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Probability of default and efficiency in cooperative banking

Citation for published version:Fiordelisi, F & Mare, D 2013, 'Probability of default and efficiency in cooperative banking' Journal ofInternational Financial Markets, Institutions, and Money, vol 26, pp. 30-45., 10.1016/j.intfin.2013.03.003

Digital Object Identifier (DOI):10.1016/j.intfin.2013.03.003

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Document Version:Author final version (often known as postprint)

Published In:Journal of International Financial Markets, Institutions, and Money

Publisher Rights Statement:This is an Author's Accepted Manuscript of an article whose final and definitive form, the Version of Record, hasbeen published in the Journal of International Financial Markets, Institutions, and Money, 26, 2013. © 2013Elsevier B.V. The final publication is available online at: http://dx.doi.org/10.1016/j.intfin.2013.03.003

Fiordelisi, F., & Mare, D. (2013). Probability of default and efficiency in cooperative banking. Journal ofInternational Financial Markets, Institutions, and Money, 26, 30-45. 10.1016/j.intfin.2013.03.003

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Download date: 26. Aug. 2014

ProbabilityofDefaultandEfficiencyinCooperativeBanking

FrancoFiordelisia,b,DavideSalvatoreMarec*

aFacultyofEconomics,UniversityofRomeIII,Italy

bBangorBusinessSchool,BangorUniversity,U.K.

cBusinessSchool,CreditResearchCentre,TheUniversityofEdinburgh,U.K.

Abstract

Cooperative banks are small credit institutions, and they aremore likely than commercialbanks to default in periods of financial stability. Focusing on Italy (one of the largestcooperativebankingmarkets),weanalysethecontributionofefficiencytotheestimationofthe probability of default of cooperative banks. We estimate several measures of bankefficiency, and we run a discrete‐time survival model to determine whether differentmanagerial abilities play different roles in predicting bank failures. We show that higherefficiency levels (both in cost minimization and revenue and profit maximization) have apositiveandstatisticallysignificantlinkwiththeprobabilityofsurvivalofcooperativebanks.Wealsofindthatcapitaladequacyreducestheprobabilityofdefault,supportingtheviewthathighercapitalbuffersprovideadditionallossabsorbencyandreducemoralhazardproblems.

JEL‐Classification:C23,G21,G28

Keywords:Bankfailure,Smallbanks,Efficiencymeasures,Hazardmodel.

*Correspondingauthor:CreditResearchCentre,UniversityofEdinburghBusinessSchool,29BuccleuchPlace,EH89JU,Edinburgh,UK.Phone:+44(0)1316515077,Fax:+44(0)1316513197,E‐mail:davide.mare@ed.ac.uk

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1 Introduction

CooperativebanksplayakeyroleintheEuropeanbankingindustry.In2010,cooperative

bankswere a driving force for socially committed business at the local level through their

3,900memberbanks,65,000branches,morethan770,000employees,50millionmembers,

and 180 million clients (European Association of Co‐operative Banks, 2011). Overall,

cooperative banks account for approximately one fifth of the European banking system

(market shares of deposits and credits are 21% and 19%, respectively). Various studies

(Groeneveld and de Vries, 2009; Cihák and Hesse, 2007; Groeneveld, 2012) suggest that

cooperativebanksare,onaverage,morestable thancommercialbanksbecausetheyhavea

great deal of soft information (which is hard to collect) on the creditworthiness of

members/customers, and therefore they are much less likely to make lending mistakes.

However,intimesoffinancialstability,regulatorsaremorepronetoletadistressedbankgo

intodefaultifitisasmallcooperativebank.ThisoutcomeisconsistentwiththeToo‐Big‐To‐

Fail policy (i.e., regulators avoid letting the largest and most powerful banks go out of

business in order to prevent panic in financial markets) and the Too‐Important‐To‐Fail

argument (i.e., regulators avoid letting the most well‐known and systematically important

banks go out of business in order to prevent the risk that many banks fail together). For

instance,thedefaultrateofItaliancooperativebankswasalmostfourtimeshigherthanthat

ofcommercialbanksintheperiodbeforethefinancialcrisis(1997–2006).Specifically,there

were 44 default cases among cooperative banks (default rate 1.04%) and 8 among

commercialbanks(defaultrate0.28%).

Ourpaperanalysesthedeterminantsoftheprobabilityofsurvivalofcooperativebanks.

What drives thedefault of banks? Is efficiency adeterminant in thedefault of banks?Does

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managerialskillplayaroleinthefinancialdistressofsmallcreditinstitutions?Thepurpose

ofthispaperistoempiricallyaddressthesequestionsinregardtocooperativebanks.Because

there is evidence thathigher efficiency reducesbank risk‐taking (e.g.,Berger andDeYoung,

1997;Fiordelisietal.,2011;CihákandSchaeck,2013),wepositthatalowerexposuretorisky

assets increases the survival time of a bank. Consequently,we argue that higher efficiency

favoursbanksoundness.Surprisingly,thereislimitedavailableempiricalevidencesupporting

this expectation.As such,weposit thatbank survival is related to themanagerial ability to

save costs (cost efficiency), maximize revenues (revenue efficiency), and maximize profits

(operatingandinterestefficiency).

Wehavethreemainresults.First,weshowthatmoreefficientbanks(efficienteither in

costsavingorinrevenuemaximization)haveahigherprobabilityofsurvival.Second,wefind

thatwhenabank’smanagerial ability tominimize costs andmaximize revenuesare jointly

considered(e.g.,efficiencyingeneratinginterestincome),moreskilfulmanagementincreases

thebank’ssurvivaltime.Third,wefindevidencetosupporttheviewthattraditionalfinancial

ratiosareconsistentpredictorsofbankdistress.Inthisregard,weshowthatcapitalisakey

determinantofbanksoundness.

Weanalysealargesamplewithmorethan4,200observations‐alltheItaliancooperative

banksbetween1997and2009.Weestimatetheprobabilityofdefaultbyrunningadiscrete‐

timesurvivalmodelthatrelatesachangeinthehazardratetoanabsolutechangeinagiven

covariate,allelsebeingequal.WefocusonItalybecausethiscase isparticularly interesting

forvariousreasons.First,cooperativebanksplayacrucialroleintheItalianbankingmarket‐

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Italian cooperative banks1have approximately 36,000 employees, 6.7 million clients, 1.1

millionmembers2,and7.3%ofthemarketshareofdeposits3.Second,theItaliancooperative

banking sector is the fourth largest inEuropeafterGermany,France, andAustria (in 2010,

6.7%4ofthetotalassetsundermanagementintheEU27cooperativebankingsector).Finally,

Italypresents auseful laboratory setting to analyse the impact of theeconomic, social, and

demographic conditions of local areas on bank efficiency. The Italian regions display very

differentconditionsthatmustbeconsideredtoaccuratelyestimatetheprobabilityoffailure.

Theremainderofthepaperisorganizedasfollows:Section2brieflyreviewstherelevant

literature. In Section 3, we formulate our research hypotheses and describe the data

employedintheempiricalanalysis.Section4summarizesthemethodology.Section5reports

the results of the analysis. Section 6 addresses the predictive accuracy of the model, and

Section7concludesandoffersfinalremarks.

2 Literaturereview

Our paper joins two separate streams of the economic literature. The first stream

concernsefficiencyestimationwiththeaimofcomparingcooperativeandcommercialbanks.

One group of studies compares cooperative and commercial banks by estimating, first, a

specific efficiency frontier for each typeof bank and, second, a common frontier that pools

togethercooperativeandcommercialbanks.Thesepapersprovidemixedevidenceaboutthe

1Notethat ItalianBanchePopolariarenotcovered in thepresentanalysisbecause, in termsofgovernance, theymorecloselyresemblejoint‐stockcompanies(Fonteyne,2007).2Sourceofdata:ItalianFederationofCooperativeBanks(Federcasse),estimateddataat31/12/2011.3Sourceofdata:EuropeanAssociationofCo‐operativeBanks(2011).4Sourceofdata:owncalculationusingdatafromtheEuropeanAssociationofCooperativeBanks(2011).Cooperativenetworks,suchastheDutchRabobankandtheFrenchCréditAgricole,arenotconsideredinthecalculation.

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costandprofitefficiencyofsuchbanks.Battagliaetal.(2010)showthatsampleheterogeneity

also occurs when estimates are obtained from a single efficient frontier estimated for

cooperativebanksonly.Cooperativebankshaveastrong linkwith thegeographicalarea in

which they operate; therefore, the levels of efficiency are influenced by the social,

demographic,andeconomicconditionsofthatspecificarea.

Various papers also compare commercial and cooperative banks by focusing on issues

other than efficiency. Cihák and Hesse (2007) use individual bank data to test whether

cooperativebanksreducethestabilityofotherbanksandrespondslowlytofinancialdistress.

Contrarytothefindingsofpreviousstudies(Brunneretal.,2004;Goodhart,2004;Fonteyne,

2007),CihákandHessefindcooperativebankstobemorestablethancommercialbanks:the

lowervolatilityof thecooperativebanks’ returnsmore thanoffsets their lowerprofitability

andcapitalization.Groeneveld(2012)comparescommercialandcooperativebanks,focusing

onthemeanvaluesofsomeindicators(returnonequity,Tier1capital,andZ‐score).Overall,

the author concludes that in Europe cooperative banks are less profitable andmore stable

thancommercialbanks.

The second stream of literature addresses the estimation of bank failures and is

characterizedbytwoapproaches:micro‐andmacro‐approaches.The“micro”strandfocuses

on individual banks’ balance sheet data, possibly integrated with financial market data, to

predict bank failures. This approach stems from the seminal papers of Altman (1968) and

Beaver(1966),whouseaccountingdatatodiscriminatebetweensoundandtroubled firms.

Sincethen,manystudieshaveassessed theabilityof financial ratios topredict the financial

health of bank operations (see, amongmany others, Meyer and Pifer, 1970; Sinkey, 1975;

SantomeroandVisno,1977;West,1985;Estrellaetal.,2000).Variouspapershavealsotested

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thesuperiorityofonespecificassessmenttechniqueoveranother(Martin,1977;Espahbodi,

1991;Shumway,2001;Glennonetal.,2002;Boyaciogluetal.,2009).Recently,Demyanykand

Hasan (2010) reviewed this extensive literature and showed that the combination of

operational research techniques with statistical methods substantially improves the

predictionofbankfailures.Otherrecentworkshavefocusedonthesubprimemortgagecrisis

andthesubsequentbankingfailures(DavisandKarim,2008a;Jinetal.,2011;ColeandWhite,

2012).

The “macro” approach investigates banking crises by focusing on macroeconomic

determinants(Demirguc‐KuntandDetragiache,1998;González‐Hermosillo,1999;Davisand

Karim,2008b).Thesestudiestypicallyanalysealargesampleofcountriestodeterminewhich

macroeconomic factors signalabankingcrisis inadvance.For instance,Demirguc‐Kuntand

Detragiache (1998) argue that GDP growth, excessively high real interest rates, and high

inflationsignificantlyincreasethelikelihoodofsystemicbankingcrises.Otherrecentstudies

(DeYoung,2003;Arena,2008;MännasooandMayes,2009;Mare,2012)haveusedboththe

micro andmacroperspectives, highlighting that combiningdifferent sourcesof information

increasestheaccuracyofpredictionsofbankfinancialdistress.

Variouspapershaveestimatedtheprobabilityofbankfailureorsurvival.Laneetal.(1986)

pioneered the field by using duration analysis. The authors were the first to use the Cox

proportional hazards model to predict US commercial bank failures. Estrella et al. (2000)

estimate the likelihood of failure using cross‐sectional logit regressions and then analyse

time‐dependency in the conditional probability of failure through a proportional hazards

model. Wheelock and Wilson (2000) use a competing‐risks hazard model to identify

characteristicsleadingtoeitherfailureoracquisition.TheauthorsdemonstratethatUSbanks

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thathavelowcapitalization,highleverage,lowliquidity,poor‐qualityloanportfoliosandlow

earningsaremorepronetofailure.Moreover,theauthorssuggestthatinefficiency,measured

throughmanagementquality,increasesthelikelihoodofbankfailure.

Shumway (2001) develops a discrete‐time hazard model to determine probability

estimates for corporationsateachpoint in time.Theauthorargues thathazardmodels are

theoreticallypreferabletosingle‐periodclassificationmodels(staticmodels)becausehazard

modelsconsiderthatfirmschangeoverandthroughtime.Hence,theresultantprobabilitiesof

defaultconsistentlyapproximatethetrueprobabilitiesoffailure.Arena(2008)performsboth

cross‐sectional logit estimation and survival time analysis to prove that bank‐level

fundamentals, the banking system, and macroeconomic variables significantly affect the

likelihood of bank failures in the case of banking crises in East Asia and Latin America. In

addition,theauthorsuggeststhatsystemicmacroeconomicandliquidityshocksdestabilized

notonlythebanksthatwerealreadyweakbeforethecrises,butalsothosebanksthatwere

relatively stronger ex‐ante. This result suggests that negative effects triggered by systemic

crisescanalsoaffectsoundbanks.MännasooandMayes(2009)useadiscretecomplementary

log‐log model to link banks’ hazard rates to macroeconomic, structural, and bank‐specific

factors.Thestudysuggeststhatchanges inbankearnings,efficiency(measuredbythecost‐

incomeratio),andtherelativesizeofthecreditportfolioarenotearlywarningindicators.

Although various studies (e.g., Berger andDeYoung, 1997; Fiordelisi et al., 2011; Cihák

andSchaeck,2013)haveanalysed therelationshipbetweenbankefficiencyandrisk‐taking,

nostudieshavedirectlyrelateddifferentmanagerialskillstotheoccurrenceofbankfailure.

This is surprising because efficiency is one of the key factors behind bank performance

(Fiordelisi,2007;FiordelisiandMolyneux,2010)anditguaranteesbanksurvivalovertime.

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The recent crises of credit institutions have shown the importance of assessing how well

managementcontributestobanksurvival(intermsofminimizingcosts,maximizingrevenues,

or maximizing various measures of profits). The accurate prediction of bank survival is

fundamentalforpractitioners,investors,academics,andregulators.Whilstthisistrueforall

banks, it is critical for cooperative banks because their failure has been historically more

likelythanthatofcommercialbanksandmightgeneratehighersocialcostsatthelocallevel.

3 Researchhypothesesanddata

Inthissection,weformulateourresearchhypotheses,andthenweoutlinethedatausedfor

theestimation.Thekeyquestionaddressedinthepaperistoverifywhetherthemanagerial

ability of a bank to reduce costs and/or increase revenues plays a role in avoiding bank

default. Our approach entails an empirical analysis of the link between various efficiency

measures and the probability of default of cooperative banks. Moreover, we estimate four

different efficiencymeasures using stochastic frontier analysis and test our results using a

balance‐sheet measure of operating efficiency (i.e., cost‐income ratio, as in Mannasoo and

Mayes,2009).Wespecifythreehypothesesthatfocusonvariousefficiencyconcepts.

First,wepositthat ifabankismorecostefficientthanitscompetitors, it is lesslikelyto

default.Theunderlyingassumptionisthatifbankmanagershavesuperiorskillsinmanaging

costsandinducinghighercostefficiency,thiswillhelpthebanksurviveduringindividualor

sector distress. We call this assumption “cost‐management excellence”. A competing

hypothesis is“cost‐skimping”(originallypositedbyBergerandDeYoung,1997,andrecently

testedbyFiordelisietal.,2011):ifabankismorecostefficientthanitscompetitors,thereisa

8

higher likelihoodofdefault.Theunderlying idea is thatcost‐efficientbanksprobablydevote

fewerresourcestocreditscreeningandmonitoring,whichimpliesatrade‐offbetweenshort‐

termcostefficiencyandfuturerisk‐taking.

HypothesisI(H1):ifabankismorecostefficientthanitscompetitors,ithasalowerprobability

ofdefault(“cost‐managementexcellence”hypothesis).

AlternativeHypothesis I (H1A): if a bank ismore cost efficient than its competitors, it has an

increasedprobabilityofdefault(“cost‐skimping”hypothesis).

Second,we argue that if a bank ismore revenue efficient than its competitors, it has a

lowerlikelihoodofdefault.Theunderlyingassumptionisthatifbankmanagershavesuperior

skills inmanagingrevenueandstimulatinghigherrevenueefficiency,thiswillhelpthebank

survive in cases of individual or sector distress. We name this assumption “revenue‐

managementexcellence”.Acompetinghypothesis is “short‐termrevenue”: if abank ismore

revenueefficientthanitscompetitors,ithasahigherlikelihoodofdefault.Theunderlyingidea

isthatrevenue‐efficientbanksprobablyhavealowerqualityloanportfolio,andcustomersare

therefore willing to pay higher interest rates. This implies a trade‐off between short‐term

revenueefficiencyandfuturebank‐soundness.

Hypothesis II (H2): if a bank is more revenue efficient than its competitors, it has a lower

probabilityofdefault(“revenue‐managementexcellence”hypothesis).

AlternativeHypothesisII(H2A):ifabankismorerevenueefficientthanitscompetitors,ithasan

increasedprobabilityofdefault(“short‐termrevenue”hypothesis).

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Third,weassumethattheprobabilityofdefaultisnotonlyrelatedtothebank’sabilityto

manageeither itscostsorrevenues,butalso to itsability toconcurrentlymanagecostsand

revenues to achieve higher profits. Specifically, a cost‐efficient bank could be disastrous at

managing revenue or the reverse. We posit that if a bank is more profit efficient than its

competitors, it has a lower likelihood of default. The underlying assumption is that higher

profitefficiencyimpliesthatbankmanagershavesuperiorskills inmanagingbothcostsand

revenues,whichwillhelpthebanksurviveintimesofindividualorsectordistress.Wecallthis

assumption“managementexcellence”.SimilartohypothesisH2A,analternativeandcompeting

hypothesisisthatof“short‐termprofits”:ifabankismoreprofitefficientthanitscompetitors,

itwillhaveahigher likelihoodofdefault (due toa lowerquality loanportfolio), implying a

trade‐offbetweenshort‐termprofitsandthefuturesoundnessofthebank.Wetestthesetwo

competingassumptionsusingtwodifferentprofitmeasures:operatingprofits(whichincludes

alloperatingcostsandrevenues)andtheinterestmargin(whichincludesonlyinterestcosts

andrevenues).

Hypothesis III (H3): if a bank is more profit efficient than its competitors, it has a lower

probabilityofdefault(“management‐excellence”hypothesis).

AlternativeHypothesisIII(H3A): ifabankismoreprofitefficientthanitscompetitors,ithasan

increasedprobabilityofdefault(“short‐termprofits”hypothesis).

Our sample comprises more than 4,200 observations and includes the financial

statements of almost all the Italian cooperative banks. The data cover the period between

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1997and2009,althoughwedonotincludetheyears2007and2008becausetheycontainno

defaultevents.EachbankcontributesTtrowsofdata, correspondingtothenumberof time

periodstinwhichitwasatriskoffailure.

Thedataset for theexplanatoryvariables iscomprehensive, combiningbank‐leveldata,

geographical information, and efficiency measures. Market information is not considered

becausecooperativebanksarenotpubliclytradedandhaveverylittlemarketactivity.

We collect data from various sources. Data on distressed banks are retrieved from the

ItalianCentralBank(BankofItaly);accountingdataareobtainedfromtheItalianAssociation

of CooperativeBanks (Federcasse); andwe garner local geographical information from the

Italian National Institute of Statistics (ISTAT). The bank‐level data, a potential leading

indicator of failure, are drawn from the banks’ financial statements. Data are publicly

available formostkey items ‐ liquidity,balance sheets,profitsand losses, off‐balance sheet

items, large depositors, and large exposures. Themajor constraints are information on the

sectorpatternoflending(includingexposuretothepropertysector)andtheinterestrateson

liabilitiesandassets.

4.Methodology

FollowingMännasoo andMayes (2009), we estimate a discrete‐time survival model to

determinetheprobabilityoffailureateachpointintime.Werunatwo‐stageanalysis.First,a

complementary log‐log model (cloglog) is estimated using various efficiency measures,

macroeconomic information, and bank risk‐taking variables. Second, we test out‐of‐sample

theaccuracyofthepredictionofthemodelandtherobustnessoftheresults.

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4.1Thehazardmodel

We estimate the survival model in discrete time because our data set only provides

observationsdiscretely.Wefocusonasingle‐statemodel,andweassumethatwehavesingle‐

spelldataforeachbank.Ourmodel implicitlyassumesthatallrelevantdifferencesbetween

banks can be summarized by the observed explanatory variables. We also assume that

bankruptcyonlyoccursatdiscretepointsintime(t=1,2,3,...,n).Moreover,eachbankeither

fails during the sample period or survives. If banks merge or are liquidated or if the

identification variable (Abi) is not available for the whole observation window, they are

omittedfromthesample.Thus,weconsiderexitsfromasinglestate(soundness)toasingle

destination(failure).

The random variable T denotes the time to exit from the sample (failure) and t the

realizationthereof.Thediscrete‐timedurationmodelimpliesthatweobservetheprobability

ofsurvivalofcooperativebanksatdistinctpointsintime.Becausethesampledatarefertoan

observationwindowof tenyears, thesurvival timedata set is right‐censored,meaning that

weobservethestartdateofthespell(year1996)butnotthetotallengthoftransitionoutof

the current state (fromsoundness to failure). It is alsoassumed that theprocess that gives

risetocensoringisindependentfromthesurvival‐timeprocess.Theprobabilityofexitwithin

thejthintervalisexpressedasfollows:

(1)

wherea1,a2,…..,akaretheintervalboundarydates(years);F(aj)isthecumulativedistribution

functionofTatdurationtime j(failurefunction);andS(aj) isthesurvivalfunctionattime j.

Thediscretehazardrateistheconditionalprobabilityofexitintheinterval(aj‐1,aj]definedas:

1 1 1Pr( ) ( ) ( ) ( ) ( )j j j j j ja T a F a F a S a S a

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(2)

Thediscrete‐timesurvivorfunctionistheproductofprobabilitiesofnotexperiencingthe

eventineachoftheintervalsuptoandincludingthecurrentone.Writtenintermsofinterval

hazardrates,itcorrespondsto:

(3)

Weallowthehazardratetovarybetweenbanksdependingontheircharacteristics,and

we summarize this information in a vector of variables. Time‐varying covariates offer an

opportunitytodynamicallyexaminetherelationshipbetweenthedistressprobabilityandthe

changing conditionsunderwhich thedistress takesplace.Thehazard rate and the selected

characteristicsarelinkedthroughanindexfunction.FollowingMännasooandMayes(2009),

weemployacomplementarylog‐logmodel(cloglog):

( , ) 1 exp[ exp( ' ' ' )]j j j j jh j X EF CAL ENV (4)

where contains time‐varying covariates; , , and are the vectors of coefficients;

denotes efficiency measures; jCAL captures bank‐level fundamentals;

represents environmental variables; and is the log of the difference between the

integrated baseline hazard evaluated at the end of the interval and at the beginning of the

interval(aj‐1;aj].Eachregressioncoefficientsummarizestheeffectonthehazardofabsolute

changesinthecorrespondingcovariates.Thecoefficientsdonotvarywithsurvivaltime.

1 11

( )Pr( | ) 1

( )j

j j jj

S aa T a T a

S a

1 2 11

( ) (1 ) (1 ) ..... (1 ) (1 ) (1 )j

j j kk

S j h h h h h

jX ' ' '

jEF jENV

j

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4.2Variables

4.2.1Eventoffailure

Following previous studies (Arena, 2008; Männasoo and Mayes, 2009, among others),

bank default is defined as the occurrence of public intervention to solve a critical distress

situation.Wemodelbankfailuresusingacategoricalvariablethatequals1ifbankifailedat

timetandequals0otherwise.FollowingItalianlaw,wedefineabankasbeingindefaultifit

underwent either of the two following events between January 1, 1997 and December 31,

2006: a) it entered extraordinary administration (e.g., conservatorship), or b) it entered

liquidation.Eachofthesegovernmentinterventionsobjectivelyshowsthatabankisunableto

continueitsoperations.

WecollectdataondistressedbanksfromtheBankofItaly.Overall,therewere44casesof

governmentintervention(eitherextraordinaryadministrationsorliquidations)intheperiod

analysed,asshown inTable1.Accountingdata forall cooperativebanksareobtained from

theItalianFederationofCooperativeBanks(Federcasse).

<InserthereTable1>

4.2.2Explanatoryvariables

Thesetofpotentialexplanatoryvariablesischoseninordertoexplaintheprobabilityof

failure as a consequence of the better management of bank operations quantified by the

efficiencymeasures.

First,weestimatecostefficiencybyusingBatteseandCoelli’s(1995)stochasticfrontiermodel,

asdetailed inAppendix1.Wealso compute the cost‐to‐income ratio as adirect test tomeasure

14

efficiency in generating operating income.We then include other variables that are likely to

contribute to the survival of a cooperative bank.We take into consideration the economic

conditionsofthelocalareaenvironment(measuredbytheannualgrowthrateinItalianGDP

percapitaandtheemploymentgrowthintheregionalworkforce)becausethesearelikelyto

affectthesurvivalofcooperativebanks(Mare,2012).Asecondgroupofvariablesfocuseson

bank‐specificfactors.Weselecttheindicatorsfollowingthewell‐knownCAMELframework5:

specifically, we measure Capital Adequacy as the ratio between the capital in excess of

regulatory requirements and the minimum capital requirement; we estimate bank Asset

Quality using the ratio of annual loan loss provisions to total loans and we quantify the

LiquidityRiskastheratioofbankdepositstocustomerdeposits.ThetworemainingCAMEL

categories(i.e.,ManagementQualityandEarnings)areexplicitlyincludedintheestimationof

the efficiency measures. We also control for a bank’s asset size and for a bank’s credit

orientation.Table2describesthevariablesemployedintheanalysisandreportstheexpected

signsoftheestimatedparameters.

<InserthereTable2>

The descriptive statistics for the explanatory variables are reported in Table 3. We

separateallbanks into twocategories: failedandnon‐failedbanks.T‐testsarecomputedto

detectstatisticallysignificantdifferencesinunivariatecomparisons.

5CAMEL is the acronym referring to the following five factors introducedbyUS regulators inNovember1979: “C” stands forCapital Adequacy, “A” for AssetQuality, “M” forManagementQuality, “E” for Earnings, and “L” for Liquidity. In 1996, CAMELevolvedintoCAMELS,where“S”istheSensitivitytoMarketRisk.Cooperativebanksengageinverylittlemarketactivity;thus,theCAMELframeworkismoreappropriatetoanalyzetheirbanksoundness.

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<InserthereTable3>

5.Results

WereporttheresultsfromthehazardfunctioninTable4.FollowingMännasooandMayes

(2009), the explanatoryvariables are laggedbyoneyear. Thediscrete‐time survivalmodel

relates a change in the hazard rate due to an absolute change in a given regressor, ceteris

paribus.Thecharacteristicsoftheeconomicenvironment(atboththelocalandnationallevel)

andbank‐specific indicators are introduced to the analysis to control for factors that could

influencethelinkbetweenbankefficiencyandtheprobabilityofdefault.Thecontrolvariables

are standardized tomake it easier to compare the individual contributions of the different

factorstothesurvivalofcooperativebanks.

<InserthereTable4>

To test our research hypotheses, we run our cloglog model (Equation 4) using five

differentspecificationstolinkefficiencyandbankfailure(respectively,oneforeachefficiency

measureandoneusingthecost‐to‐incomeratio).

Our results support the cost‐management hypothesis (H1): we find that higher cost

efficiencyengendersahigherprobabilityofsurvival.Theestimatedcost‐efficiencycoefficient

(inEstimation1ofTable4)isnegativeandstatisticallysignificantatthe1%confidencelevel.

Asaresult,wecanrejectthecost‐skimpinghypothesis(H1A).

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In regard toabank’s ability tomaximize its revenues, our results support the revenue‐

managementhypothesis (H2), suggesting thatbanks that are able to extractmore revenues

fromservicesprovidedtocustomersandachievehigherreturnsfromtheirinvestmentshave

ahigherprobabilityofsurvival.Theestimatedrevenue‐efficiencycoefficient(inEstimation2

ofTable4)isnegativeandstatisticallysignificantatthe10%confidencelevel.Consequently,

wecanrejecttheshort‐termrevenuehypothesis(H2A).

Turning to profits, our findings support the management‐excellence hypothesis (H3)

becausemoreprofit–efficientbanksarefoundtohaveahigherprobabilityofsurvival.Weuse

two measures of profitability: operating income and interest margin. In both cases, the

coefficient(inEstimations3and4ofTable4)isnegativeandstatisticallysignificantatthe1%

confidencelevel.Consequently,wecanalsorejecttheshort‐termprofitshypothesis(H3A).In

Estimation5inTable4,thecost‐to‐incomeratioispositivelyrelatedtoabank’sriskoffailure,

as banks that are less able to contain their operating costs are more likely to be poorly

managedandshowahigherhazardrate.

Wefindthat theCAMELindicatorsarestatisticallysignificant(atthe10%levelor less)

and strongly related to the hazard rate. Specifically, higher capital levels reduce the

probability of default. This supports the view that higher capitalization provides additional

lossabsorbencyandreducesabank’smoralhazard(Laneetal.,1986;Fiordelisietal.,2011;

HaqandHeaney,2012,amongmanyothers).Assuch,strengtheningthecapitalrequirement

in the cooperative banking sector, as proposed in the Basel III agreement6, may help to

preventbankdistress.

6The Basel III framework comprehends a set of documents issued by The Basel Committee on Banking Supervision (firstpublicationinDecember2010).Theaimistoreducetheimpactofbankingcrisesinthefuture.TheBaselIIIagreementfollows

17

Wealsonote thatassetquality (measuredby the loan lossprovision ratio) ispositively

related(atthe1%level)totheprobabilityofdefault.Assuch,inthecaseofadecreaseinasset

quality(i.e.,theloanlossprovisionratioincreases),theprobabilityofdefaultforcooperative

banks increases. In linewithMännasooandMayes(2009),wefindthatthe liquidityratio is

positively and statistically significantly related to the probability of default. This result

suggests that when cooperative banks rely too heavily on the interbank market, they are

exposed to the sudden freezing of funds. This can lead banks to default, especially during

periods of systemic financial distress when funding is critical. Size is negatively related to

bankfailure,aslargercooperativebankshavelessconcentratedportfoliosandcandiversify

lendingtowardsdifferentindustrialsectors.

6.TestingtheModel’sPredictiveAbility

Wetest thepredictiveaccuracyofourmodelboth in‐sampleandbyusingholdoutdata.

Theanalysisofthegoodness‐of‐fitenablesustodeterminehowwelltheeconometricmodel

fits the observed phenomena7. We again run the five models in Table 4 using only the

variables thatwere statistically significant at the 10% level; therefore,we do not consider

employment growth in our computations. In Model 5 of Table 4, we include the cost‐to‐

the publication of the first accord on capital measurement and capital standards (Basel I, July 1988) and a second, morecomprehensiveframework(BaselII,June2004).7As a further test, we run a robustness check by comparing the impact of efficiency on the probability of bank default incooperativeandcommercialbanking.We retrieveaccountingdataon Italiancommercialbanks from theBankscopedatabase.Becausedataondefaultsforcommercialbanksareinsufficienttoestimateamodel(8defaultsovertheperiod1997–2006),wefocuson2009 (6defaults). All estimated coefficients for efficiencymeasures inboth commercial and cooperativebanks havesignsthatareconsistentwiththoseestimatedinColumn5ofTable4.However,theoverallstatisticalpoweroftheestimationispoor,mainlyduetothelownumberofdefaults.Resultsfromthistestareavailableuponrequest.

18

incomeratiobecauseitisstatisticallysignificantatthe10%levelafterremovingtheliquidity

variable,employmentgrowth,andGDPgrowth.

Table5reportsthein‐samplecheckoftheaccuracyofthepredictions.InPanelAofTable

5, we report six indicators: Sensitivity, Specificity, Overall Predictive Power, ROC Area,

Accuracy Ratio, and Brier Score. Efficiency measures, estimated through the stochastic

frontieranalysis,increasethepredictiveaccuracyofthemodelwhencomparedwithModel5,

inwhichthecost‐to‐incomeratioproxiesformanagerialabilitytoreducecosts(inputs)and

toproducerevenues(output).

Sensitivity quantifies the proportion of banks in default that are correctly identified as

such; Specificity measures the proportion of safe banks (e.g., sound) that are correctly

identified.ThesetwoindicatorsarecloselyrelatedtotheconceptsofTypeIandTypeIIerrors:

all estimated models have an in‐sample Sensitivity higher than 54% (70%, if we do not

consider Estimation5,whichhas the lowestperformance) andSpecificityhigher than75%

(80%, ifwe omit Estimation 5,which has the lowest performance), values that are largely

superior to those of a naïve model (i.e., 50%). The Overall Predictive Power is the ratio

betweenthesumofallsafeanddefaultedbanksaccuratelyclassifiedandthetotalnumberof

banks.Allestimationshavein‐sampleOverallPredictivePowerhigherthan74%(80%,ifwe

omit Specification 5,which has the lowest performance, and 83% in the best specification,

which includesoperating cost efficiency), a figure that is largely superior to that of anaïve

model(i.e.,50%).

We compute the ROCCurve, which measures the impact of changes in the probability

threshold,i.e.,thedecisionpointusedbythemodelforclassification.TheareaundertheROC

Curvemeasuresthediscriminatingabilityofabinaryclassificationmodel:thelargerthisarea,

19

thehigher the likelihoodthatanactualdefault casewillbeassignedahigherprobabilityof

being in default than an actual sound case. All estimations have an in‐sample Overall

Predictive Power higher than 76% (83% if we omit Specification 5, which has the lowest

performance, and 88% in the best specification, which includes operating cost efficiency),

whichislargelysuperiortothatofanaïvemodel(i.e.,50%).

WealsocomputetheBrierScore,whichevaluatesthequalityoftheforecastsasfollows:

(5)

where is theestimateddefaultprobabilityof thebanks(from1ton),and is theactual

outcomeof theeventofdefault (equal to1 ifobligor idefaultsand0otherwise).TheBrier

Scoremustthereforealwaysbebetweenzeroandone.TheclosertheBrierScoreistozero,

thebettertheforecastofdefaultprobabilities.Allestimatedmodelshaveanin‐sampleBrier

Scoreclosetozero.

Overall, the specifications (especially Specification 1, which includes cost efficiency)

provide sound estimates in line with (or better than) the overall performance of previous

studies(Shumway,2001;MännasooandMayes,2009;Arena,2008).

<InserthereTable5>

We also run an out‐of‐sample test by estimating hazard rates using the estimated

coefficients and data from 2009. This enables us to validate our results by tackling the

problemofsample‐specificestimation.Themeaningof thegoodness‐of‐fit test is limited,as

1

1( )

n

i ii

B pn

ip i

20

we observe only six default cases in 2009 (and no defaults in 2007 and 2008). Not

surprisingly,we find that thepredictive accuracyof themodel (Table6) is lower than that

obtainedin‐sample(Table5),butthepredictivepowerofourmodelisstillhigh.Theoverall

predictivepowerishigherthan74%forall themodels,andtheBrierScorecontinuestobe

verylow(lowestvalue0.014).

<InserthereTable6>

7.Conclusions

Ourpaperanalysesthecontributionofefficiencytotheprobabilityofbankfailureamong

cooperative banks. Cooperative banks play a key role in the European banking industry.

Despite their importance, these banks experience financial distress more frequently than

commercialbanksduringperiodsoffinancialstability.ThedefaultrateofItaliancooperative

banks was almost four times that of commercial banks in the period before the recent

financial crisis (1997–2006). Specifically, there were 44 default cases among cooperative

banks(defaultrate1.04%)and8amongcommercialbanks(defaultrate0.28%).

Ourpaperanalysesthedeterminantsoftheprobabilityofsurvivalofcooperativebanksby

focusingon the role of efficiency.Our results indicate that lower risk is related to a higher

survival time forcooperativebanks.These findingscontribute to theexisting literaturethat

investigates the direct link between efficiency and risk‐taking (Chortareas et al., 2011;

Chronopoulos et al., 2011; Fiordelisi et al., 2011) by showing that prudent and skilful

managerialabilitiesincreasethesurvivaltimeofcooperativebanks.Tosupportourview,we

testthreeresearchhypothesesthatfocusonthecontributionofefficiencytotheprobabilityof

21

bankfailure.Namely,wepositthatbanksurvival isrelatedtothemanagerialabilitytosave

costs(H1),maximizerevenues(H2),andmaximizeprofits(H3).

We study a large sample of Italian cooperative banks. We show that all efficiency

measureshavelowerhazardrates,meaningthatanincreaseinthesevariablesincreasesthe

survivaltimeofbanks.Specifically,wefindthatmoreefficientbanks(eitherintermsofcost

savingorrevenueandprofitmaximization)showahigherprobabilityofsurvival,supporting

thecost,revenue,andexcellent‐managementhypotheses.

Our findings are of interest for policymakers and supervisors. Recent developments in

banking regulations stem from the idea that efficiency is a key element in assessing the

relationship between bank risk and capital levels. There is a parallel between Basel II

prescriptions regarding internal control processes andhigher efficiency gains becauseboth

contributetoanincreaseintheresilienceofbanks.Similarly,thenewcorporategovernance

directivesforbankssupportthecost,revenue,andexcellent‐managementhypotheses,inline

with the results of the paper. Moreover, we show that higher capital levels reduce the

probabilityofdefault:thissupportstheviewthathighercapitallevelsprovideadditionalloss

absorbency and reduce a bank’smoral hazard. As such, in the cooperative banking sector,

strengthening the capital requirement as proposed in the Basel III agreementmay help to

preventbankdistress.

Acknowledgements

The authorswish to thankAlessandro Carretta, OrnellaRicci, IftekarHasan, PhilMolyneux

andMariaPaulaGerardinowhokindlygavetheircommentsonearlierversionsofthispaper

22

aswellasFedercasseforprovidingthedatanecessaryfortheestimationofthemodelandfor

thehelpfulcollaboration,especially inthepersonsofAlessandraAppennini, JuanLopezand

RobertoDi Salvo. The authors are also grateful to the conference participants at the EURO

Working Group on Efficiency & Productivity analysis (EWG‐EPA, 2010) and the Infinity

ConferenceonInternationalFinance(2011).Allremainingerrorsandomissionsrestwiththe

authors.

23

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Appendix1

Efficiencymeasuresestimation

The set of potential explanatory variables is chosen in order to explain the

probability of failure as a consequence of the better management of bank operations

quantifiedbytheefficiencymeasures.Costefficiencyismeasuredusingstochasticfrontier

analysis and the Battese and Coelli (1995) stochastic frontiermodel.We use the following

translogfunctionalform:

(6)

where TC is the logarithm of the total production cost; yi (i=1, 2, 3, 4) are output

quantities; Pj (j=1, 2, 3) are input prices; ln E is the natural logarithm of total equity

capital;andTisthetimetrendtoaccountforpossiblechangesintechnologyduringthe

observed period. In order to guarantee linear homogeneity in factor prices, it is

necessary(andsufficient)toapplythefollowingrestrictions:1)thestandardsymmetry

and2)linearrestrictionofthecostfunction.Followingpreviousstudies(VanderVennet,

2002;Girardoneetal.,2004),weincludeequityasanetput,specifyinginteractionterms

withbothoutputquantitiesandinputprices.

Italian cooperative banks constitute a heterogeneous dataset. To overcome this

problem and take into consideration local market conditions, we adopt the technical

inefficiencyeffectsmodelproposedbyBatteseandCoelli(1995).FollowingBattagliaet

LnTC a0 bi lnYi i1

4

c j lnPj j1

3

e1 ln E t1T 1

2ij

j1

4

lnYij i1

4

ijj1

3

lnPij e11 ln E ln E t11T2

i1

3

ijj1

3

lnYi ln Pj i lnYi ln E i1

4

i lnYiT i1

4

j lnPj ln E j1

3

j lnPjTj1

3

i1

4

T ln E

29

al.,(2010),weincludealargesetofenvironmentalvariables(Table7)thatareestimated

attheregionallevel8.

<InserthereTable7>

To obtain a complete view of the performance of cooperative banks, we also

estimate revenue‐ and profit‐efficiency measures, which specify various measures of

profits(respectively,totalrevenue,andoperatingincomeandinterestmargin)giventhe

levelofoutputsratherthantheoutputprices.Thefrontierdefinitionisthesameasinthe

cost case, except for the dependent variable: total cost is replaced by the previously

mentionedprofitmeasure.

8Our frontiermodel includesenvironmentalvariablesthatareestimatedat theregional level (foreachof the20Italiancountry regions), but we only report summary statistics at the macro‐geographical‐area level. Statistics at the moredetailedregionallevelareavailableuponrequest.

30

Tables

Table1.Numberofbanksandhistoricaldefaultrates:cooperativevs.commercialbanks

CooperativeBanks CommercialBanks

YearNumberofBanks(A)

Liquidation(B)

Administration(C)

TotalNumberofBanksinDefault

(D=A+B)

DefaultRate(E=D/A)

NumberofBanks(A)

Liquidation(B)

Administration(C)

TotalNumberofBanksinDefault

(D=A+B)

DefaultRate(E=D/A)

1997 405 1 3 4 0.99% 291 ‐ 2 2 0.69%

1998 404 1 5 6 1.49% 299 ‐ ‐ ‐ 0.00%

1999 414 ‐ 4 4 0.97% 288 1 1 2 0.69%

2000 432 ‐ 5 5 1.16% 284 ‐ 1 1 0.35%

2001 436 ‐ 5 5 1.15% 296 ‐ ‐ ‐ 0.00%

2002 436 ‐ 6 6 1.38% 293 ‐ 1 1 0.34%

2003 430 1 6 7 1.63% 282 ‐ 1 1 0.35%

2004 434 ‐ 2 2 0.46% 279 ‐ 1 1 0.36%

2005 424 ‐ 4 4 0.94% 279 ‐ ‐ ‐ 0.00%

2006 432 ‐ 1 1 0.23% 283 ‐ ‐ ‐ 0.00%

Pre‐CrisisPeriod(1997‐2006)

4,247 3 41 44 1.04% 2,874 1 7 8 0.28%

2007 431 ‐ ‐ 0 0.00% 234 ‐ ‐ ‐ 0.00%

2008 431 ‐ ‐ 0 0.00% 255 ‐ 1 1 0.39%

2009 421 1 5 6 1.43% 285 ‐ 6 6 1.75%

CrisisPeriod(2007‐2009)

1,283 1 5 6 0.47% 774 0 7 7 0.90%

OverallPeriod(1997‐2009)

5,530 4 46 50 0.90% 3,648 1 14 15 0.41%

Source:owncalculationsusingdatafromFedercasse.Forcommercialbanks,datawereobtainedfromtheSupervisionBulletinoftheBankofItaly.Datawerenotavailableforalltheactivebanksintheperiod.Notes:ThistablepresentsthehistoricaltimeseriesofItalianbanks,subjecttotemporaryconservatorship(Administration)orclosed(Liquidation)bytheItalianbankingsupervisor(BankofItaly).Dataarepresentedseparatelyforcooperativeandcommercialbanks.Cooperativebanks'defaultrateismorethantwicethefigureforcommercialbanksduringtheoverallperiod(1997–2009)andalmostfourtimeshigherduringthepre‐crisisperiod(1997–2006).Duringthe2007–2009financialturmoil,thistendencywasreversed,withthecommercialdefaultraterisingtoalmosttwiceashighasthefailurerateforcooperativebanks.

31

Table2.Variabledefinitions

Variable Definition Representativestudies

Cost Thisisthecostefficiency,estimatedusingthemethodillustratedinAppendix1.

Variousstudies,seeareviewinHughesandMester(2010)

RevenueThisistherevenueefficiency,estimatedusingthemethodillustratedinAppendix1. FiordelisiandMolyneux(2010)

Operating Thisistheprofitefficiency,estimatedusingthemethodillustratedinAppendix1.

Variousstudies,seeareviewinHughesandMester(2010)

InterestThisistheinterestmarginefficiency,estimatedusingthemethodillustratedinAppendix1.

Cost‐Income Thisistheratiobetweenoperatingexpensesandoperatingincome.

Laneetal.(1986);MännasooandMayes(2009)

CapitalAdequacyThisistheratiobetweencapitalinexcessofregulatoryrequirementsovertheminimumcapitalrequirements. Regulatoryrequirements

CreditOrientation Thisistheratiobetweentotalloansandtotalassets. Laneetal.(1986);MännasooandMayes(2009)

AssetQualityThisistheratiobetweenloanlossprovisionsandtotalloans.

MännasooandMayes(2009);Arena(2008)

Liquidity Thisistheratiobetweenbankdepositsandcustomerdeposits.

MännasooandMayes(2009)

Size Thisisthenaturallogarithmoftotalassets. ColeandWhite(2012);Arena(2008)

EmploymentGrowthThisistheregionalworkforceemploymentgrowthoveratwo‐yearperiod. DeYoung(2003)

GDPGrowth ThisistheannualgrowthrateintheItalianGDPpercapita(atcurrentprices).

Arena(2008);Sundararajanetal.(2002)

Notes:Thistablereportsthenamesanddefinitionsofthevariablesemployedintheestimation.Thecolumn“representativestudies”listssomestudiesthathaveusedtheexplanatoryvariables.

32

Table3.Descriptivestatistics

All Non‐Failed Failed T‐testforMeans

Variables Mean S.E. Mean S.E. Mean S.E. Difference t‐statistic

CostEfficiency

0.630 0.269 0.632 0.269 0.487 0.210

0.144 3.543***

RevenueEfficiency

0.630 0.263 0.629 0.263 0.702 0.268

‐0.073 ‐1.843*

OperatingEfficiency

0.611 0.271 0.614 0.269 0.329 0.231

0.284 6.978***

InterestEfficiency 0.729 0.242 0.731 0.241 0.542 0.230 0.189 5.172***

Cost‐Income 0.780 0.127 0.779 0.123 0.900 0.310 ‐0.122 ‐6.380***

CapitalAdequacy 2.631 2.230 2.629 2.223 2.768 2.851 ‐0.139 ‐0.4107

CreditOrientation 0.642 0.122 0.641 0.122 0.716 0.128 ‐0.075 ‐4.038***

AssetQuality 0.003 0.005 0.003 0.005 0.010 0.011 ‐0.007 ‐9.083***

Liquidity 0.026 0.045 0.026 0.044 0.031 0.059 ‐0.005 ‐0.779

Size 11.663 0.983 11.675 0.971 10.490 1.324 1.185 8.016***

EmploymentGrowth 0.021 0.020 ‐ ‐ ‐ ‐ ‐ ‐

GDPGrowth 3.877 1.248 ‐ ‐ ‐ ‐ ‐ ‐

Notes:Thistablereportsthedescriptivestatisticsforthevariablesemployedtoexplainbankfailuresovertheperiodfrom1997–2006.Dataarepresentedforallbanksandseparatelyforsurvivingbanksanddefaultedbanks.Inthelasttwocolumns,wepresentthedifferenceinmeansbetweenthetwogroups(Non‐FailedandFailed)andthet‐statisticunderthehypothesisofequalityofvariancesforthetwopopulations.Thet‐statisticiscomputedastheratioofthedifferenceinmeanstothedifferenceinstandarderrors.

33

Table4.Estimationresultsofthediscrete‐timehazardregressionmodelincooperative

bankingbetween1997and2006

Models

Variables (1) (2) (3) (4) (5)Cost ‐4.34***

(1.017) Revenue ‐1.643*

(0.927) Operating ‐3.559***

(0.962) Interest ‐1.959***

(0.662)Cost‐Income 0.060

(0.051)CapitalAdequacy ‐0.752*** ‐0.548*** ‐0.493** ‐0.524*** ‐0.653***

(0.202) (0.203) (0.195) (0.191) (0.225)CreditOrientation 0.896*** 0.472** 0.425** 0.501*** 0.623***

(0.164) (0.207) (0.178) (0.178) (0.166)AssetQuality 0.453*** 0.583*** 0.489*** 0.497*** 0.544***

(0.076) (0.08) (0.077) (0.077) (0.073)Liquidity 0.322*** 0.254** 0.357*** 0.323*** 0.249**

(0.102) (0.105) (0.095) (0.099) (0.106)Size ‐0.678*** ‐1.082*** ‐0.728*** ‐0.85*** ‐0.949***

(0.208) (0.17) (0.167) (0.164) (0.183)EmploymentGrowth ‐0.311 9.325 2.743 4.064 6.631

(8.224) (8.59) (7.78) (7.913) (8.398)GDPGrowth ‐0.484*** ‐0.531*** ‐0.451*** ‐0.534*** ‐0.738*** (0.098) (0.164) (0.094) (0.103) (0.08)Observations 4215 4215 4215 4215 4215NumberofFailures 44 44 44 44 44NumberofBanks 476 476 476 476 476Notes:Thistablepresentstheresultsofthesurvivalmodelestimatedindiscretetime.Thefivemodelsincludethesamesetofvariablesapartfromtheefficiencymeasure.InModel(1),weincludecostefficiency;inModel(2)weconsiderrevenueefficiency;Model(3)comprisesoperatingincomeefficiency;inModel(4)weevaluatethecontributionofinterestmarginefficiency;andinModel(5)weconsiderthecost‐to‐incomeratio.Standarderrorsareinparenthesis.*,**,***indicatesignificanceatthe10%,5%,and1%levels,respectively,withrobuststandarderrors.

34

Table5:Predictiveaccuracy:in‐samplechecks

PanelA:Goodness‐of‐fitindicators

Measure Models1 2 3 4 5

Sensitivity 0.795 0.705 0.773 0.750 0.545Specificity 0.833 0.801 0.814 0.813 0.748OverallPredictive

0.832 0.800 0.813 0.812 0.745

ROCArea 0.879 0.832 0.866 0.845 0.765AccuracyRatio 0.757 0.664 0.733 0.689 0.531BrierScore* 0.947 0.939 0.908 0.926 1.108Source:owncalculations.*BrierScoreismultipliedby100.Notes:Thistablereportstheresultsofthemeasuresofpredictivepowerofthemodelin‐sample.

PanelB:Probabilityrankingsversusactualbankruptcies;percent*

Measure Models1 2 3 4 5

1‐5 0.068 0.136 0.045 0.114 0.0916 0.023 0.000 0.023 0.000 0.1147 0.023 0.068 0.023 0.068 0.1368 0.091 0.091 0.068 0.068 0.1599 0.114 0.091 0.091 0.182 0.13610 0.682 0.614 0.750 0.568 0.364Source:owncalculations.*Probabilityrankingsversusactualbankruptcies;percentclassifiedoutof44possible.**Decilesofthedistributionoftheestimatedhazardrate.Notes:Thistablereportstherankingofthebanksusingtheestimatedhazardrate.Noticethatthesumisnotnecessarilyequaltooneduetorounding.

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Table6:Predictiveaccuracy:out‐of‐samplechecks

PanelA:Goodness‐of‐fitindicators

Measure Models1 2 3 4 5

Sensitivity 0.500 0.167 0.167 0.167 0.000Specificity 0.793 0.894 0.878 0.749 0.998OverallPredictive

0.789 0.884 0.868 0.741 0.984

ROCArea 0.715 0.657 0.680 0.567 0.626AccuracyRatio 0.430 0.313 0.359 0.134 0.252BrierScore 0.016 0.015 0.014 0.015 0.014Source:owncalculations.Notes:Thistablereportstheresultsofthemeasuresofthepredictivepowerofthemodelout‐of‐sample.Thecoefficientsestimatedthroughthemodelaremultipliedbythevaluesoftheexplanatoryvariablesin2008toobtaintheestimatedhazardratefor2009(see§4foradetailedexplanationoftheestimationofthediscrete‐survivalmodel).

PanelB:Probabilityrankingsversusactualbankruptcies;percent*

Measure Models1 2 3 4 5

1‐5 0.167 0.167 0.333 0.500 0.3336 0.167 0.333 0.000 0.000 0.0007 0.000 0.167 0.000 0.333 0.1678 0.167 0.000 0.000 0.000 0.3339 0.167 0.167 0.500 0.000 0.00010 0.333 0.167 0.167 0.167 0.167Source:owncalculations.*Probabilityrankingsversusactualbankruptcies;percentclassifiedoutof6possible.**Decilesofthedistributionoftheestimatedhazardrate.Notes:Thistablereportstherankingofthebanksusingtheestimatedhazardrate.Noticethatthesumisnotnecessarilyequaltooneduetorounding.

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Table7:Environmentalvariablesincludedintheefficiencyestimation(meanvaluesby

macro‐geographicalarea)

Centre NorthEast NorthWest South Total

Z1 Population density (number of inhabitants persquarekilometre)(A)

194.00 132.74 337.80 214.53 192.17

Z2Index of concentration in the territory, (percentageratio between people resident in the main city of theregionandthoseresidentinthetowns)(A)

64.76 33.22 32.24 33.77 39.13

Z3Grossdomesticproductperhead(A) 24.75 27.73 28.81 15.18 24.20

Z4Entrepreneurialliveliness(ratioofthenetnumberofincorporationsintheRegistrarofCompanies)(A)

2.11 1.77 1.79 2.82 2.10

Z5 Incidence of nonperforming loans (incidence ofprecarious loans, overdue bills, groundings, andrestructured loanson the totalamountofbankassets)(B)

7.90 6.50 5.77 16.43 9.13

Z6 Number of cash points (ATM and POS) owned bycooperativebanksoverthetotalexistingintheterritory(B)

10.23 19.13 6.52 6.05 12.52

Z7 Number of bank branches owned by cooperativebanksoverthetotalexistingintheterritory(B)

9.66 37.80 8.58 9.12 21.47

Z8NumberofATMandPOS(ownedbycooperativesandotherbanks)per1,000inhabitants(B) 18.45 25.51 15.50 8.63 18.65

Z9 Number of branches (owned by cooperatives andotherbanks)per1,000inhabitants(B) 0.58 0.85 0.62 0.32 0.64

Z10 Index of firm weakness (number of bankruptciesdeclaredper1,000firms)(A)

2.97 1.75 2.53 2.66 2.31

Z11Level of criminality(number of bank robberies per1,000branches)(C)

77.06 41.40 93.44 91.45 67.52

Z12 Index of solidarity (number of blood donors per1,000inhabitants)(D)

0.22 0.35 0.34 0.12 0.27

(A)Sourceofdata:ISTAT(ItalianNationalInstituteofStatistics)(B)Sourceofdata:StatisticalBulletinsattachedtothemagazineCooperazionediCredito(C)Sourceofdata:Ministerodell’Interno(MinistryofHomeAffairs)(D)Sourceofdata:AVIS(ItalianAssociationofBloodDonors)