The effectiveness of TARP-CPP on the US banking industry: A new copula-based approach

ContentslistsavailableatScienceDirect

European

Journal

of

Operational

Research

journalhomepage:www.elsevier.com/locate/ejor

Interfaces with Other Disciplines

The

effectiveness

of

TARP-CPP

on

the

US

banking

industry:

A

new

copula-based

approach

Raffaella

Calabrese

a,∗

,

Marta

Degl’Innocenti

b

,

Silvia

Angela

Osmetti

c

a_{TheUniversityofEdinburghBusinessSchool,UnitedKingdom} b_{UniversityofSouthampton,UnitedKingdom}

c_{Università CattolicaMilano,Italy}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received1September2015 Accepted21July2016 Availableonlinexxx Keywords: Binarydata D-vinecopulamodel Banking

TARP-CPP Failure

a

b

s

t

r

a

c

t

Followingthe 2008 financialcrisis,regulatory authorities and governmentsprovided distressed banks

withequityinfusionsinordertostrengthennationalbankingsystems.However,theeffectivenessofthese interventionsforfinancialstabilityhasnotbeenextensivelyresearchedintheliterature.Inorderto un-derstandtheeffectivenessofthesebailoutsforthesolvencyofbanksthispaperproposesanewmodel: theLongitudinalBinaryGeneralisedExtremeValue(LOBGEV)model.Differingfromtheexistingmodels, theLOBGEV modelallowsus toanalysethetemporalstructure ofthe probabilityoffailureforbanks, forboththosethatreceivedabailoutandforthosethatdidnot.Inparticular,itencompassesboththe flexibilityoftheD-vine copulaandtheaccuracyofthegeneralisedextremevaluemodel inestimating theprobabilityofbankfailureandofbanksreceivingapprovalforcapitalinjection.Weapply thisnew

modeltotheUSbankingsystemfrom2008to2013inordertoinvestigatehowandtowhatextentthe

TroubledAssetReliefProgram(TARP)-CapitalPurchaseProgram(CPP)reducedtheprobabilityofthe fail-ureofcommercialbanks.Wespecificallyidentifyasetofmacroeconomicandbank-specificfactorsthat affecttheprobability ofbankfailureforTARP-CCPrecipientsand forthosethatdidnotreceivecapital

underTARP-CCP. Ourresultssuggest thatTARP-CPPprovidedonlyshort-termreliefforUS commercial

banks.

© 2016ElsevierB.V.Allrightsreserved.

1. Introduction

Monitoring and evaluating banking stability is an important

and reoccurringtheme on the agenda of policy makers. A

num-ber of recent influential studies have contributed to the

analy-sis of systemic banking crises in the operational research

liter-ature (see for a literature review Kumar & Ravi, 2007, Fethi &

Pasiouras,2010, Demyanyk & Hasan,2010,Ioannidis, Pasiouras,& Zopounidis,2010).Thesestudiesondistressedbanksdevelop

mod-els that detect risky banksprior to failure. They alsoattempt to

identify banksforwhich regulatory authoritiesmay haveto take

correctiveactions (DeYoung &Torna, 2013). However, little

atten-tionhasbeendevotedsofartotheanalysisoftheeffectivenessof

bailoutsforthestabilityofabankingsystem.Anunderstandingof

this subjectisimportant inorder tominimise the costof failure

andrescueforstakeholdersandtaxpayers.

∗ _{Correspondingauthorat:TheUniversityofEdinburghBusinessSchool,29}

Buc-cleuchPlace,EdinburghEH89JS.Tel.:+441316508074.

E-mailaddresses:[email protected] ,[email protected] (R.Calabrese),

[email protected] (M. Degl’Innocenti),[email protected]

(S.A. Osmetti).

Atpresent,thisissueisofgreatconcernforpolicymakersand

researchersbecause ofthe peculiaritiesofthe 2008 financial

cri-sis.Comparedtothepast,thefinancialcrisis ledtoextraordinary

policyinterventionsintermsofboththerangeofpolicymeasures

adopted,thespeedandscaleoftheinterventions,andthe

imple-mentation of those resolutions (Laeven & Valencia, 2010).

Start-ing from the onset of the financial crisis, US and EU regulatory

authoritiesor governments bailed-out numerouscommercial and

investment banksin order toreduce the fragility ofthe banking

systemandto restoreconfidenceinthe financialmarkets. During

thistime, severalfinancial institutionsfailed.These eventsled to

a proliferation ofnew studies on the determinants andthe

con-sequences ofbank failures andbailouts (e.g. Demyanyk & Hasan,

2010, Dam & Koetter, 2012, Bayazitova & Shivdasani, 2012, Cole & White, 2012, Berger & Bouwman, 2013, Calderon & Schaeck,

2016). Whilethe availability ofgovernmentsafetynets andrapid

interventionpoliciescanhavebeneficialeffectsinresolvingcrises,

their use is not free fromcriticism. Implicit andexplicit

guaran-teescan strengthentheperception that big-banks willbe

bailed-outifthey findthemselvesinadistressedsituation,thus

encour-agingmoralhazardbehaviour(Hakenes&Schnabel,2010),thereby

decreasing the stability of the banking system. Consequently,

http://dx.doi.org/10.1016/j.ejor.2016.07.046

0377-2217/© 2016 Elsevier B.V. All rights reserved.

understanding whether regulatory interventions and capital

sup-portenhancebankingstabilityiscriticalforregulatoryauthorities

andpolicymakers.

From a statistical perspective, many relevant theoretical and

empiricalcontributionstothistopicemploytheuseoflogistic(e.g.

BayazitovaandShivdasani,2012,ColeandWhite,2012,Bergerand Bouwman,2013orprobit models(Croci,Hertig, & Nowak, 2015).

However,theuseofprobitandlogitlinkisnotappropriatewhen

modellingrare events.Ifwe classify the rare eventsasones, the

major drawback of these approaches is that they underestimate

theprobabilityofbinaryrareeventsforvaluesclosetoone,such

asbank defaultsor bail-outs(Calabrese& Osmetti, 2015;King & Zeng, 2001; Wang & Dey, 2010). To overcome this limitation, a

model has been proposed in the operational research literature

(Andreeva,Calabrese,&Osmetti,2016;Calabrese&Osmetti, 2013; 2015;Marra,Calabrese,&Osmetti, 2014)– theBinaryGeneralised

Extreme Value Additive model, BGEVA (GEVmodel in the

para-metricform).Thisapproachisparticularlysuitable forbinaryrare

eventsdata, i.e.when theobserved number ofones inthe

sam-pleisverylow.Inparticular,theBGEVAmodelhasbeenprovento

outperform the logistic regression model when predictingfailure

events,suchasbankandfirmdefaults.

This paper adds to the operational and banking literature by

proposinganewmodelthat enablesustomeasure the

effective-ness of bailout interventions for the financial stability of banks.

Specifically,theaimofthispaperistodevelopastatisticaltoolto

betteranalyseandmonitor(i)theprobabilityofdefaultdepending

onbailoutsovertime;and(ii)thetemporaldependencestructure

oftheprobabilityofthefailureofabank.

Fromamethodologicalviewpoint,thispapercontributestothe

operationalresearchliteratureinthreeways.First,weestimatethe

probability of bank distress and the probability of being bailed

outusing theGEV model. CalabreseandGiudici (2015) showthe

advantages of the GEV model in their study of distressed

Ital-ian banks. Second, we analyse the effects of a bailout over time

onabank’s probability ofdefault.Toachieve this, wedevelop an

extension of the GEV model for use with longitudinal data. We

callthisnewmodel theLongitudinal BinaryGeneralised Extreme

value (LOBGEV)model.Third, we employ the LOBGEV toanalyse

thetemporaldependencestructureoftheprobabilityoffailurefor

banksthateitherreceivedordidnotreceivead-hocbailouts.This

enablesustoanalysehowandtowhatextentbailoutswere

effec-tiveinreducingtheprobabilityofdefaultforbanks.

Several models have been proposed for correlated responses

(outcomes) in longitudinal data (see for example Arellano & Bo,

2001). For modelling the time dependence in longitudinal data,

inthispaperwechoosea copulaapproach,analogouslyto Smith,

Min, Almeida, and Czado (2010) and Meade and Islam (2010),

because it is a simple method to estimate multivariate models

whenthe marginal responses are given. Furthermore, the copula

approach is particularly suitable to model different kinds of

de-pendence structures. In addition, the copula approach has been

usedintheregressionframeworkforcontinuousanddiscretedata.

Forexample Koleva and Paivab (2009) use a bivariate copulato

modelthedependencebetweenerrors. Radice,Marra,andWojty´s

(2015) suggest a copula-based regression model for binary

out-comesusinga parametriccopula,such asClayton, Gumbel,Frank,

Joe and Student-t. Furthermore, Kraemer, Brechmann, Silvestrini,

andCzado (2013) propose a bivariate regression model for total

lossestimation by combining marginal generalised linearmodels

forcontinuousanddiscretevariableswithacopulaapproach.

In this paperwe consider a drawablevine (D-vine) copulaas

itis an extremely flexible representationof a multivariate

distri-butionthatusesbivariatecopuladensities(pair-copula) ina

hier-archicalapproach asin Smith et al.(2010) and Smith(2015). In

the D-vine copula approach, the multivariate probability density

function is decomposedinto pair-copulae that can be chosen

in-dependentlyfromeach other,generatinga lessflexible

multivari-atedependencestructure.Onthecontrary,themultivariatecopula

models largely used inthe literature, such as multivariate

Archi-median,Gaussian,Gumbel,ClaytonandJoe,havethesame

depen-dencestructureforeachpair-copulae.Moreover,theD-vinecopula

approachissuitable formodellinglongitudinaldataandto

repre-sentthedependencestructureovertime(Smith,2015;Smithetal.,

2010). Forall thesereasons, we usea D-vinecopulaapproach to

modelthe time seriesofthefailure probabilities, previously

esti-matedbyusingtheGEVmodel.WedefinethismethodasLOBGEV

model.

We apply the proposed methodology to the USbanking

mar-ket, which isa suitable caseforour analysisfor severalreasons.

StartingfromOctober2008,theUSTreasuryutilisedseveral

initia-tivesunder the TroubledAsset Relief Program(TARP) to stabilise

theUSfinancialsystem, tospureconomicgrowth,andto prevent

unnecessaryforeclosures.Inlinewithrecentstudies(seefor

exam-ple Bayazitova& Shivdasani,2012, Berger&Roman, 2015,Duchin &Sosyura,2014),wefocusontheCapitalPurchaseProgram(CPP),

thelargest bankbailoutprogrammeunder TARPlaunched by the

Treasury.

Under the TARP-CPP, the Treasury provided capital to 707

fi-nancial institutions in 48 states, a total investment of

approxi-mately $205 billion between October2008 and December 2009.

174 of thesefinancial institutions missedone ormore TARP-CPP

dividends,and29ofthemwentbankrupt.Moreover,manyofthe

smallbanksthatreceivedcapitalinjections(372outof656banks

benefitingfrompreferredstocksinvestments)werehesitanttoexit

the programme (Wilson, 2013), raising doubts about their

long-term viability. This means that there were banksthat failed

de-spitethefactthattheyreceivedcapitalinjections.Inaddition,from

September2008toSeptember2014morethan500bankswere

re-solved by the Federal Deposit Insurance Corporation (FDIC)1_{. We}

considerthisresolutionprocessasadefaultevent.

Froman empiricalviewpoint,thisis,tothebestofour

knowl-edge,thefirstpaperthat examinestheeffectivenessofthe

TARP-CPPprogrammeonthetemporalstructureofbanks’default

prob-abilities.Previouspapersmainlyfocusontheeffectsofthe

TARP-CPPontherisk-takingandmoralhazardbehaviourofbanks(Black

&Hazelwood,2013;Dam&Koetter,2012;Duchin&Sosyura,2014),

theperformanceofbanks(Crocietal.,2015),thedistortionof

com-petition in the US banking market (Berger & Roman, 2015), and

financial and stock price recovery (Liu, Kolari, Tippens, & Fraser,

2013).Sofar, Crocietal.(2015)istheonlystudythatcomparesthe

probabilitiesoffailureforbanksthatreceivedcapitalinjections

un-derTARP-CPPandforthosethatdidnot.Weextendthisliterature

byproposinganewmodeltoassessthetemporalstructureofthe

effectsgeneratedbycapitalinjection.Inthisanalysis,wefind

evi-dencethattheTARP-CPPprogrammehelpedbankstoreducetheir

defaultprobabilitiesintheshortterm.

Weorganisetherestofthepaperasfollows.Thenext section

reviewstheliteratureontheprobabilityofbankfailuresand

capi-talinjections.Followingthis,weproposea longitudinalmodelfor

binaryrareevents. Section4describesthedataandtheempirical

results,with Section5statinganddescribingourconclusions.

2. An overview of recent studies on banks’ bailout and failure

There is a growing amount of literature on the 2008

finan-cial crisis, specifically its effects on the US banking system. A

numberof thesestudies haveinvestigatedthe likelihood ofbank

1_{Retrieved from https://www.fdic.gov/bank/individual/failed/banklist.html ,}

failures in the US during and after the financial crisis (e.g. Cole & White,2012, Berger& Bouwman,2013, DeYoung&Torna,2013, Croci et al., 2015). These authors evaluate a bank’s performance

using the CAMEL(the acronyms standsfor Capital, Asset quality,

Management,Earnings,andLiquidity)modelthatiswidelyutilised

by credit rating agencies and regulators. Their findings suggest

that low assetquality (non-performingloans), highconcentration

ofbusinessorcommercialrealestateloans,illiquidity,cost

ineffi-ciency,rapidassetgrowth,dependenceonnon-coredeposit

fund-ing andbothlow profitability andcapitalisationarekey variables

inpredictingtheprobabilityofthefailureofabank.

Morerecentstudieshavefocusedontheprobabilityofreceiving

capitalinjectionsintheUSbankingsectorduringthefinancial

cri-sis.Forexample, BayazitovaandShivdasani(2012)analysethe

like-lihoodofabankreceivingCPPcapitalinjections.Theauthorsshow

thatwholesaledebt,Tier 1ratiocapitalandcommercialloansare

allfactorsthatcanpredictifabankparticipatesintheprogramme.

Theyalsopointoutthatlargebanksaremorelikelytoreceive

cap-ital underthe TARP-CPP. Croci etal. (2015) findthat commercial

andindustrialloans,creditrisk,non-performingloans,cost

ineffi-ciencies,goodwillandsizecanenhancetheprobabilityofreceiving

capitalundertheTARP-CPP.

Additionally, a numberof studies have focused on the effects

ofpolicyinterventionsforbanks.However,despitethisresearch,it

isnot stillentirelyclearhowandtowhatextent policy

interven-tions areeffectiveinensuringthestabilityofthebanking system.

Interventions may reduce the probability of insolvency in the

short-term, but they may also create a distortion of

competi-tion and provide incentives for misleading behaviour.In this

re-gards,recentpapers(e.g. Gropp,Hakenes,& Schnabel,2011,Black

& Hazelwood, 2013, Calderon & Schaeck, 2016) have shown that

bailouts can increase themoral hazard behaviour ofbankswhen

monitoringincentivesaredistorted.Inaddition, Berger,Bouwman,

Kick,andSchaeck(2014)demonstratethatbailoutscanleadto

in-appropriate loan pricingandthe granting ofloans to riskier

bor-rowers. Furthermore, Duchin and Sosyura (2014) point out that

banksincreasedtheriskprofileofboththeirlendingactivitiesand

their portfolio investments after being enrolled in the TARP-CPP

programme. Incontrast, Koetter andNoth(2015) findthathigher

bailoutprobabilitiesarenotassociatedwithmoralhazardofbanks,

butthatinstead,bankswithahigherlikelihoodofbeingbailed-out

engagedinlessriskybehaviour. BergerandRoman(2015)provides

evidence of TARP-banks increasing their market share and

mar-ket power relativeto non-TARP banks.More recently, Crociet al.

(2015) hasshown that bailing-out more banks would havebeen

cost-efficient andwould havereduced thenumber of banksthat

went throughthe FDICresolutionprocess. Sofar,this istheonly

paper that we aware ofthat hasanalysed the probability of

de-fault of banksthat received a bailout.The authors however still

makeuseoftheprobitmodelthat,asmentionedearlier,hassome

fundamentaldrawbacks.Giventhisevidence,itisclearthatthe

de-bateon theeffectsofbailouts onthe riskprofile ofbanksisstill

ongoing.Sofar, theimpactofpolicy interventionsonthe

depen-dencestructureofthedistressprobabilitiesofbanksovertimehas

beenoverlooked.Wethereforebridgethisgapbyproposinganew

model that estimatesthe influence of the capital injections over

timeonthedependencestructureofthedistressprobabilities.

3. Methodology

Inthispaperweproposealongitudinalmodelinorderto

eval-uate the changes in the probabilities of failure over a period of

time.Specifically,we proposeaGEVlongitudinalmodel(LOBGEV)

bycombiningtheGEVmodelandtheD-vinecopula.Theproposed

model hastwo levels ofanalysis.First, we make use ofthe GEV

modelbecause ithasbeen proposedforimproving the

classifica-tionaccuracyofthecommonlyusedlogisticandprobitmodelsfor

stronglyunbalancedsamples.TheGEVmodel,describedinthe

fol-lowingsection,isusedtoestimatetheprobabilityofbankdistress

andtheprobabilityofbeingbailedoutateachtimet.Second,the

dependence across the probabilities of failure over time is

mod-elledbyamultivariatecopula.Givenitsflexibility,wechoosea

D-vinecopulaapproach,describedin Section3.2.

3.1. GEVmodel

LetYt bea responsevariablethat describesattimet abinary

rareevent,i.e.binarydependentvariablewithaverysmallnumber

ofonethanzero.Wewillbeinterestedinpredictingthe

probabil-ity

π

t=P

(

Yt=1

|

x t−1

)

given values ofcovariate vector x at time

t−1.

Theusuallystatisticalmodelsforbinaryresponsevariable,like

the logistic regression model, present several drawbacks in rare

event studies. In particular, rare events have proven difficult to

predict.When thedatais infactunbalanced,the estimate ofthe

dependentvariabletendstobe biasedtowards themajorityclass,

whichisusuallythelessimportantclasstocorrectlypredict(King

& Zeng,2001). Specifically, theuse ofa symmetric link function,

suchasthelogitorprobitfunction,mayunderestimate

π

tforthe

rareevents

{

Yt=1

}

, astheresponse curve

π

t approacheszeroat

the same rate as it approaches one (Calabrese & Osmetti, 2013;

King&Zeng,2001;Marraetal.,2014;Wang&Dey,2010).

To overcome these drawbacks Calabrese and Osmetti

(2013) propose a new flexible GLM for predicting binary rare

events. If we assume that the rare events are the outcomes

{

Yt=1

}

,2 theirfeaturesarerepresentedbythetailoftheresponse

curveforvaluesclosetoone.As theGEVrandomvariableisused

inthe literature (Falk, Husler, & Reiss, 2010) to modelthe tailof

a distribution, Calabrese and Osmetti (2013) consider a flexible

skewedlinkfunctionbasedontheGEVdistribution.Theproposed

modelisaveryflexible parametricmodel,particularlysuitable to

modelbinaryrareeventdata:

[−ln

(

π

t

)

]−τ−1

τ

=

α

+ p k=1

βk

xt−1,k, (3.1)

where

π

t=P

(

Yt=1

|

x t−1

)

isthe probability of the event(Yt=1)

at time t and where x t−1=

(

x1,x2,...,xp

)

is the vector of p

co-variatesobservedattimet−1. CalabreseandOsmetti(2015)

pro-pose the BGEVA model by including an additive component to

the GEV model. The BGEVA model has been then improved by

Calabrese, Marra, and Osmetti (2016). Several studies (Andreeva etal.,2016;Calabreseetal.,2016;Calabrese&Osmetti,2013;2015)

haveshownthat theGEVmodeloutperformsthelogistic andthe

probitmodelsevenifthepercentageofonesinthesampleisone

percent.

In this paper, we use the GEV model for different purposes.

First, we estimate the banks’ failure probability in 2008 to

anal-yse the characteristics relevant to explain banks’ distress in the

pre-interventionperiod.Second, weapplytheGEVmodelto

eval-uate the probability of receiving capital injections in 2008 and

2009. Third, we estimate the probability of failure conditionally

to the event “a bank receives a capital injection”

(

I=1

)

and“a

bank does not receive any capital injection”

(

I₌0

)

during the

post-interventionperiod (2010–2013).Therefore,let Yt be the

bi-nary r.v.such that

(

Yt=1

)

is a banksfailed at time t. We apply

the modelin Eq.(3.1) ateach time (from2010 to 2013)to

esti-mate both conditional probabilities of failure P

(

Yt=1

|

I=1

)

and

2_{TheGEVmodelissuitablealsoiftherareeventsaretheoutcomes{Y}

t=0}as

P

(

Yt=1

|

I=0

)

.Inthiswayweareabletoanalysehowandtowhat

extenttheimpactofthecovariateschangesoverthetime.

3.2.TheD-vinecopula

Definition 3.1 (Multivariatecopula). The copulais a multivariate

cumulativedistributionfunction(cdf)withU1,U2,...,Ud uniformly

distributedmarginalsrandomvariablesonI₌[0_,1]:

C

(

u1,u2,...,ud

)

=P

(

U1≤u1,U2≤u2,...,Ud≤ud

)

The importance ofcopulaein statisticalmodellingstems from

Sklar’stheorem whichshows that every multivariate distribution

canberepresentedviathechoice ofan appropriatecopulaandit

providesageneralmechanismtoconstructmultivariatemodelsin

astraightforwardmanner.

Theorem 3.1 (Sklar). LetX1,...,Xdbeasetofrandomvariableswith joint cdf F(·) and marginals cumulative distributionfunctions (cdfs) F1(·), F2(·), .., Fd(·). It exists a copula functionC: Id → I suchthat

∀

x1,x2,...,xd∈Rd

F

(

x1,...,xd

)

=C

(

F1

(

x1

)

,...,Fd

(

xd

))

. (3.2) If F1(·), F2(·), .., Fd(·) arecontinuous functionsthen the copula C(·) is unique.Conversely, if C(_·) is a copula functionand F1(·), F2(·), ..,

Fd(·)aremarginalcdfs,thentheF

(

x1,...,xd

)

in(3.2)isamultivariate cdf.

Theprincipaladvantagetouseacopulaapproachfollowsfrom

the Sklar theorem. This theorem states that each joint

distribu-tion can be expressed in terms of marginal distributions and a

copulafunction that captures the dependence structure between

themarginal probabilities.The mainadvantagesofthecopula

ap-proach are that it is a simple method to estimate multivariate

models forgiven marginal distribution functionsand it can

rep-resent different kinds of dependence structures. Simpler models

usuallyassumealineardependence,suchasthemultivariate

nor-maldistribution,orlineartaildependence,suchasthemultivariate

Student-t.Onthecontrary,thecopulamodelcanaccountfor

non-lineardependenceornon-linearupper/lowertaildependence.

In high dimensions, multivariate copula-based models have

beenemployedlargely toaccount forcomplexdependence

struc-ture in order to consider non-normality assumption (Joe, 1997;

Savu& Trede, 2010; Whelan, 2004). In the recent literature, the

multivariateprobability densityfunction hasbeen composedinto

theproductofbivariatecopulae,alsoknownaspair-copulae,that

can be chosen independently fromeach other froma wide class

ofbivariate copulae.In orderto representthe dependence

struc-ture between the pair-copulae, a graphical model is used. The

resulting approach is known as vine copulae (Czado, 2010). A

goodness of fit test can be performed to choose the

combina-tionofthepair-copulaethat bestfits todata. Smithetal.(2010),

Smith(2015)and Panagiotelis,Czado,andHarry(2012)usea

vine-copulaapproachtomodelthedependencestructurefor

longitudi-naldataandhaveshown encouragingresultson thegoodness of

fitachievedinan empiricalanalysis onheadache severity.

Differ-ent vinedecomposition, such as regular-vine (R-vine),

canonical-vine(C-vine)anddrawablevine(D-vine), havebeenproposed to

describe specific dependence between the variables. Aas, Czado,

Frigessi,andBakken (2009)and Czado (2010) extensivelyexplain

themaindifferencesamongR-vines,C-vinesandD-vines. Bedford

andCooke(2002) propose the D-vine copula formodelling time

series.As theaim ofthis paperis tomodel the failure

probabil-ity of banks over time, we use the D-vine copula approach for

their flexibility andparsimony. We do not use multivariate

cop-ula families, such as multivariate Clayton, Gumbel, Frank,

Gaus-sian andStudent-t copula, because,if we decompose these

fam-ilies inpair-copulae, they all need to belong to the same copula

family,showingthesamedependencestructure.Theconditionthat

thedependencestructureisinvariantovertimeisseldomsatisfied

by longitudinal data. This assumption is instead removed in the

D-vine copulaapproach (Smith, 2015; Smithet al., 2010).

Coher-ently,severalsimulationandempiricalstudiesforcontinuousand

discrete data (e.g. Aas & Berg,2009, Smith etal., 2010, Smith & Khaled, 2012, Kraemeretal., 2013, Panagiotelis etal., 2012) have

shown that the D-vine copula can achieve a higher goodness of

fit than the multivariate copulae, such as Clayton, Gumbel and

Gaussian.

TheD-vinecopulaapproachhaspreviouslybeenappliedin

sev-eral fields. For example, D-vine has been used to forecast

elec-tricity load (see Smith et al., 2010) and to model the

depen-dence structure between the amounts of precipitation over time

in severalgeographicareas(see Daeyoung, Jong-Min,Shu-Min, &

Yoon-Sung, 2013). In finance, Aas and Berg (2009) use them to

modelthetimeseriesoffinanciallog-returns.

We describe the D-vine model for continuous data. Let

(

X1,X2,...,XT

)

be an univariate time series of continuously

dis-tributed data observed at T possibly unequally spaced points

in time, the joint density function f

(

x1,x2,...,xT

)

can be

al-ways decomposed in a product of the conditional (to the past)

distributions: f

(

x1,x2,...,xT

)

= T t=2 f

(

xt

|

xt−1,...,x1

)

f

(

x1

)

.

Byusingapair-copula(bivariatecopula)representationwehave:

f

xt

|

xt−1,. . .,x1

= t−1 j=1 ct,j

F

xt

|

xt−1,. . .,xj+1

, F

xj

|

xt−1,. . .,xj+1

;

θ

t,j

f

(

xt

)

where F(xt| · ) is the cdf of Xt conditional to the past, f(xt) is

thedensityfunctionofthemarginalXtandct,j=ct,j|t−1,t−2,...,j+1is

the pair-copuladensitywithassociation parameters

θ

t,j between

thevariablesXtandXjconditionaltothetimesfrom j+1tot−1

(see Smithetal.,2010fordetails).

Therefore, the joint distribution of the process becomes a

D-vine copulamodel of order T,which is a product of T marginal

densitiesandT

(

T−1

)

/2pair-copuladensities:

f

(

x1,x2,...,xT

)

= T t=2

_t −1 j=1 ct,j

(

ut|j+1,uj|t−1;

θ

t,s

)

f

(

xt

)

f

(

x1

)

, (3.3) whereut|j+1=F

(

xt

|

xt−1,...,xj+1

)

anduj|t−1=F

(

xj

|

xt−1,...,xj+1

)

.

3.3. LongitudinalBinaryGeneralisedExtremeValue(LOBGEV)model

Let

π

1,

π

2,...,

π

T betheunivariateseriesoffailureprobabilities

modelledbytheGEVmodelin Eq.(3.1).Wedefinethejoint

prob-abilityof failuresover the periodst=1,...,T by a copula repre-sentationasin Eq.(3.2):

P

(

Y1=1,Y2=1,...,YT=1

)

=C

(

π

1,

π

2,...,

πt

,...,

πT

)

.

Thisrepresentationallows modellingthetemporaldependence

acrosstheprobabilitiesoffailure.Letcbethecopuladensity

func-tionofthecopulaC.Followingaproceduresimilartotheone

de-scribed forthe D-vine model inthe previous section, thecopula

densityfunctionc

(

π

1,

π

2,...,

π

T

)

canbedecomposedinaproduct

oftheconditional(tothepast)pair-copuladensityfunctions:

c

(

π

1,

π

2,...,

π

T

)

= T t=2

t−1 j=1 ct,j

(

ut|j+1,uj|t−1;

θ

t,j

)

(3.4)

Table1

Distributionofbanks’failuresfrom2008to2013intheUS.

Year TARP-CPPbanks banksnotincludedinTARP-CPP Total

Failing Non-failing Failing Non-failing

2008 0 272 12 6831 7115 2009 3 523 140 6449 7115

Year Failing Failing Total

2010 5 157 6790

2011 9 92 6721

2012 9 49 6329

2013 3 59 6048

where c_t,j=c_{t,j|t−1,t−2,...,j+1} is the pair-copula with association

parameters

θ

t,j between

π

t and

π

j conditional to the times

from j+1 to t−1 and ut|j+1=

π

t

|

π

t−1,...,

π

j+1 and uj|t−1=

π

j

|

π

t−1,...,

π

j+1.

Therefore, the joint distribution of the process becomes a

D-vine copula model of order T, which is a product of T marginal

densitiesandT

(

T−1

)

/2pair-copuladensities.Wecallthismodel

Longitudinal Binary Generalised Extreme Value model (LOBGEV).

Since theLOBGEVis basedoncopulafunction,it couldbe

differ-ent from the longitudinal modelusually based on normal

distri-bution andits dependence structure could not be linear. In this

way,aflexible,parsimonious andnotnecessarynormal

longitudi-nalmodelforbanks’probabilitiesoffailingisproposed.

4. Empirical evidence 4.1. Data

The dataonTARP-CPPcomesfromtheU.S.Departmentofthe

Treasury, whilethe data onFDIC auctions areretrieved fromthe

FDICwebsite.The accountingdataare retrievedfromthe Federal

ReservesReportsofConditionandIncome(CallReports)for

com-mercialbanksonaquarterlybasisfromthefirstquarterin2007to

the thirdquarterin2013. Callreportsdatafor commercialbanks

were downloaded from the Federal Reserve Bank of Chicago’ s

website3 _{(starting fromMarch 2011). Analogously to Croci et al.}

(2015),we focus our analysison commercialbanks. As concerns

themacroeconomicvariables,the dataongrossdomesticproduct

percapita(GDP)andthepersonalincomegrowthratecomefrom

U.S. Bureau of Economic Analysis (BEA), while those on the

un-employment ratefrom the Bureau of Labor Statistics, Local Area

UnemploymentStatistics.4

Weconsiderasadistressevent,thefailureofabankunderthe

resolutionoftheFDIC. Specifically,abank canberesolved bythe

FDICunderthreedifferenttypesoftransaction:(i)assistance

trans-actions wherethefailed/assistedinstitutionremains open andits

charter survivestheresolutionprocess;(ii)purchaseand

assump-tiontransactionswherethefailed/assistedinstitution’sinsured

de-positsare transferredto asuccessorinstitution,anditscharter is

closed;and(iii)payoff transactions,thedepositinsurer– theFDIC

or the former Federal Savings andLoan InsuranceCorporation –

pays insureddepositors, thefailed/assisted institution’scharter is

closed,andthereisnosuccessorinstitution.5 _{Inthispaper,wedo}

notmakeadistinctionbetweenthesethreecategories.

Table 1 shows the distribution offailures from 2008 to 2013

for the US banks in the data. The number of failings over time

shows differentpatterns forbanks that received capital injection

3_{https://cdr.ffiec.gov/public/ .}

4_{The data areavailableon the following website:http://www.bea.gov/iTable/}

index _ regional.cfm andhttp://www.bls.gov/lau/data.htm .

5_{Seehttps://www.fdic.gov/ formoredetails.}

andthosethatdidnotreceivesuchsupport.Inthefirstgroup,the

banksindistressachievetheirmaximumin2011and2012,inthe

secondgroupearlierin2010.

4.2.Determinantsofcapitalinjectionandbanks’failures

Inthis section we analyse the determinantsof banks’ failures

andreceivingcapitalinjections fortheyears2008 and2009.

Ad-ditionally,wecomparethecovariatesoftheprobabilityofdistress

forboththebanksthatwereenrolledintheTARPCPPprogramme

anddidnot receive anycapitalinjection. Inorder toidentify the

explanatoryvariables ofthe GEV modelforeach yearfrom 2008

to2013,wefollowtheCAMELframeworkinthelinewithprevious

studies(e.g. Wheelock& Wilson,2000,Rossi,2010,Cole&White, 2012,Dam&Koetter,2012,Berger&Bouwman,2013,Calabrese& Giudici,2015).

Ourmodelconsistsofacombinationofvariablesthatprevious

andrecentstudieshaveidentifiedtoberelevantfortheprediction

ofabankfailure orbailoutduringthe2008–2009financialcrisis.

Inparticular,inaccordancewith DamandKoetter(2012)and Cole

andWhite(2012)weincludeequity-to-assetratio,totalloans/total

assets,other real estate owned/total assets,cost inefficiency,

liq-uidity,size andholdingcompanies inour model.We expectcost

inefficiencytohaveadirectinfluenceonthelikelihoodofabank’s

failing. Since other real estate owned/total assets have been

ex-traordinarilyriskyforbanksinthepast,weexpectthisvariableto

impact directly on failure. In addition, consistent with Wheelock

andWilson(2000),apositivevaluefortheliquidityvariablecould

lead to the possibility of liquidity problems for a bank. Banks

witha liquidityproblemaremorelikelytofail.Therefore,we

ex-pectthatliquidity hasa directeffectontheprobability offailure

of a bank. In contract, the level of capitalisation, size and being

partofaholdingcompanyshouldshowaninverserelationshipon

the likelihood offailure. As maintained by Bergerand Bouwman

(2013),membershipofabankholdingcompanyshouldreducethe

probability of failure because it strengthens its competitive

posi-tionasaconsequenceofthecapitalsupportprovidedbythe

hold-ingcompany. Furthermore,assuggestedby CalabreseandGiudici

(2015),wealsoaddTier1capitalratioandperformanceas

predic-torsofbankfailuretoourmodel.Weexplainthatweexpectthese

variables tohave an inverserelationship withthelikelihood ofa

bankfailing.

Next,drawingon theUSliterature (e.g. ColeandWhite,2012,

Crocietal., 2015,we selectcommercialandindustrial loans asa

key variable to predict banks’ failure during the recent financial

crisis. We also take into account the brokered deposit over total

andnon-interestincomeoverbothoperatingincomeandtotal

as-setsassetfollowing BergerandBouwman(2013)and DeYoungand

Torna (2013). Boththesevariables appear to be important

deter-minantsofbankfailureduringtherecentcrisisastheyarerelated

eitherto high-risk activities orto tradingpositions that are easy

tochangebutdifficulttomonitor.Finally,weacknowledgethe

im-portanceoflocalandregionaleconomicconditions.Inthisregard,

weexplainthatinaccordancewith Koetteretal.(2007)and Arena

(2008) we include gross domestic product per capita (GDP), the

unemploymentrate andthe personal income growth ratein our

model.Inthesamemanner,afewrecentstudieshavefocused on

probability of capital injections in the US banking sector during

therecent 2007–2009financial crisis. Specifically, Bayazitovaand

Shivdasani(2012) analyse the likelihoodof banks’ applicationfor

CPPcapitalinjections.Theauthorsshowthat thatwholesaledebt,

Tier 1ratio,commercial loans andthestate macroindexgrowth

are all factors that predict a bank’s participation decision to the

programme. Theyalsopoint out that large banksaremore likely

tobe acceptedinto theTARPCCP.Thisisin linewith Crocietal.

Table2

TheestimatesoftheGEVmodelfortheprobabilityoffailureandthe prob-abilityofreceivingcapitalinjectionin2008and2009intheUS.

Variables 2008 2009 Failure TARP-CPP TARP-CPP Holding −0.23(∗∗∗) _−2.89(∗∗∗) EQTA Size 0.17(∗∗∗) _0.14(∗∗∗) OtherRE −6.21(∗) _−5.44(∗) C&Iloans 1.11(∗∗∗) _1.47(∗∗∗) ROA Loans 0.69(∗∗∗) ROE −0.80(∗∗∗) NIM −17.60(∗∗∗) Noninterestincome1 0.004(∗∗∗) Noninterestincome2 Costinefficiency

Loanlossreserves 46.03(∗∗∗)

Tier1ratio −58.84(∗∗∗) _−2.84(∗∗∗) Liquidity −18.95(∗∗∗) Nonperformingloans 15.97(∗∗∗) _−2.05(∗∗∗) Brokereddeposit Age −0.11(∗) GDP UR 0.04(∗∗∗) PI 20.89(∗∗) _15.96(∗∗∗)

Thenumberof“∗” denotesthesignificantlevel:

(∗∗∗) _p≤0.000. (∗∗) _p≤0.001. (∗) _p≤0.01.

non-performing loans, cost inefficiencies, goodwill and size

en-hancetheprobabilityofbeingacceptedforTARP-CCP.

In order to have annual data, we compute a 4 quarter

mov-ingaverage.Thedependent variableisforecastedone yearahead.

Therefore,allexplanatoryvariables are measuredone yearin

ad-vance,withrespecttotheyearinwhichthedependentvariableis

observed.Toavoidmulticollinearity in theregression models,we

removetheexplanatoryvariables withthe VarianceInflation

Fac-tor(VIF)higherthan5.Weinitiallyconsider37variables;only22

ofthemaresignificantatthelevelof5percentorlowinatleast

oneGEVmodel.Thelistofthevariablesincludedinthemodelsis

reportedbelow:

• Holding:adummyvariablethatequals oneifthebankispart

ofabankholdingcompany,otherwiseitiszero;

• EQTA:equityovertotalassets;

• Size:logarithmoftotalassets;

• OtherRE:allotherdirectandindirectinvestmentsinrealestate

overtotalasset;

• C&ILoans:commercialandindustrialloansovertotalassets;

• ROA:netincomeovertotalassets;

• Loans: loans andleases, net unearnedincome and allowance

overtotalassets;

• ROE:netincomeovertotalequity;

• NIM:netinterestincomeovertotalassets;

• Non Interest Income 1: non-interest income over operating

income;

• NonInterestIncome2:non-interestincomeovertotalassets;

• LoanLossReserves:loanlossallowanceovertotalassets;

• Tier1Ratio:Tier1overriskyassets;

• Liquidity: federal funds purchased in domestic offices net of

fundssoldindomesticofficesovertotalassets;

• NonPerformingLoans:pastdueandnonaccrualloansovertotal

assets;

• Brokereddeposit:brokereddepositovertotalassets;

• Cost Inefficiency: noninterest expenses over non-interest

in-comeandinterestincome;

• Age:Differencebetweensampleyearandtheyearofopening;

• GDP:GDPgrowthrateatthestatelevel;

• UR:unemploymentrateatthestatelevel;

• PI:personalincomegrowthrateatthestatelevel.

We apply the GEV model by estimating Eq. (3.1) using the

maximumlikelihood method.The estimationprocedure is

imple-mented intheR package BGEVA(Marraetal., 2014)available on

CRAN. Table2reportsthefindingsoftheGEVmodelforthe

prob-abilityof failure andthe probability ofreceiving capitalinjection

in2008and2009.

In line with previous studies (e.g. Wheelock & Wilson, 2000,

Cole&White,2012,DeYoung&Torna,2013)ourresultsshowthat

bankswithlessliquidity(LoanLossReservesovertotalloans),low

assetquality(highnonperformingloans),poorperformance (ROE)

and low capitalisation (Tier 1 ratio) were more likely to fail in

2008. We also find that banks withhigh non-traditional income

sources(Non-interestincome1)hadahighprobability offailing.

In this regards, DeYoung andTorna (2013) point out that banks

thatengageinriskynontraditionalactivitiesaremorelikelytotake

risksintheirtraditionallinesofbusiness.

Columns2and3of Table2reportthedeterminantsfor

receiv-ing thecapital injectionin2008 or2009.Banks withlarge

com-mercialandindustrialloans(C&ILoans)andlowrealestate(Other

RE)weremorelikelytobebailedoutin2008and2009.This

find-ing is unsurprising given that loans are typically theleast liquid

andriskiestassets.Inlinewiththeparadigmtoobigtofail,large

banksweremorelikelytoreceivecapitalinjection.Inaddition,we

findthat bank holdingcompany membershipreduced the

proba-bility of capitalinjection in 2008. As pointed out by Bergerand

Bouwman(2013),commercialbankscanbenefitfromthefinancial

support provided by the holdingcompany and thereforethere is

lessneedtogetfurtherfunds.In2009,banksthat investedmore

in a tradition portfolio ofactivities (high loans over total assets)

and that suffered from an economic viewpoint (low net interest

margin) had a high probability of receiving capital injection.

Fi-nally, concerning the macroeconomic variables, banks located in

theStateswithhighpersonalincomegrowthrate(PI) and

unem-ploymentrate(UR)weremorelikelytobebailedout.

Table 3 displays the determinants of the probability of

fail-ure conditionally to the event intervention

(

Ii=1

)

and

non-intervention

(

Ii=0

)

and the relative explicative variables forthe

periodpost-intervention2010–2013.Capitalisationlevel(EQTA,

eq-uityover total assets)appears to be an importantvariableto

re-duce theprobability of failingforthebanksthat received capital

injectionforalltheyearsunderinvestigation.Instead,Sizewas

as-sociatedwithahighprobabilityoffailingforallthebanksin2012,

while only for the banksthat didnot receive TARP-CPPin 2011.

As concerns the probability conditionally to thenon-intervention

(

Ii=0

)

, low capitalisation (EQTA, Tier 1 ratio), and performance

(ROA)werekeyvariablesfortheoccurrenceofthefailurein2010–

2011.Liquidityappearstodiminishtheprobabilityoffailingofthe

banksthatreceivedcapitalinjectionin2012.Moreover,asin2008,

totalnon-interestincomeandnonperformingloanswereboth

im-portantpredictive variablesforbankruptcyin2010. Theexcessive

increaseofnon-interestexpensesandthereductionoftheinterest

incomesources havethen impactednegatively ontheprobability

offailure(costinefficiency)subsequentlyin2011and2013.Finally,

withregardstothemacroeconomicvariables,bankswithhigh

per-sonalincomegrowthrateweremorelikelytofailintheStatesin

2010and2013.

4.3. DidtheTARPCPPincreasethestabilityofthebankingsystem?

In this section we analyse the effectiveness of TARP-CPP in

Table3

TheestimatesoftheGEVmodelfortheprobabilityoffailureforthetwogroupsofbanksthatareincludedandnotintheTARP-CPPproject fortheperiod2010−2013intheUS.

Variables 2010 2011 2012 2013

TARP NoTARP TARP NoTARP TARP NoTARP TARP NoTARP Holdingdummy −4.80(∗∗∗) _−0.11 EQTA −53.72(∗∗) _−35.67(∗∗) _−46.82(∗∗∗) _−93.45(∗∗∗) _−4.85(∗) _−2.27(∗∗) _−20.11(∗∗) _−198.65(∗∗∗) Size 0.37(∗∗∗) _0.36(∗∗∗) _0.32(∗∗∗) OtherRE C&Iloans ROA −29.32(∗∗∗) _−12.25(∗∗) _−21.59(∗∗∗) _−172.29(∗∗) Loans −3.84(∗∗) _5.03(∗∗) _0.79(∗∗∗) ROE −0.32(∗∗∗) NIM Noninterestincome1 Noninterestincome2 32.52(∗∗) Costefficiency 0.71(∗∗) _0.57(∗) Loanlossreserves Tier1ratio −42.75(∗∗∗) _−15.08(∗∗∗) Liquidity −2.81(∗) Nonperformingloans 10.70(∗∗∗) Brokereddeposit Age 0.34(∗∗∗) _−0.13(∗∗∗) GDP −2.54(∗) _97.47(∗) UR PI −175.77(∗∗∗) _−239.69(∗∗) Tradingassets

Thenumberof“∗” denotesthesignificantlevel:

(∗∗∗) _p≤0.000. (∗∗)_p≤0.001. (∗) _p≤0.01.

LOBGEV model proposed in this paper6 _{Thismodel allows usto}

estimate thetype andthe level ofdependence betweenthe

dis-tressprobabilitiesovertime.

Specifically,we applytheGEVmodel,presentedin Section 3.1,

to all the banks in 2008 and to the two groups of banks

-those that received capital injections and those that did not –

for each year from 2009 to 2013. The dependent variable is

bank failure or non-failure in a given year. Using the

parame-ters estimates of the GEV model, we assess the distress

proba-bilities P

(

D2008=1

)

, P

(

Dt=1

|

I=0

)

and P

(

Dt=1

|

I=1

)

for t=

2009_,2010_,2011_,2012_,2013. Afterwards, we measure the

depen-dence betweenthe distressprobability in2008 P

(

D2008=1

)

and

theconditionalprobability P

(

Dt=1

|

I=0

)

orP

(

Dt=1

|

I=1

)

after

theintervention(2010–2013)usingtheD-vinecopuladescribedin

Section 3.2. The level of dependence is given by the association copulaparameter

θ

t,jdefinedin Section3.3.Toevaluatethe

effec-tivenessofthecapitalinjections,weanalysethetemporalstructure

of thefailure probabilitiesfor thebanks that benefitfrom

TARP-CPPinterventionsP

(

Dt=1

|

I=1

)

andforthosethatdidnotreceive

suchfundsP

(

Dt=1

|

I=0

)

.

Thepair-copulafamiliesthatmaximisetheGoodnessofFitTest

or the Akaike information criterion are chosen in order to

pro-vide thebestfittothedata.Gaussiancopulaachievesthebestfit

to data ifwe are interested in modelling the dependence

struc-turebetween thefailure probability in 2008and thesame

prob-abilityin2010, 2011,2012and2013forbothnon-TARPandTARP

recipients. Sincethe estimatedpair-copulaeare Gaussian,the

de-pendence between the failure probabilities is linear. Instead, we

obtained that differentpair-copula families, such as the

Student-tandtheGumbelcopulae,providethebestfittodataifwemodel

the dependencebetweenthefailure probabilitiesafterthe

begin-ningoftheimplementationoftheTARP-CPPprogramme,i.e.from

2009to2013.ItisinterestingthatbothStudent-tandtheGumbel

6_{TheLOGBEVmodelisimplementedinRandthecodeisavailableuponrequest}

fromtheauthors.

copulaeshowataildependence,inthefirstframeworkthetail

de-pendence is linear, in the latter it is an upper tail dependence.

Table4 reportsthe association parameter estimatesof the

Gaus-sian copula, that are the intensityofthe dependenceof the

fail-uresprobabilitiesovertimeforthetwogroupsofbanksthatwere

either included or not in the TARP-CPP programme. At the first

glance,wenotethatin2010theTARP-CPPprogrammeconsistently

decrease the default probability dependence with the default of

probability inOctober2008,whenthe programmewaslaunched.

Specifically, in 2010, the correlation between the P

(

Dt=1

|

I=1

)

andP

(

D2008=1

)

was0.04whilethosefortheP

(

Dt=1

|

I=0

)

and

P

(

D2008=1

)

was 0.4286. This result suggeststhat the TARP-CPP

programmehasprovidedanimmediaterelieftothebanksenrolled

intheprogrammethroughadecreaseoftheirprobabilityoffailing.

However,thecorrelationbetweentheP

(

Dt=1

|

I=1

)

in2011and

P

(

D2008=1

)

was0.1330andhigherin 2012,0.2254. Inthe same

manner,the correlation betweenthe P

(

Dt=0

|

I=1

)

in 2012and

P

(

D2008=1

)

hasincreased.In2013,the correlationbetweenboth

P

(

Dt=1

|

I=1

)

andP

(

Dt=1

|

I=0

)

,andP

(

D2008=1

)

havereached

almostthesamelevel(respectively,0.0753and0.0923).

Theseresultspotentially haveimportantandsignificant

impli-cations. In particular, capital injections helped banks to reduce

theirdefaultprobabilitiesintheshortterm.However, suchan

ef-fectislessstrongafter2010 until2012, whenbanksthatdidnot

receivecapitalinjectionsshowsimilar patterns.Thissuggeststhat

the TARP was effective in reducing the default probability

espe-cially during the peak of the global financial crisis. Our findings

areinlinewith BergerandBouwman(2013)’spaper,whichshows

that capital is an effective tool in enhancing banks performance

(intermsalsoofsurvival asdistanceto default)especiallyduring

crisesandeconomic downfall. Theeffectiveness oftheTARP

pro-grammeintheshorttermcouldbeduetothecompetitive

advan-tagesandtheincreaseofmarketsharesandmarketpowerforthe

TARP banks, asshown by Berger and Roman (2015). From 2010,

the dependences between the probabilities of defaults for banks

thatwereeithersupportedornotbytheTARP-CPPprogrammeare

Table4

The levelofdependence betweenthefailure probability P(D2008=1) andthe conditionalfailureprobabilities

P(Dt=1|I=0)orP(Dt=1|I=1)forthetwogroupsofbanksthatareincludedandnotintheTARP-CPPproject

fortheperiod2009–2013.

Time Dependencebetween

P(Dt=1|I=1)andP(D2008=1) Dependencebetween P(Dt=1|I=0)andP(D2008=1) 2009–2008 0.6548 0.7858 2010–2008/2009 0.0443 0.4286 2011–2008/(2009–10) 0.1330 0.0691 2012–2008/(2009—10–11) 0.2254 0.1955 2013–2008/(2009–10–11–12) 0.0753 0.0923

typically large banks with high market power have appeared

to have taken on more risk as a consequence of capital

injec-tions duringthe TARP programme, aspointedout by Berger and

Roman (2015), Black and Hazelwood (2013) and Duchin and Sosyura (2014). Secondly, TARP banks could have struggled with

the costs of TARP-funds which could have harmed their market

powerandsoundness(Berger&Roman,2015).

Inaddition,wefindalineardependencestructurebetweenthe

probabilitiesoffailurein2008andafterthat.Thismeansthat the

likelihood of failure after 2008 depends on the level of distress

ofthe bank at the peak of the financial crisis fornon-TARP and

TARP recipients, regardless of whethera bank is healthy or not.

Onthe contrary,after2008, the dependencebetweenthe

proba-bilities of failure becomesa tail dependencefor the two groups

ofbank. These resultscould be dueto a distortion of the

finan-cialmarketcausedbythegovernmentsupport.Asshownby Black

andHazelwood(2013)and DuchinandSosyura(2014),banksthat

receive government assistance tend to increase their risk taking

for both lending and investment activities as a general attitude.

Forthis reason, we find that the time series ofthe probabilities

offailures after2008 show dependence onlyfor distressedTARP

banks. DuchinandSosyura(2014)alsoshowthatahigherrisk

atti-tudeisassociatedmorewithasignalofgovernmentsupportrather

thanwiththecapitalinjectionitself.Inlinewithourresults,they

specificallyfindthat ahigherrisk-taking attitudeismoreevident

forbanksthatareclosertofinancialdistressorthatwereallowed

toskipped dividend payments requiredby the TARP programme.

Furthermore,bankslearnedaboutthegovernmentforbearance

at-titudeduring therunning of the TARP-CPPprogramme(overthe

period2008–2009). Therefore, itis reasonableto find a different

risk-attitude for a specific group of banks after the beginning of

theTARPprogramme.Aspointedoutby BergerandRoman(2015),

marketpowerbanks,whicharetypicallythelargeones,appearto

have takenon more risk because of capital injection duringthe

TARPprogramme.Thismeansthatbankswithhigherriskexposure

tended to take on morerisk after2008. In addition,it is

plausi-bletofindataildependenceforthenon-TARPrecipientsafterthe

peakofthefinancialcrisis. Thesebankswerenot considered

suf-ficientlyhealthy orsystemicallyimportanttobe integratedinthe

programme.Hence,thedistressedandthehealthybanksmaintain

theirrisk performance afterthebeginning ofthe implementation

oftheTARP-CPPprogramme,i.e.from2009to2013.

5. Conclusion

The 2008financialcrisishashighlightedtheimportance of

re-liableandrobust modelstomonitorandassessbanks’stabilityin

ordertoreducethesocialcostsoffailuresandrescuepolicies.This

issueis of particular interest because the financial crisis hasled

toavast amountofcostly policyinterventionstostabilise the

fi-nancialsystem. Whiletheseinitiatives haveprovided relieftothe

banking system, their effects onthe stabilityof thebanking

sys-temoveraprolongedperiodoftime isstill controversial.Bailouts

can favourmoral hazardbehaviour ofbanksandinturn increase

theirriskprofileovertime(Black&Hazelwood,2013;Dam& Koet-ter, 2012; Duchin & Sosyura, 2014; Hakenes & Schnabel, 2010).

Eventhough there isan increasing number ofstudies on capital

injectionstobanksduringthefinancialcrisis, theeffectivenessof

bailoutsinreducingtheprobabilityoffailureovertimeisrelatively

unexplored.

This paper contributes to the operational research literature

by covering thisgap. In particular, we propose a new

longitudi-nal model forbinaryrare events, the Longitudinal Binary

Gener-alised Extreme Value (LOBGEV) model.This model uses the GEV

model(Calabrese&Osmetti, 2013) to representthe marginal

dis-tributions of the D-vine copula (Smith et al., 2010). We employ

this new model to analyse the impact of the TARP-CPP capital

injections on the probability of failure of US commercial banks

from2008to2013.Ourresultsprovidethreeimportantempirical

contributions.

First,usingtheGEVmodel,weanalysethedeterminantsof

re-ceivingcapitalinjectionsundertheTARP-CPPandofbankfailures

over the period 2008–2009.Our results show that low liquidity,

low assetquality, poor performance and low capitalisation, high

non-traditional income sources increase the probability of bank

distress.Moreover, we findthatbankswithhighcommercialand

industrialloans, largesize, andlowreal estatearemore likelyto

bebailed-out.

Second, we apply the GEV model to identify the

characteris-ticsthatarerelevanttodescribebanks’failureaftertheTARP-CPP

projects.Ourfindingsshow thathigherlevelsofcapitalisation

re-duce theprobability ofbankruptcy forbanksthatreceived

TARP-CPPfundsforalltheyearsunderinvestigation.Moreover,both

cap-italisation andperformance ofbanksare pivotalvariables forthe

distressprobability conditionally tothe non-intervention. As

con-cerns the macroeconomicvariables, USbankswithhighpersonal

incomegrowthratewerelesslikelytofailin2010and2013.

Third,weproposetheLOBGEVmodeltoinvestigatethe

tempo-raldependencestructureofthefailureprobabilitiesforbanksthat

received TARP-CPP capital injections and for those that did not.

This newmodelcan be used by regulators andpolicy makers to

assesstheeffectiveness ofcapitalinjectionsover time in

improv-ing banks performance. In particular, our investigation is driven

bya simplebutpowerfulquestion:didtheTARP-CPPprogramme

reduce banksdefaultprobabilities?Ourresultssuggest that,after

an initial relief, the correlation between the probabilities of

fail-ure forTARP-CPP recipients over a periodof fiveyears is almost

thesameasthecorrelation forbanksthatdidnot receivecapital

injections.Therefore,theTARP-CPPprogrammewaseffectivein

re-ducing banksdefault probabilities onlyin the shortterm, during

thepeakoftheglobalfinancialcrisis.

Acknowledgments

The authors would like to thank the editor and the referees

paper.WewouldalsoliketothankPaul Wagner,JaapBosand

Et-toreCrocifortheirsuggestionsduringthedraftingofthepaper.

References

Aas, K. , & Berg, D. (2009). Models for construction of multivariate dependence: A comparison study. TheEuropeanJournalofFinance,15(7), 639–659 .

Aas, K. , Czado, C. , Frigessi, A. , & Bakken, H. (2009). Pair-copula constructions of mul- tiple dependence. Insurance:Mathematics & Economics,44(2), 182–198 . Andreeva, G. , Calabrese, R. , & Osmetti, S. (2016). A comparative analysis of the UK

and Italian small businesses using generalised extreme value models. European JournalofOperationalResearch,249(2), 506–516 .

Arellano, M. , & Bo, H. (2001). Panels data models:some recent developments. In J. J. Heckman, & E. Learner (Eds.), Handbookofeconometrics:5 (pp. 3229–3296). Elsevier Science B V .

Arena, M. (2008). Bank failures and bank fundamentals: A comparative analysis of Latin America and east asia during the nineties using bank-level data. Journalof Banking & Finance,32(2), 299–310 .

Bayazitova, D. , & Shivdasani, A. (2012). Assessing tarp. ReviewofFinancialStudies, 25(2), 377–407 .

Bedford, T. , & Cooke, R. (2002). Vines: A new graphical model for dependent ran- dom variables. AnnalsofStatistics,30(4), 1031–1068 .

Berger, A. N. , & Bouwman, C. H. (2013). How does capital affect bank performance during financial crises? JournalofFinancialEconomics,109(1), 146–176 .

Berger,A.N.,Bouwman,C.H.,Kick,T.K.,&Schaeck,K.(2014).Bankrisktakingand liquiditycreationfollowingregulatoryinterventionsandcapitalsupport. Avail-ableatSSRN1908102.

Berger, A. N. , & Roman, R. A. (2015). Did TARP Banks get competitive advantages?

JournalofFinancialandQuantitativeAnalysis,50(6), 1199–1236 .

Black, L. K. , & Hazelwood, L. N. (2013). The effect of tarp on bank risk-taking. Journal ofFinancialStability,9(4), 790–803 .

Calabrese, R. , & Giudici, P. (2015). Estimating bank default with generalised extreme value regression models. Journal of the Operational Research Society, 66(11), 1783–1792 .

Calabrese, R. , Marra, G. , & Osmetti, S. A. (2016). Bankruptcy prediction of small and medium enterprises using a flexible binary generalized extreme value model.

JournaloftheOperationalResearchSociety,67(4), 604–615 .

Calabrese, R. , & Osmetti, S. (2013). Modelling small and medium enterprise loan defaults as rare events: the generalized extreme value regression model. Journal ofAppliedStatistics,40(6), 1172–1188 .

Calabrese, R. , & Osmetti, S. (2015). Improving forecast of binary rare events data: A gam-based approach. JournalofForecasting,34(3), 230–239 .

Calderon, C. , & Schaeck, K. (2016). The effects of government interventions in the fi- nancial sector on banking competition and the evolution of zombie banks. Jour-nalofFinancialandQuantitativeAnalysis. (Forthcoming)

Cole, R. A. , & White, L. J. (2012). Déjà vu all over again: The causes of us commercial bank failures this time around. JournalofFinancialServicesResearch, 42(1–2), 5–29 .

Croci, E. , Hertig, G. , & Nowak, E. (2015). Decision-making during the crisis: Why did the treasury let commercial banks fail?. In ProceedingsofEuropeancorporate governanceinstitute(ECGI). Law working paper no. 281/2015.

Czado, C. (2010). Pair-copula constructions of multivariate copulas. In Copulatheory anditsapplications(pp. 93–109). Springer .

Daeyoung, K. , Jong-Min, K. , Shu-Min, L. , & Yoon-Sung, J. (2013). Mixture of d-vine copulas for modeling dependence. ComputationalStatistics& Data Analy-sis,64(2), 1–19 .

Dam, L. , & Koetter, M. (2012). Bank bailouts and moral hazard: Evidence from ger- many. ReviewofFinancialStudies,25(8), 2343–2380 .

Demyanyk, Y. , & Hasan, I. (2010). Financial crises and bank failures: A review of prediction methods. Omega,38(5), 315–324 .

DeYoung, R. , & Torna, G. (2013). Nontraditional banking activities and bank failures during the financial crisis. JournalofFinancialIntermediation,22(3), 397–421 . Duchin, R. , & Sosyura, D. (2014). Safer ratios, riskier portfolios: Banks response to

government aid. JournalofFinancialEconomics,113(1), 1–28 .

Falk, M. , Husler, J. , & Reiss, R.-D. (2010). Lawsofsmallnumbers:Extremesandrare events. Springer .

Fethi, M. D. , & Pasiouras, F. (2010). Assessing bank efficiency and performance with operational research and artificial intelligence techniques: A survey. European JournalofOperationalResearch,204(2), 189–198 .

Gropp, R. , Hakenes, H. , & Schnabel, I. (2011). Competition, risk-shifting, and public bail-out policies. ReviewofFinancialStudies,24(6), 2084–2120 .

Hakenes, H. , & Schnabel, I. (2010). Banks without parachutes: Competitive effects of government bail-out policies. JournalofFinancialStability,6(3), 156–168 . Ioannidis, C. , Pasiouras, F. , & Zopounidis, C. (2010). Assessing bank soundness with

classification techniques. Omega,38(5), 345–357 .

Joe, H. (1997). Multivariatemodelsandmultivariatedependenceconcepts. CRC Press . King, G. , & Zeng, L. (2001). Explaining rare events in international relations.

Interna-tionalOrganization,55(3), 693–715 .

Koetter, M. , Bos, J. W. , Heid, F. , Kolari, J. W. , Kool, C. J. , & Porath, D. (2007). Ac- counting for distress in bank mergers. Journal of Banking & Finance,31(10), 3200–3217 .

Koetter, M. , & Noth, F. (2015). Did tarp distort competition among sound unsup- ported banks? EconomicInquiry.

Koleva, N. , & Paivab, D. (2009). Copula-based regression models: A survey. Journal ofStatisticalPlanningandInference,139(11), 3847–3856 .

Kraemer, N. , Brechmann, E. C. , Silvestrini, D. , & Czado, C. (2013). Total loss esti- mation using copula-based regression models. Insurance:Mathematicsand Eco-nomics,53(3), 829–839 .

Kumar, P. R. , & Ravi, V. (2007). Bankruptcy prediction in banks and firms via statisti- cal and intelligent techniques–a review. EuropeanJournalofOperationalResearch, 180(1), 1–28 .

Laeven, L. , & Valencia, F. (2010). Resolutionofbankingcrises:Thegood,thebad,and theugly. International Monetary Fund .

Liu, W. , Kolari, J. W. , Tippens, T. K. , & Fraser, D. R. (2013). Did capital infusions en- hance bank recovery from the great recession? JournalofBanking & Finance, 37(12), 5048–5061 .

Marra,G.,Calabrese,R.,&Osmetti,S.A.(2014).Packagebgeva.

Meade, N. , & Islam, T. (2010). Using copulas to model repeat purchase behaviour an exploratory analysis via a case study. EuropeanJournalofOperationalResearch, 200(3), 908–917 .

Panagiotelis, A. , Czado, C. , & Harry, J. (2012). Pair copula constructions for mul- tivariate discrete data. Journal oftheAmericanStatisticalAssociation,499(107), 1063–1072 .

Radice,R.,Marra,G.,&Wojty´s,M.(2015).Copularegressionsplinemodelsfor bi-naryoutcomes.StatisticsandComputing.doi:10.1007/s11222-015-9581-6 .

Rossi,C.V.(2010).Decomposingtheimpactofbrokereddepositsonbankfailure: theoryandpractice.StudyPreparedfortheAnthonyT.Cluff Fund:http://www. fsround.org/publications/pdfs/2011/brokereddepositsreport _ rev.pdf .

Savu, C. , & Trede, M. (2010). Hierarchies of archimedean copulas. Quantitative Fi-nance,10(3), 295–304 .

Smith, M. (2015). Copula modelling of dependence in multivariate time series. In-ternationalJournalofForecasting,31, 815–833 .

Smith, M. , & Khaled, M. (2012). Estimation of copula models with discrete margins via bayesian data augmentation. JournaloftheAmericanStatisticalAssociation, 107(497), 290–303 .

Smith, M. , Min, A. , Almeida, C. , & Czado, C. (2010). Modeling longitudinal data us- ing a pair-copula decomposition of serial dependence. JournaloftheAmerican StatisticalAssociation,402(105), 1467–1479 .

Wang, X. , & Dey, D. K. (2010). Generalized extreme value regression for binary re- sponse data: An application to b2b electronic payments system adoption. The AnnalsofAppliedStatistics,4(4), 20 0 0–2023 .

Wheelock, D. C. , & Wilson, P. W. (20 0 0). Why do banks disappear? The determinants of us bank failures and acquisitions. ReviewofEconomicsandStatistics,82(1), 127–138 .

Whelan, N. (2004). Sampling from Archimedean copulas. Quantitativefinance,4(3), 339–352 .

Wilson, L. (2013). Tarp’s deadbeat banks. ReviewofQuantitativeFinanceand Account-ing,41(4), 651–674 .