Endogenous Currency of Price Setting in a Dynamic. Open Economy Model *

Transcription

1 Endogenous urrency of rice Seing in a Dynamic Open Economy Model Michael B. Devereux Universiy of Briish olumbia and ER harles Engel Universiy of Wisconsin and NBER June 5, 200 Absrac Many papers in he recen lieraure in open economy macroeconomics make differen assumpions abou he currency in which firms se heir expor prices when nominal prices mus be pre-se. Bu o dae, all of hese sudies ake he currency of price seing as exogenous. This paper ses up a simple wo-counry general equilibrium model in which exporing firms can choose he currency in which hey se prices for sales o foreign markes. We make wo alernaive assumpions abou he srucure of inernaional financial markes: one where here are complee markes for hedging consumpion risk inernaionally, and he oher wihou risksharing possibiliies. Our resuls are quie sharp: exporers will generally wish o se prices in he currency of he counry ha has he mos sable moneary policy. When moneary sabiliy is similar among counries, here is an equilibrium where firms from all counries se heir price in he currency of he buyer (local currency pricing. Bu excep for a special case where money variances are exacly idenical across counries, here is no equilibrium where all firms se expor prices in heir own currencies (producer currency pricing. We hank paricipans a a workshop a he Federal Reserve Bank of New York for commens. Devereux hanks SSHR for financial suppor. Engel hanks NSF for suppor.

2 The new Keynesian macroeconomics provides a raionale for sicky nominal prices. When here are menu coss o changing prices, imperfecly compeiive firms migh find i more profiable o leave prices unchanged when here is a shock o coss or demand han o change he price. There is a growing lieraure in inernaional macroeconomics building on he new Keynesian sicky price framework ha provides microeconomic foundaions for analysis of open economies. In a much-cied paper, Obsfeld and Rogoff (995 assumed ha firms se prices in heir own currency when selling abroad. Subsequenly, a long lis of papers has invesigaed he effecs of alernaive assumpions abou he currency in which firms se prices when selling o foreign markes. Bu o dae, all of hese sudies have aken he currency of price seing as exogenous. Realisically however, a firm is unlikely o be indifferen beween pricing in domesic or foreign currency. When he firm sells abroad, would i prefer he price o be sicky in he producer s currency or he currencies of consumers? Tha quesion has been addressed previously in he lieraure, bu always in a parial equilibrium seing. The parial equilibrium seing is problemaic because i akes as exogenous variables ha are influenced by he equilibrium price-seing configuraion. For example, he behavior of labor coss or aggregae demand migh depend on how prices are se. We address he quesion of opimal choice of currency for price seing in a framework closely relaed o ha of Obsfeld and Rogoff ( Their model is a wo-counry general equilibrium framework in which here are sicky nominal prices. The Obsfeld-Rogoff (OR model makes many simplifying assumpions in order o be able o derive analyical soluions ha are helpful for developing inuiion. Thus i makes fairly specific assumpions abou household s preferences; abou producion funcions; abou he probabiliy disribuions of shocks o he A parial lis is Bes and Devereux (996, Tille (2000, Devereux and Engel (2000, Devereux, Engel and Tille (999, Bacchea and Van Wincoop (2000, orsei and eseni (200, and Suherland (200,

3 economy; and abou price seing behavior (specifically ha prices are rese every period. We will follow heir framework, which allows us o derive some very simple condiions under which firms will eiher se prices in advance in heir own currency ( producer-currency pricing or, or in consumers currencies ( local-currency pricing or L. We emphasize he imporance of moneary sabiliy in deermining he pricing choice in equilibrium. We find ha when here are large differences beween he variance of money supplies across counries, here is a endency for all firms o price in he currency of he counry wih he mos sable money supply. As Guillermo Oriz (999, he governor of he Banco de México, has commened: The pass-hrough of exchange raes o inflaion was much higher in Mexico han in anada, Ausralia or New Zealand. And his has o do a lo wih hisory, wih credibiliy of moneary policies, and his is one of he big challenges ha we are facing oday in Mexico in he conduc of moneary policy. And we have o really build sufficien credibiliy so ha his passhrough from exchange rae movemens o inflaion ceases o be such an auomaic reacion. In relaed work, Taylor (200 argues along similar lines, making he case ha passhrough from boh exchange raes and general coss may be endogenously deermined by a counry s inflaion performance. The essenial message of our resuls may be encapsulaed as follows. The more sable is a counry s moneary process, relaive o is neighbors, he more likely i is ha foreign exporers will se heir prices in ha currency, and he more sable will be ha counry s price level. By he same oken, because his counry s exporers will also end o se heir expor prices in he 2 Bacchea and van Wincoop (2000a, Devereux and Engel (2000, and Devereux, Engel, and Tille (999 have exended he Obsfeld-Rogoff model wih uncerainy o he local-currency pricing case, and o pricing schemes ha mix local-currency pricing and producer-currency pricing. 2

4 home currency, he price level of he counry s rading parners, wih less sable moneary processes, will be less sable. A he same ime, he resuls depend in an imporan way on he srucure of inernaional financial markes. When inernaional financial markes allow for full consumpion risk-sharing across counries, i is only relaive moneary sabiliy ha maers. The counry wih he more sable moneary process will have all world expors priced in is currency, even if neighboring counries also have quie sable moneary processes. Bu when markes for inernaional risksharing are absen, hen absolue moneary volailiy becomes imporan. In his case, as long as all counries have reasonably sable money supplies, we find ha he equilibrium configuraion of price seing will be ha all counries follow L, and exchange rae pass-hrough is zero. Bu his equilibrium will be eliminaed if moneary volailiy rises in one counry. In ha case, all world expors will be priced in he currency of he mos sable money supply. Bacchea and van Wincoop (2000b have also recenly addressed he quesion of opimal choice of currency for pricing in a general equilibrium model ha differs from ours only slighly in he preference assumpions. They find, as we do, ha in he absence of risk-sharing an equilibrium emerges in which all firms in boh counries are follow L pricing when agens are sufficienly risk averse. 3 However, hey confine hemselves o he case of idenical home and foreign money supply processes, so hey do no uncover he key resul of our paper ha he pricing equilibrium is deermined by differences in moneary variances across counries. Also, heir resuls are all from numerical simulaions, while our analyical resuls allow us o precisely characerize he condiions for various equilibria o emerge. In secion, we lay ou he model. In secion 2, we derive he equilibrium price-seing behavior under he assumpion of complee markes in nominal financial claims. We es he 3 In conras o us, hey find ha under complee markes in heir se-up here are no pure-sraegy equilibria. 3

5 sensiiviy of our findings o he assumpion of financial marke compleeness by reexamining, in secion 3, our conclusions in a seing where no financial claims are raded. Then in secion 4, we discuss broader consideraions ha are lef ou of our sylized model.. The model Here we ouline he feaures of he models we examine. There are wo counries. Infiniely-lived consumers in each counry maximize expeced lifeime uiliy, which is a funcion of consumpion, real balances and labor. They ake prices and wages as given. There is a coninuum of monopolisic firms in each counry. Each firm ses prices one period in advance. Firms can se differen prices for home and foreign consumers, and can se prices eiher in heir own currency or consumers currencies. Labor markes are compeiive and nominal wages are flexible. We will consider wo differen asse marke srucures. In one, here are complee markes in nominal coningen claims. In he oher, here is no inernaional rade in asses, and all firms are locally owned. Moneary auhoriies in each counry increase he money supply randomly and nominal exchange raes are floaing. Moneary randomness is he only source of uncerainy in he model. 4 roducers mus se prices prior o he realizaion of moneary shocks. This is an insiuional consrain in our model. In secion 4 we discuss how menu coss migh generae nominal price sickiness. rices fully adjus o moneary shocks afer one period; i.e., here is no persisence o he price-adjusmen process. 4 Our resuls are compleely unaffeced in boh he full risk-sharing and no risk-sharing case if we inroduce produciviy shocks o he producion process. Inuiively, i is because in boh cases he equilibrium exchange rae is unaffeced by produciviy shocks. We omi hose shocks from he paper o keep hings clean. 4

6 onsumers The represenaive consumer in he home counry is assumed o maximize = s U E β us, 0 < β < s= where u s = s M + χ ln s s ηl s, > 0. is a consumpion index ha is a geomeric average of home and foreign consumpion: n n = h f n n n ( n. We assume ha here are n idenical individuals in he home counry, 0 < n <. h and f are indexes over consumpion of goods produced a home and in he foreign counry, respecively: h = n 0 n h di f = ( n f n di The elasiciy of subsiuion beween goods produced wihin a counry is, which we assume o be greaer han. There is a uni elasiciy of subsiuion beween he home goods and foreign goods indexes. M are domesic real balances, and L is he labor supply of he represenaive home agen. The price index,, is defined by = n n h f, where h n = n 0 h di f = f n n di 5

7 There are n idenical individuals in he foreign counry. Their preferences are similar o home counry residens preferences. The erms in he uiliy funcion involving consumpion are idenical in he home and foreign counries. The funcional form for real balances and labor are he same as for he home counry residens, bu, for foreign residens, hey are funcions of foreign real balances and foreign labor supply. The opimal inra-emporal consumpion demands are given by: h h = n h h f f = n f f n h h = n = ( n f f h h di = h h f f di = f 0 n f We allow for wo alernaive asses marke srucures. In one, residens of each counry can purchase a full se of sae-coningen nominal bonds: here is full inernaional risk-sharing. In he oher, he polar opposie, here is no asse rade a all. Residens of one counry can only rade in commodiies a spo exchange raes, and here are no possibiliies for inernaional risksharing in asses markes. While boh cases are exremes, his comparison serves o highligh he role of inernaional risk-sharing mechanisms in deermining he form of price seing 5. Full risk-sharing When consumers have access o a full se of sae coningen bonds, hari, McGraan, and Kehoe (2000 show ha he following risk-sharing condiion (he M condiion obains 6

8 ˆ S = Γ 0, (. where S is he home currency price of foreign currency, and Γ 0 is a consan, depending on iniial condiions. 6 ˆ is he foreign-currency denominaed foreign price level. Throughou his paper, he ^ aop a nominal price indicaes ha i is denominaed in foreign currency, while a superscrip indicaes a foreign quaniy. onsumpion will differ across he wo counries only o he exen ha here are changes in he real exchange rae. No risk-sharing Wihou any risk-sharing possibiliies, commodiy rade mus balance across counries, or, equivalenly, domesic consumpion mus equal domesic income. Given our simple specificaion of preferences, his implies ha he nominal value of consumpion mus be equalized across counries, when evaluaed in any one currency: S ˆ = (.2 In addiion o he consumpion demand equaions lised above, we can derive he money demand equaion for he represenaive home-counry residen: M χ =, (.3 E ( d+ where E is he inverse of he gross nominal ineres rae, and ( d + d + = + + β is he pricing kernel for one period ahead dollars. Also, he rade-off beween consumpion and leisure is given by: 5 When he law of one price holds (as i does when all firms follow pricing, consumpion risk is compleely shared, even wihou complee asses markes, as OR (998 show. Bu under he L specificaion, he law of one 7

9 W =η. (.4 Governmen Governmen increases he money supply wih direc ransfers. The governmen budge consrain (in per capia erms is simply M = M + T. In addiion, we assume he money supply follows a random walk: M E ( =. (.5 M + An analogous equaion holds for he foreign money supply. Firms where Firms are monopolisic compeiors. The producion funcion for firm i is given by: Y i = L i, L i is employmen of firm i a ime. The objecive of he domesic firms is o se prices o maximize he expeced uiliy of he owners. When here is full risk-sharing, i does no maer wheher he owners of firms are home or foreign residens. Wihou risk-sharing, he naural assumpion o make is ha domesic firms are all owned by domesic residens. Bu under eiher asse marke srucure, prices mus be se before informaion abou random money supplies and produciviy shocks is known. The opimizaion problem can be expressed as one of maximizing he expeced presen value of profis using he marke nominal discoun facor for he owners of he firm. price does no hold. 8

10 While he firm mus se prices in advance, i has he opion of seing prices in one of wo ways: : roducers se he price in heir own currency. The price ha foreigners pay for domesic goods, and he price ha home residens pay for foreign goods flucuae when he exchange rae changes. L: roducers se he price in he consumers currency. rices consumers face do no respond a all o exchange rae changes. No sae-coningen pricing is allowed. Equilibrium relaionships The goods-marke equilibrium in he home counry is wrien as: L = n + ( n. h h There is an analogous condiion for he foreign counry. I is easy o verify from he money demand equaion, (.3, and he random-walk assumpion for money supplies ha: M = ( β. (.6 χ This implies ha he nominal ineres rae is consan, in equilibrium. An analogous equaion holds for he foreign counry. The soluion for he exchange rae depends on he degree of inernaional risk-sharing. Under full risk-sharing, (i.e. condiion (., equaion (.5 give us a soluion for he exchange rae: 6 We assume Γ 0 =. 9

11 M S =. (.7 M Wihou risk-sharing, we may use equaion (.2 and (.6 o obain he following soluion for he exchange rae: M ˆ S =. (.8 M While under full risk-sharing, he exchange rae will depend only on he exogenous sochasic realizaions of money, while in he economy wihou risk-sharing he exchange rae will depend on he way in which home and foreign price levels respond o moneary shocks. Finally, he leisure-consumpion radeoff, (.4, and equaion (.6 give us ηχ W = M. (.9 β 2. Opimal price seing wih full risk-sharing Now we look a he decision ha firm s make when hey se prices in advance. This decision has wo pars. The firs par concerns which currency he firm should se prices in. Then, given his decision, he firm mus choose a price. In each case, he firm maximizes profis evaluaed a he discoun facor relevan o heir owners. We firs examine he price seing decision under full risk-sharing. The quesion of which currency o choose for price seing can be examined for one firm in isolaion. When prices mus be se in advance, he currency of price seing will maer for expeced discouned profis of he firm. Bu he decision over which currency o se prices 0

12 will also depend upon he acions of all oher firms, for wo reasons. Firs, he firm (for insance he home firm selling o he foreign counry will compee wih all oher home firms wihin he indusry, and he currency in which hey price in will be relevan. Second, as shown in Devereux and Engel (2000, he currency in which prices are se has macroeconomic implicaions for aggregae demand, he consumer price index, employmen and GD. Boh he volailiy and mean of hese variables will differ in an economy wih relaive o an economy wih L. This may affec he decision faced by any one firm. Thus, in principle he decision over which currency o se prices in is a complex one, depending on he decision made by all oher firms. In fac, we will see ha our model produces a very simple and inuiive soluion. We adop he following procedure. Firs, looking a he home counry firm, we ask wheher if all home counry firms se heir expor prices in home currency (, is here an incenive for a single home firm o deviae, and se is expor price in foreign currency (choose L? 7 If he answer is yes, hen we can conclude ha is no an equilibrium oucome for home counry firms. Then we reverse he quesion by asking wheher if all home counry firms were o se heir expor prices in foreign currency (L, here is an incenive for any one home firm o deviae and se is price in domesic currency (choose. If he answer o his is yes, hen L is no an equilibrium for all home counry firms. By looking a he answer o boh quesions we can see wheher or L (or possibly boh consiue an equilibrium for home firms. Wha we find is ha he condiion o choose L when all oher firms choose L is he same as he condiion o choose L when all oher firms follow. So, if ha condiion is me, we conclude here is an equilibrium in which all firms follow L. 7 In principle, his decision migh depend on he pricing decisions of foreign producers also. In fac, as we ll see, i does no, so we can ignore his issue in our descripion.

13 Then by employing symmery, we can look a he decision of foreign firms. Finally, using he resuls for boh home and foreign firms, we can idenify an equilibrium configuraion of price seing in he world economy. Home firms follow The opimizaion problem can be expressed as maximizing he expeced presen value of profis using he marke nominal discoun facor for he owners of he firm. Since here is no ineremporal aspec o he firms opimizaion problems (see, Obsfeld and Rogoff (998, his reduces o maximizing one period ahead expeced profis in each case. Moreover, because we allow he firm o segmen markes by counry, we can focus exclusively on he decision over pricing in he foreign marke. In he case he firm s expeced profi on foreign sales is: ( E d h ( i Xh ( i W ( Xh ( i, where X = ( n is oal sales of firm i o foreign residens. Here, h ( is he h h home-currency price for he sale of home firm i o foreign consumers. Recall ha he nominal i discoun facor is d ˆ =, where he second equaliy makes use of he S β = β ˆ S risk-sharing condiion. From secion, foreign demand for he home good is X h = ( n h ˆ = h ( ˆ h i h ˆ = n h ( ˆ h i ˆ ˆ h = n h ( h i S ˆ h. Recall ha a ^ indicaes he price is denominaed in foreign currency. So h is he foreigncurrency price paid by foreign residens for home-produced goods, and S h = h. ˆ ˆ When all firms follow, he firs-order condiion for he price of goods sold o foreign consumers is: 2

14 E( W h = h =. (2. E ( Noe ha he derivaion of equaion (2. does no depend on he price-seing decisions of foreign firms, confirming ha we can ignore he foreign firms pricing sraegy. Using (2., we can esablish ha he expeced discouned profi of firm i in he home marke earns in period is given by [ d ( W X ] K E ( E, (2.2 h h = where K = nβ. ondiional on period - variables, expeced discouned profi depends only on foreign consumpion. Now consider he poenial benefi for firm i if i deviaes from all oher firms, and ses he price in he foreign currency. Isolaing he firm s profis from foreign sales, i maximizes: ˆ dev E [ ˆ dev dev d ( S W X ( ] h h i, X dev where h is he foreign-currency price se by he deviaing firm, and h is demand for is produc given by: ˆ dev ˆ dev ˆ dev dev h ( i Sh ( i S h ( = ( h ( = ˆ h = h h h X i n i n. If firm i ses is price in he foreign currency, a home counry nominal depreciaion will reduce foreign demand for firm i s produc, relaive o demand for all oher home goods. ˆ dev The firs-order condiion for he opimal choice of h is given by: ˆ dev E( W S h =. (2.3 E ( S 3

15 Noe ha he deviaing price depends direcly upon he disribuion of he exchange rae, while he opimal price for producers (2. does no. Using (2.3 we may esablish ha he expeced discouned profi for he deviaing firm is: h K E. (2.4 ˆ dev S h Subsiuing in for he opimal prices from expressions (2. and (2.3, expression (2.4 can be rewrien as: K ( E ( W S ( E ( S ( E( W ( E ( If wages, consumpion and he exchange rae are lognormally disribued, his reduces o: {( E ( W S ( E ( S ( E ( W } E ( K (2.5 If all oher firms are follow pricing, hen firm i would prefer o deviae and follow an L pricing sraegy if expeced discouned profis by doing so were higher. omparing expression (2.5 o profis under pricing, given by (2.2, his reduces o he condiion > ( E ( W S ( E ( S ( E ( W. (2.6 Under he lognormaliy assumpion, his can be furher reduced o he simple expression: ov w, s Var ( s 0, (2.7 ( 2 > where lower-case leers are he naural logs of heir upper-case counerpars. We hus obain a very simple condiion deermining wheher he home firm would wish o deviae from a equilibrium and se prices in foreign currency. The logic behind his condiion is easy o obain. learly if here were no variaion in he exchange rae, here would be no difference beween pricing in domesic and foreign currencies. Thus, he main quesion is how exchange rae volailiy impacs on he expeced profi of he deviaing firm. Focusing on expression (2.4, we see ha exchange rae volailiy on is own, holding prices and foreign 4

16 consumpion consan, would end o raise expeced discouned profis. For given prices and foreign consumpion, expeced discouned profis are increasing in exchange rae volailiy. Bu exchange rae volailiy also affecs he opimal price ha he deviaing firm ses. Looking a expression (2.3 we see ha exchange rae volailiy increases he opimal price for he deviaing firm. The impac of exchange rae volailiy on he firm s opimal deviaing price in fac ouweighs he direc effec of exchange rae volailiy on expeced discouned profis, so ha we find he ne impac of exchange rae volailiy on expeced discouned profis of he deviaing firm is negaive. Were his he complee picure, a firm would never wish o deviae from. Bu exchange rae volailiy also has a second indirec effec insofar as exchange raes are correlaed wih marginal cos. If he exchange rae is posiively correlaed wih marginal cos for he firm, hen he opimal price of he deviaing firm will be lower (see 2.3, and expeced profis higher, given a deviaion. ondiion (2.7 hen jus represens he sum of he direc and wo indirec effecs of exchange rae volailiy on expeced discouned profis for he deviaing firm. How does condiion (2.6 and (2.7 relae o he earlier sudies of he currency of price seing decision, based on parial equilibrium analysis (e.g. Giovannini, 988, Friberg, 998? These sudies differed in mainly hree ways. Firs, hey ook aggregae variables (such as foreign demand and he foreign I as given. Second, hey were focusing on he decision of a single producer facing a demand curve in isolaion, where implicily he price of all oher goods is fixed in foreign currency. Finally, hese sudies for he mos par assumed risk neuraliy, so he firm wishes o maximize expeced profis alone. In his seing Giovannini (988 shows ha when he demand curve is convex (concave in own price, he home firm would wish o se price in domesic (foreign currency. By conras, our environmen is general equilibrium, where boh demand and all oher prices are endogenous. In addiion however, he firm compees agains oher domesic firms, so 5

17 he currency in which hese oher firms se heir prices is relevan. In our model, he elasiciy of demand beween he home good and foreign goods is uniy, so under he parial equilibrium analysis of Giovannini (and risk neuraliy, his would imply ha he home firm would be indifferen o pricing in home or foreign currency. Bu he relevan comparison for he firm in our environmen is beween her prices and he prices of domesic compeiors. Finally, insead of having risk neuraliy, we explicily condiion profis wih he sochasic discoun facor relevan for he firms owners. In combinaion wih our full risk-sharing assumpion, his in fac eliminaes he direc imporance of he exchange rae in deermining overall demand for home goods, relaive o foreign goods. Again, wha maers for he firm is he demand for her variey of he home good, relaive o he varieies of oher home firms. Following from his discussion, we can make some observaions abou (2.6 and (2.7. Alhough we are allowing for he full general equilibrium effecs of alernaive pricing policies, he condiions governing he opimaliy of deviaing are remarkably simple. In paricular, he fac ha foreign consumpion demand is endogenous is no imporan o he decision over which prices o se. This is somewha surprising, since boh for pricers in equaion (2. and L deviaors in equaion (2.3, he covariance of rae maers for he opimal ex ane price. The covariance of wih home nominal wages and he exchange wih he exchange rae also affecs expeced discouned profis of he L deviaor, beyond is influence on prices, as can be seen in equaion (2.4. As we noed, he parial equilibrium models of he opimal choice of currency for pricing, such as Giovannini (988, rea aggregae variables as exogenous and so ignore hese covariances. Bu if were reaed as exogenous and uncorrelaed wih wages and exchange raes in equaions (2., (2.3, and (2.4, we would sill derive equaions (2.6 and (2.7 as he condiion for choosing L when all oher firms choose. 6

18 To see his, noe ha if ind were independen, we would have h = E ( W, and ˆ devind h E = E ( W S ( S. rofis of he deviaor would hen be given by: n E ind h E ˆ dev ind S h The condiion for deviaion o be profiable is hen ind h E > ˆ, dev ind S h ( which is exacly equivalen o condiions (2.6 or (2.7. Thus, he condiion o swich o L pricing is ha he expeced value of he opimal price relaive o he opimal dollar value of he L price (raised o he power be greaer han one. ondiion (2.7 was derived wihou making reference o he soluion for he nominal exchange rae and nominal wages in erms of he money supplies. Now, combining expression (.7 for he exchange rae, and (.9 for he nominal wage wih condiion (2.7, a firm will deviae and follow an L pricing sraegy when all oher firms in he home counry follow a sraegy if and only if:. Var ( m > Var ( m. (2.8 Tha is, he home firm will wish o deviae from pricing if and only if he volailiy of home money exceeds ha of foreign money. Moreover, his condiion holds irrespecive of he covariance of home and foreign money supplies. Wha maers is only he oal moneary volailiy, no he covariance across counries. Now from he resuls so far, we can sae he following proposiions: 7

19 roposiion : An equilibrium exiss in which all home firms are pricers if and only if ov w, s Var ( s 0. ( 2 roof: If his condiion is me, hen no firm will wish o swich o L pricing when all oher firms are pricing, from condiion (2.7. orollary: An equilibrium exiss in which all home firms are pricers if and only if Var ( m Var ( m. Home firms follow L Now assume ha all home producers se prices in he foreign currency for sales o foreign consumers, and ask wheher an individual producer has an incenive o deviae. We can follow he same logic as before. The discouned expeced profis from sales o he foreign marke are given by: E [ ˆ d ( S W X ( ] h h i, where foreign demand is given by X h ˆ h h = n ˆ h ˆ ˆ h = ( n h = ˆ. ˆ h h The opimal price for he L firm is: ˆ ˆ E ( W S h = h = (2.9 E ( The expeced discouned profis of hese L price seers is given by: K E ( (2.0 8

20 Noe ha his is exacly he expeced discouned profi level for firms if hey are all price seers. Thus, for a given disribuion of foreign consumpion, expeced profis will be he same if eiher all home firms follow rules or L rules 8. If all oher home firms are seing prices in he foreign currency for foreign consumers, firm i migh consider seing he price in he home currency. Expeced profis for he deviaing firm are hen given by: E dev dev [ d ( W X ( ] h h i, where X dev h dev h h = n ˆ S h dev ˆ dev h = ( n h = ˆ. ˆ S h h The opimal price for he deviaor is given by: dev ( E( W S h i =. (2. ( E S Using his, he equilibrium expeced discouned profis for he deviaor are: S ˆ h K E dev (2.2 h Subsiuing he expressions for opimal prices, (2.9 and (2., ino equaion (2.2, he expeced discouned profis of he firm ha follows he sraegy when all ohers follow L are: K ( E ( W S ( E( S ( E ( W S ( E( Again, under lognormaliy, his can be simplified o: 8 In fac however, expeced foreign consumpion will no be he same. As shown in Devereux and Engel (2000, he presence of L (for all firms, boh home and foreign will generae a very differen process for oupu and consumpion for boh he home and foreign economies han would. Bu in any case, a comparison of profis from his perspecive is no relevan o he quesion of wheher eiher or L consiues an equilibrium. 9

21 {( E ( W S ( E ( S ( E ( W S } E ( K (2.3 omparing equaion (2.3 o he profis for firms ha L price, i will pay o deviae from L pricing if and only if: This condiion can be expressed as: ( E ( W S ( E ( S ( E ( W S (2.4 > ov w, s Var ( s 0. 9 (2.5 ( 2 < If we use he expressions for equilibrium wages and exchange raes, (.7 and (.9, hen he necessary and sufficien condiion for a firm o swich o pricing when all oher firms follow an L pricing sraegy is: The following proposiions follow: Var ( m < Var ( m. (2.6 roposiion 2: An equilibrium exiss in which all home firms follow an L pricing sraegy if and only if ov w, s Var ( s 0. ( 2 orollary: An equilibrium exiss in which all home firms are follow L pricing if and only if Var ( m Var ( m. omparing proposiions and 2, we see ha here is an equilibrium in which all home firms are L pricers if ( ov ( w, s Var ( s 0 or Var ( m Var ( m, and here is 2 9 areful examinaion reveals ha he expression on he lef-hand side of equaion (2.4 equals he inverse of he expression on he lef-hand side of equaion (2.6 under log normaliy. 20

22 an equilibrium in which all home firms are pricers if he reverse relaionship holds. Moreover, excep for he special case of equal moneary variances, he wo canno overlap. When here is an equilibrium where all home firms se prices under, here is generically no equilibrium where hey will se prices under, wih he reverse saemen holding also. So far, we have looked only a he decision facing home firms. Bu i urns ou ha he decision facing foreign firms is idenical, given he symmery of he model. Foreign firms will wish o pre-se prices in foreign currency if he volailiy of foreign currency is less han ha of domesic currency, and will wish o se prices in home currency if he reverse holds. Then we can go on o sae he following proposiion: roposiion 3: There is an equilibrium in which all home and foreign firms se prices in he home currency if and only if: Var ( m Var ( m. There is an equilibrium in which all home and foreign firms se prices in he foreign currency if and only if: Var ( m Var ( m. The paern is ha firms choose o se prices in he currency of he counry wih he lowes moneary variance. Noe ha if one of hese inequaliies is sric, hen here canno be an equilibrium in which all firms in boh counries follow, nor here can here be an equilibrium where all firms in boh counries follow L. The following proposiion follows immediaely: 2

23 ropoposiion 4: A necessary and sufficien condiion for heir o be an equilibrium in which all firms in boh counries follow a sraegy, or in which all firms follow an L sraegy, is Var ( m = Var ( m. roposiion 4 represens a case where here is no unique equilibrium for he choice of price seing currency. Individual firms in he home and foreign counries are indifferen beween pricing in eiher currency. 3. Opimal price seing wihou risk-sharing To wha exen do he resuls in he previous secion depend upon he assumpion of full risk-sharing? We invesigae his quesion by moving o he polar opposie assumpion of no risk-sharing, so ha commodiy rade mus be balanced in every period. This is represened by condiion (.2. An imporan effec of using he rade balance condiion insead of complee markes is ha he exchange rae is no longer deermined by equaion (.7. In he previous analysis, equaion (.7 was imporan because i obained irrespecive of he pricing decisions of firms. When equaion (.2 holds, hen equaion (.8 gives us he equilibrium expression for he exchange rae. I is clear ha (excep when = he exchange rae will in depend on how home and foreign price levels respond o moneary shocks. We will show ha we can derive proposiions ha are similar o roposiion and roposiion 2, in he absence of asse rade. However, he corollaries o boh proposiions do no in general hold in his case. Tha is, he deerminans of he currency of pricing involve more han jus he rankings of moneary variances. We follow he same se of seps. 22

24 23 Home firms follow If all firms follow pricing, hen expeced discouned profi earned in foreign markes, foreign demand, and he discoun facor are all defined as before. 0 When all firms follow, he he firs-order condiion for he price of goods sold o foreign consumers is: ( ( ( = = h h E W E i. Noe ha his differs from he opimal price wih full risk-sharing, c.f. equaion (2., since i is domesic and no foreign consumpion now ha weighs marginal cos in he pricing rule. The expeced discouned profi ha firm i in he home marke earns in period is given by ( E K, where β = n K. Now if an individual home firm deviaes and ses is price in foreign currency, i will choose price ( ˆ i dev h given by: ( ( ( ˆ = dev h S E W S E i. The expeced discouned profi for he deviaing firm is: ( ˆ dev h h i S E K. 0 However, in he absence of full risk sharing, home and foreign discoun facors are no longer idenical.

25 24 Following he same seps as in he previous secion (wih equaions (2.5-(2.7, we conclude ha under he lognormal assumpion, if all oher firms are pricers, firm i would prefer o deviae and follow an L pricing sraegy if and only if: 0 (, ( ( 2 > s Var s w ov. (3. This is he same condiion as (2.7 in he previous secion. However, here is no in general a simple relaionship equivalen o equaion (2.8 ha can be derived from condiion (3.. This is because he exchange rae from (.8 now depends on he pricing sraegies followed by he home and foreign firms. We shall analyze some possible oucomes shorly. Home firms follow L Following seps analogous o hose of secion 2, we find ha he opimal price charged o foreign consumers of he home good when all home firms follow an L pricing sraegy is: ( ( ˆ ( ˆ = = h h E W S E i The expeced discouned profis of hese L price seers is given by: ( E K The opimal price for a home firm ha chooses o deviae and price in is own currency when all oher home firms price in he foreign currency is given by: ( ( ( = dev h S E W S E i. The expeced discouned profi for he firm ha deviaes from pricing is: ( ˆ dev h h i S E K

26 I will pay o deviae from L pricing if and only if: ov w, s Var ( s 0. ( 2 < Likewise, given he symmery of he model, we can show ha he foreign firm will find i advanageous o deviae from if he following condiion is me ov ( w, s Var ( s > 0, 2 On he oher hand, he foreign firm will find i advanageous o deviae from L if ov ( w, s Var ( s < 0. 2 How do hese condiions ranslae ino resricions on he underlying moneary variances? To invesigae his, we make some conjecures abou pricing sraegies. Then from he implied behavior of exchange raes, we can esablish wheher hese conjecures represen equilibrium sraegies. Firs, conjecure ha all firms in boh counries followed pricing. Then i is easy o show ha he law of one price holds for all goods, and given idenical preferences, purchasing power pariy holds: ˆ. From equaion (.8, his implies S = M S = M. Then using equaion (.9 for he nominal wage, he necessary and sufficien condiion for a home firm o follow pricing when all oher home firms follow pricing is: 2 ov ( w, s Var ( s = Var ( m Var ( m 0. In he same way, he necessary and sufficien condiion for a foreign firm o follow when all oher foreign firms follow is: ( 2 ov w, s Var ( s = Var ( m Var ( m 0. 25

27 These wo condiions are incompaible, and so here can be no equilibrium in which all firms follow sraegies, excep in he special case where Var ( m = Var ( m. So we have he following proposiion, which is analogous o roposiion 4 for he case of pricing: ropoposiion 5: A necessary and sufficien condiion for he exisence of an equilibrium in which all firms in boh counries follow a sraegy is Var ( m = Var ( m. Now conjecure ha all firms in boh counries follow L sraegies. In his case, boh and ˆ are deermined a ime, and ˆ Var ( Var ( 0. Then using equaion = = (.8 and (.9, a necessary and sufficien condiion for a given home firm o follow L pricing if all oher home firms follow L pricing is: ov (, w s Var ( s = (2 Var ( m Var ( m 2( ov ( m, m 0. 2 Similarly, if all foreign firms follow L pricing, a necessary and sufficien condiion for any given foreign firm o follow L pricing is: ov ( w, s Var ( s = (2 Var ( m Var ( m 2( ov( m, m 0. 2 If boh of hese condiions are me, all firms in boh counries will follow L pricing. roposiion 6: There is an equilibrium in which all firms in boh counries follow L pricing if and only if he following wo condiions are me: Var Var ( m + Var ( m 2 Var ( m 2( ov ( m, m, ( m + Var ( m 2 Var ( m 2( ov ( m, m. 26

28 learly for large enough, boh condiions can be me. So, in conras o he case of full risk-sharing, here i is possible for an equilibrium o exis in which all firms price in he consumers currencies, even when Var ( m Var ( m. roposiion 6 herefore allows for a case where all expor firms would like o keep heir prices fixed in he local currency of sale, raher han heir own currency. I requires ha consumers be relaively risk averse. The inuiion behind he proposiion can be developed in ligh of he discussion of he previous secion. We saw here ha exchange rae variance, holding marginal coss consan, led o a reducion in profis for he L firm relaive o he alernaive, and reduced he incenive o se prices in he buyer s currency. On he oher hand, a posiive covariance beween he exchange rae and marginal coss ends o raise profis for he L firm, and increases he incenive o price in he buyer s currency. Bu when all firms follow L pricing rules, and he coefficien of relaive risk aversion exceeds uniy, he impac of moneary variance on he exchange rae is dampened, relaive o he covariance of he exchange rae and marginal coss. This increases he incenive o follow L pricing, and, if he condiions of proposiion 6 are me, suppors he L pricing rule for boh counries as an equilibrium, even wihou idenical moneary variances. Noe however, ha if moneary variances move ou of line oo much, hen he global L pricing equilibrium is eliminaed. The condiions of proposiion 6 will no hold if one counry s moneary variance is oo high, relaive o he oher. We have shown ha generically, global pricing is no an equilibrium. Global L pricing can be an equilibrium for high risk aversion, and as long as moneary variances are no oo far apar. Wha abou asymmeric pricing equilibria? Is here an equilibrium where all world exporing firms price in home (foreign currency? 27

29 Firs, conjecure ha all home firms follow pricing and all foreign firms follow L pricing. If all foreign firms se prices in advance for home consumers in erms of domesic currency, hen is predeermined. Bu, wih home firms following a pricing sraegy, varies wih he exchange rae. We have, expressing prices in logs, p ˆ = ns + z, where z represens predeermined componens of he price index. Using his soluion for he foreign I in he equaion for he exchange rae (.8, we can esablish ha a home firm will follow pricing when all oher home firms follow pricing if and only if he following condiion is me (using (.9 and (3.: (2( ( n + Var ov ( w, s ( m Var ( m 2 Var ( s = 2( ( n ov ( m, m 0 Likewise, a foreign firm will follow L pricing if all oher foreign firms follow L pricing if and only if: (2( ( n + Var ov ( m ( w Var We herefore have he following proposiion:, s 2 ( s = ( m 2( ( n ov Var ( m, m 0 ˆ roposiion 7: There is an equilibrium in which all home and foreign firms se prices in he home currency if and only if he following wo condiions are me: Var Var ( m Var ( m 2( ( n( Var ( m ov ( m, m, ( m Var ( m 2( ( n( Var ( m ov ( m, m. A necessary condiion for hese wo condiions o be me is Var ( m Var ( m. 28

30 The symmery of he home and foreign counry allows us o derive he following proposiion for he alernaive case, where all expors are priced in foreign currency: roposiion 8: There is an equilibrium in which all home and foreign firms se prices in he foreign currency if and only if he following wo condiions are me: Var Var ( m Var ( m 2( n( Var ( m ov ( m, m, ( m Var ( m 2( n( Var ( m ov ( m, m. A necessary condiion for hese wo condiions o be me is Var ( m Var ( m. roposiions 7 and 8 canno boh be me, excep in he special case in which he log money supplies are equal. Tha is, i is generically no possible o have one equilibrium in which all firms price in he home currency and simulaneously anoher equilibrium in which all firms price in he foreign currency. Noe also ha for eiher proposiion 7 or proposiion 8 o hold, i is necessary ha he moneary variances are quie far apar. Tha is, he condiion Var ( m Var ( m ( Var ( m Var ( m is no a sufficien condiion for proposiion 7 (proposiion 8. If risk aversion is greaer han uniy, and reasonably large, and he moneary variances differ only slighly, hen neiher of hese proposiions will apply. In ha case, proposiion 6 will represen he only pricing equilibrium in he economy wihou full risksharing. 2 Anoher case in which boh proposiions could be me is = and equal moneary variances. 2 Neverheless, i is possible for he condiions of roposiion 6 o be me a he same ime ha he condiions of eiher roposiion 7 or roposiion 8 are me. Tha implies here can be siuaions of muliple equilibria. If home moneary variance is smaller han foreign moneary variance, hen i is possible ha here will exis boh an equilibrium in which all firms price in he home currency and one in which hey all follow L pricing. And, if home moneary variance exceeds foreign moneary variance, i is possible ha here will exis boh an equilibrium in which all firms price in he foreign currency and one in which hey all follow L pricing. 29

31 The economy wihou full risk-sharing hen offers us some ineresing conclusions regarding he equilibrium configuraion of inernaional pricing. Firs, i is generically no possible o have exporers in all counries se prices in heir domesic currency. I is possible ha exporers will choose o se prices in he currency of he buyer, so long as risk aversion is relaively large, and he moneary variances are no oo far apar. Bu if he moneary variance of one counry is oo high, hen his equilibrium will be eliminaed, and i will be replaced by one in which he counry s exporers will se heir prices in he currency of he oher counry, as will he exporing firms in he oher counry. In addiion, if risk aversion is relaively low, we end o move owards he resuls of he previous secion: all world expors will be se in he prices of he counry wih he lowes moneary variance. 4. Discussion and conclusions The resuls of he las wo secions depend on he ype of inernaional financial markes in exisence, and also depend on he degree of risk aversion. I is possible o have muliple equilibria in inernaional price seing arrangemens; in he full risk-sharing case his is possible if moneary variances are exacly idenical; in he no risk-sharing case his is possible if he moneary variances are differen, bu no oo far apar. Neverheless, a very srong message comes ou of he resul of boh secions. A counry ha has highly volaile moneary policy will find ha is impor prices will be pre-se in foreign currency, and as a resul i will experience a high rae of pass-hrough from exchange raes o impored good prices. A counry wih a low volailiy of moneary policy is more likely o have is impor goods prices se in is own currency, wih a very low rae of exchange rae passhrough. When all counries have very low moneary policy volailiy, and inernaional financial 30

32 markes are incomplee, we are likely o see emerge a low rae of exchange rae pass-hrough generally. These resuls are consisen wih he conenion of Oriz (999 and he discussion of Taylor (2000, suggesing no only ha exchange rae pass-hrough is endogenous, bu ha i may depend direcly on he degree of predicabiliy in moneary policy. Thus, he resuls would raionalize why exchange rae pass-hrough would be high in a counry ha has hisorically had quie unsable moneary policy, such as Mexico, and low in counries such as New Zealand and anada, which have hisorically benefied from very sable moneary policy. While our resuls do lend some suppor o he view ha exchange rae pass-hrough depends on moneary policy, here are a number of feaures lef ou of he presen analysis. As in he previous lieraure in he `new open economy macroeconomics, we have no discussed why firms mus se nominal prices one period in advance. The answer from he new Keynesian lieraure is ha small menu coss make i more profiable for a firm o se prices ahead of ime: he loss in profis from no alering prices opimally when here are small demand shocks are second-order, so even very small menu coss imply i is opimal no o change prices. In he inernaional seing, he firm may necessarily have o incur coss of adjusing prices. If prices are se in he home currency, here may be coss associaed wih adjusing foreign-currency prices, and vice-versa. One can jusify he analysis of he paper, which does no explicily consider menu coss, by assuming ha he coss of adjusing prices are he same wheher prices are se in home or foreign currency. If he coss are very differen, menu cos consideraions migh aler he opimal choice of currency for price seing. Bu i may be ha hese coss are all quie small, so ha he consideraions of he previous secions dominae menu cos consideraions. I is unforunaely 3

33 difficul o quanify menu coss and compare hem o he gains in expeced discouned profis ha we have focused on. Therefore, we view his paper as giving only a parial answer o he quesion of he opimal currency for price seing. Our analysis has expanded on he previous parial equilibrium modeling and we have found ha he parial equilibrium resuls may well be overurned in general equilibrium. Bu furher heoreical and empirical work is needed o incorporae consideraions of ransacions coss, disribuion and inermediae producs. 32

34 References Bacchea, hilippe, and Eric van Wincoop, 2000a, Does exchange rae sabiliy increase rade and welfare?, American Economic Review 90, Bacchea, hilippe, and Eric van Wincoop, 2000b, Trade flows, prices and he exchange rae regime, Sudy ener Gerzensee, mimeo. Bes, aroline and Michael B. Devereux, 996, The exchange rae in a model of pricing o marke, European Economic Review, 40, ampa, José M., and Linda S. Goldberg, 200, Exchange rae pass-hrough ino impor prices: a macro or micro phenomenon?, Federal Reserve Bank of New York, mimeo. hari, V.V., arick J. Kehoe, and Ellen R. McGraan, 2000, an sicky price models generae volaile and persisen real exchange raes?, Naional Bureau of Economic Research, working paper no orsei, Giancarlo and aolo eseni, 200, Opimal ineres rae rules and exchange rae passhrough, Federal Reserve Bank of New York, mimeo. Devereux, Michael B., and harles Engel, 2000, Moneary policy in he open economy revisied: rice seing and exchange rae flexibiliy, Naional Bureau of Economic Research, working paper no Devereux, Michael B., harles Engel, and édric Tille, 999, Exchange rae pass-hrough and he welfare effecs of he euro, Naional Bureau of Economic Research, working paper no Friberg, Richard, 998, In which currency should exporers se heir prices?, Journal of Inernaional Economics 45, Giovannini, Albero, 988, Exchange raes and raded goods prices, Journal of Inernaional Economics 24, Obsfeld, Maurice, and Kenneh Rogoff, 995, Exchange rae dynamics redux, Journal of oliical Economy 03, Obsfeld, Maurice, and Kenneh Rogoff, 998, Risk and exchange raes, Naional Bureau of Economic Research, working paper no Oriz, Guillermo M., 999, Dollarizaion: fad or fuure for Lain America?, IMF Economic Forum, ranscrip. Suherland, Alan, 200, Incomplee pass-hrough and he welfare effecs of exchange rae variabiliy, Universiy of S. Andrews, mimeo. 33

35 Taylor, John B., 2000, Low-inflaion, pass-hrough, and he pricing power of firms, European Economic Review 44, Tille, édric, 2000, Beggar-hy-neighbor or beggar hyself? The income effecs of exchangerae flucuaions, Federal Reserve Bank of New York, Saff Repor 2. 34