - -^ h that exited bankers had transferredout in theirfinaloperatingperiod.Thus, in theaggregate level, afractionofnewenteringbankerscanbewrittenas

1 1N Q Z Q Z1 1 1 1nt t t t t{~

{ ~=-

- =- - - -^^

hh (26)

Combiningequation(25)andequation(26),onceyieldsthefollowingequationofmotionfornetworth:

N R R R N Q Z1 1 1 1t tK

tL

t tL

t t t{ z ~= - + +- - - -^ h6 @ (27)

Notethat~helpspinningdownthesteadystateofleverageratioQZ/N.


2.3 Non-financial firms

Next,weturntotheproductionandinvestmentsidesoftheeconomy.There are competitive non-financial firms engaged in the production of a singletradableretailgoodwhichservesasanumeraire.Producerscombinecapital and labor into theCobb-Douglas production function to produce a finalconsumptiongood,whichisgivenby

Y A K H1t t t t tp= a a-^ h ,0 11 1a (28)

whereKtisthecapitalstockandHtdenotesthelaborinput.Thetotalfactorproductivity and the capital quality shocks are assume to followanAR(1)processasfollows:

ln lnA A 1 ,t A t A tt f= +-^ ^h h (29)

ln ln 1 ,t t tp t p f= +p p-^ ^h h (30)

withEt(At)=1and, . . . 0,i i d N,2

A t A+f v^ h, 1Et tp =^ h and . . . 0,i i d N,2

t +f vp p^ h.

Following Gertler and Karadi (2011), the capital quality shock pt providesanexogenoussourceofvariationinthecapitalvalue.Inthecontextofthemodel,itcorrespondstoeconomicdepreciationofcapitalsothat(ptKt)isaneffectivecapitalquantityatperiodt.Thecapitalqualityshockcausesthedevaluationofbank’scapitalanddeterioratesthebalancesheet.Thus,banksfaceafinancialdistressconditionandeventuallythecrisis.

Whenoutputsareavailabletothefirmsattheendoftheperiod,thewagebill (WtHt)willbepaid to thehouseholds.Firmshaveoptions toselldepreciatedcapital(1 - d)KttothecapitalproducersattheunitarypriceofQt and the new capital stockKt + 1 is purchased for production in subsequent period.The firms finance its capital acquisition each period by borrowingfunds from the financial intermediaries. To acquire the funds to purchase capital,firmsissueclaimsZjtwhichisequaltothenumberofunitsofcapitalKt + 1, and price each claim at a unit price of capitalQt. The relationship betweenthevalueofcapitalacquiredandthevalueofclaimsagainstcapitalisgivenby

Q Z Q K 1t jt t t= + (31)


Thisconditionequatesthepriceofaunitofcapitaltothepriceoffinancialclaim.Thearisingequitycontractbetweenthefinancialintermediaryandthenon-financialfirmyieldsthegrossinterestrateRtK.ThisimpliesthatfirmswillpayR Q Z 1t

Kt jt-^ h, a zero profit condition in the non-financial sector, to the

bank.Assumingthatthereisfrictionlessbetweenthiscontractswhichisanunderlyingassumption,theintermediarieshaveperfectinformationaboutthefirmsandhavenoproblemenforcingpayoffs.Thus,firmsofferaperfectlystate-contingent debt to financial intermediaries, best interpreted as firms’ equity. However, since banks suffer from the agency problem in financialmarkets, physical capital purchases are indirectly affected through this constraint. Within the model, only financial intermediary faces capital constraints to obtain funds and, these constraints affect the supply of fundsavailabletonon-financialfirms.Therequiredrateofreturnoncapitaleventuallyrises.

Afirmprofitmaximizationproblemyieldsthefollowingoptimalcon-ditionsforfactorsdemand:

1 HY

Wt

tta- =^ h (32)

1

E R Q

E KY

Q1

11 1

11

t tK

t

t tt t

ttp a

pd

=

+ -

+

++ +

++^ ^h h; E' 1

(33)

The labor demand equation (32) shows that the marginal productivity of laborequal to thewage rate.Thecapitaldemanddependson themarginalproductivityofcapitalandcapitalgains.

2.4 Capital producers

The capital producers are set alongwithBernanke et al. (1999) todetermine thevariation in theendogenouspriceofcapital. Inaddition, thecapitaladjustmentcostsareadded into thesmallopeneconomymodels toreducetheinvestmentvolatility.

Thereisacompetitivesectorofidenticalcapitalproducerswhichisowned by the households. At the end of period t, a competitive capital


producer buys depreciated capital from firms at price Qt and quantities of capital stock 1 Kt td p-^ ^h h. The investment amount It yields the gross newlybuiltcapital I K Kt t tU^ h .Onlynet investment issubject toquadraticadjustmentcosts,whichisgovernedbyafunction I Kt tU^ hwith,thesteadystate d dU =^ h .Thecapitalproducerscombineaquantityofcapitalandnewinvestment,It,withalineartechnologytogetcapitalKt + 1.ThentheysellthenewlyproducedcapitalstockKt + 1tonon-financialfirmswithacompetitivepriceQtperunitofcapital.

Thecapitalproducersprofitmaximizationproblemisgivenby

(1 ) ( )Max E Q K Q K I,

, 10I K

ti

t t i t i t i t i t i t i t ii1t t

b d pK - - -3

+ + + + + + + +=+

6 @" ,

/ (34)

subjecttothelawofmotionofthecapitalstock

1K K KIK1t t t

t

ttd p U= - ++ ^ ^ ch h m (35)

with 2KI

KI

KI 2

t

t

t

t K

t

txdU = - -c cm m; E

The capital producers choose an optimal level of investment tomaximizeprofityieldstheTobinQequationasfollows:

1Q KI 1

t Kt

tx d= - -

-

c m; E (36)

The capital producers choose an optimal capital stocks tomaximize profityieldstheinvestmentdemandequationasfollows:

1I KI

K KI

11

11

1

11

tt

tt K

t

tx dU= - -+

+

++

+

+-

c ^ cm h m; E (37)

where 0K 2x isthedegreeofcapitaladjustmentcosts.Themeaningofassetpriceequationisthatcapitalproducerssellcapitalatpriceequaltoadjustmentcost.

2.5 Closing the model

Finally, the exogenous processes for a foreign interest rate and itsshockneedtobespecified.Assumingthataforeigninterestratedependsonalast-periodforeigninterestrateanditsshock,whichisgivenby


R R*1

*,t R t R t* *t f= +- (38)

Themarketclearingconditionsforasmallopeneconomyaregivenby

Y C It t t= +

D D1 1tH

tB=+ +

L D B1 1 1

*

jt jtB

jt= ++ + +

3. The model analysis

3.1 Calibration

Table1liststhechoiceofparametervaluesforthebaselinemodel.Eleven parameters govern the steady state and six parameters govern the dynamics.Westartadiscussionabouttheconventionalparameters.Wesetadiscountfactorasanannualgrossrealinterestrateb=0.9926,implyingthatan annual realized interest rate is 3%.This parameter canbe computed as1.03 0.9926

0.25 =-^^ h h.Thedegreeofriskaversionisassumedtobev=0.2which is, consistent with the evidence of low sensitivity of expected consumptiongrowthtorealinterestrates.visassumedtobe3.0303,implyingthattheelasticityoflaborsupplyishigh.|issettobe1,implyingthatthereisnoscalingdisutilityoflaborsupply.Theprobabilityofbankssurvivingintothenextperiodissettobe{=0.979whichiscloseto1.Thisimpliesthatbanksaredifficulttobebankruptcy.Thefractionofhouseholdstransferringtonewentrybankersissettobe~=0.005meaningthatonlyasmallamountoftheassetswillbetransferredintothebankingsystematthebeginningoftheperiod.The capital income share is assumed to bea = 0.35 implying that domestic firms are labor intensive in production. The depreciation rate of capitalcanbederived from theaverageannualdepreciation rateofcapitalstockoftheyear1970to2012basedon1988prices,theNationalEconomicsand Social Development Board. The average annual depreciation rate is4.17%whichisd=(0.042/4)=0.0105perquarter.

The technologyshockpersistence is set tobetA=0.80. It implies thatabout80%oftechnologyimprovementfromthelastperiodaffectstheproduction in the current period.According toGertler andKaradi (2011), the initial decline in capital quality shocks is fixed at five percent and the


autoregressive factor istp = 0.66.Absent any changes in investment, theshocksgenerateroughlyatenpercentdeclineineffectivecapitalstocks.Thatisthesourceoffinancialcrisisisadeclineinassetvaluesasopposedtothephysicalcapitaldestruction.Theforeigninterestrateshockpersistenceissettobet~=0.80.Itimpliesthatabout80%offoreigninterestratefromthelastperiodaffectsthecurrentinterestrate.

Table 1Parameters

Household Value Assigned Description

b

v

o

|

0.99260.203.0303

1

DiscountfactorDegreeofrelativeriskaversionTheelasticityoflaborsupplyDisutilityweight

Financial intermediary

{

x

j

~

0.9790.0042

10.005

ProbabilityofbankersurvivalPortfolioadjustmentcostDesirelevelofdebtratioFractionofnewentrytransfer

Non-financial firm

a

d

xK

0.350.01050.028

ShareofcapitalincomeCapitaldepreciationrateCapitaladjustmentcost

Dynamic parameters

tA

tp

ts

tx

ly

lx

0.800.660.80(-5,5)0.50.1

PersistenceoftechnologyshockPersistenceofcapitalqualityshockPersistenceofforeigninterestshockDegreeofresponsivenessPreferenceoveroutputPreferenceoverpolicychange


3.2 Experiment

The experiment is set to a downturn economy with a negative technologyshockbyonepercentofstandarddeviationandanegativecapitalquality shock by five percent of standard deviation.The first orderTaylor approximationisusedinapproximationprocess.ThemodelissimulatedbyusingDynare.Theimpulseresponsefunctionshowninapercentagechangeofdecimalpointandtimingisusedwithquarterlydata.

Anegative shockof technologybyonepercent standarddeviationwithautoregressivefactor0.80dampenssignificantlythedomesticeconomy,theoutputand inputdemandsdropsharply.This leadsweakens thebank’sbalancesheet.Specifically,theleveragerisesimmediately,whilethenetworthandcapitaltoassetsratiosignificantdeclineasshownintheFigure1.

Theinitialtechnologyshockinducesasharpcontractionofoutputsby 0.01 percent.A drop in productions induces a reduction of labor and investment demands, so the return to capital declines. The nominal wage decreasesabout0.01percent.Areductioninthenominalwageleadsfurther adeclineinhouseholdconsumptionabout0.015percentpoint.Asthereturntocapitaldeclines, thehouseholdoptimal savingsdecisionby increasingadepositintothebank.Inthefinancialsector,areductioninspreadsleadstoareductionofliabilitiesdemandedbythebankbecausethebankshaveahighborrowing cost and less expected profits. Therefore, the net worth drops dramatically,whereastheleverageandtheassetriseimmediately.Itinduces a significant drops capital to assets ratio. The high leverage of the bank incorporatingwithlowcapitalofthebankleadstoahighriskandthebank’sbalance sheet weakening. Thus, the banking sector will face a financial distress condition and, if they borrow external funds, they will face high externalfinancialcosts.Thesecondeffectloopwillstartwhenbanksfaceadistressconditionandahighexternalfinancepremium.Finally,theimpactsonbothfinancialactivityandrealactivitybecomemoreseverebecauseofasharpcontractionintheaggregateoutputandinvestment.


Figure 1 ANegativeTechnologyShock


Figure 2 ANegativeCapitalQualityShock


Anegativecapitalqualityshockbyonepercentofstandarddeviationwithautoregressive factor0.66 inducesasharpcontractionof theeffectivecapitalquantity.Itleadsfurthertoasignificantdropintheaggregateoutputand investment immediately. The shock contracts outputs by about 0.01 percent,whilethecapitalstockandinvestmentdemanddropby0.03percent.A reduction inoutputs inducesadecline in the labordemandandnominalwage.Asignificantdropininvestmentdemandinducesadeclineinthereturntocapitalandassetprice.Areductionintheeffectivecapitalquantityleadstoafurthercontractioninthenetworthandcapitaltoassetsratio.Adeclineincapitalinducesahighleverageofthebankandadropinspreadsandassets.Itleadstoafurtherdecreasefurtherinprofitsandnetworth.Sothebanksfacebalancesheetconstraintandthefinancialproblemarises.Thisisaroughwayto introduce a banking crisis into themodel. The second impacts becomemoreseverewhenbankshaveabalancesheetconstraintandhighleverage.Thisamplifiestheeffectsoffinancialproblemtotheeconomy.

3.3 Capital requirement

Withinthisframework,therearetwomotivesofthecapitalrequire-ment that aim to encourage banks to increase the quality and quantity of capitalandtodiscouragethemtoextendmoreriskyassets.Asassetpricesaffect theborrowingconstraintsandbalancesheet, thereexistsapecuniaryexternalitythatbanksdonotproperlyinternalizewhentheymakedecisionsontheirbalancesheetstructure.Theparticipantstakeassetpricesasgivenandsince the asset price is determinedby an aggregate level. In the aggregatelevel, their joint behavior determines asset prices and, by implication, the extent of balance sheet effect and the degree of financial fragility in the economy.Inparticular,theyinducebankstoraisetoomuchdebt,suchastopurchaseexcessivelyshortmaturityassetsandthusthebankstakeexcessiverisk. In this sense, financial fragility is uninternalized by the product of externalfinancemadebyindividualinstitutions.

For policymakers, if we impose Pigouvian taxes or regulation to an individual institution to realize theexternality thathecontributes to the financialsystem.Asaresult,thedecentralizedmarketequilibriumisefficientandmakeseverybody in theeconomybetteroff.Anumberofpapershave


emphasizedthisexternalitytointroducetheimpactofregulation,taxationandsubsidies to the banks’ balance sheetswhich finally reward the networth.(DiamondandRajan(2009)Korinek(2011)andJeanandKorinek(2013)).

Inthismodel,thecapitalrequirementisaregulatorypolicyimposedto thebank’sbalancesheet toreducethefinancialexternalityandsystemicrisk,butrewardsthenetworth.Anincreaseinthetotalnetworth(equity)tothetotalassetratioimpliesanincreaseinthecapitalrequirement.Inparticular,wesupposethatthegovernmentsubsidizesbanks tsx perunitofnetworth.Thesubsidyisfinancedbyataxonanincrementoftotalliabilities.Asregulatorsimposethecapitalrequirement,theflowoffundsconstraintforthebankisnowgivenby

1N R Q Z R L1 1 1 1t tK

t t ts

tL

tx= - ++ + + +^ ^h h (39)

Thenetworthevolutionbecomes:

1 1N R R Q Z R N1 1 1 1t tK

ts

tL

t t ts

tL

tx x= - + + ++ + + +^^ ^h h h (40)

with

1 1l E R R x l, 1 1 1 , 1 , 1 1t t t t tK

ts

tL

t t t t t{ b x b {K K= - - + ++ + + + + +^ ^^h h h" ,

1 1n E R z n, 1 1 , 1 , 1 1t t t t ts

tL

t t t t t{ b x b {K K= - + ++ + + + +^ ^^h h h" ,

Thecapitalrequirementissetinrespondingtothecapitalrequirementinthesteadystateandthedeviationfromtheaggregatecreditlevelasfollows:

ln QZQ Z

ts

ssss

t tx x t= + x c m (41)

wheretheparameterxssdenotesthesteadystateofcapitalrequirement.QtZt denotes aggregate of credit andQZss is the steady state level of aggregatecredit.Theparameter 5,5!t -x

^ histhedegreeofresponsivenessofcapitalrequirement.

The performance of capital requirement can be determined by theeconomicloss.Thelossfunctiondependsonunconditionalvarianceofoutputandthetermofpolicychangeasfollows:

L 2 2cap y yl v l v= + x xD (42)


where y2v is theasymptoticunconditionalvariancesofoutputand 2v xD is the

variancesofthecapitalrequirementchanges,respectively.lyisaweightofpolicymakers’preferenceonvariancesofoutputandlxdenotesaweightofpolicymakersonvariancesofcapitalrequirementchanges.Theleastvalueoflossfunctionisthebestpolicyperformance.

Anegativetechnologyshockinducesacontractioninthenetworthandweakensthebalancesheet.Itleadsfurthertoafinancialdistressconditionand a significant drop in investment. Introducing capital requirement in respondingtotheassetgrowthdeviatingfromitssteadystateaffectsdirectlythebank’sbalancesheet.Anincreaseincapitalrequirementbyonepercentofitssteadystatelevelwiththelowerdegreeofresponsiveness(tx=1.5)totheassetgrowthinducesanincreaseintheleverageratioandassetgrowth.Thecapital requirement increases the costs to the financial intermediaries for additionalexternalfunds,thereforethespreadsdecline.Thisreducesfurtherthedemandforliabilities.Thecapitalrequirementacceleratesthenetworthgrowthwhichinduceslateranimprovementofnetworthandbalancesheet.Inaddition,thecapitalrequirementreducesthebanker’sincentivetodivertmore assets for their personal purposes. However, the capital requirementdoesnotaffectrealactivities.Theimpactsofthetechnologyshockonoutput,investment, and consumption aswell as inputs demand remain unchangedfromthebaselinemodel.

The negative capital quality shock affects the economy through a reductionof effective capital quantity and therefore output and investmentcontractsharply.Areductioninvaluesofcapitalandassetsleadstoadeterio-ration of the bank’s balance sheets. Banks face a higher external finance premiumandthusincreaselendingrates.Thisinducesfirmstocutbackallinvestmentprojects.Thebalancesheetconstraintandhighleverageamplifythe impacts of financial problem on the economy. Introducing the capital requirement with more aggressiveness (tx = 3.5) in response to the assetgrowththatdeviatesfromitssteadystatelevelis themosteffectivepolicy.Thecapitalrequirementchangesthebankbehavior.Thatis,itreducesbankleverageby0.1percentandleadstoadropinassetgrowth.Itincreasesthespreadsbyover0.05percent.Itincreasesthebanknetworthbyabout0.05percentandimprovesthebank’scapitaltoassetsratio.Finally,itstrengthensthebank’sbalancesheetandreducesthefinancialdistresscondition.


Figure 3 CapitalRequirementandTechnologyShock

Figure 4 CapitalRequirementandCapitalQualityShock


The negative foreign interest rate shock by five percent induces a contractionintheliabilitiesdemandbecauseadropinthereturntoliabilities.Itleadsfurtherareductionintheassetgrowthandleverage.Areductionin theassetgrowthandleverageinduceadeclineinthenetworthgrowthanddeterioratethebank’sbalancesheet.Banksfurtherfaceahighexternalfinancepremium and thus increase the lending rates.This leads firms to cut back an investment. Introducingacapital requirementwithmoreaggressiveness(tx=5)inresponsetotheassetgrowthisbeneficialtothebanks.Thecapitalrequirementstabilizesthebank’sleverage.Thatis,itincreasesthebank’snetworth by 0.01 percent and the spreads rises over 0.02 percent. Finally, an aggressive capital requirement rewards the capital to asset ratio.Thus, thebanks’capitalrisesandreducesfinancialdistresscondition.Inaddition,wefind that thecapital requirement regulationaffects to thebankers’behaviorandtheirbalancesheets.

Figure 5 CapitalRequirementandForeignInterestShock


Theperformanceofthepolicycanbedeterminedbytheabilityofthepolicyinstabilizingthebankbalancesheet.Toachievethisobjective,wevarythepolicychoiceagainstassetgrowthandfindthedegreeofresponsivenessthatcanstabilizethevalueoflossfunctionandbalancesheetvariables.Thefinancialprobleminducesahighvariationofnetworthandleverageratio.

Table 2 TheImpactofCapitalRequirement

Shock Capitalrequirement0.5yl = , 0.1l =x

L 2 2cap y yl v l v= + x xD

Loss 2yv

2v xD2NWv

2vz

Technologyshock 0,5!tx ^ h 0.0040 0.0080 0.000 0.0086 0.000

Capitalqualityshock . , .0 5 2 5!tx ^ h 0.0026 0.0052 0.0002 4.4106 0.0003

Foreigninterestshock 5!tx ^ h 0.0000 0.0000 0.0000 0.0000 0.0000

Source:Author’sCalculation

Thevariancesofoutput,policychanges,networthandleverageratio,respectively,areshowninTable2.Specifically,thecapitalrequirementislesseffective in response to the technology shock because varying the policy parameter does not reduce the loss function and variance of net worth. However,theresponseofcapitalrequirementtothefinancialshockismoreefficient.Thatis,lessdegreeofresponsivenessofcapitalrequirement(tx=0.5) totheassetgrowthgeneratestheminimumvaluesoflossfunction.Also,ithelpsstabilizingthebankbalancesheetandgeneratestheminimumvarianceofnetworthandleverageratio.

4. Conclusion and remarks

The objective of this paper is to investigate the impact of capital requirement inresponse to theshocks,whichdampensdowntheeconomy.Also,weaimtofindhowit improves thebank’sbalancesheet.Anegativeshockoftechnologyhasasignificantnegativeeffectonthedomesticeconomy,particularly,adropintheoutputandinputdemandsharply.Thisleadstothe


bankbalancesheetweakening.Theleveragerisesimmediately,whilethenetworth and capital to assets ratio significantlydecline.Hence, banks face a financialdistresscondition.Anegativecapitalqualityshockinducesasharpcontractionoftheeffectivecapitalquantity.Itdecreasesanaggregateoutputand investment immediately. The significant drop in investment demand inducesadecline in thereturn tocapitalandassetprice.Areduction inan effectivecapitalquantityleadstoafurthercontractioninthenetworthandcapitaltoassetratio.Adeclineincapitalinducesahighleverageofthebankincorporatingwithadropinspreadsandassets.Itleadstoadecreasefurtherinprofitsandnetworth.Sobanksfacebalancesheetconstraintandthefinancialproblemarises.Thecapitalrequirementisefficientinresponsetothefinancialproblem.Itincreasesthebanknetworthandreducestheleverageratio.Finally,alessaggressivepolicygeneratestheminimumlossandstabilizesvariationofnetworthandbankleverage.Ahighdegreeofresponsivenessisrequiredifauthorities aim to accelerate a networth accumulation and overcomes thebankingcrisis.However,thecapitalrequirementislesseffectiveinresponsetothetechnologyshock,sothecapitalrequirementcannotstabilizenetworthandbalancesheetinthiscase.

References

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Gertler,M.,&Karadi,P.(2011).Amodelofunconventionalmonetarypolicy.Journal of Monetary Economics,58(1),17-34.

Gertler,M.,Kiyotaki,N.,&Queralto,A.(2012).Financialcrises,bankriskexposure and government financial policy. Journal of Monetary Economics,59,17-34.

Jeanne,O.,&Korinek,A.(2013).Macroprudentialregulationversusmoppingup after the crash. Working Paper 18675, National Bureau of EconomicReasearch.

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