CREDIT RISK AND EFFICIENCY IN THE EUROPEAN BANKING SYSTEMS: A THREE-STAGE ANALYSIS*

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1 CREDIT RISK AD EFFICIECY I THE EUROPEA BAKIG SYSTEMS: A THREE-STAGE AALYSIS* José M. Pastor WP-EC 99-8 Correspondenca a: José M. Pastor: Departamento de Análss Económco, Unverstat de Valènca, Campus dels Tarongers, s/n, Ed. Departamental Orental, Valenca (SPAI), e-mal: ose.m. Edtor: Insttuto Valencano de Investgacones Económcas, S.A. Prmera Edcón Dcembre 999. IVIE workng-papers offer n advance the results of economc research under way n order to encourage a dscusson process before sendng them to scentfc ournals for ther fnal publcaton. * The author wshes to express hs grattude to Mr. Davd Humphrey for hs suggestons and comments. Ths study was carred out durng the author's tme as a vstng lecturer n Florda State Unversty. The author also wshes to thank the Fundacón Caa Madrd and SEC for fnancal support, and the IVIE for provdng the data base.

2 CREDIT RISK AD EFFICIECY I THE EUROPEA BAKIG SYSTEMS: A THREE-STAGE AALYSIS José M. Pastor ABSTRACT Increased competton and the attempts of European banks to ncrease ther presence n other markets may have affected the effcency and credt rsk. The frst of ths aspects s based on the ncentve to the banks to reduce cost n order to gan n compettveness. The second s assocated to ther lack of knowledge of such markets and/or acceptance of a hgher rsk n order to ncrease ther market share. Despte the mportance of these aspects, bankng lterature has usually analyzed the effects of competton on the effcency of bankng systems wthout consderng these aspects. The few studes that attempt to obtan rsk adusted effcency measures do not consder that part of the rsk s due to exogenous crcumstances. Ths artcle proposes a new three stage sequental technque, based on the DEA model and on the decomposton of rsk nto ts nternal and external components, for obtanng effcency measures adusted for rsk and envronment. It s seen that the technque allows the use of any exstng technque of ncorporaton of envronmental varables n DEA analyss. Key words: DEA, credt rsk, bad loans, effcency, envronmental varables. RESUME El ncremento de la competenca y los ntentos de los bancos europeos por aumentar su presenca en otros mercados pueden haber afectado tanto al nvel de efcenca bancara como al resgo de crédto. El prmero de los aspectos se fundamenta en el ncentvo que tenen los bancos a reducr los costes para ganar compettvdad. El segundo, está asocado a la ausenca de competenca en tales mercados y/o a la aceptacón de nveles mayores de resgo con el fn de ncrementar la cuota de mercado. A pesar de la mportanca de estos aspectos, la lteratura bancara tradconalmente ha analzado los efectos de la competenca en la efcenca de los sstemas bancaros sn consderar estos efectos sobre el resgo. Los escasos estudos que ntentan obtener meddas de efcenca austadas por el resgo no consderan que parte del resgo es debdo a crcunstancas exógenas. Este artículo propone una nueva técnca secuencencal en tres etapas, basado en el modelo DEA y en la descomposcón del resgo en sus componentes externo e nterno, para la obtencón de meddas de efcenca austadas por el resgo y el ambente. La técnca se aplca al análss de la efcenca de los sstemas bancaros europeos y permte el uso de cualquera de las tecncas exstentes para la ncorporacón de varables ambentales en un contexto DEA. Palabras clave: DEA, resgo de crédto, morosdad, efcenca, varables ambentales. 2

3 . ITRODUCTIO The ncreased competton assocated wth the process of lberalzaton and globalzaton and the attempts of European banks to ncrease ther presence n other markets may have affected the effcency and credt rsk of the European bankng nsttutons. The frst of these aspects, already analyzed n other studes, s based on the ncentve to the banks to reduce costs and to mprove the management of ther resources n order to gan n compettveness. The second aspect, whch has not yet been analyzed, s explaned by the poorer knowledge of the new markets by the newly entered banks and/or the greater permssveness n the acceptance of rsk wth a vew to ncreasng the market share n certan sectors and/or regons. Despte the mportance of these two aspects, bankng lterature has usually analyzed bankng effcency wthout consderng them together. Tradtonal effcency measures, based on the consderaton of outputs and nputs, are usually a good nstrument of analyss of the performance of frms; however, t s sometmes necessary to consder other factors. In the case of bankng, one of the most mportant of these s rsk, as t s desrable not only that a bankng frm should be effcent, but also that t should be secure. Ths s certanly not exclusve to the bankng sector, but t s of greater mportance than n other sectors, gven the potental economc repercussons of bankng falures. However, despte ts mportance, the relatonshp between rsk and effcency has hardly been studed n the lterature. Only the studes by Berg et al. (992), Hughes et al. (993 and 996) and Mester (994a, 994b) have attempted to obtan rsk-adusted effcency measures. However, ther approaches may be unsutable nsofar as they are based on the ncluson of rsk (measured by means of total bad loans) as an addtonal nput, mplctly assumng that all bad loans are caused by the bad management of banks, wthout consderng that some may be due to adverse economc crcumstances beyond the banks' control. If these exogenous or uncontrollable factors are not fltered out, the effcency of those frms whose bad loans are due to an adverse economc envronment wll be underestmated. Furthermore, none of the exstng studes attempts to decompose total bad Toevs and Zzka (994) affrm that standard ratos, normally used by fnancal analysts as ndcators of effcency, do not consder rsk. Furthermore, they affrm that to try to mprove effcency can be counterproductve, as banks may do so by transferrng ther actvtes towards hgh-rsk busness, wth low operatng costs and hgh proftabltes. 3

4 loans nto these two components: bad loans due to bad management (nternal factors) and bad loans due to economc envronment (external factors) 2. Internatonal comparsons of bankng effcency have not loomed large n the lterature. The lack of homogeneous accountng data and the exstence of dfferent regulatory frameworks notably complcate these comparsons. The very few studes n ths feld, based on the constructon of a common fronter for all countres, have tradtonally found hgh degrees of neffcency. Ths result may be due to the fact that the procedure used mplctly assumes that any dfference of effcency between countres s exclusvely due to bad management, wthout also consderng the possble exstence of technologcal dfferences (Pastor, Pérez and Quesada, 997) or dfferences n the economc envronment (Pastor, Lozano and Pastor, 997) whch may bas the results and provde under-estmated effcency measures for those bankng systems that are subected to less favorable economc envronments. To avod ths problem t s necessary to ntroduce envronmental varables to control for the dfferent economc crcumstances under whch the bankng frms of dfferent countres carry out ther actvty. In ths respect, the most notable exceptons are the recent studes by Detsch and Lozano (996) and Pastor, Lozano and Pastor (997) whch ncorporate envronmental varables wth the am of establshng a common standard of comparson for all frms. However, unlke parametrc fronter models, the ncorporaton of envronmental varables n DEA models s a feld stll beng researched, offerng a wde varety of proposals whch have to be consdered and compared. In ths context, and n order to solve these problems, ths study proposes a new (three stage) sequental technque, based on the DEA technque, to dentfy and decompose the orgn of bad loans and to obtan effcency measures adusted for rsk and envronment, more refned than those htherto proposed n other studes, to allow analyss of how not only the evoluton of effcency, but also rsk management, have responded to lberalzaton measures. The procedure proposed enables the total bad loans of each bank to be decomposed, n a frst phase, nto ts two components: one part due to bad rsk management and another due to exogenous economc and envronmental factors. For ths purpose we use varous approaches for ncorporatng envronmental varables nto DEA, wth the am of 2 Only Pastor (999) and Saurna (998) analyse the determnants of bad loans dstngushng between nternal and external factors, though the latter does not use the results to decompose bad loans. 4

5 testng whether ths leads to sgnfcant dfferences n the results. In the second phase, ncorporatng nto the model only the proporton of bad loans due to bad management, we obtan the rsk-adusted effcency measures. Fnally, n the thrd phase, by ncorporatng economc envronment varables, we obtan ndcators of effcency whch, as well as beng adusted for rsk, are adusted for the economc envronment. The results are used to determne the nfluence on effcency of rsk ("rsk effect") and of envronment ("envronment effect"). The paper s organzed as follows. The second secton revews the exstng studes on rsk and effcency, the studes that analyze nternatonal comparsons of effcency and the dfferent proposals for ncorporaton of envronmental varables nto DEA. Secton 3 lays out the methodology proposed for decomposng bad loans and calculatng the rsk management effcency and the rsk and envronment-adusted effcency measures. Ths methodology allows the applcaton of the dfferent proposals for ncorporaton of envronmental varables nto DEA models. Ths secton also descrbes the procedure for decomposng the overall effcency measure nto the rsk and envronment-adusted effcency, the rsk effect and the envronment effect. Secton 4 descrbes the data used, secton 5 gves the results, and fnally secton 6 presents the conclusons. 2. LITERATURE REVIEW 2.. The relatonshp between rsk and effcency There are many aspects n whch credt rsk (usually measured through bad loans, problem loans or provsons for loans losses) s related to effcency. They have all been excellently analyzed by Berger et al. (997) who fnd that there s a negatve relatonshp between cost effcency and rsk n faled banks 3. Berger et al (997) offer several reasons for ths negatve relatonshp. Frst, neffcent banks, as well as havng problems of controllng ther nternal costs, may have 3 Other studes fnd that faled banks are usually cost neffcent (Berger et al., 992; Barr et al., 994; Wheelock et al., 995 and Becher, et al., 995), or that an ncrease n bad loans s usually preceded by an ncrease n cost neffcency (De Young et al., 994). 5

6 problems n the assessment of the credt rsk, so that a bad management of costs goes together wth greater credt rsk. Berger et al (997) call ths orgn of rsk "bad management hypothess". Second, bad loans may arse because of adverse economc crcumstances beyond the bank's control, so that banks have to spend more resources to recover the problem loans. Ths orgn of credt rsk they call "bad luck hypothess". Alternatvely, there could be a postve relatonshp between cost effcency and credt rsk when banks decde not to spend suffcent resources on analyzng loan applcatons. In ths way they would appear to be effcent but wth a hgh level of bad loans. Berger et al (997) call ths "skmpng hypothess". In spte of the extensve analyss by Berger et al. (997), ther procedure, based on the Granger causalty test, does not enable the orgns of rsk to be found at ndvdual level, but reaches very broad conclusons for the ndustry as a whole. Also, the conclusons wll depend on the proporton of banks actng on each partcular hypothess, so the results obtaned wll always be underestmated because frms do not act unformly 4. Furthermore, as they themselves affrm, the Granger causalty test measures statstcal assocatons that n no way mply economc causaton. In the lterature on bankng there s no study that decomposes the orgns of bad loans and, although some studes have attempted to obtan rsk-adusted effcency measures 5, the method used s unsutable for two fundamental reasons. Frst, these studes attempt to obtan rsk-adusted effcency measures by ntroducng the measurement of credt rsk (bad loans) drectly n the model as an addtonal nput. Ths procedure would characterze banks adequately only f bad loans orgnated exclusvely n the "bad management" of rsk. However, ths stuaton s not reasonable, as the economc envronment also nfluences banks' levels of bad loans, so that part of them s due to what Berger et al. (997) call "bad luck". If what s wanted s to evaluate the effcency of banks whle controllng for rsk, only the proporton bad loan caused by nternal factors ("bad management") should be consdered, whle the proporton of bad loan caused by external factors ("bad luck") should be excluded. 4 Berger and De Young fnd that some hypotheses are only consstent wth sub-sets of data, as when the whole set of data s consdered there s a mxture of effects. 5 The frst study was by Berg et al (992) usng the DEA technque. Subsequently Hughes et al. (993 and 996), Mester (994a, 994b) used parametrc technques. 6

7 Second, not all bad loans have the same probablty of beng recovered. The European central banks, followng the European Unon drectves, regulate the provsons to be made n each partcular crcumstance. Therefore, gven that these provsons are drectly related to the probablty of recoverng the loans, t seems more approprate to measure the rsk by usng the provsons for loans losses (PLL) nstead of loans losses tself, as the frst mplctly consders the rsk assocated wth each problem loan. Therefore, unlke the approach of Berger et al. (997), whch only enables generc conclusons to be reached, ths study proposed a technque for dentfyng the causes of bad loan at ndvdual level (usng ther termnology, "bad management" or "bad luck") and, unlke Hughes et al. (993 and 996) and Mester (994a, 994b) who obtan measurements of effcency adusted for rsk by consderng total bad loans, ths study only ncorporates that proporton caused by nternal factors ("bad management"). The method proposed s appled to the commercal banks of the prncpal European bankng systems wth the am of analyzng how the effcency of bankng frms and ther behavor have evolved n the face of the rsk mplct n the creaton of the Sngle Market and the processes of de-regulaton Internatonal comparsons of bankng effcency Internatonal comparson of bankng effcency, although t has been researched before, has not loomed large n the lterature. The only studes 6 are those by Berg et al., Førsund, Halmarson and Suomnen (993), Berg, Bukh and Førsund (995) and Bergendahl, (995), who compare the effcency of the bankng systems of the Scandnavan countres, Fecher and Pesteau (993) who appled free dstrbuton fronter technques to the analyss of eleven countres of the OECD, Pastor, Pérez and Quesada (997) who appled the DEA technque and the Malmqust ndex to the analyss of the effcency and productvty of eght countres of the OECD, Allen and Ra (996) who used the free dstrbuton and parametrc stochastc fronter technques to compare the effcency of ffteen developed countres, Detsch and Lozano (996) who used a parametrc fronter to test whether the technology of the French and Spansh bankng systems s smlar when envronmental varables are consdered, and Pastor, Lozano and Pastor (997) who analyze the effcency fltered for envronmental factors of ten communty countres. 6 See Berger and Humphrey (997). 7

8 Wth the only excepton of Pastor, Pérez and Quesada (997), all these studes share the characterstc of beng based on the constructon of a common fronter for all countres and assume, at least mplctly, that the dfferences of effcency among bankng systems are due only to dfferences n management. evertheless, t s possble that the technology underlyng the producton of bankng servces may be dfferent, and that the dfferences n effcency reflect the exstence of dfferent technologes, as shown by Pastor, Pérez and Quesada (997) or alternatvely t s possble that the technology may be very smlar, so that the effcency s n fact reflectng dfferences specfc to the envronment of each country, as shown by Detsch and Lozano (996) and Pastor, Lozano and Pastor (997). If ths s so,.e. f there exst mportant dfferences n the envronment, the constructon of a common fronter that does not consder these dfferences wll generate underestmated measurements of effcency, because effcency would not only be ncorporatng bad management but also the exstence of an unfavorable envronment. Indeed, except for the cases where very smlar bankng systems are beng analyzed (Berg et al., 993 & 995), the measurements of effcency obtaned are usually very low. One way of solvng these problems, wthout havng to resort to the constructon of a specfc fronter for each bankng system, s to consder a homogeneous lne of bankng busness n order to ensure that the technology of the banks specalzng n that busness wll be smlar, and to ncorporate envronmental varables n order to guarantee that the comparson wll be made consderng exclusvely frms subect to a smlar envronment 7. Thus, n ths study, as n Pastor, Pérez and Quesada (997) and Pastor, Lozano and Pastor (997), only banks specalzng n commercal bank busness are consdered, and as n Detsch and Lozano (996) and Pastor, Lozano and Pastor (997) a set of envronmental varables are consdered. 7 Pastor, Pérez and Quesada 997) use only commercal banks, Pastor, Lozano and Pastor (997) lkewse use commercal banks and ncorporate envronmental varables. However, n both cases the heterogenety of the sample s stll hgh, and consequently the measurements of effcency are stll very low. 8

9 2.3. DEA Model: Incorporaton of envronmental varables nto DEA models Measurements of effcency n tradtonal DEA models are obtaned by solvng problems of the type (Banker et al., 984): [] Mn = = ϑλ, = λ y y ; r =,..., R r λ x ϑ x ; s =,..., S s ϑ λ = ; λ 0; where y ( y, y,..., y ) s the vector of R outputs, x ( x x x ) = 2 R,,..., s the vector of = 2 S S nputs. Solvng the above problem for each of the banks we obtan optmum solutons. Each optmum soluton ϑ * s the effcency measure of bank and, by constructon, satsfes ϑ *. Those banks wth ϑ * < are consdered neffcent, whle those wth ϑ * = are consdered effcent 8. Unlke parametrc models, n whch ncorporaton of envronment varables s drect, snce they entry as addtonal explanatory varables, n DEA ths s a feld n whch research s stll beng done and about whch there s no consensus. The problem arse because there s not nformaton about the negatve or postve nfluence of each envronment varable, n other words, the researcher does not know f a gven varable should be consdered as output or as nput. The proposals are very vared (Rouse, 996) and can be classfed nto methods of one, two and three stages. The one-stage approach s the most drect and most easly nterpreted, and conssts of consderng together outputs, nputs and envronmental varables, restrctng the problem of 8 From an ntutve pont of vew, to analyse the effcency of the productve scheme of frm (y, x ) the problem constructs a feasble scheme as a lnear combnaton of the schemes of the frms of the sample whch, usng ϑ x nputs produce at least y. In ths way, (-ϑ ) ndcates the maxmum radal reducton to whch the nput vector of frm can be subected wthout alterng the observed levels of nput, so that ϑ s the ndcator of techncal effcency. In the event that ϑ =, what occurs s that t s not possble to fnd any lnear combnaton of frms whch, wth less nput, obtans at least as much output, so that the frm s catalogued as effcent. In the other cases, ϑ <, ndcatng that the productve scheme followed by frm s neffcent, snce another feasble alternatve scheme exsts whch obtans the same amount of output usng ϑ x nput, quantfyng ts overuse of resources n comparson wth the alternatve scheme as (-ϑ )x. 9

10 optmzaton to only the outputs and/or nputs. Ths method, proposed by Banker et al. (986a & 986b), has the am of lmtng the feld of comparson to only those unts of decson subect to equal or worse envronmental condtons. However, despte beng easy to nterpret and to apply, t poses three fundamental problems: ) the nfluence of each envronmental varable has to be known a pror n order to orentate ts nfluence on the optmzaton; 2) Those unts of decson n worse condton are, by defnton, consdered to be effcent; and 3) the number of effcent unts grows wth the number of envronmental varables ntroduced (restrctons) 9. The commonest two-stage method conssts of regressng n a second stage the ndces of effcency obtaned n the frst stage aganst the set of envronmental varables 0. It has usually been crtczed for the fact that the ndces of effcency generated are not contaned n the nterval (0,]. However, ths crtcsm s groundless f we apply lmted dependent varable models (Tobt) or smply regress an exponental functon n order to prevent predctons above unty. The advantages of ths procedure are: ) easy mplementaton; 2) possblty of consderng many envronmental varables smultaneously wthout ncreasng the number of effcent unts; 3) there s no need to know the orentaton of the nfluence of each envronmental varable; and 4) possblty of use when some (or all) of the envronmental varables are common to sub-sets of ndvduals. Lastly, Fred and Lovell (996) propose a three-stage method. In the frst stage they propose usng a DEA model wth nputs and outputs. In the second stage, they nclude the slacks obtaned n the frst stage and the envronmental varables n a stochastc fronter 9 The frst problem s not usually very mportant, as on most occasons the nfluence of the envronmental varables s well known. However, the second problem s especally serous n those cases where a broad set of ndvduals share the same envronmental condtons, as n ths case ths whole sub-set would be consdered effcent. Pastor, Lozano and Pastor (997) propose a soluton to ths problem, consstng of groupng the envronmental varables nto ntervals n order to wden the feld of comparson. Ray (988), Golany et al. (993) and Cooper et al. (996) 0 The frst to apply ths technque was Tmmer (97). After hm, lmted dependent varable models have been used profusely (McCarty et al., 993). Ths procedure has tradtonally been used to explan dfferences n effcency rather than to flter ther mpact. An alternatve two stage method s that of Pastor (995b). Ths method s based on the applcaton of DEA only to nputs (or outputs) and to the envronmental varables n a frst stage. In the second stage Pastor (995b) proposes radal expanson of the nputs (or outputs) top elmnate the effect of the envronmental varables. The procedure, though t has the advantage of generatng predctons contaned wthn the nterval (0,], presents the dsadvantage that n the frst stage outputs are not consdered, and frms that use more nputs are assumed to do so because of unfavourable crcumstances, wthout consderng that t s because they produce more output. 0

11 approach (SFA) model or n a DEA model. The am s to obtan slacks fltered for the nfluence of the envronmental varables. These fltered slacks are used to adust the nputs (and/or outputs) whch wll be used n the thrd stage to obtan the defntve ndces of effcency fltered for the envronmental varables. It s not clear whether the hgh cost of ths method n terms of tme and computaton requrements s compensated by a notable mprovement n the results. Only the stochastc fronter verson, by ncorporatng randomness, could present certan vrtues n comparson wth other methods. In order to test the vrtues and dsadvantages of each of these methods (see table ), n ths study all of them are used and compared. 3. METHODOLOGY 3.. Phase : Rsk management effcency and decomposton of bad loans It has been shown n prevous sectons that bad loans can appear due to two dfferent causes: nternal and external. Gven that external causes are beyond the control of the frms, the effcency measure n the management of rsk must be calculated by elmnatng the effect of these external factors on bad loan. Ths secton descrbes the method, based on the DEA technque and on the ncorporaton of envronmental varables, for estmatng effcency n rsk management and decomposng our measurement of credt rsk (PLL) nto the part due to nternal factors assocated wth bad management and the part due to external factors. The procedure conssts of comparng each bank wth a lnear combnaton of banks whch, wth an equal (or hgher) volume of loans, have a smaller (or equal) amount of PLL gven the envronmental condtons. The proposed technque enables the use of any of the exstng technques of ncorporaton of envronmental varables nto DEA. Snce allowance s made for the envronment (or the state of the economy) the ndcator of effcency obtaned (γ ) ndcates the potental reducton of PLL that could be acheved wthout reducng the total amount of loans granted, gven the exstng state of the economy. We call ths measurement "rsk management effcency" because t measures the proporton of bad loans (measured by

12 Table : Methods to nclude envronmental varables n a DEA model. Method Stage 2 Stages 3 Stages Advantages Dsadvantages References Stage Incorporate envronmental varables together wth nputs and outputs n order to lmt the comparson to the unts that are subect to equal or worse envronmental condtons. ) Easly appled, 2) Easly nterpreted. 3) Speed. ) The nfluence of each varable must be known a pror. 2) Problems caused when some (or all) varables are common to sub-sets of ndvduals. 3) The number of effcent unts ncreases wth the number of envronmental varables ntroduced. Banker et al (986a y 986b), Lozano et al. (996), Ray (988), Golany et al. (993), etc. 2 Stages The effcency ndces obtaned n The DEA model only consders nputs stage are regressed usng an OLS, and outputs. Tobt or non-lnear logstc regresson. ) Easly appled. 2) Easly nterpreted. 3) Speed. 4) Can be used when some (or all) of the varables are common to sub-sets of ndvduals. 5) Varables can be ntroduced wthout ncreasng the number of effcent unts. 6) Does not requre the orentaton of the envronmental varables to be known beforehand. ) If OLS s used n the second stage, the effcency ndces may not be contaned wthn the nterval (0,]. Tmmer (97), McCarty et al. (993), etc. 3 Stages (SFA) The DEA model only consders nputs and outputs. The slacks are regressed aganst the envronmental varables usng a stochastc fronter approach (SFA) n order to obtan slacks wth the envronmental effect fltered out. Those frms that obtan effcency scores of less than one are n a favourable envronment and nputs are therefore adusted (ncreased) by that proporton to flter out the envronmental effect The nputs, corrected for envronment, and the outputs, are used n the fnal DEA model. ) Incorporates randomness nto DEA. Very mportant n cases where there may be outlers. 2) Can be used when some (or all) of the varables are common to sub-sets of ndvduals. 3) Varables can be ntroduced wthout ncreasng the number of effcent unts. 4) Does not requre the orentaton of the envronmental varables to be known beforehand. ) A very tme-consumng procedure. 2) Large number of problems to be solved and hgh computaton requrements. If = number of frms, the number of problems s *2. Fred et al. (996), Rouse (996). 3 Stages (DEA) The DEA model only consders nputs and outputs. The slacks, treated as nputs, together wth the envronmental varables are ncorporated nto a DEA model n order to obtan effcency ndces that reflect the effect of envronmental varables. Those frms that obtan effcency ndces of less than one are n a favourable envronment and nputs are therefore adusted (ncreased) by that proporton to flter out the envronmental effect. The nputs, corrected for envronment, and the outputs, are used n the fnal DEA model. ) Can be used when some (or all) of the varables are common to sub-sets of ndvduals. ) The nfluence of each envronmental varable must be known a pror. 2) Large number of problems to be solved and hgh computaton requrements. If I = number of nputs and = number of frms, the number of problems s *(2+I). Fred et al. (996), Rouse (996).

13 means of the PLL) that s attrbutable to bad rsk management. If a partcular frm has an ndcator γ = t means that there s another frm (or lnear combnaton of frms) that grants an equal or greater amount of loans wth a lower degree of bad loan (-γ )PLL <PLL 2. Ths ndcator of "rsk management effcency" (γ ) can be obtaned by any of the three methods descrbed before whch wll now be set out n greater detal Sngle stage method The ndcator of "effcency n rsk management" (γ ) s obtaned n the sngle stage methods by solvng the followng problem for each bank, wth varable returns to scale (VRS): [2] Mn = = = = γ γ, λ = λ PLL γ PLL λ L L λ Z λ Z Z Z λ = ; λ 0; + p q + p q ; p =,.., P ; q =,..., Q n whch s the number of frms (=,..,), λ s the vector of weghts, PLL s the provsons for loans losses, L s the volume of loans, and Z = ( Z Z2 ZP) ( ) = 2 Q,,..., and Z Z, Z,..., Z are the vectors of envronmental varables (economc cycle) wth postve or negatve nfluence respectvely 3. 2 ote that greater neffcency n the management of rsk may reflect a lower averson to rsk on the part of frms, so that certan frms may prefer to accept a lower probablty of repayment of the loan provded they obtan a hgher rate of nterest. In any case, the ndcator obtaned here measures frms' mplct rsks, whether due to bad management or to reduced averson to rsk. 3 Envronmental varables are treated n the model as nputs or outputs by nvertng ther nfluence. Thus, for example, f an envronmental varable has a postve nfluence (more means better) t s consdered as nput n the model (see Cooper et al, 996). ote that all the envronmental varables are treated as non-dscretonal varables (see Banker et al, 986a). 2

14 3..2. Two-stage method In the frst stage of two stage models, the ndcators of "rsk management effcency" (γ ) are obtaned by calculatng effcency ndces wthout correctng for envronmental SC varables ( γ ) on the bass of the followng problem: [3] Mn = = γ SC SC γ, λ = λ PLL γ λ L L PLL λ = ; λ 0; SC In the second stage these uncorrected effcency ndces are regressed, takng the envronmental varables (Z) as ndependent varables. In order to contan the effcency ndces wthn the nterval (0,], ether a Tobt model or a logstc regresson model can be used. In the latter case a non-lnear regresson should be performed as follows: [4] γ SC = exp( Z ; β) ε + exp( Z ; β) + The predctons of the regresson model would be the defntve effcency ndces adusted for envronmental varables whch n our case would be the ndcators of "effcency n rsk management" (γ ) Three-stage methods The three-stage method s based on obtanng the slacks resultng from problem [3]. These slacks (s ) are calculated as the dfference between the optmum values and the real values for each frm, s = = λ PLL PLL In the second stage the slacks are fltered for envronmental varables usng a stochastc fronter model (SFA) or a DEA model. In the frst case Fred et al (996) proposed addng the corrected slacks to the orgnal nputs, n our case to the PLL, and ncorporatng them nto the thrd stage of the conventonal DEA model. If DEA s used, the slacks obtaned n the frst stage are ncluded wth the envronmental varables n the second stage to obtan corrected nputs, n our case the corrected PLL. In the thrd stage the corrected nputs, n ths case the corrected PLL, are ncluded n the fnal DEA 3

15 model. For greater detal see the appendx. In all cases the optmum soluton, γ offers the proporton of PLL that bank could reduce f t mproved ts rsk management wthout alterng the amount granted n loans. If γ = t means that there s no bank or lnear combnaton of banks whch wth equal (or greater) amount of loans, and gven the envronmental condtons, has a lower volume of PLL than bank. In ths case, all the PLL would be due to external factors and bank would be effcent n rsk management, even though t had a certan degree of rsk (PLL) as ths would orgnate n the unfavorable economc condtons. In general, γ, lower values of γ mean lower proportons of PLL due to nternal factors, so that γ represents the proporton of PLL of bank that s due to external factors and -γ s a measurement of the proporton due to nternal factors. 3.2 Phase 2: Effcency adusted for rsk However, these tradtonal measurements of effcency ϑ do not consder rsk. If we wsh to consder rsk, as well as effcency, to evaluate the performance of frms, t s necessary to "reward" (by ncreasng effcency) those banks that are good managers of rsk. For ths purpose, Hughes et al (993 and 996) and Mester (994a, 994b) ncorporated total bad loan as a measurement of frms' rsk management. However, for the reasons gven above, ths measurement may be contamnated by economc shocks exogenous to the frms, whch must be dscounted so as not to penalze banks that are subected to an adverse envronment. In ths study t s proposed to ncorporate only that part of bad loan that s due to nternal factors or bad management 4. More specfcally, gven that γ measures the effcency of rsk management and (-γ ) measures the proporton of bad loan whch s due to bad rsk management, t s obvous that (-γ )PLL measures the volume of PLL that s due to the rsk polcy of the frm (nternal factors). Therefore, the effcency measure adusted for rsk would be obtaned by solvng the followng problem: 4 ote that we nclude the PLL due to bad management and not the totals as n other studes. 4

16 [5] Mn = = = = ρ, λ λ y λ x y ; r =,..., R ρ x ; s =,..., S λ ( γ ) PLL ρ r s λ = ; λ 0; ( γ ) PLL ρ n whch only the part of PLL due to nternal factors, (-γ )PLL (obtaned n phase by any of the procedures descrbed) have been ncluded. The effcency measure adusted for rsk ρ s a more sutable measurement of bankng frms' performance than those of Berg et al (992), Hughes et al. (993, 996) or Mester (994a, 994b), as t only penalzes those banks whose bad loans are due exclusvely to bad rsk management. Comparson of the effcency measure not adusted for rsk (ϑ ) obtaned n problem [] wth the effcency measure adusted for rsk (ρ ) obtaned n problem [5] offers a measurement of the mpact of rsk management on the effcency of bankng form,.e. ths comparson s a measurement of the "prze" or "penalty" n the effcency measure awarded to t dependng on how t manages rsk. We call ths mpact the "rsk management effect" (RME) and t s obtaned from the followng rato: [6] RME ϑ = ρ If a bank has RME< ths means t manages rsk well, takes few rsks and consequently has "won a prze" n terms of a effcency measured adusted for rsk (ρ ) hgher than the unadusted measure (ϑ ). If, on the other hand, RME=, t means that addng rsk to the model has no effect on effcency snce the banks manage rsk as well as better than other nputs 5. 5 ote that the rsk effect s always less than or equal to unty, meanng that the added restrcton benefts the ndces of effcency or leaves them as they were. However ths does not necessarly occur n the other procedures. 5

17 3.3 Effcency adusted for rsk and envronment: Phase 3 Although measurements of effcency adusted for rsk (ρ ) offer a more sutable evaluaton of frms' performance, further refnement s stll requred, as the envronment n whch frms carry out ther actvty nfluences effcency, sometmes decsvely. To acheve a effcency measure n whch all frms are evaluated by the same standard, t s necessary to refne the effcency measure adusted for rsk by ncludng other envronmental varables. Ths effcency measure adusted for rsk and the envronment (Ω) would be obtaned by ncorporatng the effect of envronmental varables by any of the procedures descrbed earler, wth two reservatons: ) ow nstead of PLL all nputs have to be corrected, and 2) the envronmental varables that nfluence bad loan are not necessarly the same as those that nfluence effcency. The optmum solutons that nclude rsk and envronment wll provde measurements of effcency adusted for rsk and envronment (Ω ). As before, the rato between the measurements of effcency adusted for rsk (ρ ) and the effcency measures adusted for rsk and envronment (Ω ) offer us nformaton on the degree of nfluence of the envronment on the effcency of the banks. We call ths coeffcent the "envronment effect" (EE) and t s expressed as follows: [7] EE = ρ Ω If EE <, ths means that the envronment s unfavorable for the frm, as when t s compared only wth the set of frms that are subect to the same condtons or worse, the effcency measure mproves. If, on the other hand, EE >, ths means that the effcency measure has penalzed the frm, snce the unadusted measurements of effcency attrbuted to effcency what n fact was only a favorable envronment 6. Reformulatng the above expressons, t s possble to decompose the effcency measure wth varable returns to scale of bank nto several components: 6 ote that, unlke the rsk effect, except n the sngle stage models, the envronment effect may be a rsk greater than unty. 6

18 ρ ϑ [8] ϑ = Ω = Ω EE RME Ω ρ Expresson [8] offers nformaton on the orgns of the effcency measure under VRS (ϑ ), so that ths can be explaned n terms of the effcency measure adusted for rsk and envronment (Ω ), of the envronment effect (EE ) and of the rsk management effect (RME ). 4. DATA AD VARIABLES Internatonal comparsons of effcency must be very careful n the selecton of data. ot only the possble accountng heterogenety of the varables used has to be consdered, but also the dfferent specalzatons and the dfferent envronment. In ths study the data base was obtaned from IBCA Ltd., an nternatonal ratng agency whch homogenzes the nformaton and classfes frms n terms of specalzaton, so that the accountng unformty s guaranteed. Homogenzaton of specalzaton was acheved by consderng only commercal banks, therefore excludng other categores such as savngs banks, state-owned banks, ndustral and development banks, etc. Snce the key varable of the analyss s the provsons for loans losses (PLL) only those countres that report ths varable as a separate tem from other provsons could be selected 7. Ths lmts the analyss to Span, Italy, France and Germany 8. The total sample conssts of 2598 observatons from 988 to 994: 44 observatons of French commercal banks, 387 Italan, 524 Spansh and 543 German. In the case of Germany, due to the lack of PLL data the perod studed s Inputs and outputs. In the bankng lterature there s no general agreement as to the proper defnton of nputs and outputs. In ths study, as n Pastor (995a, 996), Pastor, Pérez and Quesada (997) and Pastor, Lozano and Pastor (996), we opted to use the "value added" 7 Unfortunately, nformaton about loan losses s avalable only for a very small sample of banks. Ths fact makes mpossble the comparson of the results obtaned usng PLL wth those obtaned usng loans losses, whch s the varable often used n the lterature. 8 Although only four countres form the European Communty are consdered, the sample chosen represented n % of the total assets of the European Communty's commercal banks. 7

19 approach (Berger and Humphrey, 992) and selected three outputs: y =loans, y 2 =deposts, y 3 =other earnng assets; and two nputs: x =personnel expenses and x 2 =operatng costs (excludng personnel expenses and ncludng fnancal costs). Envronmental varables 9 : The envronment varables were selected for ther nfluence both on bad loan and on effcency. A pror, only economc cycle varables nfluence bad loans, whereas other structural varables nfluence effcency. Wth regard to the former, t was assumed that greater varablty of the economc cycle has a postve nfluence on bad loan. To capture ths nfluence the nter-annual coeffcent of varaton of nomnal GDP was consdered. Lkewse, a hgher growth rate of GDP has a negatve nfluence on bad loan, so both the annual growth rate of GDP and the cumulatve growth rate were ncluded. These three varables were ntroduced wth dfferent lags and the recursve procedure n Pastor (995b) was used to determne whch varables are most nfluental. The results of ths procedure determned that the most nfluental varables are the coeffcent of varaton of the nomnal GDP of the perod, the growth rate of nomnal GDP of the perod, and cumulatve annual growth rate n the last 5 years. The selecton of varables nfluencng effcency s, a pror, a much more complcated task because of the wde range of possbltes. To lmt the possbltes n ths study we consder ntally the envronmental varables that were found by Pastor, Lozano and Pastor (997) to be nfluental, usng the procedure n Pastor (995b): per capta wages, densty of deposts, natonal ncome per branch and captal adequacy rato RESULTS 5. Rsk management effcency and decomposton of bad loans The results obtaned wth regard to rsk management effcency, ncorporatng the envronmental varables ndcated above and usng the dfferent versons, are presented n 9 The data on envronmental varables s taken from the Economc Bulletn of the Bank of Span, Bank Proftablty, Eurostat and IE (atonal Statstcal Insttute of Span). All the varables were expressed n dollars. See Frexas et al. (994) for the macroeconomcs determnants of loan losses. 20 Pastor, Lozano and Pastor (997) ntally consdered the followng varables: ncome per capta, wages per capta, populaton densty, densty of demand, ncome per, deposts per branch, branches per nhabtant, branches per square klometre, captal adequacy rato and average proftablty of the sector. 8

20 fgure. The evoluton of rsk management effcency of each of the countres s very smlar n all technques, wth the sole excepton of the one stage method (represented on the rght-hand axs) 2. Excludng the one stage method because of ts lmtatons n ths partcular case, t can be concluded that effcency n rsk management has evolved dfferently n each country. Whle n Italy and Germany t has evolved wthout a partcular trend, France shows a reducton n the rsk management effcency. In the case of Span, after a descent of rsk management effcency durng the perod , t apprecably mproved, and by 994 was at levels hgher than n 988. In general, the average porton of PLL due to nternal factors stands at between 3% and 26%. Span and Germany are the most effcent countres n rsk management, wth an annual average among methods of around 26% followed by France wth 8% and Italy wth 3%. On the bass of the evoluton of effcency n rsk management, nstead of the overall evoluton of bad loans, the conclusons on the evoluton of rsk n bankng systems are very dfferent. Thus, although bad loan has ncreased snce 990 n all countres (graph.), bad loan due to rsk management, wth the excepton of France where t worsens, ether mproves (Span) or remans steady (Italy and Germany). It s possble, therefore, to conclude that the ncrease n competton generated by Communty de-regulaton processes does not seem to have pushed frms nto rsker busness and/or behavor. Table 2 shows the values of the proportons of bad loans (PLL) attrbuted to nternal factors ( γ ) n each of the methods, excludng the sngle stage method. Obvously those bankng systems that are less effcent n rsk management have hgher proporton of bad loan due to nternal factors. Thus, for the case of Italy the proporton of bad loan due to nternal factors s 87%, whereas n other bankng sectors such as those of Span or Germany these proportons are lower (around 73%). 2 In the fnal nstance, gven that the envronmental varables are common to all the frms of the same country, t s suffcent for a partcular country to have a more unfavourable envronment n one partcular varable for all the frms of that country to be consdered effcent. In the extreme case n whch each country has an unfavourable stuaton n one of the envronmental varables consdered, all the frms of all the countres wll be consdered effcent by excluson, as has occurred n many years. 9

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