Master s Thesis. Comparing the Monetary Policies of the Fed and the ECB: A New Keynesian Approach. Arda Özcan

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1 Maser s Thesis Comparing he Moneary Policies of he Fed and he ECB: A New Keynesian Approach Arda Özcan Maser of Economics and Managemen Science Humbold Universiy of Berlin Suden Number: 5375 Examiner: Prof. Harald Uhlig Ph. D. Augus 2, 27

2 Absrac In his paper a Dynamic Sochasic General Equilibrium (DSGE) model is described for he closed and open economy case wih incomplee exchange pass-hrough in he so-called "New Keynesian" framework following Chrisiano, Eichenbaum and Evans (25) and Adolfson, Laseén, Lindé and Villani (27), respecively. The main focus of his paper are he di erences and similariies beween US and EU moneary policies. A less imporan focus is aribued o he implicaions of open and closed economy models in moneary policy analysis. The models are solved and log-linearized and nally calibraed based on Smes and Wouers (24a, 24b and 27). We found ha moneary ransmission mechanism has similar for US and EU in boh models. 2

3 Conens Inroducion 5 2 Theory and Relaed Lieraure 6 3 The Model 8 3. Households Inermediae Goods Firms Imporing Firms Exporing Firms More Open Economy Aspecs The Governmen The Cenral Bank Marke Equilibrium Solving he Model Seady Sae Log-linearized equaions Calibraion Impulse Response Analysis 32 6 Concluding Remarks 36 7 References 38 8 Appendix 4 8. Parameer values Figures

4 Lis of Figures Ineres rae shock, EU, closed economy model () Ineres rae shock, US, Closed economy model () Ineres rae shock, EU, Open economy model () Ineres rae shock, US, Open economy model () In aion arge shock, EU, Closed economy model () In aion arge shock, US, Closed economy model () Ineres rae shock, EU, Closed economy model (2) Ineres rae shock, US, Closed economy model (2) In aion arge shock, EU, Closed economy model (2) In aion arge shock, US, Closed economy model (2) Ineres rae shock, EU, Open economy model (2) Ineres rae shock, US, Open economy model (2) In aion arge shock, EU, Open economy model (2) In aion arge shock, US, Open economy model (2) Preference shock, EU, Closed economy model Preference shock, US, Closed economy model Labor supply shock, EU, Closed economy model Labor supply shock, US, Closed economy model Technology shock, EU, Closed economy model Technology shock, US, Closed economy model Preference shock, EU, Open economy model Preference shock, US, Open economy model Labor supply shock, EU, Open economy model Labor supply shock, US, Open economy model Technology shock, EU, Open economy model Technology shock, US, Open economy

5 Inroducion In his paper a Dynamic Sochasic General Equilibrium (DSGE) model is described for he closed and open economy case in he so-called "New Keynesian" framework. The closed economy model is based on he work of Chrisiano, Eichenbaum and Evans (25) whereas he open economy model is based on he work of Adolfson, Laseén, Lindé and Villani (27). Boh papers allow for nominal and real rigidiies, such as price and wage sickiness, variable capial uilizaion, capial adjusmen coss and habi formaion as common feaures. Following Adolfson, Laseén, Lindé and Villani (27), incomplee exchange rae pass-hrough is inroduced in order o capure he di erences in moneary policy implemenaion in open and closed economy models. Furhermore, consumpion, labor income and capial income axes are incorporaed for boh models and accordingly, scal policy is rule is inroduced following Traband and Uhlig (26). The main focus of his paper are he di erences and similariies beween US and EU moneary policies. A less imporan focus is aribued o he implicaions of open and closed economy models in moneary policy analysis. This paper can be di ereniaed from ha of Adolfson, Laseén, Lindé and Villani (27), as wihin his paper he open economy model for boh he EU and US are modelled ogeher allowing for ineracions and subsequenly puing forward furher challenges. Boh models are no esimaed bu insead calibraed based on Smes and Wouers (24a, 24b and 27) esimaions. In he absence of benchmark large-open economy models incorporaing US and EU economies in he same model, calibraion also pus forward furher challenges. Boh models have similar e ecs on moneary ransmission mechanism. However, due o he arising miscalculaions, he models presened here fails o generae sandard impulse response funcions for some paricular shocks. Therefore, he nex sep, following his paper will be xing he calculaion problems and using Bayesian echniques for he esimaion procedure. The paper is organised as follows. In Secion 2, a brief inroducion is given abou he New Keynesian principles and he evoluion of such models. The open and closed economy models are described in Secion 3. Furher, in Secion 4 he seady sae de niions along wih he model soluion is presened. This is followed by calibraion of he model. Calibraion is based on Smes and Wouers (24a, 24b and 27). The model is evaluaed in Secion 5 by analyzing impulse response funcions. Finally, concluding remarks are made in Secion 6. 5

6 2 Theory and Relaed Lieraure For a leas pas wo decades here is a growing ineres in he so-called "New Keynesian" synhesis in analyzing moneary policies. The New Keynesian synhesis came ino popular usage in he 98 s. Earlier in he pre-keynes world compeiive markes and perfec exibiliy of prices and wages were assumed. Keynes s argumen was he exisence of rigidiy in prices and wages. One of he reasons for he prevailence of involunary, prolonged unemploymen was aribued o his sickiness in wages which causes marke imperfecions. Laer on from 95 s unil mid-97 s neoclassical synhesis, which is based on uiliy based maximisaion of households and rms, was he dominan framework. The essence of neoclassical synhesis was "Walrasian" equilibrium (i.e. perfecly exible prices and wages and compeiive markes) in he long-run and reamen of wages and prices as given in he shor-run. Along wih his shor-run rigidiy in prices and wages, he expecaions were also assumed o be xed in he shor-run or subjec o ad-hoc adjusmen as under he adapive expecaions hypohesis. Furher, 97 s winessed he rise of raional expecaions or New Classical approach, originally proposed by Muh (96) and laer developed by Lucas (976). New Classicals assumed perfec exibiliy for prices and wages, whereas informaion available o economic agens was reaed as imperfec. This implies ha agens could use he informaion hey had opimally bu sill markes could deviae from he full informaion equilibrium. Lucas (976) argued ha he parameers of radiional macroeconomeric models depended implicily on agens expecaions of he policy process and were unlikely o remain sable as policymakers changed heir behaviour. As Rudebusch (22) saes, his criique was in uenial in wo respecs. Firs, i helped re-orien macroeconomic research oward models wih explici expecaions and "deep" parameers of ase and echnology. These models, which were o be invarian o policy shifs, included esimaed rs-order condiions or Euler equaions, calibraed general equilibrium models wih explici opimizaion. Second, he Lucas criique helped change he focus of policy evaluaion from consideraion of alernaive pahs of he policy insrumen o consideraion of alernaive policy rules, which allowed individual agens o formulae forward-looking dynamic opimizaion problems. New Keynesian economics adoped he raional expecaions approach as well as nominal rigidiies in prices and wages. Di erences beween he New Classicals and New Keynesians exis more in erms of modeling he supply-side and less in modeling he demand-side. (Gordon, 99). Addiionally, Romer (993), Greenwald and Sigliz (993), Taylor (997) give insighs ino undersanding he basic principles of New Keynesian perspecive. Goodfriend and Woodford (997) give an insigh ino he evoluion of moneary policy analysis along wih he evoluion of economic houghs saring from neoclassical synhesis. 6

7 In he long run growh pah of oupu is deermined by he supply-side. In he long run here is no radeo beween in aion and unemploymen, i.e. moneary neuraliy in he long run. In he shor run here is a radeo beween in aion and unemploymen as described by he Phillips curve. Given he price/wage sickiness, shor run ucuaions are caused by changes in aggregae demand. Policy measures are a eced by he expecaions of privae agens. Equilibrium, which does no imply cleared markes, is possible when hese expecaions are ful lled. These principles innaely consiues he Taylor (993) rule which is he essence of he New Keynesian moneary policy analysis framework. Taylor rule speci es ha he cenral bank ses is insrumen, which is he shor erm ineres rae, in order o reac o wo key variables: he deviaions in aion from a arge and he deviaions of real oupu from is poenial level or from is seady sae. Therefore, by focusing on policy responses o hese key variables, he Taylor rule implicily capures policy responses o economic facors ha a ec he evoluion of hese key variables. Furher, Dynamic Sochasic General Equilibrium (DSGE) models provided he necessary ools for he sudy of he opimal conduc of moneary policy, design and implemenaion of simple ineres rae rules (Monacelli, 23). In his maer, sicky price closed economy model of Roemberg and Woodford (997) became he workhorse for moneary policy analysis. Smes and Wouers (23), on he oher hand, showing ha Bayesian mehods can be applied succesfully o closed economy analysis, provided a new perspecive on he subjec. And more recenly he research was exended ino open economy analysis, i.e., New Open Economy Macroeconomics (NOEM) analysis. Moneary policy analysis in he early NOEM lieraure was assuming complee exchange rae pass-hrough. However, Gali and Monacelli (22) show ha opimal moneary policy is idenical in open and closed economy analysis when here is complee exchange rae pass-hrough o domesic prices. Accordingly, Lubik and Schorfheide (25) develops a small open economy model wih wo counries, namely US and EU. They inroduce endogenous deviaions from purchasing power pariy (PPP) via monopolisic price-seing imporers ha lead o imperfec pass-hrough. Adolfson, Laseén, Lindé and Villani (27) provides a large-scale open economy model for EU, also assuming incomplee exchange rae pass-hrough boh in impor and expor secor. The esimaed model have a moneary ransmission mechanism well in line wih he common lieraure. 7

8 3 The Model In his secion he closed and he open economy models for he EU and he US economy are derived from he opimizing behaviour of households and rms. Closed economy model is a sandard New Keynesian DSGE model wih a scal policy incorporaing sicky wages and prices, adjusmen coss in invesmen, habi persisence in preferences and variable capial uilizaion. Fiscal policy is inroduced following Traband and Uhlig (26). Furher, open economy model builds on he srucure of Adolfson, Laseén, Lindé and Villani (27) wih exending he foreign economy framework. In his paper, boh economies are modelled wih symmeric preferences and echnologies allowing for di erences in price-seing, policies and exogenous shocks raher han being modelled as exogenous shocks. Households maximize a uiliy funcion consising of consumpion and leisure in boh models. The real cash balances is absen from he uiliy funcion, in line wih he pracice in modern New Keynesian lieraure. Woodford (23) jusi es he reason concepually on he grounds of a bookkeeping cashless economy. Noe also ha in he open economy model, consumpion and invesmen is composed of domesic and impor goods which are supplied by he domesic and imporing rms, respecively. Furher, he households can save in domesic bonds and/or foreign bonds depending on he model, i.e., open versus closed. Accordingly, his decision of he households resuls in he uncovered ineres rae pariy condiion in open economy analysis. In boh models, he households ren capial o he inermediae goods producers. In urn, given he coss o adjusing he invesmen rae and he coss of varying uilizaion rae of he physical capial sock, hey decide on how much o inves in physical capial sock. Furher, each household ses his wage in Calvo(983) seing. This is in line wih he assumpion ha each household is a monopoly supplier of a di ereniaed labor service. Firms in he boh economy models, i.e, inermediae goods rms (only rm in he closed economy model), exporing rms and imporing rms, produce a di ereniaed good and herefore, operae in a monopolisically compeiive environmen. They se heir respecive prices according o a Calvo seing, i.e., only a cerain fracion of rms can reopimize heir prices in each period. Moreover, while di ereniaed inermediae goods are aggregaed by a nal good producer in he Home economy, imporing rms buy he homogenous good in he Foreign economy and afer di ereniaing i by brand-naming sells i o a nal impor good producer o be aggregaed. On he oher hand, exporing rms buy he homogenous good from he nal good producer, di ereniaes i by brand-naming and sells i (by local currency pricing) o he imporing rms operaing in he Foreign economy. Assuming price sickiness in he shor run implies ha exchange rae pass- 8

9 hrough is no complee in he shor run. 2 Inherenly, deviaions from PPP are assumed o exis in he shor run, bu no in he long run. However, monopolisic imporers charge a consan mark-up o consumers causing a l.o.p. gap even afer adjusing for exchange rae movemens. Below, he closed and he open economy models will be presened along wih each oher. Since symmeric preferences and echnologies are assumed for boh economies, describing he model for he EU ( as Home economy in open economy analysis) will su ce. In his respec, variables wih a " " denoes he US economy variables. Noe also ha economic agens in boh economies make idenical decisions, i.e. in equilibrium individual decisions coincide wih he aggregae decision. 3. Households There is a coninuum of households, indexed by j 2 [; ], opimize X E j = d c log(c j H j ) d h A L (h j ) + l + l () where C j and h j denoe he j h household s consumpion and labor e or levels, respecively. Consumpion smoohing behaviour of he households are capured by including a habi formaion, H = hc where h capures he level of habi persisence. is he discoun facor and wo srucural shocks d c and d h are persisen preference shocks o consumpion and labor supply, respecively. Boh of he shocks follow a rs order auoregressive process, AR(), given by: d c = c d c + " dc; and " dc; N(; ) ; d h = h d h + " dh; and " dh; N(; ) For he open economy analysis, aggregae consumpion is assumed o consis of domesically produced goods and impor goods given by he following echnology C = ( w c ) c C d c c c + w c (C m ) c c c where C d and C m are consumpion of he domesic and impored good respecively. w c is he share of impors in consumpion and c is he elasiciy of 2 See, for example, Devereux and Engle (22), Corsei and Peseni (22) and Lubik (26) (2) 9

10 subsiuion beween consumpion goods. The oal expendiure on consumpion is he sum of domesic and impor good purchases. P c C = P C d + P m C m where P c, P and P m denoes consumer price index (CPI), domesic producer prices and impor prices, respecively. Maximizing he above budge consrain subjec o equaion (2), demand funcions for domesic and impor goods can be derived. c C d P = ( w c ) P c C ; (3) C m = w c P m P c c C (4) Plugging (3) and (4) ino he budge consrain, CPI can be obained P c = h i ( w c ) P c + w c (P m ) c c (5) The j-h household s budge consrain is: (+ c )C j +I j +a(u j ) K j + e Bj + B j (R + k )B j + (R )e Bj P P P = ( y ) w j h j + ( k )r k u jkj + e R Bj + R B j + T R + D j P P (6) where w j is he real wage, r k is he real renal price of capial, u j is he varying capial uilizaion rae, a(u j ) is he physical cos of u j in resource erms, T R is a lump-sum ransfer from he governmen and D is he pro of he rms in he economy. All ineres raes are expressed in gross raes, i.e. R = + r and R = + r : The households inves eiher in governmen bonds B or foreign bonds B a ime. Noe ha in closed economy analysis B =. k ; c ; and y denoes axes on capial income, consumpion and labour income, respecively. Moreover, households pay y w j h j amoun of labor income ax, k r k u jkj amoun of capial income ax on e cienly used capial, c C j amoun of consumpion ax and k (R )B j + (R )e Bj amoun of capial income ax on domesic and foreign bonds. Finally, e is he nominal exchange rae (domesic currency per uni of foreign currency). The households can increase heir capial sock by invesing in addiional physical capial, waiing one period o come in acion, or by direcly increasing he uilizaion rae of capial, u. However, he laer is delivered facing a

11 cos funcion, a (u ) wih a () =, u =. As seen in he budge consrain equaion (6), adjusmen coss of varying uilizaion rae of capial are paid by he households. Furher, following Alig e al (24), he household s sock of physical capial evolves according o K j = ( ) K j + F (I j ; I j ) (7) where denoes he physical rae of depreciaion and I j denoes ime invesmen goods. The funcion F (:) is he echnology used o ransform curren and pas invesmen ino insalled capial for use in he following period. F (:) is given by F (I j ; I j ) = S ~ Ij I j I j Furhermore, funcion S(:) is assumed o be increasing, convex and sais es: S = S = and S > in seady sae. The seady sae of he model does no depend on he value of S, however, he dynamics do. 3 In a similar way as in consumpion, oal invesmen is assumed o consis of domesically produced goods and impor goods given by he following echnology I = ( w i ) i I d i i i + w i (I m ) i i i (8) where w i is he share of impors in invesmen and i is he elasiciy of subsiuion across invesmen goods. Also as in he consumpion goods case, he demand for domesic and impor invesmen goods are as follows 4 i I d P = ( w i ) P c I ; (9) I m = w i P m P c i I () Noe ha for simpliciy same prices are assumed for invesmen and consumpion goods. 3 For an explici de niion of invesmen and uilizaion adjusmen coss, see Chrisiano, Moo and Rosagno (27). 4 In conras o Adolfson, Laseén, Lindé and Villani (27) he oal expendiure on invesmen, assuming same price levels for invesmen as for consumpion goods, is given by P c I = P I d + P m I m

12 By using (), (6) and (7), households solve he Lagrangian problem. The rs order condiions wih respec o C j, B j, B j ; u j, K j and I j are as follows: = dc (C H ) ( + c ) " # + R (R ) k + = E + " # + R (R ) k + e + = E + r k = a (u j ) ( k ) e () (2) (3) (4) + Q = E (Q + ( ) + ( k +)r+u k + a(u + )) = Q S ~ I I ~S I I I I +E " + Q + ~ S I+ I (5) # 2 I+ I (6) where, Q = and + = P+ P :Noe ha he rs order condiions does no depend on j, since households aggregae decisions are assumed o coincide in equilibrium. Combining he wo rs order condiions wih respec o B j and Bj, he uncovered ineres rae pariy along wih he log-linear version can be obained R R e + E = k + e + e k E ; + e ^R ^R = k E ^e + (7) This ineres rae pariy condiion is slighly di eren from he sandard case wihou axes. Noe ha > due o he inroducion of axes. The k ax on capial income causes he households o require an exra ineres rae premium on heir domesic bond holdings. The reason is ha here is no ax paid on expeced exchange rae pro s. Consequenly, when he exchange rae is expeced o depreciae, he households anicipae larger gains from holding foreign bonds compared o holding domesic bonds since he e ecive ax rae di ers beween hese posiions. For he expeced earnings on he domesic and foreign bond holdings o be equivalen, he domesic-foreign ineres rae di erenial mus hen be larger han one when he capial ax is posiive (Adolfson, Laseén, Lindé and Villani, 27). 2

13 Wage decision of he households is more involved. Households supply di eren ypes of labour allowing hem o have monopolisic power over individual wages. Labor supplied by he households are ransformed ino aggregae labor by he given echnology: Z L = h j dj (8) where L denoes he aggregae labor and conrols he elasiciy of subiuion among di eren ypes of labor. Labor aggregaor maximizes his pro s subjec o (8) aking as given all di reniaed labor wages w j and he wage w. Consequenly, his maximisaion problem is: max w L h j Z o w j h j dj From his maximisaion problem, demand for j-h household s labor can be derived: wj h j = L (9) w Zero pro condiion for labor aggregaor s maximisaion problem delivers he aggregae wage rae which depends on he individual wage rae: Z w = w j dj (2) Households se heir wages following a Calvo s seing. In each period, a fracion ( w ) of households reopimise heir wages. All oher households can only parially se heir wages by pas CPI in aion. Indexaion is conrolled by he parameer w 2 [; ]. When w = here is no indexaion and when w = here is oal indexaion. This implies ha if he household canno reopimize is wage for s periods, his normalised wage afer s periods is sy h= cw +h w w j Therefore, he relevan par of he Lagrangian for he j-h household is: " # X max E ( w ) s d h h + l j+s A L + +s y Y s +s cw w ~w +h ~w h j+s + s= l h= 3

14 subjec o h j+s = sy h= cw w +h ~w w +s! L +s Noe ha opimized wage, ~w ; does no depend on j, since i is assumed ha households who can opimize heir wages, choose he same wage rae. Following is he rs order condion o he above problem: P E s= ~w = ( w) s d h A L h + l j+s P E s= ( w) s +s y sq +s h= cw +h w h j+s (2) Finally, given equaion (2) and indexaion, he law of moion of he real wage rae can be de ned as: w = w w cw + ( w ) ( ~w ) (22) 3.2 Inermediae Goods Firms There is a coninuum of inermediae goods rms indexed by i 2 [; ]; each producing y i unis of goods o be used by he nal good rm o produce Y a period. Final good producion is given by he following echnology: Z Y = y di (23) where is he elasiciy of subsiuion. Final good rms are perfecly compeiive and maximize pro s subjec o he producion funcion (23), aking as given all inermediae goods prices p i and he nal good price p. Consequenly, heir maximizaion problem is: Z max p Y p i y i di y in From he above maximizaion problem, demand for i-h inermediae goods rm s oupu can be derived: y i = pi p Y (24) 4

15 where Y is he aggregae demand and he zero pro condiion delivers he aggregae price level: Z p = p di (25) i Each inermediae good i is produced by he following Cobb-Douglas producion funcion: y i = A KiL i (26) where denoes he xed cos of producion and i is se o deliver zero pro in seady sae. L i is he labor demanded o produce he inermediae good i and K is he capial services sock raher han physical capial sock K, since variable capial uilizaion is inroduced in he model. A is he oal facor produciviy shock which follows a AR() process, given by A = A A + " A; and " A; N(; ) Inermediae goods producers face a wo-sage problem. In he rs sage, given facor prices w and r k, rms ren L i and K i in order o minimize he real cos: min L i,k i w L i + r k K i subjec o A K y i = i L i if A Ki L i > oherwise The rs order condiions for his problem are: w = ( )A K il i or w = ( ) (y i + ) L i r k = A K i L i or r k = (y i + ) K i Furhermore, oal cos is given by: T C = w L i + r k K = w L w L i : Given ha he rms has consan reurns o scale, by r k where K i = seing he level of labor and capial o produce one uni of good, real marginal cos, mc can be derived as: 5

16 w mc = A (r k ) Noe ha he real marginal cos does no depend on i: all rms receive he same echnology shock and all rms ren inpus a he same price. In he second sage, inermediae good producers choose he price ha maximizes discouned real pro s in a Calvo s seing. In each period, a fracion ( p ) of rms can reopimize heir prices. All oher rms can only index heir prices by pas in aion p i = p p i. Indexaion is conrolled by he parameer p 2 [; ] where p = implies no indexaion and p = implies oal indexaion. I is assumed ha all rms ha can reopimize heir prices, choose he same price ~p :Maximizaion of he rm i is as follows: "!# X sy max ( p ) s +s p ~p E ~p s= y i+s h= +h p +s mc +s subjec o y i+s = sy ~p p +h p +s h=! Y +s and he rs order condiion o above problem is: P E s= ~p = ( p) s +s p +s mc +s y i+s P E s= ( sq p) s +s h= p +h y i+s (27) Furhermore, given equaion (25) and indexaion, he law of moion of price level can be de ned as: p = p p p + ( p ) (~p ) (28) Log-linearizing he equaions (27) and (28), he New Keynesian Phillips curve can be derived: ^ = + p E ^ + + p + p ^ + ( p) ( p ) p + p m^c where "ha" variables denoe percenage deviaions from heir seady saes. Noe also ha if p =, above equaion boils down o a sandard New Keynesian Phillips curve wih no backward-looking feaure. 6

17 3.3 Imporing Firms There is a coninuum of imporing rms ha purchase a homogenous good a world marke prices Pi which are se by heir respecive producers in heir own currency. These foreign goods are di ereniaed ( i.e brand naming) by imporing rms and hen aggregaed by a nal impor good producer. Finally, hese impor goods are sold o he households as consumpion and invesmen goods. As menioned above, deviaions from purchasing power pariy (PPP) are assumed o exis in he shor run due o he exisence of monopolisically compeiive imporers. The nal impor good is a composie of i di ereniaed impored goods, supplied by imporing rm i, and is producion is given by he echnology: Z M = m M m i m m di where M = C m + I m. Similar o he nal good producer, from he maximizaion problem of he nal impor good producer, i can be shown ha each imporing rm i, faces he demand for impored consumpion goods and impored invesmen goods which are given by P m C i = i P m P m I i = i P m m C m (29) m I m (3) The imporing rms choose he price ha maximizes discouned real profis in a Calvo s seing. In each period, a fracion ( m ) of rms can reopimize heir prices. All oher rms can only index heir prices by pas in- aion p m i = m m p m i. Indexaion for non-opimized impor prices is conrolled by he parameer m 2 [; ] where m = implies no indexaion and m = implies oal indexaion. I is assumed ha all rms ha can reopimize heir prices, choose he same price ~p m :Marginal cos for rm i is given by mc m = e P and law of one price (l.o.p.) gap is de ned by m = P e P. If PPP m holds, hen m =. However, impored goods are subjec o price discriminaion as monopolisic imporers charge a mark-up o consumers a he border. This implies ha he same good can have di eren prices depending on where i is sold even afer adjusing for exchange rae movemens (Lubik, 26). Maximizaion problem of he rm i is as follows: " X sy max E ( m ) s +s M i+s m m ~p m +h s= h= ~p m p m +s m +s!# 7

18 subjec o M i+s = sy h= m +h ~p m p m +s! m M +s Similar o domesic inermediae good producers, rs order condiion o above maximizaion problem and he law of moion for impor prices (p m ) m = m m m p m m + ( m ) (~p m ) m resuls in he Phillips-curve relaionship beween impor-price in aion and he l.o.p. gap for impor goods. ^ m = + m E ^ m + + m ^ m + ( m) ( m ) + m m ( + m ) ^ m Furher, in order o nd he seady sae o be used in he log-linearizaion procedure, exible price equilibrium can be de ned in he following way. In a exible price environmen he maximizaion problem of he imporing rms is given by max P m i e P (Ci m + Ii m ) P i m subjec o he demand equaions (29) and (3) and P i m denoes he opimal exible price of rm i. Firs order condiions, afer rearranging and dropping he subscrip i (since all rms make idenical decisions), yield P m i = m m e P (3) Noe also ha as m!, implying a horizonal demand curve for impored goods, he markup over he world marke price P goes o zero. Due o nominal rigidiies in he impor secor incomplee exchange rae pass-hrough occurs Exporing Firms Similar o impor secor, here is a coninuum of exporing rms, which purchase he homogenous good a P from he nal good producer and di ereniae i by brand naming. The di ereniaed good is hen sold a Pi x (local currency pricing) in he foreign marke as consumpion and invesmen goods. So he marginal cos of exporing rms is mc x = P =e. Deviaions from l.o.p. is also assumed for he expor goods and accordingly l.o.p. gap is de ned by x = P P. x The exporing rm i faces he following demand for is produc X e i P x x X i = i X P x 5 Noe also ha in conras o Adolfson e al (27), he seady sae markup for impored consumpion and invesmen goods are assumed o be idenical. 8

19 where X = C x +I x and P x is he aggregae expor price level. The exporing rms choose he price ha maximizes discouned real pro s in a Calvo s seing. In each period, a fracion ( x ) of rms can reopimize heir prices. All oher rms can only index heir prices by pas in aion p x i = x x p x i. Indexaion for non-opimized impor prices is conrolled by he parameer x 2 [; ] where x = implies no indexaion and x = implies oal indexaion. I is assumed ha all rms ha can reopimize heir prices, choose he same price ~p x : The expor rms maximize pro s (denoed in local currency) according o he following maximizaion problem "!# X sy max E ( x ) s +s X i+s x x ~p x x ~p x +h +s s= h= p x +s subjec o X i+s = sy h= x x +h ~p x p x +s! x X +s Combining log-linearized rs order condiion of he above maximizaion problem wih he log-linearized version of he law of moion for he expor prices (p x ) x = x x x p x x + ( x ) (~p x ) x, he Phillips-curve relaionship beween expor-price in aion and he l.o.p. gap for expor goods can be derived. ^ x = + x E ^ x + + x ^ x + ( x) ( x ) + x x ( + x ) ^ x Furhermore, given he similar seing for foreign aggregae consumpion, foreign demand for he home expors is given by C m P + I m = C x + I x x n c = P (C + I ) (32) where C and I are foreign consumpion and invesmen, respecively and P denoes foreign price level. Noe ha equaion (32) allows for shor run deviaions from he l.o.p. which occur because of he price sickiness. 3.5 More Open Economy Aspecs In his secion various relaive prices, which ener he model, will be discussed. Relaive prices beween domesic goods and impored goods is given by m;d = P m P (33) 9

20 There is also he relaive price beween home expors and he foreign goods x; = P x P (34) where P F; is he world-marke price of impors. Deviaions from he l.o.p. for he expor goods and impor goods are given by x = m P P x e ; (35) = P e P m (36) Combining (34) and (35) anoher relaive price which is used by he exporing and imporing rms can be obained P f = P e = x x; (37) Noe ha l.o.p. gap for impor goods can be wrien as = m = = P e P m f m;d x x; m;d Finally, he producer price and impor price relaive o CPI is as follows c;d = P c P (38) c;m = P c P m (39) 3.6 The Governmen The governmen budge consrain is given by G + T R + R B = B + T (4) 2

21 where T denoes ax revenues and i is as follows T = c C + k (R ) B + R e B + y w L + k r k u K (4) The hree ax raes, namely labor income, capial income and consumpion ax, and lump-sum ransfers, T R are reaed as shocks and follow an AR() process. Following Traband and Uhlig (26) governmen deb is assumed no o deviae from is balanced growh pah, i.e. B = B, 8 > and herefore governmen budge consrain can be wrien as G = B( R ) + T T R where is se equal o.75 which is consisen wih he annual growh of real GDP in boh economies of roughly 3 percen. 3.7 The Cenral Bank Adjusing he Taylor (993) rule, moneary policy auhoriy is assumed o adjus he shor run ineres rae in response o deviaions in CPI in aion from he in aion arge ( ar ), deviaions in oupu from is seady sae value and. Addiionally, in open economy analysis, moneary policy rule is also assumed o be a funcion of real exchange rae. Accordingly, moneary policy rule is given by ^R = R ^R + ( R )(^ ar + r (^ c ^ ar ) + y ^y + x^x ) + " R (42) which is a generalized backward-looking Taylor rule 6. ^R is he shor run ineres rae, ^ c is he CPI in aion, ^y is he oupu deviaion from is seady sae and ^x denoes real exchange rae, which is given by ^x = ^e + ^ ^ c + ^x (43) The cenral bank responds o he log-linearized model-consisen measure of he CPI in aion which can be derived from he equaion (5). ^ c = ( w c ) d;c c ^ + w c ( m;c ) c ^ m (44) where he seady sae domesic goods prices and impor goods prices relaive o seady sae CPI are given by d;c P = P c and m;c P = m, respecively. P c Furher, ^ ar is a ime-varying in aion arge of he cenral bank and " R is an ineres rae shock. The moion of he in aion arge is de ned as an AR() process. ^ ar = ^ ar + " ar 6 For a more deailed analysis on exchange rae e ecs on moneary policy rule, see Ball(999) and Svensson(2). 2

22 3.8 Marke Equilibrium Final goods marke equilibrium condiion in closed economy is given by C + G + I A K L a(u ) K (45) To clear he nal goods marke and foreign bond marke in open economy analysis, he following wo consrains mus hold in equilibrium: where ~C + ~ I + G + ~ X ~ M A K L a(u ) K (46) e B = e R B + e P x (C x + I x ) e P F; (C m + I m ) (47) ~C = C d + C m ~I = I d + I m ~M = C m + I m ~X = C x + I x Also, noice ha nal good marke condiion can be rearranged as C d + I d + G + C x + I x A K il i a(u ) K By using he demand equaions (3), (4), (9), () and (32), consumpion, invesmen, oal impors and expors can be arranged,respecively, as c! ~C = C d + C m P P m c = ( w c ) P c + w c P c C (48) ~I = I d + I m = ( w i ) P ~M = C m + I m = w c P m P c P c ~X = C x + I x = P x P i + w i P m P c c C + w i P m P c i! I (49) i I (5) n c (C + I ) (5) Dividing (47) by P and de ning a = eb P, he foreign bond marke equilibrium condiion can be wrien as a = a where x = R e + ( x ) (C x + I x ) ( f ) (C m + I m ) e P P and x f e = P P = x e x; 22

23 4 Solving he Model In his secion, rs, seady sae equaions are given. Second, all he loglinearized equaions are presened. This is followed by model calibraion and calculaion of he seady sae values o ge an insigh ino he equilibrium condiions for boh economies and models. 4. Seady Sae In seady sae, he economy is assumed o reach equilibrium. Dropping he subscrips in he rs order condiions for variables and in he marke equilibrium equaions, seady sae values of ineres, o be used in he analysis, can be calculaed. Using he consumpion Euler equaion (2), seady sae gross ineres rae is calculaed as R = k k where k is he average capial income ax rae. I is also clear o see in seady sae R = R from equaion (3) assuming e =. Furher, using capial Euler equaion (5), seady sae renal rae of capial can be obained r k = ( ) k Cos minimizaion of he rms imply in he seady sae which delivers w L = ( ) Y + (52) and r k Y = + (53) K K Y = k + ( ) Y where Y is he share of xed cos in oal producion. Assuming S =, capial accumulaion consrain (7)in seady sae yields K = I which in urn gives I Y = k + ( ) Y 23

24 Now consider he Euler equaion associaed wih he household s capial uilizaion decision. In seady sae full capaciy uilizaion is assumed, i.e. u = and his implies a () = r k k = ( ) Marke equilibrium condiions for he closed economy and open economy implies in seady sae C = Y + G Y + I (54) Y C = ~ Y + I ~ Y + G Y = C d Y + I d Y + G Y + C x Y + I x Y where seady sae values C ~ and I ~ can be derived from equaions (48) and (49) and are given by ~C = ( w c ) c;d c + w c ( c;m ) c C ~I = ( w i ) c;d i + w i ( c;m ) i I where c;d = P c P and c;m = P c P m are seady sae relaive prices. Tax revenue of he governmen in seady sae is given by T Y = c C Y + k R B Y + y w L Y + k rk K Y (55) Using equaions (52), (53) and (54) above equaion (55) can wrien for he closed economy case as T Y = c ( G Y I Y ) + k R B Y + y ( ) + k + Y whereas in open economy case his di ers slighly T Y = c ( G Y (56) ( w i ) c;d i + w i ( c;m ) i I Y ) (57) + k R B Y + y ( ) + k + Y Governmen budge consrain in seady sae is as follows G Y = ( R) B Y + T Y T R Y 24

25 Plugging equaions (56) and (57) ino he above equaion, seady sae values for he governmen expendiure o oupu raio for closed and open economy can be calculaed, respecively G Y = + c G Y = + c c 2 4 I Y + y ( ) + k + Y + k R + ( R) B Y c ( w i ) c;d i + w i ( c;m ) i IY + y ( ) + k + Y + k R + ( R) BY 3 5 Now consider he seady sae values for relaive prices. Equaion (5), which de nes he CPI, can be wrien as P c P = P c P m = " " ( w c ) + w c P m P ( w c ) P P m c # c (58) c + w c # c (59) Combining (58), (59) and (3), evaluaed in seady sae gives " P c P = m ( w c ) + w c m e P c # c (6) P " P c P = m c # P c ( w m c ) m e P + w c (6) where e is he seady sae exchange rae and is assumed o equal, i.e., e =. Furher, he producer price level equals he foreign price level in seady sae, i.e., P = P F;. Therefore, equaions (6) and (6) can be described as " P c # c c P = m ( w c ) + w c m " P c P = ( w m c ) m m Noe ha if < c < and < m <, w c >. Accordingly, above gives P c P m c + w c # c P c P will be greaer han wih will be smaller han. Combining boh equaions 2 P m 6 ( w c ) + w m c P = 4 ( w c ) m c m m c + w c c = m m 25

26 In addiion o he above assumpion P = P F;, noe also ha he expor price equals he foreign price level in seady sae, i.e., P x = P F;. This implies ha here are no deviaions from he l.o.p. in expor secor in seady sae equilibrium. x P = P x e = On he oher hand, imporing rms charge a markup of heir cos and herefore, exchange rae pass-hrough in domesic impor prices is imperfec in seady sae. m P = e P m = x x; m;d = P P m = m m Finally, seady sae values for he remaining relaive prices are as follows m;d = P m P x; = P x P = f = P e P = 4.2 Log-linearized equaions For he dynamics, he equaions of he model are log-linearized around heir seady seady values, i.e. z = ze^z z( + ^z ) and he sysem is solved following Uhlig (999). All he model equaions are given below. Afer combining equaions () and (2) and log-linearizing, he dynamics for consumpion can be obained " ^C = E ^C +h + + h ^C +h + h c +h + (^ c c + ^ c ) + h +h ( ^d # c ^d c +) + h +h ^ + h +h ( k h )R +h ( R)^ k + (62) 26

27 In he absence of consumpion and capial income axes, above equaion boils down o he sandard consumpion equaion wih habi formaion used in New Keynesian models. Boldrin, Chrisiano and Fisher (2) argue ha he abiliy of sandard general equilibrium models o accoun for he equiy premium and oher asse marke saisics is considerably enhanced by he presence of habi formaion in preferences. The invesmen equaion is given by ^I = E + ^I + + ^I + + ' + ^Q (63) where ' = S is he elasiciy of invesmen wih respec o a one percen emporary increase in he curren price of insalled capial. A more persisen change in he price of capial implies a larger percenage change in invesmen because adjusmen coss induce agens o be forward looking (Chrisiano e al, 25). As menioned before, S does no a ec he seady sae analysis, bu he dynamics depend on he value of S. Using (4) and (5), log-linearized version of Euler equaion for capial can be obained ^Q = E ^ + k ^R + ( ) ^Q k + k ^ k + + ( ( )) ^r + k (64) Inroducion of capial income ax implies ha ineres rae changes have less e ec on he curren price of capial and accordingly, on he invesmen level compared o he case wihou capial income ax. Furher, an expeced increase in fuure capial income ax causes he curren price of capial o decrease whereas an increase in expeced in aion, renal rae of capial and price of capial implies an increase in curren price of capial. Capial accumulaion is as follows ^K = ( ) ^K + ^I (65) New Keynesian Phillips curves for all he rms in he economy are derived by assuming Calvo s conrac model in he economy wih some price-seers being backward-looking. ^ m = ^ = + p E ^ + + p + p ^ + ( p) ( p ) p + p m^c (66) + m E ^ m + + m ^ x = + x E ^ x + + x ^ m + ( m) ( m ) + m m ( + m ) ^ x + ( x) ( x ) + x x ( + x ) 27 ^ m (67) ^ x (68)

28 where ^ is he domesic producer price in aion, ^ m is he impor price in aion and ^ x is he expor price in aion. Real marginal coss for domesic producers and l.o.p. gap for imporing rms and exporing rms are given by ^ m = ^ m ^x m^c = ( ^ x; ) ^w + ^r k ^ m;d ^A (69) = ^ m + ^ + ^e ^ m (7) ^ x = ^ x + ^ ^ x ^e (7) Since rms in he Calvo model would like o keep heir price as a xed markup over marginal cos, an increase in real marginal cos will spark in aionary pressures in domesic prices and accordingly, in expor prices. Furher, due o he parial indexaion of all hree rms by pas in aion, New Keynesian Phillips curve implies ha in aion raes depend no only on he expeced in- aion bu also on he pas in aion. Indexaion is capured by he parameers p, m and x for domesic producers, imporing rms and exporing rms, respecively. Noe ha j =, j [p; m; x] implies ha all hree New Keynesian Phillips curves are only forward-looking. Remaning log-linearized relaive prices are given by ^ x; ^ m;d ^ f = ^ f ^ c;d = ^ x; + ^x ^ (72) = ^ m;d + ^m ^ (73) + ^x + ^ x; (74) = ^ c;d + ^c ^ (75) Similar o rms, households se wages in a Calvo seing. Log-linearizing and rearranging (2) and (22), he wage dynamics can be obained & ^w + & ^w + & 2 ^w + + & 3^ + & 4^ + + & 5^ c + & 6^ c = E +& 7 ( ^d c ^C h + h ^C c h + ^ c ) + & c 8 ^L + & 9^ y (76) + & ^dh where w = [ l ( )] [( w)( w)] and &= w w l w + 2 w w w w w w w w w w = w w w ( ) ( ) l C B ( ) y ( y ) ( ) & & & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & C A 28

29 Uncovered ineres rae pariy is given by ^R ^R = k E ^e + Capial uilizaion rae is as follows ^u = ^K b K where ^k is he deviaion of capial services sock from is seady sae value and b K is he deviaion of physical capial sock from is seady sae value. Furher, afer log-linearzing he Euler equaion associaed wih he household s capial uilizaion decision, i.e. equaion (4), following expression can be obained ^u = k ^rk k ^ k where is he inverse elasiciy of capial uilizaion wih respec o he renal rae of capial. Moreover, rs order condiions o he cos minimizaion problem of he inermediae goods rms implies ^L = ^r k + ^K ^w Real exchange rae is given by ^x = ^e + ^ ^ c + ^x = w c ( c;m ) ( c ) ^ m;d ^ x; ^ x In open economy analysis supply and demand is given by + ^A + Y ^K + ( ) ^L k r k K ^K Y K b ( w c ) c;d c C Y ^C + c^ c;d G + Y ^G X + ^M Y f ^ x; + ( w i ) c;d ii I Y ^I + i^ c;d by In closed economy analysis, he di erence is in he demand side. I is given ^Y = C Y ^C + I Y ^I + G Y ^G + k r k K Y ^K b K Governmen budge consrain G Y ^G = T Y ^T B Y R ^R T R Y d T R 29

30 and accordingly, ax income is given by T Y ^T C = Y c ^C + ^ c + k R B Y + + ^ Y k + k B Y R ^R + y + Y ( ) ^ y + y ( ) + k ^Y Ne foreign asse dynamics is as follows ^a = R^a ^x X + f ^ x; ^M + C m + I m ^ f C m ^C c ( w c ) c;d ( c ) ^ m;d I m ^I i ( w i ) c;d ( i ) ^ m;d CPI in aion is given by ^ c = ( w c ) c;d ( c ) ^ + w c ( c;m ) ( c ) ^ m Finally, moneary policy is given by ^R = R ^R + ( R )(^ ar + (^ c ^ ar ) + y ^y + x^x ) + " R 4.3 Calibraion Alhough he model parameers are no deermined by esimaion, i is found ha cerain parameer combinaions generae sandard impulse response funcions. For allowing such combinaions, parameer calibraion, which is done a a quarerly frequency, is based mainly on Smes and Wouers (24a, 24b); for impor and expor secor and he share of capial in producion on Adolfson e al. (27); for scal policy parameers on Traband and Uhlig (26). The discoun facor is se equal o.99 which below implies a seady sae quarerly gross real ineres rae of.53 and.6 for he EU and US, respecively. This di erence is due o he capial income ax on domesic and foreign bonds. However, above we assume R = R. This problem, which could be solved by seing US discoun facor in niesimally higher or EU discoun facor in niesimally lower, is negligible. Parameer, de ning he habi persisence 3

31 in consumpion is se so ha h EU = :59 and h US = :69. The share of capial in producion is.29 and.24 for he EU and US economy, respecively. Furher, he depreciaion of capial is se equal o.5 for boh economies which implies an annual depreciaion rae of 6 percen. For he moneary policy rule paramaers, R, and y, in he open economy case he esimaes of Smes and Wouers (24a) and for he exchange rae parameer, x he esimaes of Adolfson e al. (27) is used. On he oher hand, for closed economy case Smes and Wouers (24b) and Smes and Wouers (27) are used. Moneary Policy Rule Parameers R y x Open Economy EU US Closed Economy EU US Furher, Traband and Uhlig (26) give a deailed explanaion for he consumpion, labor income and capial income ax raes along wih he quarerly seady sae governmen deb and ransfers o GDP raio for boh economies. 7 These values are as follows EU US Labor ax rae y Capial ax rae k Consumpion ax rae c.7.5 Gov. ransfers o GDP raio T R Y.9. Gov. deb o GDP raio B Y For he res of he parameers, see Appendix. 3

32 % deviaion from S % deviaion from S 5 Impulse Response Analysis In secion four, closed and open economy models for he EU and US are described in a DSGE framework. Accordingly, in his secion he impulse response analysis, using Toolki, will be based on open versus closed economy comparison. Firs, he e ecs of a shock in ineres rae and in aion arge will be invesigaed. Second, our analysis will be focused on preference, labour supply and echnology shocks. Furhermore, he size of shocks are se equal o one sandard deviaion as in Smes and Wouers (23). Concerning he moneary policy rule, a few hings are worh menioning. In he common lieraure, ineres rae smoohing parameer, R is esimaed o be higher for he ECB policy rule compared o he US. 8 This implies ha i akes longer for he ECB o converge o is ineres rae arge afer an ineres rae shock. This can be seen in Figure () and (2), alhough he model canno capure he desired hump-shaped impulse response funcions. Furhermore, a decrease in consumpion, invesmen and governmen expendiures, which can be seen in Figure (7) and (8) for boh economies, respecively, leads o an increase in oupu. These resuls are in line wih Smes and Wouers (24a).. ResponseomonearyEU.4 ResponseomonearyEU..2 R GDP ResponseomonearyEU i n f mc ResponseomonearyEU Figure : Ineres rae shock, EU, closed economy model () 8 See, for example, Chrisiano, Moo and Rosagno (27) and Lubik and Schorfheide (25). 32

33 % deviaion from S % deviaion from S GDP ResponseoIn.RaeUS R ResponseoIn.RaeUS ResponseoIn.RaeUS i n f i n f mc ResponseoIn.RaeUS Figure 2: Ineres rae shock, US, Closed economy model () Figure (3) and (4) depics he impulse response funcions in open economy model following an ineres rae shock. The resuls are similar o closed economy resuls, however, he deviaions are bigger his ime. Accordingly, similar o he resuls in Adolfson e al (27), Figure () and (2) has implicaions abou he open economy variables. In he EU economy, impor price in aion decreases more han he domesic in aion decreases. Furher, an increase in he marginal cos of he exporing rms, mc x = P =e, due o a real appreciaion of EU currency, pus an upward pressure on expor price in aion. In his respec, given he price sickiness, l.o.p. gap for expor secor, x = P P, increases. EU x e expors decrease, while impors increase causing a ne foreign asse de ci. On he oher hand, for he US economy, he e ecs are he oher way around. The real appreciaion is no ha srong and expor prices fall causing an increase in expors. The US ne foreign asse acquisiion increases. 33

34 % deviaion from S % deviaion from S % devi a i on f r om S S % devi a i on f r om S S % devi a i on f r om S % devi a i on f r om S ResponseomonearyEU GDP EU ResponseomonearyEU RE U ResponseomonearyEU NFx EU I n f EU I n f EU ResponseomonearyEU Figure 3: Ineres rae shock, EU, Open economy model ().2 ResponseomonearyUS GDP US ResponseomonearyUS RUS ResponseomonearyUS I n f US ResponseomonearyUS NFx US Figure 4: Ineres rae shock, US, Open economy model () Following gures (5) and (6) presens he deviaions of oupu, gross real ineres rae, in aion and real marginal coss from heir seady sae values for he EU and US economies in he closed economy model. E ecs are in he same direcions for boh economies. Consumpion, invesmen, governmen expendiures and accrodingly, oupu increases. An upward pressure in he wages and renal rae of capial causes an increase in marginal cos in real erms and in urn in aion increases. The cenral banks reac o his by increasing ineres raes. For furher di erences and similariies, we now urn o he e ecs of preference, labor supply and echnology shocks. Figure (5) and (6) depics impulse response funcions afer a shock in preferences in closed economy case for boh economies. As i is shown, consumpion, governmen expendiures and GDP 34

35 % devi a i on f r om S S % devi a i on f r om S S % devi a i on f r om S % devi a i on f r om S % devi a i on f r om S S % devi a i on f r om S S % devi a i on f r om S % devi a i on f r om S GDP ResponseopinflarEU ResponseopinflarEU i n f ResponseopinflarEU R ResponseopinflarEU mc Figure 5: In aion arge shock, EU, Closed economy model () GDP ResponseopinflarUS ResponseopinflarUS i n f ResponseopinflarUS R ResponseopinflarUS mc Figure 6: In aion arge shock, US, Closed economy model () 35

36 increases, while invesmen decreases. In he EU, he reurn on capial and real wage raes increase and accordingly, real marginal coss increase. This, in urn, creaes a cos-push in aion. However, in he US, real wage rae increases only slighly while reurn on capial decreases. This implies ha in he US real marginal coss decrease and in urn, in aion decreases. Furher, he ECB reacs o his in aion increase by increasing he ineres raes and he Fed reacs o his drop in in aion by decreasing he ineres raes. Open economy implicaions of a preference shock are presened in he gures (2) and (22). This ime in he EU, he decrease in domesic in aion and impor price in aion pulls CPI in aion downward. However, expor price in aion increases. These changes in impor and expor price in aion aler he demand schemes for impors and expors in he shor run causing a loss in he ne foreign asse posiion of he EU. On he conrary, in he US he e ecs imply an opposie responses. Figure (7) and (8) presens he e ecs of a labor supply shock in he EU and US in he closed economy case. In boh economies, real wage raes increase, causing marginal coss o increase and accordingly an increase in in aion. This rise in in aion engenders a rise in ineres raes in boh economies. In open economy case, seen in Figure (23) and (24), labor shock acs as a negaive shock and generaes he opposie impulse response funcions for he closed economy case for boh economies. Finally, we analyse he e ecs of a echnology shock. In Figure (9) and (2) he deviaions of seleced variables from heir seady sae values are shown. For boh of he economies in closed economy case, echnology shock causes he labor supply o fall and real wage raes o increase. On he oher hand, real marginal coss along wih he reurn on capial decreases. Due o he downward pressure on in aion, which is caused by he fall in marginal coss, ineres raes decrease. Furher, in he open economy case, which is depiced in Figure (25) and (26), consumpion and oupu increases for boh economies. Domesic and impor price in aion pus an upward pressure on CPI in aion in he EU bu no in he US. As l.o.p gap for he expor secor decreases, accordingly, here is an increase in expors and a fall in impors in boh economies. The di erence beween he US and EU is he response of he ineres rae. In he former i decreases as a reacion o a fall in CPI in aion and in he laer i increases due o a rise in CPI in aion. 6 Concluding Remarks In his paper, for US and EU we have desribed a closed economy and an open economy model following Chrisiano, Eichenbaum and Evans (25) and Adolfson, Laseén, Lindé and Villani (27), respecively. Furhermore, he ax srucure was inroduced following Tranband and Uhlig (26). Boh models, in line 36