Endogenous exchange rate pass-through when nominal prices are set in advance $

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1 Jounal of Intenational Economics 63 (2004) Endogenous exchange ate pass-though when nominal pices ae set in advance $ Michael B. Deveeux a,b Chales Engel c,d, *Pete E. Stogaad e a Depatment of Economics, Univesity of Bitish Columbia, Vancouve, BC, Canada, V6T 1Z1 b Cente fo Economic Policy and Reseach, London EC1V 7RR, UK c Depatment of Economics, Univesity of Wisconsin, 1180 Obsevatoy Dive, Madison, WI , USA d National Bueau of Economic Reseach, Cambidge, MA 02138, USA e Danmaks Nationalbank, Havnegade 5, DK-1093, Copenhagen, Denmak Received 31 July 2001; eceived in evised fom 25 Febuay 2003; accepted 20 Apil 2003 Abstact This pape develops a model of endogenous exchange ate pass-though within an open economy macoeconomic famewok, whee both pass-though and the exchange ate ae simultaneously detemined, and inteact with one anothe. Pass-though is endogenous because fims choose the cuency in which they set thei expot pices. Thee is a unique equilibium ate of pass-though unde the condition that exchange ate volatility ises as the degee of pass-though falls. We show that the elationship between exchange ate volatility and economic stuctue may be substantially affected by the pesence of endogenous pass-though. Ou key esults show that pass-though is elated to the elative stability of monetay policy. Counties with elatively low volatility of money gowth will have elatively low ates of exchange ate pass-though, while counties with elatively high volatility of money gowth will have elatively high pass-though ates. D 2003 Elsevie B.V. All ights eseved. Keywods: Exchange ate pass-though; Expot pices JEL classification: F3; F4 $ This pape is a combination and compehensive evision of Deveeux and Engel (2001) and Stogaad (2001). * Coesponding autho. Tel.: ; fax: addess: cengel@ssc.wisc.edu (C. Engel) /$ - see font matte D 2003 Elsevie B.V. All ights eseved. doi: /s (03)

2 264 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Intoduction A lage body of empiical evidence has found that pass-though of exchange ate changes to impot pices is less than complete 1. Howeve, the degee of pass-though is not unifom acoss counties o industies 2. Exchange ate pass-though mattes fo many questions; fo instance the pedicted volatility of the eal exchange ate, the intenational tansmission of macoeconomic shocks, and the welfae benefits of intenational policy coodination 3. It is, theefoe, impotant to undestand the undelying deteminants of pass-though. While thee is a lage liteatue that has examined long-un pass-though the optimal picing choice of fims when makets ae segmented and competition is impefect consideably less study has been undetaken of pass-though in the shot un when thee may be some nominal pice stickiness. We analyze the deteminants of an expoting fim s choice of cuency in which to peset pices. With nominal pice stickiness, the aggegate degee of exchange ate passthough is detemined by this decision. The pape theefoe develops a model of endogenous exchange ate pass-though, in a famewok in which the exchange ate itself is endogenously detemined. We find that thee is a two-way inteaction between exchange ate pass-though and exchange ate volatility. Exchange ate volatility detemines the pice-setting choices of a fim, and theefoe, the degee of aggegate exchange ate passthough. But in tun, the degee of exchange ate pass-though itself detemines the volatility of the exchange ate. The stating point of ou analysis is the assumption that pices ae sticky in the shot un. Thee is a long tadition of nominal pice stickiness in models of macoeconomics. But in an open economy, the question of pice stickiness is moe poblematic. Clealy, the exchange ate is not sticky. As a esult, when a good is taded between counties with flexible exchange ates, the cuency in which the pice of the good is fixed becomes an impotant facto in detemining the effect of exchange ate changes. If pices ae sticky in the cuency of the expote (we denote this as PCP, o poduce cuency picing ), then pass-though fom exchange ate changes to final consumes will be complete, and impoted goods will display consideable pice flexibility. On the othe hand, if goods pices ae fixed in consume s cuency (LCP, o local cuency picing ), thee is no passthough at all, and impoted goods pices ae unaffected by exchange ate changes. When a fim sells aboad, would it pefe to follow PCP o LCP? This question has been addessed befoe, but mostly in patial equilibium settings, which take as exogenous key vaiables that ae influenced by the pice-setting configuation itself. Fo instance, in geneal equilibium, the behavio of exchange ates, labo costs, and demand may themselves depend on how pices ae set. 1 A shot list of citations includes Kugman (1987), Knette (1989, 1993), Feensta (1989), Feensta et al. (1996), Goldbeg and Knette (1997), Goldbeg (1995) and Goldbeg and Veboven (2001) fo studies of passthough to impot pices. Engel (1993), Engel and Roges (1996) and Pasley and Wei (2001) among many othes, have studied pass-though to consume pices. 2 This point was emphasized in the suvey of Goldbeg and Knette (1997). 3 See fo example, Betts and Deveeux (1996, 2000), Deveeux and Engel (2000), Tille (2000) and Lane (2001).

3 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Ou analysis poceeds in thee stages. In the fist stage, we examine the choice of cuency of pice setting fo a fim that has local maket powe in a stochastic envionment, taking as given the distibution of exchanges ates, maket demand, and pices of othe fims. We establish a vey simple ule fo the choice of pice-setting cuency. If a fim is choosing its pices optimally, then up to a second ode appoximation, its decision depends only on the vaiance of the exchange ate and the covaiance of the exchange ate with maginal costs. The highe is the vaiance of the exchange ate, the moe incentive the fim has to set pices in its own cuency. The highe is the covaiance of the exchange ate and maginal costs, the moe the fim would wish to set its pice in foeign cuency. A emakable aspect of the esult is that the cuency of picing decision is independent of the vaiance of maket demand and the pices of all othe fims. We then place the fim in a two-county intetempoal geneal equilibium envionment whee the exchange ate and maginal costs ae detemined by andom money shocks. Each county has a continuum of fims that expot goods to the othe county. The degee of exchange ate pass-though is detemined by the measue of fims that choose to follow PCP. While fims decisions with espect to cuency of picing depend on the distibution of exchange ates and maginal costs, these distibutions in tun depend on the degee of aggegate exchange ate pass-though. Thee is thus a two-way inte-elationship between exchange ate volatility and exchange ate pass-though. Is thee a unique equilibium degee of exchange ate pass-though? If pass-though depends on exchange ate volatility, and exchange ate volatility depends on pass-though, thee aises the possibility of multiple equilibia 4. Roughly speaking, the condition fo a unique equilibium is that exchange ate volatility is highe in an economy whee exchange ate pass-though is lowe. On the othe hand, if declining pass-though is associated with a decline in exchange ate volatility, then multiple equilibia may exist. We show that in ou model, multiple equilibia ae unlikely to occu. The oveall degee of exchange ate pass-though depends on vaious stuctual featues of the economy. Pass-though is highe the moe stable ae maginal costs in each county, and the lowe is the elasticity of substitution between domestic and foeign goods. Moeove, in an envionment of endogenous exchange ate pass-though, conventional esults on the deteminants of exchange ate volatility must be applied with caution. In paticula, ou model of exchange ate detemination implies that low exchange ate passthough can poduce substantial exchange ate volatility. But when pass-though is endogenous, the pesence of high exchange ate volatility will itself incease the incentive fo fims to follow PCP. By inceasing the ate of aggegate pass-though, this dampens exchange ate volatility. In the thid stage of ou analysis, we examine the elationship between monetay policy and pass-though. Ou key esults elate to the impact of diffeential monetay shocks on the degee of exchange pass-though. When counties have diffeences in the volatility of money gowth, ou model pedicts that expoting fims in both counties will tend to pe-set thei pices in the county that has the moe stable money gowth. This leads to an impotant 4 This was pointed out by Deveeux and Engel (2001). A slightly diffeent pespective on multiple equilibia in the decision ove invoicing cuency is pesented by Bacchetta and van Wincoop (2002). We discuss Bacchetta and van Wincoop (2002) moe fully below.

4 266 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) link between monetay policy and pice stability. A county that follows a successful policy of monetay stabilization, educing the vaiance of its money gowth, will expeience a pice-stability bonus. This is because foeign expotes will begin moe and moe to set thei pices in that county s cuency, theeby educing the impact of exchange ate changes on the county s CPI. But the flip side of this is that the foeign county expeiences less stable pices, since expotes in the stabilizing county will also begin to pe-set thei pices in domestic cuency. Thus, thee is a begga-thy-neighbo aspect to policies of monetay stabilization in an envionment of endogenous pass-though. This pape is pat of a wide liteatue on sticky pice open economy macoeconomic models 5. Recently, seveal studies have looked at the detemination of the degee of exchange ate pass-though in geneal equilibium models with endogenous exchange ates. Deveeux and Engel (2001) and Stogaad (2001) pesent a vey simila analysis of the decision with espect to PCP vesus LCP, in sepaate woks that have been combined to fom the pesent pape. Bacchetta and van Wincoop (2001) pesent numeical esults on equilibium pass-though in a static envionment. They find a positive connection between isk-avesion and LCP. In some cases they find that thee ae no pue stategy equilibia fo fims picing decisions, a theme we take up below. Bacchetta and van Wincoop (2002) focus on the choice of invoicing cuency (o cuency of pice setting) in a static geneal equilibium famewok, poviding analytical esults. Thei patial equilibium esults take on much of the flavo of theoetical conclusions of Feensta et al. (1996) that passthough is geate when expoting fims have a high degee of maket powe. They emphasize the possibility of multiple equilibia that aise because of stategic complementaities between the pice-setting decisions of fims. They also exploe the ole of multiple counties, and the impact of a monetay union on the equilibium invoicing cuency in intenational tade. In thei pape, multiple equilibia aise due to diminishing etuns to scale in a manne that is absent in ou wok. But they do not focus on the twoway inteaction between exchange ate pass-though and exchange ate volatility, no do they examine the implication of diffeences in monetay policies acoss counties. The next section sets out the poblem of a single fim in a stochastic envionment, and establishes a simple ule fo the detemination of the cuency of picing. Section 3 sets out the geneal equilibium model. Section 4 combines Section 2 and Section 3 to detemine the degee of exchange ate pass-though. Section 5 exploes the implications of diffeences in the vaiance of money gowth among counties. 2. The decision of a fim in a stochastic envionment In this section, we examine the choice of cuency of pice setting fo a monopolistic expoting fim in a patial equilibium setting. We develop a condition on vaiables (exchange ates and wages) that ae exogenous to the fim, unde which the fim will choose to pice in its own cuency o the cuency of the impoting county. In the next section, we exploe the popeties of a specific macoeconomic model. Embedded in that 5 See Obstfeld and Rogoff (1995, 1998, 2000), Lane (2001), Bacchetta and van Wincoop (2000) and Deveeux and Engel (2001) and many othes.

5 model ae fims that face pecisely the same type of demand cuve and cost function as does the fim in this section. Take a fim i in the home county selling a diffeentiated good to a foeign maket. Assume that the fim faces the CES demand cuve: Y ðpðiþþ ¼ PðiÞ k P h Y *, k > 1: ð1þ P P* P(i) is the pice the foeign consume pays fo good i. P is the pice index fo all home goods puchased by the foeign consume, and P* is the foeign county consume pice index. Without loss of geneality let P(i), P and P* be denominated in foeign cuency. Y* is a demand shift vaiable that is independent of pice. k is the pice elasticity of demand facing the domestic fim i. h is the foeign pice elasticity of demand fo domestic goods. Fim i is a small enough supplie that it ignoes the impact of its picing decision on P. Eq. (1) imposes a paticula functional fom on the fim s demand schedule so as to be consistent with the geneal equilibium model developed below. But we make no specific assumptions about the distibution of P, P* and Y*. These vaiables may be stochastic, and may be coelated with the exchange ate. The fim has a constant etuns to scale poduction function, and faces the (possibly stochastic) maginal cost W. The fim evaluates pofits using the (stochastic) discount facto d. In the model below, we detemine the exact fom of d PCP vesus LCP M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) The fim has to decide whethe to set its pice in domestic o foeign cuency. Whateve cuency it chooses, it must set the pice befoe the state of the wold is known. If fim i sets its pice in its own cuency, (PCP), then expected discounted pofits ae " EP PCP ¼ E dðp PCP P PCP k # ðiþ P h ðiþ WÞ Y *, ð2þ SP P* whee S is the exchange ate (home-cuency pice of foeign cuency). If the fim sets its pice in the foeign cuency (LCP), then expected discounted pofits ae " EP LCP ¼ E dðsp LCP P LCP k # ðiþ P h ðiþ WÞ Y * : ð3þ P P* In Eqs. (2) and (3), undiscounted pofits ae denominated in the home cuency. We shall see in Poposition 1 (below) that the optimal cuency of pice setting does not depend on the chaacteistics of the discount facto, d. The only estiction we impose is that the discount facto is exogenous to the fim. In the macoeconomic model we pesent below, the discount facto is specified so that fims ae maximizing the expected utility of fim ownes. Nominal pofits ae deflated by the exact consumption pice index of the epesentative fim owne, and weighted by the maginal utility of consumption of fim ownes. Howeve, ou esults (Poposition 1) ae moe geneal and hold iespective of how fim manages evaluate the maginal value of futue nominal income to fim ownes.

6 268 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) The pofit-maximizing pice fo the fim, unde PCP and LCP, espectively, may easily be deived as follows: P PCP ðiþ ¼ k EðWS k ZÞ k 1 EðS k ZÞ, PLCP ðiþ ¼ k EðWZÞ k 1 EðSZÞ, whee Z = dp k h P* h Y*. Using these solutions, the expessions fo expected discounted pofits ae: EP PCP ¼ k½eðs k ZÞŠ k ½EðS k ZW ÞŠ 1 k ð4þ EP LCP ¼ k½eðszþš k ½EðZW ÞŠ 1 k k. Fom expessions (4) and (5), we may establish: whee k ¼ 1 k 1 k k 1 ð5þ Poposition 1. The home fim sets its pice fo the foeign maket in home (foeign) cuency if vaðsþ covðw, sþ > 0, ð< 0Þ, 2 whee s = ln(s), and w = ln(w). Poof. See Appendix A. 5 This condition says that (log) exchange ate vaiance leads the fim to set its pice in tems of home cuency. But a positive covaiance between (the log of) the exchange ate and (the log of) maginal costs leads the fim to set its pice in foeign cuency. To explain this condition, take expessions (2) and (3) again. In any given state of the wold, unde eithe picing policy, pofits ae inceasing in the exchange ate. Unde PCP, a ise in the exchange ate will incease demand fo the fim s good, holding othe fims pices constant. Unde LCP, a ise in the exchange ate will incease the home cuency value of sales. But unde PCP, the pofit function in any state of the wold is stictly convex in the exchange ate, fo k >1, while with LCP the pofit function is linea in the exchange ate. This means that, holding othe vaiables constant, an incease in exchange ate vaiance inceases pofits unde PCP elative to LCP. If this wee the only consideation, the fim would follow PCP if thee wee any exchange ate uncetainty. But thee is a seconday channel, aising fom the uncetainty of maginal costs. If the covaiance between the exchange ate and maginal cost is positive, this tends to incease expected total costs unde PCP, since the fim s demand is highe pecisely when the cost of poduction is highe 6. Unde LCP, howeve, demand is independent of the exchange 6 Thee is a link between the conditions fo picing in consume s cuency and the conditions fo low passthough when pices ae set ex post. We have noted the similaity between the conditions in Bachetta and van Wincoop s (2002) model, and Feensta et al. s (1996) model of picing to maket. Fibeg (1998) daws a link between Giovannini s (1988) model of choice of cuency fo setting pices and models of picing to maket such as Kugman s (1987). Hee we note that the picing to maket liteatue especially the empiical liteatue has dawn the link between coelation of wages with exchange ates, and the esponse of impot pices to exchange ate changes. See Goldbeg and Knette (1997, p. 1251) fo a discussion.

7 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) ate (holding othe vaiables constant), so that expected total costs do not depend on the covaiance between the exchange ate and maginal cost. This channel, theefoe, inceases the incentive to choose LCP. When we add both of these channels togethe, we aive at exactly the condition descibed in the poposition. Note a stiking featue of Poposition 1. The condition does not depend on the vaiance of Z (which itself depends on total demand, the pices of othe home fims, the foeign CPI, and the stochastic discount facto), o the covaiance of Z with S o W. It follows that Poposition 1 holds in any envionment in which the fim s demand schedule can be descibed by Eq. (1). In paticula, it will apply in the same fom fo the geneal equilibium model that we constuct below. Thus, given va(s) and cov(w, s), the fim s optimal cuency of picing is independent of the picing policies of othe fims, the assumptions about intenational financial makets, o the chaacteistics of any othe maco vaiables in the domestic o foeign economies. Why does the condition in Poposition 1 not depend on the distibution of Z? Rewite (2) and (3) as: EP PCP ¼ EðX 1 ZÞ, whee X 1 ¼ðP PCP P PCP k ðiþ ðiþ WÞ, ð6þ S EP LCP ¼ EðX 2 ZÞ, whee X 2 ¼ðSP LCP ðiþ WÞðP LCP ðiþþ k. ð7þ An incease in S inceases both X 1 and X 2, so in both the PCP and LCP cases, expected pofits ae highe when the covaiance of S and Z is positive 7. In the PCP case, when thee is a depeciation, pofits incease because demand fo the good inceases. In the LCP case, as S ises, pofits incease because the pofit magin on each unit ises. Intuitively, the eason why the comovements of S and Z have appoximately no effect on the compaison of expected pofits in the LCP and PCP cases is that a small deviation in S (aound the point of appoximation) has equal effects on X 1 and X 2. That can be undestood by ecognizing that unde cetainty, fims incease pices until the point whee the incease in total pofit fom aising the pice on each unit is equal to the loss in pofit fom the lost demand as pice inceases 8. 7 It is clea fom inspection of (6) and (7) that the mean and vaiance of Z and the covaiance of Z with W affect expected pofits equally in the PCP and LCP cases. 8 How does the condition of Poposition 1 elate to the patial equilibium models of Giovannini (1988) (see also Fibeg, 1998)? In Giovannini (1988), it is assumed that the exchange ate is the only souce of uncetainty in the fim s picing poblem. He then shows that if pofits unde PCP ae concave (convex) in the exchange ate, then LCP (PCP) is pefeed to PCP (LCP) by the fim. Pofits ae concave (convex) in the exchange ate if the maket demand cuve is concave (convex). In ou analysis, holding maginal cost constant, pofits must be convex in the exchange ate, because we use a CES demand system in which the demand schedule is convex by constuction. Theefoe, wee the exchange ate the only souce of uncetainty, all fims would wish to follow PCP (as we have shown). But ou inteest is in analyzing the two-way inteaction between exchange ate passthough and exchange ate detemination. Since the exchange ate and maginal costs ae both diven by the undelying aggegate shocks to the economy, we cannot assume that maginal costs ae constant. Hence the condition undelying Poposition 1.

8 270 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) The situation of a foeign fim expoting to the domestic maket is entiely analogous, so long as demand can be descibed as in Eq. (1). Thus we may state: Coollay to Poposition 1. The foeign fim sets its pice fo the home maket in foeign (home) cuency if vaðsþ 2 þ covðw*, sþ > 0, ð< 0Þ. 3. The geneal equilibium model While the last section examines the decision on cuency of picing taking as given the distibution of the exchange ate, in this section we constuct a geneal equilibium model of exchange ate detemination, taking as given the cuency of picing followed by fims. The model is taken entiely fom the ecent liteatue on monopolistic competition in (open economy) macoeconomics (e.g. Blanchad and Kiyotaki, 1987; Obstfeld and Rogoff, 1995), so ou desciption is kept bief. (The full details of the model ae given in a Mathematical Appendix that is available in Deveeux et al., 2003.) Thee ae two counties, home and foeign, with consumes, fims and govenments in each county. Thee ae n households and fims in the home county, and 1 n in the foeign county. All fims have a monopoly ove sales of thei good, and all wokes (households) have a monopoly in setting thei wage Pefeences and maket stuctue Each consume k in the home county maximizes expected lifetime utility U t ðkþ ¼E t X l s¼t! b s t u s ðkþ, 0 < b < 1, whee u s ðkþ ¼ 1 1 q C1 q s ðkþþv ln M sðkþ P s g 1 þ w L1þw s ðkþ, q > 0. C(k) is a consumption index, M(k)/P ae domestic eal balances, and L(k) is the labo supply of the epesentative home agent. Consumption is decomposed into the consumption of home and foeign composites, with elasticity of substitution h between composites. In tun, the home (foeign) composite is defined ove a continuum of n (1 n) goods, with elasticity k between individual goods. 1 The consume pice index may be witten as P t =(np h 1 ht +(1 n)p h ft ) 1/(1 h), whee P it epesents the pice index of county i s goods fo sale in the home county. Pices set in foeign cuency ae denoted with an asteisk. Pices fo each peiod ae set befoe all infomation about the peiod is known. All goods sold by local fims ae piced in local

9 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) cuency, but when expoting, fims can follow PCP o LCP. Let the faction of home (foeign) fims that engage in LCP be z (z*). Fo now we take these values as given. Using this notation, the home county pice index of foeign goods is P ft ¼½ 1 1 n þ 1 1 n Z nþð1 z*þð1 nþ n Z 1 nþð1 z*þð1 nþ ðs t P fht * ðiþþ 1 k di P fht ðiþ 1 k diš 1=ð1 kþ, whee the notation P fht (i) and P fht * (i) epesents the domestic-cuency and foeigncuency pice of foeign goods sold in the home maket. Holding goods pices fixed, the pass-though fom exchange ate changes to home pices depends on the numbe of foeign fims following LCP. As z*! 1, pass-though is zeo. Home households expenditue consists of consumption and the accumulation of money balances and bonds. Thei evenues come fom wage income, the eanings of pofits fom home county fims, payment on pe-existing bonds, money balances caied ove, and tansfes fom the monetay authoity. They choose consumption, thei wage ate (given thei individual monopoly powe ove thei diffeentiated labo), bonds and money balances to maximize utility. We make the assumption that intenational financial makets ae impefect. Consumes can tade aboad only in non-contingent nominal bonds. Thus, thee is incomplete intenational isk shaing. Within the domestic economy, howeve, we assume that thee is full isk shaing acoss households. This eliminates the specific uncetainty in wage income acoss types of households. Because utility is additively sepaable between consumption and labo, this implies that households will have equal consumption, whethe o not they adjust wages ex-post. Fims poduce using labo only, with constant etuns to scale. Since we wish to allow fo some stickiness in wages, we follow Obstfeld and Rogoff (2000) in assuming that poduction uses diffeentiated labo, with elasticity of demand x between types of labo. To maintain symmety in the model, assume that any individual fim uses wokes of each type. Theefoe, the poduction function fo fim i in the home county is " 1 1=x Z # 1=ð1 ð1=xþþ n Y ðiþ ¼ Lðk, iþ 1 ð1=xþ dk n. 0 Given a distibution of wages W(k), it is easy to show that the fim s maginal cost of poduction is given by ðð1=nþðm n 0 WðkÞ1 x dkþþ 1=ð1 xþ. Each woke then faces a specific labo demand cuve with wage elasticity of demand x. The fim will choose its pice to maximize the state-contingent value of pofits. Since fims ae owned by domestic households, they evaluate pofits at the same state-contingent pices that ae used fo tading between domestic agents Equilibium conditions Table 1 outlines the main equations of the model. Table 1a descibes the optimality conditions fo the consume and the fim. The consume chooses a stock of domestic

10 Table 1 Equations of the model (a) Optimal conditions fo consume and fim Ct q Eule equation: P t Money demand: Flexible wage: Fixed wage: ¼ bð1 þ tþ1 ÞE t C q tþ1 P tþ1 Home pice: P ht ¼ k k 1 E t 1 ðd t 1 C ht W t Þ E t 1 ðd t 1 C ht Þ M t ¼ vc q 1 þ tþ1 PCP pice: P hft ¼ k E t 1 ðz t St kw tþ t P t tþ1 k 1 E t 1 ðz t St kþ Wt a ¼ xg x 1 P tct q Law t LCP pice: P hft * ¼ k E t 1 ðz t W t Þ k 1 E t 1 ðz t S t Þ W f t ¼ xg x 1 E t 1 ðl f ð1þwþ t Þ Definition: Z t = d t 1 P* (k h) ht P* h t C t * E t 1 L f t PtC q t (b) Pice and wage index Wage index: W t ¼ðvðWt aþ1 x þð1 vþðw f t Þ 1 x Þ 1=ð1 xþ CPI: P t ¼ðnPht 1 h Impot pice index: P ft ¼½ð1 z*þðsp fht * Þ 1 k þ z*p 1 k Š 1=ð1 kþ (c) Maket equilibium Employment (flex wage): L a t ¼ v W t a x ½Y ht þð1 zþy hft þ zy hft * Š W t fht þð1 nþpft 1 h Þ 1=ð1 hþ! Employment (fix wage): L f W f x t t ¼ð1 vþ Y ht þð1 zþy hft þ zy hft * W t Home sales: Y ht ¼ C ht ¼ n P h ht P k hft P ht * h C t Foeign sales (PCP): Y hft ¼ð1 nþ C P t S t P ht * P t * t * Foeign sales (LCP): * ¼ð1 nþ P hft * k P ht * h C * P t * t * Y hft P ht 272 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Balance of payments: P t C t þ B tþ1 ¼ P ht Y ht þð1 zþp hft Y hft þ zs t P hft * Y hft * þð1þ t ÞB t

11 cuency denominated bonds to maximize utility, given the nominal inteest ate 9 t +1. Money demand depends positively on consumption and negatively on the nominal inteest ate. Each consume-woke sets the wage as a makup ove the maginal ate of substitution between consumption and leisue. A faction v of the total n wokes set wages ex-post, afte the state of the wold is ealized, while the faction 1 v set wages in advance. The nominal discount facto used by fims in thei evaluation of expected pofits q is now defined as d t 1 = b((c t 1 P t 1 )/(C q t P t )). Wage and pice indices ae descibed in Table 1b. Table 1c descibes the maket cleaing elationships. Employment of fixed wage and flexible-wage wokes will in geneal diffe (although the income effects of this ae divesified away). The home county cuent account (pe capita) is equal to total income pe capita less consumption. B t +1 epesents the home county s stock of net foeign assets (denominated in the home cuency). All home consumes eceive the same income, whee income comes fom sales to domestic consumes and sales to foeign consumes, though both PCP and LCP fims Model solution M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Let the money stock in each county follow a andom walk in logs 10. Fo the home county: ln M tþ1 ¼ ln M t þ u tþ1, E t ðu tþ1 Þ¼0: We may solve by linea appoximation aound an initial non-stochastic equilibium. The full linea appoximation is deived in Appendix B. In ode to detemine the cuency in which fims set thei pices, the only infomation we need is the second moment popeties of the log of the exchange ate and wages. But this is exactly what is obtained fom the linea appoximation. Let x t + j =lnx t + j E t 1 ln X t + j epesent the log deviation fom time t 1 expectation fo any vaiable X t + j, j z 0. A vey convenient popety of the money demand specification, in combination with the assumption about the money supply pocess, is that the nominal inteest ate is constant. This is because, given that the log of the money stock follows a andom walk, so does the log of the tem P t C t q. Using this fact, taking the money maket equilibium fo the home county fom Table 1a, and the analogous conditions fo the foeign county, lineaizing, and taking diffeences, gives c t c t * ¼ m t m t * q ð1 zn z*ð1 nþþs t q. ð8þ When thee is full pass-though of exchange ates into pices, i.e. z = z* = 0, puchasing powe paity holds at all times, and (8) epesents a simple monetay model of the 9 We omit the pesentation of the conditions ove the choice of within-county state-contingent assets, because fom the Mathematical Appendix we know this just leads to full consumption insuance acoss agents within a county. 10 We take the monetay policy shocks as exogenous. But since we allow fo abitay covaiance between home and foeign money shocks, ou famewok in pinciple allows fo any exchange ate outcome, anging fom fee floats (when shocks ae independent), to a pegged exchange ate (when shocks ae collinea).

12 274 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) exchange ate. Altenatively, with z = z* = 1, shocks to elative consumption ae detemined by shocks to elative money supplies alone. Fom time t + 1 onwads, in expectation, thee is full money neutality (in the linea appoximate model). Then, using the time t + 1 balance of payments condition, labo maket and poduct maket cleaing (and using the notation db t +1 = B t +1 B t ), we may establish that E t ðc tþ1 c tþ1 * Þ¼ db tþ1 ð1 nþ P C, ð9þ whee =(wh+(1 q)+qh)/(wh + 1), epesents the steady state inteest ate (equal to (1/b) 1), and P C descibes the initial steady state value of nominal consumption. This condition says that, if the home county is expected to have an incease in net foeign assets, beginning in time t + 1, then it is also expected to have an incease in its elative consumption 11. Using the balance of payments condition fo time t, the expessions fo foeign and domestic sales, and the pice indices fom Table 1b, we obtain the following c t c t * þ db tþ1 ¼ ðh 1Þð1 zð1 nþ z*nþþð1 nþz* þ nz ð1 nþ P C ½ Šs t. ð10þ This equation says that shocks to the exchange ate, by affecting the elative income of the home and foeign county, affect the path of elative consumption and the cuent account. Then, putting (9) and (10) togethe, we obtain c t c t * þ E tðc tþ1 c* tþ1 Þ¼½ðh 1Þð1 zð1 nþ z*nþþð1 nþz* þ nzšs t : ð11þ Eq. (11) says that the income effects of exchange ate changes ae spead ove cuent and expected futue elative consumption. Finally, fom the home and foeign Eule equations (Table 1a), we may obtain the following condition elating consumption gowth acoss the two counties (using E t s t +1 = s t ): E t ðc tþ1 c tþ1 * Þ¼c t c t * ðzn þ z*ð1 nþþ s t : q Eq. (12) says that an unanticipated exchange ate depeciation in peiod t, by causing a eal exchange ate depeciation fo the home county (when z, z* p 0), educes the elative home county inteest ate, and causes a fall in expected consumption gowth in the home county, elative to the foeign county. We may put (8) (12) togethe to obtain a solution fo the impact of money shocks on the cuent exchange ate. This is given by: 1 þ ðm t m t *Þ s t ¼, ð13þ D ð12þ 11 Since ou linea appoximation is taken aound an initial symmetic steady state with B = 0, the net foeign assets tem entes in tems of ates of change, athe than popotional ates of change.

13 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) whee h D ¼ 1 þ i þðzn þ z*ð1 nþþðq 1Þþqðh 1Þð1 zð1 nþ z*nþ : The esponse of the exchange ate to unanticipated money shocks depends on the elasticity of demand fo home goods, the inte-tempoal elasticity of substitution, and the measue of LCP fims in the home and foeign counties. Two special cases of (13), epoted in Table 2 ae of paticula inteest. With full pass-though fom exchange ates to pice (z = z* = 0), the esponse of the exchange ate is lowe, the geate is the elasticity of demand between home and foeign goods. On the othe hand, when pass-though is zeo (z = z* = 1), the exchange ate esponse is negatively elated to q, the consumption elasticity of money demand. Fom Table 1 we also deive the esponse of maginal cost to a money shock as: w t ¼ vðm t þ wl a t Þ: ð14þ The employment esponse to a money shock is: l a t ¼ xð1 vþw a t þ nc t þð1 nþc t * þð1 nþhð1 nz* zð1 nþþs t : ð15þ Employment depends negatively upon the wage of the flexible wage settes, positively on the movement in aggegate wold consumption, and, though expenditue switching effects, positively on the nominal exchange ate, so long as thee is some pass-though of exchange ates into pices (i.e. when z, z*< 1). Fom the money maket equilibium conditions in Table 1a, the movement in wold consumption is: nc t þð1 nþc t * ¼ nm t þð1 nþm t * ð1 nþnðz z*þs t q An unanticipated incease in home o foeign money aises wold consumption. But in addition, when z p z*, an exchange ate depeciation has a compositional impact on total consumption. Fo instance, when z > z*, a depeciation aises the home CPI moe than it educes the foeign CPI. Ceteis paibus, this implies that a weighted sum of home and foeign consumption will fall. We now put the components of Sections 2 and 3 togethe, examining the inteaction between the detemination of exchange ates and exchange ate pass-though.. Table 2 Exchange ate solutions: special cases ðm t m t *Þ 1 þ 1 ðm t m t *Þ 1 þ z = z*= 0 s t ¼ qðh 1Þþ 1 þ z = z*= 1 s t ¼ q þ

14 276 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Equilibium pass-though with identical monetay policies We evaluate the conditions undelying Poposition 1 and its coollay, using the esults fom (13), (14) and (15). Fist, define the function U(z, z*, 2 u, 2 u* ) as the elative benefit to the fim of picing by LCP as opposed to PCP. That is: Uðz, z*, 2 u, 2 u* Þ¼cov t 1ðw t, s t Þ va t 1ðs t Þ : 2 Because exchange ate vaiance and the covaiance of maginal cost and the exchange ate depend on the undelying monetay shocks, as well as on the measue of fims in each county following LCP, we may wite the function in this way. In the same way, we define U*(z, z*, 2 u, 2 u* ) as: U*ðz, z*, 2 u, 2 u* Þ¼ cov t 1ðw* t, s t Þ va t 1ðs t Þ : 2 Table 3 uses the esults fom Section 3 to define the conditional vaiance of the exchange ate and the conditional covaiance of exchange ate and maginal costs. We fist focus on symmetic equilibia, whee n = 0.5, 2 u = 2 u*, U = U*, and z = z*. Counties ae, theefoe, identical in all espects, and fims in the home and foeign county follow the same picing policy. Thee ae thee candidate symmetic equilibia, descibed as follows: (A) Symmetic PCP, z = z* = 0. This equies U(0, 0, 2 u, 2 u )<0, (B) Symmetic LCP, z = z* = 1. This equies U(1, 1, 2 u, 2 u )>0, (C) Symmetic mixed, 0 V z = z*v 1. This equies U(z, z, 2 u, 2 u )=0. In the thid case, at the equilibium value of z, fims ae indiffeent between picing in the home and foeign cuency 12. To establish the existence of equilibium we need to evaluate the U function at each value of z. It is easy to establish that in the symmetic case: h Uðz, z, 2 u, 2 u Þ ~ ṽ qðh 1Þþwh 1 þ i ð1 zþþðq 1Þz 1 þ ð1 ṽþ, ð16þ whee the tem ~ denotes popotional to, and ṽ ¼ v=ð1 þ wxð1 vþþ < How would fims coodinate on a mixed equilibium, when they ae indiffeent between the two policies? One possibility is that they play a mixed stategy, choosing to follow LCP (PCP) with pobability z (1 z), befoe choosing pices (Bacchetta and van Wincoop, 2001 give this intepetation). An altenative possibility is that thee ae small diffeential fim-specific costs (e.g. menu costs) of choosing LCP as opposed to PCP. If we ank fims in ode of inceasing costs, then the mixed equilibium would be a limit outcome as the scale of these diffeential costs appoaches zeo.

15 Table 3 Conditional vaiances and covaiances va t 1 (s t ) 1 þ 2ð 2 u þ 2 2 u* uu*þ D 2 cov t 1 (w t, s t ) v cov t 1 (w a t, s t ) cov t 1 (w a t, s t ) ¼ H cov t 1 ðu t ; s t Þ 1 þ wn q cov t 1 (w t *, s t ) cov t 1 (w t * a, s t ) þ w 1 n cov t 1 ðu t *; s t Þ q þwð1 nþ hð1 nz* zð1 nþþ n ðz z*þ q v cov t 1 (w t * a, s t ) wð1 nþ ¼ H cov t 1 ðu t *; s t Þ 1 þ þ w q wn hð1 nz* zð1 nþþ þ n q ð1 nþ ðz z*þ q va t 1 ðs t ÞŠ; cov t 1 ðu t ; s t Þ va t 1 ðs t ÞŠ 1 H ¼ 1 þ wxð1 vþ M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004)

16 278 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Using expession (16), we may establish the following poposition Poposition 2. Symmetic equilibium (a) If 1 þ 1 þ ð1 ṽþ qṽ h > 1 þ w q 1 þ, and q > 1 þ 1 þ ð1 ṽþ, ṽ LCP is the unique equilibium. (b) If 1 þ 1 þ ð1 ṽþ qṽ h < 1 þ w 1 þ, and q < 1 þ 1 þ ð1 ṽþ, ṽ q PCP is the unique equilibium. (c) If 1 þ 1 þ ð1 ṽþ qṽ h > 1 þ w q 1 þ and q < 1 þ 1 þ ð1 ṽþ, ṽ the unique equilibium is za(0, 1), such that U( z, z, 2 u, 2 u )=0. (d) If 1 þ 1 þ ð1 ṽþ qṽ h < 1 þ w q 1 þ, and q > 1 þ 1 þ ð1 ṽþ, ṽ thee ae thee equilibia: PCP, LCP, and an inteio (unstable) equilibium ẑ a (0, 1) such that U(ẑ, ẑ, u 2, u 2 )=0. Poof. The poposition follows diectly fom applying the paamete estictions to the conditions fo the diffeent types of candidate equilibia given above. 5 If the two inequalities given in pat a hold, each fim has an incentive to set expot pices in tems of the local cuency, whateve othe fims do. Thus, the only equilibium can be one whee all fims follow LCP. Fo LCP to be a unique symmetic equilibium, the consumption elasticity of money demand must be at least unity, and the elasticity of substitution between home and foeign goods must be sufficiently high. The esults ae sensitive to the flexibility in maginal cost. If most wages ae pe-set, then LCP cannot be an equilibium. But if v =1,so that all wages ae adjusted ex-post, then LCP is the unique equilibium when q>1 and h >1. If the two inequalities of pat b hold, then each fim will follow PCP, no matte what othe fims do. This outcome is moe likely, the lowe is v, and the lowe ae h and q. In the fist case, the calculation the fim makes is dominated by the vaiance of the exchange ate,

17 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) since the covaiance of maginal costs and the exchange ate is small when most wages ae pe-set. In the second case, the lowe ae h and q, the highe is the volatility of the exchange ate, elative to the cov t 1 (w t, s t ) tem, whateve picing policy is chosen. As a esult the optimal policy fo all fims is to choose PCP. In pat c, the incentives fo picing will depend on what othe fims do. If all fims follow PCP, then any one fim would have an incentive to deviate and choose LCP. But if all fims follow LCP, then again, any one fim would have an incentive to deviate and choose PCP. Thus, thee is no equilibium whee all fims follow the same picing policy. By continuity, an intemediate equilibium exists in which some fims follow PCP and some fims LCP. Fo a given value of v, this outcome is moe likely, the highe is h and the lowe is q. In that case, exchange ate volatility is quite low unde PCP, elative to cov t 1 (w t, s t ), giving fims an incentive to engage in LCP. But if all fims follow LCP, then with a low value of q, exchange ate volatility is high, elative to cov t 1 (w t, s t ). This means that LCP is not an equilibium. In the intemediate equilibium ð1 zþ fims follow PCP and z fims follow LCP. No fim has an incentive to deviate fom this outcome. The key featue giving ise to a unique equilibium is the pesence of a negative elationship between pass-though and exchange ate volatility. Pat d is the opposite of pat c. In this case, all fims have an incentive to follow PCP if all othe fims do also. Convesely, all fims have an incentive to follow LCP if all othe fims do also. Fo a given value of v, this outcome is moe likely, the lowe is h and the highe is q. Exchange ate volatility is then quite high unde PCP, elative to cov t 1 (w t, s t ), giving fims and incentive to engage in PCP, when all othe fims do so. But if all fims follow LCP, then with a high value of q, exchange ate volatility is low. This encouages fims to engage in LCP when othe fims also follow LCP. Thus, both z = 0 and z = 1 ae equilibia 13.Apositive elationship between exchange ate pass-though and exchange ate volatility thus gives ise to the possibility of non-uniqueness. Can thee be pue stategy asymmetic equilibia in the symmetic model? No. In the symmetic model, cov(w, s) and cov(w*, s) diffe only in the z z* tem that appeas in each expession in Table 3. Ifz > z*, then cov(w, s)< cov(w*, s) implying that U < U*. The latte inequality cannot be consistent with home fims choosing LCP (U > 0) and foeign fims choosing PCP (U*< 0). Hence, assuming z > z* leads to a contadiction. Fig. 1 descibes the fou possible equilibium configuations, in tems of the value of the U(z, z, 2 u, 2 u ) function ove the ange of z. Fig. 1a descibes the unique LCP outcome. Fig. 1b shows the unique PCP outcome. In each case the equilibium is unique because the gain to following LCP is positive (negative) iespective of the choice of othe fims. Fig. 1c shows the unique intemediate outcome, while Fig. 1d illustates the possibility of multiple equilibia. We note fom the figues that multiple equilibia ae possible only when the U(z, z, 2 u, 2 u ) function is upwad sloping. The slope of the function is (positively) popotional to h ṽ qðh 1Þþwh 1 þ i þ 1 q : As suggested by the poposition, this is moe likely to be positive, the highe is q, and the lowe is h. Moe infomally, multiple equilibia ae moe likely when LCP tends to be 13 Thee is also an intenal equilibium. This equilibium is unstable, howeve, since if a small measue of fims deviate by inceasing (deceasing) z, then all othes will wish to follow, so that z goes to 1 (0).

18 280 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Fig. 1. Equilibium configuations in the symmetic case. associated with low exchange ate volatility, and PCP tends to be associated with high exchange ate volatility. Empiically, howeve, multiple equilibia ae not vey likely in ou model. The empiically elevant ange of h exceeds unity, and should cetainly exceed the consumption elasticity of money demand q. Note that Poposition 2 does not depend on distibution of the money supplies. With identical monetay vaiances, both the vaiance of the exchange ate and the covaiance of exchange ates and maginal costs ae affected equally by monetay vaiability. In case (c), the equilibium z is given by qðh 1Þþ 1 þ wh ð1 ṽþ ṽ z ¼ qðh 1Þþwh 1 þ : ð17þ þ 1 q Inspection of (17) indicates that z is inceasing in ṽ. As a geate faction of wages ae set ex-post, the equilibium degee of pass-though declines. Similaly, z is inceasing in q and h. Both paametes tend to educe exchange ate volatility fo any given z, inceasing the numbe of fims who engage in LCP. This case illustates an impotant implication of Poposition 2; the elationship between exchange ate volatility and economic stuctue may be substantially alteed by the endogeneity of exchange ate pass-though. To illustate, take a special case whee w = 0 and ṽ ¼ 1. With pass-though taken as given, we may e-wite the expession fo exchange ate volatility as 1 þ 2ð 2 u þ 2 u* 2 uu* Þ 1 þ 2. þðq 1Þzþqðh 1Þð1 zþ

19 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) If we begin in a situation whee h>1, q>1, so that z = 1 holds (pat a of the poposition), then all fims follow LCP. In this case, the exchange ate volatility is 1 þ! 2 þ q ð 2 u þ 2 u* 2 uu* Þ. Hee, exchange ate volatility is less than the vaiance of monetay fundamentals, ( 2 u + 2 u* 2 uu* ). Now let q fall below unity. Ignoing the esponse of pass-though, we would pedict that this would incease exchange ate volatility, so that volatility exceeded the vaiance of monetay fundamentals. But in ou model, this will not happen. When q falls below unity, pat c of the poposition (o Fig. 1c) applies. Now we have passthough falling, so that z ¼ qðh 1Þ qðh 1Þþ1 q : Exchange ate volatility is now given by ( 2 u + 2 u* 2 uu* ). In this example, when endogenous pass-though is taken into account, exchange ate volatility will neve exceed the monetay fundamentals. 5. Pass-though with diffeential monetay policies We now allow fo diffeences in money gowth volatility acoss counties. To focus on the effects of diffeent volatilities, we assume in this section that the money shocks ae uncoelated acoss counties. Without loss of geneality, assume that the home county has lowe monetay gowth volatility than the foeign county. As discussed in, footnote 12, we may think of equilibia whee fims employ mixed stategies. Thus, if U(z, z*, 2 u*, 2 u* ) = 0 and U*(z, z*, 2 u*, 2 u* ) = 0 we say {z, z*} is an equilibium whee each home (foeign) fim chooses a pobability z (z*), ex ante, of setting its expot pice in foeign (home) cuency, and 1 z (1 z*) of setting its pice in home (foeign) cuency. To simplify the pesentation of esults, we fist make the additional assumption that pefeences display lineaity in labo supply, so that w = 0. This assumption is commonly used in the liteatue on exchange ates and pice stickiness (Deveeux and Engel, 2001; Cosetti and Pesenti, 2001). Qualitatively, none of the esults ae affected by the assumption. The geneal case whee w > 0 is used in the simulations below. In addition, futhe to ou discussion of the last section, we focus only on the cases of unique equilibium. Thus, we estict attention to the set of equilibia whee the U and U* functions ae downwad sloping In the specific case whee w = 0, this equies that q(h 1)(1 n) (q 1)n> 0 and q(h 1)n (q 1)(1 n)>0.

20 282 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) Using Table 3, it may be established that h U ~ ṽ 1 þ i þðzn þ z*ð1 nþþðq 1Þþqðh 1Þð1 zð1 nþ z*nþ 1 þ ð 2 u þ 2 u* Þ 2 2 u h U* ~ ṽ 1 þ i þðzn þ z*ð1 nþþðq 1Þþqðh 1Þð1 zð1 nþ z*nþ 1 þ ð 2 u þ 2 u* Þ 2 2 u* Fom these two expessions, we may establish the following poposition. Poposition 3. Let X ¼ 1 þ ð 2 u þ 2 u* Þ 2 2, X* ¼ 1 þ ð 2 u þ 2 u* Þ u 2 2, and u* h Cðz; z*þ ¼ṽ 1 þ i þðzn þ z*ð1 nþþðq 1Þþqðh 1Þð1 zð1 nþ z*nþ. 2 Note that fom ou assumption that u* > 2 u, we have X > X*. The equilibium is descibed by the set l ={z, z*}. The equilibium has the following popeties: (a) If Cð1,1Þ ¼ṽ þ q > X, (b) If then l={1, 1}. Cðẑ; 1Þ ¼ṽ 1 þ þð1 nþẑnþðq 1Þþqðh 1Þð1 nþð1 ẑþ ¼ X and 0 < ẑ < 1, then l ¼fẑ; 1g: (c) If X* < Cð0; 1Þ ¼ṽ 1 þ þð1 nþðq 1Þþqðh 1Þð1 nþ < X, then l = {0, 1}.

21 M.B. Deveeux et al. / Jounal of Intenational Economics 63 (2004) (d) If X* ¼ Cð0,ẑ*Þ ¼ ṽ 1 þ þ ẑ*ð1 nþðq 1Þþqðh 1Þð1 nẑ*þ and 0 < ẑ* < 1, then l ={0; ẑ*}. (e) If Cð0; 0Þ ¼ṽ 1 þ þ qðh 1Þ < X*, then l = {0, 0}. Poof. Fo each pat, the poof follows by diect constuction. In case (a), if C(1, 1) exceeds X, then full LCP is an equilibium fo both the home and foeign fims. Moeove, because we assume that C(z, z*) is deceasing in both vaiables (i.e. because we ule out multiple equilibia), this is the only equilibium outcome. In case (b), a measue ẑ of home county fims follow LCP, while all foeign fims follow LCP. Note that ẑ is implicitly defined by the equality C(ẑ,1)=X. In case (c), all home county fims follow PCP, wheeas foeign fims all follow LCP. In case (d), all home county fims follow PCP, while a measue ẑ* of foeign fims follow LCP. Finally, in case (e), all fims, both home and foeign, follow PCP. 5 Poposition 3 implies that the exchange ate pass-though into the home economy is always less than o equal to that into the foeign economy. A fall in the volatility of home money gowth will eithe leave exchange ate pass-though into the home economy unchanged, o decease it. Convesely, exchange ate pass-though into the foeign county eithe emains unchanged, o inceases. Thus, fims tend to set thei expot pices in the cuency that is associated with the moe stable monetay gowth. Which of the five categoies of Poposition 3 will come about depends on paamete values, and the elative size of money gowth vaiances. As in Section 4, the smalle is v, the faction of wage contacts that ae subject to ex-post adjustment, the moe likely that fims in both counties will follow PCP, since maginal costs will tend to have a smalle covaiance with exchange ate movements. Fo a given q, the geate is the elasticity of substitution between home and foeign poducts, h, the moe likely is LCP, since exchange ate vaiance will, ceteis paibus, be smalle. When the vaiance of money gowth, elative to foeign money gowth, falls to zeo, exchange ate passthough into the foeign county becomes complete. The eason is that educing home money gowth vaiance to zeo tends to fully stabilize maginal cost fo the home county. With a positive exchange ate vaiance detemined by foeign monetay instability, it is, theefoe, always optimal fo home county fims to set pices in thei domestic cuency. Fo foeign fims on the othe hand, the vaiance of the exchange ate tends to fall, elative to the covaiance of the exchange ate and maginal cost,