MNB Working papers 21/5 Karin Rabisch The role of financial marke srucure and he rade elasiciy for moneary policy in open economies
The role of financial marke srucure and he rade elasiciy for moneary policy in open economies April 21
The MNB Working Paper series includes sudies ha are aimed o be of in e res o he academic communiy, as well as researchers in cenral banks and elsewhere. Sar ing from 9/25, aricles undergo a refereeing process, and heir publicaion is supervised by an ediorial board. The purpose of publishing he Working Paper series is o simulae commens and suggesions o he work prepared wihin he Ma gyar Nem ze i Bank. Ciaions should refer o a Ma gyar Nem ze i Bank Working Paper. The views expressed are hose of he auhors and do no necessarily reflec he official view of he Bank. MNB Working Papers 21/5 The role of financial marke srucure and he rade elasiciy for moneary policy in open economies* (A ôkepiaci szerkeze és a külkereskedelmi rugalmasságok haása a nyio gazdaságok moneáris poliikájára) Wrien by: Karin Rabisch** Published by he Ma gyar Nem ze i Bank Sza bad ság ér 8 9, H 185 Bu da pes hp://www.mnb.hu ISSN 1585 56 (online) * I hank Rober Kollmann, Margaria Rubio and Péer Benczúr for useful discussions, as well as paricipans a he MNB-CEPR Workshop 29, he Vienna MacroeconomicsWorkshop 29 and ASSET 29. ** Deparmen of Economics, Cenral European Universiy and Research Deparmen, Magyar Nemzei Bank. E-mail: rabischk@ceu.hu.
Conens Absrac 5 1 Inroducion 6 2 The Model 9 Households 9 Firms 12 Resource Consrains and Aggregae Budge Consrains 13 Relaive Prices and The Terms of Trade 14 3 Opimal Moneary Policy and Inernaional Risk Sharing 15 Definiion of Equilibrium and Descripion of Consrains for Ramsey Problem 16 Definiion of Ramsey problem under cooperaion 18 Definiion of Ramsey problem under independenly acing moneary auhoriies 18 4 Parameerizaion 2 5 Resuls 21 Ramsey Seady Sae 21 Transmission under flexible versus sicky prices 21 The Role of Financial Marke Srucure and he Trade Elasiciy for Sabilizaion 23 The Role of Risk Sharing for Gains from Policy Coordinaion and Gains over he Flexible Price Allocaion 25 Sensiiviy Analysis 26 6 Conclusion 27 References 28 Appendices 3 A Tables and Figures 3 mnb working papers 21/1 21/5 3
Absrac The degree of inernaional risk sharing maers for how moneary policy should opimally be conduced in an open economy. This is because risk sharing affecs he way in which moneary policy is affeced by erms of rade consideraions. In a sandard wo-counry model wih monopolisic compeiion and nominal rigidiies I consider differen assumpions on inernaional financial markes complee markes, financial auarky and a bond economy and a large region for he crucial parameer of he rade elasiciy. There are hree main resuls: one, he prescripion of (producer) price sabiliy as he opimal policy is obained only as a special case, while in general i is opimal o deviae from a sricly zero inflaion rae. Two, while gains from inernaional policy coordinaion are generally small, hey become poenially subsanial when inernaional risk sharing is poor and wealh effecs from shocks across counries are large. And, hree, when inernaional financial markes are incomplee, here are also (someimes considerable) gains over he flexible price allocaion achievable. JEL: E52, E58, F42. Keywords: moneary policy, risk sharing, price sabiliy, policy coordinaion, financial marke srucure, rade elasiciy. Összefoglalás A nemzeközi kockázamegoszás méréke fonos meghaározója a nyio gazdaságok opimális moneáris poliikájának. A kockázamegoszás foka ugyanis ha arra, hogy a moneáris poliika mikén veszi figyelembe a cserearány-megfonolásoka. Egy szenderd, kéországos modellben monopoliszikus verseny és ragadós áraka feléelezve vizsgálom a nemzeközi őkepiacra vonakozó különböző leheséges felevéseke (eljes piacok, pénzügyi auarkia, illeve egyelen kövény esee), valamin a kereskedelmi rugalmasság paraméereink széles skálájá. A három fő eredmény a kövekező: (i) a ermelői árindex sabilizálása csak egy speciális eseben opimális, álalában célszerű elérni a szigorú inflációs célköveésől; (ii) a nemzeközi moneáris poliikai kooperáció előnyei álalában kicsik, kivéve alacsony nemzeközi kockázamegoszás és erős országok közöi jövedelemhaások eseén; (iii) ha a nemzeközi őkepiacok nem eljesek, a rugalmas árak mellei allokáció (néha jelenős mérékben) elmarad az opimálisól. mnb working papers 21/5 5
1 Inroducion This paper presens a unifying framework o sudy he role of he degree of inernaional risk sharing for opimal moneary policy in open economies. The main resuls are hreefold: one, he prescripion of (producer) price sabiliy as he opimal policy is obained only as a special case, while in general i is opimal o deviae from a sricly zero inflaion rae. Two, while gains from inernaional policy coordinaion are generally small, hey become poenially subsanial when inernaional risk sharing is poor and wealh effecs from shocks across counries are large. And, hree, when inernaional financial markes are incomplee, here are also (someimes considerable) gains over he flexible price allocaion achievable. The framework used o address hese issues is a relaively sandard wo-counry imperfecly-compeiive sicky-price model of he open economy. In such a seup, a number of imperfecions characerize he economy ha ypically exer influence on he way moneary policy should opimally be conduced. As in he closed economy boh counries are characerized by wo inernal disorions: because of monopolisic compeiion oupu is inefficienly low, and he economy s adjusmen is subjec o nominal rigidiies in he form of quadraic price adjusmen coss (assumed o be se in producer currency), which opens up an oupu gap relaive o a world of flexible prices. In addiion, here is an exernal disorion which sems from a counry s monopoly power on he relaive price of is expors o impors, ha is, on is erms of rade (T OT ). 1 The presen paper shows ha his inernaional dimension of moneary policy, ha is, he size and direcion in which movemens in he erms of rade ener ino he consideraion of moneary policy, depends crucially on he degree of inernaional risk sharing. The degree of risk sharing in urn, is deermined by he srucure of inernaional financial markes assumed, as well as by he precise parameerizaion of he rade elasiciy. For his purpose, I conras hree sylized assumpions on he inernaional financial marke srucure namely, complee markes (CM), financial auarky (FA) and an incomplee markes-bond economy (IM) and consider a wide range of he rade elasiciy. The laer is of imporance as i governs he srengh in which relaive wealh is affeced in response o counry specific shocks. In he special case of a uniary elasiciy (combined wih log-uiliy) movemens in he erms of rade provide full auomaic risk sharing independen of he financial marke srucure assumed. 2 An analysis of he role of he degree of risk sharing for opimal moneary policy can herefore only be addressed a values of he elasiciy away from uniy. In he previous lieraure here has been no consensus on he choice of he value of he rade elasiciy i has been all over he place. Therefore, I choose no o calibrae his parameer o a specific fixed value, bu consider insead a large range for i, where domesic and foreign consumpion goods are allowed o be eiher subsiues or complemens. Moreover, I consider also very low elasiciies in my analysis which have been shown o be necessary o reproduce ogeher wih an incomplee financial marke srucure he empirically observed low degrees of inernaional risk sharing. I sudy opimal moneary policy using a Ramsey approach and assuming ha policymakers can commi. Gains from inernaional policy coordinaion are compued by conrasing welfare achieved by a world social planner wih he welfare achieved under uncoordinaed (Nash) policy compeiion. On he mehodological side, he presen paper conribues o he lieraure by laying ou a well defined Nash policy game in a dynamic economy in he framework of he Ramsey approach. In he following, I briefly discuss each of he hree resuls found and posiion and conras hem wih respec o he lieraure. Turning o he firs resul in more deail, I find ha for almos all cases of financial marke assumpions and policy regimes considered he implicaions are ha full sabilizaion is no he opimal moneary policy. By 1 Throughou he paper, I refer o he erms of rade when alking abou he influence of inernaional prices on policy decisions. However, i should be noed ha, equivalenly, I could have referred o he real exchange rae as he relevan inernaional price o consider (which in his model always moves proporionally o he erms of rade). 2 In his case any income effecs from shocks are offse by proporional movemens in he inernaional relaive price (see, Cole & Obsfeld (1991), Corsei & Peseni (21)). 6 mnb working papers 21/5 MNB WORKING PAPERS 21/5 5
Inroducion full sabilizaion I refer o a policy of achieving fully sable producer prices, such ha he erms of rade behave exacly as in he world wihou nominal rigidiies and he flexible price allocaion is replicaed (fully closing he oupu gap). Only in he case of complee markes under coordinaion and in he case of he uni-elasiciy- auomaic perfec risk sharing producer prices should be kep fully sabilized. 3 Moreover, I documen he precise paerns when i is opimal o fully sabilize, undersabilize or oversabilize he economy. An ineresing resul is ha he opimal policy is found o be exacly he opposie under CM and FA: when i is opimal for an independenly acing policymaker o undersabilize he economy under CM (full risk sharing), he finds i opimal o oversabilize he economy under FA (no risk sharing). 4 In a recen conribuion De Paoli (29) documens a relaed resul. She sudies he role of financial marke srucure on opimal moneary policy in a small open economy in he form of comparing differen argeing rules and finds ha he welfare based ranking of hese rules is in opposie order for he case of CM and FA. 5 In paricular, he above resul can be undersood as follows: le us consider a emporary domesic produciviy increase as an example. Also, consider ha domesic and foreign goods can easily be subsiued in consumpion. In response o he shock, an independenly acing policymaker under CM finds i opimal o somewha undersabilize he economy. Tha is, while he lowers he ineres rae o make oupu supply deermined he does so no o he full degree o replicae he flexible price allocaion and leaves a small oupu gap open. This also means ha he resuling erms of rade depreciaion is somewha less pronounced and he policymaker enjoys a more favorable relaive price compared o he flexible price world. By expanding oupu a lile less he can reduce his labor effor a he prospec of keeping his uiliy from consumpion as perfec inernaional risk sharing holds and goods can easily be subsiued. 6 The siuaion is a differen when counries are in financial auarky. In such a seup he policymaker finds i opimal o iniiae an oupu increase ha more ha closes he oupu gap and ha depreciaes he erms of rade even more ha under flexible prices, ha is, he oversabilizes he economy. He does so because under FA oupu and consumpion are very closely linked, so even hough labor effor has o be increased, his is worh i as consumpion can be raised as well. Furhermore, even he coordinaed policymaker under FA will follow his policy, in fac, will iniiae an even larger erms of rade depreciaion. This is because he policymaker under FA, coordinaed or uncoordinaed, has o consider an addiional disorion in his design of moneary policy, he fac ha he degree of risk sharing is oo low and can be improved hrough a larger adjusmen in inernaional relaive prices. A second resul is he dependence of welfare gains from policy coordinaion on he degree of risk sharing. The wo-counry seup allows for an explici consideraion of Nash versus coordinaed opimal policies, which allows o also draw conclusions abou he gains from policy cooperaion. These are found increasing for elasiciies of subsiuion away from uniy and are ypically an order of magniude larger in he case of complemenariy beween domesic and foreign goods, paricularly when risk sharing is low (FA and IM). In addiion, I find ha welfare gains from coordinaion are bigger under complee markes when goods are subsiues, bu urn ou o be bigger under financial auarky/ incomplee markes when goods are complemens. This is due o he fac ha he lack of risk sharing becomes even more imporan when, because of a low elasiciy, inernaional prices move srongly and wealh effecs are large. Suherland (24) has previously sudied he role of marke srucure for he gains of policy coordinaion in a simple saic model, finding ha welfare gains are raher small. In addiion he only considers he case when goods are subsiues. On he one hand welfare gains are likely o be larger under more realisic, dynamic price rigidiies 7, on he oher hand he case of low subsiuion elasiciies is of paricular ineres as i is precisely he specificaion 3 This is he isomorphism and inward-looking resul of early conribuions (see, e.g., Clarida e al. (21), Galí & Monacelli (25), or Corsei & Peseni (21), Benigno & Benigno (23)). 4 This finding is summarized graphically in Figure 2, which plos he impac responses (o a produciviy shock) of producer price inflaion as a funcion of he rade elasiciy. 5 The simple rules she considers are producer price inflaion argeing, consumer price inflaion argeing, and a fixed exchange rae regime. 6 Under Nash policy compeiion, however, boh counries behave in his fashion and he oo low erms of rade volailiy does no longer provide full risk sharing, leading o welfare losses. 6 MNB WORKING PAPERS 21/5 mnb working papers 21/5 7
INTRODUCTION needed o reconcile he predicions of he heoreical model wih he low degree of risk sharing observed in he daa. I is ineresing o noe, ha even if policymakers ac coordinaely price sabiliy is, in general, no found o be he opimal oucome. The reason for his finding is ha he flexible price financial auarky economy (or bond economy) is no efficien as counries do no involve in any (oo lile) risk sharing. A policymaker ha can, because of sicky prices, influence he erms of rade/ he real exchange rae finds i opimal o le i respond more closely o he way i would under complee financial markes, such ha he equilibrium responses of he real exchange rae under he opimal policy is also doing some risk sharing. 8 This desire o improve inernaional risk sharing can be very srong, such ha even in he Nash case, welfare gains over he flexible price allocaion can be made, when financial markes are incomplee. The res of he paper is organized as follows. Secion 2 describes he model, secion 3 discusses he role of moneary policy in a world wih various degrees of inernaional risk sharing and ses up he relevan Ramsey problems. Secion 2 discusses he model s parameerizaion. Secion 5 discusses he resuls for opimal moneary policy depending on he degree of inraemporal elasiciy and depending on he financial marke srucure, looking a he implicaions for he opimaliy of price sabiliy and he gains from policy coordinaion. Secion 6 concludes. 7 Faia & Monacelli (24) also sudy he role of he erms of rade on opimal policy in a model wih Roemberg adjusmen coss, bu only consider he case of complee markes. 8 A relaed poin is made recenly by Corsei e al. (29). 8 mnb working papers 21/5 MNB WORKING PAPERS 21/5 7
2 The Model The world economy consiss of a Home counry (H) and a Foreign counry (F ), each of which is specialized in he producion of one ype of radable good. Households and firms are defined over a coninuum of uni mass. Home and Foreign households are indexed by j ε [,1] and j ε [,1] respecively. Each good is produced by firms in a number of varieies, indexed by h in he Home counry and by f in he Foreign counry. Each variey is an imperfec subsiue o all oher varieies and is produced under condiions of monopolisic compeiion. Firms face quadraic adjusmen coss in heir price seing decision and are assumed o se he price in he foreign marke in heir own currency (producer currency pricing). I absrac from modeling moneary fricions by considering a cashless economy. Unless necessary oherwise, in he following I only discuss he problem of Home agens, wih an undersanding ha he problem for Foreign agens is symmeric variables of Foreign agens are marked wih an aserisk. HOUSEHOLDS Preferences and Budge Consrain Household j maximizes her lifeime expeced uiliy: E β U C, L = E = β = C 1 σ ( j ) 1 σ L1+κ ( j ) 1 + κ, (1) where β is he discoun facor, C ( j ) is consumpion and L(j) is labor effor. Consumpion C ( j ) is a consan-elasiciy-of-subsiuion (CES) baske over domesic and foreign goods: C ( j ) = γ 1ω ω 1 C ω H, ( j ) + (1 γ) 1 ω C ω 1 ω F, ω ω 1 ( j ), (2) where ω denoes he rade elasiciy, ha is, he inraemporal elasiciy of subsiuion beween domesic and foreign goods, and where parameer γ 1 is he degree of home bias in consumpion. For each household j 2 he consumpion indices of Home varieies and Foreign varieies are defined as: C H, = 1 C (h, j ) θ 1 θ d h θ θ 1, C F, = 1 C ( f, j ) θ 1 θ d f θ θ 1, (3) where C (h, j ) and C (f, j ) are respecively consumpion of Home variey h and Foreign variey f by agen j a ime. Household j maximizes equaion (1) subjec o he budge consrain. Each period household j receives wage income, W L ( j ), and dividends from he monopolisic firms hey own, Π ( j ), and has consumpion expendiure P C (j). The availabiliy of any asses of domesic household j depends on he assumpions of he srucure of inernaional financial markes. Throughou he paper, I consider hree possible scenarios: complee markes (CM), financial auarky (FA) and an incomplee markes bond economy (IM). 8 MNB WORKING PAPERS 21/5 mnb working papers 21/5 9
THE MODEL Under complee markes he household has access o a full se of sae-coningen (Arrow-Debreu) securiies. Le Q s +1 s denoe he price of one uni of Home currency delivered in period + 1 coningen on he sae of naure a + 1 being s +1. Wih complee markes, Q s +1 s is he same for all individuals. Le B H, j, s+1 denoe he claim o BH, unis of Home currency a ime + 1 in he sae of naure s +1, ha household j buys a ime and brings ino ime + 1. Q s +1 s and BF, j, s+1 are defined similarly in erms of unis of Foreign currency. ɛ denoes he nominal exchange rae (unis of Home currency per uni of Foreign currency). The budge consrain under complee markes is hen given by: Q s +1 s BH, j, s+1 + Q s+1 s ɛ B F, j, s+1 s +1 s +1 B H, 1 j, s + ɛ B F, 1 j, s + W L ( j ) + Π ( j ) P C ( j ). (4) If he wo economies are in financial auarky no asses can be raded inernaionally. Le B H, ( j ) and B F, ( j ) denoe bonds denominaed in eiher domesic and foreign currency. Under inernaional financial auarky, he domesic currency bond, B H,, ha can be raded only domesically. Equivalenly, foreign agens can rade a foreign currency bond, B F,, bu also only wihin heir counry.9 The budge consrain of domesic household j under financial auarky hen becomes: B H, ( j ) = B H, 1 (j) R 1 + W L ( j ) + Π ( j ) P C ( j ). (5) Finally, I consider he case of he incomplee markes-bond economy. I now assume ha boh counries can now engage in financial rade hrough one of he one-period nominal bonds. In paricular, I assume ha he foreign currency denominaed bond, B F,, can be raded inernaionally (and ne foreign wealh is iniially zero). 1 While his assumpion inroducing a small asymmery ino he oherwise symmeric seup, I do so because he domesic and foreign currency bond holdings are no separaely idenified. 11 Following Schmi-Grohé & Uribe (23) and Benigno (21), o render he incomplee markes economy saionary, I assume ha domesic agens face a quadraic adjusmen cos when aking on an inernaional asse posiion differen from heir long-run (zero) posiion. The budge consrain under he assumpion of he incomplee markes-bond economy is: B H, ( j ) + ɛ B F, 1 ( j ) + φ ɛ B F, 1 ( j ) 2 P (6) 2 P B H, 1 (j) R 1 + ɛ B F, 1 ( j ) R 1 + W L ( j ) + Π ( j ) P C ( j ). 1 1 9 Tha is, he asse marke clearing condiions under FA are B H, ( j ) d j = and B ( j ) d j =. F, 1 The nominal bonds are in zero ne-supply worldwide, so ha: 1 1 1 B H, ( j ) d j = and B F, ( j ) d j + B ( j ) d j = F, 11 Moreover, i is imporan o noe ha he inernaionally raded asse is exogenously resriced o be he foreign currency bond only, for which a long-run zero posiion is simply assumed. In paricular, his seup does no ener he recen lieraure on issues of porfolio choice and endogenous non-zero posiions (see, e.g. Devereux & Suherland (28) and Tille & van Wincoop (27)). 1 mnb working papers 21/5 MNB WORKING PAPERS 21/5 9
The Model Households Inraemporal Consumpion Allocaion Household j minimizes, each period, is consumpion expendiure subjec o obaining a uni of he final consumpion good. Denoing wih P he Lagrange muliplier o ha problem 12 gives he following opimal demand funcions: c (h, j ) = θ θ p (h) p C ( j ) = γ (h) ω PH, H, C ( j ), (7) P H, P H, P θ θ p ( f ) p c ( f, j ) = C ( j ) = (1 γ) ( f ) ω PF, F, C ( j ), (8) P F, For given Home-currency prices of varieies, p (h) and p ( f ) he uiliy-based CPI, P, is given by: P = γ P 1 ω H, P F, P 1 + (1 γ) P 1 ω F, 1 ω, (9) where P H, = 1 p (h) 1 θ d h 1 1 θ, P F, = 1 p ( f ) 1 θ d f 1 1 θ. (1) Households Labor Supply and Ineremporal Allocaion Denoe wih λ ( j ) he Lagrange muliplier of he household s budge consrain. Household j s firs order condiions wih respec o C ( j ) and L ( j ) are idenical for all possible financial marke assumpions and are given by: P C σ ( j ) L κ ( j ) = W. (11) Under complee financial marke, he firs order condiion w.r.. home and foreign Arrow-Debreu securiies are given by: Q C+1 ( j ) σ s +1 s = βe C ( j ) P P +1 which can be combined o obain he risk sharing equaion:,q C+1 ( j ) σ s +1 s = βe C ( j ) P ɛ +1, (12) P +1 ɛ ɛ P C = ( j ) σ. (13) P C ( j ) 12 Formally, 1 min 1 p (h)c (h, j ) d h + p ( f )C ( f, j ) d f P C ( j ). 1 MNB WORKING PAPERS 21/5 mnb working papers 21/5 11
THE MODEL Under financial auarky he domesic currency bond can only be held domesically such ha 1 = βe C+1 ( j ) σ R C ( j ) P P +1. (14) Under he incomplee markes bond economy, he firs order condiion w.r.. home and foreign bond are similarly given by: 1 = βe C+1 (j) σ R C ( j ) P P +1,1 = βe R C+1 ( j ) C ( j ) σ P ɛ +1. (15) P +1 ɛ The nominal ineres rae R and R he wo economies. can be hough of as he underlying insrumens of moneary policy in FIRMS Producion and Price Seing The producion funcion is assumed o be linear in labor: Y (h) = Z L (h), (16) where Z is he level of produciviy, which is given by a counry-specific AR(1) process wih persisence parameer ρ Z and sandard deviaion σ Z. Firms operae under condiions of monopolisic compeiion aking ino accoun he downward-sloping demand for heir produc and se prices o maximize heir profi. They are assumed o se he prices in he foreign marke in heir own currency, ha is, I consider he scenario of producer currency pricing (PCP). Firms are small, in he sense ha hey ignore he impac of heir pricing and producion decisions on aggregae variables and price indices. When firms se heir prices hey have o ake ino consideraion a quadraic adjusmen cos, where parameer α measures he degree of price sickiness: φ (h) = α 2 p (h) 2 p 1 (h) 1. (17) The presence of Roemberg adjusmen coss makes he firms price seing decision dynamic, which inroduces richer and arguably more realisic equilibrium dynamic effecs of moneary policy han in a seup where prices are se one period in advance. The richer descripion of price sickiness is also likely o be more appropriae for quaniaive welfare analysis. I assume hroughou ha he law of one price holds, such ha for each variey h we have ɛ p (h) = p (h). Each producer chooses is price p (h) such as o maximize is oal marke value: E Ω, p (h)(1 + τ) MC (h) p (h) = P H, θ CH, + C H, α p (h) 2 p 1 (h) 1 2 P H,, (18) 12 mnb working papers 21/5 MNB WORKING PAPERS 21/5 11
The Model where MC is he marginal cos ha minimizes labor inpu, which is equal o all firms, M C (h) = MC = W /Z, Ω,s is he household s sochasic discoun facor beween ime and s, and where τ sands for a producion subsidy ha can be used o offse he disorion from monopolisic compeiion. Firms Opimaliy Condiions The firm s opimal price seing condiion is derived as: = θ p (h) CH, P + C 1 p (h) H, θ MC (h) (θ 1)(1 + τ) (19) H, P H, P H, p (h) PH, p+1 α p 1 (h) 1 p 1 (h) + E Ω,+1 α (h) p+1 (h) P H,+1 1 p (h) p 2 (h). Parameer α = corresponds o he case of flexible prices, in which case he price is se as he a simple markup over curren marginal coss. I focus aenion on a symmeric equilibrium where all domesic producers charge he same price, adop he same echnology and herefore choose he same demand for labor. This implies p (h) = P H,, p (h) = P H,, L (h) = L, Π (j) = Π. RESOURCE CONSTRAINTS AND AGGREGATE BUDGET CONSTRAINTS The resource consrain for each variey h and each variey f are given by: 1 Y (h) = 1 c (h, j )d j + c (h, j )d j + 1 φ ( j ) d j = C H, + C H, + φ, (2) 1 Y (f ) = 1 c ( f, j )d j + c ( f, j )d j + 1 φ ( j ) d j = C F, + C F, + φ. (21) Symmery across all households j gives C ( j ) = C, L ( j ) = L, λ ( j ) = λ, and implies ha condiions (7)-(8), (11)-(13), (14) and (15) mus also hold for aggregae variables and indices j can be dropped. In addiion, using equilibrium in he asse markes he aggregae budge consrain under he case of financial auarky, having imposed clearing condiions, can be expressed as: = W L + Π P C. (22) In he incomplee markes bond economy, afer imposing asse marke clearing condiions he budge consrain becomes: ɛ B F, + φ ɛ B 2 F, 1 P = B F, 1 2 R 1 + W L + Π P C. (23) P 12 MNB WORKING PAPERS 21/5 mnb working papers 21/5 13
THE MODEL RELATIVE PRICES AND THE TERMS OF TRADE The erms of rade is defined as he price of impors o expors, be wrien as: P F, ɛ P H,, which given he law of one price can T OT = P F, P H,. (24) Using he opimal consumer price level resuling from he inraemporal allocaion problem, i is possible o express all relaive prices as a funcion of he erms of rade only. In paricular, he real exchange rae, which is he price of a foreign consumpion bundle relaive o domesic consumpion bundle, ha is, RER = ɛ P /P, is relaed o he erms of rade by: RER = f RER γ + (1 γ )T OT 1 ω 1 1 ω T OT = γ + (1 γ)t OT 1 ω 1 1 ω. (25) The PPI-o-CPI raios are defined as p H, P H, /P and p F, P F, /P of he erms of rade only: and can also be wrien as funcions p H, = f p H p F, = f p F T OT = γ + (1 γ)t OT 1 ω 1 1 ω, (26) T OT = γ T OT ω 1 + (1 γ ) 1 1 ω. 14 mnb working papers 21/5 MNB WORKING PAPERS 21/5 13
3 Opimal Moneary Policy and Inernaional Risk Sharing Having compleed he descripion of he model economy, I now urn o sudying he opimal moneary policy in his wo-counry imperfecly compeiive sicky price economy. The paricular focus will lie on how he degree of inernaional risk sharing affecs he scope and goals of moneary policy and if he predicions for opimal moneary policy in his oherwise sandard model are alered. For his reason, i is useful o firs reflec on he disorions ha characerize he economy. As in he closed economy boh counries are characerized by wo inernal disorions: price sickiness and monopolisic compeiion. The laer produces an inefficien level of oupu. The oher inernal disorion, price sickiness, prevens efficien adjusmen o he disurbances ha affec he economy and opens up a gap of oupu relaive o he flexible price allocaion. The consensus resul of he lieraure is ha a procyclical policy can remove he sicky-price disorion by making producion supply-deermined and can resore he flex-price equilibrium if desirable. In addiion o he wo inernal disorions, here is an exernal disorion which sems from counries monopoly power on he inernaional relaive price, ha is, on heir erms of rade. The srengh and direcion in which erms of rade consideraions ener moneary policy crucially depends on he amoun of inernaional risk sharing, which in urn depends on a) he assumpions on asse markes and b) he degree of subsiuabiliy beween domesic and foreign goods. In order o sudy his exernal dimension of moneary policy, ha is, he role of he monopoly power over he erms of rade for moneary policy I follow Suherland (24) and Benigno (29) in considering a seup in which he presence of a producion subsidy fully offses he disorion from monopolisic compeiion. This allows me o isolae he influence of erms of rade consideraions for he conduc of moneary policy. 13 In he seup of complee financial markes, a policymaker herefore only faces he disorion of sicky prices and he fac ha he has monopoly power over he erms of rade. While a coordinaed policymaker fully akes ino accoun he effec of movemens in he erms of rade on world welfare, a non-coordinaed policymaker will seek o use his monopoly power o maximize his own counry s welfare, ignoring he effec of such a sraegy on he oher counry. Under incomplee markes (FA or IM) policymakers also face a siuaion in which he degree of inernaional risk sharing is oo low. Therefore a coordinaed policymaker will aim a using his insrumen, on he one hand, as before, o make demand supply-deermined, on he oher hand, o ry o improve inernaional risk sharing. A non-coordinaed policymaker s erms of rade consideraions are now influenced by boh his desire o il he erms of rade in his favor, bu also by improving risk sharing properies o some degree. For all financial marke assumpions considered, he single mos imporan parameer ha influences boh size and direcion of erms of rade consideraions is he inraemporal elasiciy of subsiuion beween domesic and foreign goods, he rade elasiciy. I deermines he srengh of expendiure swiching effecs of he exchange rae/ erms of rade and herefore he impac of moneary policy on goods demand in differen counries. I also influences he degree o which counries are subjec o asymmeric income shocks. If he elasiciy is close o uniy hen relaive price changes are largely offse by changes in oupu volumes and he erms of rade provide srong auomaic risk sharing (see Cole & Obsfeld (1991)). I assume hroughou ha policymakers can credibly commi in he sense ha hey can choose he enire fuure (sae-coningen) evoluion of he conrol variables, once and for all, a dae zero. The assumpion of commimen is imporan, as privae secor expecaions abou he evoluion of prices affec he forward 13 Sensiiviy analysis will be conduced in secion 5 and will allow for a relaxaion of his simplifying assumpion. 14 MNB WORKING PAPERS 21/5 mnb working papers 21/5 15
OPTIMAL MONETARY POLICY AND INTERNATIONAL RISK SHARING looking erms in he dynamic pricing equaions. I sudy hese issues by employing a Ramsey ype approach, following closely he seps oulined in Schmi-Grohé & Uribe (29) o obain he seady sae and dynamics implied by he Ramsey equilibrium. 14 In his seup he opimal moneary policy enails a Ramsey planner which maximizes a social objecive funcion subjec o he privae secor s consrains. 15 I compare opimal commimen policy under Nash compeiion and under cooperaion, and compue welfare gains from coordinaion from a second order approximaion o he Ramsey equilibrium equaions. DEFINITION OF EQUILIBRIUM AND DESCRIPTION OF CONSTRAINTS FOR RAMSEY PROBLEM An equilibrium requires ha households and firms behave opimally, as described by he above opimaliy condiions. Specifically, given exogenous processes for Z and Z, a policy for R and R and given iniial condiions, a symmeric world compeiive equilibrium is a se of prices and quaniies ha saisfy he Home and Foreign consumers opimaliy condiions, equaions (7)-(11), and heir foreign counerpars, ogeher wih: he risk sharing equaion (13) under complee financial markes equaion (14) and he budge consrain, equaion (23), under he incomplee markes-bond economy he budge consrain, equaion (22), under he financial auarky maximize firms profis, meaning ha prices are se according o (19) and similarly in he foreign economy, saisfy he marke clearing condiions for each asse and each good, in all he markes where i is raded, and saisfy he resource consrains. I is possible o reduce he sysem of equilibrium condiions o a sysem of equaions in C, C, L, L, π H,, π F,, and T OT only given exogenous processes for Z and Z, and for a policy for R and R. In paricular, plugging in for he demand funcions (7) and (8) ogeher wih heir foreign counerpars, making use of he fac ha π = p H, 1 p H, π H,, π = p F, 1 π, and by using he funcional relaionships beween he real exchange p F, F, rae and he erms of rade (equaion (25)) and he PPI-o-CPI raio and he erms of rade (equaion (26)), i is possible o wrie he equilibrium as being described by equaions (27)-(33) below. Equaions (27)-(28) are he wo Euler equaions, equaions (29)-(3) he wo price seing equaions, equaions (31)-(32) he wo resource consrains, and equaions (33a), (33b) or (33c) are he relevan opimaliy condiions ha hold under complee markes, financial auarky or he bond economy respecively. 1 = βe σ C+1 1 R C π +1, (27) 14 This builds on previous work on he sudy of opimal policy in dynamic economies, see e.g., (Ramsey (1927)), Akinson & Sigliz (1976), Lucas & Sokey (1983), Chari e al. (1991). 15 While mos sudies of opimal moneary policy in he recen lieraure build on a linear-quadraic approximaion approach in he spiri of Roemberg & Woodford (1997), Woodford (23), and Benigno & Woodford (25), recenly, he Ramsey ype approach has been employed in an increasing number of dynamic equilibrium models wih monopolisic compeiion and nominal rigidiies. Examples include, among ohers, Khan e al. (23), Schmi-Grohé & Uribe (25, 27), and Faia & Monacelli (24). 16 mnb working papers 21/5 MNB WORKING PAPERS 21/5 15
Opimal Moneary Policy and Inernaional Risk Sharing MAGYAR NEMZETI BANK 1 = βe R C σ +1 1 C π +1, (28) α π H, 1 π H, = ω p H, C + RER ω C L κ θ C σ (θ 1)(1 + τ) (29) Z p H, σ C+1 p H,+1 +E α π H,+1 1 π H,+1, C p H, α π F, 1 π F, = p F, ω RER ω C + C θ L κ C σ Z p F, (θ 1)(1 + τ) (3) σ C+1 p F,+1 +E C p α π F,+1 1 π F,+1, F, Z L = p H, ω C + RER ω C, (31) Z L = p F, ω RER ω C + C, (32) under complee markes: RER = C σ, C (33a) under financial auarky: p H, Z L φ = C, (33b) under incomplee markes, bond economy 16 : RER b F, + φ 2 1 + ψrer b F, = βe R C+1 C RER b F, 2 = RER b F 1 R 1 π σ 1 π +1 RER +1 RER + p H, Z L C φ., (33c) 16 The budge consrain is also expressed in real erms, where bf, = B F, /P. 16 MNB WORKING PAPERS 21/5 mnb working papers 21/5 17
OPTIMAL MONETARY POLICY AND INTERNATIONAL RISK SHARING DEFINITION OF RAMSEY PROBLEM UNDER COOPERATION To derive he Ramsey opimal moneary policy under cooperaion, I se up he problem of a world social planner ha aims a maximizing he counry-size weighed average measure of welfare, which are given by he lifeime expeced uiliies: ave ra g e W = 1 2 E = β U C, L + U C, L. (34) Le i = C M, FA, I M denoe he hree assumpions on financial marke srucure. Define he vecor of Ramsey consrains as RC i, by verically sacking equilibrium equaions (27)-(33). Also, le superscrip C refer o he case of policymakers acing under coordinaion. I define he vecor of Lagrange mulipliers a ime aached o consrains (27)-(33) by Λ i,c, where Λ i,c =[λ i,c H1,, λi,c F 1,, λi,c H2,, λi,c F 2,, λi,c H3,, λi,c F 3,, λi,c 4, ].17 In his dynamic economy i is no possible o solve in closed form he decenralized economy as a funcion of policy insrumens only. Differen from Chari & Kehoe (1999) he Ramsey problem is herefore se up by carrying he model s equilibrium condiions as consrains, ha implicily define he economy s allocaion as a funcions of he insrumens, R and R. In paricular, following Schmi-Grohé & Uribe (29), I find he porion of he Ramsey problem ha is relevan for he purpose of compuing he opimal policy from he imeless perspecive by: L C M C =... + 1 2 U C, L + U C, 1 L + 2 βe U C+1, L +1 + U C +1, L +1 + 1 β Λi,C 1 RC i 1 + Λi,C E RC i + βe Λi,C +1 RC i +1. (35) The opimal policy can hen be described by he firs order condiions of he Lagrangian wih respec o Λ i,c, and C,C, L, L,π H,,π F,,T OT, R, R. DEFINITION OF RAMSEY PROBLEM UNDER INDEPENDENTLY ACTING MONETARY AUTHORITIES If moneary auhoriies ac uncoordinaed, he home and foreign policymaker each maximize heir respecive naional welfare, aking as given he oher counry s choice of policy, ha is, eiher ineres rae R or R. In paricular, he objecive of he domesic and he foreign policymaker are given, respecively, by: W = E β U C, L, (36) W = = E β U C, L. (37) = A Nash equilibrium is defined as a siuaion in which boh counries choose he level of consumpion, labor and inflaion, and he policy insrumen o maximize heir objecive, bu where he oher counry s consumpion, labor and inflaion depend hemselves on he policy choice of he firs (no simply aken as given). 17 As he incomplee markes-bond economy he he vecor of consrains includes wo financial marke specific equaions and he size of Lagrange mulipliers is accordingly enlarged. 18 mnb working papers 21/5 MNB WORKING PAPERS 21/5 17
Opimal Moneary Policy and Inernaional Risk Sharing MAGYAR NEMZETI BANK As such, he home Ramsey policymaker should ake as consrains is own Euler equaion, pricing equaion and resource consrain and financial marke equilibrium condiion as he relevan Ramsey consrains, plus he foreign consumpion, labor and inflaion choices as a funcion of is choice of he policy insrumen. Bu hese are nohing else han implici funcions defined by he foreign Euler equaion, pricing equaion and resource consrain. Therefore, each policymaker akes he enire compeiive equilibrium condiions, given by equaions (27)-(32) and he relevan financial marke equilibrium equaion, equaion (33a), (33b) or (33c), as consrains o he Ramsey policy problem. 18 The vecor of consrains for he domesic and he foreign auhoriy is given, as under coordinaion, by RC i for i = C M, FA, I M. Also, define he sequence of he vecor of Lagrange mulipliers aached o consrains in RC i by Λ i,n λ i,n F 3,, λ i,n 4, =[λ i,n H1,, λi,n F 1,, λi,n H2,, λi,n F 2,, λi,n H3,, λi,n F 3,, λi,n ] and Λ i,n = [λ i,n 4, H1,, λ i,n F 1,, λ i,n H2,, λ i,n F 2,, λ i,n H3,, ], where superscrip N refers o he scenario of complee markes and Nash policymakers. The relevan porions of he Ramsey problems of he Lagrangians of he opimal policy problem of he domesic and foreign policymaker are hen given by: L i,n =... + U C, L + βe U C +1, L +1 + 1 β Λi,N 1 RC i 1 + Λi,N E RC i + βe Λi,N +1 RC i L i,n =... + U C, L + βe U C +1, +1 L +1, (38) (39) + 1 β Λ i,n 1 RC i 1 + Λ i,n E RC i + βe Λ i,n +1 RC i +1. Taking derivaives of L i,n wih respec o Λ i,n, and C,C, L, L,π H,,π F,,T OT, and R summarizes he opimal policy of he domesic moneary auhoriy, condiional on a foreign policy R. Equivalenly, he derivaives of L i,n wih respec o Λ i,n, and C,C, L, L,π H,,π F,,T OT, and R summarize he opimal policy of he foreign moneary auhoriy, condiional on domesic policy R. The full Nash equilibrium can hen be obained by combining he Ramsey opimaliy condiions of he domesic and foreign policymakers (i should be noed, ha he firs order condiion w.r.. he vecor of Lagrange mulipliers of boh policymakers are idenical, ha is, hey simply reurn he equaions of he compeiive equilibrium). 19 18 This is in conras o Faia & Monacelli (24) and Liu & Pappa (28) who ake he each counry s own opimaliy condiions as a consrains in he uncoordinaed Ramsey problem (aking as given he oher counry s consumpion, labor and inflaion choices in addiion o he policy insrumen). 19 As in he case of coordinaion, he incomplee markes bond economy consiss of wo financial marke relaed equilibrium condiions, and he vecors of Lagrange mulipliers are correspondingly expanded o Λ I MN =[λ I MN MN MN MN MN MN MN, λi, λi, λi, λi, λi, λi, λ I MN I MN ] and Λ = [λ I M N, H1, F 1, H2, F 2, H3, F 3, 4, 5, H1, λ I M N F 1,, λ I M N H2,, λ I M N F 2,, λ I M N H3,, λ I M N F 3,, λ I M N 4,, λ I M N ]. 5, 18 MNB WORKING PAPERS 21/5 mnb working papers 21/5 19
4 Parameerizaion The baseline parameerizaion of he model is summarized in Table 1, in secion 5 I consider some parameer variaions. The discoun facor β is aken o be.99, implying an annual ineres rae of abou 4 percen. Parameer θ is aken o be 6, which implies a markup over marginal cos of abou 2 percen. Parameer γ (γ ), which is he weigh on domesic good in he domesic (foreign) consumpion baske, is se o.75 (.25) in he baseline case, implying ha here is posiive home bias. The value of he parameer of he quadraic adjusmen cos in price seing, α, is 6, which corresponds, ogeher wih he chosen value for θ, o a parameer of abou.75 in a Calvo syle price seing or a price sickiness of abou four quarers, based on he slope coefficien in he linearized pricing equaions (see, e.g. Faia & Monacelli (28)). The degree of risk aversion, σ, is considered o be 1 in he baseline parameerizaion (which implies log uiliy in consumpion). The inverse Frisch elasiciy of labor supply, κ, is equal o 2, a value ha lies well in he region used in he lieraure (e.g. Roemberg & Woodford (1997) sugges a value of.47, while micro daa on (low) esimaed Frisch elasiciies sugges values as high as 5, which is chosen e.g. by Benigno (29). The producion subsidy parameer is se such ha i offses he monopolisic compeiion disorion, ha is, τ, is se equal o 1/(θ 1). As for he exogenous processes, I consider, in line wih mos of he inernaional business cycle lieraure, a raher persisen echnology shock wih auocorrelaion coefficien of ρ =.95, and wih sandard deviaion of he shock of σ ɛ, σ ɛ =.1. Finally, I consider a wide range for he value of he rade elasiciy, ranging from goods being very complemenary in consumpion o goods being very subsiuable. As I show, he value of he rade elasiciy is a mos crucial parameer in deermining he influence of erms of rade consideraions in shaping opimal moneary policy in an open economy. Also, here is no consensus on he choice for his parameer in he lieraure. In he rade lieraure, Lai & Trefler (22) esimae, for individual goods, rade elasiciies of around 5 and higher. In he business cycle lieraure, he rade elasiciy is ypically aken o be lower. Backus e al. (1995) use elasiciies beween and 5, Chari e al. (22) assume a value of 1.5. A number of recen conribuions have also emphasized he role of a low elasiciy of inraemporal subsiuion (well in he complemenariy region) ogeher wih an incomplee financial markes srucure in he ransmission of produciviy shocks across counries, in paricular in addressing sylized facs on inernaional relaive prices and he low degrees of inernaional risk sharing observed in he daa (see e.g., Heahcoe & Perri (22), Corsei e al. (28), Thoenissen (28), Enders & Mueller (29)). In paricular, as Corsei e al. (28) show, he volailiy of he erms of rade or he exchange rae becomes paricularly high around a hreshold of he rade elasiciy ha is relaed o he degree of home bias and lies a 1 1 2γ.2 For values of he rade elasiciy close o ha hreshold he erms of rade under incomplee financial markes behave markedly differen han under complee financial markes, leading o low degrees of risk sharing. Thus, an analysis of he effecs of varying degrees of inernaional risk sharing for opimal moneary policy should also specifically consider his region of low elasiciies. 2 Moreover, hey show ha for values of he rade elasiciy below he hreshold, he T OT appreciae in response o a home produciviy increase which leads o a decrease in foreign consumpion (which is in line wih empirical response for he case of he US), whereas above he hreshold he T OT depreciae and ransmission o he oher counry is posiive. 2 mnb working papers 21/5 MNB WORKING PAPERS 21/5 19
5 Resuls RAMSEY STEADY STATE Secion 2 has shown ha he Ramsey equilibrium under he various financial marke assumpion and under coordinaion or Nash is obained as he sysem of equaions of firs order condiions derived from he appropriae Ramsey problem. To deermine he long-run inflaion rae associaed o he opimal policy problems above, one needs o solve he seady-sae versions of he se of efficiency condiions. In all economies and regimes considered, he seady sae (gross) inflaion rae associaed o he opimal policy problem is found o be equal o 1, as can be seen from he firs order condiion wih respec o π H, and π F,.21 Hence he Ramsey planner would like o generae an average (ne) inflaion rae of zero. The inuiion for his resul is simple. Under commimen, he planner canno sysemaically affec he economy hrough moneary surprises and, hus, here is no a erms of rade exernaliy as he one discussed in Corsei & Peseni (21) and Clarida e al. (21). Tha is, he planner canno on average resor o movemens in inflaion o aler he relaive purchasing power of is residens. The planner herefore aims a choosing a long-run inflaion rae ha minimizes he cos of adjusing prices, which is summarized by he quadraic erm. The openness dimension of he desire of adjusing he erms of rade can, herefore, drive he planner s behavior only in he presence of equilibrium flucuaions (as induced by counry-specific shocks) around he same long-run seady sae. TRANSMISSION UNDER FLEXIBLE VERSUS STICKY PRICES To faciliae he analysis of opimal moneary policy, I firs examine a useful benchmark in which price adjusmen is flexible, and hen describe he dynamics under sicky prices. In his flexible price environmen, here is no scope for moneary policy. I sudy his case in deail however, as he flexible price allocaion is a naural reference case, and I will, in he following, ofen relae he opimal moneary policy o such a benchmark. Under flexible prices a produciviy increase in he domesic economy leads o a higher abundance of domesic goods. This ranslaes ino a decrease in he price of domesic goods resuling in a depreciaion of he domesic erms of rade, making domesic goods relaively cheaper and channeling world demand owards domesic goods. Figure 1 shows he responses o he domesic produciviy shock of major variables for he hree financial marke srucures (CM, FA, and IM-Bond) and for he case where goods are eiher subsiues (ω = 3), complemens (ω =.7) or are uni-elasic (ω = 1). Le s focus firs on he case of goods being subsiues and consider he scenario of complee financial markes. The increase in domesic produciviy leads o a domesic consumpion increase, labor effor rises as he home economy ges more producive and he erms of rade deeriorae. Enjoying a more favorable price and because i is easy o subsiue o he now more abundan domesic good he foreign counry also benefis 21 This is he case even if he monopolisic disorion were no offse. In paricular, he Ramsey firs order condiion w.r.. πh, is given by: = ξ i α π 2H, H, 1 + ξ i ξ i C 3H, 3H, 1 α 2πH, 1 ξ i R 1H, 1 1 C 1 σ f p H (T OT) f p H (T OT 1) C C 1 σ f p H (T OT) f p H (T OT 1) which, a seady sae (as ξ i = ξ i = ξ i 3H, 3H, 1 3H and ξ i = ξ i = ) implies 1H, 1H = ξ i 2H α (π H 1). 2 MNB WORKING PAPERS 21/5 mnb working papers 21/5 21
RESULTS from he domesic produciviy shock. In paricular, under complee markes, he erms of rade depreciae jus enough o equalize he marginal uiliy benefi from he produciviy shock in boh counries, as dicaed by he risk sharing equaion. In he oher exreme case of financial auarky, he response of he erms of rade is somewha less pronounced. While he erms of rade sill depreciaes as an equilibrium response o he now more abundan domesic goods, i does so o a much lesser exen han in he case where marginal uiliy had o be equalized. As no sae-coningen asses have been raded promising he Foreign counry par of he benefis, Home labor effor does no increase, he expansion in domesic oupu is herefore lower han in he complee markes case, and he fall in he price of domesic goods relaive o foreign goods (ha is, he erms of rade deerioraion) in urn less pronounced. When goods are subsiues he TOT and labor move oo lile under incomplee financial markes relaive o CM. The ransmission of he produciviy shock is somewha differen when goods are complemens. Generally speaking, a lower elasiciy of subsiuion implies ha for any given change in quaniies, higher movemens in he price are necessary o bring abou hese movemens in quaniies. Tha is, under all financial marke srucures, he erms of rade responses are now much sronger han in he case where goods are subsiues. In addiion, he TOT now depreciaes more in he case of incomplee financial markes han under complee markes. Because home and foreign goods are complemenary in uiliy from consumpion, he (produciviy-induced) higher abundance of domesic goods also leads o a higher demand for foreign goods. If markes are complee he foreign counry is herefore bound o expand is oupu by increasing is labor effor which ends o ake some of he pressure of he erms of rade increasing. Under financial auarky such an increase in foreign oupu is absen, as a resul he increased demand for he foreign goods wihou a counerbalancing increase in supply for i leads o a deerioraion of he erms of rade ha is even sronger. The lower he rade elasiciy, he sronger is he erms of rade depreciaion, and he foreign counry increasingly benefis from he domesic produciviy increase. Summarizing, now, when goods are complemens he TOT move oo much under incomplee markes relaive o CM. Finally, le s urn o he case in which goods are uni-elasic. If he elasiciy is uniy hen relaive price changes are compleely offse by changes in oupu volumes. In his knife-edge case, he income effec of he required erms of rade depreciaion (given he relaively higher produciviy in Home) balances he incenive o swich expendiure owards Home goods: relaive wealh is always unaffeced in response o counry specific shocks and ha complee risk sharing is always obained independen of he financial marke srucure assumed. 22 Under sicky prices, i is cosly for firms o change heir prices which as a resul don adjus insananeously. As is well known in he lieraure, a policy of producer price argeing would, however, lead o an exac replicaion of he flexible price allocaion. If producer prices P H and P are rigid, he policymaker can iniiae F he necessary policy response a decrease in he nominal ineres rae ha booss demand and depreciaes he home erms of rade, such ha is response behaves as if here were flexible prices. Home goods are hen cheaper relaive o Foreign goods in boh Home and he Foreign counry. As demand shifs in favor of he goods wih he lowes relaive price, world consumpion of Home goods increases relaive o consumpion of Foreign goods, ha is, here is "expendiure swiching". While he replicaion if he flex-price allocaion is possible, he adjusmen under sicky prices requires acion on he par of he moneary policymaker. Also, if i is he opimal moneary policy o exacly replicae he flexible price allocaion depends on he disorions ha characerize he economy. As described in secion 3 i should be expeced ha open economy aspecs he fac ha counries have some degree of monopoly power over he erms of rade, and ha he degree of inernaional risk sharing may be oo low will generally have an influence on he degree of opimal sabilizaion ha moneary policy should provide. The nex secions sudies hese issues in deail. 22 Sricly speaking, he hreshold where relaive price changes are compleely offse by changes in oupu volumes lies only a uniy because of my assumpion of log-uiliy (ha is a coefficien of relaive risk aversion, σ = 1). More generally his hreshold depends on he inraemporal elasiciy, he ineremporal elasiciy and he degree of home bias and is given by ω = (2γ 1 + σ)/(2γσ). 22 mnb working papers 21/5 MNB WORKING PAPERS 21/5 21