Accepted Manuscript. The Mechanics of Commercial Banking Liberalization and Growth. Alessandra Dal Colle

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1 Acceped Manuscrp The Mechancs of Commercal Bankng Lberalzaon and Growh Alessandra Dal Colle PII: S ( DOI: hp://dx.do.org/ /j.jbankfn Reference: JBF 4943 To appear n: Journal of Bankng & Fnance Receved Dae: 15 Augus 2014 Acceped Dae: 21 Aprl 2016 Please ce hs arcle as: Dal Colle, A., The Mechancs of Commercal Bankng Lberalzaon and Growh, Journal of Bankng & Fnance (2016, do: hp://dx.do.org/ /j.jbankfn Ths s a PDF fle of an uneded manuscrp ha has been acceped for publcaon. As a servce o our cusomers we are provdng hs early verson of he manuscrp. The manuscrp wll undergo copyedng, ypeseng, and revew of he resulng proof before s publshed n s fnal form. Please noe ha durng he producon process errors may be dscovered whch could affec he conen, and all legal dsclamers ha apply o he journal peran.

2 The Mechancs of Commercal Bankng Lberalzaon and-growh Alessandra Dal Colle CeFMS, SOAS, Unversy of London, UK and Chef Lendng Un, Banca Prossma, Pazza Paolo Ferrar 10, 20121, Mlan, Ialy. Emal: JEL classfcaon: E44; F43; G2 Keywords: Commercal Bankng; Fnancal Servce Lberalzaon; Economc growh

3 The Mechancs of Commercal Bankng Lberalzaon and Growh.. Absrac Ths paper aemps o formalze he effecs of lberalzaon across he border of depos-akng and lendng acves on he regme of compeon n he bankng marke as well as on he rae of growh of he economy. We exend a heorecal model by Dedda (2006 where wo economes - Home and F oregn - hos a leas one operang bank each. The dfferen mpacs on such seng of wo GATS-defned modes of commercal bankng lberalzaon - namely he Commercal P resence mode and he Cross-Border mode - wll hen be modeled. Fnally, he possbly of sraegc behavor by compeng banks n equlbrum wll also be nroduced. The model lnks n a causal chan he cos srucure of he bankng ndusry, he regme of compeon n he lberalzed bankng secor and fnally he rae of growh of he economy under alernave modes of lberalzaon. The model specfcally denfes a hreshold level of economc developmen, above whch he bankng secor would operae compevely, whch s sensve o dfferen modes of commercal bankng lberalzaon. Fnally, compeve bankng s shown o suppor an accelerang rae of growh, generang a bdreconal, self-renforcng lnk beween commercal bankng lberalzaon and growh. The pace of growh s furher ncreased, wh respec o a scenaro where such behavor s no presen, by he presence of sraegc behavor by compeng banks n equlbrum. Polcy-wse he paper suggess o look a he relaonshp beween macroeconomc fundamenals and he cos srucure of commercal bankng acvy raher han clamng ha lberalzaon s growh-enhancng per se. JEL classfcaon: E44; F43; G2 Keywords: Commercal bankng, Fnancal Servce Lberalzaon, Economc growh Preprn submed o Nuclear Physcs B May 27, 2016

4 1. Inroducon The leraure on he relaonshp beween fnancal lberalzaon and economc growh s que wde and dfferenaed 1. Economcs scholars and polcy makers alke have offered dsconnuous suppor o fnancal lberalzaon as an engne of growh. The era afer he Second World War sared wh calls for resrcve nervenons n he fnancal secor 2. By he early 1970s, hs fnancal represson polcy came under severe crcsm and n he Eghes, he so-called Washngon Consensus called for lberalzaon of capal flows and deregulaon n he recpen fnancal sysems, as hs would smulae a szeable flow of nvesmens from rch counres o poor ones and could accelerae developmen n he laer counres. A new bou of crses n he Nnees 3 gave suppor o crcs of he Washngon Consensus, among whom Krugman (1993, who mananed ha as capal was no accounable for cross-counry dfferences n economc growh raes and no hsorcal evdence suggesed ha lberalzng polces were followed by large flows of capal from rch o poor counres, herefore fnancal lberalzaon was no o be consdered as an engne of growh. By he end of he Nnees fnancal lberalzaon was recommended agan as a polcy o enhance he funconng of domesc fnancal sysems hrough s posve effecs on producvy. Even on he more specfc feld of commercal bankng lberalzaon - ha s he openng o nernaonal rade of depos akng and loan granng acves - polcy leraure s almos equally dvded. Some conclude ha cross-border bankng,.e. he supply of fnancal servces from abroad, suppors he developmen of an effcen and sable fnancal sysem ha offers a wde access o qualy fnancal servces a low cos for he hos counry, as revewed by Claessens (2006. Beck e al. (2014 n a repor on bankng n Afrca underlne he benefs of cross-border bankng, however empered by a wde-rangng array of polcy recommendaons n he felds of naonal and supranaonal regulaon and supervson. Levne (2001 revews ler- 1 Tornell and Weserman (2004 and Balag e al. (2009, ogeher wh her conrbuon o he debae, offer very updaed revews of he leraure boh on he heorecal and on he emprcal sde. 2 For a comprehensve revew see Andersen and Tarp ( Capro and Honohan (1999 repor ha he average cos of 59 bankng crashes n developng counres durng he perod was 9% of GDP. 2

5 aure n favour of foregn bank esablshmen n he hos counry whereas Deragache, Poonam and Tressel (2006 express crcsm of foregn banks presence especally n low-ncome counres manly because of o he possble cred shrnkage and ncreased operang coss. Tamrsa e al. (2000 express reservaons on he lberalzaon of bankng acves boh under he cross-border bankng - because of he consequences on he sably of sngle domesc fnancal sysems - and under he esablshmen of foregn banks, because of he possbly of cherry-pckng lenders by foregn nermedares. The orgnal queson on how commercal bankng lberalzaon does ncrease economc growh s hence sll unresolved and hs paper wll presen a dynamc model whose am s o offer an analycal framework o denfy he conrbuon of commercal bankng lberalzaon o compeon n he bankng secor and hence o economc growh. The model n hs paper akes s general seng from Dedda (2006. The model n fac keeps he overlappng generaon framework where ndvduals share her ncome beween consumpon and savngs whch hey depos wh banks. The laer hence borrow from savers and lend o frms - whch produce accordng o a consan reurn echnology only f exernally funded - hrough a echnology nvolvng economes of scale and of specalzaon. The man addons o he seng of Dedda (2006 are hree-fold. Frs, he model s assumed o work n an economy whch s a leas as developed as o supply enough resources o make one bank workng. I s hence a scenaro nvolvng no sorage echnology o make up for he lack of fnancal nermedaon; herefore a seng suable o sudy economes a a laer sage of developmen han hose argeed by Dedda (2006. Second, he model s se n an nernaonal framework nvolvng wo regons of a federal sae nsead of a sngle counry. Under Domesc Bankng (DB from now on resden savers n each of he wo regons of he federal sae fund, hrough domesc banks, loans exclusvely o resden frms,. Followng bankng lberalzaon, n he federal sae nvesmens may be fnanced by he whole (n he Commercal P resence mode of fnancal lberalzaon or segregaed (n he Cross-Border mode pool of savngs of he formerly Domesc Bank-only regons. Coss of bankng acvy change dependng on whch mode of lberalzaon s mplemened. And fnally he possbly of compeng agens enacng sraegc behavor n equlbrum s nroduced. The core conrbuon of he paper s o underlne how dfferen modes of commercal bankng lberalzaon mpac on he cos srucure of he ndusry, hence on s regme of compeon and her effecs on he rae of 3

6 growh of he economy. Secondly, he paper also denfes a hreshold of economc developmen 4, measured by capal per capa, above whch he bankng secor would operae n monopolsc compeon susanng an accelerang rae of growh. Ths s o say ha below he hreshold he dynamcs of economc growh manly susan bankng developmen, whle above he hreshold a bdreconal, self-renforcng lnk beween bankng acvy and economc growh s envsaged. Bankng lberalzaon modfes he seng of he hreshold n so far as changes he cos srucure n he bankng ndusry. More specfcally, he hgher are he fxed coss of bankng acvy, he hgher he level of developmen of he economy has o be n order o susan monopolsc compeon n he bankng secor as an equlbrum oucome. The model also supples formal condons o he hess of Pagano (1999 and Classens (2006, sang ha openng he fnancal secor usually brngs more compeon. Fnally, he model deermnes ha sraegc behavor by compeng banks permanenly rases he number of banks operang n equlbrum, hence may push up he pace of growh wh respec o a scenaro where such behavor s no presen, as s he case n Dedda (2006. Secons 2 and 3 wll nroduce he framework of Domesc Bankng and descrbe s equlbrum. In secon 4 wo dfferen modes of fnancal lberalzaon wll be skeched ou, namely Commercal P resence and Cross-Border mode of lberalzaon and hey wll be subsequenly emboded n formal models n secons 5 and 6 respecvely. 2. The model Suppose a federal naon sae exss and s composed by wo regons = F, H each populaed by a connuum of sze of households and a connuum of sze of nfnely-lved frms whose behavor s descrbed n wha follows. 4 Threshold effecs are used n he mos dfferen ways n he leraure. They can be deermnsc, as n hs hs model and n n Dedda (2006, as well as sochasc, as n he soveregn deb defaul leraure of Malk (2014 and Muller (2015 among ohers. However, hey all share a common naure and role. They paron he se of possble values of a key varable n subses deermnng a swchng n he behavour of he model and, consequenly, n equlbrum resuls. 4

7 2.1. Households Indvduals lvng n regon nelascally supply labor durng he frs perod of lfe and receve a salary w whch s parly saved and parly consumed accordng o subjec o U(c 1, c 2+1 = lg c ρ lg c 2+1 c 1 = w d and c 2+1 = R d, d where c 1 s he consumpon of he presenly young generaon, d s young people s savng ha s enrely deposed, c 2+1 s he consumpon of he same people when old a + 1, ρ s he dscoun rae and R d s he gross reurn on deposs from o + 1. Ths framework resuls n opmal savngs whch are a consan fracon of wage as d = (2 + ρ 1 w = sw ( Frms Frms have no nal endowmen. They operae f and only f hey are exernally funded. I s also assumed ha hey are prce akers and demand loans a he lowes rae, beng ndfferen across banks for all oher aspecs of he lendng conrac. The producon funcon for he represenave frm operang n regon s Y = α ( A ( K β ( l 1 β (2 where α s he exogenous producvy coeffcen, l s labor; K s capal, A = (k 1 β, wh k = K, and 1 < β < 1 s an exernaly effec assocaed l 2 wh capal accumulaon. The represenave frm s demand for loans sems from he producon funcon as b R l, = Y +1 K +1 = ( R l, +1 αβa +1 1 β 1 where R l, s he reurn on lendng n regon when full capal deprecaon s assumed. The equaon makes explc ha for he borrowng frm he cos of fnance R l, s he only choce varable vs-à-vs banks. 5

8 In equlbrum he prce of he facors of producon wll be and w = (1 βα ( A ( K β ( l β = (1 βαk (3 R l, = βα ( A ( K β 1 = βα (4 n he marke for labor and capal respecvely. The consan rae of reurn on capal n equlbrum mples consan reurns o scale n he cumulable facor, whch s he dsngushng feaure of endogenous growh Commercal Bankng Commercal bankng s defned as he bundle of depos-akng and lendng acves. In hs paper, n any regon, banks are acve 5 and fund hemselves by ssung depos conracs o households and generae her revenues by lendng o frms. They also consume real resources for a fxed amoun E each perod and for z q(zdz per un of lendng o ndvdual 0 frms, where z s he mass of funded frms. Ths generaes economes of scale and of specalzaon n bankng acvy. Formally, z fnanced frms generae coss equal o q ( z = qz + q (5 where 0 < q < 1 and lm q(z = q > 0. The lendng echnology hence z 0 nvolves he consumpon of a fracon q per un of allocaed loan o he ndvdual frm. q s he consan margnal effec of specalzaon, hence a low z decreases oal coss. Also, he mnmal marke share nvolves posve coss. In fac, cred analyss mus be carred ou for every sngle poenal cusomer a cred orgnaon before a loan s graned,.e. before he poenal borrower becomes an acual cusomer, hence when z 0. In hs seng oal varable coss are Q ( z z = q (z dz = q ( z qz and average varable coss are 5 Ths s he reason why no alernave sorage echnology s assumed. For a formal defnon of he condons for bankng acvy see noe 8. 6

9 Q (z = q z 2 z + q For any gven z, margnal coss are hgher han he average varable cos, formally q (z > Q(z. So a margnal ncrease n he marke sze z wll z rase average varable coss by dampenng he workng of he economes of specalzaon. The leraure offers several examples of economes of boh scale and specalzaon n he bankng secor such as hose orgnaed by he delegaon o specalzed agens whch need a fxed nvesmen n each perod 6,7 and economes of specalzaon ha are rggered by cusomers varey, as n Sussman (1993. As o economes of scale and of specalzaon specfc o lendng echnologes, Berger (2004 shows ha hese echnologes can be arranged n a connuum rangng from hose ha are prmarly based on hard quanave daa such as fnancal saemen lendng, asse-based lendng, and cred scorng sysems o relaonshp-based lendng, whch, n conras, s based n large par on sof nformaon, such as he characer and relably of he frm s owner, hs specfc experence n he secor, he hsory of he frm s relaonshps wh s supplers, and he busness prospecs n he marke n whch he frm operaes. Quanave-based lendng orgnaes economes of scale as s capacy lms are que large, n fac, s cenred on accessng, sorng and elaborang quanave daa hrough he use of compuer sysems and daabases,.e. bg cke ems. On he oher hand, n relaonshp-based lendng nformaon s generally gahered hrough conac over me by he bank loan offcer wh he frm, s owner, s supplers and s oule marke on a varey of dmensons. In acual lendng pracce, analyss a cred orgnaon s carred ou usng boh echnques n a complemenary fashon. Only when quanave daa are no avalable or are 6 Frexas and Roche (2008 offer an updaed revew of he role of economes of scale boh on he lendng and on he depos gahrerng sde, n para These auhors summarze her poson cng Benson and Smh (1976 sang The rason d êre for hs ndusry s he exsence of ransacon coss. (page Were such economes of scale no presen, hen any sngle lender would have o bear he fxed coss wh neffcen duplcaons across he economy. Then drec lendng by ndvduals could be susaned as an equlbrum soluon. Greenwood and Jovanovch (1990, among ohers, jusfy he exsence of nsuons, as opposed o drec lendng, because of her ably o pool resources among ndvduals, o ake up nformaon gaherng and conrac-wrng effcenly and o dversfy rsk. 7

10 of poor qualy, lendng s acually carred ou purely on sof nformaon. The larger s he share of borrowng frms evaluaed on sof nformaon only, he lower wll be he exploaon of economes of specalzaon. Formalzng he fxed and varable coss jus exemplfed, he balance shee of he represenave bank orgnang n regon can be represened as D = z b + z 0 q(zb dz + E = ( 1 + Q (z z z b + E (6 where D are deposs orgnaed n regon,.e. he bank s source of fundng. The RHS represens he bank s use of funds as b s he amoun of loans per frm and (Q (z b + E are he resources consumed by he bankng acvy n her varable and fxed componens respecvely. From (6 he prof of he n-h bank operang n regon can be wren as π n, = R l b z R d D = R l b z R d [ ( zb 1 + Q ] (z + E z (7 where R u, wh u = l, d are reurns on loans or deposs respecvely. Hence prof s he dfference beween revenues R l, b z ( and all he resources needed o cover loan supply (.e. b z, Q(z varable coss b z and fxed ones (E mes he cos of fundng R d,. Compeon n bankng acvy s characerzed by lenders who choose prces and he marke share hey wsh o serve o maxmze her profs and by frms who, gven he prce of loans, demand a quany of cred o maxmze her profs. More precsely, s assumed ha: 1. banks ac as prce akers n he marke for deposs. In he marke for loans each bank ses he neres rae R l, as well as s marke share z n order o maxmze (7, subjec o z, gven he opmal behavor n by compeors. Banks do no o dscrmnae across borrowers and charge he same neres rae o any of hem; 2. here s free enry n commercal bankng. The number of banks operang n regon s n and s aken as gven by each sngle bank; z 8

11 3. frms are prce-akers n he marke for loans and hey demand as much cred as hey need o maxmze her profs a he lowes rae avalable from banks. Focus wll be on symmerc equlbra where all banks se he same neres rae and serve he same marke share. In each MOde of lberalzaon (M O = Domesc Bankng, Commercal P resence and Cross-Border rade equlbrum s defned as a se of values Ω MO = ( R MO,l ; z MO ; n MO for a gven rae of reurn on deposs R MO,d such ha: each bank offers a rae R MO,l and serves a marke share z MO whch s he bes response o compeors offers; n MO s such ha profs of each operang bank s zero; frms demand he prof maxmzng quany of cred. Eher a monopoly or a compeve equlbrum wll resul dependng on nal condons. Boh equlbra wll be suppored boh n Domesc Bankng and n he lberalzed regmes. 3. General equlbrum and economc growh n Domesc Bankng In Domesc Bankng nvesmens n each regon are funded exclusvely by savngs of resden ndvduals. I wll also be assumed ha each regon s nally endowed wh suffcen capal o develop bankng acvy 8. The nerplay beween he regme of compeon n he bankng secor, as deermned by he free enry condon, and prof-maxmzng choces by banks sems from he equaly beween he sources and uses of funds n he economy. Formally, s(1 βαk = [ n DB z DB + n DB Q(z DB ] b DB + n DB E = F, H (8 deermnes wo possble equlbra for he each of he wo regons n Domesc Bankng, dependng on he level of economc developmen k, ha read respecvely 8.e. k,=0 > E αs(1 β 2. 9

12 Ω DBm = R l,dbm = R d,dbm 1 Q(z DB,c β z DB,c q(2β 1 wh Γ = and 1 2(1+qs(1 β 3 2 monopols and Ω DBc = wh η DB = R l,dbc = R d,dbc z DB,c = z DBm = 1 Γs(1 β 2 n DBm = s(1 β2 αk E 1 β n DB,c = s(1 βαk E 1+ Q (z DB,c z DB,c (1+q(z DB,c = Rd,DBm (1+q 2β 1 when k k DB = Γ α E (9 < β < 1 when each bank operaes as a ( 1 + q ( z DB,c n DB,c ( 1 βη DB < 1 when banks compee. when k > k DB = Γ α E (10 Each of he wo equlbra shows a value for he reurns on loans R l,db, one for he banks marke share z DB as well as he number of operang banks n DB. The reurns on loans s a mark-up on he cos of fundng R d whch depends on varable coss of he bankng secor. As expeced, he mark-up s on average coss hen he bankng secor s monopolsc, whle s on margnal coss when he bankng secor s compeve. The number of operang banks s an ncreasng funcon of he level of economc developmen k and an nverse funcon of he fxed coss of bankng acvy E. The developmen hreshold k DB, whch spls bankng opmal behavor beween monopolsc and compeve, s hgher he hgher are he fxed coss of bankng acvy and he lower are producvy α, propensy o save s and share of labor ncome n he economy (1 β. Ths mples ha, gven a se of macroeconomc fundamenals, namely α, s and (1 β, a hgher (lower fxed coss of bankng acvy E, requres a hgher (lower level of developmen of he economy n order o gran a compeve bankng secor. The number of banks operang n equlbrum n any compeon regme s a drec funcon of he macroeconomc fundamenals of he economy and an nverse funcon of he fxed coss E. Please noe ha he equlbrum number of operang banks s permanenly hgher han would have been 10

13 whou conflcng marke shares, as s n Dedda ( Specfcally, when k grows above k DB, he number of operang banks ncreases and because of conflcng marke shares, sraegc neracon ses off. Specfcally, a R l,dbm each bank would be able o reap a monopoly prce from a marke share ha s acually smaller han he prof maxmzng ( one z DBm, so each bank could earn an addonal marke share of z DBm by lowerng he rae charges n equlbrum by ε 0 wh a drop n revenues of n DB,c ε 0. Ths wll sar a process of undercung unl he possbly of n DB,c = R l,dbc and he correspondng oper- ( = s(1 βαk E 1 βη DB. The banks undercung behavor squeezes he mark-up n he compeve regme and more banks can operae han would be he case, were he marke shares no conflcng. Formally, n DB,c = s(1 β2 αk < n DB,c E = s(1 βαk (1 βη DB, E where n DB,c s he equlbrum number of operang banks when here s no sraegc neracon n equlbrum and η DB < 1. exra profs drops o zero,.e. R l,db ang banks n equlbrum are n DB,c The exsence of equlbra formalzed n (9 and (10 can be saed 10 n he followng lemmas. Lemma 1. A local monopoly symmerc equlbrum exss f and only f he mass of frms whch are acually served by all banks s lower han he oal marke,.e. f n DB,m z DBm. Lemma 2. A monopolsc compeon symmerc equlbrum exss f and only f he mass of frms whch are acually served by all banks s such ha n DB,c z DB,c >. Fundamenally, when he economy s no suffcenly developed, he number of banks operang n equlbrum s oo low relave o he number of borrowng frms. In fac, s so low ha he resulng marke shares for operang banks wll no conflc and each bank wll operae lke a local monopols. In oher words, each bank has a poenal marke share larger han 9 In noe 7 on page 237 of Dedda (2006, s assumed ha (... (he mass of frms H, s suffcenly hgh. H s assumed o be large enough so ha here are no sraegc neracons when such compeon (among fnancal nermedares sars. 10 All calculaons for he demonsraon of lemmas and he proofs of proposons n he nex secons are avalable from he auhor on reques. 11

14 he prof maxmzng one, as a consequence each can offer a monopoly rae wh no danger of compeors undercung hem, as no one has an neres n lowerng prof o gan a marke share ha s larger han he prof maxmzng one. In hs equlbrum no all demand for loans s sasfed and he marke share z,m and R l,m are ndependen of banks coss. On he oher hand, n monopolsc compeon all he poenally borrowng frms are acually served, and bankng has reached s effcency lm. Banks marke shares z,c are conflcng and her sze s an nverse funcon of her number, hence a drec funcon of fxed coss per capa. All equlbrum values are sensve o he level of developmen as measured by he level of capal per capa. Suppose he wo regons have he same level of developmen k and E H < E F, hen he equlbrum (gross growh raes read: g+1 DB = k +1 = k s(1 βα(2β 1 (1+q, s(1 βα(2β 1 (1+q for k k DBH and = F, H s(1 βαβ 1+q(z DBH for k DBH < k k DBF and = F, H s(1 βαβ 1+q(z DB for k > k DBF and = F, H (11 Equlbrum growh raes are deermned boh by macroeconomc fundamenals and bankng secor srucure. In fac, he hgher are he savng rae s, exogenous producvy α and capal share n he economy β, he faser s growh, ndependenly of he compeon regme n bankng. On he oher hand, he hgher are banks varable coss, he slower s growh. Because of he separaon of he bankng marke n he wo regons, boh on he depos and on he lendng sde, he pah of developmen runs hrough hree dfferen sages characerzed by combnaons of dfferen regmes of compeon n he bankng secors of he wo regons. When he level or developmen s low,.e. k k DBH k DBF, each regon has a monopolsc bankng secor as here are no enough resources o fund many operang banks. The demand for nvesmens s no fully funded and he federal sae wll grow a a consan rae. In essence, a vcous cycle ses n: he less regons are developed, he fewer he operang banks n equlbrum, he larger z DBm. As a consequence, lowly developed regons wh a bankng sysem only operang domescally, grow more slowly also because her neffcen bankng secors use up oo many resources o cover 12

15 her coss. Causaly runs from economc growh o bankng developmen as z DBm s consan. For k DBH < k k DBF a leas regon H - he one wh he lowes fxed coss of bankng acvy - enjoys a compeve bankng secor. In hs regon an ncreasng number of operang banks wll n urn decrease he avalable marke share z DB,c 11 and suppor growh. Ths s a consequence of he economes of specalzaon as he smaller s z, he lower are margnal coss q(z DB,c. DBF When boh regons are developed,.e. k > k he bankng secor s compeve everywhere, hen economc growh s self-renforcng. In fac an accelerang rae of growh wll be fed by he ncreasng number of operang banks ha wll n urn decrease he avalable marke share z DB,c, lower he margnal coss of he bankng acvy and suppor growh whch n urn ncreases k and n DB,c furher squeezng z DB,c. Ths s a consequence of he economes of specalzaon. Hence, he lnk beween bankng developmen and economc growh becomes bdreconal. Fnally noe ha sraegc neracon has also a lasng mpac on growh as g DB,c +1 = sβ(1 βα < g DB,c +1 = sβ(1 βα η DB f η DB < 2β 1 where g DB,c β Q(zDB z DB 1+ Q(zDB z DB s he growh rae when here s no sraegc neracon n equlbrum. 4. Lberalzaon of Trade n Bankng Servces Trade n bankng servces can be lberalzed n dfferen modes wh reference o dsncve combnaons n sourcng he funds -.e. domesc or foregn depos - and usng hem -.e. lendng o resden or non resden frms. A recen conrbuon by Maoo e al. (2006 underlnes ha lberalzaon of servces mples ha he relevan acves mus, a some lengh, be locally produced and lberalzaon of rade n hese servces leads o enhanced compeon, boh a home and abroad. In fac, f he degree of compeon remans unchanged, hen he auhors manan ha here canno be a posve mpac on growh on accoun of he scale effec. Conversely, a larger scale acheved merely by elmnang domesc barrers o enry and aracng domesc resources from oher secors would suffce o generae larger endogenous growh. 11 Formally g F A,c +1 wll ncrease as gf A,c +1 z F A,c = q 2 s(1 βα (1+q(z F A,c < 0 13

16 Tryng o apply hs concep o bankng servces, able 1 clusers he wo man acves,.e. depos-akng and lendng, no modes of lberalzaon. Specfcally he Commercal P resence (CP mode of lberalzaon s defned as a mode of operaon whereby a foregn enran bank gans access o depos-akng acves from foregn savers. Ths s because depos-akng s characerzed by he smulaney of producon and consumpon whch mples he proxmy beween he consumer and producer,.e. he need o se up shop n he deposors counry. In hs mode of lberalzaon a frm can arrange a loan wh a foregn bank locally. The bank, however, has o nves n order o ensure physcal presence and fully-fledged operaons on se. By conras, he Cross-Border (CB mode of lberalzaon s defned as a mode of operaon whereby loans o local borrowers can be arranged wh banks abroad va elephone or some oher way of communcaon. Ths s he case when nvesmens o se up shop are eher forbdden - and hs s usually he case when domesc banks receve proecon as hey were a sraegc nfan ndusry - or oo cosly for he enran bank, so supply by dsance s he preferred roue. Ths mples ha foregn banks do no have access o local deposs and hey are acually channellng domesc deposs o fnance foregn loans as he possbly of nerbank lendng s no allowed n hs model. Table 1: Modes of fnancal lberalsaon Depos from Domesc Savers Non Resden Savers Loan provded by Domesc bank Domesc Bankng No Allowed Foregn bank esablshed Cross-Border No Allowed n s home Mode: Bankng counry Servces rade only Foregn bank esablshed Commercal Presence: Bank- n he hos ng Servces rade + Foregn Drec counry Invesmens Adaped from Kono - Schuknech (1998 In wha follows, commercal bankng lberalzaon wll be appled across he wo regons of he federal sae wh a oal populaon of (H + F and wll be refleced n modfcaons of (8 boh on he supply and on he 14

17 demand for funds. More precsely: n he CP mode of lberalzaon he fxed coss of bankng acvy wll change o E CP, rrespecve of he orgn of he enran bank. Ths s due o nvesmens needed o se up shop abroad, such as bg cke n erms of lendng echnology o operae locally as well as buyng/renng premses for acvy on se. As a resul of hese nvesmens, he lendng marke and he depos marke wll be fully negraed; n he CB mode of lberalzaon he fxed coss of bankng acvy wll reman unchanged. Lendng acvy can n fac be organzed wh ways of communcaon - such as elephone, and/or nerne - whch do no requre major revsons n lendng pracces whle depos-akng remans reserved o local banks. In each of he wo regons of he lberalzng federal sae only hose banks wll operae, ha he sngle regon s own pool of savng can suppor. As a consequence, only (6 wll be changed o he sum of he respecve funcons across he wo regons. Summarzng, n commercal bankng lberalzaon he lendng marke s always fully negraed whle he depos marke may or may no be fully negraed. Fnally, he choce of he CB or CP mode of commercal bankng lberalzaon s assumed o be aken by he federal auhores so he possbly of asymmeres across he wo regons s ruled ou. 5. General equlbrum and economc growh n Commercal Presence (CP In he Commercal Presence (CP mode boh he loan and he depos markes are perfecly negraed and (8 changes o (H + F s(1 βαk = n CP [(1 + Q(zCP z CP ] z CP b CP + E CP (12 where b CP s he amoun of loans acually graned by a bank, Q(zCP z CP b CP z CP and E CP are respecvely oal varable and fxed coss of commercal bankng. 15

18 In hs seng, for any gven k, he maxmum poenal marke share avalable o a sngle bank s he rao of he oal number of frms n he lberalzng federal sae (H + F o he number of banks n CP. Along he same lnes of he Domesc Bankng seng, he nerplay beween he free enry condon and he opmzng behavor of banks n he Commercal P resence mode resuls n a se of equlbrum values for he reurn on loans, he marke share and he number of operang banks ha read ( R l,cp m = R d,cp m Q (z CP,m Ω CP β z CP,m m = z CP,m 1 = (13 Γs(1 β 2 n CP,m = (H+F α(1 β2 k E CP when k k CP = Γ α ECP 12,.e. when each bank operaes as a monopols, and a se of values equal o ( ( R l,cp c = R d,cp c 1 β 1 + q z CP c Ω CP c = z CP,c = H+F ncp c (14 ( 1 βη CP CP c n when k > k CP wh η CP = 1 = (H+F s(1 βαk E CP 1+ Q (z CP c z(zcp c CP c (1+q(z when banks compee. Therefore, for any gven k, n CP banks wll be operang n he lberalzng federal sae wh an avalable marke share no larger han H+F each, as n CP (H + F s he number of operang frms n he economy. If he represenave bank serves H+F cusomers n equlbrum, s marke share wll conflc n CP and sraegc neracon wll occur among compeng banks. Should hs no be he case, each bank wll operae as a local monopols. One of he frs effecs of commercal bankng lberalzaon under he CP mode vs DB s o change he level of economc developmen needed for a compeve bankng secor,.e. kcp k DB f E E CP. Also, he 12 As n CP,m z CP,m CP (H + F for k k 16

19 number of banks ncreases or decreases relave o Domesc Bankng n proporon o per capa fxed coss of bankng acvy.e. n CP ndb f ( E 1. CP (H+F (1 βη CP (1 βη DB Ths s o say ha lberalzaon smulaes bankng acvy, by ncreasng he number of operang banks, f he E fxed coss n per capa erms n he lberalzng federal sae are lower han he sum of he correspondng raos n he wo formerly auarkc regons. Fnally, subsung n CP from (13 or (14 n (12 one obans he growh rae as: g+1 CP = k +1 1 = k sβ(1 βα 1+ Q(zCP m z sβ(1 βα CP m 1+q(z CP c 1 for k k CP 1 for k > k CP (15 The queson wheher he CP mode of commercal bankng lberalzaon s growh-enhancng vs Domesc Bankng mode s examned n he nex proposon. Proposon 3. A lberalzng economy whose bankng secor operaes under he CP mode wll grow faser han under he DB mode f lberalzaon brngs abou more compeon n he bankng secor n equlbrum n he form of: lower level of developmen needed o susan a compeve bankng secor,.e. k CP < k DBH < k DBF as E CP < E DBH < E DBF smaller marke share for operang banks,.e. z CP c kdbf. < z DBc when k > The nuon behnd Proposon 3 les agan n he effecs of he change n he fxed coss of bankng acvy n he CP mode, due o he need o se up shop abroad. For any gven level of economc developmen, f E CP < E DB, hen he banks orgnang n regon are operang as monopols n DB and, because wh lberalzaon fxed coss have decreased, hey now sar o compee and se off an accelerang rae of growh. Should he European Unon be hough of as a federal sae, hs case mgh be exemplfed by counres whose commercal bankng secor was over-regulaed and proeced agans foregn compeon by naonal legslaon, causng hgh E per capa. The access o he European Unon has called for smplfcaon 17

20 n regulaons, whch has decreased fxed coss. Banks can hus compee on a level wh he oher European parners General equlbrum and economc growh n Cross-Border rade n Bankng Servces (CB In he Cross-Border (CB mode of lberalzaon, banks face a demand for loans from all he frms locaed n he whole lberalzng federal sae, bu hey canno access he depos-akng acvy n he oher regon of he lberalzng federal sae. The paron of he depos marke requres wo equlbrum condons and specfcally s(1 βαk = n CB, [ z (1 CB + Q(zCB z CB b CB, + E ] = F, H (16 where b CB, = (H+F k +1, as well as wo free enry condons, one for each [ z CB n CB, ] regon,.e. R l,cb R d,cb (1 + Q(zCB b CB, z CB k+1 = R d,cb E = F, H. In addon o ha, as he marke for loans s unque n he CB mode, equlbrum mus also hold for he whole federal sae, hence (H + F s(1 βαk = (1 + Q(zCB (H + F k z CB +1 + n CB E (17 =F,H Smlarly o he prevously analyzed mode of lberalzaon, he nerplay beween he free enry condon and he prof maxmzng behavor of banks n he Cross-Border mode resuls n ( R l,cbm = R d,cbm Q (z CB,m β Ω CBm = z CB,m = 1 Γs(1 β 2 n CB,m = s(1 β2 αk E z CB,m (18 13 The oppose case,.e., E CP > E F A for he European Unon mgh be exemplfed by counres whch were acually fnancal cenres akng he benef of a very low level of regulaon, hence a low E. Access o he Unon n hs case has called for more regulaon whch has resuled n an ncrease n fxed coss of fnancal nermedaon o E CP. 18

21 when k k CB = Γ α E and n CBm = s(1 β 2 αk f banks ac as E local monopolss. If he bankng marke s compeve he equlbrum s Ω CBc = R l,cbc n CB,c when k > k CB wh η CB = = R d,cbc 1 β z CBc = H+F n CBc = s(1 βαk E 1+ Q (z CBc z ( z 1 CBc (1+q(z CBc ( ( 1 + q z CBc ( 1 βη CB and n CBc (19 = s(1 ( βαk 1 βη CB. E Smlarly o he CP mode, for any gven k, each bank wll be facng a demand for loans from all of he frms locaed n he lberalzng federal H+F sae. Each bank wll be argeng a poenal marke share of. If he ncb represenave bank serves hese cusomers n equlbrum, s marke share wll conflc and sraegc neracon wll occur among compeng banks. Should hs no be he case, each lender wll operae as a local monopols. Wh CB commercal bankng lberalzaon he developmen hreshold for he bankng secor o behave compevely lowers he hgher s he sum of fxed coss of bankng acvy,.e. k CB > k DB as E > E. Subsung n CB from (18 or (19 n (17 one obans a growh rae of sβ(1 βα CB 1 for k k g CB +1 = k +1 k 1 = 1+ Q(zCBm z CBm sβ(1 βα 1+q(z CBc 1 for k > k CB (20 The nex proposon examnes wheher he CB mode s growh-enhancng for he new lberalzng federal sae vs Domesc Bankng. Proposon 4. A lberalzng economy whose bankng secor operaes under he CB mode wll grow faser han under he DB mode f lberalzaon brngs abou more compeon n he bankng secor n equlbrum n he form a smaller marke share for operang banks,.e. z CBc < z DBc when k > k DB. The comparsons n Proposon 4 rely on he same mechancs as Proposon 3. In erms of he defnon of he regme of compeon n he bankng secor he CB mode of lberalzaon fares mdway beween he DB and he CP mode of lberalzaon. Smlarly o Domesc Bankng, 19

22 ncb ncb banks wll be acve n he whole lberalzng federal sae, wh > ( ( ndb f E η CB η DB < η DB E η CB where = F, H and = H, F. Please noe ha as he lberalzng federal sae has o suppor all he banks operang n he wo regons, he level of developmen needed for a compeve bankng secor s necessarly hgher han ha n DB. As a consequence, lberalzaon under CB mode can generae he hghes mpac on growh, once he regons and he federal sae are developed enough o susan a compeve bankng secor. 7. Concluson Followng Ceorell (1997, Claessens (2006 and Tornell and Wesermann ( who denfy he change n he coss of fnancal nermedaon, and evenually of he regme of compeon n he fnancal secor as one of he man channels of ransmsson of he effecs of fnancal lberalzaon on economc growh - he model n hs paper also esablshes a drec lnk beween commercal bankng lberalzaon and economc growh whch s essenally shaped by he coss of bankng acvy and he regme of compeon n he bankng secor 14. The orgnal conrbuon of hs paper may be found n he specfcaon of he mechancs of commercal bankng lberalzaon lnkng he varaon n cos srucure of he bankng ndusry undergong alernave modes of lberalzaon, he regme of compeon n he lberalzed bankng secor and he rae of growh of he economy. Summarzng, he lnk beween compeon and commercal bankng lberalzaon fundamenally ress on he basc dea ha he more players n he marke n hs case on he supply sde of loans he hgher he level of compeon. The equlbrum number of operang banks depends on fxed coss of bankng acvy and resources avalable, as measured by capal per capa. Commercal bankng lberalzaon, n he dfferen modes of Commercal Presence and Cross- Border bankng, changes he fxed coss of bankng acvy and herefore 14 Blackburn and Hung (1998 descrbe a bdreconal lnk beween fnancal and economc developmen based on he reducon of coss of projec apprasal and ulmaely of lendng and on an ncrease n he number of such projecs, whch reduces he coss of esablshng fnancal nermedares. 20

23 he equlbrum number of operang banks, gven he avalable resources, and consequenly he regme of compeon. Also, he model denfes a pah-dependency beween commercal bankng lberalzaon and economc growh as specfes a hreshold level of developmen above whch he bankng secor becomes compeve, susanng an accelerang rae of growh. Such hreshold level of economc developmen ncreases wh he level of fxed coss of bankng acvy. As long as commercal bankng lberalzaon lowers he fxed coss of bankng acvy, he bankng secor may see an ncrease n compeon. Ths gves formal suppor o he vew ha openng he fnancal secor usually brngs more compeon, as underlned n Pagano (1993 and Claessens (2006 among ohers, and hence suppors faser growh. Anoher conrbuon by he paper s o pon ou he effecs of sraegc behavor by banks on he degree of compeon n he bankng secor and hence on economc growh. More specfcally, dfferenly from Dedda (2006, he model underlnes ha undercung behavor by acve banks ncreases her number wh respec o hose ha would have operaed were he marke shares no conflcng and hs may have a posve mpac on growh. The models hence offer mulfaceed and qualfed answers o he queson wheher commercal bankng lberalzaon s acually growh-enhancng. More specfcally, commercal bankng lberalzaon does ncrease economc growh only f he level of fxed coss of bankng acvy n he lberalzed economy s more favorable han ha under Domesc Bankng. Should hs no be he case, hen commercal bankng lberalzaon could sll prove growh-enhancng for he economy bu only for hgh levels of economc developmen. Dal Colle (2010 offers some suppor o hese resuls as causaly s found o run from economc o fnancal developmen n low ncome regons, as s he case modelled n hs paper when he hreshold level of developmen leadng o compeon n he bankng secor s ye o be reached. The man polcy recommendaon ha seems o emerge from he model s ha n order o smulae economc growh va commercal bankng lberalzaon s no parcularly useful o lower barrers o enry n he form of fxed coss per se, bu proper accoun has o be aken of her relaonshp o macroeconomc fundamenals of he lberalzed economy. In fac he hresholds delmng a compeve bankng secor - gvng way o self-renforcng growh - are a funcon no only of he fxed and varable coss of bankng acvy, bu also of exogenous producvy α, propensy o save s share of labor ncome n he economy (1 β. Non neglgble caveas should be 21

24 added o such polcy recommendaon 15, n so far as he model presened here does allow neher for he workngs of he nerbank depos marke nor for macroeconomc or dosyncrac rsk. Furhermore, he coss of bankng acvy are modeled as flow only and herefore hey are unrelaed o he performance of he sock of old loans. 15 Such polcy recommendaon would also grealy benef from he emprcal suppor from he esmaon of equlbrum relaonshps (11, (15 and (20. Ths calls for he developmen of an orgnal compose ndcaor relaed o loans from non-resden banks (amoun ousandng o GDP and bank concenraon rao from Beck e al. (2000 as well as an ndex of he qualy of regulaon. Also, accordng o I-TIP Servce daabase hese daa should be reflecng rade n bankng servces from 2008, a perod where qualy of daa may be mpared by he effecs of he global fnancal crss. Furher deals are avalable from he auhor on reques. 22

25 [1] Andersen, T. P. and Tarp, F., Fnancal Lberalsaon, Fnancal Developmen and Economc Growh n LDCs, Journal of Inernaonal Developmen, 2003, 15, [2] Balag, B.H., Demerades, P.O. and Hook Law, S., Fnancal Developmen and openness: Evdence from panel daa, Journal of Developmen Economcs, 2009, 89, [3] Beck, T., Fuchs, M., Snger, D. and We, M., Makng cross-border bankng work for Afrca. Washngon, DC ; World Bank Group, 2014 [4] Beck, T., Demrgüç-Kun, A., Levne, R., A New Daabase on Fnancal Developmen and Srucure, World Bank Economc Revew, 2000, 14, hp://seresources.worldbank.org/intres/resources/ /fnsrucure November 2013.xlsx [5] Benson, G. and Smh, C.W., A ransacon cos approach o he heory of fnancal nermedaon, Journal of Fnance, 1976, 31, [6] Berger, A.N., Poenal Compeve Effecs of Basel II on Banks n SME Cred Markes n he Uned Saes, Board of Governors of he Federal Reserve Sysem, mmeo, 2004 [7] Borcher, I., Gooz, B., Maoo, A., Polcy Barrers o Inernaonal Trade n Servces: Evdence from a New Daabase, World Bank Economc Revew, 2014, 28, 1, [8] Blackburn, K. and Hung V. T. Y., A Theory of Growh, Fnancal Developmen and Trade, Economca, 1998, 65, 257, [9] Capro G. and Hohohan P., Resorng bankng sably: beyond supervsed capal requremens, Journal of Economc Perspecves, 1999, 13, 4, [10] Ceorell N., The Role of Cred Marke Compeon on Lendng Sraeges and on Capal Accumulaon, Federal Reserve Bank of Chcago, Workng Papers Seres, Research Deparmen WP 14,

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27 [24] Mueller, A., Soresleen, K., Zlbo, F., Soveregn Deb and Srucural Reforms, CEPR Dscusson paper no , 2015 [25] Pagano, M., Fnancal Marke and Growh. An Overvew, European Economc Revew, 1993, 37, [26] Sussman, O., A heory of fnancal developmen, n Govannn, A. (Eds, Fnance and developmen: ssues and experence, Cambrdge Unversy Press, Cambrdge, (UK, 1993 [27] Tamrsa, N. T., Sorsa, P., Bannser, G. J., McDonald, B. J. and Weczorek, J., Trade Polcy n Fnancal Servces, IMF, Workng paper WP/00/31, 2000 [28] Tornell, A. and Wesermann, F., The Posve Lnk beween Fnancal Lberalzaon, Growh and Crses, CESfo, Workng Paper no. 1165,

28 Appendx o The Mechancs of Commercal Bankng Lberalzaon and Growh Appendx A. Appendx Please noe ha number beween parenheses refer o equaons n he paper whereas (A.# refer o equaons n hs Appendx. Appendx A.1. Sac Opmzaon Omng DB for smplcy, frs order condons from (7 are π n, R l, = 1 β 1 π n, z b R l = { R l, } R d, z + b z 1 β 1 ( ( R l, R d, 1 + Q (z z b R l b R d, and from (A.1 he opmal rae of reurns on loans s ( R l, = R d, Q (z β z R d, z Q (z z = 0 (A.1 b z q 2 = 0 (A.2 Appendx A.2. Number of banks operang n equlbrum n Domesc Bankng The aggregae supply of funds, defned from (1 and (3 mulpled by he sze of he economy, equals he resources from (6 used up by all he n DB operang banks, hence s(1 βαk = [ n DB z DB + n DB Q(z DB ] b DB + n DB E = F, H (A.3 Preprn submed o Nuclear Physcs B May 27, 2016

29 The separaon n he depos markes requres wo accumulaon funcons and wo free enry condons, one for each regon, mplyng ha for any gven k, n DB, nermedares are operang. In equlbrum each nermedary wll se he neres rae on loans and choose he marke share so as o maxmze (7 subjec o z DB as each of hem canno have more han = n DB marke share as a poenal cusomer base, as s he number of operang frms n he regon whch resul n R l,db R d,db n DB [ (1 + Q(zDB R d,db E = F, H hence n DB = s(1 βαk E 1 R d,db, (1 + Q(zDB R l,db z DB z DB ] b DB k +1 = = F, H (A.4 where subsung b DB = k +1 n DB z DB n (A.3 resuls n E k+1 = s(1 βαk n DB ] = F, H (A.5 [1 + Q(zDB z DB The accumulaon equaon s he rao of ndvdual savngs s(1 βαk (ne of per capa fxed cos for fnancal nermedaon n DB E o varable resources for fnancal nermedaon, whch are he sum of acual loans and average varable coss (1 + Q(zDB. z DB Hence k +1 k = sβ(1 βα 1+ Q(zDB z DB sβ(1 βαη DB 1+ Q(zDB z DB = F, H (A.6 Appendx A.2.1. Local Monopoly Symmerc Equlbrum Supposng he consran s no bndng frs order condons from he maxmzaon of (7 subjec o z = resul n n DB R l,f Am d,f Am 1 = R (1 + Q ( z F Am (A.7 β z F Am 2

30 and z F Am = q(2β 1 2(1+qs(1 β 3. 1 Γs (1 β 2 wh 1 < β < 1 and Γ = 2 Fnally, subsung (A.7 and (A.8 n (7 valued a zero one obans n DB,m = s(1 β2 αk E (A.8 (A.9 Proof of Lemma 1. Gven z DBm and n DB,m from (9 and he fac ha n DB,m s ncreasng n k, hen here mus exs a hreshold level of capal k DB below whch n DB,m z DBm s verfed. In fac n DB,m z DBm can be rewren as s(1 β2 αk 1 ha s k E Γs(1 β 2 k DB = Γ α E. k DB, hen he margn on he z DBm -h cusomer, ha s zero a R l, = R l,dbm and Havng esablshed s ( R l,dbm R ( d,dbm 1 + q ( z DBm b DBm z DB = z DBm from (9. Banks are no keen o compee by undercung on he prce of loans and n DB,m z DBm ensures her marke shares are no conflcng, so (9 can be consdered an equlbrum for k k DB. On he oher hand, when k > k DB, n DB,m z DBm s no longer lower han and he margn on he z DBm -h cusomer calculaed a R l,dbm from (9 s posve for any z < 1 Γs(1 β 2, hen he prof-maxmzng behavor of banks would drve hem o undercu he prce. Consequenly, R l,dbm, z and n from (9 canno be consdered an equlbrum for k > k DB. Appendx A.2.2. Monopolsc Compeon Symmerc Equlbrum Evenually, economc growh wll make he acual level of capal per capa grow above k DB. As a consequence he number of operang nermedares wll ncrease above n DB. Should banks behave lke under local monopoly, marke share would be conflcng n equlbrum, makng equlbrum unenable. In such an envronmen, equlbrum has o susan a marke share poenally avalable o a sngle nermedary of n DB,c as s he number of operang frms n he regon. Wh such a marke share and a monopoly rae of reurn each nermedary would earn an exra-prof, as he would be able o reap a monopoly prce from a marke share ha s acually smaller 3

31 han he prof maxmzng one n monopoly. As a consequence, each nermedary, by lowerng he rae he( charges n equlbrum by ε 0, could earn an addonal marke share of z F Am wh a drop n revenues of n DB,c ε 0. Ths wll sar a process of undercung by nermedares unl n DB,c he possbly of exra profs drops o zero,.e. R l,dbc = R d,dbc 1 ( ( 1 + q β z DB,c Fnally, subsung (A.10 and z DB,c = n DB,c obans n DB,c = s(1 βαk E ( 1 βη wh η DB = (A.10 n (7 valued a zero one ( 1 + Q (z DBc z DBc (1 + q (z DBc < 1 (A.11 Proof of Lemma 2. Should k k DB, here would be no compeve equlbrum as Lemma 1 would apply. Should k > k DB, Lemma 1 would no apply, and he compeve equlbrum would have o be such as here were no ncenve for banks o devae from. No alernave equlbrum wh z = n DB,c and R l dfferen from (10 can however be calculaed. Appendx A.2.3. Monopolsc equlbrum whou sraegc behavor n equlbrum Were sraegc behavor absen n equlbrum - as n Dedda ( he number of banks n he compeve equlbrum would have been n DB,c s(1 β 2 αk E n DB,c and growh g DB,c +1 = sβ(1 βα (1 β. (1 βη DB Hence n DB,c as 1 β < 1 βη DB and 1 > η DB = s(1 β2 αk E 1+ Q(zDB z DB < n DB,c wh z DB = n DB,c = s(1 βαk E (1 βη DB = = and n DB,c Also g DB,c +1 = sβ(1 βα 1+ Q(zDB z DB < g DB,c +1 = sβ(1 βα η DB 1+ Q(zDB z DB 4

32 as 1 + qz DB + q < 1 + q 2 zdb + q and n DB,c 2n DB,c < 1 2 < n DB,c n DB,c 2 2β < 1 βη DB 1 2β < βη DB f η DB < 2β 1 β Appendx A.3. Number of banks operang n equlbrum under Commercal Presence In he federal sae seng he pool of deposs equals he sum of savngs n prevously domesc bank-only regons. Also, he demand for loans s ncreased by he larger sze of he economy and he hgher fxed coss of fnancal nermedaon. So he equlbrum s descrbed by (12 whch, subsung b CP = (H+F k +1, generaes he accumulaon equaon n CP z CP of he form E CP k +1 = s(1 βαk ncp (H+F (A.12 (1 + Q(zCP z CP The opmal [ number of banks] s found by mposng a free enry condon of he ype R l R (1 d + Q(zCP (H+F k z CP n CP +1 = R d E CP. Subsung (A.12 one obans (1 + Q(zCP n CP = (H + F s(1 βαk E CP 1 R d R l z CP (A.13 Appendx A.4. Number of banks operang n equlbrum under Cross-Border rade n Fnancal Servces = (H+F k +1 z CB n CB, Equlbrum n he marke for funds n each regon of he economy yelds a demand for loans of b CB, and requres he wo equlbrum condons n (16 and wo accumulaon funcons and wo free enry condons, one for each [ regon, ].e. R l,cb R d,cb (1 + Q(zCB b CB, z CB k+1 = R d,cb E = F, H whch resul n 5

33 n CB, = s(1 βαk E 1 R d,cb (1 + Q(zCB R l,cb z CB = F, H (A.16 In addon o ha, as he marke for loans s unque n he CB mode, equlbrum mus also hold for he whole federal sae, hence (H + F s(1 βαk = (1 + Q(zCB (H + F k z CB +1 + n CB E (A.17 =F,H By summng up equaons (16 across regons on he lef-hand sde one obans he same supply of savng as n he CP mode 1,.e. he lef-hand sde of (A.17. Ths s furher evdence ha he sze of he fnancal marke n he CB mode s he same as n he CP and ha he modes of lberalzaon dffer only by he nernal dsrbuon of marke shares. The aggregae accumulaon funcon s hence z CB ncb E (H+F k +1 = s(1 βαk (A.18 (1 + Q(zCB whch, subsung n (16 or (A.16, denfes he equlbrum number of operang banks. 1 I s easy o verfy ha b CP = =F,H b CB, 6 = (H+F k+1 z CB n =F,H