Financial Frictions and Policy Cooperation: A Case with Monopolistic Banking and Staggered Loan Contracts *

Transcription

1 Federal Reserve Bank of Dallas Globalizaion and Moneary Policy Insiue Working Paper No. 37 hp:// Financial Fricions and Policy Cooperaion: A Case wih Monopolisic Banking and Saggered Loan Conracs * Ippei Fujiwara Keio Universiy and Ausralian Naional Universiy Yuki Teranishi Keio Universiy April 05 Absrac Do financial fricions call for policy cooperaion? This paper invesigaes he implicaions of simple financial fricions, monopolisic banking ogeher wih saggered loan conracs, for moneary policy in open economies in he linear quadraic (LQ) framework. Welfare analysis shows ha policy cooperaion improves social welfare in he presence of such financial fricions. There also exis long-run gains from cooperaion in addiion o hese by joinly sabilizing inefficien flucuaions over he business cycle, ha are usually found in models wih price rigidiies. The Ramsey opimal seady saes differ beween cooperaion and noncooperaion. Such gains from cooperaion arise irrespecive of he exisence of inernaional lending or borrowing. JEL codes: E50, F4 * Ippei Fujiwara, Faculy of Economics, Keio Universiy, Mia, Minao-ku, Tokyo Japan. [email protected]. Yuki Teranishi, Faculy of Business and Commerce, Keio Universiy, Mia, Minao-ku, Tokyo Japan. [email protected]. Formerly circulaed as Financial Sabiliy in Open Economies. The auhors hank he edior Giancarlo Corsei and wo anonymous referees for useful commens. We have also benefied from discussions wih Kosuke Aoki, Pierpaolo Benigno, Marin Bodensein, Larry Chrisiano, Richard Dennis, Bianca De Paoli, Mary Eichenbaum, Takeo Hoshi, Gunes Kamber, Jinill Kim, Federico Mandelman, Tomoyuki Nakajima, Sefan Niemann, Maury Obsfeld, Bruce Preson, Lars Svensson, Cedric Tille, Mike Woodford, and seminar and conference paricipans a he Universiy of Bonn, Hiosubashi Universiy, FRB Alana, Bank of Korea, Universiy of Zurich, Vicoria Universiy of Wellingon, Reserve Bank of New Zealand, Kyoo Universiy and Naional Universiy of Singapore. Fujiwara graefully acknowledges financial suppor from he Muraa Science Foundaion. The views in his paper are hose of he auhors and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem.

2 Inroducion The recen global nancial crisis has renewed ineres in he poenial of policy cooperaion. In order for he global economy o recover, he need for policy cooperaion is now a opic of discussion for leaders in major policy insiuions. Academic sudies, however, do no usually emphasize he imporance of cooperaion in sabilizaion policies. Wha causes hese divergen views on policy prescripions during he global nancial crisis? Perri and Quadrini (0) emphasize he imporance of nancial fricions in explaining he unprecedened degree of business cycle synchronizaion across di eren counries during he recen global nancial crisis. In his paper, we ackle his problem by invesigaing he implicaions of simple nancial marke imperfecions on moneary policy in open economies. For his purpose, we exend he sandard new open economy macroeconomics (NOEM) model a la Clarida, Gali, and Gerler (00) or Benigno and Benigno (003, 006), o incorporae an imperfecly compeiive banking secor as examined in Kobayashi (008), Teranishi (05), Mandelman (00, 0), and Fujiwara and Teranishi (0). The banking secor of our model has hree feaures: a cos channel, monopoly power by banks over loan rae seings, and saggered loan conracs. Gerali, Neri, Sessa, and Signorei (00) esimae a similar model o ours, where monopolisic banking and sicky loan raes are incorporaed in a prooypical dynamic sochasic general equilibrium (DSGE) model, in order o quanify he conribuion of shocks originaing from nancial fricions o he slowdown during he recen global nancial crisis. Firms need o borrow working capial from privae banks in advance o nance wage Dr. John Lipsky, Acing Managing Direcor of he IMF, saed on June 0, A second success is he remarkable increase in global policy cooperaion ha has aken place in he wake of he global nancial crisis. When he world las faced such grave danger during he Grea Depression counries aced in heir own, perceived self-ineres wih beggar-hy-neighbor policies ha in fac deepened he downurn. This ime, counries aced ogeher o ackle he crisis. Corsei, Dedola, and Leduc (00) conclude ha, [i]n welfare erms, he gains from cooperaion are close o zero. Indeed, he lieraure has presened numerical assessmens of he benchmark model under he complee markes ha do no generae appreciable quaniaive welfare gains from coordinaing policies, relaive o opimal sabilizaion pursued by independen policy makers (engaging in sraegic manipulaion of erms of rade).

3 bills. Barh and Ramey (00) and Ravenna and Walsh (006) empirically demonsrae he imporance of his cos channel in moneary policy ransmission in he US. Each bank is assumed o be in a long-erm relaionship wih each inermediae-goods producing rm. Thus, banks have monopoly power over loan rae seings. Gropp and Kashyap (00), van Leuvenseijn, Sorensen, Bikker, and van Rixel (03) and Mandelman (00, 0) explore he imporance of bank compeiions on loan rae seings. Finally, dynamic fricions in he nancial marke are capured by saggered loan conracs, ha follow he Calvo (983) - Yun (996) framework. Sickiness in loan rae conracs is repored by many sudies, as Slovin and Sushka (983) and Berger and Udell (99) for he U.S., Sorensen and Werner (006) and Gambacora (008) for he Euro area, and he Bank of Japan s Financial Sysem Repors for he Japanese economy. 3 Their explanaions rely on credi raioning during recession. There are, however, oher aspecs relaing o sickiness in loan raes. For example, he Bank of Japan s Financial Sysem Repors show ha he duraion of xed loan conracs ends o be very long. Also, Graham and Wrigh (007) repor ha a signi can proporion of ineres rae paymens in some European counries are a a xed rae. Furhermore, hey noe ha []he associaed deb conracs are almos always wrien in nominal erms, have quie signi can associaed ransacions coss and as a consequence are renegoiaed relaively infrequenly. 4 We hen use a NOEM model wih such nancial fricions o analyze he opimal 3 For he US, using micro level daa, Slovin and Sushka (983) and Berger and Udell (99) show ha i akes wo or more quarers for he privae banks o adjus loan ineres raes. For he Euro area, Sorensen and Werner (006) esimae he incompleeness in he pass-hrough from he policy ineres rae o loan ineres raes in an error correcion model using macro daa. They furher show ha he degree of he incomplee pass-hrough signi canly di ers among counries. Gambacora (008) conducs similar analysis for Germany and shows he exisence of sicky adjusmen in loan ineres raes. For Japan, according o Bank of Japan s Financial Sysem Repors published in March 007 and 008, he major ciy banks need ve quarers and he local banks seven quarers o adjus loan ineres raes. 4 Several sudies provide empirical evidences behind hese infrequen negoiaions, for example, Hannan and Berger (99) for menu coss, Berger and Udell (99) for implici conracs and Calem, Gordy, and Meser (006) for swiching coss. 3

4 moneary policy under boh cooperaion and noncooperaion. In order o undersand how simple nancial fricions as explained above may aler gains from cooperaion, a linear quadraic (LQ) approach is employed. The second order approximaed welfare meric following Benigno and Woodford (005) and Benigno and Benigno (006) is also derived. Saggered loan conracs under monopolisic compeiion in he banking secor creae dispersion in loan raes when a shock his he economy. Since labor supply is ighly linked o loan raes due o he working capial loan, his resuls in ine cien allocaions in labor among ex pos symmeric rms. Consequenly, similarly o he case wih price rigidiies, dispersion in loan raes works as if i were a negaive echnology shock. The role of he cenral bank is o reduce welfare loss semming from such dispersion in loan raes and he working capial loan. Welfare analysis shows ha here are boh long-run and shor-run gains in cooperaion. Seady sae welfare becomes higher under cooperaion. Under noncooperaion, each cenral bank has long-erm incenives o raise loan ineres raes. This is because high ineres raes reduce labor supply via he cos channel. This resul is similar o he one obained in Cooley and Quadrini (003). Over he business cycle, here also exis gains from cooperaion when he global economy is subjec o markup shocks. This is because he erms of rade exernaliy, where each counry aemps o manipulae he erms of rade in is favor, is no inernalized under noncooperaion. 5 These resuls hold regardless of he exisence of inernaional lending or borrowing. Unless here is fricion in inernaional nancial ransacions, neiher inernaional lending nor borrowing makes any di erence o he case in which only domesic nancial ransacions are allowed. The res of he paper is srucured as follows. Previous sudies wih similar banking secors o ours in a dynamic general equilibrium framework are summarized in Secion 5 The mechanism behind his resul is similar o he one in Benigno and Benigno (006) wih sicky prices. 4

5 . Secion 3 derives he model used in his paper and displays is dynamic properies. Secion 4 solves he equilibrium under he Ramsey opimal moneary policy in boh cooperaive and noncooperaive regimes. Secion 5 derives he quadraic loss funcions around he Ramsey opimal seady saes obained in Secion 4. These are he welfare measures ha cenral banks aim o minimize. We also invesigae he naure of he opimal moneary policy in open economies wih nancial fricions. Secion 6 exends he basic model o cases wih inernaional lending and borrowing. Finally, Secion 7 summarizes he ndings of his paper and inroduces possible fuure exensions of his paper. Monopolisic Banking and Saggered Loan Conracs Nominal conracs ogeher wih infrequen renegoiaion are commonly observed in many counries. Thus, he sickiness of loan raes ogeher wih imperfec compeiion in he banking secor are poenially imporan mechanisms in accouning for he daa. Several previous sudies incorporae a similar banking secor in a dynamic general equilibrium framework. Gerali, Neri, Sessa, and Signorei (00), Mandelman (00, 0) and Fujiwara and Teranishi (0) develop models wih an imperfecly compeiive nancial secor. They all conclude ha an imperfecly compeiive banking secor conribues o a beer of he model o he daa. Gerali, Neri, Sessa, and Signorei (00) provide empirical evidence of he sickiness in loan conracs in his vein. They esimae he prooypical new Keynesian model, a la Smes and Wouers (003, 007) and Chrisiano, Eichenbaum, and Evans (005), and exend o replicae he aforemenioned feaures wih a monopolisic banking secor and loan rae sickiness. Shocks semming from he banking 5

6 secor explain he major par of he conracion in he recen nancial crisis. Mandelman (00, 0) nds ha he incorporaion of a monopolisic banking secor increases he volailiy of real variables and ampli es he business cycle. Counercyclical bank markups generaed from sraegic limi pricing aimed a proecing reail niches from poenial compeiors increases he model s o he daa in developing economies. Fujiwara and Teranishi (0) explain he persisence of he real exchange rae by incorporaing an imperfecly compeiive nancial secor. Also, Ravenna and Walsh (006) repor empirical evidence of a direc ineres rae e ec on in aion where marginal coss are a eced boh by real wages divided by he produciviy and nominal ineres raes. On implicaions of such nancial fricions on moneary policy, Ravenna and Walsh (006) inroduce he cos channel ino an oherwise sandard new Keynesian model in closed economy. The opimal moneary policy under he cos channel faces rade-o beween in aion and oupu gap sabilizaion even wih he IS shocks. Cooley and Quadrini (003) hin ha he decline in ineres raes afer he adven of Euro can be explained by moneary cooperaion in a wo-counry model wih he cos channel. No sudy, however, has invesigaed wheher nancial marke imperfecions call for policy cooperaion no only in he long-run bu also over business cycles. Such mechanisms can also replicae one of he imporan characerisics of moneary policy, ineres rae smoohing. Woodford (003) explains his hrough he hisory dependen policy under commimen. Graham and Wrigh (007), Kobayashi (008), and Teranishi (05) demonsrae ha rigidiies in loan rae dynamics can also necessiae ineres rae smoohing as he opimal policy reacion o shocks. 6 Fujiwara and Teranishi (0) also emphasize ha he sicky loan mechanism can produce hump-shaped 6 Conrary o Kobayashi (008), and Teranishi (05), sickiness in ineres raes is imposed on consumers in Graham and Wrigh (007). Thus, he loan ineres rae in he IS curve is sicky in Graham and Wrigh (007), while in our model, ha in he Phillips curve is sicky. Also, Graham and Wrigh (007) do no conduc welfare analysis bu show an ineresing resul on moneary policy. Low ineres raes are mainained even afer in aionary shocks hi he economy under sicky deb conracs. 6

7 responses o many srucural shocks including moneary policy shock. As previous lieraure on moneary policy ransmission mechanism using he Vecor Auoregressive models as represened by Chrisiano, Eichenbaum, and Evans (999) shows, he abiliy o produce hump-shaped responses is considered o be imporan for he dynamic sochasic general equilibrium model. As a resul, many sudies using he dynamic sochasic general equilibrium incorporae habi formaion in consumpion or invesmen growh adjusmen coss as examined in Chrisiano, Eichenbaum, and Evans (005). Sicky loan raes can have hump-shaped properies wihou relying on hese mechanisms. For a posiive analysis of nancial marke imperfecions, many sudies employ he - nancial acceleraor mechanism of Bernanke, Gerler, and Gilchris (999) in he dynamic sochasic general equilibrium framework. In he nancial acceleraor mechanism, ne worh as he sae variable causes he deviaions of loan raes from he policy ineres rae. In our model, insead of ne worh dynamics, he wedge beween he loan rae and he policy rae arises due o imperfec compeiion in rms and hus banks. Accordingly, he dynamics of loan raes are creaed by saggered loan conracs. The consequences are, however, similar. A shock relaed o nancial marke imperfecions evenually resuls in an increase in he cos of goods producion. 7 The bene of our approach is ha he naure of opimal moneary policy can be undersood analyically and herefore inuiively. 8 3 Model This secion describes a wo counry model wih nancial fricions. There are four agens in wo symmeric counries: consumers, rms, privae banks, and cenral banks. We rs display he problems solved by each agen and hen summarize equilibrium condiions. 7 This is also rue for he model wih collaeral consrains as in Kiyoaki and Moore (997). 8 For numerical analysis on opimal moneary policy in open economies wih such nancial fricions, see Bodensein, Guerrieri, and LaBriola (04). 7

8 The main model does no allow banks o lend and borrow inernaionally. Sill, nancial shocks spill over inernaionally, hrough expors and impors. Thus, nancial fricions in one counry can aler he dynamics of endogenous variables in he oher counry. The exension of he main model o inernaional lending and borrowing will be discussed in Secion Consumers A represenaive consumer in he home counry H maximizes welfare W : W E X T = T u (C T ) Z 0 v [l T (h)] dh ; () where E is he expecaions operaor condiional on he sae of naure a dae and [0; ) is he subjecive discoun facor. The funcions u and v are increasing in he consumpion index C and he labor supply l, respecively. l (h) denoes he labor supplied o inermediae-goods producing rm h. The budge consrain is given by P C + E [X ;+ B + ] + D B + ( + i ) D + + B + F T ; Z 0 w (h)l (h)dh () where P is he aggregae consumer price index, B is he Arrow securiy, D is he deposi o he privae banks, i is he nominal ineres rae se by he cenral bank from o, w is he nominal wage, B = R 0 B (h)dh is he nominal dividend from he ownership of he privae banks in he home counry, F = R 0 F (h)dh is he nominal dividend from he ownership of inermediae-goods producing rms in he home counry, X ;+ is he sochasic discoun facor, and T is he lump sum ax. 9 9 The resuls obained in his paper will no change even if a deposi o foreign banks or ownership of foreign rms and banks is allowed. 8

9 Because a complee nancial marke beween he wo counries is assumed, consumers in each counry can inernaionally rade he sae coningen securiies o insure agains counry-speci c shocks. Consequenly, consumers in boh counries encouner a unique discoun facor. Assuming a complee inernaional nancial marke in he presence of nancial marke imperfecions may seem unreasonable. These are, however, hough o be imporan ingrediens in explaining economic developmens during he recen global nancial crisis, in paricular, he signi can synchronizaion of he business cycles across di eren counries. Perri and Quadrini (0) explain his unprecedened degree of synchronizaion using a model wih credi shocks ( nancial marke imperfecions) under complee inernaional nancial markes. 3. Firms 3.. Inermediae-goods producer Inermediae-goods producer h produces a di ereniaed inermediae good y using he di ereniaed labor: y (h) + y (h) = f [l (h)] ; (3) and needs o borrow loans q o nance labor compensaion: q (h) = R (h) w (h) l (h); (4) where R is gross loan raes. The inermediae-goods producer h ses prices in boh domesic and foreign markes under he law of one price: 0 p (h) = S p (h) ; (5) 0 There is no need o assume eiher producer currency pricing or local currency pricing as here is no price sickiness. 9

10 o maximize he pro F : F (h) = ( + ) [p (h) y (h) + S p (h) y (h)] R (h) w (h) l (h); (6) where he aserisk denoes foreign variables. p and p denoe prices o home and foreign markes, respecively. S is nominal exchange raes. is he sales subsidy. Wih his ime-varying sales subsidy nanced by he lump-sum ax, he markup shock is de ned as exp ( ) ss markupime-variaion z } { z } { + ; where denoes he elasiciy of subsiuion beween di ereniaed inermediae goods. can capure ime-variaion in he markups. This is a speci caion following Benigno and Benigno (006) and creaes ine cien ucuaions in he marginal rae of subsiuion beween consumpion and goods producion. The same oucome is obained by using oher speci caions: ime-varying monopoly power of wage seers as in Clarida, Gali, and Gerler (00) and Woodford (003); a ime-varying elasiciy of subsiuion as in Giannoni (04). Under he curren seings, domesic (foreign) rms borrow only from domesic (foreign) banks. This assumpion will be relaxed laer in Secion 6 o check wheher inernaional lending and borrowing aler our main resuls. In his paper, sicky prices are no assumed o solely concenrae on he role of he nancial fricions on policy cooperaion. There is a rade-o beween price sabiliy and nancial sabiliy wih sicky prices. For deails of his rade-o, see Kobayashi (008) and Teranishi (05). 0

11 3.. Final-goods producer A nal consumpion goods producer minimizes he oal cos: P H; Y H; + P F; Y F; ; subjec o he following producion echnology: YH; YF; Y ; (7) where (0 ) denoes he home bias. is se o 0.5 since symmery beween wo counries is assumed. Goods produced in he domesic counry Y H; and hose produced in he foreign counry Y F; are de ned, respecively, as Z Y H; 0 y (h) dh ; (8) and Z Y F; 0 y (h ) dh : (9) 3.3 Privae Banks There is a coninuum of privae banks in each counry locaed over [0; ]. Each privae bank collecs deposis from consumers in is counry given saving ineres raes. Each bank h is in a long-erm relaionship wih each inermediae-goods producing rm h. This follows a segmened banking sysem assumed in such previous sudies as Kobayashi (008), Andrés and Arce (0) and Mandelman (00, 0). As a resul, i ses di ereniaed nominal loan ineres raes according o heir individual loan demand curves. A di ereniaed nominal loan ineres rae applies o di ereniaed inermediae-goods producers. Thus, wihin his segmened environmen, privae banks mainain monopoly

12 power over he loan ineres rae deerminaion. In addiion, each bank reses is loan ineres raes wih probabiliy following he Calvo (983) - Yun (996) framework as examined in Teranishi (05) and Fujiwara and Teranishi (0). Due o saggered loan conracs beween rms and privae banks, privae banks end up xing nominal loan ineres raes for a cerain period. Saggered loan conracs also generae dispersion in loan ineres raes, which resul in welfare coss, which will be explained in deail. The privae bank h ses he loan ineres rae o maximize he presen discouned value of pro : where X E T = T X ;T B T (h) ; (0) B (h) = q (h) [( + ) R (h) ( + i ) exp (u )] : () u denoes he loan premium shock. Noe ha goods prices are exible in his model. In addiion, he moneary auhoriy does no adjus nominal ineres raes on deposis i wih a Taylor rule arrangemen - a ypical feaure in he NOEM seup, alhough such an arrangemen is indeed possible. Nominal ineres raes on deposis are given by he opimal moneary policy discussed below Summary: Financial Markes In his economy, he benevolen cenral bank deermines nominal ineres raes i o maximize social welfare. Households ake i as deposi ineres raes and smooh consumpion hrough ineremporal opimizaion. Banks in he monopolisically compeiive marke borrow from households as deposis or loanable funds D wih deposi ineres raes i, Almos idenical resuls are obained wih he assumpion of he monopolisically compeiive banking secor as examined in Teranishi (05), Gerali, Neri, Sessa, and Signorei (00) and Fujiwara and Teranishi (0).

13 and lend o rm h wih lending raes R (h). A he beginning of he period, banks receive deposis and lend funds o rms. A he end of he period, hey receive repaymens from rms. If loan raes are exible, lending and borrowing are deermined by he inra-emporal opimizaion problem by privae banks, which is similar o he sandard saic pro maximizaion problem by rms. 3 When loan raes are sicky, rms solve he dynamic opimizaion problem o maximize he presen discouned value of he pro s as shown in equaions (0) and (). This is also analogous o he opimal price seing problem by rms under sicky prices in he sandard new Keynesian model. Wih he possibiliy ha rms may no be able change loan raes in he fuure, opimal loan rae seing becomes forward-looking. To focus on he role of nancial fricions, prices are assumed o be exible. I is herefore possible o assume ha he cenral bank can direcly conrol real (deposi) ineres raes. 4 The real ineres rae se by he cenral bank in his manner, however, is usually di eren from ha arising in he fricionless (e cien) economy, which can be called as he naural rae of ineres on deposis. The naural rae of ineres on deposis is deermined hrough he consumpion Euler equaion: C = E + i + C + = E ( + r + ) C +: r + becomes he naural rae of ineres on deposis when consumpion is always a is e cien (naural) level. 5 A wedge beween he curren deposi ineres rae and he naural rae of ineres on deposis may emerge afer (real) shocks hi he economy. 6 The cenral bank s role is 3 The di erence beween a monopolisic banking secor wih exible loan conracs and a perfecly compeiive banking secor is found only in he exisence of he seady sae markup in he former. No di erence arises in dynamics. 4 To be precise, as will be explained below, CPI in aion raes are lef o be indeerminae, bu CPI in aion expecaions are uniquely pinned down hrough he consumpion Euler equaion. 5 As is he case wih he sandard new Keynesian model, consumpion Euler equaions are no included in cenral banks welfare maximizaion problem since hey are redundan. 6 Shocks creae a wedge beween curren loan raes and hose under e cien economy. This will 3

14 how o minimize his wedge in order o maximize social welfare. Thus, reacions by he cenral bank o shocks aler deposi ineres raes, while loan ineres raes adjus only gradually due o saggered loan conracs. As will become clearer, compleely eliminaing he e ecs from shocks o loan raes is no necessarily he opimal moneary policy. Even if loan raes are exible, he cenral bank can improve social welfare in his model. Changes in he level of loan raes lead o ine cien ucuaions in oupu (and herefore consumpion evenually) under he working capial loan. Thus, exibiliy in loan raes does no preven he cenral bank from eliminaing ine cien ucuaions in oupu by adjusing nominal ineres raes o shocks. 3.4 Preference and Parameer u() and v() are iso-elasic funcions: u (c) = c ; and v (l) = l: Firms are equipped wih a linear producion echnology: f (l) = exp (z ) l; where z denoes he echnology shock. Appendix A displays he deailed derivaion for he sysem of equaions. evenually produce a wedge beween curren deposi raes and he naural rae of ineres on deposis. The naural rae of ineres is de ned so ha i corresponds o he policy ineres rae as is convenion in he sandard new Keynesian model. 4

15 3.5 Marke Clearing Condiions Equaion (3) ogeher wih he foreign counerpar depic he marke clearing condiions for inermediae goods. The marke clearing condiions for nal goods are simply C = Y ; () and C = Y : (3) Financial markes clear when oal deposis equal o oal loans: Z 0 q (h) dh = D ; and ne supply of he Arrow securiies is zero: B = 0: 3.5. Welfare Coss The saggered loan conrac creaes dispersion in loan ineres raes. Wih he working capial loan, loan raes are ighly linked wih labor supply. Dispersion in loan raes leads o ine cien allocaions of labor among ex pos symmeric rms like price dispersion in he sandard new Keynesian model. Similarly o Yun (005) for price dispersion, he relaive loan rae dispersion is de ned as Z R (h) dh; (4) 0 R 5

16 where R is he average loan raes: Z R R (h) 0 dh : (5) Then, aggregaing he resource consrains over h leads o P Y + P P H; Y PH;! = exp (z ) l : Any dispersion of loan raes, namely R (h) 6= R, works as if i were a negaive echnology shock. represens he welfare cos semming from saggered loan conracs. For he deails of he derivaion, see Appendix A, in paricular, equaion (85). 3.6 Sysem of Equaions equilibrium condiions below, ogeher wih he opimal moneary policy de ned in he nex secion deermine he opimal pahs for R, F, K, Y, R, F, K, l, l,,, i and i : 6 R 4 R F = K ; (6) F = + E Y + R Y R + K = ( + i ) exp ( ) exp (u ) Y + + E R R 6 R F +; (7) Y R R + K +; (8) F = K ; (9) Y + R = + E F Y R + F +; (0) 6

17 K = + i R Y + R + E Y 6 R = ( ) 4 Y R + K +; () exp ( ) R = l ; () R R R ; (3) Y R R 6 R = ( ) 4 = l ; (4) R + R ; (5) and = Y exp ( ) R exp (z ) R : (6) Similarly o Yun (005), equaions (6) o (8) and equaions (9) o () represen he recursive represenaions for domesic and foreign loan Phillips curves, respecively. The rs-order log-linear approximaion on hese equaions around he Ramsey opimal seady saes (^x log (X =X) (X X) =X, where X is he Ramsey opimal seady sae value) leads o he domesic loan rae Phillips curve: ^R ^R = E ^R+ ^R + ( ) ( ) i + u + ^R ; (7) and he foreign loan rae Phillips curve: ^R ^R = E ^R + ^R + ( ) ( ) i ^R : (8) Equaions (7) and (8) are analogous o he new Keynesian Phillips curve. Insead of in aion raes, which are de ned as ^ = ^P ^P, here in aion raes for gross loan raes 7

18 ( ^R ^R ) are deermined by loan in aion expecaion E ( ^R + ^R ) and (nominal) marginal coss of loan creaion (i + u + ^R ). Loan ineres raes a ec marginal coss wih he presence of he cos channel as equaions (4), (7) and (8) illusrae. Thus, conrary o he sandard new Keynesian model, in aion raes (of loan raes) as well as he price level (of loan raes) are pinned down by he model. Consequenly, backward-looking componens in equaions (7) and (8), namely ^R and ^R, become he endogenous sae variables in his model. Noe also ha seady saes do no maer for linearized aggregae supply condiions. Equaions (3) and (5) show he dynamics of relaive loan rae dispersion, which is de ned in equaion (4) and Z R (h ) dh : (9) 0 R Since each bank only reses is loan ineres raes wih probabiliy, equaions (3) and (5) are derived from he de niion of he average loan raes in equaion (5) and Z R 0 R (h ) dh : As is well-known in he lieraures wih he new Keynesian model, relaive price dispersion maers only under higher order han linear approximaion. This is because wih linear approximaion, ^ = ^ = 0: Equaions () and (4) are derived from he marke clearing condiions for inermediae goods in equaion (3) and is foreign counerpar. As is he case wih he sandard new Keynesian model, relaive price dispersion erms in equaions (4) and (9) ac as if hey were negaive echnology shocks. As a resul, price sabiliy, or loan rae sabiliy in his paper, becomes he opimal moneary policy. 8

19 Equaion (6) is he marke clearing condiion for he nal goods in equaions () and (3) under he complee inernaional nancial marke. This can be also expressed as log-deviaion from he Ramsey opimal seady saes as 0 = + ^Y + ^R z + ^R : (30) The consumpion Euler equaion for he domesic counry: Y Y + = ( + i ) E ; (3) + and ha for he foreign counry: " Y (Y ) = ( + i ) E + + # ; can be included in addiion o equilibrium condiions (6) o (6). These will deermine CPI in aion expecaions in boh counries. In such a model, however, indeerminacy in in aion raes arises. In order o avoid his indeerminacy, a sicky price mechanism mus be incorporaed in inermediae goods rms pro maximizaion problem in equaions (6). This will, however, complicae he analysis, especially in open economies. Thus, nominal price rigidiies are omied from he model and CPI in aion raes are lef o be indeerminae in his model. In his economy, here are hree disorions: subopimally low producion due o monopolisic rens, working capial loans, and saggered loan conracs. The rs disorion is eliminaed by an appropriae subsidy. The opimal moneary policy aims o minimize he welfare coss semming from he second and he hird disorions. 9

20 Figure : Responses o Moneary Policy Shock 3.7 Dynamic Properies Here, we display he dynamic propery of his model o he moneary policy shock. Even hough he model is quie simple and sylized, i can capure imporan properies in he moneary ransmission mechanism: namely, he delayed responses in loan raes and hump-shaped responses of oupu and consumpion. In he simples form, he linearized equilibrium condiions in equaions (7), (8) and (30) given policy ineres raes can deermine he equilibrium pahs for domesic loan raes R, foreign loan raes R and nal goods producion (consumpion in boh domesic and foreign counries) Y. The exisence of lagged loan raes in equaions (7) and (8) and he absence of he deerminaion of in aion raes give he model quie di eren implicaions regarding indeerminacy semming from moneary policy rules. The model can have unique raional expecaions equilibrium wihou moneary policy feedback rules. Figure illusraes he responses of hese variables o a moneary policy shock or an increase in policy ineres raes i, which is evenually deposi ineres raes in he consumpion Euler equaion in (3). The parameers are calibraed as in Table. and are aken from Seinsson (008), and is he average value of loan rae sickiness 0

21 Table : Parameer Values Parameers Values Explanaion 0.99 Subjecive discoun facor Coe cien of relaive risk aversionec o real ineres rae 0.57 Probabiliy of loan ineres rae change 7.66 Subsiuabiliy of di ereniaed consumpion goods across he counries esimaed in Fujiwara and Teranishi (0). The moneary policy shock follows an AR() process wih a parameer of 0.9. Due o he exisence of saggered loan conracs, he iniial response of domesic loan raes becomes signi canly smaller compared o changes in domesic policy ineres raes. Thus, delayed responses on loan raes repored by such previous sudies as Slovin and Sushka (983), Berger and Udell (99), Sorensen and Werner (006), Graham and Wrigh (007), Gambacora (008) and Gerali, Neri, Sessa, and Signorei (00) maerialize in his model. In addiion, he responses of Y, ha is he nal oupu and herefore consumpion in boh domesic and foreign counries, demonsrae humpshaped dynamics, ofen considered an imporan propery for he dynamic sochasic general equilibrium model o replicae. Hump-shaped responses sem from lagged loan raes in equaions (7) and (8) as endogenous sae variables. Unlike he sandard new Keynesian model wih sicky prices, he level of nominal variables price levels in he new Keynesian model and he levels of loan raes in our model consrain real variables hrough he working capial loan. The foreign loan rae Phillips curve in equaion (8) conains only foreign loan and policy ineres raes. A shock also only impacs upon domesic policy ineres raes. Thus, foreign loan raes remain a a seady sae level in his simulaion. Through an increase in domesic loan raes, however, consumpion in he foreign counry also decreases due o he cos channel of moneary policy under he complee inernaional nancial marke. We will consider opimal reacions by boh domesic and foreign cenral

22 banks in he following secions. 4 Ramsey Policy In his secion, he Ramsey opimal moneary policy under boh cooperaion and noncooperaion will be discussed. There are wo main aims of deriving he allocaions under he Ramsey opimal moneary policy in his secion: o compue he opimal Ramsey opimal seady sae around which he model should be approximaed, and o undersand wheher here are gains from cooperaion in he long-run. 4. Cooperaion Under cooperaion, wo cenral banks aim o maximize global welfare ogeher: W + W E " X T T = = E X T = C T + (C T ) Y T T l T l T ; Z 0 l T (h) dh Z 0 l T (h ) dh # (3) where equaions () and (3) are subsiued, subjec o equilibrium condiions in equaions (6) o (6). Appendix B provides all equilibrium condiions involving Lagrange mulipliers on he consrains of his problem. These deermine he allocaions under he opimal moneary policy in cooperaion. 4. Noncooperaion Under noncooperaion, he game beween wo cenral banks mus be well-de ned. In paricular, we mus clarify he acion of he opponen which is aken as given. In his paper, we solve he open-loop Nash equilibrium, where he domesic (foreign) cenral bank maximizes welfare of domesic (foreign) counry given he policy ineres rae in

23 he foreign (domesic) counry. Clarida, Gali, and Gerler (00) assume oupu in he oher counry o be given, while producer price in aion raes in he oher counry are considered o be given in Benigno and Benigno (003, 006). In he model considered in his paper, here is neiher counry speci c oupu nor in aion as can be seen in equaions (6) o (6). Consequenly, he naural variable o be given as exogenous o each cenral bank is he policy ineres rae in he counerpar counry. Given he policy ineres rae in he foreign counry i, he domesic cenral bank maximizes welfare in he domesic counry: W E X T = = E X T = C T T Y T T Z 0 l T ; l T (h) dh (33) subjec o equilibrium condiions in equaions (6) o (6). Similarly, he foreign cenral bank akes he policy ineres in he domesic counry i as given and maximizes welfare in he foreign counry: W E X T = Y T T l T ; (34) subjec o equilibrium condiions in equaions (6) o (6). Appendix B provides all equilibrium condiions involving Lagrange mulipliers on he consrains in his problem under noncooperaion. These deermine he allocaions under he opimal moneary policy in noncooperaion. 4.3 Ramsey Opimal Seady Sae The Ramsey opimal seady saes are compued from equilibrium condiions by eliminaing ime subscrips. The aim of compuing he Ramsey opimal seady saes is 3

24 wofold. Firs, we will derive he opimal moneary policy in he LQ framework following Benigno and Woodford (005) and Benigno and Benigno (006). This is because inuiion for he opimal moneary policy can hardly be undersood from he non-linear equilibrium condiions shown in Appendix B. LQ approximaion mus be conduced around he Ramsey opimal seady saes. Second, he di erences beween cooperaive and noncooperaive regimes imply he exisence of gains from policy cooperaion in he long-run. Appendix B shows he Ramsey opimal seady sae for all variables under boh cooperaion (wih subscrip C) and noncooperaion (wih subscrip N), where seady sae markups are eliminaed by subsidy. Here, only he Ramsey opimal seady saes of endogenous variables excep for auxiliary variables and he Lagrange mulipliers are displayed. The Ramsey opimal seady saes of policy ineres raes, oupu, labor supply and loan ineres raes under cooperaion are as follows: + i C = + i C = ; Y C = l C = l C = ; and R C = R C = : (35) Ne ineres raes are zero so he welfare coss semming from he working capial loan becomes zero. This is considered he Friedman rule in he presence of he cos channel. Zero ne nominal ineres raes ogeher wih negaive in aion raes become opimal in eliminaing nominal disorions. Thus, he second disorion can be eliminaed by he appropriae seady sae condiions wih negaive in aion argeing. 4

25 On he oher hand, hose under noncooperaion are + i N = + i N = + ; and Y N = l N = l N = ; + R N = R N = + : Since he coe cien of he relaive risk aversion, or, he inverse of he ineremporal elasiciy of subsiuion, is posiive ( > 0), boh policy and loan ineres raes are higher under he noncooperaive regime (i N > i C, R N > R C ). Regarding oupu and labor supply, since d + d = d exp log + d + = exp log + + log ( + ) > 0; (36) wheher or no i becomes larger under cooperaion depends on he size of. Appendix C proves ha seady sae welfare is indeed higher under cooperaion Cooperaion vs Noncooperaion in he Long-Run The Ramsey opimal seady saes under cooperaion are di eren from hose under noncooperaion. In addiion, seady sae welfare is naurally higher under cooperaion. Togeher hese imply ha here is welfare gain from cooperaion in he long-run. Here, we aim o undersand he sources of his long-run welfare gain. In he absence of shocks and nominal (loan rae) rigidiies, equilibrium condiions in 7 The model involves endogenous sae variables, namely R and R. Thus, seady sae welfare comparison may no be a good measure for evaluaing he (policy) regimes. In paricular, when he seady saes for endogenous sae variables are di eren, he seady saes under he Pareo opimal allocaion can be lower han hose under alernaive policy. For a deailed discussion on his poin, see Bilbiie, Fujiwara, and Ghironi (04). 5

26 equaions (6) o (6) collapse o he ve equaions below: Y f; + i f; = l f; ; (37) Y f; + i f; = l f;; (38) = Y f; ( + i f; ) + i f; ; (39) R f; = + i f; ; and R f; = + i f;; where he variables in his economy are denoed wih subscrip f. They can be also obained by eliminaing ime subscrips in equilibrium condiions in equaions (6) and (6). Thus, opimal policy analysis here can be considered o compue he golden rule allocaion in he erminology of King and Wolman (999). The problem under cooperaion is o maximize welfare de ned in (3) subjec o equaions (37) o (39), while he domesic (foreign) cenral bank under he noncooperaive regime aims o maximize welfare de ned in (33) and (34) subjec also o equaions (37) o (39). The opimal allocaions obained from hese problems are idenical o he Ramsey opimal seady saes, derived in he previous secion. The di erences in he Ramsey opimal seady saes beween cooperaion and noncooperaion can be undersood from his simpli ed opimizaion problem for he golden rule allocaions. Equaions (37) o (39) clarify he reason behind he di erences. Equaions (37) and (38) demonsrae ha each cenral bank has an incenive o keep policy ineres raes high o reduce he dis-uiliy semming from labor supply. Corsei and Peseni (00) call his incenive he de aionary bias. Wih he working capial loan and he complee nancial marke, he erms of rade T ot can be expressed as he raio of domesic over 6

27 foreign loan raes: 8 T ot = S P H; P F; = R : (40) R Thus, each cenral bank aims o keep higher ineres raes o improve he erms of rade. On he oher hand, equaion (39), which is derived from he marke clearing condiion for nal goods in equaions () and (3) under he complee inernaional nancial marke, shows ha wih globally lowered ineres raes, boh counries can enjoy more consumpion and herefore higher welfare. Under he complee inernaional nancial marke, i is no he policy ineres rae in each individual counry, bu global ineres raes, ha is he arihmeic mean of ineres raes of wo counries, which deermines global consumpion and herefore consumpion in each counry. This becomes he source of he exernaliy, which creaes incenives for cenral banks o keep ineres raes higher. Cenral banks under cooperaion can inernalize his exernaliy. Consequenly, ineres raes under cooperaion are lower han under noncooperaion. Thus, here are gains in cooperaion wih he cos channel in he long-run. 9 5 Opimal Moneary Policy in LQ Framework The previous secion clari es ha here are gains in cooperaion in he long-run. In his secion, we delve ino wheher gains exis even in he shor-run, in paricular, in opimal responses o srucural shocks. For his, we need o compare he opimal pahs o shocks of all endogenous variables beween cooperaion and noncooperaion using equilibrium condiions in Appendix B. 0 Ye, here are oo many equaions, in paricular, for auxiliary variables and co-sae variables. Insead, in his secion, we invesigae he naure of he Ramsey opimal 8 For he deailed derivaion, see Appendix A, in paricular, equaions (89) o (9). 9 Cooley and Quadrini (003) explain he decline in ineres raes afer he adven of Euro were caused by moneary cooperaion. 0 Naurally, he same impulse responses are obained under boh non-linear and LQ Ramsey problems. 7

28 policy using he LQ framework proposed by Benigno and Woodford (005) and Benigno and Benigno (006). 5. Loss Funcion under Cooperaion Firs, welfare under cooperaion in (3) is approximaed up o he second order. We use he second order log approximaion: X X X ^x + ^x : Then, welfare under cooperaion in (3) is approximaed around he Ramsey opimal seady sae as W + W E X T = E X =0 Y T T l T l T ^Y ^l ^l + ( ) ^Y ^l ^l : (4) Noe ha erms ha are of he higher order han second order and independen from policy will no be shown hereafer. By aking logs for equaions () and (4), we have ( ) ^Y ^R + ^ = ^l ; (4) and ( ) ^Y ^R + ^ = ^l : (43) Benigno and Benigno (006) is he applicaion of Benigno and Woodford (005) o a wo counry model. De Paoli (009) derives he quadraic loss funcion in a small open economy using his echnique. 8

29 In addiion, second order approximaion o equaions (3) and (5) leads o E X =0 E X =0 ^R ^R ; (44) ( ) ( ) and E X =0 E X =0 ( ) ( ) ^R ^R : (45) By subsiuing equaions (4) o (45) ino (4), he quadraic loss funcion under cooperaion is derived: (W + W ) L E X =0 8 >< >: ^R ^R ( )( ) + ( )( ) + ^R + + ^R h ^R + + ^R + i ^R ^R 9 >= : >; (46) The loss funcion in equaion (46) shows ha global welfare is represened by no only he loan in aion rae, namely he di erence ( ^R ^R ), bu also he level of loan ineres raes ^R. The former capures welfare coss semming from relaive loan rae dispersion in equaions (4) and (9). The laer represens welfare losses from unsmoohed consumpion. The cos channel conrols he equilibrium dynamics in consumpion and herefore, loan raes remain in he approximaed loss funcion o represen welfare gain from consumpion smoohing. 5. Loss Funcions under Noncooperaion Under noncooperaion, he loss funcions for boh domesic and foreign cenral banks are compued separaely. The domesic welfare under noncooperaion in (33) is approx- 9

30 imaed up o he second order as W E X T = + Y T T E X =0 l T ( + ) ^Y ( + ) ( ) ^l + ^Y ^l : (47) Afer subsiuing equaions (4) o (44) and ignoring he parameers before he summaion, his collapses o E X =0 8 >< >: 4 ^R ^R ( )( ) ^R + ^R + ^R z + ^R >= >; : (48) Conrary o he loss funcion under cooperaion in (46), he linear erm ^R sill remains. ^R represens he erms of rade exernaliy. The domesic cenral bank prefers ^R o be lower since his reduces social loss in (48). This is because lower ^R improves he erms of rade for he domesic counry as shown in equaion (40). A linear erm in he welfare meric will resul in a spurious welfare evaluaion in he LQ framework. Here, following Benigno and Woodford (005) and Benigno and Benigno (006), we ake he second order approximaion o equilibrium condiions and obain he approximaed equaions where linear erms are expressed only by quadraic erms. By using such second orderly approximaed equilibrium condiions, we can subsiue ou linear erms in he welfare meric wih quadraic erms. Appendix D shows furher deail of how o derive he quadraic approximaion of he loan rae Phillips curves in equaions (6) o (8) or (9) o (). From he second order approximaion of he loan rae Phillips curve in he foreign counry in equaions (9) o For deails on his, see, for example, Suherland (00), Kim and Kim (003, 007), Benigno and Woodford (005, 0) and Kim, Kim, Schaumburg, and Sims (008). 30

31 (), we can derive E X =0 i ^R E X =0 6 4 ( ) ^Y i ( )( ) ^R ^R i ^R ^R : (49) By subsiuing his approximaed relaionship in (49) ino he approximaed welfare measure in (48), we can derive he quadraic loss funcion which he domesic cenral bank aims o minimize: L D E X =0 8 >< >: ^R ^R ( )( ) + + ( )( ) i + ^R + + ^R h ^R + + ^R i ^R i ^R 9 >= : (50) >; Similarly, from he second order approximaion of he loan rae Phillips curve in he domesic counry in equaions (6) o (8), we can obain 8 hz + ( ) ^Y i i + + u ^R 9 E X =0 i ^R + u + E X =0 >< >: i + u + ^R ^R ^R ( )( ) >= : >; (5) By using his approximaed relaionship in (5), we can derive he quadraic loss funcion for he foreign cenral bank as L F E X =0 8 >< >: ^R ^R ( )( ) + ^R ( )( ) h + ^R (i + + u )i + ^R nh ^R (i + + u )i + ^R + o ^R 9 >= : (5) >; 3

32 5.3 Cooperaion vs Noncooperaion in he Shor-Run We rs de ne he opimal allocaions in he LQ framework as follows. 3 De niion The opimal cooperaive allocaion is he sequence of endogenous variables f ^R ; ^R ; i ; i ; ^Y g ha minimizes (46) under he consrains (7), (8), and (30), given he sequence of shocks fu ; z ; g and he iniial condiions: ^R0 and ^R 0. De niion The opimal noncooperaive allocaion is he sequence of endogenous variables f ^R ; ^R ; i ; i ; ^Y g, ha minimizes (50) under he consrains (7), (8), and (30), given he sequence of he foreign policy ineres rae i, shocks fu ; ; z g and he iniial condiions: ^R0 and ^R 0, and ha minimizes (5) under he consrains (7), (8), and (30), given he sequence of he domesic policy ineres rae i, shocks fu ; z ; g and he iniial condiions: ^R0 and ^R 0. Noe ha parameers in equaions (7), (8) and (30) do no rely on seady sae values. Also, regarding he loss funcions in (46), (50) and (5), he di erence in seady saes only maers for he parameers before he summaion as in (47), which can be ignored when compuing he opimal moneary policy. Therefore, even hough he Ramsey seady saes are di eren beween cooperaion and noncooperaion, opimal responses are no a eced by his di erence. Below, we describe how he opimal moneary policy under boh cooperaion and noncooperaion will reac o he echnology shock, he loan premium shock and he markup shock, respecively Technology Shock Noe ha he echnology shock z is no included in he loss funcions under boh cooperaion and noncooperaion, as shown in equaions (46), (50) and (5). This fac implies 3 ^Y is passively deermined via equaion (30). Thus, i can be excluded from he deerminaion of opimal moneary policy. 3

33 ha he level of loan raes or loan in aion raes, ha he cenral banks aim o achieve, are independen from he echnology shock. In a sandard new Keynesian model, due o sicky prices, he echnology shock alers he naural rae, namely oupu under he exible price equilibrium. Therefore, he oupu gap, which is de ned as he di erence in oupu beween he sicky and exible price equilibria and hus he cenral banks aim o minimize, also shifs as he echnology shock changes. In conras, in our model, due o he exibiliy in price seings, he echnology shock does no change he oupu gap. Thus, for he cenral bank, i is opimal o sabilize ucuaions in loan raes deermined by equaions (7) and (8). These equaions do no conain he echnology shock as a componen of marginal coss for supplying loans. Under boh cooperaion and noncooperaion, i is opimal o compleely sabilize he ucuaions in loan raes in boh domesic and foreign counries. Any ucuaions in oupu ^Y according o equaion (30) under ^R = ^R = 0, namely, ^Y = z are opimal and should no be correced by policy acions. Thus, here is no addiional gain from cooperaion Loan Premium Shock Conrary o he echnology shock, he loan premium shock is included in he loss funcion in he foreign counry as in equaion (5) as well as in he domesic loan rae Phillips curve in equaion (7). Despie his, he loan premium shock does no require policy cooperaion eiher. Under cooperaion, since he loan premium shock is no included in he global loss funcion in equaion (46), cenral banks in boh counries should aim o achieve complee 33

34 loan rae sabiliy as ^R = ^R = 0. This can be achieved by seing he domesic policy ineres rae o eliminae he domesic loan premium shock in he domesic loan Phillips curve in equaion (7) such ha i = u. Under noncooperaion, he domesic cenral bank aims o compleely sabilize loan raes since he loss funcion does no conain he loan premium shock. To achieve his, again, he domesic policy rae is se o eliminae he loan premium shock. By doing so, loan raes are compleely sabilized, since he marginal coss of supplying domesic loans in equaion (7) are no ucuaing. Alhough he loan premium shock is included in he foreign loss funcion in equaion (5), he domesic policy ineres rae is no conrollable by he foreign cenral bank. Consequenly, he complee sabilizaion of loan raes by he domesic cenral bank su ces o achieve he opimal allocaions. Again, here is no gain from cooperaion Markup Shock The markup shock is repored o be an imporan driver of he business cycles in many sudies wih he prooypical DSGE model following Chrisiano, Eichenbaum, and Evans (005) and Smes and Wouers (003, 007). Bayesian maximum likelihood esimaion of he DSGE model of he Euro area by Gerali, Neri, Sessa, and Signorei (00) provides sizable esimaes of sandard errors in he banking secor markup shocks. Also, he auhors repor signi can conribuions from markup shocks in he banking secor in he ucuaions of nancial (and herefore real economic) variables beween 004 and 009 including he peak of he recen global nancial crisis. The opimal responses o he markup shock under boh cooperaion and noncooperaion are shown in Figures and 3. The markup shock follows an AR() process wih a parameer of 0.9. Responses o shocks are derived under commimen ogeher wih he assumpion ha he iniial endogenous sae variables are se a heir opimal seady 34

35 Figure : Opimal Responses o Markup Shock: = sae values. 4 The parameers in Table are again employed, bu for he coe cien of he relaive risk aversion, we examine wo values; Figures and 3 show hose when =, and = 0:5, respecively. Terms of Trade vs Risk Sharing As equaion (8) implies, his is a shock o reduce he markup. Wih sicky loan raes, as implici in equaions () and (4), and explici in loss funcions in (46), (50) and (5), ucuaions in loan ineres raes resuls in resource coss. Consequenly, under boh cooperaion (blue lines) and noncooperaion (red lines), in order o avoid resource coss semming from loan rae dispersion, loan ineres raes gradually change afer a negaive markup shock. When =, foreign loan and policy ineres raes move in he opposie direcion o domesic ineres raes. On he oher hand, when = 0:5, hey boh move in he same direcion. In his model, since he inra-emporal elasiciy of subsiuion beween domesic and foreign goods is se a uniy as in equaion (7), he coe cien of relaive risk aversion solely deermines wheher goods produced in he wo counries are Edgeworh 4 This is he imeless opimal moneary policy in he erminology of King and Wolman (999). 35

36 Figure 3: Opimal Responses o Markup Shock: = 0:5 complemens or subsiues. 5 When > ( < ), for insance, he ineremporal elasiciy of subsiuion becomes lower (higher) han he inra-emporal elasiciy of subsiuion. In his siuaion, home goods and foreign goods are Edgeworh subsiues (complemens). Consequenly, oupu in he domesic counry moves in he opposie (same) direcion o ha of he foreign counry. This mechanism can be undersood by analyzing he relaionship beween marginal coss and he erms of rade. By combining he resource consrain wih he labor marke equilibrium condiion, only marginal coss wih he presence of he markup shock are given by where is MC = w l ( ) = T ot ; (53) P H; Improvemens of he erms of rade have wo opposing e ecs o marginal coss. Firs, by a ecing oupu prices, improvemens in he erms of rade direcly 5 For more deail on his poin, see, for example, Tille (00), Clarida, Gali, and Gerler (00), Benigno and Benigno (003, 006), Fujiwara, Nakajima, Sudo, and Teranishi (03) and Fujiwara and Ueda (03). When =, namely wih he log uiliy, wo counries become insular and hre is no spillover beween he wo counries. 6 Equaions (59), (66), (7) and (85) in Appendix A are used. 36

37 decrease marginal coss in he home counry. Second, hese resul in producion swiching from domesically-produced o foreign-produced goods. Given domesic oupu, his requires a rise in oupu in he foreign counry. Toal consumpion rises in boh counries, and due o risk sharing, boh domesic and foreign consumpion rise by he same amoun. A rise in domesic consumpion raises marginal coss in he home counry, and o o se he rise in prices, home employmen mus decrease. In he erminology of Clarida, Gali, and Gerler (00), he former is he erms of rade e ec while he laer is he risk sharing e ec. For example, when >, he laer dominaes he former channel. A negaive shock o he markup in he domesic counry reduces domesic loan ineres raes. As shown in equaion (40), his worsens he erms of rade for he domesic counry and herefore improves he foreign erms of rade. The negaive markup shock spills over o he foreign counry as if i were a posiive shock o marginal coss. Consequenly, in his case, foreign loan raes should increase. Flexible Loan Raes Green lines represen he opimal responses when here are no rigidiies in loan rae seings. Under exible loan raes, he rs wo erms in he loss funcions in (46), (50) and (5) disappear. Since no welfare cos sems from he ucuaions in loan in aion raes ( ^R ^R ), here exiss no rade-o beween sabilizing he di erence or he level of loan raes. Thus, cenral banks under boh cooperaion and noncooperaion can solely concenrae on sabilizing oupu ucuaions, which are capured by he hird o he fh erms in (46), (50) and (5). Noe ha changes in he level of loan raes can lead o ine cien ucuaions in oupu and herefore consumpion evenually, under he working capial loan. 7 When loan raes are exible, namely = 0, loan rae Phillips curves in equaions 7 When prices are exible, no role is lef for moneary policy in he sandard new Keynesian model. In conras, in our model, he cenral bank can sill improve social welfare even wih exible loan raes. The price level does no maer under exible prices in he sandard model, bu he level of he loan raes maers under he working capial loan. 37

38 (7) and (8) collapse o ^R f; = i f; + ; and ^R f; = i f;: Wheher cenral banks are under cooperaion or noncooperaion, by conrolling i f; and i f;, cenral banks can se loan ineres raes o eliminae ine cien ucuaions semming from he markup shock, ha are represened by he hird o he fh erms in (46), (50) and (5). The opimal dynamics wihou loan rae sickiness under boh cooperaion and noncooperaion are derived as follows: ^R f; = ; (54) ^R f; = 0; i f; = ; i f; = 0; and ^Y f; = 0: When a negaive shock is applied o he domesic markup, equaion (54) implies ha in he absence of saggered loan conracs, domesic loan raes should be decreased immediaely. There is no di erence in he opimal responses under exible loan seings beween cooperaion and noncooperaion. Alhough seady saes are di eren, cenral banks under boh cooperaion and noncooperaion have he same goal for heir sabilizaion policies o srucural shocks. The markup shock changes he arge level of loan ineres raes di erenly beween wo counries under noncooperaion, bu moneary pol- 38

39 icy can compleely eliminae social loss de ned in (46), (50) and (5) semming from he mark up shock by achieving equaion (54). Gains from Cooperaion When loan raes are revised infrequenly, signi can differences beween cooperaion (blue lines) and noncooperaion (red lines) are observed in he responses of foreign loan and policy ineres raes. This is because under noncooperaion, cenral banks in boh counries are unable o inernalize he erms of rade exernaliy as discussed above and in such papers as Corsei and Peseni (00) and Benigno and Benigno (006). The domesic (foreign) cenral bank aims o reduce R (R ) o minimize social loss in (48) in order o improve he erms of rade in equaion (40). Consequenly, agains a posiive markup shock, as eviden in he domesic loss funcion (50), he domesic cenral bank wans o have lower domesic loan raes ( ^R = ) agains a posiive markup shock, while as he foreign loss funcion (5) shows, he foreign cenral bank ries o mainain domesic loan raes o be higher ( ^R = i + ). This incenive o manipulae he erms of rade is absen wihou loan sickiness. When loan raes are exible, here is no need for he domesic (foreign) cenral bank o in uence foreign (domesic) loan raes. Moneary policy can compleely eliminae social loss semming from he markup shock. On he oher hand, when loan raes are sicky, he foreign (domesic) loan rae Phillips curve becomes a binding consrain for he domesic (foreign) cenral bank. Thus, he domesic (foreign) cenral bank has an incenive o conrol foreign (domesic) loan raes o improve he erms of rade for he domesic (foreign) counry. Achieving equaion (54) is no opimal any more, since his creaes dispersion in loan raes. Room emerges for he domesic (foreign) cenral bank o manipulae loan raes in he foreign (domesic) counry. Through he relaionship of domesic marginal coss and he erms of rade in equaion (53), when > ( < ), increases (decreases) in policy ineres raes in he foreign counry alleviae he problem of he domesic counry semming from a shock o reduce 39

40 he markup. Foreign moneary policy under noncooperaion only reacs o he spillover e ecs on foreign marginal coss from he markup shock in he domesic counry. As a resul, under noncooperaion, he reacions of foreign variables o he domesic markup shock are lessened. 6 Inernaional Banking So far, we have omied inernaional lending and borrowing. Financial globalizaion has been expanding quie rapidly. We can easily observe his rend from recen nancial and economic developmens. Gadanecz (004), McGuire and Tarashev (006), and Lane and Milesi-Ferrei (007, 008) formally show ha more funds from foreign counries are owing ino he domesic nancial markes of oher counries. In his subsecion, we exend our model o incorporae inernaional lending and borrowing. Two cases will be examined, namely, inernaional funding and inernaional lending and borrowing. 6. Inernaional Funding As equaion () implies, domesic privae banks borrow solely from he domesic nancial marke. Assume insead ha privae bank h can now borrow a porion from he domesic nancial marke as well as a porion from he foreign nancial marke. Then, he pro de ned in equaion () can be re-wrien as B S + (h) = q (h) ( + ) R (h) ( + i ) ( ) E ( + i ) : (55) S The complee inernaional nancial marke implies he UIP (uncovered ineres rae pariy) condiion: + i = E S + S ( + i ) exp (" ) ; (56) where we add he so-called UIP shock ", he imporance of which has been emphasized by 40

41 many empirical sudies on inernaional macroeconomics, such as Lubik and Schorfheide (006). By combining equaions (55) and (56), we have he modi ed pro equaion under inernaional lending and borrowing: B (h) = q (h) ( + ) R (h) ( + i ) + exp (" ) : Our resuls so far will no change even when privae banks can borrow inernaionally. Furhermore, he UIP shock works similarly o he loan premium shock. 6. Inernaional Lending and Borrowing Nex, le us consider he siuaion where rms can borrow inernaionally. Suppose ha domesic rms borrow a porion from he domesic privae bank as well as a porion from he foreign privae bank. 8 Then, he pro equaion of he domesic rm h in equaion (6) is re-wrien as F (h) = ( + ) [p (h) y (h) + S p (h) y (h)] R (h) w (h) l(h) S + ( ) E R (h) w (h) l (h): S The second erms can be ransformed ino R (h) w (h) l(h) = MU R (h) ( + i ) w (h) l(h) exp (u ) ; while, by using equaion (56), he hird erm can be wrien as ( ) E S + S R (h) w (h) l (h) = ( ) MU R (h) ( + i ) w (h) l (h) exp (" ) : 8 For deailed analysis on his issue, see our working version of his paper: Fujiwara and Teranishi (009). 4

42 MU R (h) and MU R (h) are ime-varying markups for lending raes o domesic rm h semming from monopolisic compeiion and saggered loan conracs. As long as he UIP holds and he foreign bank lends o domesic rms in he foreign currency uni, he funding rae urns ou o be he same as he domesic saving rae irrespecive of he exisence of inernaional or domesic lending. Inernaional lending and borrowing do no aler he naure of he opimal moneary policy under boh cooperaion and noncooperaion discussed in his paper. 9 7 Conclusion We show ha policy cooperaion increases social welfare in a model wih simple nancial fricions wih monopolisic banking and saggered loan conracs in a racable framework. In order o undersand he implicaions of nancial fricions for policy cooperaion, we employ a simple nancial sysem consising only of cos channel, monopoly power by banks and saggered loan conracs. Recenly, here have been many aemps o posiively analyze he role of nancial fricions wih more deailed modeling of nancial secors, following such sudies as Kiyoaki and Moore (997), Bernanke, Gerler, and 9 The working paper version of his paper: Fujiwara and Teranishi (009) also considers inernaional lending for domesic rms in he domesic currency. There, for example, he pro equaion of he domesic rm h can be wrien as F (h) = ( + ) [p (h) y (h) + S p (h) y S + (h)]!e + (!) R (h) w (h) l (h): S while ha foreign bank h is B (h) = q (h) S + ( + )! + (!) E R (h) S i : The parameer! deermines how much is borrowed in he foreign currency uni. For example, if! =, he domesic rm borrows in he foreign currency uni and herefore incurs all exchange rae risks. Under his seing, he cenral bank under noncooperaion has an addiional incenive o appreciae domesic currency in order o reduce loan paymens. Consequenly, di erences arise in he opimal allocaions and prices beween cooperaive and non-cooperaive regimes even wih oher shocks han he markup shock. 4

43 Gilchris (999), Gerler and Kiyoaki (00), or Gerler and Karadi (0). Opimal moneary policy analysis ogeher wih a complex banking secor becomes increasingly di cul wih he exisence of he endogenous sae variables. 30 Will his exension drasically change our main resuls? This issue is lef for fuure research. 30 Bodensein, Guerrieri, and LaBriola (04) repor numerical resuls on opimal moneary policy analysis wih nancial fricions based on Gerler and Karadi (0). Analysis wih he LQ framework becomes complicaed wih he endogenous sae variables. See, for example, Edge (003). 43

44 References Andrés, J., and O. J. Arce (0): Banking Compeiion, Housing Prices and Macroeconomic Sabiliy, Economic Journal, (565), Barh, M. J., and V. A. Ramey (00): The Cos Channel of Moneary Transmission, in NBER Macroeconomics Annual 00, Volume 6, NBER Chapers, pp Naional Bureau of Economic Research, Inc. Benigno, G., and P. Benigno (003): Price Sabiliy in Open Economies, Review of Economic Sudies, 70(4), (006): Designing argeing rules for inernaional moneary policy cooperaion, Journal of Moneary Economics, 53(3), Benigno, P., and M. Woodford (005): In aion Sabilizaion and Welfare: The Case of a Disored Seady Sae, Journal of he European Economic Associaion, 3(6), (0): Linear-quadraic approximaion of opimal policy problems, Journal of Economic Theory, 47(), 4. Berger, A. N., and G. F. Udell (99): Some Evidence on he Empirical Signi - cance of Credi Raioning, Journal of Poliical Economy, 00(5), Bernanke, B. S., M. Gerler, and S. Gilchris (999): The Financial Acceleraor in a Quaniaive Business Cycle Framework, in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford, vol. of Handbook of Macroeconomics, chap., pp Elsevier. Bilbiie, F. O., I. Fujiwara, and F. Ghironi (04): Opimal moneary policy wih endogenous enry and produc variey, Journal of Moneary Economics, 64(C), 0. 44

45 Bodensein, M., L. Guerrieri, and J. LaBriola (04): Macroeconomic Policy Games, Finance and Economics Discussion Series 04-87, Board of Governors of he Federal Reserve Sysem (U.S.). Calem, P. S., M. B. Gordy, and L. J. Meser (006): Swiching coss and adverse selecion in he marke for credi cards: New evidence, Journal of Banking & Finance, 30(6), Calvo, G. A. (983): Saggered Prices in A Uiliy-Maximizing Framework, Journal of Moneary Economics, (3), Chrisiano, L. J., M. Eichenbaum, and C. L. Evans (999): Moneary Policy Shocks: Wha Have We Learned and o Wha End?, in Handbook of Macroeconomics, ed. by J. B. Taylor, and M. Woodford, vol. of Handbook of Macroeconomics, chap., pp Elsevier. (005): Nominal Rigidiies and he Dynamic E ecs of a Shock o Moneary Policy, Journal of Poliical Economy, 3(), 45. Clarida, R., J. Gali, and M. Gerler (00): A Simple Framework for Inernaional Moneary Policy Analysis, Journal of Moneary Economics, 49(5), Cooley, T. F., and V. Quadrini (003): Common Currencies vs. Moneary Independence, Review of Economic Sudies, 70(4), Corsei, G., L. Dedola, and S. Leduc (00): Opimal Moneary Policy in Open Economies, in Handbook of Moneary Economics, ed. by B. M. Friedman, and M. Woodford, vol. 3 of Handbook of Moneary Economics, chap. 6, pp Elsevier. Corsei, G., and P. Peseni (00): Welfare And Macroeconomic Inerdependence, The Quarerly Journal of Economics, 6(),

46 De Paoli, B. (009): Moneary Policy and Welfare in a Small Open Economy, Journal of Inernaional Economics, 77(),. Edge, R. M. (003): A Uiliy-Based Welfare Crierion in a Model wih Endogenous Capial Accumulaion, Finance and Economics Discussion Series , Board of Governors of he Federal Reserve Sysem (U.S.). Fujiwara, I., T. Nakajima, N. Sudo, and Y. Teranishi (03): Global Liqudiy Trap, Journal of Moneary Economics, 60(8). Fujiwara, I., and Y. Teranishi (009): Financial Sabiliy in Open Economies, IMES Discussion Paper Series 09-E-09, Insiue for Moneary and Economic Sudies, Bank of Japan. (0): Real exchange rae dynamics revisied: A case wih nancial marke imperfecions, Journal of Inernaional Money and Finance, 30(7), Fujiwara, I., and K. Ueda (03): The scal muliplier and spillover in a global liquidiy rap, Journal of Economic Dynamics and Conrol, 37(7), Gadanecz, B. (004): The Syndicaed Loan Marke, BIS Quarerly Review. Gambacora, L. (008): How do banks se ineres raes?, European Economic Review, 5(5), Gerali, A., S. Neri, L. Sessa, and F. M. Signorei (00): Credi and Banking in a DSGE Model of he Euro Area, Journal of Money, Credi and Banking, 4(s), Gerler, M., and P. Karadi (0): A model of unconvenional moneary policy, Journal of Moneary Economics, 58(),

47 Gerler, M., and N. Kiyoaki (00): Financial Inermediaion and Credi Policy in Business Cycle Analysis, in Handbook of Moneary Economics, ed. by B. M. Friedman, and M. Woodford, vol. 3 of Handbook of Moneary Economics, chap., pp Elsevier. Giannoni, M. P. (04): Opimal ineres-rae rules and in aion sabilizaion versus price-level sabilizaion, Journal of Economic Dynamics and Conrol, 4(C), 0 9. Graham, L., and S. Wrigh (007): Nominal Deb Dynamics, Credi Consrains and Moneary Policy, The B.E. Journals of Macroeconomics, 7(). Gropp, R., and A. K. Kashyap (00): A New Meric for Banking Inegraion in Europe, in Europe and he Euro, NBER Chapers, pp Naional Bureau of Economic Research, Inc. Hannan, T. H., and A. N. Berger (99): The Rigidiy of Prices: Evidence from he Banking Indusry, American Economic Review, 8(4), Kim, J., S. Kim, E. Schaumburg, and C. A. Sims (008): Calculaing and using second-order accurae soluions of discree ime dynamic equilibrium models, Journal of Economic Dynamics and Conrol, 3(), Kim, J., and S. H. Kim (003): Spurious welfare reversals in inernaional business cycle models, Journal of Inernaional Economics, 60(), (007): Two Pifalls of Linearizaion Mehods, Journal of Money, Credi and Banking, 39(4), King, R., and A. L. Wolman (999): Wha Should he Moneary Auhoriy Do When Prices Are Sicky?, in Moneary Policy Rules, NBER Chapers, pp Naional Bureau of Economic Research, Inc. 47

48 Kiyoaki, N., and J. Moore (997): Credi Cycles, Journal of Poliical Economy, 05(), 45. Kobayashi, T. (008): Incomplee Ineres Rae Pass-Through and Opimal Moneary Policy, Inernaional Journal of Cenral Banking, 4(3), Lane, P. R., and G. M. Milesi-Ferrei (007): The Exernal Wealh of Naional Mark II, Journal of Inernaional Economics, 73(), (008): The Drivers of Financial Globalizaion, American Economic Review, 98(), Lubik, T., and F. Schorfheide (006): A Bayesian Look a he New Open Economy Macroeconomics, in NBER Macroeconomics Annual 005, Volume 0, NBER Chapers, pp Naional Bureau of Economic Research, Inc. Mandelman, F. S. (00): Business cycles and moneary regimes in emerging economies: A role for a monopolisic banking secor, Journal of Inernaional Economics, 8(), 38. (0): Business Cycles and he Role of Imperfec Compeiion in he Banking Sysem, Inernaional Finance, 4(), McGuire, P., and N. Tarashev (006): Tracking Inernaional Bank Flows, BIS Quarerly Review, 7(4). Perri, F., and V. Quadrini (0): Inernaional Recessions, NBER Working Papers 70, Naional Bureau of Economic Research, Inc. Ravenna, F., and C. E. Walsh (006): Opimal moneary policy wih he cos channel, Journal of Moneary Economics, 53(),

49 Slovin, M. B., and M. E. Sushka (983): A Model of he Commercial Loan Rae, Journal of Finance, 38(5), Smes, F., and R. Wouers (003): An Esimaed Dynamic Sochasic General Equilibrium Model of he Euro Area, Journal of he European Economic Associaion, (5), Smes, F., and R. Wouers (007): Shocks and Fricions in US Business Cycles: A Bayesian DSGE Approach, American Economic Review, 97(3), Sorensen, C. K., and T. Werner (006): Bank Ineres Rae Pass-Through in he Euro Area: A Cross Counry Comparison, Working Paper Series 580, European Cenral Bank. Seinsson, J. (008): The Dynamic Behavior of he Real Exchange Rae in Sicky Price Models, American Economic Review, 98(), Suherland, A. (00): A Simple Second-Order Soluion Mehod for Dynamic General Equilibrium Models, Discussion Paper Series, Deparmen of Economics 00, Deparmen of Economics, Universiy of S. Andrews. Teranishi, Y. (05): Smoohed Ineres Rae Seing by Cenral Banks and Saggered Loan Conracs, Economic Journal, 5(58), Tille, C. (00): The Role of Consumpion Subsiuabiliy in he Inernaional Transmission of Moneary Shocks, Journal of Inernaional Economics, 53(), van Leuvenseijn, M., C. K. Sorensen, J. A. Bikker, and A. A. van Rixel (03): Impac of bank compeiion on he ineres rae pass-hrough in he euro area, Applied Economics, 45(), Woodford, M. (003): Ineres and Prices: Foundaions of a Theory of Moneary Policy. Princeon Universiy Press, Princeon. 49

50 Yun, T. (996): Nominal Price Rigidiy, Money Supply Endogeneiy, and Business Cycles, Journal of Moneary Economics, 37(-3), (005): Opimal Moneary Policy wih Relaive Price Disorions, American Economic Review, 95(),

51 Appendix A: Equilibrium Condiions Consumers From he consumer s uiliy maximizaion problem given by equaions () and (), he ineremporal opimaliy condiion is derived: C +P P + = ( + i ) E C ; (57) and + i = E (X ;+ ) : (58) Also, he opimaliy condiion for di ereniaed labor supply is given by C = w (h) P = w P : (59) Linear dis-uiliy in labor supply resuls in a homogenous wage rae. Similarly for he foreign counry, we have " C (C ) # = ( + i ) E + P ; (60) P+ + i = E (X ;+ ) S + S ; (6) and (C ) = w (h ) P = w P ; (6) where S denoes he nominal exchange rae. By combining (57), (58), (60) and (6), under he assumpion where boh counries are equally wealhy iniially, he following 5

52 inernaional risk sharing condiion deermines he real exchange rae e. C = e (C ) ; (63) where e = S P : P Final Goods Producers The cos minimizaion problem by he nal goods producer leads o P H; = P Y H; Y F; Y ( ) = P ; (64) Y H; and By plugging hem ino producion funcion (7), P F; = ( ) P Y Y F; : (65) P = P H; P F; : (66) By solving similar cos minimizaion problem on equaion (8), he sandard de niion of aggregae price index and relaive demands are derived as Z P H; = p (h) 0 dh ; (67) and p (h) y (h) = Y H;: (68) P H; 5

53 Similarly, in he foreign counry, Y F; = ( ) P F; Y P ; (69) Y H; = P H; Y P ; (70) P = P H; P F; ; (7) Z PH; = p (h) 0 dh ; (7) and y (h) = " # p (h) Y P H;: (73) H; Inermediaed Goods Producers From he pro maximizaion problem in equaion (6) by inermediae-goods producer h, ogeher wih equaions (3) and (68), he opimal price seing condiions are derived as p (h) = where we also assume R (h) w ( + ) ( ) exp (z ) = exp ( ) R (h) w ; (74) exp (z ) ( + ) ( ) = : Similarly, for he foreign rms, p (h ) = R (h ) w ; (75) and he law of one price implies p (h ) = S p (h ) : 53

54 Banks The loan demand is expressed by combining equaions (3), (4), (5), (59), (67), (68), (7), (73) and (74) as q (h) = w exp (z ) R (h) R Y H; + Y H; : (76) To maximize he pro maximizaion in equaion (0) ogeher wih equaion (76), he privae bank opimally ses is loan rae ~ R o saisfy X E T = () T P C T w T exp (z ) Y H;T + YH;T P T C w exp (z T ) Y H; + YH; R R T " ~R R R R T # ( + i T ) u T = 0: ( + ) ( ) R T (77) From equaion (5), ~R 6 R = 4 R R : (78) By combining equaions (77) and (78), 6 R 4 R F = K ; (79) where X F E () T T = = + E P C P C T w T exp (z ) Y H;T + YH;T P T C w exp (z T ) Y H; + YH; +w + exp (z ) Y H;+ + Y H;+ P + C w exp (z + ) Y H; + Y H; R R T R R + (80) F +; 54

55 and X K E () T T = = ( + i ) exp ( ) exp (u ) R P C T w T exp (z ) Y H;T + YH;T R ( + i T ) u T P T C (8) w exp (z T ) Y H; + YH; R T ( + ) ( ) R T P C + E +w + exp (z ) Y H;+ + Y H;+ R P + C K +: w exp (z + ) Y H; + YH; R + Similarly, for loan rae seings in he foreign counry, R 6 R F = K ; (8) where F P = + E C+ w Y + F;+ + Y F;+ R P+ (C ) w Y F; + YF; R + F +; (83) and K = ( + i ) R P + E C+ w Y + F;+ + Y F;+ R P+ (C ) w Y F; + YF; R + K +: (84) Aggregaion Wih equaions (3), (5), (5), (64), (67), (70), (68), (73) and (74), P Y + P P H; Y PH;! = exp (z ) l ; (85) where l Z 0 l (h) dh; 55

56 By using equaions (5) and (78), his can be expressed as a dynamic equaion. Z 0 R (h) dh (86) R 6 R = ( ) 4 R R R : Similarly for he foreign counry, P Y + P P F; Y PF;! ( ) = l ; (87) and R 6 R = ( ) R + R : (88) By combining (67), (74) and (5), he price index is relaed o marginal coss: P H; = exp ( ) w R ; (89) exp (z ) Wih equaion (5), Similarly, for price seings by he foreign rms, P H; = exp ( ) w R S exp (z ) : (90) P F; = w R ; (9) and P F; = S w R : (9) 56

57 Sysem of Equaions 7 Equaions (), (3), (57), (59), (60), (6), (63), (64), (65), (66), (67), (70) (7), (79), (8), (80), (8) (84), (83), (85), (86), (87) (88), (89), (7), (9) and (9) deermines dynamic pahs of,, ~w, ~w, e, Y H;, Y F;, Y, Y H;, Y F;, Y, R, F, K, R, F, K, l,, l,, p H;, p H;, p F;, p F;, C and C under he opimal moneary policy for i and i. Nominal variables are de-rended as P P ; ~w w ; ~w w P P ; p H; P H; P ; p H; P H; ; p P F; P F; ; p F; P F; : P P C C + = ( + i ) E + ; C = ~w ; " C (C ) # = ( + i ) E + ; (C ) = ~w ; + C = e (C ) ; Y H; = (p H; ) Y ; Y F; = ( ) (p F; ) Y ; YF; = ( ) p F; Y YH; = p H; Y 6 R 4 R ; ; F = K ; 57

58 C F = + E + ~w + exp (z ) Y H;+ + Y H;+ R C F +; ~w exp (z + ) Y H; + YH; R + K = ( + i ) exp ( ) exp (u ) C +E + ~w + exp (z ) Y H;+ + Y H;+ R R C ~w exp (z + ) Y H; + YH; R 6 R F = K ; R + K +; C + ~w + Y F;+ + Y F;+ R = + E (C ) ~w Y F; + YF; R+ C + ~w + Y F;+ + Y F;+ R + E (C ) ~w Y F; + YF;! Y + Y = exp (z ) l ; p H; F K = + i R p H; 6 R = ( ) 4 R R R! Y + Y ( ) = exp (z ) l ; p F; p F; R 6 R = ( ) R + R R + F +; ; ; K +; p H; = ~w R exp ( ) ; exp (z ) p H; = ~w R exp ( ) ; e exp (z ) p F; = ~w R ; p F; = e ~w R ; C = Y ; 58

59 C = Y ; = p H; p F; ; and = p H; p F; : Under he assumpion = 0:5, hese collapse o equaions (6) o (6). 59

60 Appendix B: Ramsey Policy Cooperaion The opimal moneary policy under cooperaion is deermined by equaions below: Y E +Y + + Y Y ( ) Y Y = 0; exp ( ) R R Y exp ( ) R R exp (z ) 0 + E Y exp ( ) R = 0; R E +R + R + exp ( ) R Y exp (z ) + Y R = 0; + E + Y + R = 0; R +R + (R ) + exp ( ) R exp (z ) + Y (R ) = 0; Y + 5 ( ) g F " + 0 # = 0; + 8 ( ) g ( ) F 8 " < : ( ) ( ) + # 9 = ( ) ; = 0; ( ) exp (z ) g exp (z ) F + 8 ( ) g ( ) F = 0; g = 0; 60

61 8 + 8 g ( ) = 0; 4 = 0; 6 = 0; 7 = 0; 9 = 0; 3 = ; and 4 = : i denoes he Lagrange muliplier for he consrains (6) o (6), respecively. Noncooperaion The opimal moneary policy under noncooperaion is deermined by equaions below: Domesic Y + ~ 3 E ~ 3 Y ( ) Y = 0; exp ( ) R +Y + Y ~ 0 + E ~ ~ Y Y exp ( ) R = 0; exp ( ) R R exp (z ) ~ R E ~ +R + R + ~ exp ( ) R Y exp (z ) + Y exp ( ) R = 0; ~ + E ~ + + = 0; 6

62 ~ R E ~ +R 9 + ~ ( + i ) exp (u ) (R ) (R ) + ~ R exp (z ) Y = 0; ~ + ~ 5 ( ) g F " + ~ 0 # = 0; ~ ~ 7 " ( ) # ( ) F + ~ 8 ( ) g ( ) F + ~ 9 g ( ) K 8 + ~ < : ( ) " ( ) # 9 = ( ) ; = 0; ~ 3 + ~ 5 ( ) g F + ~ 8 ( ) g ( ) F + ~ 9 ( ) g ( ) K = 0; ~ 7 " ( ) ~ 5 + ~ 5 g = 0; # ~ 8 + ~ 8 g ( ) = 0; ~ 7 ~ 9 + ~ 9 g ( ) = 0; ~ 4 = 0; ~ 6 = 0; ~ 3 = ; and ~ 4 = 0: 6

63 ~ i denoes he Lagrange muliplier for he consrains (6) o (6) for he domesic cenral bank s maximizaion problem. Foreign Y + 3 E 3 +Y + + Y exp ( ) R R Y Y exp (z ) exp (z ) ( ) ( ) Y = 0; R 0 + E = 0; R E +R + R 6 ( + i ) exp ( ) exp (u ) R + exp ( ) R Y = 0; exp (z ) + E + Y + R = 0; + R R + + (R ) + Y R exp (z ) + Y (R ) = 0; + 8 ( ) g ( ) F 8 " + < : ( ) ( ) # 9 = ( ) ; = 0; ( ) g F + 6 ( ) g K + 8 ( ) g ( ) F = 0; g = 0; g ; g ( ) = 0; 63

64 7 = 0; 9 = 0; 3 = 0; and 4 = : i denoes he Lagrange muliplier for he consrains (6) o (6) for he foreign cenral bank s maximizaion problem. Ramsey Opimal Seady Sae Cooperaion The Ramsey opimal seady saes under cooperaion is as follows: F = K = F = K = ; = = ; + i = + i = ; Y = l = l = ; R = R = ; = = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 0; 0 = = = ; 64

65 and 3 = 4 = : Noncooperaion On he oher hand, he Ramsey opimal seady saes under noncooperaive framework are as follows: F = K = F = K = ; = = ; + i = + i = ( + ) ; Y = l = l = ; + R = R = + ; ~ = ~ = ~ 3 = ~ 4 = ~ 5 = ~ 6 = 0; ~ 7 = ( ) ; + ~ 8 = ; + ~ 9 = ~ = ; + ~ 0 = ; + ~ = 0; ~ 3 = ; ~ 4 = 0; = = 3 = 7 = 8 = 9 = 0 = 0; 65

66 4 = ( ) ; + 5 = ; + 6 = = ; + = ; ( ) + 3 = 0; and 4 = : 66

67 Appendix C: Seady Sae Welfare Comparison When 6=, welfare under cooperaion is given by W C = WC = ; while ha under noncooperaion is W N = WN = + : Thus, he seady sae welfare di erence is W C W N = = " + + # : Equaion (36) depics ha is always increasing in and i akes + Thus, W C W N > 0 when =. when 0 < < and > : When =, welfare under cooperaion is W C = W C = ; 67

68 while ha under noncooperaion is W N = WN = = log log () + < W C : 68

69 Appendix D: Second Order Approximaion of Loan Phillips Curve Here, he second order approximaion of he loan Phillips curve in he domesic counry will be described. Firs, we denoe Then, equaion (79) can be wrien as r = ~ R R : (93) r F = K ; or ^r + ^F = ^K : (94) where F and K are slighly di erenly de ned from equaions (7) and (8): F E K E X T = X T = () T f ;T ; () T k ;T ; f ;T Y T exp ( T ) R ;T ; (95) k ;T Y T ( + i T ) exp (u T ) R ;T ; (96) R T and R ;T R R T 69

70 Second order approximaion leads o F ^F + ^F X = E () T T = ^F + ^F = ( ) E f T = ^f T + ^f T X () T ^f T + ^f T ; and ^K + ^K X = ( ) E () ^k T T + ^k T : T = Then, equaion (94) can be ransformed ino X ^r = ( ) E () T ^k;t ^f;t + E T = X ^r E T = X T = () T ^k;t + ^f ;T ^k;t ^f;t () T ^k;t + ^f ;T : (97) This is because ^F ^K ^F + ^K = ^r E X T = () T ^ft + ^k T ; where he higher order erms are ignored. Equaions (95) and (96) are expressed in log exac form as f ;T ( ) ^Y T T + ( ) ^R ;T ; and k ;T = ( ) ^Y T + i T + u T ^RT ^R ;T : 70

71 Thus, ^k ;T ^f;t = i T + T ^RT ^R;T z T ^R;T and ^k ;T + ^f ;T = ( ) ^Y T + i T ^ T ^RT + ( ) ^R ;T x T + ( ) ^R ;T : Then, equaion (97) furher collapses o ^r = + E X ^r Z + ( ) E () T z T ^R;T X T = T = () T h x T + ( ) ^R ;T i z T ^R;T : (98) where Wih equaions: Z E X T = () T h x T + ( ) ^R ;T i : (99) ^r + = ^r +Z + + E + E X T =+ X T =+ () T (+) z T ^R+;T () T (+) h x T z T x T ^R+;T + ( ) ^R +;T z T ( ) ^R +;T i ; ^k +;T ^f+;t = z T ^R+;T ; and ^r + = ^K + ^F+ = E X T =+ () T (+) z T ^R+;T ; 7

72 Equaion (98) is furher ransformed ino ^r ^r + + ^R +; = z + E + x z ^r + + ^R +; ^r Z Z + + E ( ) ^r E ^R + +; ( ) ( ) ^R +; E : ( ) (00) Second order approximaion of equaions (78) and (93) leads o r ^R ; ( ) ^R ; ( ) : (0) Subsiuion of he approximaed equaion (0) ino (00) resuls in = ( ) ^R ^R ; ; + ( ) ^R ; Z ( ) ( ) ( ) E ( ) ( ) + X X T T = X E T T = z T x T z T + ^R ; (0) + E T ^R T;T T = On he oher hand, Z in (99) can be expressed recursively as ( ) Z = x + E ^R +; + Z + : (03) 7

73 Finally, solving equaions (0) and (03) a ime 0 leads o K 0 = ( ) ( ) E X =0 i + + u ( ) ( ) X + E ^z + ( ) ^Y + i ^ ^R i + + u =0 + X E ^R ^R ; =0 ^R ^R where K 0 = ^R 0; ( ) ^R 0; ( ) + ( ) ^R 0;0 Z 0 + ^R 0;0 : Thus, E X =0 E X =0 i + + u 8 >< >: ^R h( ) ^Y i i ^ ^R ( )( ) ^R ^R i + ^R 9 >= >; : 73