WP/5/ Monon and Commmen n Bank Lendn Behavo Rodolhe Blavy
5 nenaonal Moneay Fund WP/5/ MF Wokn Pae Wesen Hemshee Deamen Monon and Commmen n Bank Lendn Behavo Peaed by Rodolhe Blavy Auhozed o dsbuon by Tevo S. Alleyne Novembe 5 Absac Ths Wokn Pae should no be eoed as eesenn he vews o he MF. The vews exessed n hs Wokn Pae ae hose o he auho(s and do no necessaly eesen hose o he MF o MF olcy. Wokn Paes descbe eseach n oess by he auho(s and ae ublshed o elc commens and o uhe debae. The ae ooses a heoecal aumen on he naue o bank lendn, based on he dea ha, houh commmen and monon, banks ovecome basc nomaonal asymmees wh boowes. By bnn oehe loan commmen heoes and ced aonn heoes, he ae shows ha, whn a amewok o asymmec nomaon beween lendes and boowes and unde cosly emnaon o lendn aanemens, commmen may exlan he accumulaon o noneomn loans by banks. Two addonal esuls ollow: ( ha banks avo boowes wh well-known oducon uncons and lon-em ced hsoy; and ( ha nees ae seads may be lae sncan make meecons eval. JEL Classcaon Numbes: D45, D8, E44, G Keywods: Bank, ced, monon, commmen, asymmey o nomaon Auho(s E-Mal Addess: blavy@m.o would lke o hank Mchael Kuczynsk, Elena Loukoanova, Govann dell Acca, Doulas Damond, Phll Schellekens, Tevo Alleyne, Mwanza Nkusu, Rchad Blavy, Pablo Duck, Enque Floes, and Ryan Hammond o he helul commens and suesons; and Kae Jonah and Loudes Cuado o edoal asssance.
- - Conens Pae. noducon.... Conces, Denons, and Theoecal Famewok...6. Monon and Bank Lendn... V. Temnaon Coss and Commmen n Bank Lendn...5 V. Monon and Commmen wh Ced Hsoy... V. Conclusons...5 Aendx mlc Commmen wh Ced Hsoy: Fomalzaon...7 Reeences... Fue mac o Monon on he Execed Po o he Bank and on Ced Allocaon...4
- -. NTRODUCTON One o he ocuses o he vas leaue on ced and bank behavo has been nancal nemedaon as a majo exlanaon o he exsence o banks. The deb conac emees as key o he bank-boowe elaonsh. Rescons on ull nomaon and eec nomaon envonmens ae noduced o exlan secc chaacescs o ha elaonsh. Semnal woks on hese ssues nclude Benson and Smh (976 on ansacon coss; Leland and Pyle (977, Slz and Wess (98, Damond (984, and Fama (985 on asymmec nomaon, ced aonn, and snaln; and Damond and Dybv (98 on lqudy nsuance. Ths ae uos ha he monon ocess undeaken by banks may deemne he naue o he lendn behavo, n acula n economes whee nomaon abou boowes s scace and he coss o exn a lendn elaonsh ae hh. The accumulaon o noneomn loans on he balance shees o banks s shown o be a lausble esul o hh ex coss. Two addonal chaacescs emee unde he oosed amewok, boh commonly acceed esuls n he bank lendn leaue. The s s ha banks ee o nance comanes n he omal seco wh ae and small devaons om hsoc aveae euns and wh whch hey have well-esablshed elaonshs. The second s ha he sead beween deos and lendn aes may be wde. These hee chaacescs esul om a heoecal aumen based on he dea ha banks ovecome some basc nomaonal oblems houh lon-em elaonshs wh boowes and commmen. Tansosed no a amewok o asymmec nomaon beween lendes and boowes, he ae shows ha unde lausble condons, monon o boowes by banks nceases he ecency o he ced make by lowen he nees ae chaed o boowes and/o nceasn he execed o o he bank, and by oenally nceasn he level o ced n he economy owad s s-bes level. A muleod sen s modeled by ocusn on he condons ha nduce banks no a eallocaon o he oolo n nem eods. n he envonmen o he model, banks ae assumed o eceve, a each nem eod, an nomal snal om boowes ha educes asymmees o nomaon and allows o an ncease n he execed eun o he bank. Howeve, commmen o unomsn boowes, necessay o he aal evelaon o nomaon a each nem eod, s a cosly ocess ha educes ans om monon. The bank may heeoe ee o emnae he lendn conac coss o commmen ae hhe han ex coss. Wh hs aoach, he ae bns oehe wo heoes o bankn behavo.e., loan commmen heoes and ced aonn heoes. Some o he consans commonly mosed n modeln boh heoes ae elaxed, noably he escon o models o a oneeod amewok and he assumon o cosly sae vecaon. An addonal conbuon s o use a smle and oeaonal denon o he deb conac. The deb conac s a conac ha seces a loan o nancal esouces om one aen (he lende o anohe (he boowe a an nal eod, aans aymen n he nex eod o he len caal lus
- 4 - he nees due. A each eod, he lende can ese he ce and ossbly he ohe ems, on he undesandn ha he loan s enewable o an ndene eod o me. By ocusn on an nem eod n he le o he conac, he ae aems o ovde a ealsc modeln o he monon ocess. The monon acvy consss o he combnaon o hee elemens: he aleness o nomaon snals, he neeaon o snals, and he adjusmen o ncenves. As a esul, he assumon o ex os cosly sae vecaon used n models o bank ced and monon s no used hee. A each nem eod, boowes send new nomaon abou he eomance o he ojecs, whch noms banks on he boowes execed eomance n he one eod ahead. Ths amewok s adoed o elec wo eaues o he loan conac: ( ha banks may eneally obseve ex os he euns ealzed by boowes on he ojecs, and ( ha loan conacs end o cove he mulle eods o he le o a ojec. The ssue o commmen s noduced om a deen anle han n evous loan commmen models. These models have exloed he easons o he emeence o muleod loan commmens om he on o vew o boh boowes and lendes. They have emhaszed he ole o make meecons n he emeence o lendn commmens, n acula, ansacon coss, asymmey o nomaon, and make domnance. n a conex whee banks ncu coss o emnaon when lqudan a loan, hey ae shown o be mlcly commed o some boowes, even when hey exec neave euns om such boowes. The esence o commmen and ex coss s cenal o he aumen oosed n hs ae. Commmen coss coesond o he educon n he bank s execed evenue due o commmen o unomsn boowes. n ohe ems, hey ae he bank s nvesmen n he ocess o nomaon acquson. Ex coss ae, o smlcy, assumed o be elaed o a numbe o meecons n he unconn o he bankn m. These meecons ane om nsuonal and admnsave des, aency oblems (noably, a dveence o neess beween he aen conacn he loan and he manaemen o he bank, o weaknesses n he judcal and law enocemen sysems. Banks ae dened, ollown Fexas and Roche (998, as nsuons whose cuen oeaons conss n ann loans and ecevn deoss om he ublc (.. James (98 aued ha ansacon coss assocaed wh he seach o and selecon o new boowes ae hhe han coss o connun a eexsn lendn elaonsh, and hence a move o loan commmen. Melnk and Plau (986 develo a model whee lendn s moe ecen unde loan commmen conacs han n he so make. The esuls ae deenden on he assumon ha whle he loan ae s xed unde loan commmens, vaes n lne wh a loan-sze sk emum n he so make. Boo and ohes (99 also esen a model whee loan commmen yelds a moe ecen allocaon o ced han conacn decly n he so make. n he envonmen o he model, moal hazad due o asymmec nomaon leads o nvesmen n second-bes ojecs o o ced aonn. Loan commmens, because hey ae based on an u-on commmen ee ha comensaes o below-make nees aes, educe he dsoons assocaed wh moal hazad. Moan (994 obans comaable esuls n a model whee commmens educe he deaul sk o boowes and hence educe ced aonn.
- 5 - The key esuls ae as ollows. A each eod, he monon o nomaon snals by he bank allows o so boowes no wo caeoes omsn and unomsn boowes wh he bank execn osve euns om he ome and neave om he lae. The bank consequenly maxmzes s one-eod-ahead execed o by eallocan s oolo away om unomsn boowes o boowes n he so make. Howeve, because he bank ncus coss o conac emnaon when neun a lendn elaonsh, s consaned n s ably o eallocae s oolo and emans commed o a numbe o unomsn boowes. Ths esul ovdes a s juscaon o he ac ha bank lendn ends o be n he om o muleod mlc deb conacs. Commmen o unomsn boowes, by educn he execed o o he bank, lms s ably o educe nees aes on omsn boowes and nces he bank o ass on he cos o deosos, n he om o lowe deos nees aes. 4 The model suess ha seads beween lendn and deos nees aes wll be lae n an envonmen whee he bank sues om moan aency oblems, has weak nenal conol sysems, and whee he leal sysem s weak and conac enocemen and emnaon dcul and cosly, because coss o conac emnaon wll be hh and so wll commmen o unomsn boowes. The ossbly o he bank o esablsh a ced hsoy o boowes noduces no he model an addonal chaacesc o bank lendn: ha he ocess o nomaon neeaon s mosly backwad-lookn. n he conex o he model, hs chaacesc s shown o make he bank eslen o nose n nomaon snals and o even undue and cosly emnaon o loan conacs. Howeve, backwadlookn nomaon neeaon educes he ably o he bank o deec sucual chanes n he qualy o boowes, wh he oenal o a subsanal deeoaon n s oveall oolo. The emande o he ae s oanzed n ou secons. Secon dscusses conces and denons n lh o he exsn leaue. Secon esens he amewok o ou model. Secon V develos a model o monon and commmen n banks lendn behavo whou ced hsoy, whch s exended n Secon V o allow o he consuon o ced hsoes by banks. Fnally, Secon V ovdes a summay and concluson. 4 Ths esul o he model may un coune o emcal evdence ha banks wh hh noneomn loan aos may acually oe hhe deos aes. n eec, he sk o nsolvency ovdes ncenves o ncease deos collecon, even a a hh cos. Ths asec s no modeled n he ae. The esul esened hee ollows noably om he assumons ha he bank has a xed ool o deoss ha does no vay om eod o eod and ha he bank oeaes n a monoolsc envonmen.
- 6 -. CONCEPTS, DEFNTONS, AND THEORETCAL FRAMEWORK The deb conac s a he coe o he bank-boowe elaonsh n he bankn leaue. n a ull nomaon amewok, boh aes would secy n he conac evey ossble uue connency (o sae o naue and he esuln oblaons n each o hem, ncludn he amoun o eaymen o o addonal loan, he nees chae o he nex eod, any adjusmen n he collaeal equed by he lende, and he se o acons equed om he boowe. n a muleod sen, a comlee connen conac would be vey lenhy and could be ohbvely cosly. Fo hs eason and because o unceany abou uue connences, deb conacs usually dene eaymen oblaons and collaeal o he whole duaon o he conac, wheeas acons o be undeaken by he boowe ae le o s own aecaon (see, o examle, Fexas and Roche, 998. The denon o he deb conac adoed n hs ae eans some lexbly n he adjusmen o he ems o he conac n he vaous saes o naue, whle monon ovdes he bank wh he ably o nluence he acons o he boowes ove me. The deb conac s dened as a conac beween a lende and a boowe, enewable o an ndene eod o me, whee he lende can ese he ce and ossbly he ohe ems. The lende eans he ably o emnae he conac and eneoae s ems o smlcy, eneoaon s houh he ossbly o chann nees aes ove me. We assume ha hs ably s lmed aally by mlc coss o conac emnaon, ncludn ( nsuonal and admnsave des (o examle, he coss o ocessn he chanes n he ems o he conac, ( aency oblems (noably a dveence o neess beween he aen conacn he loan and he manaemen o he bank, and ( weaknesses n he judcal and law enocemen sysems. The model ocuses on he ably o nancal nemedaes o mono boowes houhou he le o he conac, n he esence o coss o conac emnaon. The monon acvy consss o he combnaon o hee elemens: he aleness o nomaon snals, he neeaon o snals, and he adjusmen o ncenves. The s wo elemens coesond o he bank s eos n educn asymmees o nomaon wh boowes. The hd elemen eesens he ably o mody he ems o he conac o ensue ood eomance o he boowe. An alenave denon has commonly been dened n he bankn leaue, whee monon s a ocess o oucome dscovey, n whch he lende has o mono he boowe n ode o have some ndcaons on he ealzed euns on he ojecs undeaken. Ths denon o monon s cenal o he cosly sae vecaon aadm s develoed by Townsend (979 and lae exended by Gale and Hellw (985 and Wllamson (987. Cosly sae vecaon models assume ha lendes canno obseve euns on ojecs undeaken by boowes unless cosly auds ae eomed. Boowes, o maxmze he euns, may alsy he ealzed euns n ode o lowe eaymens o he bank, hey can oably do so. Conacs wh ex os asymmey o nomaon eneally secy a hh enouh enaly o even successul boowes om declan aled euns. Auds only ake lace when cash lows ae oo low o boowes o eay caal and nees o he bank, snce enales even chean n all ohe saes o naue. Fo successul saes, eaymen o he bank s ndeenden o he
- 7 - eun on he ojec. Wllamson (987 showed ha hs envonmen endoenously denes he omal conac as ben he deb conac. 5 Some muleod models have mosed sce escons on ex os asymmey o nomaon, by assumn ha ex os aud o euns by he bank s no ossble. 6 The boowe only eays he lende he s ovded wh ncenves o do so. n Bolon and Schasen (99, he hea o conac emnaon nduces he eaymen o he loan n a eeaed boowe-lende elaonsh. n a one-eod model, hee would be no lendn because he boowe would always declae alue o s ojec and nably o eay he loan. Unde he assumon ha he bank s unable o aud euns ex os, s execed o would always be neave. n a muleod sen, 7 he bank may comm o enew he loan he m eays he conacual amoun n he nem eod. Whle boowes wll always deaul on he las aymen when he ncenve o eay s emoved, he bank may yeld sucen o om nem aymens o comensae o he ulmae loss. Slz and Wess (98 also develoed a model whee conac emnaon and eneoaon ae used as ncenve mechansms. Haubch (989 exended he models n Bolon and Schasen (99 and Damond (984 by combnn he wo ncenve devces n an nne hozon model: wh dynamc conacn, chean boowes ae dened and unshed, ehe houh conac emnaon o eneoaon o he conac ems ha s, hhe nees aes. The assumon o ex os cosly sae vecaon s no used n he model oosed hee. Fomally, monon s undeaken as ollows. mane an economc envonmen whee aens ae sk neual and comosed o a bank oean n a monoolsc envonmen and a ou o undsnushable boowes. The le o a deb conac s smled o hee saes: he allocaon o caal o he new boowe, nem eods dun whch he loan s enewed, and he emnaon o he conac. The model ocuses on nem eods, denoed. Assume ha he nal allocaon o caal has been made unde condons o ex ane asymmey o nomaon. Unde such condons, he bank has lmed nomaon abou boowes. The bank may obseve only 5 The same esul was obaned by Damond (984 n a model whee cash lows ae no obsevable and mechansms o uhul evelaon esablsh he omaly o he deb conac. Damond exanded he model o show ha, wh a nonecunay cos assocaed wh unuhul evelaon o euns, a sandad deb conac s sll obaned. 6 The mossbly o obseve euns ex os s shaed wh he Damond (984 model. Howeve, Damond s soluon was o mose nonecunay coss o aled boowes, and eecvely o emove he lmed lably consan. 7 Gomb (994 exended he wo-eod model o Bolon and Schasen (99 o a muleod sen (see also Dewaon and Maskn, 995.
- 8 - he aveae chaacescs o a ou o boowes aveae obably o success and aveae execed euns bu no he secc chaacescs o ndvdual boowes. Assume uhe ha he bank nally allocaes all s nancal esouces o boowes. The bank s oal nancal esouces ae a xed ool o deoss ha do no vay dun nem eods. ollows ha he bank may ene new loan aanemens n he so make and only emnaes some conacs wh s cuen boowes n he same eod. As a esul, he bank decdes o emnae some conacs n an nem eod, ees esouces o ene no new loan aanemens wh boowes wh whch has no evous lendn elaonsh. A any ven eod, he bank eassesses s loan oolo, ae ecevn an nomaon snal om boowes. The snal s emed a each eod. n eec, unde he assumon ha loans ae enewed evey eod o an nne numbe o mes, each eod coesonds o he eaymen o nees and caal by he boowes and o he enewal decson by he bank. On he bass o he newly accumulaed nomaon, he bank decdes whehe o mody he sucue o ncenves o boowes. Chanes n he condons o loans ovde ncenves o boowes o eom accodn o he nal ems o he conac. Amon an aay o ossble chanes o he conac, only wo ae eaned, o smlcy: ( he nees ae may be moded because ood boowes may be oeed bee ems; and/o ( he volume o ced allocaed may be moded, ehe by emnaon o he conac o by nceased ced aonn n he case o unomsn boowes o loan enewal n he case o omsn boowes. The model ollows he omulaon oosed by Slz and Wess (98, wh boowes undeakn wo-oucome ojecs. Assumons abou he chaacescs o boowes ae as ollows: Fo smlcy, each boowe has a snle ojec. Thee s no advese selecon. Boowes and ojecs have he same sk-eun chaacescs, and he wo ems ae used nechaneably. The ndvdual obably o success,, and he coesondn successul eun o he h s boowe, R, ae unobsevable o lendes; R s he eun on a aled ojec and s consan acoss boowes, unde he assumon ha a aled ojec yelds a eun equal o he lqudan value o he m. The value o ne asses mnus bankucy coss, ndeendenly o he skness o he ojec sel, s consan o all boowes;
- 9 - R s he aveae execed eun on boowes ojecs. R s obsevable o he bank s and s consan acoss boowes: R ( R R. ollows ha sky ojecs yeld hhe euns n case o success han sae ones. 8 The aveae obably o success o boowes,, oehe wh he aveae, ae obsevable by he bank. dsbuon o euns ( G wh densy uncon ( n hs envonmen, boowes have no nal wealh and seek nance o he ojecs. Whou loss o enealy, he nal nvesmen equed o each ojec s nomalzed o. A sandad deb conac s ssued, wh eaymen o caal and nees ( n nonbankucy saes and maxmum ecovey o deb n bankucy saes ( R. The model assumes ha he bank may no ully oec sel aans bankucy and obans a neave eun n case o alue o he boowe. Fomally, he boowes aled eun s neo o R. he loan eaymen: ( he ojec s successul, he boowe eceves he ayo o he ojec ne o eaymens o he bank. he ojec als, he boowe ays he aled eun o he bank and eceves no ayo. The eun o he h s boowe s π max ( R ;. Gven he obably ha he ojec s successul, he execed eun o he h boowe, ne o deb eaymen o he bank, s: s E( π ( R. The execed eun o he boowe s a deceasn uncon o he obably o success. 9 The esul ha execed ne euns o he boowe ae hhe o ske ojecs can be exlaned by he ac ha o ske ojecs, he execed nees aymens ae lowe because he loan s ead less oen (Enlsh, 986,. 7. n he model, hs s he case s because aveae execed euns ( R ae held consan and because R s assumed o ncease wh he deee o sk. 8 s Gven R ( R R, and R and R consan acoss boowes, >, s R ( R R ( R s R < R. 9 The esul s obaned by devn he o uncon o he boowe wh esec o he E( π obably o success. We oban: [ R ( ]. The devave uncon s neave aled euns ae neo o he loan eaymen, whch s ue unde he assumons o he model.
- - A sk-neual eneeneu s wlln o undeake s ojec, nanced by a deb conac, and only E( π. Boowes choose o aly o loans and only he ojec yelds sucenly hh euns, whch, ven he nvese elaonsh beween euns and obably o success, means ha boowes aly o loans only he ojecs ae sucenly sky o yeld a mnmum successul eun ha ensues nonneave execed euns. Thee s a lm obably o success,, above whch he eneeneu decdes no o boow, such ha: R R ( R. The lm obably o success s deceasn wh he nees ae. The qualy o he ool o boowes hence wosens as he bank ases nees aes. As n Slz and Wess (98, boowes wh hh obably o success oessvely do ou o he ool o boowes as he bank ases he lendn nees ae. The nal allocaon o caal s deemned by he execed eun o he bank om lendn o ha ou o boowes a nees ae, omally: ( ( [( ( R ] ( ( ( b ( d d, ( whee b s he nees ae ad o deosos by he bank. Equaon ( eesens he eun o he bank om loan alcans ven he nees ae. Whn he subse o loan alcans wh obably o success below (, he s a o he equaon eesens he aveae eun om boh successul and aled ojecs. The second a o he equaon coesonds o he oblaons o he bank o s deosos, snce ( value o aned loans. Slz and Wess (98 have shown ha a ced-aonn ( d s he oal [ ] s s s such ha E( π R (. Fom R R R s R R ( R. Relacn o no E( π and solvn o E( π R R ( R. n he emande o he ae, ( s denoed o concseness. s R (, ollows ha, ves
- - equlbum may exs when some boowes wh osve execed euns ae excluded om he ced make. Once he bank has eneed a lendn elaonsh wh boowes, eodcally eceves nomaon snals and monos boowes. Pomsn boowes send a osve snal ha suess ha hey have a hhe obably han he aveae (undsnushable boowe o eomn well n he nex eod. Unomsn boowes, on he ohe hand, send a neave snal and have a lowe obably o success n he nex eod. 4 The bank s heeoe able o eassess he qualy o s ced oolo ae eceon o a snal. Wh addonal nomaon, he chaacescs o boowes as obseved by he bank a me chane. The eceon and neeaon o nomaon by he bank s omalzed as ollows: The nomaon snal, s emed a me by boowe. A osve snal s such ha. A neave snal s such ha,., nomaon s only aally evealed o he bank. The bank obseves only whehe he snal s osve o neave. The bank may dsnush amon evously undsnushable boowes wo seaae ous. Pomsn boowes, whch send a osve nomaon snal, consue he s ou; and unomsn boowes he second one. The exsence o a ced-aonn equlbum s elaed o he wosenn o he ool o boowes as he nees ae ses. Suose ha, a some nees ae ', he bank s evenues om he ncease n he nees ae ae moe han ose by he moal hazad eec, he bank wll no lend a nees aes above '. ' s such ha he execed o o boowes s osve, ced aonn ollows. Fomally, he esul s obaned by shown ha equaon ( s a nonmonoonc uncon o he nees ae. By devn equaon ( wh esec o, and shown ha he lm o he devave as he nees ae ends o nny s neave, nonmonooncy ollows. One ossble omulaon o nomaon snals s o elae hem o he eomance o boowes n he evous eod, obseved by he bank dun monon. Peomance could, o examle, be dened as he ably o boowes o ay deb sevce due n a ven eod. 4 The model assumes hee ha he aveae obably o success o he ool o boowes emans unchaned a each nem eod.
- - The eceon o he snal modes he bank s eceon o he obably o success o. 5 Hence, boowes. A nem eod, he obseved obably o success s: (, ( he snal s osve and (, he snal s neave. <, The nomaon snal s a uncon o he obably o success o boowes, conssen wh he ac ha he snal eveals nomaon abou he qualy o boowes. Hence,. s denoed (,, The aveae execed eun on he ojecs o boowes and he aveae obably o success eman consan. The ndvdual obably o success,, and he assocaed s successul eun, R, eman unobsevable o lendes.. MONTORNG AND BANK LENDNG n hs secon, he mac o boowes nomaon snals on bank lendn s examned n a conex whee nomaon snals ae uncoelaed acoss eods, whch evens he bank om esablshn a ced hsoy o s boowes. The esuls ovde heoecal suo o he dea ha he bank benes om eeaed lendn o boowes and develos an exese ha allows o allocae ced moe ecenly han n a ycal one-eod model. The decson o he bank o enew o susend ced o boowes s modeled whn he amewok esablshed n Secon. The aumen oceeds by analyzn he mac o nomaon on he execed o o he bank and on ced allocaon, successvely. The equaons esened n Secon ae ewen and moded o ake no accoun he addonal nomaon avalable o he bank n he om o he nomaon snal. 6 As he bank eceves nomaon abou boowes, can so evously undsnushable boowes no wo subous, omsn and unomsn. The bank adjuss s execaons o o om boowes. Pomsn boowes ae execed o yeld hhe execed euns han unomsn ones. PROOF. The execed eun o he bank om a snle boowe, ne o nees aymens o deosos, s: ( ( ( ( R ( b. (,,, 5 A osve snal s such ha,. Ths escon ensues ha he obably o success s no sueo o. 6 The boowe does no mody s behavo ollown he snal because he nomaon eleased wh he snal was avalable o ex ane.
- - The execed eun o he bank om lendn o ha ou o boowes a nees ae may be wen as: ( [( ( ( ( ( ( R ( b ] ( The eceon o he nomaon snal modes he execed eun o he bank by (subacn ( om (: ( [( R ] ( ( d. ( d. (4 The sn o he deence wll deend on he sn o. Fo omsn boowes, he bank wll exec hhe euns han o he nal ou o boowes. Fo unomsn boowes, execed euns wll be lowe. Pooson. Peod o eod son o boowes allows he bank o mody s ced oolo o maxmze s execed o. Concuenly, he bank monos boowes, ovdn eomance ncenves o boowes n he om o conac emnaon o connuaon and/o chanes n he nees ae. A any ven eod, wh no modcaon o he bank s oolo, he execed eun o he nex eod s he aveae beween execed os om omsn boowes and aled euns om unomsn boowes. Ae ecevn he snal, he bank may maxmze s execed o by keen omsn boowes n s oolo, emnan conacs wh unomsn boowes, and eallocan s oolo o boowes o whch has no vae nomaon bu whch yeld hhe aveae execed euns, equal o (see equaon (4. Because he oveall sze o he bank s loan oolo does no chane n nem eods, 7 he bank can exand new loans only elaces cuen boowes by new boowes, hence he subsuon o unomsn boowes by undsnushable boowes. Deendn on s o objecves, he bank may also decde o kee nees aes consan, nceasn s o uhe by enean excess euns om omsn boowes, o educe nees aes on omsn boowes, ovdn hem wh a eomance ncenve. 8 PROOF. he bank decdes no o mody s loan oolo, s execed o s unchaned comaed wh he evous eod. By assumon, he aveae obably o success emans consan, and he aveae execed eun o he bank s unchaned. 7 Ths s ue unde he assumon ha he bank has a xed sock o deoss and unde he addonal assumon ha any o eneaed by he bank s no envesed bu ad o as dvdend o shaeholdes. 8 The bank does no chae ndvdual boowes wh deenaed nees aes because o aal evelaon o nomaon. does no dsnush ndvdual boowes amon he wo ous o omsn and unomsn boowes.
- 4 - The shae o omsn boowes n he bank s loan oolo s denoed. By keen s nees ae consan on omsn boowes, he bank nceases s o on hose boowes by ( [( R ] ( ( d. Ths suaon may be obseved omsn boowes ae cave boowes,.e., he nomaon snal s only obsevable by he bank ha has nanced hose boowes nally, o, as s he case n he model oosed hee, he bank oeaes n a monoolsc envonmen. The bank may also o o lowe he nees ae n ode o ewad omsn boowes and enoce ncenves o ood eomance. The shae o unomsn boowes ben (, he execed o o he bank om hose boowes s equal o: ( [ ] ( ( ( ( ( ( ( ( R ( b d. Follown eceon o he nomaon snal, he bank leaves nees aes unchaned, kees omsn boowes, and elaces unomsn boowes by ndsnushable boowes. The bank eneaes an excess o equal o ( [( R ] ( ( d. 9 Fue llusaes he oucome o nem monon. Fue. mac o Monon on he Execed Po o he Bank and on Ced Allocaon Unchaned nees aes o omsn boowes Pomsn boowes Reducon o nees aes o omsn boowes ρ ( ρ ( e Excess o Pomsn boowes nees ae educon Relacemen o unomsn boowes by undsnushable boowes ncease n he bank s execed o Undsnushable Unomsn boowes boowes 9 n hs envonmen, he bank eneaes excess execed o a each nem eod. The esul s a dec consequence o s monoolsc suaon. allows o exac a en om omsn boowes, unless he bank decdes o lowe nees aes o ovde hem eomance ncenves.
- 5 - V. TERMNATON COSTS AND COMMTMENT N BANK LENDNG Ths secon looks a how he ably o he lende o eallocae s oolo n ode o maxmze s o and mono boowes s consaned by he exsence o coss assocaed wh he emnaon o loans. Fo nsuonal, admnsave, and euaon easons, s cosly o he bank o ex a loan conac ha s eomn ooly. As a esul, he bank may decde no o ac on mxed nomaon snals, bu ahe accommodae hem ove me, and ac only on vey neave snals. Coss o conac emnaon ae exoenous and denoed C. A any eod, he bank emnaes a loan conac and only he cos o emnaon s smalle han he o loss, PL, ncued by he bank om commn o unomsn boowes; ha s, and only PL C. The o loss esuls om he nably o he bank o eallocae s oolo away om unomsn boowes o undsnushable boowes due o mlc commmen. The o loss coesonds o he nvesmen undeaken by he bank o acque vae nomaon abou boowes a each nem eod. The ex cos a whch PL C s he maxmum nvesmen he bank s wlln o undeake o oban nomaon abou boowes. The o loss PL s calculaed as he deence beween he execed euns o he bank om undsnushable boowes and he execed eun om unomsn boowes. n ohe wods, he o loss s equal o he chane n he execed o ae eceon o a neave snal by he bank, as omalzed n equaon (4: PL ( d. [ ] [ ( R ] ( ( Pooson. Commmen by he bank o unomsn boowes wll deend on he elave manude o mlc coss o conac emnaon and o he nomaon snals eceved om boowes a nem eod. PROOF. The decson aken by he bank o emnae conacs s subjec o PL C, o: C ( ( d ( [( R ] ( ( d. (8 Thee s a heshold o nomaon snals below whch he bank does no comm o boowes. Fo hose boowes, vae nomaon abou he obably o success n he eod ahead s so neave ha he bank ees o ncu he emnaon cos, lqudae s loans, and lend o nance he ojecs o undsnushable boowes. The heshold s such ha equaon (8 holds wh equaly: C ( heshold s calculaed by solvn o : ( d ( [( R ] ( d. The
- 6 - C ( (. (9 ( [( R ] ( The heshold s neave, snce he bank wll only emnae conacs wh unomsn boowes. The manude o he heshold snal leadn o conac emnaon s a osve uncon o C, and a neave uncon o he eun o he bank om undsnushable boowes. n a bankn envonmen whee banks sue moan aency oblems, have weak nenal conol sysems, whee he leal sysem s weak and enocemen o conac emnaon dcul and cosly, and whee he bank s euaon s assessed on s ably o ean cusomes and allocae ced ecenly, mlc coss o conac emnaon wll be hh. As a esul, only he bank eceves convncn evdence ha he execed euns o a boowe ae vey low wll oceed o emnae a loan conac. Fo nomaon snals such ha >, he bank wll ee o eman commed o boowes, even ncus a, o loss n he om o oone evenues. Pooson. By commn o unomsn boowes, he bank acces a educon n s execed o a each eod, howeve neo o he o loss would ncu by emnan s loans on all unomsn boowes. PROOF. Denoe as he shae o boowes sendn a osve snal ; he shae o, boowes sendn a neave snal such ha > > s,,, and he shae o boowes sendn a neave snal such ha >,, s, wh. The las ou o boowes s desnaed as vey unomsn boowes n he emande o he ae. n he esence o coss o conac emnaon, he bank wll enew loans o omsn and unomsn boowes (as shown n ooson and emnae loans wh vey unomsn boowes o elace hem wh undsnushable boowes. The execed o o he bank,, s comaed wh wo heoecal alenave suaons o assess he mac o boh he eceon o he nomaon snal and o he coss o conac emnaon. The alenave suaons ae when he bank elaces all unomsn and vey d d The nomaon snal heshold s ndeenden o nees aymens o deosos. nees aymens eman consan whehe he bank comms o unomsn boowes o elocaes o undsnushable boowes because he oal sze o he loan oolo emans unchaned.
- 7 - unomsn boowes by undsnushable boowes ( n he absence o coss o conac emnaon ( and ( n he esence o coss o conac emnaon (. n he esence o coss o emnaon and o a heshold below whch he bank decdes o emnae loans, he execed o o he bank s equal o: ( ( ( ( ( ( ( [ ] ( ( ( ( ( ( ( ( ( [ ] ( ( ( ( ( [ ] ( ( ( ( ( ( ( ( ( ( [ ] ( ( ( ( ( d b C d R d C b R d b R d b R, ( ( ( [ ] ( ( ( ( ( ( [ ] [ ] ( ( d C R d b R ( ( ( ( [ ] [ ] ( ( d C R. ( The execed o o he bank s equal o he execed o om undsnushable boowes lus he excess o he bank yelds om omsn boowes, mnus he lowe o yelds om unomsn boowes o whch comms and mnus he emnaon coss ncued o he shae o boowes o whch emnaes conacs. n he absence o coss o conac emnaon, he bank emnaes all loans wh unomsn and vey unomsn boowes and elocaes s oolo o undsnushable boowes. The execed eun o he bank s: ( ( ( ( ( ( ( [ ] ( ( ( ( ( ( [ ] ( ( ( ( ( ( ( [ ] ( ( ( ( ( d b d R d b R d b R ( ( ( [ ] ( ( ( ( [ ] ( ( d R d b R
- 8 - ( [( R ] ( ( d. ( By keen omsn boowes and subsun unomsn ones by undsnushable boowes, he bank eneaes an excess o o he shae o boowes ha ae omsn. he bank wee o emnae conacs wh all unomsn boowes, s execed o om lendn n eod would be equal o: ( ( [ ( ( ( ( R ( b ] ( ( ( [ ( ( ( ( ( R ] ( ( [ ( ( R ( b ] ( d d ( ( ( [ ( ( R ( b C] ( ( C ( b ( ( d [ ( ( [ R ] ( C] ( d ( [ ( ( [ R ] ( C] ( d. ( The execed os o he bank vay deendn on whehe decdes o emnae loans wh unomsn boowes. The deences beween,, and ae comued as ollows: ( ( [ R ] ( ( ( [( ( ( ( [ R ] C] ( eaann yelds: d d; d d ( [ R ] ( ( ( ( ( d C d. ( Commmen and emnaon coss aec he execed o o he bank n wo ways, as omalzed n equaon (. Fs, he bank ooes evenues o he shae o boowes ha could elace by moe oable undsnushable ones. Second, he bank ncus coss o conac emnaon o he shae o boowes.
- 9 - Howeve, he bank, houh commmen, saves on emnaon coss and yelds hhe os han had emnaed conacs wh all unomsn and vey unomsn boowes, as shown n equaon (4: ( eaann yelds: ( [( ( ( ( [ R ] C ] ( [ ( ( [ R ] ( C ] ( d ; d ( [ R ] ( ( ( ( ( d C d (4 By emnan all conacs and no commn o unomsn boowes, he bank ncus an addonal emnaon cos (he second em o equaon (4 and eneaes a sueo evenue by swchn o undsnushable boowes (he s em o equaon (4. The sueo evenue eneaed om oolo eallocaon s, howeve, nsucen o comensae o he emnaon coss ncued. The bank would heeoe exec lowe evenues om emnan all conacs comaed wh commn o hose unomsn boowes who dd no send such bad snals. Pooson 4. The ably o he bank o mono boowes s consaned by he manude o mlc coss o conac emnaon and by he ooons o omsn, unomsn and vey unomsn boowes. The bank may allevae hs consan by assn a o he coss o mlc commmen o deosos. Assume ha he bank ollows an exlc objecve o s execed o. As shown unde ooson, he bank may eneae an excess o ae eceon o he nomaon snal. The excess o may hen be used n hee ways: ( o ncease he oal execed o o he bank; ( o educe he lendn aes on omsn boowes; and ( o ncease nees aes ad o deosos, heeby osen nancal nemedaon. Howeve, he sze o he excess execed o s educed by he coss o conac emnaon because he bank needs o eneae enouh excess euns o comensae o he execed o loss om unomsn boowes. Ths educes he ably o he bank o mono boowes by educn he hea o conac emnaon and lowen nees aes on omsn boowes. Hence, commmen esuls n omsn boowes mlcly subsdzn unomsn boowes. Ths ollows om he ac ha, o boowes, coss o conac emnaon ae hhe han coss o commmen, as demonsaed wh equaon (9.
- - n a cave envonmen whee he bank manans lendn and deos nees aes consan, he bank ealzes an excess o ollown eceon o he nomaon snal. Pomsn boowes ae chaed a consan nees ae n se o he lowe obably o alue, enean an excess o sucen o comensae om he o losses elaed o mlc commmen and conac emnaon. PROOF. Unde he assumons o he model, he eceon o he nomaon snal does no aec he aveae execed o o he bank bu only ovdes nomaon abou he dsbuon o boowes. ollows ha: ( ( [ ( ( ( ( R ] ( ( ( [ ( ( ( ( ( ( R ] ( ven, and e-aann, yelds: ( [ ( ( ( ( R ] ( ( ( ( [ ( ( ( ( R ] ( ( ( ( [ ( ( R ( b ] ( d ( d d d d ( ( [ ( ( ( ( R ] ( ( ( ( ( b ( d ( ( ( d [ ( ( R ( b ] ( [ ( ( ( ( R ] ( ( ( b ( d ( [ ( ( R ( b ] ( [ ( ( R ( b ] ( d d d d; ( [( R ] ( ( ( [( R ] ( ( d d ( [( R ] ( (. d (5 Equaon (5 omalzes he ac ha when he bank leaves s oolo unchaned ae eceon o he nomaon snal, s execed o emans unchaned. The excess o eneaed by omsn boowes, he s a o equaon (5, comensaes exacly o he lowe execed o om unomsn and vey unomsn boowes, he second and hd as o equaon (5, esecvely. Howeve, as suesed n he above dscusson, he bank modes s oolo when eceves nomaon om boowes, by keen omsn boowes, commn o unomsn boowes, and elacn vey unomsn boowes by undsnushable
- - boowes. The deence,, beween he nal execed o and he execed o ae eallocaon o he bank s ced oolo s equal o: ( ( [ ( ( ( ( ( ( R ] ( [ ( ( R C] ( eaann yelds: d ( ( b ( d d ( [ ( ( ( ( R ] ( ( ( ( [ ( ( R ( b ] ( d ; d ( [ ( R ] ( ( d [( R ] ( ( d C ( d (6 Reaann (6 usn (5, one obans ( ( C ( ( d ( [( R ] ( ( d ( ( C ( d [( R ] ( ( d. (7 As shown n ooson and ven he denon o vey unomsn boowes, C ( ( d ( [( R ] ( ( d. Equaon (7 s heeoe osve, suesn ha he bank execs an excess o n he nem eod due o oolo eallocaon. The manude o he excess o wll deemne he exen o whch he bank may educe nees aes on omsn boowes. coss o conac emnaon ae low and/o he ooon o vey unomsn boowes s hh, he bank wll have moe leeway o educe such nees aes. Deendn on he lexbly o deos nees aes, he bank may ass a o all o he cos o mlc commmen o deosos. By lowen deos nees aes, he bank modes s execed excess o: ( ( [ ( ( ( ( R ] ( ( ( [ ( ( R ( b ] ( d C ( d ( d ( ( ( [ ( ( ( ( R ] ( ( ( b ( d ( d [ ( ( R ( b ] ( d
- - Gven, and e-aann, one has: ( [( R ] ( ( d ( [( R ] ( ( d C ( ( d ( ( b b ( d ( ( b b ( d. (8 s sueo o when he bank may lowe he deos nees ae, hence ovdn he bank wh moe leeway o educe aes on omsn boowes whou modyn s execed o objecve. The esul ovdes an exlanaon o lae seads beween lendn and deos aes, n an economc envonmen whee coss o conac emnaon ae hh. Follown on he aumen develoed n hs secon, a deen neeaon o he heshold and he elaed mlc coss o emnaon C may be ovded, as he maxmum oleance o omsn boowes o comensan unomsn boowes, and o deosos o bean he coss o he bank s commmen o s ced oolo, esecvely. V. MONTORNG AND COMMTMENT WTH CREDT HSTORY n hs secon, he mac o mlc commmen on he lendn behavo o he bank s nvesaed uhe, by lookn a he ocess o accumulaon ove me o nomaon snals eceved a each eod. The assumon used n secon V ha nomaon snals ae no seally coelaed s abandoned, allown he bank o esablsh a ced hsoy o each boowe, denoed e,. Commmen o boowes ove me allows he bank o aally allae he asymmey o nomaon aces when lendn and o allocae ced moe ecenly han n he absence o ced hsoy. Monon by he bank s deemned by a ocess o backwad-lookn accumulaon and neeaon o nomaon based on mlc commmen o boowes. The decson o he bank o enew o susend ced o boowes s modeled whn he amewok esablshed n secon and, aan, he equaons n secon ae ewen and moded o ake no accoun he nomaon accumulaed by he bank. The ocess o nomaon accumulaon s omalzed as ollows. Successve nomaon snals buld he bank s exese wh eads o ndvdual boowes. The denon o omsn and unomsn boowes s amended o accoun o accumulaed nomaon, and omsn/unomsn boowes ae boowes who have a hsoy o osve/neave nomaon snals.
- - The nomal snal, s eceved a me. The nomaon snal has he same chaacescs as n he evous secon; Accumulaed nomaon s denoed e,., s aeaed wh as nomaon houh, avean: e, e,, wh e, ; he accumulaon o snals s osve, and e, < he accumulaon s neave. Pomsn / unomsn boowes have < a hhe / lowe obably o success han he ou as a whole, esecvely; The aveae obably o success o he boowes s emans unchaned a. Fo each subou o boowes, he bank esmaes he secc obably o success as wh N e e,,,, whee N s he oal numbe o boowes n he bank s oolo. and s R, he ndvdual obably o success and he assocaed successul eun ae unobsevable by lendes. One chaacesc o he nomaon accumulaon ocess emees om he seccaon o e, : as he bank-boowe elaonsh exends ove me, as nomaon domnaes ove he snal sel. The bank s able o eassess he qualy o s ced oolo a each nem eod, ae aeaes he new snal wh as nomaon. A each nem eod, he bank can so evously undsnushable boowes no wo subous, omsn and unomsn. Ove me, he bank may move s nem son o boowes hanks o he successve eceon o nomaon snals. Pomsn boowes yeld hhe execed euns han unomsn ones. The bank maxmzes s o by elacn unomsn boowes by undsnushable boowes. The omalzaon and oos ollow exacly secon V and ae esened n aendx. Pooson 5. As a esul o boh backwad-lookn nomaon neeaon and mlc commmen o boowes, nomaon snals have an asymmec mac on he bank s lendn behavo, deendn on he naue o he snal and on he boowes ced hsoes. Fs, he bank acs deenly he snal eceved s osve o neave. When he bank eceves a osve snal om boowes, hee s no chane n s lendn behavo: boowes havn sen he snal ae eaned whn he bank s oolo. The only oenal chane ollows om he ac ha he bank may wan o lowe nees aes on such omsn boowes o ovde eomance ncenves. The mac o a neave nomaon snal may, on he ohe hand, om he bank no acon emnaon o he lendn elaonsh. Second, he mac o he nomaon snal deends on he ced hsoy o boowes. Boowes wh a lon hsoy o neave nomaon snals wll be moe exosed o he sk o conac emnaon han boowes wh a lon osve hsoy. Ths asymmey s due o backwad-lookn nomaon neeaon. Thouh avean,
- 4 - he bank educes he manude o each new nomaon snal, wh he ollown mlcaons. The ocess o accumulaon o nomaon educes he manude o each ndvdual nem nomaon snal houh avean, and educes he mac o he snal on he execed o o he bank. PROOF. A eceon o he snal, he bank evses s assessmen o he qualy o boowes by ncooan he snal no as nomaon. As dened eale, he nomaon used by he bank ollows om hs ncooaon o he snal as, e, e,, whch s sueo o e, he snal s osve and neo o e, s neave. The nomaon snal modes he o o he bank by: ( [( ] ( R ( d. (9 The chane n execed o s smalle by a aco o comaed wh wha s n he absence o nomaon accumulaon (equaon (4. The boowes bene om he lon-em elaonsh wh he bank. ( The hea o conac emnaon dmnshes ove me o omsn boowes. ( The dsclnay ole o monon becomes moe elevan o unomsn boowes because he hea o emnaon s moe bndn. PROOF. The emsson o a neave snal om boowes wll have a dsnc mac deendn on he naue o accumulaed nomaon. Fo boowes wh a sascal hsoy o bad news, a small snal may suce o nduce conac emnaon. Fo omsn boowes, a successon o neave snals may be needed beoe he bank decdes o ac. Fomally, he bank wll ac unde an nomaon snal he snal s such ha, e, < e o, < ( e e,, whee e s he heshold ha deemnes whehe he bank connues o no o lend o a secc boowe. The manude o he snal equed o he bank o ac wll be small e s close o e ha s, as nomaon has conssenly oned owad he unomsn naue o he boowes and lae e s sncanly hhe o e ; lae he bank-boowe elaonsh exends ove a lon eod o me. Wh s nsuonal memoy, he bank s less subjec o volaly n nomaon snals. Fo examle, he bank would comm o a omsn boowe even ha boowe s on houh dcul mes. The bank also evses only oessvely s assessmen o unomsn boowes when ood news ae eceved. Because conac emnaon s cosly, he bank s nsuonal memoy has he osve mlcaon o evenn undue conac emnaon and nceasn he execed o o he bank.,
- 5 - PROOF. n he absence o ced hsoy, he execed o o he bank would sue om hh volaly o nomaon snals, as would om he bank no eulaly emnan conacs on omsn boowes due o occuences o bad news. Wh no ced hsoy, he bank emnaes s conac wh a boowe he nem nomaon snal s such ha, <. Howeve, he boowe has a omsn ced hsoy, wh e, >, he nomaon snal mh eesen an exceonal occuence. The boowe s ced hsoy may be son enouh o he bank o connue o comm o he boowe n se o he e e., <, neave snal. As shown above, he snal would have o be such ha ( Denon β as he shae o boowes ha send such neave snals, he bank would ealze hhe execed os om commn o he boowes equal o: β ( [( e ( ( e ( R ] ( ( [( ( R ] ( ( d d C ( d. The ohe consequence o he ocess o backwad-lookn nomaon neeaon and mlc commmen s he nably o he bank o deec sucual chanes n he chaacescs o boowes, whehe omsn o unomsn. PROOF. Assume ha he qualy o a boowe wh a omsn ced hsoy deeoaes suddenly a eod T, so ha he boowe conssenly sends snals such ha,,. Wh no ced hsoy, he bank would mmedaely emnae s lendn elaonsh wh he boowe. Howeve, due o he ocess o nomaon accumulaon houh avean, may ake a subsanal numbe o eods beoe he bank decdes o ac on he neave snals. Seccally, he bank wll ac when e, e. The numbe M o eods s: e et, M M. T V. CONCLUSONS n a amewok o nomaon asymmey beween lendes and boowes, he model esened n hs ae shows ha a numbe o eaues o he deb conac ae cenal n exlann he naue o bank monon. Those eaues nclude he oessve evelaon o he qualy o boowes houh successve nomaon snals; he backwad-lookn ocess o nomaon accumulaon and neeaon; he esence o coss o conac emnaon o he bank; and, nally, he mlc commmen o he bank o enew he deb conac ove me. Seveal chaacescs o he bank lendn ocess ae shown o emee unde he assumons o he model. The need o comm o boowes o allevae oblems o asymmec nomaon and he esence o hh coss o conac emnaon ovde an exlanaon o he accumulaon o noneomn loans on he balance shees o banks. n an envonmen wh oo nomaon dssemnaon, hh nsuonal and admnsave des, and aency oblems, he model shows ha coss o conac emnaon may be so
- 6 - hh ha banks ee o kee noneomn boowes on he balance shees. Ths behavo would be amled easons o commmen ae noneconomc, such as ed ae and conneced lendn. Fuhe, hese coss exlan he eeence o banks o boowes wh well-known oducon uncons and lle vaably n euns ove me. Fnally, n he envonmen o he model, he exsence o a sead beween deos and lendn aes ollows om commmen o unomsn boowes. n eec, he bank may only susan commmen execs excess o om ohe boowes. As a esul, wll manan hh nees on omsn boowes, and low nees aes ad o deosos, wdenn he sead beween he wo aes. may do so moe easly comeon n he bankn seco s lmed, as s he case n a monoolsc envonmen. The model oens avenues o uhe eseach. An mmedae exenson would be o consde a comeve bankn envonmen. Comeon would aec he aumen n wo ways. Fs, he bank s make owe wh deosos would subsde, educn he ably o banks o ass he cos o commmen o deosos. Second, he mac on lendn wll deend on he ably o boowes o cedbly snal nem saus (omsn o unomsn o comen banks. hs nomaon s vae o he bank wh whch he boowe has a eexsn lendn elaonsh, he esuls o he model ae unchaned. s omal o he boowe o eman loyal o s bank. The bank ceaes an ex os nomaonal monooly, o whch ays he coss o commn o unomsn boowes. nomaon s aally o oally avalable o comen banks, omsn boowes may oban lowe lendn aes, whch even banks om comensan commmen coss by excess euns on omsn boowes. Wh nomaon ublcly avalable, banks would lose he benes o commmen. On a boade macoeconomc level, he ae shows ha, when dsoons o he unconn o he ced make ae hh hh asymmey o nomaon beween lendes and boowes, lle comeon n he bankn seco, hh mlc coss o conac emnaon he economc coss assocaed wh bank lendn may be hh. Fs, he soundness o banks may be a sk due o lae volumes o noneomn loans. Second, he nancn o economc owh may be concenaed o a ew well-esablshed nduses. Thd, he volume o ced may be consaned by hh nees aes on boowes, and low nees aes o deosos.
- 7 - APPENDX Aendx. mlc Commmen wh Ced Hsoy: Fomalzaon The ocess o nomaon accumulaon and mlc commmen s modeled ollown closely he omalzaon n Secon V. Fs, wh accumulaed nomaon, he bank educes he asymmey o nomaon beween sel and he boowes and may so he lae no ous o omsn and unomsn boowes. The execed eun o he bank om a snle boowe, ne o nees aymens o deosos, s: E e e R b. (A ( ( ( ( ( e,,, The execed eun o he bank om lendn o ha class o boowes a nees ae may be wen as: e ( [( e ( ( e ( R ] ( ( ( b ( d d. (A The accumulaon o nomaon modes he execed eun o he bank by: e ( [( R ] e ( ( ( The sn o he deence wll deend on he sn o ( e d. (A. Fo omsn boowes, he bank wll exec hhe euns han o he nal ou o boowes. Fo unomsn boowes, execed euns wll be lowe. Second, he bank modes s loan oolo o maxmze s execed o. The bank maxmzes o by keen omsn boowes n s oolo, and eallocan s oolo away om unomsn boowes, o boowes o whch has no vae nomaon, as hose yeld hhe aveae execed euns han unomsn boowes. The shae o omsn boowes n he bank s loan oolo s denoed. By keen s nees ae consan on omsn boowes and elacn unomsn boowes by undsnushable boowes, he bank nceases s o by ( [ ( R ] ( e ( ( d. On he shae ( o undsnushable boowes ha elace unomsn ones, he execed o o he bank s equal o he nal execed o, so he ncease n o s due o he excess eun made on omsn boowes. Thd, he bank has o ncu coss o conac emnaon when exn a conac wh a boowe. Coss o conac emnaon, denoed C, ae assessed elavely o he o loss PL he bank aces when comms o unomsn boowes. The o loss s esmaed as he deence beween execed o om undsnushable boowes and execed o
- 8 - APPENDX om unomsn boowes: PL ( om equaon (A. ( [ R ] ( e ( ( d, whch ollows Thee exss a heshold based on he accumulaed nomaon below whch he bank does no comm o boowes. The heshold, denoed e, s such ha C PL, o C o ( e : ( d ( [( R ] ( e ( d. The heshold s calculaed by solvn e ( ( C d. (A4 ( [( R ] ( The heshold s neo o, conssen wh he ac ha he bank wll only emnae conacs wh unomsn boowes. The manude o he nsuonal memoy leadn o conac emnaon s a osve uncon o C, and a neave uncon o he eun o he bank om undsnushable boowes. Fouh, commmen o unomsn boowes lowes he execed o o he bank, bu no as much as he emnaon o conacs on all unomsn boowes would. The shae o boowes wh a osve ced hsoy s denoed, and he accumulaed nomaon e ; he shae o boowes wh neave ced hsoy e such ha > e > e s ; and he shae o boowes wh vey neave ced hsoy e such ha > s ; wh.. n he esence o coss o emnaon and o a heshold e below whch he bank decdes o emnae loans, he execed o o he bank s equal o: ( ( [( e ( ( e ( R ( b ] ( [( e ( ( e ( R ( b ] ( ( [( R ] e ( [ ( ( e ( ] ( d d ( d [ ( ( R ( b C] ( d C ( ( d. The execed o o he bank s equal o he execed o om undsnushable d
- 9 - APPENDX boowes lus he excess o he bank yelds om omsn boowes, mnus he lowe o yelds om unomsn boowes o whch comms, and mnus he emnaon coss ncued o he shae o boowes o whch emnaes conacs.. n he absence o coss o conac emnaon, he bank emnaes all loans wh unomsn boowes and elocaes s oolo o undsnushable boowes. The execed eun o he bank s: ( [( e ( ( e ( R ( b ] ( ( ( [( ( R ( b ] ( ( [( R ] e ( ( ( d d. By keen omsn boowes and subsun unomsn ones by undsnushable boowes, he bank eneaes an excess o o he shae o boowes ha ae omsn.. he bank wee o emnae conacs wh all unomsn boowes, s execed o om lendn n eod would be equal o: ( [( e ( ( e ( R ( b ] ( ( [( R ] e ( ( ( d d ( C ( ( d ( [( ( R ( b C] ( The execed o o he bank vaes deendn on whehe decdes o emnae loans wh unomsn boowes. The deences beween,, and ae comued as ollows: ( d. d ( [( R ] e ( ( ( ( ( d C d. (A5 Commmen and coss o conac emnaon aec he execed o o he bank n wo ways, as descbed n equaon (A5. Fs, he bank oeoes evenues o he shae o boowes ha could elace by moe oable undsnushable. Second, he bank emnaes conacs o he shae o boowes, and ncus coss o conac emnaon.
- - APPENDX Howeve, he bank, houh commmen, saves on emnaon coss and yelds hhe os han had emnaed conacs wh all unomsn boowes, as shown n equaon (A6. ( [( R ] e ( ( ( ( ( d C d. (A6 By emnan all conacs and no commn o unomsn boowes, he bank ncus an addonal emnaon cos (he second em o equaon (A6, and eneae a sueo evenue by swchn o undsnushable boowes (he s em o equaon (A6. The sueo evenue eneaed om oolo eallocaon s howeve nsucen o comensae o he emnaon coss ncued. The bank would heeoe exec lowe evenues om emnan all conacs comaed o commn o hose unomsn boowes who dd no send such bad snals, as ndcaed by he osve sn o equaon (A6. Fh, he mac o he ced hsoy o boowes deends on he ooons o omsn, unomsn and vey unomsn boowes and on he manude o he mlc coss o emnaon. The mac o he eceon o he nomaon snal on he execed o o he bank s comued as he deence beween s execed o n he absence o vae nomaon and he execed o ae eceon o nomaon snals: ( [( R ] e ( [ ( ( e ( ] ( ( ( d C d ; eaann yelds: ( [ ] ( [( R ] ( e ( ( e ( d C ( d. (A7 ( ( ( The s em n equaon (A7 s osve. e ( e unde he assumons ha he aveae eun o he ool o boowes emans unchaned ae eceon o he nomaon snal and ha ( R. (
- - REFERENCES Benson, G., and Smh, C., 976, A ansacons cos aoach o he heoy o nancal nemedaon, Jounal o Fnance, vol. (,. 5. Bolon, P., and D. Schasen, 99, A heoy o edaon based on aency oblems n nancal conacn, Amecan Economc Revew, vol. 8(,. 9 6. Boo, A., A. Thako, and G. Udell, 99, Cedble commmens, conac enocemen oblems and banks: nemedaon as cedble nsuance, Jounal o Bankn and Fnance, vol. 5, PP. 65. Damond, D., 984, Fnancal nemedaon and deleaed monon, Revew o Economc Sudes, vol. 5,.9 44., and Dybv, P., 98, Bank uns, deos nsuance, and lqudy, Jounal o Polcal Economy, Vol. 9 (,. 4 9. Dewaon, M., and E. Maskn, 995, Ced and ecency n cenalzed and decenalzed economes, Revew o Economc Sudes, vol. 6(4,. 54 56. Fexas, X., and J-C. Roche, 998, Mcoeconomcs o Bankn, MT Pess, Cambde: USA. Gale, D., and M. Hellw, 985, ncenve comable deb conacs: The one-eod oblem, Revew o Economc Sudes, vol. L,.647 6. Gomb, D., 994, Conbuon à l économe nancèe e nduselle, Ph.D dsseaon, Laboaoe d économée de l Ecole Polyechnque, Pas. Haubch, J., 989, Fnancal nemedaon: deleaed monon and lon em elaonshs, Jounal o Bankn and Fnance, vol. (,. 9. James, C., 98, An analyss o bank loan ae ndexaon, Jounal o Fnance, Vol. 7 (,. 89 5. Melnk, A., and S. Plau, 986, Loan commmen conacs, ems o lendn, and ced allocaon, Jounal o Fnance, vol. 4 (,. 45 5. Moan, D., 994, Bank ced commmens, ced aonn, and moneay olcy, Jounal o Money, Ced and Bankn, vol. 6 (,. 87. Leland, H., and D. Pyle, 977, nomaonal asymmees, nancal sucue, and nancal nemedaon, Jounal o Fnance, Vol. (,. 7 87. Slz, J. E., and A. Wess, 98, Ced aonn n makes wh meec nomaon, Amecan Economc Revew, vol. 7(,. 9 4.
- -, 98, ncenve eecs o emnaons: Alcaons o he ced and labo makes, Amecan Economc Revew, vol. 7(5,. 9 7. Townsend, R., 979, Omal conacs and comeve makes wh cosly sae vecaon, Jounal o Economc Theoy, vol.,. 65 9. Wllamson, S, 987, Cosly monon, loan conacs, and equlbum ced aonn, Quaely Jounal o Economcs, Vol. (, Feb.,. 5 46.