Market-oriented interest rate, deposit insurance system and bank runs: A dynamic model perspective

Tian, Guoqiang; Zhao, Yupu; Gong, Rukai A icle Ma ke -o ien ed in e es a e, deposi insu ance sys em and bank uns: A dynamic model pe spec i e China Poli ical Economy (CPE) P o ided in Coope a ion wi h: School o Economics, Nanjing Uni e si y Sugges ed Ci a ion: Tian, Guoqiang; Zhao, Yupu; Gong, Rukai (2019) : Ma ke -o ien ed in e es a e, deposi insu ance sys em and bank uns: A dynamic model pe spec i e, China Poli ical Economy (CPE), ISSN 2516-1652, Eme ald, Leeds, Vol. 2, Iss. 1, pp. 53-72, h ps://doi.o g/10.1108/CPE-04-2019-0004 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/319395 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ Ma ke -o ien ed in e es a e, deposi insu ance sys em and bank uns A dynamic model pe spec i e Guoqiang Tian School o Economics, Shanghai Uni e si y o Finance and Economics, Shanghai, China and Texas A&M Uni e si y, College S a ion, Texas, USA Yupu Zhao School o Economics, Shanghai Uni e si y o Finance and Economics, Shanghai, China, and Rukai Gong Glo ious Sun School o Business and Managemen , Donghua Uni e si y, Shanghai, China Abs ac Pu pose –In he ansi ional p ocess o p omo ing ma ke -o ien ed in e es a e, China is con on ed wi h an impo an heo e ical and p ac ical issue: how o a oid bank uns and ealize he smoo h ope a ion o he inancial sys em. The pu pose o his pape is o cons uc a bank- un dynamic model by aking in o accoun a ma ke en i onmen wi h he ansmission o mul iple ounds o noise in o ma ion, a comp ehensi e conside a ion o deposi o s’expec a ion o e u n on asse s (o ea ning a e/yields o asse s), he e iciency o in o ma ion p ocessing and dissemina ion, and he di e en mo i es o p ema u e wi hd awal. Design/me hodology/app oach –The au ho s discussed he dynamic p ocess o bank uns, u nished he a io and numbe o each ound o bank un, and cha ac e ized he co esponding dynamic equilib ium as well. Fu he mo e, he au ho s expanded he benchma k model by inco po a ing he deposi insu ance sys em (DIS) o discuss he ac ion mechanism o DIS o e uns. Findings –The esul s show ha DIS implemen a ion has wo opposi e e ec s: s abilized expec a ion and mo al haza d, by i ue o i s in luence o e he wo ypes o p ema u e wi hd awal mo i es o deposi o s; he implemen a ion e ec o DIS es s wi h he dual-e ec compa ison, which is endogenous o he ins i u ional en i onmen . O iginali y/ alue –The policy implica ions a e as ollows: while implemen ing DIS, i is necessa y o es ablish and imp o e he co esponding ins i u ional cons uc ion and suppo ing measu es, o consolida e ma ke discipline and imp o e he supe iso y ole o he bank’s in e nal go e nance mechanism, so as o educe he po en ial mo al haza ds. The inancial sys em e o m shall be u he ed and he p ocessing and dissemina ion e iciency o in o ma ion be ele a ed o p omp deposi o s o o m s able wi hd awal expec a ions, he eby enhancing he s abilizing e ec o DIS. Keywo ds Mo al haza d, Bank uns, Deposi insu ance sys em, Ma ke -o ien ed in e es a e Pape ype Resea ch pape China Poli ical Economy Vol. 2 No. 1, 2019 pp. 53-72 Eme ald Publishing Limi ed 2516-1652 DOI 10.1108/CPE-04-2019-0004 The cu en issue and ull ex a chi e o his jou nal is a ailable on Eme ald Insigh a : www.eme aldinsigh .com/2516-1652.h m © Economic Resea ch Jou nal. Published in China Poli ical Economy. Published by Eme ald Publishing Limi ed. This a icle is published unde he C ea i e Commons A ibu ion (CC BY 4.0) licence. Anyone may ep oduce, dis ibu e, ansla e and c ea e de i a i e wo ks o his a icle ( o bo h comme cial and non-comme cial pu poses), subjec o ull a ibu ion o he o iginal publica ion and au ho s. The ull e ms o his licence may be seen a h p://c ea i e commons.o g/licences/by/4.0/legalcode. O iginally published in Simpli ied Chinese in Economic Resea ch Jou nal. 53 Deposi insu ance sys em and bank uns 1. In oduc ion Since he e o m and opening up, he ela i e de elopmen lag o China’s inancial indus y has been ega ded as one o he majo issues con on ing China’s economic ansi ion. I is becoming mo e and mo e u gen o imp o e he capi al alloca ion and u iliza ion e iciency ia ini ia ing inancial sys em e o ms, whe ein he in e es a e ma ke iza ion (ma ke -o ien ed in e es a e) e o m cons i u es an impo an ini ia i e o inancial sys em ans o ma ion (Yi, 2009). Howe e , in e na ional expe ience shows ha inancial ma ke iza ion, while imp o ing he e iciency o inancial esou ce alloca ion, may exace ba e he agili y o he inancial sys em, leading o bank c ises and e en economic c ises (Bekae e al., 2005). In e na ional Mone a y Fund (IMF) s a is ics show ha since he p e alence o inancial de egula ion (libe aliza ion) in he 1990s, mo e han 100 banking c ises ha e occu ed all o e he wo ld. O he 181 membe s a es o he IMF, 130 ha e expe ienced di e en le els o banking c ises. How o a oid he banking c isis in he p ocess o p omo ing in e es a e ma ke iza ion (libe aliza ion) and ealize he smoo h ope a ion o he inancial sys em is a majo heo e ical and p ac ical p oblem aced by he economies in ansi ion. The expe ience and esea ch o a ious coun ies show ha , conside ing he s ong ex e nali ies o inancial indus y, while p omo ing ins i u ional e o ms such as in e es a e libe aliza ion (ma ke iza ion), i is necessa y o es ablish a se ies o suppo ing sys ems, such as deposi insu ance sys ems (DISs), o p omo e he smoo h implemen a ion o inancial sys em e o m[1]. China’s cen al decision-making le el has been explo ing and p omo ing he in oduc ion o DIS as a suppo ing condi ion o he s eady implemen a ion o in e es a e libe aliza ion[2]. In Ma ch 2015, China’s S a e Council p omulga ed he “Regula ions on Deposi Insu ance,”which was o icially implemen ed on May 1 in he same yea , ma king he ansi ion om implici ull gua an ee (blanke gua an ee) o explici DIS in China. The exis ing esea ch and p ac ice show ha he eme gence o DIS mainly s ems om he bank’s conce n abou he deposi o s’bank uns; he po en ial in o ma ion asymme y be ween deposi o s will u he lead o panic in he banking sys em and expand he chain eac ion o he un, causing sys emic banking c isis and ex emely ad e se e ec s on economic de elopmen . DIS can e ec i ely es ain he beha io o deposi o s, educe he occu ence o deposi o s’ un-o (bank un) beha io , and s abilize he inancial sys em e o m (Fama, 1980; Diamond and Dyb ig, 1983). Howe e , DIS may also cause se ious mo al haza d p oblems in banks, mainly in h ee aspec s: Fi s , DIS has no made i necessa y o banks o pay highe in e es a es o deposi o s o addi ional isks o in es men . Fo highe e u ns, banks ha e incen i es o in es in high- isk p ojec s, hus inc easing he ins abili y o bank ope a ions. Second, deposi insu ance (DI) ins i u ion p o ides epaymen gua an ees o banks acing liquidi y c isis; hence, DIS weakens he banks’in e nal go e nance mechanism, educes he isk managemen abili y o banks and inc eases he p obabili y o bank ailu es. Thi d, deposi o s expec DI ins i u ions o p o ide wi hd awal gua an ees; hence, hei incen i es o supe ise bank in es men beha io s wane, leading o weak ma ke discipline and p omp ing banks o op o high- isk in es men p ojec s (Demi güç-Kun and Kane, 2002, 2004). Based on his, while implemen ing DIS, all coun ies ace a ade-o be ween he s abilizing e ec o p e en ing bank uns and he po en ial mo al haza d. Fu he mo e, whe he DIS can be e ec i ely implemen ed is o en closely ela ed o he ins i u ional en i onmen . In an economy wi h a ela i ely sound inancial sys em, he go e nmen in e enes li le and p o ides less gua an ees in banking business; hus, he un-o beha io poses a g ea h ea o banks. The e o e, DIS implemen a ion can p o ec he in e es s o deposi o s and he s abili y o he banking sys em. Howe e , in he inancial ma ke s o ansi ion economies su ei ed wi h go e nmen in e en ion, he go e nmen usually ac s as a hidden gua an o o exe in luence on banking business. The e o e, DIS implemen a ion may lead o se ious mo al haza d p oblems. Wi h he g adual ad ancemen o he inancial sys em e o m, he go e nmen ’s implici gua an ee mechanism shall be law idden and no longe applicable. On he con a y, he explici DIS has become he wo ld-wide ins i u ional p o ocol. 54 CPE 2,1 Then, in he ansi ion pe iod o he inancial sys em, how o es ablish and e ec i ely implemen he explici DIS is an issue wo hy o u he s udy. Exis ing esea ch shows ha explici DIS ends o inc ease he likelihood o banking c ises, he mo e so when he design cha ac e is ics o DI is aken in o accoun (Demi güç-Kun and Kane, 2002). A na u al ques ion is why, in he p ocess o ma ke iza ion o in e es a es in he economies wi h impe ec inancial sys em, DIS implemen a ion is o en shadowed by bank uns. I is necessa y o discuss he ela ionship be ween DIS and bank un in he con ex o in e es a e libe aliza ion. As a as he ac s a e conce ned, DIS i s appea ed in de eloped coun ies in Eu ope and Ame ica, whe e he economic en i onmen and mechanism o demand aced by DIS a e signi ican ly di e en om de eloping coun ies in he ansi ion pe iod (Fan and Cao, 2006). The Uni ed S a es can be aken as an example. When he Uni ed S a es es ablished he explici DIS, i aced he inancial c isis o 1929‒1933. I s mechanism o demand was “ inancial c isis→ o es ablish DIS→ o main ain inancial s abili y.” In ansi ional economies such as China, while implemen ing DIS, i aces a inancial sys em e o m whose mechanism o demand is “ o e o m inancial sys em→ o es ablish an explici DIS→ o es ablish a ma ke -based isk managemen mechanism.”Among hem, one o he majo measu es o inancial sys em e o m is ma ke -o ien ed in e es a e e o m. Di e en mechanisms o demand a e bound o ace di e en mechanisms o in e ac ion. The e o e, when we discuss he ela ionship be ween DIS and bank un, i is necessa y o closely ollow his ins i u ional backg ound. In iew o his, his pape cons uc s a gene al dynamic model o bank un o analyze he basic logic o deposi o s’ uns in he p ocess o in e es a e ma ke iza ion and u he inco po a es DIS in o he benchma k model o examine he impac o DIS on bank uns. The p ocess is in wo s eps: Fi s , o clea ly cha ac e ize he p ocess o bank uns, in he dynamic model, we b eak down he deposi o un p ocess in o mul iple ounds and he un-o beha io in o wo ypes o mo i a ions. Gi en an expec ed decline o long- e m e u n on asse s (ROA/ asse s ea ning a e), in ound o he un, he ma ginal eplacemen a e o deposi o s in he wo pe iods o consump ion changes, causing hem o wi hd aw money in ad ance, he eby eleasing a signal upon which deposi o s will p ocess and o m new judgmen s, and decide whe he o un in he nex ound. This p ocess las s o se e al ounds, and as a esul , banks ace he isk o unning ou o liquidi y. I should be no ed ha he i s ound o he un is o en di e en om he subsequen un: in he i s ound o he un, he deposi o ealizes he imp o emen o pe sonal wel a e by aking ou he long- e m deposi o consump ion in pe iod 1, de ined as he i s ca ego y o mo i a ion; in o he ounds o uns, deposi o s ake long- e m asse s o u u e consump ion, which is a panic beha io , de ined as he second ca ego y o mo i a ion. Fu he mo e, he e o caused by in o ma ion asymme y has a las ing in luence, which is endowed by he deposi o ’s choice o ime weigh while p ocessing in o ma ion, and i is o en ela ed o he ins i u ional en i onmen such as he deg ee o go e nmen in e en ion and he le el o in e es a e ma ke iza ion (Demi güç-Kun e al., 2008). Then, DIS is in oduced in o he benchma k model o analyze i s impac on he beha io o banks and deposi o s, espec i ely, and hus he impac mechanism o DIS on bank- un p ocess and he dynamic equilib ium. The es o he pape is a anged as ollows: Sec ion 2 e iews he li e a u e; Sec ion 3 cons uc s a gene al heo e ical model o bank- un benchma k and sol es and analyzes dynamic equilib ium; Sec ion 4 in oduces DIS o expand he benchma k model and explo e he ac ion mechanism o DIS on bank uns; Sec ion 5 concludes and gi es policy implica ions; he p oo s o he lemma and p oposi ions in he ex a e shown in he Appendix. 2. Li e a u e e iew In he wake o he 2008 wo ld inancial c isis, he bank- un p oblem has once again become a ho opic in academic esea ch. The ele an li e a u e ocuses mainly on wo aspec s. 55 Deposi insu ance sys em and bank uns Fi s , he decline o he banks’ eal ROA gi es ise o bank uns, which was an emphasis o he ac ual impac i s p oposed by B yan (1980). Second, he D&D Model was i s p oposed by Diamond and Dybi g, who held ha he bank un is based on he he d beha io caused by “Sunspo ”(Diamond and Dyb ig, 1983), ha is, unce ain y o indi idual beha io in an impe ec ma ke . The ule o “Fi s -come, Fi s -se ed”s ipula ed by he deposi con ac igge s bank uns, and he es ic ion o “sequen ial se ice” o deposi o s leads o nega i e payo ex e nali y e ec s. Pos lewai e and Vi es (1987) desc ibed bank uns as an equilib ium o a s a ic game wi h incomple e in o ma ion; Wallace (1988) poin ed ou ha demand deposi s and he “ i s come, i s se ed”sequen ial ule a e he wo essen ial ac o s ha lead o bank uns; Jacklin and Bha acha ya (1988) compa ed wo ypes o bank un models caused by panic and eal e u n, and p o ed ha he c i ical poin o bank un depends on he a iance o long- e m ROA by using squa e oo u ili y unc ion and he model speci ica ion wi h in a ian consume expec a ion o long- e m ROA; Scho e and Yo ulmaze (2009) es ablished a dynamic bank- un model o in o ma ion ansmission, o examine he impac o in o ma ion ex e nali ies and he he d e ec in bank uns on he equilib ium ou come. A he same ime, a se ies o s udies ha e been conduc ed o discuss he ela ionship be ween DIS and he isk o bank uns. Diamond and Dyb ig (1983) a gued ha he isk o bank uns b ough abou by demand deposi s would lead o bank ailu es and eal economic losses, whe eas he implemen a ion o a DIS would acili a e an equilib ium; Chen (1999) posed a DIS design idea ha could elimina e he bank un panic and guide deposi o s o ocus on accu a e in o ma ion. DIS may c ea e mo al haza d p oblems while p e en ing bank uns, whe eas liquidi y suppo policies can p e en bank uns and cu ail mo al haza d issues. S a and Yilmaz (2007) s udied he bank un in Tu key in 2001 and poin ed ou ha he use o DIS in eme ging economies can educe he wi hd awal beha io o deposi o s who lack in o ma ion when bank liquidi y is unce ain, and hus help p e en he occu ence o bank uns. I can be seen ha he exis ing esea ch has made ins uc i e discussions on bank uns and he impac o DIS on bank uns. Howe e , mos o hese models a e ca ied ou in he con ex o s a ic in o ma ion ansmission, wi hou conside ing he dynamic p ocess o in o ma ion ansmission in eali y, and especially he po en ial bank uns in he p ocess o inancial sys em e o m in ansi ional economies. Below we will build a bank- un model based on dynamic pe spec i es conside ing he di e en p ema u e wi hd awal mo i es o deposi o s and he p ocess o p ocessing and dissemina ion o expec a ion bias, o analyze he p ocess o bank uns in dep h, which cons i u es a help ul complemen o he exis ing esea ch. Wi h he ac i e p omo ion o ma ke -o ien ed in e es a e e o m and DIS in ecen yea s, many Chinese schola s ha e emba ked upon p elimina y esea ch on issues such as in e es a e libe aliza ion and he in oduc ion and implemen a ion o DIS. Xie e al. (2001) in oduced he ele an heo e ical esea ch and in e na ional compa ison o DIS. Huang (2001) di ided he isks b ough by in e es a e libe aliza ion in o ansi ional isk and e e las ing isk, poin ing ou ha a e in e es a e libe aliza ion, deposi in e es a es will ise signi ican ly in he sho e m. Qian (2004) held ha he p e equisi es o es ablishing an e ec i e DIS include imp o ing bank go e nance s uc u e, p uden bank supe ision and popula ized DI concep s, e c., and p oposed e ec i e ins i u ional a angemen measu es o DI design. Su (2005) ook in o accoun he p ac ical p oblems exis ing in China’s inancial de elopmen and made p oposi ions on he na u e o DI ins i u ions, sou ces o unds and paymen me hods. Wang (2006) s udied and summa ized he expe ience o he US Fede al Deposi Insu ance Co po a ion (FDIC), and pu o wa d sugges ions on he es ablishmen and supe ision unc ions o China’s DI ins i u ions. Tang (2008) in es iga ed, om he pe spec i e o DIS in a ious coun ies, how o imp o e he co po a e go e nance mechanism o o e come he po en ial mo al haza d o in oducing a DIS. Yao and Xia (2012) pu o wa d he design idea o DIS wi h minimum cos and incen i e compa ibili y based on he empi ical analysiso DISinGe many,B azilandRussia.By employing he p incipal-agen model, Yao e al. (2013) discussed he p os and cons o he implici 56 CPE 2,1 and explici DIS unde sys emic isk om he pe spec i e o he in e nal go e nance le el o comme cial banks. I can be seen ha he exis ing Chinese esea ch mainly ocuses on d awing on he in e na ional expe ience. I discusses he necessi y o in oducing DIS and p oposes he co esponding design ideas, bu a ely in ol es he ela ionship be ween DIS and bank un agains he backd op o in e es a e ma ke iza ion, which is he ocus o his pape . In summa y, he exis ing esea ch mainly conside s he economic en i onmen aced by de eloped economies, and conside s less he demand egime (mechanism) o DIS in ansi ional economies, and he economic en i onmen o in oducing DIS. In addi ion, mos o he exis ing esea ches use he esea ch amewo k o he classic D&D model, ha is, an idea o explo e DIS implemen a ion wi h he goal o maximizing social u ili y o he u ili y o deposi o s, bu lacking conside a ion o he bank’s own beha io . The mo e ealis ic si ua ion is ha banks, as independen decision-making bodies, ha e beha io al cha ac e is ics ha pu sue hei own u ili y maximiza ion. Fu he mo e, in e ms o deposi o beha io al limi s, he D&D model assumes ha deposi o s do no know whe he hey a e spending in he i s o second pe iod a he beginning o he pe iod, bu in eali y, deposi o s will o m he op imal consump ion plan h ough con inuous collec ion and p ocessing o in o ma ion. In iew o his, his pape will expand he exis ing model om wo aspec s. Fi s , he pa icipan s’beha io al assump ions a e expanded. Assuming ha he bank’sgoalis o maximize i s expec ed u ili y, a liquidi y managemen s a egy is a ached and he deposi o ’s consump ion decisions a e in e nalized, depending on hei expec a ions o deposi a es in di e en pe iods. Second, he exis ing bank- un model is expanded by he ollowing me hod. Fi s , he dynamic bank- un model o mul i- ound noise in o ma ion ansmission is es ablished; he deposi o ’s p ema u e wi hd awal mo i es a e di ided in o wo ca ego ies, and he impac o long- e m ROA dis ibu ion, in o ma ion p ocessing and e ec o sp eading e iciency on equilib ium is analyzed. Second, he o de ing ule in he dynamic model is de ined, and he concep o s ong equilib ium is p oposed o cha ac e ize he in luence o he unce ain y o he signal ob ained by he deposi o in each ound o he un on he equilib ium esul , he eby boos ing he eali y emula ion o bank- un equilib ium. Thi d, DIS is in oduced in o he model and he impac mechanism o he sys em implemen a ion on he dynamic un is analyzed. The esul s o his pape show ha DIS has wo opposi e e ec s o o ming a s able expec a ion and causing mo al haza d by a ec ing he wo mo i es o deposi o s’p ema u e wi hd awal, and he s eng h o he wo e ec s depends on he ins i u ional en i onmen . Whe he he in oduc ion and implemen a ion o DIS can imp o e he e iciency o social inancing, educe he p obabili y o bank uns and p omo e he smoo h ans o ma ion o he inancial sys em elies on he es ablishmen and imp o emen o ma ke discipline, he in e nal go e nance mechanism o banks, he e iciency o ma ke in o ma ion p ocessing and dissemina ion, and o he suppo ing sys ems ela ed o he inancial ma ke iza ion e o m. 3. The dynamic bank- un model This sec ion expands he exis ing model o es ablish a bank- un dynamic model wi h a wide co e age. The speci ic analysis idea is o desc ibe he economic en i onmen , as well as he decision-making sequence o deposi o s and banks, o cha ac e ize he beha io al assump ions o banks and deposi o s, o analyze he speci ic dynamic p ocess o bank uns, and o de ine and discuss he dynamic equilib ium. 3.1 Economic en i onmen Conside an economic en i onmen wi h h ee pe iods (0, 1, 2), whe e he e is a bank and a con inuum o deposi o s in he [0, 1] ange. The bank has p op ie a y echnology o con e ing pe iod 0 asse s in o pe iod 1 and pe iod 2 consume goods, and in es ing he acqui ed deposi s in wo ypes o asse s: sho - e m secu i y asse s and long- e m isk 57 Deposi insu ance sys em and bank uns asse s, o which secu i y asse s can be conside ed as a s o age echnology ha con e s a uni o asse s o pe iod 0 in o a ce ain uni o asse s o pe iod 1. Long- e m isk asse s a e de e mined by a speci ic and unce ain echnology, and hey can gene a e uni s o consume goods in pe iod 2, he e, is a andom a iable. A he beginning, he deposi o owns all he asse s and he asse s a e no classi ied and con e ed. In pe iod 0, he bank p o ides wo ypes o con ac s: he i s ype is a demand deposi . I he bank has a su icien liquidi y, in pe iod 1, a uni asse will ecei e R 1 uni s o consume goods; i he bank has insu icien liquidi y, he bank’s liquid asse s will be e enly dis ibu ed among deposi o s. The second ype o con ac is a ixed ime deposi . I he long- e m asse s held by he bank ha e a highe ROA, a uni asse will ecei e R 2 (WR 1 ) uni s o consume goods in pe iod 2, o R 1 uni s in pe iod 1; i he bank’s liquidi y in pe iod 1 is insu icien , i will be e enly dis ibu ed among all he wi hd awals o pe iod 1. Conside ing he eali y o China’s dual- ack in e es a e sys em, he ROA o long- e m isk asse s is a andom a iable, which can be ega ded as he equilib ium in e es a e in he ma ke o loanable unds. I is he embodimen o in e es a e ma ke iza ion, and he co esponding p obabili y densi y unc ion is q( ). Taking in o accoun he eali ies o in e es a e con ol, he bank’s deposi in e es a es o R 1 and R 2 in he wo pe iods change ela i ely li le, and hey a e subjec o he cons ain s o he ceiling on deposi a es as well as he loo on lending a es (Yi, 2009; He and Wang, 2011). Wi h he g adual ad ance o in e es a e ma ke iza ion, R 1 and R 2 will be mo e lexible. The decision sequence o he bank and deposi o is shown in Figu e 1. 3.2 Pa icipan ’s beha io se ing 3.2.1 Bank. In pe iod 0, he bank p o ides wo ypes o con ac s o abso b deposi s and in es s he acqui ed deposi s in Luni s o sho - e m (cu en ) asse and Xuni s o long- e m ( isk) asse s, espec i ely. Assuming ha he bank is isk-neu al, he goal is o maximize he expec ed u ili y by asse alloca ion o he abso bed deposi s. Suppose ha in pe iod 0, he in o ma ion se aced by he bank is I 0 . Gi en he ROA o long- e m asse s, he bank’s p oblem o maximizing he expec ed u ili y is: max L;X g ΕLD1R1þsX D2R2 ðÞ I0  s: :LþXpD; whe e σis he bank’s in e empo al isk adjus men ac o , which measu es he expec ed e u n and isk p e e ence (appe i e) o he bank o long- e m in es men , and sa is ies σ⩾ (1/ ), ha is, he adjus men o yield o long- e m isk asse s a leas ealizes he p esen discoun ed alue. The op imiza ion p oblems acedbybankscanbe u he cla i iedas he ollowing: max L;XgE1s ðÞ LþsD D1R1sD2R2 ½ : = 0 The bank p o ides wo ypes o con ac s: demand deposi s and ime deposi s; deposi o s make deposi decisions = 0.5 The bank will make in es men s decisions on he acqui ed deposi : de e mining he quan i y o sa e ( iskless) and isk asse s = 2 When he deposi con ac expi es, he deposi o ob ains he p incipal and in e es and makes a consump ion decision = 1 The deposi o judges he ROA o asse s in es ed by he bank and decides whe he o wi hd aw money in ad ance o he cu en o u u e consump ion Figu e 1. Bank and deposi o decision sequence 58 CPE 2,1 Since 1s p0 and is independen o o he a iables, i is di ec ly in e ed ha banks will p e e o in es in long- e m isk asse s, ha is, he e is a “ma u i y misma ch”p oblem. To ensu e he sa e y o he ope a ion, i is assumed ha he bank implemen s a liquidi y managemen s a egy ρ(E 1 R 1 +E 2 R 2 ), whe e he pa ame e ρindica es he bank’s p e-judgmen o he p obabili y o un-o beha io , and i can also be used o indi ec ly cha ac e ize he deposi o ’s belie in he long- e m ROA. The e o e, sho - e m liquid asse s can be exp essed as L¼max{ρ(D 1 R 1 +D 2 R 2 ), D 1 R 1 }, co esponding o he capi al equi ed by he go e nmen ’s banking egula o y policies. Acco ding o he Basel Acco ds, he ele an p o isions on bank capi al shall sa is y ρD 2 R 2 W(1−ρ)D 1 R 1 ,soL¼ρ(D 1 R 1 + D 2 R 2 ) will be ob ained. In his way, he bank’s in es men decision becomes he p oblem o maximizing he expec ed u ili y o he addi ional liquidi y managemen s a egy. 3.2.2 Deposi o (consume ). Acco ding o he pa icipan ’s decision-making sequence in Figu e 1, in he ace o he wo ypes o deposi con ac s p o ided by he bank, he deposi o will selec D 1 uni s o demand deposi s and D 2 uni s o ime deposi s. D 1 and D 2 a e all unc ions o R 1 and R 2 , and Dis he sum o he o al deposi s. The wo asse alloca ions ha e ce ain subs i u abili y D¼D 1 (R 1 ,R 2 )+D 2 (R 1 ,R 2 ). I is assumed ha he ep esen a i e deposi o has a u ili y unc ion in Go man’s Fo m: u(c 1 )+βu(c 2 ), whe e u(·) sa is ies he Inada Condi ion, βis a deposi o ’s in e empo al discoun ac o . In pe iod 0, he deposi o and he bank ha e he same in o ma ion se I 0 , based on which he p oblem o maximizing he expec ed u ili y aced by he ep esen a i e deposi o can be exp essed as: max D1;D2 g Euc 1;c2 ðÞ I0  ¼uD 1R1 ðÞþbuD 2R2 ðÞ ½ s: :D1þD2pD: Sol ing he abo e maximiza ion p oblem, he Eule equa ion is ob ained, u0(c 1 )¼βu0(c 2 ), namely, u0(D 1 R 1 )R 1 ¼βR 2 u0(D 2 R 2 ). I shows ha he deposi o ’s ma ginal u ili ies in he wo pe iods o consump ion a e equal, ha is, he ma ginal u ili ies o he deposi o ’s sho - e m o long- e m capi al alloca ion a e equal; he expec ed u ili y is maximized. 3.2.3 The dynamic p ocess o bank uns. Reali ies and esea ches ha e shown ha he eme gence o bank uns o en in ol es wo aspec s: he decline o long- e m ROA and w ong con ac ual a angemen s. Fi s , wo ypes o p ema u e wi hd awal mo i es a e de ined: in he ace o declining expec ed long- e m ROA, deposi o s ake ou long- e m deposi s o consump ion in pe iod 1, which is de ined as he Type 1 mo i a ion. As deposi o s a e wo ied abou he sa e y o bank deposi s, hey will choose o wi hd aw money in pe iod 1 o consump ion in pe iod 2 in he u u e, which is de ined as he Type 2 mo i a ion. I can be seen ha al hough he deposi o s a e aking ou deposi s in ad ance because o he expec ed educ ion in he yield o long- e m asse s, he Type 1 mo i a ion will inc ease he deposi o ’s consump ion in pe iod 1 and imp o e hei own wel a e, while he Type 2 mo i a ion may cause a bank un panic and lead o economic dis u bances. The ollowing wo s ages will examine he bank- un p ocess caused by he deposi o ’s wo ypes o p ema u e wi hd awal mo i es. The ollowing scena io can be conside ed: deposi o s ha e incomple e in o ma ion abou he a e o e u n on long- e m asse s held by banks. Re e ing o he ideas o Golds ein and Pauzne (2005), he signals ob ained by ep esen a i e agen (deposi o ) ia e exp essed as ^ i 1¼ þei 1, whe e ei 1deno es he po en ial e o o deposi o ’s in e p e a ion o he in o ma ion, which has a p obabili y densi y unc ion q1ðei 1Þde ined wi hin he suppo [−e 1 , e 1 ], and acco dingly, he p obabili y densi y unc ion q1ð^ i 1 Þo ^ i 1is de ined wi hin he in e al [ −e 1 , +e 1 ], and q 1 (·) sa is ies he condi ion R þe1 e1q1ð^ i 1 Þd^ i 1¼1. Lemma 1 gi es 59 Deposi insu ance sys em and bank uns he na u e o he condi ional p obabili y densi y unc ion o long- e m asse e u n ha he deposi o judges based on in o ma ion: Lemma 1. Fo any deposi o iand j, i he p obabili y densi y unc ions q1be1 ðÞand q2be2 ðÞ o he in e ence e o a e independen o each o he , hen he e is a posi i e numbe δsuch ha j 2b j7d  ¼ i 2b j  , ha is, o deposi o iand j, he in e ed in o ma ion o he long- e m asse e u n is symme ical. In pe iod 1, he sho - e m and long- e m deposi s o he asse alloca ion o deposi o ia e exp essed as ollows: Di 1þDi 2¼Di. I he deposi o iobse es o p edic s ha he long- e m ROA is educing, based on he Type 1 mo i a ion, pa o he long- e m deposi , Di 1X0, will be wi hd awn in ad ance in pe iod 1, o he consump ion o pe iod 1, and he Eule equa ion o he maximum expec ed u ili y o he deposi o de i es: u0Di 1þDi 1  R1  R1¼EbR2u0Di 2Di 1  R2 hi :(1) He e, he igh side o he equa ion can be exp essed as: Z þe1 ðÞ e1 ðÞ bu0Di 2Di 1  R2 hi R2q1^ i 1  d^ i 1; whe e R2¼ðX^ i 1=1 ðÞ Di 2ÞðDi 1=Di 2ÞR1. Fo any long- e m ROA, i is in e ed om he abo e o mula (1) ha Di 1¼gð ;e1;Di 1;Ri 1Þ. Only he Type 1 mo i a ion is conside ed o cause he deposi o o wi hd aw in ad ance, and he e o e only Di 1appea s in he expec ed u ili y unc ion o he deposi o in pe iod 1, and he amoun o p ema u e wi hd awal Δ 1 is uniquely de e mined by D1¼R1 0Di 1ðUÞdi. Speci ically, in he case ha deposi o i ega ds he signal i 1as he ROA dis ibu ion cen e , n 1 ep esen s he h eshold alue o he long- e m ROA upon which he bank un will (no ) jus happen, de e mined by D2R2¼ D1R1 ðþD2R2ÞD1R1þX n 1. The e a e h ee scena ios o discuss he numbe o bank uns ha occu : (1) I X n 1þ2e1, hen Δ 1 ¼0, namely, when he long- e m ROA is high enough, no bank un will occu ; (2) I n 1p o n 1þ2e1, hen D1¼lim Di 1-0R n 1þe1 n 1e1 Di 1q1ð^ i 1 Þd^ i 1¼lim Di 1-0R n 1þe1 n 1e1gð ;e1;Di 1; Ri 1Þq1ð^ i 1 Þd^ i 1; and (3) I o n 1, hen D1¼lim Di 1-0R þe1 e1gð ;e1;Di 1;Ri 1Þq1ð^ i 1 Þd^ i 1. In he case o a gi en deposi con ac , we u he ha e Δ 1 ¼h( ,e 1 ), and @D1=@  o0;@D1=@e1  40, indica ing ha he numbe o uns mo es in e sely o he long- e m ROA and in he same di ec ion wi h deposi o s’in e p e a ion e o o he ROA in o ma ion. In he second pe iod, deposi o i ecei es a un signal wi h noise, and he judgmen on he long- e m ROA is upda ed as 0i 1. The deposi o s p ocess he in o ma ion in he same way as desc ibed abo e, bu hei expec a ions o he signal change. A his ime, deposi o iexpec s he long- e m ROA as 0i 1¼ þei 2,whe eei 2indica es he e o o he in e ence deposi o i makes based on he in o ma ion o he p e ious ound. I has a p obabili y densi y unc ion q2ðei 2Þde ined wi hin he in e al [−e 2 ,e 2 ], and hen he p obabili y densi y unc ion o 0i 1is q2 0i 1  ,de inedwi hin ei 2; þei 2  . In o de o clea ly cha ac e ize he deposi o ’s in o ma ion upda ing p ocess, we conside using adap i e expec a ion equa ion o weigh he 60 CPE 2,1 he hi d sec ion, he deposi o uses he adap i e expec a ion model o weigh he in o ma ion o he wo adjacen pe iods o o m a new in e ence. Conside ing a mo e gene al case, we de ine n d;nþ1as he h eshold alue o he long- e m ROA igge ing a bank un in ound n, which sa is ies he ollowing condi ions: Z i nþ1þu i nþ1u X^ iþ D1R1þD2R2 ðÞD1R1X n i¼1 DiR1 "# i nþ1^ i n i nþ1¼ n nþ1  d^ 1¼D2X n i¼1 Di ! R1þF; whe e i nþ1ð^ i n9 n nþ1;FÞ ep esen s he condi ional p obabili y densi y unc ion o he deposi o i′s in e ence e o on he long- e m ROA in ound n⩾2, and ^ i n¼ þun. Gi en he deposi composi ion o a deposi o , i can be in e ed om he mon onici y o he le side o he abo e equa ion ha n d;nþ1o n nþ1, ha is, DIS implemen a ion will cause a decline o he h eshold alue o he long- e m ROA upon which he bank un will (no ) jus happen, hus educing he p obabili y o a bank un. In u n, he a io and numbe o bank uns o deposi o s a any ound a e ob ained, which is exp essed as he ollowing p oposi ion: P4. In he case o DIS implemen a ion, o any ound n,n⩾2, gi en he h eshold alue o he long- e m ROA igge ing a bank un, n nþ1, he a io o bank uns is hus: lnð n d;nþ1;un;FÞ¼Z n d;nþ1 un nþ1ð^ i n9 n nþ1;FÞd^ i: The co esponding numbe o bank uns is Dn¼D2Pn1 i¼1Di  ln n d;nþ1;un;F  . In he con ex o in e es a e libe aliza ion, he impac o DIS on he second ype o p ema u e wi hd awal mo i es o deposi o s in ol es h ee aspec s. Fi s , DIS implemen a ion will a ec he h eshold alue o he long- e m ROA igge ing a bank un, which is simila o he impac o he Type 1 mo i a ion. Second, he in e ence e o o he deposi o on he long- e m ROA will be educed, and he weigh ing p ocess o he in o ma ion becomes mo e a ional and clea , ha is, aking in o accoun he small p obabili y o la ge de ia ions, i is gi en a ligh e weigh . Con e sely, a hea ie weigh is gi en o he smalle de ia ions, which leads o s able expec a ions and decision-making o wi hd awal. Thi d, he bank may adjus he asse alloca ion s uc u e and educe liquid asse s, inc ease en u e capi al, which igge s mo al haza d issues ha a e simila o he impac o he Type 1 mo i a ion. Speci ically, in any ound, he impac o DIS implemen a ion on he bank- un a iocanbeb okendownin o h eepa s: @ln n d;nþ1;un;F  @F¼@lnðUÞ @ n d;nþ1 @ n d;nþ1 @F zfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflffl{ A þ@lnðUÞ @un @un @F zfflfflfflfflfflffl}|fflfflfflfflfflffl{ C |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} D:s abilizing e ec ðÞ þ@lnðUÞ @L @L @F |fflfflfflfflfflffl{zfflfflfflfflfflffl} B:mo al haza d e ec ðþÞ ;(5) whe e he i s pa (A) indica es ha DIS implemen a ion di ec ly a ec s he h eshold alue o he long- e m ROA igge ing a bank un, which, in u n, a ec s he a io o deposi o s’bank uns. F om @lnðUÞ=@ n d;nþ140and@ n d;nþ1=@Fo0, we de i e Ao0; he second pa (C) analyzes he impac o DIS implemen a ion on he deposi o p e-judgmen bias sequence and weigh sequence as a channel o in luence he bank- un a io. F om ∂λ n (⋅)/∂u n W0and∂u n /∂F o0, we de i e Co0. I can be seen ha bo h esul s show ha DIS implemen a ion has a es aining e ec on bank uns, namely, D¼A+Co0. Thus, hey join ly o m a s abilizing e ec . The hi d pa (B) indica es he ansmission pa h o mo al haza ds in banks a e DIS implemen a ion when he banks a e mo e inclined o in es in high- isk asse s because hey expec he DI ins i u ions o p o ide epaymen gua an ees o po en ial c ises. A he same 67 Deposi insu ance sys em and bank uns ime, he na owing o bank in e es sp eads b ough abou by he ad ancemen o in e es a e ma ke iza ion will s eng hen his e ec . Ce e is pa ibus, i is bound o inc ease he p obabili y and a io o bank uns, namely, BW0. Based on he analysis o he abo e wo pe iods and mul iple ounds o bank- un p ocess, and he esul s o Equa ions (4) and (5), DIS implemen a ion has wo opposi e e ec s o s abilizing wi hd awal expec a ion and inducing mo al haza d, which a e mainly e lec ed in he ollowing h ee aspec s. Fi s , DIS implemen a ion can educe he h eshold alue o bank uns when deposi o s expec changes in long- e m ROA, and i can cu down he p obabili y and a io o bank uns, which a e e lec ed in Equa ion (4) o Type 1 mo i a ion and he i s pa o Equa ion (5) o Type 2 mo i e. Second, wi h he ad ancemen o he in e es a e ma ke iza ion, DIS implemen a ion will educe he deposi o ’s in e ence e o sequence o he long- e m ROA, and a he same ime, he weigh ed sequence o weigh s used in in o ma ion p ocessing also becomes mo e a ional and clea , he eby educing he popula ion de ia ion o he deposi o ’s p e-judgmen and educing he p obabili y and a io o bank uns, which a e e lec ed in he second pa o Equa ion (5) o Type 2 mo i e. Thi d, DIS implemen a ion encou ages banks o ha e g ea e incen i es o engage in high- isk businesses o eap g ea e yields, and i upli s deposi o s’expec a ions o DIS p o iding all o pa o he deposi paymen secu i y, hus weakening hei o e sigh o he banks and elici ing mo e mo al haza d beha io s in he la e . These a e e lec ed in he second pa o Equa ion (4) o Type 1 mo i a ion and hi d pa o Equa ion (5) o Type 2 mo i a ion. The i s and second aspec s abo e show ha DIS implemen a ion has a s abilizing e ec on bank uns, whe eas he hi d aspec will lead o mo al haza d p oblems in banks. The o al e ec depends on he s eng h compa ison be ween he wo. As de ined by dynamic equilib ium, we need o de e mine a h eshold ound * ;a e ⩾ * ounds, any deposi o s no longe ini ia e a bank un. F om he abo e analysis, i can be seen ha DIS implemen a ion can a ec he h eshold ound igge ing a bank un. Speci ically, he s abilizing e ec achie ed by DIS implemen a ion can educe he h eshold ounds, so ha he bank un ends ea ly. Con e sely, he mo al haza d e ec can augmen he p obabili y and a io o bank uns, and e en ually he uns end la e. The e o e, policy make s need o in eg a e and balance he s abilizing e ec s and mo al haza ds while in oducing and implemen ing DIS. 5. Conclusions and policy implica ions As one o he h ee pilla s o he inancial sa e y ne , DIS, oge he wi h p uden ial supe ision, and he cen al bank as lende o las eso , p omo es he heal hy de elopmen o he inancial sys em, helps p e en and esol e isks in a imely manne , and main ains he s abili y o he inancial sys em. In May 2015, he “Regula ions on Deposi Insu ance”o icially came in o o ce, ma king he o mal en y in o he implemen a ion le el o DIS ha he go e nmen and academia ha e discussed o many yea s. Then, in he con ex o in e es a e ma ke iza ion, how o e ec i ely pu DIS “in place”and achie e he expec ed goal is an u gen p oblem o be s udied. In iew o he in e es a e ma ke iza ion, we comp ehensi ely conside ed he economic en i onmen o banks’in es men decision-making and deposi o s’consump ion decision- making. Based on he dynamic pe spec i e, his pape cons uc ed a bank- un model o mul i- ound noise in o ma ion ansmission, discussed he dynamic p ocess o bank un in s ages, and sepa a ely conside ed he wo ypes o p ema u e wi hd awal mo i es o he deposi o s. The a io and quan i y o bank uns a e de i ed om he luc ua ions o long- e m ROA held by he bank, he so ing ule o he deposi o ’s p e-judgmen e o , he in o ma ion p ocessing and dissemina e e iciency unde in o ma ion asymme y and o he ac o s, and he co esponding dynamic equilib ium is cha ac e ized. We u he inco po a ed he DIS in o ou benchma k model, desc ibed he impac o DIS implemen a ion on bank and deposi o beha io al decision- making, and hen s udied he in luence mechanism o DIS on bank- un p ocess and he co esponding dynamic equilib ium by analyzing i s impac on deposi o s’ wo ypes o 68 CPE 2,1 p ema u e wi hd awal mo i es. The esea ch esul s show ha DIS implemen a ion has wo opposi e e ec s o s abilizing expec a ion and elici ing mo al haza ds, which a e mainly e lec ed in he ollowing h ee aspec s. Fi s , DIS implemen a ion can educe he h eshold alue o bank uns when deposi o s expec changes in long- e m ROA, and i can cu down he p obabili y and a io o bank uns. Second, wi h he ad ancemen o he in e es a e ma ke iza ion, DIS implemen a ion will educe he deposi o ’s in e ence e o sequence o he long- e m ROA, and a he same ime, he weigh ed sequence o weigh s used in in o ma ion p ocessing also becomes mo e a ional and clea , he eby educing he popula ion de ia ion o he deposi o ’sp e- judgmen and educing he p obabili y and a io o bank uns. Thi d, DIS implemen a ion encou ages banks o ha e g ea e incen i es o engage in high- isk businesses o eap g ea e yields, and i upli s deposi o s’expec a ions o DIS p o iding all o pa o he deposi paymen secu i y, hus weakening hei o iginal o e sigh o he banks and elici ing mo e mo al haza d beha io s in banks. The e ec o implemen ing a DIS depends on he compa ison o s abilizing e ec s and mo al haza ds, which es s wi h he ins i u ional en i onmen , hus equi ing policy make s o comp ehensi ely conside he ade-o be ween s abilizing e ec s and mo al haza ds while in oducing and implemen ing DIS. DIS is an impo an g oundwo k sys em o na ional inance. I p o ides ins i u ional gua an ee o he e o m o he inancial sys em, especially he p omo ion o in e es a e ma ke iza ion, and i imp o es he ope a ional e iciency o he inancial ma ke . Howe e , in he implemen a ion p ocess o DIS, i is necessa y o ake in o accoun he mo al haza ds caused by impe ec suppo ing policies and measu es. This equi es p ope handling o he dynamic ela ionship be ween in e es a e ma ke iza ion, DIS and inancial ans o ma ion and de elopmen . The s udy has he ollowing policy implica ions. While implemen ing DIS, on he one hand, e o s should be made o ein o ce he cons uc ion o inancial egula o y mechanisms, s eng hen ma ke discipline, imp o e he ole o he bank’s in e nal go e nance mechanisms, and educe he nega i e impac o po en ial mo al haza ds. On he o he hand, e o s should be made o u he deepen he e o m o he inancial sys em, imp o e he e iciency o p ocessing and dissemina ion o in o ma ion, educe he de ia ion o deposi o s’p e-judgmen o bank yield in o ma ion, and encou age deposi o s o o m s able wi hd awal expec a ions in he ace o changes in long- e m asse yields o banks, he eby enhancing he s abilizing e ec o DIS. Acknowledgmen s The au ho s a e indeb ed o he Na ional Na u al Science Founda ion o China Eme gency Managemen P ojec (G an No. NSFC-71850002), he NSFC Gene al P og am (G an Nos: NSFC- 71371117 and NSFC-71271129), he NSFC You h P ojec (G an No.: NSFC-71503037) and he Minis y o Educa ion (Shanghai Uni e si y o Finance and Economics) Key Labo a o y o Ma hema ical Economics. In pa icula , The au ho s would like o hank he wo anonymous e iewe s o hei cons uc i e commen s and sugges ions. The au ho s ake sole esponsibili y o he consequences o his pape and he iews he eo . No es 1. Gi en he s ong ex e nali ies o he inancial indus y, he inancial indus y is he mos egula ed indus y, e en in ma u e de eloped ma ke economies. 2. Fo he demons a ion p ocess o DIS implemen a ion, e e o Su (2005). Re e ences Bekae , G., Ha ey, C.R. and Lundblad, C. (2005), “Does inancial libe aliza ion spu g ow h?”,Jou nal o Financial Economics, Vol. 77 No. 1, pp. 3-55. B yan , J. (1980), “A model o ese es, bank uns, and deposi insu ance”,Jou nal o Banking and Finance, Vol. 4 No. 4, pp. 335-344. 69 Deposi insu ance sys em and bank uns Chen, Y. (1999), “Banking panics: he ole o he i s -come, i s -se ed ule and in o ma ion ex e nali ies”,Jou nal o Poli ical Economy, Vol. 107 No. 5, pp. 946-968. Demi güç-Kun , A. and Kane, E.J. (2002), “Deposi insu ance a ound he globe: whe e does i wo k?”, Jou nal o Economic Pe spec i es, Vol. 16 No. 2, pp. 175-195. Demi güç-Kun , A., Kane, E.J. (2004), “Deposi insu ance: handle wi h ca e”, in Ahumada, L.A., Fuen es, J.R., Loayza, N. and Schmid -Hebbel, K. (Eds), Cen al Banking, Analysis, and Economic Policies Book Se ies, 1 ed., Banking Ma ke S uc u e and Mone a y Policy, Cen al Bank o Chile, Vol. 7, pp. 345-358. Demi güç-Kun , A., Kane, E.J. and Lae en, L. (Eds) (2008), “Deposi insu ance a ound he Wo ld: issues o design and implemen a ion”, MIT P ess Books, 1s ed. Vol. 1 No. 11, p. 363. Diamond, D.W. and Dyb ig, P.H. (1983), “Bank uns, deposi insu ance, and liquidi y”,Jou nal o Poli ical Economy, Vol. 91 No. 3, pp. 401-419. Fama, E.F. (1980), “Agency p oblem and heo y o he i m”,The Jou nal o Poli ical Economy, Vol. 88 No. 2, pp. 288-307. Fan, X. and Cao, Y. (2006), “Bank-o ien ed deposi insu ance :a scheme o unde de eloped coun ies”, China Economic Qua e ly, Vol. 6 No. 1, pp. 171-186, 187, 188. Golds ein, I. and Pauzne , A. (2005), “Demand-deposi con ac s and he p obabili y o bank uns”, Jou nal o Finance, Vol. 60 No. 2, pp. 1293-1327. He, D. and Wang, H. (2011), “Dual- ack in e es - a e sys em and he conduc o mone a y policy in China”,Jou nal o Financial Resea ch, Vol. 378 No. 12, pp. 1-18. Huang, J. (2001), “Ma ke -o ien ed in e es a e and isk con ol o comme cial banks”,Economic Resea ch Jou nal, No. 1, pp. 19-28. Jacklin, J.C. and Bha acha ya, S. (1988), “Dis inguishing panics and in o ma ion-based bank uns: wel a e and policy implica ions”,Jou nal o Poli ical Economy, Vol. 96 No. 3, pp. 568-592. Pos lewai e, A. and Vi es, X. (1987), “Bank uns as an equilib ium phenomenon”,Jou nal o Poli ical Economy, Vol. 95 No. 3, pp. 485-491. Qian, X. (2004), “Mo al haza d, cons ain condi ions and sys em design o deposi insu ance”,Jou nal o Financial Resea ch, Vol. 290 No. 8, pp. 21-27. Scho e , A. and Yo ulmaze , T. (2009), “On he dynamics and se e i y o bank uns: an expe imen al s udy”,Jou nal o Financial In e media ion, Vol. 18 No. 2, pp. 217-241. S a , M.A. and Yilmaz, R. (2007), “Bank uns in eme ging-ma ke economies: e idence om u key “s special inance houses”,Sou he n Economic Jou nal, Vol. 73 No. 4, pp. 1112-1132. Su, N. (2005), “D aw on in e na ional expe ience and accele a e he es ablishmen o a DIS ailo ed o China’s na ional condi ions”,Jou nal o Financial Resea ch, Vol. 306 No. 12, pp. 1-5. Tang, H. (2008), “Deposi insu ance sys em and bank co po a e go e nance”,Jou nal o Financial Resea ch, Vol. 337 No. 7, pp. 154-159. Wallace, N. (1988), “Ano he a emp o explain an illiquid banking sys em: he Diamond and Dybi g model wi h sequen ial se ice aken se iously”,Fede al Rese e Bank o Minneapolis Qua e ly Re iew, Vol. 12 No. 4, pp. 3-16. Wang, Z. (2006), “FDIC expe ience and cons uc ion o China’s deposi insu ance sys em”,Jou nal o Financial Resea ch, Vol. 309 No. 3, pp. 124-130. Xie, P., Wang, S. and Yan, W. (2001), “Theo e ical esea ch and in e na ional compa ison o deposi insu ance”,Jou nal o Financial Resea ch, Vol. 251 No. 5, pp. 1-12. Yao, D., Yan, J. and Yin, Y. (2013), “Deposi insu ance sys em o he cen al bank’s bailou ? –A dynamic-game pe spec i e”,Economic Resea ch Jou nal, No. 10, pp. 43-54. Yao, Z. and Xia, F. (2012), “Op imal deposi insu ance design –in e na ional expe ience and heo e ical analysis”,Jou nal o Financial Resea ch, Vol. 385 No. 7, pp. 98-111. Yi, G. (2009), “The p ocess o in e es a e ma ke iza ion in China’s 30 yea s o e o m and opening-up”, Financial Resea ch, Vol. 343 No. 1, pp. 1-14. 70 CPE 2,1 Appendix (1) P oo o P1: P oo : by Equa ion (1), we ha e: Bi¼Z 2 iþu ðÞ 2 iu ðÞ ^ i i 2^ ij 2 i¼ n 2  d^ i: By Lemma 1, o deposi o s iand j, we ha e: j 2^ jd  ¼ i 2^ j  : He e: d¼ 1ei 1þ1 1 ðÞei 2 1ej 11 1 ðÞej 240; and hus: Bi¼Z þ 1ei 1þ1 1 ðÞei 2þu þ 1ei 1þ1 1 ðÞei 2u ^ i i 2^ i ðÞd^ i; Bj¼Z þ 1ej 1þ1 1 ðÞej 2þu þ 1ej 1þ1 1 ðÞej 2u ^ j j 2^ j  d^ j: Le ^ i¼^ jþd, and by placing i in equa ion B j , we ha e: Bj¼Z þ 1ej 1þ1 1 ðÞej 2þu þ 1ej 1þ1 1 ðÞej 2u ^ jd  j 2^ jd  d^ j¼Z þ 1ei 1þ1 1 ðÞei 2þu þ 1ei 1þ1 1 ðÞei 2u ^ idðÞ i 2^ i ðÞd^ i¼BidoBi: The e o e, o deposi o s wi h signal 2 io n 2, Z þ 1ei 1þ1 1 ðÞei 2þu þ 1ei 1þ1 1 ðÞei 2u ^ i i 2^ i ðÞd^ i¼BioBn: He e: Bn¼Z n 2þu n 2u ^ i i 2^ i ðÞd^ i; whe e n 2is he h eshold alue o a un. Also, 2^ ðÞ¼ Z1 1 ðÞ þe2 ðÞ 1 1 ðÞ e2 ðÞ q1 y 1   q2 1 1 ðÞ 1 1  dy: Thus, he a io o deposi o s who conduc bank uns is l1¼R n 2 u 2^ j ðÞd^ .∎ (2) P oo o P2: P oo : Conside n¼2, le : Ci¼Z i 3þu i 3u ^ i 3^ ij i 3¼ n 3  d^ i: He e, u¼ 1 2 e 1 +(1− 1 ) 2 e 2 +(1− 2 )e 3 . 71 Deposi insu ance sys em and bank uns As pe Lemma 2, le : d¼1 2 ðÞei 3þ 2 1ei 1þ1 1 ðÞei 2  1 2 ðÞej 3 2 1ej 1þ1 1 ðÞej 2 hi 40: We ha e: Ci¼Z þ1 2 ðÞei 3þ 2 1ei 1þ1 1 ðÞei 2 ½ þu þ1 2 ðÞei 3þ 2 1ei 1þ1 1 ðÞei 2 ½ u ^ i i 3^ i ðÞd^ i; Cj¼Z þ1 2 ðÞej 3þ 2 1ej 1þ1 1 ðÞej 2  þu þ1 2 ðÞej 3þ 2 1ej 1þ1 1 ðÞej 2  u ^ j j 3^ j  d^ j: Replacing ^ i¼^ jþdin o equa ion C j yields: Cj¼Z þ1 2 ðÞei 3þ 2 1ei 1þ1 1 ðÞei 2 ½ þu þ1 2 ðÞei 3þ 2 1ei 1þð1 1Þei 2 ½ u ^ idðÞ j 3^ idðÞd^ i ¼Z þ1 2 ðÞei 3þ 2 1ei 1þ1 1 ðÞei 2 ½ þu þ1 2 ðÞei 3þ 2 1ei 1þ1 1 ðÞei 2 ½ u ^ idðÞ i 3^ i ðÞd^ i¼CidoCi: Thus, o deposi o s wi h signal i 3o n 3, i de i es: Z þ1 2 ðÞ ei 3þ 2 1ei 1þ1 1 ðÞ ei 2 ½ þu þ1 2 ðÞei 3þ 2 1ei 1þ1 1 ðÞei 2 ½ u ^ i i 3^ i ðÞd^ i¼CioCn; whe e: Cn¼Z n 3þu n 3u ^ i i 3^ i ðÞd^ i: n 3is he h eshold o he un and sa is ies he ollowing: 3^ ðÞ¼ Z1 2 ðÞ þe2 ðÞ 1 2 ðÞ e2 ðÞ 2 ^ y 2  q3 y1 2 ðÞ 1 2  dy: The e o e, he a io o deposi o s pa icipa ing in bank uns is l2¼R n 3 u 3^ j ðÞd^ . When nW2, by he abo e simila analysis p ocess, we ob ain: ln n nþ1;u  ¼Z n nþ1 u nþ1^ nj i nþ1¼ n nþ1  d^ n:Q:e:d: (3) P oo o P3: P oo : (⇐) Ob iously holds. (⇒) Fo deposi o s wi h a signal sa is ying ei 1¼e1;ei 2¼e2;ei 3¼e3;..., i can be in e ed ha no one can ge a wo se signal. Since all deposi o s p ocess in o ma ion acco ding o he same me hod, i can be seen om he p oo p ocess o Lemma 2 and P2 ha he expec ed alue o he long- e m ROA o he deposi o co esponding o he wo s -so ing me hod is he lowes . I he deposi o does no un, no o he deposi o s will, and i is hus a s ong equilib ium. ∎ Co esponding au ho Guoqiang Tian can be con ac ed a : [email p o ec ed] Fo ins uc ions on how o o de ep in s o his a icle, please isi ou websi e: www.eme aldg ouppublishing.com/licensing/ ep in s.h m O con ac us o u he de ails: pe missions@eme aldinsigh .com 72 CPE 2,1