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
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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
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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
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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).
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70
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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