Does the Exchange Rate Belong in Monetary Policy Rules? New Answers from a DSGE Model with Endogenous Tradability and Trade Frictions

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1 Does he Exchange Rae Belong in Moneary Policy Rules? New Answers from a DSGE Model wih Endogenous Tradabiliy and Trade Fricions Michael Kumhof Inernaional Moneary Fund Douglas Laxon Inernaional Moneary Fund July 7 Kanda Naknoi Purdue Universiy Absrac This paper develops a -region DSGE model ha inegraes he heory of comparaive advanage or endogenous radabiliy ino a moneary model wih nominal and real rigidiies. We nd ha wihou endogenous radabiliy here is no role for he exchange rae in opimized moneary policy rules. Bu wih endogenous radabiliy he exchange rae can play a much more fundamenal role in faciliaing or slowing down adjusmens in he real economy, and i eners he opimized policy rule. JEL Classi caion Numbers: C; E3; E Keywords: Moneary Policy; Taylor Rule; Flexible Exchange Raes; To be presened a an ECB Conference on Globalisaion and he Macroeconomy, July 3-34, 7 in Frankfur, Germany. The auhors wish o hank Gian Maria Milesi-Ferrei for providing commens on an earlier version of his paper. We graefully acknowledge he invaluable suppor of Michel Juillard, Heesun Kiem and Susanna Mursula in developing he procedures used in he model simulaions. The views expressed herein are hose of he auhors and should no be aribued o he IMF, is Execuive Board, or is managemen Correspondence: mkumhof@imf.org; dlaxon@imf.org; and knaknoi@exchange.purdue.edu

2 I Inroducion The bene s of exchange rae exibiliy lie in is abiliy o change he relaive prices of goods in he presence of nominal rigidiies. Friedman (93) rs argued ha a exible exchange rae regime is desirable as a shock absorber, and his has been followed by a long subsequen lieraure. The implicaions for he conduc of domesic moneary policy have however been he subjec of much debae. In he closed economy lieraure, several imporan papers have found ha welfare opimizing moneary policy resuls in a complee sabilizaion of he domesic price level, wih no rade-o beween oupu gap sabilizaion and domesic price sabiliy. Many key conribuions o he recen open economy lieraure have found condiions (bu also excepions) under which hese resuls carry over o an open economy seing, which means speci cally ha here is no need for moneary policy o explicily consider he exchange rae. However, hese papers share an imporan se of common assumpions ha may be violaed in pracice. They include producer currency pricing, perfec exchange rae pass-hrough, and a lack of real rigidiies in inernaional rade. The lieraure has hus far concenraed on he pricing assumpion, by replacing he producer currency pricing assumpion wih local currency pricing. I can hen be shown ha i becomes opimal o eiher have a compleely xed exchange rae, or a leas o have a very signi can role for he exchange rae in he moneary policy rule. 3 The empirical evidence for he pricing assumpion is a subjec of much debae, wih Corsei and Peseni () arguing ha an inermediae degree of pass-hrough may be mos appropriae, wih developing counries likely closer o a high pass-hrough han indusrialized counries. 4 In his sudy we will argue ha anoher and hus far overlooked se of facors may play a key role in deermining wheher he exchange rae should ener moneary policy rules. They concern he endogenous deerminaion of he range of goods ha a counry expors and impors, ogeher wih real rigidiies in boh exporing and imporing. For imporing we assume ha here are coss, in erms of boh cos and ime, of iniiaing and reversing new impor supplier relaionships. For exporing, here is a cos o swiching beween purely domesic producion on he one hand and producion for boh domesic and foreign markes on he oher. We nd ha in a baseline model wih producer currency pricing bu wihou hese feaures he opimized linear moneary policy rule has a zero weigh on deviaions of he real exchange rae from is long-run rend. When endogenous deerminaion of he range of expors and impors is added ogeher wih expor swiching coss, he exchange rae assumes an imporan role, wih real appreciaions requiring moneary easing. exchange rae. Adding real impor rigidiies signi canly increases he opimal coe cien on he real To derive hese resuls we develop a wo-counry DSGE model ha inegraes he heory of comparaive advanage of Dornbusch, Fisher and Samuelson (977) ino a moneary model wih real rigidiies and wih sicky prices and wages. In his model he nominal exchange rae can play a much more fundamenal role in faciliaing or slowing down adjusmens in he real economy. To illuminae he implicaions for moneary policy we subjec he model o sandard ypes of shocks. We hen sudy macroeconomic performance using The key papers are King and Wolman (996), Goodfriend and King (997) and Roemberg and Woodford (997). See Gali and Monacelli (), Benigno and Benigno (3) and Obsfeld and Rogo (). 3 See Smes and Wouers (), Devereux and Engel (3) and Corsei and Peseni (). 4 Goldberg and Kneer (997) and Campa and Goldberg () nd ha in indusrialized counries he degree of shor-run pass-hrough o impor prices is roughly percen, and close o percen in he long run. Bu for many developing counries he consensus is ha pass-hrough o impor prices is very much higher, for example Bursein, Eichenbaum and Rebelo ().

3 moneary policy ineres rae rules ha add a erm for real exchange rae deviaions from rend o he convenional in aion and oupu gap erms. The model builds on he moneary, sochasic general equilibrium model of comparaive advanage of Naknoi (4). Heerogeneiy in produciviy and proporional rade coss deermine which goods are expored, impored or no raded in equilibrium. In his environmen rade is signi canly more responsive o shocks han in convenional models, which end o underpredic he volailiy of rade ows relaive o GDP. In he shor run, his endogeneiy of he rade paern ampli es he expendiure swiching e ec of exchange raes, as rms ransi ino and ou of exporing. A he same ime, he ransiions cause aggregae produciviy o ucuae, in he same manner as in he real models of Ghironi and Meliz (). These ransiions generae addiional oupu volailiy ha moneary policy mus sabilize. We also assume ha i is cosly o belong o he se of exporers. The cos is ime-varian and generaes smaller rade responses in he shor run han in he long run. I is similar o he xed cos of enering ino exporing in Ghironi and Meliz (). Exporers ha ransi in and ou of exporing in he shor run is no a far-feched assumpion. Trade economiss have ideni ed year-o-year ransiions ino and ou of exporing from micro daa in he U.S., Colombia and Mexico. For example, he duraion of rade relaionships of he U.S. wih is rading parners a he produc level is found o vary from 3 o years. These sudies indicae ha he exporing decision is no a long-run issue. I is beer viewed as a medium-run phenomenon wih some degree of persisence. The model makes hree deparures from Naknoi (4). Firs, we assume ha imporers ake ime and nd i cosly o build new relaionships wih foreign suppliers. This ime o build markes assumpion is similar o ime o ship in Backus, Kehoe and Kydland (994). I generaes a low shor-run elasiciy of subsiuion beween domesic goods and impored goods, despie a high long-run elasiciy. Because his fricion reduces he shor-run real rade response, i has imporan implicaions for moneary policy. Second, we inroduce verical inegraion, wih endogenous radabiliy only observed a he level of inermediae goods. 6 This was inroduced parly for realism, as i allows he model o generae observed rade o GDP raios wihou posulaing unrealisically high impor shares in producion and consumpion. Bu in addiion i doubles he e ecs of he ime-o-build-markes assumpion, which we make a boh he inermediae and nal goods levels. Third, o obain a fully speci ed business cycle model we inroduce invesmen and capial accumulaion. We assume ime o build in invesmen subjec o quadraic invesmen adjusmen coss. Togeher wih he assumpion of habi persisence in consumpion his implies ha domesic demand responds sluggishly, hereby generaing plausible responses o sandard shocks. To he bes of our knowledge, our model is he rs wo-counry moneary business cycle model ha embeds endogenous radabiliy in a seing wih signi can nominal and real rigidiies. Nominal rigidiies in price and wage seing allow for a meaningful analysis of opimal moneary policy, which would no be possible in he exible-price models of Bes and Kehoe (), Bergin and Glick (3) and Ghironi and Meliz (). We can herefore compare our resuls o hose of he large lieraure on opimal moneary See Bernard and Jensen (4), Robers and Tybou (), Aiken, Hanson and Harrison (997), and Besedes and Prusa (6). 6 Obsfeld and Rogo () argue ha he expendiure swiching channel largely operaes hrough relaive prices in he inermediae goods secor. 3

4 policy in open economies cied above. We describe our model in he nex secion. Secion III discusses calibraion, Secion IV presens our resuls, and Secion V concludes. II The Global Endogenous Tradabiliy Model (GETM) The model economy consiss of wo counries, referred o as Home and Foreign. The counries have idenical preferences and idenical nal and inermediae goods echnologies bu di eren echnologies in primary producion. Counries di er in size, wih he populaion of Home being and ha of Foreign ( ). We concenrae on he economic decisions of Home agens, as he corresponding decisions of Foreign agens are mirror images. Noe ha we express variables in absolue raher han in per capia erms, as his simpli es he exposiion. Each economy consiss of a represenaive household, a governmen, and muliple layers of rms. Households consume, supply labor, and accumulae capial. The mos upsream level of rms is primary producers, who obain capial and labor inpus from households, he laer subjec o sicky nominal wages. Primary producers di er by heir level of produciviy relaive o producers in he oher counry. They endogenously decide on hree modes of aciviy, quiing producion if hey are no compeiive wih impors from abroad, producing only for he domesic marke if hey are compeiive domesically bu no abroad, and producing for boh he domesic and he foreign marke if heir compeiors abroad are no compeiive. The nex layer of producion is inermediaes rms, which combine domesic and foreign varieies and hen sell hem eiher domesically or abroad. The nal layer is nal goods producers, who combine domesic and foreign inpus wih an exogenously nonradable xed inpu o produce nal oupu for domesic consumers, invesors, and he governmen. We assume ha inernaional rade a any sage is subjec o an iceberg ype rading cos, where a fracion of goods is los in shipping. The governmen is Ricardian and decides on an ineres rae rule for moneary policy. The srucure of he model economy in erms of goods and facor ows is illusraed in Figure. A Households Each individual household i maximizes lifeime uiliy which has hree argumens, consumpion C i which exhibis exernal habi persisence ha is parameerized by v, leisure ( L i ), where L i is labor e or and is he ime endowmen, and real money balances m i = M i =P, where P is he price of nal oupu. Denoing he ineremporal elasiciy of subsiuion by, we have 8 X < () Max E S c C i C : = + Li m i + n 9 = ; ; where E is he expecaion condiional on informaion available a ime, and S c is a preference or demand shock given by () S c = c S c + ( c ) + u c : Capial accumulaion is subjec o a ime-o-build echnology, wih a T + -period lag beween a new invesmen sar I i and he poin a which ha invesmen leads o an addiion o he currenly producive 4

5 capial sock K i : (3) K i + = ( )K i + I i T S inv T : The erm S inv represens a shock o he produciviy of invesmen spending, speci cally o he rae a which such spending is ranslaed ino addiions o he capial sock. I is given by (4) S inv = inv S inv + ( inv ) + u inv : Changes in invesmen sars are subjec o an exernal quadraic adjusmen cos () I = I I i : I This and all oher adjusmen coss are assumed o be redisribued back o households in lump-sum fashion. Each invesmen sar represens a commimen o a spending plan over T + periods, saring in he period of he invesmen sar and ending one period before capial becomes producive. The shares of he invesmen projec o be disbursed in each period are given by! j ; j = ; :::; T, wih T j=! j =. The acual invesmen J i is herefore given by (6) J i = T j=! j I i j : In wha follows we choose nal oupu as our numeraire, and he lower case price and reurn variables p and r are in erms of his numeraire. The nominal exchange rae is S, and he real exchange rae is s = (S P )=P. The gross rae of currency depreciaion is denoed by ", and and are he gross domesic and foreign in aion raes. Households in Home can hold money M i and wo oher ypes of nancial asses. Nominally nonconingen domesic currency governmen bonds, bough in period and mauring in +, and paying o i unis of domesic currency in +, are denoed by ~ F i, wih a real sock of ~ f i = ~ F i =P. Nominally non-coningen foreign currency bonds are denoed by F i, wih a real sock of f i = (S F i )=P. They are assumed o pay o i unis of foreign currency in +, where i is he gross nominal ineres rae in he res of he world and is a shock o uncovered ineres pariy given by (7) = + ( ) + u : The inernaional bond is assumed o be he only inernaionally raded asse. Households face a quadraic cos associaed wih holding he sock of his bond. This is required in he usual fashion o ensure saionariy of he economy s ne foreign asse posiion. The cos is given by (8) f = f f i + f ca i ; gdp gdp where he rs erm represens a cos of deviaing from a zero ne foreign asse o GDP posiion, and he second a cos of deviaing from a zero curren accoun o GDP posiion, where ca = f i f ". While his is mosly a compuaional device, here are also good empirical jusi caions, as for example emphasized by Kollmann (4). In addiion o nancial asses, households own wo ypes of real asses, domesically produced capial K i and a facor V i ha is in xed supply a he aggregae level. The laer is inroduced o capure he role

6 of exogenously nonraded goods in he economy, as he assumpion ha all goods are radable under zero rading coss seems oo exreme. Households real income consiss of real wages w L i, real reurns on capial r k K, i rens on he xed facor r v V i, ineres on inernaional bonds f i i " and on domesic bonds f ~ i i, lump-sum governmen ne axes T x i =P, pro redisribuions i =P from rms, and lump-sum redisribuions of adjusmen coss A i =P. The household also earns he ne capial gains from appreciaions of he price of he xed facor p V. Household expendiure consiss of consumpion spending C i, invesmen spending J i, spending on invesmen adjusmen coss, and a quadraic cos of adjusing nominal wages along he lines of Roemberg (98). The laer is exended o coss of adjusing he rae of change of he wage relaive o he pas observed aggregae wage in aion rae, as pioneered by Ireland () and also used by Laxon and Peseni (3). Speci cally, he real wage adjusmen cos is given by (9) w = w w wi L w! ; where wi = W i =W i is he (gross) household speci c rae of wage in aion and w is he aggregae rae of wage in aion. The period budge consrain, whose muliplier is denoed by, is herefore given by () f i + f ~ i + m i = f i i " + f ~ i i + mi +w L i + r K K i + r v V i + p V V i V i C i J i I f w +( i =P ) + (A i =P ) (T x i =P ) : We assume ha iniial holdings of bonds, money, capial and xed facors are idenical for all households. This implies ha each household has he same presen discouned value of income, and ha all households marginal condiions are idenical, including a synchronizaion of wage seing behavior. We can herefore drop he index i from he household problem. Every household maximizes () subjec o (3), (), (6), (8), (9), (), and he demand for heir labor. The rs-order condiions for consumpion, bonds and he xed facor are given by () S c C vc = ; v () = E + i + (3) + f f + f ca + i = E " + ; gdp gdp + + p V + + r V + (4) = E p V : Opimal invesmen and capial accumulaion are given by () T j=! j j +j + I I I I 6 ; = T +T q +T S inv ;

7 (6) q = E + r k + + q + ( ) : Nex, we consider an individual household s wage seing decision. We assume ha primary producers demand a labor composie ha is a CES aggregae over all labor varieies supplied by households, wih ime-varying elasiciy of subsiuion w. The cos minimizaion problem of an individual varieies producer indexed by z is given by (7) Min L i (z);i[;] Z Z W i L i (z)di s:: L (z) = L i (z) w w w w di : This produces a se of labor demand equaions for each labor variey L i (z) ha, given idenical relaive wages facing each producer, is sraighforward o aggregae so as o obain oal demand for each variey L i : W (8) L i i = W w Z L ; W = W i w w di : Households maximize heir uiliy from leisure subjec o labor demand (8), he budge consrain () and he wage in aion adjusmen cos (9). We obain he following equaion for wage dynamics: w L ( w ) + w L w w w w w E + w + L + w w + w w + w = (9) w L ( L ) : We allow for wage markup shocks. In paricular, he exogenously ime-varying wage markup is given by () w = w w ; which is subjec o i.i.d. shocks () w = w ( + u w ) : B Primary Producers Primary producion follows he speci caion of Naknoi (4), adding capial inpus and coss of swiching beween exporing and producing only for he domesic marke. Speci cally, here is a coninuum of goods varieies indexed by z [; ]. Firms endogenously decide wheher o belong o one of hree ypes of rms depending on heir produciviy. The mos producive ones, indexed by H, produce boh for he domesic marke and for expors because hey are more compeiive han foreign rms in he foreign marke even afer incurring a proporional rading cos. Those wih inermediae produciviy, indexed by N, produce only for he domesic marke because hey are su cienly compeiive domesically agains foreigners handicapped by he rading cos, bu for he same reason hey canno compee wih foreigners in he foreign marke. Finally, hose wih he lowes produciviy choose o qui producion because hey canno compee wih foreign impors in he domesic marke. For each variey here is a large number of perfecly compeiive rms producing oupu y from labor `(z) and capial k (z) using he following echnology: () y (z) = a(z)x `(z) k (z) ( ) : 7

8 The rs wo elemens on he righ hand side are rm-speci c produciviy a(z) and aggregae or oal facor produciviy (TFP) x. Firm-speci c produciviy deermines he paern of comparaive advanage beween counries. We normalize produciviy in Foreign o one, a (z) = 8z, and for Home we assume a produciviy schedule ha is exponenially declining in z as follows: (3) a(z) = Ne nz : The long run relaive produciviy of he mos producive Home variey is herefore Nx=x, while n is he rae a which relaive produciviy declines, a parameer ha will generally have o be larger for smaller counries. Comparaive advanage of course implies ha Home does no need o have an absolue advanage in any good in order for i o produce some par of world oupu. This means ha Nx < x is feasible. Comparaive advanage ogeher wih rading coss make radedness of inermediae goods endogenous. For each producer, opimaliy requires ha he price of is variey equals marginal cos, which in urn equals marginal facor cos divided by produciviy. Marginal facor cos is given by (4) mc = (w ) r k ( ) and he opimaliy condiion becomes ( ) ; () p (z) = mc x a(z) : A Home producer of variey z will produce so long as he price P (z) he is able o charge given his marginal cos does no exceed he price (S P (z))=( ) ha an imporer from Foreign of he same variey is able o charge given his marginal cos and rading coss. Given he declining relaive produciviy paern in Home here will herefore be a maximum level of z above which Home will rely enirely on impors from Foreign. We denoe his ime-varying level by z h. Equally, a Foreign producer of variey z will produce so long as his price P (z) does no exceed he price (P (z))=(s ( )) ha an imporer from Home of he same variey is able o charge. There will herefore be a minimum level of z, denoed z l, below which Foreign will rely enirely on impors from Home. We can combine hese wo condiions on prices wih he marginal cos condiions for Home and Foreign producers (). Bu before doing so we need o discuss expor adjusmen coss. We assume ha enering he expor rade involves addiional coss such as exra markeing coss and coss of building a geographically larger disribuion nework. Conversely, exiing he expor rade involves bene s ha can be concepualized as he scrap value of overseas sale operaions as in he indusrial organizaion lieraure. The funcional form of hese coss and bene s is of he iceberg-ype, ha is coss which mel a fracion of produciviy a(z) or a (z) for new enrans, and which conversely freeze addiional waer ha adds o he produciviy iceberg for rms ha exi. The dependence of such coss on enry and exi is capured by making hem a funcion of he change in he range of varieies produced for expors beween las period and his period. In paricular, for Home exporers he e ecive relaive produciviy is given by (x =x ) l a(z), 7 where (6) l = a z l z l z l 7 Noe our assumpion ha hese coss or bene s apply o all exporers ex-pos, regardless of wheher hey swiched saus. This is done for analyical racabiliy bu wihou loss of generaliy, as i only a ecs he inerpreaion and calibraion of he parameer a. : 8

9 For Foreign exporers he e ecive relaive produciviy is given by (x =x )(= h ), where (7) h = a z h z h z h The e ec of hese coss is o make exporers relaive produciviy schedule seeper around he cuo poins z l and z h of las period. For he example of a favorable domesic produciviy shock, his means ha some formerly nonraded varieies coninue o only be produced for he domesic marke even hough before aking accoun of expor adjusmen coss he producer could now produce more cheaply han foreigners. Bu as soon as ha nonraded goods producer decides o become an exporer he faces a lower level of produciviy. Combining he above discussion we obain he following condiions for he range of Home and Foreign produced varieies: : (8) wih equaliy a z = z h, and mc mc x Ne nz s x ( ) h for z [; z h ] ; (9) mc mc = x Ne nz ( s x ) l for z [z l ; ] ; wih equaliy a z = z l. The rs expression says ha a Home producer s marginal cos has o be below is Foreign compeior s marginal cos, bu allowing for he fac ha a poenial Foreign compeior s cos also includes he rade cos and expor adjusmen cos hurdles. The second condiion expresses he equivalen requiremen for he Foreign producer. We de ne = z h z l. Having deermined he ranges of goods produced by he expors and nonraded goods secors, i is hen rivial o deermine hese secors demand for inpus. Leing L ;H = R z l `(z)dz, K ;H = R z l k (z)dz and Y ;H = R z l y (z)dz, and similarly for secor N, we can wrie, for j = H; N: (3) w L ;j = Y ;j ; (3) r k K ;j = ( ) Y ;j : C Inermediaes Producers The producer of inermediaes D is a price-aker in boh his inpu and his oupu markes, wih his ( exible) oupu price given by P D. He uses inpus of expor goods D ;H, 8 nonraded goods D ;N and impor goods D ;F, wih he following CES producion funcion: (3) D = = Z D y (z) D D D dz D z l D (D ;H ) D D + ( ) D (D ;N ) D D + ( z h ) D (D ;F ) D D D : 8 These are goods in he varieies range z [; z l ) ha are boh expored and used a home. 9

10 The sub-baskes of inermediae goods are given by (33) D ;H = D ;N = " z l " Z D z l Z D z h z l (y (z)) D D dz (y (z)) D D dz # D D # D D ; ; D ;F = " z h Z D z h (y (z)) D D dz # D D ; where he price sub-indices for each of hese baskes can be shown o be " Z # z l D (34) P ;H = P (z) D dz ; P ;N = P ;F = z l " " Z z h z l z h P (z) Z z h P (z) # D D dz ; # D D dz : Using our resuls on he pricing of individual varieies, and dividing hrough by he numeraire price level, we can rewrie hese price indices in erms of aggregae variables as (3) and similarly for Foreign. p ;H = mc x a ;H ; p ;N = mc x a ;N ; p ;F = p s ;F ; The secorial produciviy erms in he denominaors of he rs wo expressions can be derived hrough analyical inegraion over he appropriae sub-inervals of goods varieies produciviies. 9 We have (36) a ;H = " z l Z z l a(z) D dz # D 3 e n(d )z l = N l 4 n( D )z l D ; (37) a ;N = = " 4 Z z h z l a(z) D dz # D e n(d )z l e n(d )z h n( D ) 3 D : 9 Noe again ha a criical implicaion of endogenous radabiliy is ha he aggregae produciviy level of a counry is endogenous o he producion choices of is rms. The Foreign aggregae produciviy erms are simpler, wih a ;F = h and a ;N =.

11 Inermediaes producers face a cos, in erms of boh ime and resources, of adjusing he impored goods componen of producion D ;F. Firs, i akes ime o build up new supplier relaionships ha allow he volume of impors o increase. We model his by assuming ha he sock of impor orders D ;F ha is lled in any given quarer is predeermined, while i akes T periods for new orders O DF o add o he exising order sock. Furhermore, we assume for simpliciy ha he exising order sock declines a he rae df = =( + T ), so ha he enire sock of orders urns over compleely wihin T + periods. We herefore have (38) D ;F = ( df )D ;F + O DF T : In addiion o hese ime coss here is also a resource cos o changing he amoun of orders, which represens he resources spen on foreign eld o ces and marke reconnaissance. Le he impor orders of inermediaes producer i equal O DF;i erms of impored inermediaes: (39) DF, and lagged aggregae orders O DF. Then we have he following real resource cos in = df O DF;i D O DF D Le he marginal uiliy of an addiional uni of domesic currency be given by = =P. Then he pro maximizaion problem for a represenaive inermediaes producer is (4) Max E X = P D +( z h ) D (D ;F ) D D A z l D (D ;H ) D D + ( ) D (D ;N ) D D D D +q DF P ;F ( df )D ;F + O DF T D ;F : The soluion o his problem for D ;H and D ;N is : P ;H D ;H P ;N D ;N P ;F D;F + DF (4) p D z l D D ;H D = p ;H ; (4) p D D D ;N D = p ;N : The condiion for D ;F is (43) p ;F q DF = + p +;F q DF +( df ) + "p D ( z h )D D ;F D p ;F # ; wih an opimaliy condiion for new impor orders of (44) df p O DF D O DF D O DF D O DF D A = T +T p +T;F q DF +T : Alernaive assumpions for df are of course feasible and a ec he rae a which new orders can change he sock of exising orders.

12 Noe ha he shadow price of he exising order sock q DF is zero in seady sae, bu posiive when here is a posiive shock o he demand for impors ha emporarily raises he marginal produc of impors above he real impor price. This speci caion of inermediaes impors ensures boh a delayed and gradual response of impor volumes o shocks. Overall real rade rigidiies of course also include he expor adjusmen coss menioned above. On he oher hand, endogenous radabiliy will push owards an ulimaely larger response of rade volumes o real exchange rae changes, because rms can choose no only he quaniy of expors hey produce bu also wheher hey wish o ener he expor marke in he rs place. D Final Oupu Producers Final oupu producers are perfecly compeiive price akers in heir inpu markes and monopolisically compeiive in heir oupu marke. Their producion decisions are idenical across producers, and we will herefore omi a rm speci c index. The rs sep in nal oupu producion is o combine radables produced by domesic inermediaes producers Z ;H wih radables produced by foreign inermediaes producers Z ;F o produce he radables composie T, wih he following echnology: (4) T = T ( T ) T (Z ;H ) T T + ( T ) T (Z ;F ) T T T : As for inermediaes producers, changing he level of impors Z ;F echnology. We le P T be he marginal cos of he composie T, P ZH impored inpus, and we de ne ZF as (46) ZF The impor order sock evolves according o = zf O ZF;I T O ZF T (47) Z ;F = ( zf )Z ;F + O ZF T : Then he opimizaion problem is 8 X < (48) Max E : P T = P ZH Z ;H P ZF A is subjec o a ime o build markes : and P ZF ( T ) T (Z ;H ) T T + ( T ) T (Z ;F ) T T Z;F + ZF The soluions o his problem for Z ;H and Z ;F are given by he prices of domesic and T T + q ZF P ZF ( zf )Z ;F + O ZF T Z ;F : (49) p ZH = p T T T Z ;H T ; () p ZF q ZF = + p ZF +q+( ZF zf ) + "p T ( T )T Z ;F T p ZF # ; The excepion is in adjusmen cos erms, where we need o disinguish beween lagged exernal aggregae erms and curren rm-speci c erms.

13 wih an opimaliy condiion for new impor orders of () zf p ZF and a price of impors O ZF T O ZF T O ZF T O ZF T A = T +T p ZF +T q ZF +T ; () p ZF = p ZF s ( ) : Final oupu is a composie of he sock of he nonradable xed facor V and of radables T, wih he CES producion funcion given by (3) = O ( O ) O (V ) O O + ( O ) O (T ) O O O : We denoe he nominal/real marginal cos of by P O =p O and he nominal/real renal cos of he xed facor by R V =r V. Then cos minimizaion implies he following demands for radables and nonradables: (4) T = ( O ) p T p O O ; () V = O r V p O O : Final oupu producers price seing is subjec o sicky in aion as in he wage seing decision oulined above. Speci cally, we assume ha all users of nal oupu demand a CES composie of varieies supplied by nal goods producers, wih ime-varying elasiciy of subsiuion p. The cos minimizaion problem of an individual user of nal oupu indexed by z is given by (6) Min i (z);i[;] Z P i i (z)di s:: (z) = Z p i (z) p di! p p : This produces a se of goods demand equaions for each variey i (z) ha, given idenical relaive prices facing each user of nal oupu, is sraighforward o aggregae so as o obain oal demand for each variey i : P (7) i i = P p Z ; P = P i p p di Final oupu producers maximize he presen discouned value of heir cash ow subjec o heir goods demand (7) he in aion adjusmen cos (8) p = p i ; and a xed cos in erms of nal oupu! O ha is given by (9)! O = p ( ) : : 3

14 When =, his xed cos exacly o ses he seady sae markup pro s = p. For (; ) he parameer denoes he share of markup pro s ha are reained as pro s by he rm afer xed coss have been paid. We inroduce his xed cos erm, which is familiar from Alig, Chrisiano, Eichenbaum and Linde () who se =, o be able o beer calibrae invesmen and capial income shares in GDP, as explained in he calibraion secion. The pro maximizaion problem is herefore ( X (6) Max E P i P O P i p ) P p P O! O : P = Afer recognizing ha all rms behave idenically and herefore dropping he rm-speci c indices i, he rs order condiion wih respec o P i is given by p (6) p po = p p p p : We allow for price markup shocks. In paricular, he exogenously ime-varying price markup is given by (6) p = p p ; which is subjec o i.i.d. shocks (63) p = p ( + u p ) : E Governmen Fiscal policy in boh counries is Ricardian in ha scal lump-sum axes are endogenously adjused o nance governmen spending, afer aking seigniorage ino accoun. To correcly calibrae seady sae shares of consumpion and invesmen in GDP, we assume a xed amoun of governmen spending G in each period. We also assume ha he iniial sock of nominal governmen deb is zero. Ne axes are deermined by (64) T x + M M = G ; which mainains he sock of governmen deb a zero a all imes. The benchmark policy rule ha we consider for he Home economy is an exended version of he Taylor (993) rule ha allows for ineres rae smoohing and ha adds an addiional real exchange rae feedback erm: (6) i = (i ) i i 4; gdp gdp y s s : s The in aion arge is given by so ha = is he long-run nominal ineres rae. The cenral bank is assumed o respond o deviaions of he he year-on-year in aion rae 4; = ( 3 ) 4 from is arge, and o he oupu gap and he real exchange rae gap. The oupu gap is a de ned as he deviaion of GDP from a -sided cenered moving average of GDP wih weighs aken from he Hodrick-Presco (HP) ler. While his measure of he oupu gap is imperfec, i helps o avoid some of he pifalls wih using alernaive measures such as he ex-price oupu gap, or purely backward-looking measures ha are based on one-sided versions of he HP ler ha exclude he model s prediced levels of fuure GDP see Appendix I for more deails abou he HP ler and he weighs ha we use. In e ec, because we are using he model s 4

15 predicions o help measure he underlying rend level of oupu i will produce measures of he business cycle ha can accoun parly for supply shocks ha shif he level of poenial oupu. The measures will also be much less erraic and jumpy han ex-price measures of he oupu gaps ha are in uenced by daa measuremen problems. 3 In addiion, in empirical versions of hese models ha produce compeiive forecass, following his approach in real ime will resul in signi canly smaller revisions in he measures of he business cycle han wha is obained from one-sided applicaions of Hodrick-Presco ler, which ignore informaion from he model s forecas of fuure oupu see Juillard, Kamenik, Kumhof and Laxon (7). Finally, and criically for his paper, he las erm of he Taylor Rule includes a measure of he real exchange rae gap measured in exacly he same way as we measure he oupu gap. Including he real exchange rae gap is no sandard, bu he purpose of his paper is of course o analyze wheher his erm should be included in a world wih endogenous radabiliy and real rade fricions. The Foreign cenral bank is assumed o follows a similar ineres rae feedback rule, bu wihou a real exchange rae feedback erm. F Equilibrium and he Curren Accoun In equilibrium households maximize lifeime uiliy, rms a all levels of producion maximize he presen discouned value of heir cash ows, and he governmen follows is policies as oulined in he previous secion. In addiion, he following marke clearing condiions hold (wih an equivalen se of condiions for Foreign): 4 (66) L = L ;H + L ;N ; (67) K = K ;H + K ;N ; (68) Y ;H = p ;H D ;H + s p ;HD;H ; (69) Y ;N = p ;N D ;N ; (7) D = Z ;H + Z ;H ( ) ; (7) V = V ; (7) = C + J + G +! O : Togeher wih household and governmen budge consrains hese clearing condiions imply he following curren accoun equaion: i (73) f " + s p ;HD;H + s p ZH Z;H = f + p ;F D ;F + p ZF Z ;F : Finally, inernaional bond marke clearing is given by (74) f + f s = : 3 Wage and price indicies conain signi can noise componens ha induce measuremen errors ino ex-price measures of he oupu gap, which is one reason why hey have no had much of an impac in policymaking deliberaions. Anoher reason is ha hey ypically are consruced by assuming ha all of he economy s sae variables such as he capial sock have always been deermined by a ex-price economy. 4 Noice ha he presence of relaive prices in he marke clearing condiions for varieies composies in secors H and N is due o he fac ha he oupu composies Y are de ned as addiive in quaniies while he inpu quaniies D are de ned as CES aggregaes.

16 III Calibraion We calibrae he model wih he euro area in mind, and herefore se he size of Home o be percen of he world economy ( = :). Unless oherwise menioned, parameers are assumed o be he same across he wo counries. Consumers discoun he fuure a he rae of percen per quarer (4 percen per year) ( = :99). The ineremporal elasiciy of subsiuion ( ) and he degree of habi persisence () are. and.8, respecively. These coe ciens, ogeher wih adjusmen coss on consumpion and invesmen, generae he lagged and hump-shaped responses o ineres hikes ypically found in empirical models. Frisch elasiciy of labor supply, which is implied by and he seady sae proporion of ime worked, 6 is se equal o., which is sandard for he macroeconomic lieraure, bu a he high end of microeconomic esimaes. Average markups for boh he euro area and he res of he world are aken from Bayoumi, Laxon and Peseni (4). The seady-sae labor marke markup is se o 3% in Home and 6% in Foreign and in he goods markes i is se a 3% in Home and 3% in Foreign. Coe ciens de ning wage and price sickiness parameers have all been se o 4. These values were chosen o produce plausible impulse responses o sandard shocks. Elasiciies of subsiuion beween Home and Foreign raded goods D and T The were se equal o., as is sandard in he macroeconomic lieraure. The elasiciy of subsiuion beween raded and exogenously nonraded goods O is se o.8, following he evidence surveyed in Mendoza (). Turning o ime-o-build lags, following Murchison, Rennison and Zhu (4), we assume ha i akes one quarer o plan an invesmen projec and quarers o complee i. 7 We assume ha invesmen expendiure is spread equally over he (T + )-period life of he invesmen projec. In addiion, we se he adjusmen cos parameers ha govern invesmen dynamics o be consisen wih he hump-shaped paern seen in response o ineres rae cus ha peak a around 4-6 quarers. The depreciaion rae of privae capial is. percen per quarer ( = :). To re ec he di culies of building and mainaining inernaional supplier relaionships compared o domesic supplier relaionships, we assume a ime-o-build markes lag of quarers in boh inermediae and nal goods. This implies ha he wo depreciaion raes df and zf of exising impor orders equal =3. We choose adjusmen cos parameers o generae plausible dynamics of impors following shocks. Similarly, seing a = : generaes plausible ransiions beween exporing and non-exporing rms following shocks. The model herefore generaes small changes in rade volumes in response o emporary real exchange rae ucuaions, bu large changes in response o permanen shocks, as has been observed in pracice see Erceg, Guerrieri, and Gus (3) and Laxon and Peseni (3). Finally, we se he parameers ha deermine Wihou he adjusmen coss, higher parameer esimaes may be needed. For example, Bayoumi, Laxon and Peseni (4) show ha esimaes as high as. and.97 are required for and o generae he hump-shaped responses o ineres rae shocks ha can be found in he ECB s Area-Wide Model (AWM) of he moneary ransmission mechanism see Fagan, Henry and Mesre (). 6 As usual for his ype of uiliy funcion one can calibrae eiher he Frisch elasiciy or he proporion of ime worked in seady sae. We choose he former as i more signi can for macroeconomic dynamics. 7 Time-o-build dynamics are becoming an imporan feaure of he new generaion of macro models ha are being designed inside cenral banks. For example, he work by Murchison, Rennison and Zhu (4) a he Bank of Canada builds on earlier work a he Fed by Edge (a, b). For more informaion on he imporance of ime-o-build dynamics for he inernal propagaion mechanism of DSGE models, see Casares (4). In paricular, Casares (4) provides a very useful sudy showing he e ecs on macroeconomic dynamics of adding ime-o-build lags ha range beween and 8 quarers. 6

17 he endogenous risk premium on bonds o ensure ha changes in he risk premium are su cien o preven implausibly large curren accoun de cis. The model is calibraed so ha sandard componens of GDP have sizes compaible wih heir average shares in GDP in he daa. The only di culy here is he share of exogenously nonraded goods in GDP, which we assume o be percen. Relaive GDP in boh counries is xed by adjusing he Home aggregae produciviy parameer x in accordance wih relaive GDP in he daa, leaving x =. Governmen spending and privae invesmen are each assumed o represen 8 percen of seady sae GDP in each counry, where he privae invesmen raio is xed by choosing he producion funcion parameer. Noe ha our previous choices of and would ypically make i impossible o independenly x he seady sae capial share. There is however a soluion o his in models wih monopolisic compeiion, because he capial share does no only depend on he reurn o capial bu also on he monopoly pro s of rms minus heir xed coss. We herefore x he seady sae capial share in GDP a 36 percen in boh Home and Foreign, by appropriaely seing he xed cos parameer. Expors and impors are assumed o be balanced in seady sae, wih an overall percen expors and impors o GDP raio in Home (and of course correspondingly smaller raios in he larger Foreign), half of which is accouned for by inermediae goods and half by nal goods. To calibrae rade in his way he parameers a our disposal are di eren from convenional models, a leas a he level of inermediae goods. The parameer here is no an exogenous share parameer (like T a he level of nal oupu) bu he slope n of he relaive produciviy schedule. 8 We rs choose rading coss o equal = :, and hen obain n = :4 as consisen wih percen expors and impors o GDP raios. This relaively a slope re ecs he fac ha we assumed Home o represen a fairly large share of he world economy. Finally, we se he parameers ha deermine he endogenous risk premium on bonds o ensure ha changes in he risk premium are su cien o preven implausibly large curren accoun de cis. For moneary policy, we assume ha he in aion arges in boh Home and Foreign equal percen per annum. The coe ciens of he moneary policy rule are of course he subjec of our analysis. We work wih a fairly sylized represenaion of he shock processes, which are assumed o be idenical in boh economies. The wage and price markup shocks are assumed o be equal in magniude and heir magniudes have been calibraed so ha hey deermine mos of he variaion in he in aion process a he business cycle frequency. Following recen empirical work we assume ha here is no serial correlaion in hese shocks see Smes and Wouers (4), Juillard and ohers (6) and Juillard and ohers (7). In same empirical work demand shocks o consumpion and invesmen have been found o be very signi can for explaining variaion in he real economy a business cycle frequency. Following Juillard and ohers (6) we assume ha he consumpion and invesmen shocks are posiively correlaed (.) and ha here exiss signi can posiive serial correlaion in he consumpion shocks. We also consider shocks o he UIP equaion, which have been found o be very imporan for explaining exchange rae variabiliy and for hese shocks we assume ha hey are highly serially correlaed (.7). In he secion on sensiiviy analysis we consider di eren assumpions abou he shock processes o examine how he resuls change under alernaive assumpions. We do no consider oher sources of shocks such as permanen produciviy shocks or shocks ha a ec specializaion and openness, bu leave he analysis of hese addiional shocks unil he model has been fully esimaed. 8 The inercep N canno be se independenly of he aggregae produciviy parameer x, whose calibraion was discussed above. 7

18 Figure repors he responses of GETM o a persisen basis poin hike in ineres raes in he Home economy. The magniude and hump-shaped response of GDP and consumpion is similar o sandard DSGE models such as he IMF s Global Economy Model (GEM) as well as reduced-form economeric models such as he ECB s Area-Wide Model (AWM) model compare Figure wih Table. However, GETM shows signi canly smaller invesmen responses for emporary shocks. This mainly re ecs he ime-o-build capial assumpion in GETM, which ends o weaken he response of invesmen in response o emporary shocks. Convenional DSGE models such as GEM assume quadraic adjusmen coss associaed wih changing he level of invesmen and absrac from ime-o-build consideraions for a discussion of model properies wih ime-o-build dynamics see Murchison, Rennison, and Zhu (4). Reduced-form models such as AWM are compleely backward looking and so he responses o shocks should in principle represen an average response o emporary and permanen shocks. GETM s responses o permanen shocks will ypically be larger as i akes longer o increase he capial sock and rms have he incenive o incur he adjusmen coss. Ineresingly, he responses of impors and expors are signi canly sronger in GETM han in GEM and are more in line wih he sronger responses of AWM. 9 Again, his re ecs he key assumpion in GETM ha he supply of expors is more responsive o relaive prices as rms are allowed o choose o produce goods for eiher he expor or domesic marke. IV Resuls The main goal of his secion is o assess under wha condiions sandard moneary policy reacion funcions such as he Taylor rule need o be modi ed o include informaion abou he exchange rae. However, before proceeding o his analysis we rs sar by showing how GETM is di eren from oher sandard DSGE models and why endogenous radabiliy maers. A How is GETM Di eren from Oher Models? Convenional moneary business cycle models canno accoun for srong rends in rade volumes, nor can hey explain how he moneary ransmission mechanism changes over ime as economies exploi greaer specializaion. The objecive of GETM has been o develop a model ha inegraes rade heory ino a moneary business cycle model. The basic assumpion of he model is ha rading coss resric rade and resul in lower levels of specializaion and produciviy. Figure 3 repors resuls ha show he long-run e ecs on welfare, rade, GDP, consumpion, invesmen and labor e or of lower rading coss. In he base-case calibraion a reducion in rading coss of percenage poins raises he expor-o-gdp raio by almos 4 percenage poins. As rading coss represen pure deadweigh losses welfare improves signi canly in boh economies. In he Home economy GDP and invesmen rise by 9. percen and 8.4 percen, respecively. The increases in consumpion in he Home economy are even larger (.7 percen) han he gains in GDP as he erms of rade improves in favor of he Home economy. The welfare improvemen in he Foreign economy is signi can, bu much smaller han in he Home economy. This re ecs he assumpion ha he Foreign economy is much larger han he Home economy (.7 versus.) so here are smaller poenial gains from rade. In boh economies higher welfare is a resul of higher levels of produciviy, which increase 9 These responses are repored in Fagan, Henry and Mesre () and Bayoumi, Laxon and Peseni (4). 8

19 he susainable level of real income. This resuls in an increase in he consumpion of leisure reducion in labor e or ha is one half as large as he increase in consumpion of goods and services. Figures 4 o 7 provide some sensiiviy analysis. The base-case calibraion of he Home economy assumes ha is relaive size is.. Figure 4 considers he case of a small open economy ha only represens percen of he world s populaion. In his case he bene s of lower rading coss mainly accrue o he smaller economy and become larger. Indeed, in his case a percenage poin reducion in rading coss raises GDP by 4.8 percen, abou percenage poins more han in he base case when i represened percen of he world. Figures and 6 repor resuls for cases where he elasiciy of subsiuion beween impored goods and domesically produced goods is. and 3., insead of he base-case assumpion of.. As can be seen in he Figures, higher rade elasiciies srenghen he responsiveness of rade ows, bu have very lile addiional e ecs. For example, in he base case a reducion in rading coss of percenage poins increases he expor-o-gdp raio by 4.9 percenage poins and his e ec declines o 4.3 percenage poins when he elasiciy of subsiuion is. and rises o 44. percenage poins when i is 3.. However, in hese cases he e ecs on GDP and consumpion are almos idenical. To isolae he di eren supply-side e ecs Figure 7 repors he resuls for a smaller labor supply elasiciy (. insead of he. ha was used in he base case). A lower elasiciy of labor supply srenghens he e ecs on GDP (. versus 9. percen in he base case), consumpion (.7 versus 3. percen) and invesmen (8.4 versus 9. percen) as workers increase leisure relaively less in response o higher produciviy. B Opimal Simple Policy Rules We now opimize he feedback and smoohing coe ciens in he moneary policy rule (6). To do so we consider a general loss funcion where policymakers are assumed o care abou variabiliy in in aion, oupu, and expors: (7) L = L var(4) + L var(ygap) + L 3 var(xgap) : The rs wo erms ha place weighs on in aion and oupu variabiliy are sandard. We argue here may be good reasons why policymakers migh also care abou variabiliy in expors if here are signi can fricions in shifing resources ino he expor secor. However, we do no make his elemen of he loss funcion criical for our resuls, raher we simply repor resuls for alernaive ses of weighs and discuss he implicaions. In fuure exensions of he paper we plan o explore higher-order approximaions of he model and possibly welfare analysis so ha we can analyze he level e ecs on welfare and oher variables ha may arise from excessive variabiliy in expors. Bu, i should be recognized ha loss funcions are a more exible approach ha is no dependen on he speci c form chosen for he uiliy funcion. In addiion, i allows for a simple characerizaion of preferences for policymakers, whose objecives may no wholly coincide wih hose of privae agens, a phenomenon ha is imporan in accouning for real-world policymaking. For exposiional purposes we de ne in aion nuers as policymakers ha place a weigh of on in aion and zero weighs on oupu and expor variabiliy. We de ne oupu gappers as policymakers ha place equal weighs on in aion and oupu gap variabiliy; and oupu-expor gappers as policymakers ha place equal weighs on variabiliy in in aion, oupu gaps and expor gaps. To rule ou implausibly large magniudes for ineres rae variabiliy we also assume ha he objecive funcion is minimized subjec o a consrain 9

20 ha he sandard deviaion of he rs di erence of ineres raes is less han or equal o basis poins. B. Base-Case Resuls The op row of Table repors he base-case resuls for in aion nuers when he exchange rae is in he reacion funcion and he second row repors he resuls for in aion nuers when i is excluded from he reacion funcion. The 3rd row repors he di erence beween he rs rows so ha i is easier o see he addiional variabiliy imposed on he economy by ignoring variaion in he exchange rae. The nex 6 rows in he Table repea he analysis for oupu gappers and oupu-expor gappers. In each line we repor he value of he loss funcion, he opimal parameers in he reacion funcion as well as he sandard deviaions for year-on-year in aion, oupu, expors and he real exchange rae, all measured as deviaions from rend. The resuls for in aion nuers produce a large weigh on in aion in he reacion funcion and signi can posiive weighs on he oupu gap and he exchange rae. This suggess ha he oupu gap and exchange rae gaps have signi can informaion conen ha is useful for helping o reduce variabiliy in in aion. However, when we focus on he role of he laer by comparing he di erences beween he rs rows we can see ha excluding he exchange rae resuls in a very small increase in he in aion variabiliy of wo basis poins. Noe, however, ha here are signi can increases in he variabiliy of oupu and especially expors by ignoring exchange rae developmens, so ha while he losses of in aion nuers are lile a eced by ignoring oupu and exchange rae gaps, in aion nuers would impose signi can losses on oupu gappers and oupu-expor gappers. Indeed, he parameer esimaes on in aion are much larger han wha is ypically observed in reacion funcions, suggesing ha policymakers are no in aion nuers, bu insead place signi can weigh on real variables when hey deliberae abou ineres rae decisions. Indeed, when we move o he cases of oupu gappers and oupu-expor gappers we observe a signi can decline in he weigh on he in aion erm and an increase in he weigh on he oupu gap in he case of oupu gappers and an increase in he weigh on he real exchange rae gap for he case of oupu-expor gappers. For he case of he oupu-expor gappers here is a signi can reducion in variabiliy in boh oupu and expors a he cos of higher variabiliy in in aion while for he oupu gappers excluding he exchange rae increases variabilily in boh oupu and in aion. A his poin he obvious quesion o ask is how hese resuls are di eren from convenional moneary business cycle models ha absrac from endogenous radabiliy. The nex subsecion answers ha quesion. B. The Role of Endogenous Tradabiliy I is sraighforward in GETM o exclude endogenous radabiliy from he model by simply deleing he equaions ha deermine he evoluion of z l and z h, and hen exogenizing hese variables. This and eliminaing rade fricions urns GETM ino he sandard open economy model ha has been used exensively in he lieraure. Table 3 repeas he analysis above when we exclude endogenous radabiliy. Srikingly, he parameers on he exchange rae gap decline o pracically zero and here is very lile di erence in all cases beween he loss funcions where he exchange rae gap eners he reacion funcion and hose cases where i does no. This con rms earlier resuls obained from oher DSGE models ha assume producer currency pricing, where he exchange rae has no been found o play a signi can conribuion in convenional mon- This is only slighly higher han he sandard deviaion of he rs di erence of shor-erm ineres raes in he euro area.