Monetary Union and Macroeconomic Stabilization. Dominik Groll

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1 Moneary Union and Macroeconomic Sabilizaion Dominik Groll No November 2013

2 Kiel Insiue for he World Economy, Hindenburgufer 66, Kiel, Germany Kiel Working Paper No November 2013 Moneary Union and Macroeconomic Sabilizaion Dominik Groll Absrac: I is convenionally held ha counries are worse off by forming a moneary union when i comes o macroeconomic sabilizaion. However, his convenional view relies on assuming ha moneary policy is conduced opimally. Relaxing he assumpion of opimal moneary policy no only uncovers ha counries do benefi from forming a moneary union under fairly general condiions. More imporanly, i also reveals ha a moneary union enails he inheren benefi of sabilizing privaesecor expecaions abou fuure inflaion. As a resul, inflaion raes are more sable in a moneary union. Keywords: Moneary union; macroeconomic sabilizaion; welfare analysis; hisory dependence; inflaion expecaions. JEL classificaion: F33, F41, E52. Dominik Groll Kiel Insiue for he World Economy Kiel, Germany Telephone: dominik.groll@ifw-kiel.de The responsibiliy for he conens of he working papers ress wih he auhor, no he Insiue. Since working papers are of a preliminary naure, i may be useful o conac he auhor of a paricular working paper abou resuls or caveas before referring o, or quoing, a paper. Any commens on working papers should be sen direcly o he auhor. Coverphoo: uni_com on phoocase.com

3 MONETARY UNION AND MACROECONOMIC STABILIZATION Dominik Groll Kiel Insiue for he World Economy, Hindenburgufer 66, Kiel, Germany. This version: November 19, 2013 I is convenionally held ha counries are worse off by forming a moneary union when i comes o macroeconomic sabilizaion. However, his convenional view relies on assuming ha moneary policy is conduced opimally. Relaxing he assumpion of opimal moneary policy no only uncovers ha counries do benefi from forming a moneary union under fairly general condiions. More imporanly, i also reveals ha a moneary union enails he inheren benefi of sabilizing privae-secor expecaions abou fuure inflaion. As a resul, inflaion raes are more sable in a moneary union. Keywords: Moneary union; macroeconomic sabilizaion; welfare analysis; hisory dependence; inflaion expecaions. JEL classificaion: F33, F41, E52. dominik.groll@ifw-kiel.de. Phone:

4 2 1 Inroducion 1 Inroducion When do counries benefi from forming a moneary union? This quesion is a leas as old as he Opimum Currency Area OCA) lieraure iniiaed by Mundell 1961). One of he key insighs of his lieraure is ha for asymmeric counries o benefi from forming a moneary union, prices and wages have o be flexible and producion facors have o be mobile. More recenly, he New Keynesian lieraure, by using dynamic sochasic general equilibrium DSGE) models, has come o he consensus ha, from he perspecive of macroeconomic sabilizaion, forming a moneary union makes counries generally worse off in erms of welfare. 1 This is because counries relinquish one of heir mos imporan policy insrumens for macroeconomic sabilizaion, namely he shor-erm nominal ineres rae conrolled by naional cenral banks. However, his consensus is based on he assumpion ha he cenral bank conducs moneary policy opimally. While he concep of opimal moneary policy consiues an imporan heoreical benchmark from a normaive perspecive, is pracical limiaions are widely acknowledged. 2 More imporanly, he assumpion of opimal moneary policy in he OCA conex has led o he conclusion ha he exchange rae regime is irrelevan for sabilizaion policy if opimal moneary policy is complemened by opimal fiscal policy Adao, Correia, and Teles, 2009). Thus, i seems a leas debaable wheher opimal moneary policy is he bes modeling choice o describe he behavior of cenral banks when one wans o know he condiions under which counries benefi from forming a moneary union. Agains his background, I ake a differen approach in his paper by assuming ha moneary policy follows Taylor-ype ineres rae rules, according o which i responds only o macroeconomic variables ha are observable, such as inflaion or oupu. My main finding is ha in he sandard wo-counry New Keynesian DSGE model, in which moneary policy follows ineres rae rules, counries may gain in welfare by forming a moneary union. The gain in welfare comes from a higher sabiliy of inflaion raes, which ouweighs he coss of higher oupu-gap and erms-of-rade-gap insabiliy. Wheher counries gain in welfare depends srongly on he degree of price sickiness. When prices are relaively sicky, counries are beer off forming a moneary union; when prices are relaively flexible, counries are beer off mainaining a flexible exchange rae. Two effecs are responsible for his higher sabiliy of inflaion raes. Firs, he benefi of mainaining a flexible exchange rae diminishes as prices become sickier, since he nominal exchange rae inheris he sickiness of goods prices. As a resul, an increasing degree of price sickiness reduces he effeciveness of he nominal exchange rae as a sabilizaion mechanism. Second, forming a moneary union enails an inheren benefi. 3 Since he nominal exchange rae is fixed, he erms of rade and, herefore, he inflaion raes display an inerial or hisory-dependen behavior. This hisory dependence has he advanage of affecing he inflaion expecaions of price seers in such a way as o lower he responsiveness of inflaion o changing economic condiions. The 1 See surveys by Corsei 2008), Dellas and Tavlas 2009), and Beesma and Giuliodori 2010). 2 For example, he cenral bank needs o be able o observe he flexible-price equilibrium. For more pracical shorcomings of opimal moneary policy, see Gali 2008, Ch ). 3 "Inheren" refers o he fac ha he benefi is no modeled explicily, like a reducion in ransacion coss, bu emerges from wihin he model.

5 1 Inroducion 3 higher he degree of price sickiness is, he sronger his effec is. As a resul, inflaion raes are more sable in a moneary union. This second effec corresponds o an effec ha is well-known from he analysis of opimal moneary policy in a closed economy. There, opimal moneary policy under discreion is inferior o opimal moneary policy under commimen because he former does no influence he inflaion expecaions of price seers in a favorable way. I suffers from he so-called sabilizaion bias. In conras, opimal moneary policy under commimen induces hisory dependence ino he economy and, herefore, explois he fac ha price seers are forward-looking. The inuiion in his paper is compleely analogous. Forming a moneary union may be superior o mainaining a flexible exchange rae because fixing he exchange rae induces hisory dependence. This benefi, which manifess iself in a higher sabiliy of inflaion raes and which is relaed o he sabilizaion bias, obains in addiion o he benefi of eliminaing a poenial inflaion bias, which is sressed by Alesina and Barro 2002) and Cooley and Quadrini 2003). 4 Whereas he laer benefi has been acknowledged in he lieraure e.g., Dellas and Tavlas, 2009; Beesma and Giuliodori, 2010), he former sill seems o be unknown. I is imporan o realize ha boh effecs described above are endogenous o he model. The firs effec is due o he presence of he uncovered ineres pariy condiion on he one hand and moneary policy following Taylor-ype ineres rae rules on he oher hand. 5 The second effec is due o he fac ha price seers are forward-looking in he presence of nominal price rigidiies. All hese feaures belong o he core of new open economy macroeconomics NOEM) models and, herefore, are presen also in many medium-o-large-scale models ha are buil around his core. 6 The oher imporan finding of his paper is ha wheher forming a moneary union is beneficial or no depends heavily on he way moneary policy is conduced. When moneary policy responds o inflaion aggressively or when i implemens a high degree of ineres rae smoohing, hen mainaining a flexible exchange rae is superior. Thus, i is he qualiy of moneary policy ha is crucial for he welfare ranking beween he moneary union and he flexible exchange rae regime. Since moneary policy is more powerful under he flexible exchange rae regime, i is also more harmful when no conduced properly. This is because he qualiy of moneary policy is reinforced by he nominal exchange rae. In his sense, a moneary union provides a hedging mechanism agains moneary policy misakes. Clearly, he finding ha counries benefi from forming a moneary union when prices are relaively sicky bu no when prices are relaively flexible sands in conras o he predicions of he radiional OCA heory. Probably he mos imporan reason for his discrepancy is he fac ha expecaions are reaed as endogenous in New Keynesian models, unlike in he heoreical framework of he radiional OCA lieraure, in which expecaions are reaed as exogenous. Since he inheren benefi 4 Giavazzi and Pagano 1988) s "advanage of ying one s hands" follows he same logic, alhough hey refer o he former European Moneary Sysem ). 5 Noably, he uncovered ineres pariy condiion need no hold exacly for his effec o exis. I suffices for he ineres raes and he nominal exchange rae o be linked. 6 The inroducion of nominal price rigidiies in he spiri of Calvo 1983) ino NOEM models goes back o Kollmann 2001), Gali and Monacelli 2005), and Clarida, Gali, and Gerler 2002).

6 4 1 Inroducion of moneary unions works hrough expecaions, his channel is naurally missing in models wihou such an expecaional feedback mechanism. 7 This paper is relaed along several dimensions o he New Keynesian lieraure ha analyzes he condiions under which counries benefi from forming a moneary union. In his lieraure, only a few sudies have considered an environmen wihou opimal moneary policy: Devereux 2004), Dellas and Tavlas 2005), Dellas 2006), and Ferreira-Lopes 2010). The models used in hese sudies, as well as heir findings are, on he one hand, quie diverse. On he oher hand, none of hese sudies addresses he inheren benefi of moneary unions, he role of he degree of price sickiness, nor he closely relaed issue of he inheried sickiness of he exchange rae, all of which are crucial for he welfare ranking beween he moneary union and he flexible exchange rae regime. Several sudies have inroduced explici benefis of moneary unions o creae a counerpar o he cos of giving up naional moneary policy as a sabilizaion device. Such explici benefis of moneary unions include he eliminaion of shocks o he uncovered ineres pariy condiion Kollmann, 2004), he gain in poenial oupu Ca Zorzi, De Sanis, and Zampolli, 2005), he gain in cenral bank credibiliy Clerc, Dellas, and Loisel, 2011), and he possibiliy of higher consumpion risk sharing across counries Ching and Devereux, 2003). In conras, no explici benefis are inroduced ino he model employed in his paper. The benefi of sabilizing inflaion expecaions is inheren o moneary unions as a resul of a fixed nominal exchange rae. This paper is also relaed o Monacelli 2004). 8 Among oher hings, he finds ha in a small open economy a fixed exchange rae regime induces ineria ino he economy. On he one hand, I show ha his benefi carries over o a wo-counry environmen and is inheren o moneary union regimes as well. 9 On he oher hand, I show ha i does no hinge upon he saionariy of he price level, as sressed by Monacelli 2004). Saionariy of he price level is a special feaure of he small open economy environmen and does no carry over o a wo-counry seing employed here. Also, Monacelli 2004) does no address he role of he degree of price sickiness, he relaed issue of he inheried sickiness of he exchange rae, nor he role of moneary policy. The res of his paper is organized as follows. Secion 2 oulines briefly he srucure of he model. Secion 3 provides imporan analyical resuls in he case of symmeric counries and presens he welfare resuls graphically. Secion 4 presens he resuls in he case of asymmeric counries. Secion 5 relaes he resuls o he radiional OCA heory. Secion 6 concludes. 7 See King 1993) for a criical assessmen of he Old-Keynesian, IS-LM models wih respec o heir reamen of expecaions. 8 For a small open economy, a fixed exchange rae regime may dominae a flexible exchange rae regime wih opimal moneary policy under discreion. A flexible exchange rae regime wih opimal moneary policy under commimen, however, always dominaes he oher wo regimes. Comparing he same hree regimes, Soffrii and Zanei 2008) come o a differen conclusion, namely ha a fixed exchange rae regime fares worse han he wo flexible exchange rae regimes. One possible explanaion for he differen finding could be he differen weigh aached o he oupu-gap variance relaive o he weigh aached o he inflaion variance in he welfare loss funcion, which is ad hoc in boh sudies. Anoher explanaion could be he differen assumpion abou wheher he res of he world is also subjec o shocks or no. 9 In general, fixed exchange rae regimes and moneary union regimes do no coincide. This depends on how he fixed exchange rae regime is implemened.

7 2 Model 5 2 Model The model I use is a compleely sandard wo-counry New Keynesian DSGE model and hus I keep he descripion very brief. I feaures wo inernaional moneary regimes: 1. A moneary union MU) regime: Boh counries share he same currency. A common moneary policy governs he common nominal ineres. 2. A flexible exchange rae FX) regime: Each counry mainains is naional currency and conducs is own, independen moneary policy. Nominal ineres raes are counry-specific. The nominal exchange rae beween he wo currencies is flexible. The model is described in deail in Benigno 2004) and in Benigno and Benigno 2008) and i includes a microfounded, linear-quadraic welfare measure. Under boh regimes, he model economy feaures wo counries wih rade in consumpion goods as opposed o rade in inermediae goods). Consumpion preferences are of he Cobb-Douglas ype and are, in addiion, idenical across counries, i.e., here is no home bias in consumpion. These preferences imply ha risk sharing is perfec in he sense ha consumpion is equal across counries a all imes. Purchasing power pariy holds, i.e., he real exchange rae is consan. While hese assumpions are clearly resricive, hey grealy simplify he analysis, and relaxing hem o allow for a home bias in consumpion i.e., no purchasing power pariy and a variable real exchange rae) does no aler he findings significanly. The only facor of producion is labor, which is immobile beween counries. The only rigidiy is he nominal price rigidiy in he spiri of Calvo 1983). Under he FX regime, prices are se in he currency of he producer s counry "producer currency pricing"), i.e., he producer does no discriminae he price beween counries. The nominal exchange rae convers he price ino foreign currency, i.e., he law of one price holds and exchange rae pass-hrough is complee. Given he same consumpion preferences as under he MU regime, purchasing power pariy holds as well. The nominal exchange rae is deermined by he uncovered ineres pariy. In boh regimes, moneary policy is conduced via Taylor-ype ineres rae rules. Imporanly, I assume ha moneary policy is no able o observe he flexible-price equilibrium of he economy, in paricular he flexible-price ineres rae and flexibleprice oupu. Thus, moneary policy reacs o inflaion and o oupu deviaion from he seady sae), no o he oupu gap deviaion from flexible-price oupu). The only shocks considered are counry-specific produciviy shocks. However, he findings are robus wih respec o oher shocks, such as governmen-spending shocks or cos-push shocks Model equaions The equaions of he complee log-linearized model are displayed below for he full derivaion, see Appendices B and C). Deviaions of he logarihm of a variable X from is seady sae are denoed by X under flexible prices and by ˆX under sicky prices. 11 Variables and parameers are defined in Table 1 and Table 2, respecively. 10 In fac, under cos-push shocks he case for a moneary union becomes even sronger. 11 Noaion is adoped from Benigno 2004).

8 6 2 Model C Y i Y W π i π W π R R i R T S Y i ν i Consumpion idenical across counries) Oupu of counry i = H, F World oupu weighed average of counry-specific oupu) Producer price inflaion in counry i = H, F World inflaion weighed average of counry-specific inflaion) Inflaion differenial beween he wo counries π F π H Nominal ineres rae in counry i = H, F Nominal ineres rae in moneary union Terms of rade Nominal exchange rae Produciviy shock in counry i = H, F Whie noise process in counry i = H, F Table 1: Variables ρ n β η σ α i φ π φ Y φ R ρ i Inverse of elasiciy of ineremporal subsiuion in consumpion Counry size measured by populaion Discoun facor Inverse of elasiciy of producing he differeniaed good Elasiciy of subsiuion beween differeniaed goods Probabiliy of no being able o rese he price in counry i = H, F Inflaion coefficien in ineres rae rule Oupu coefficien in ineres rae rule Ineres rae smoohing coefficien in ineres rae rule Persisence of produciviy shock in counry i = H, F k i C k i C = 1 αi β)1 α i ) α i ρ+η 1+ση k i T k i T = 1 αi β)1 α i ) α i 1+η 1+ση Table 2: Parameers Flexible-price equilibrium under boh regimes Under compleely flexible prices, he model equaions are idenical for boh he FX and MU regime and are given by wih i = H, F. C = η ρ + η YW 2.1) T = η 1 + η YR 2.2) Ỹ W = η ρ + η YW 2.3) Y W = ny H + 1 n)y F 2.4) Y R = Y F Y H 2.5) Y i = ρ i Y i 1 + ν i, 2.6)

9 2.2 Model descripion Sicky-price equilibrium under he MU regime Under sicky prices, he model equaions for he MU regime are given by E Ĉ +1 = Ĉ + 1 ρ ˆR E π W +1 ) 2.7) Ŷ H = 1 n) ˆT + Ĉ 2.8) Ŷ F = n ˆT + Ĉ 2.9) π H = 1 n)k H T ˆT T ) + k H C Ĉ C ) + βe π H ) π F = nkt F ˆT T ) + kc FĈ C ) + βe π+1 F 2.11) ˆT = ˆT 1 + π F π H 2.12) ˆR = φ R ˆR φ R )φ π π W + φ Y Ŷ W ) 2.13) π W = nπ H + 1 n)π F. 2.14) Sicky-price equilibrium under he FX regime The model equaions for he FX regime are given by E Ĉ +1 = Ĉ + 1 ρ n ˆR H E π H +1 ) + 1 n) ˆR F E π F +1 ) ) 2.15) Ŷ H = 1 n) ˆT + Ĉ 2.16) Ŷ F = n ˆT + Ĉ 2.17) π H = 1 n)k H T ˆT T ) + k H C Ĉ C ) + βe π H ) π F = nkt F ˆT T ) + kc FĈ C ) + βe π+1 F 2.19) ˆT = ˆT 1 + π F π H + Ŝ 2.20) E Ŝ +1 = ˆR H ˆR F 2.21) ˆR H = φ R ˆR 1 H + 1 φ R)φ π π H + φ Y Ŷ H ) 2.22) ˆR F = φ R ˆR F φ R)φ π π F + φ Y Ŷ F ). 2.23) 2.2 Model descripion Consumpion is equal across counries a all imes and is described by only one Euler equaion, equaion 2.7) under he MU regime and equaion 2.15) under he FX regime. The only difference beween he wo Euler equaions is ha under he MU regime he nominal ineres rae is common o boh counries. The srucure of aggregae demand is he same under boh regimes and given by equaions 2.8), 2.9), 2.16), and 2.17). Also, he counry-specific New Keynesian Phillips curves are he same under boh regimes and are given by 2.10), 2.11), 2.18), and 2.19). In conras o a closed-economy framework, no only he consumpion gap bu also he erms of rade gap difference beween sicky-price and flexible-price erms of rade) maers for producer price inflaion. 12 The erms-of-rade ideniy is given by 2.12) under he MU regime and by 2.20) under he FX regime, he difference beween he wo being he 12 Noe ha he consumpion gap is equal o he world oupu gap: Ĉ C = Ŷ W Ỹ W. Accordingly, he New Keynesian Phillips curves can be expressed in erms of he world oupu gap as well.

10 8 2 Model presence of he nominal exchange rae in he laer. Equaion 2.21) is he uncovered ineres pariy condiion. The expeced change in he nominal exchange rae corresponds o he ineres rae differenial across counries. Finally, moneary policy is conduced via Taylor-ype ineres rae rules, given by equaion 2.13) under he MU regime and by equaions 2.22) and 2.23) under he FX regime. Under flexible prices, prices are se as a markup over marginal coss, moneary policy is neural, and consumpion, oupu, and he erms of rade are driven by produciviy shocks only, given by equaions 2.1), 2.2), and 2.3). Since money is neural under flexible prices, he inernaional moneary regime does no affec real variables, which herefore behave idenically under boh moneary regimes. 2.3 Welfare loss funcion The welfare analysis follows he logic of he familiar linear-quadraic approach, according o which he log-linear model equaions are used o evaluae a quadraic welfare loss measure Woodford, 2003). The world welfare loss funcion is given by he discouned value of a weighed average across counries of he average uiliy flow of agens using a second-order Taylor series expansion. 13 Throughou he paper, i is assumed ha he disorion induced by monopolisic compeiion is compleely offse by an appropriae subsidy see Appendix D for he full derivaion). Thus, W = 1 2 ρ + η) varĉ C ) η)n1 n) var ˆT T ) α H + σ1 + ση)n 1 α H )1 α H β) var π H α + σ1 + ση)1 n) F ) 1 α F )1 α F β) var π F +.i.p. + O ξ 3 ). 2.24) As in he closed economy, he welfare loss depends on he inflaion rae and he consumpion gap. 14 In he open economy, he welfare loss depends addiionally on he erms of rade gap. Inuiively, when he erms of rade deviae from he erms of rade ha would prevail under flexible prices, he resuling allocaion of producion across counries is inefficien due o he presence of price sickiness. 13 Compuing counry-specific welfare would complicae he calculaions significanly because more accurae approximaions of he non-linear model equaions would be necessary Benigno and Woodford, 2005). This is beyond he scope of his paper. 14 In he basic closed-economy framework, consumpion usually equals oupu. Noe also ha he welfare loss funcion 2.24) can be expressed alernaively in erms of he world oupu gap or he counryspecific oupu gaps see equaion D.72). The specificaion in erms of he consumpion gap was chosen for analyical convenience.

11 2.4 Calibraion 9 In he special case when prices are equally rigid in boh counries α H = α F = α), he welfare loss funcion simplifies o W = 1 2 ρ + η) varĉ C ) η)n1 n) var ˆT T ) α + σ1 + ση) 1 α)1 αβ) [ var π W + n1 n) var π R +.i.p. + O ξ 3 ). 2.25) ] ) 2.4 Calibraion The values for he baseline calibraion are aken from Benigno 2004), excep for he ineres rae rule coefficiens Table 3). A value of 0.99 for he discoun facor β implies a seady sae real ineres rae of around 4.1 percen annually. A value of 7.66 for he elasiciy of subsiuion beween differeniaed goods σ implies a seady sae markup of prices over marginal coss of 15 percen. A value of 0.75 for he probabiliy of no being able o rese he price α i implies an average duraion of price conracs of 4 quarers. Following Roemberg and Woodford 1998) and Benigno 2004), he inverse of he elasiciy of producing he differeniaed good η is calculaed as η = ɛ wy ρ + 1 γ γ, 2.26) where ɛ wy denoes he elasiciy of he average real wage wih respec o producion and γ denoes he labor income share. ρ 1/6 Inv. of elasiciy of ineremporal subsiuion in consumpion n 0.5 Counry size measured by populaion β 0.99 Discoun facor η 0.67 Inv. of elasiciy of producing he differeniaed good ɛ wy 0.5 Producion elasiciy of average real wage γ 0.75 Labor income share σ 7.66 Elasiciy of subsiuion beween differeniaed goods α i 0.75 Probabiliy of no being able o rese he price φ π 1.5 Inflaion coefficien in ineres rae rule φ Y 0 Oupu coefficien in ineres rae rule φ R 0 Ineres rae smoohing coefficien in ineres rae rule ρ i 0.9 Persisence of produciviy shock var ν i 1 Variance of whie noise process corrν H, νf ) 0 Correlaion beween counry-specific whie noise processes Table 3: Baseline calibraion Under he baseline calibraion, moneary policy responds o inflaion φ π = 1.5), bu i does no reac o oupu φ Y = 0) and does no engage in ineres rae smoohing φ R = 0). I assume hroughou he paper ha all ineres rae rule coefficiens are idenical across counries and regimes.

12 10 3 Resuls under symmery I consider a broad range of values for he parameers of he model o check for he validiy of he resuls Table 4). In paricular, he ineres rae rules will also feaure a reacion o oupu and ineres rae smoohing. ρ [0.1,1.1] Inv. of elasiciy of ineremporal subsiuion in consumpion n [0.05,0.95] Counry size measured by populaion β [0.9,1.0] Discoun facor η [0.2,3.0] Inv. of elasiciy of producing he differeniaed good ɛ wy [0.2,1.2] Producion elasiciy of average real wage γ [0.5,0.9] Labor income share σ [5,25] Elasiciy of subsiuion beween differeniaed goods α i [0.05,0.95] Probabiliy of no being able o rese he price φ π [1.1,3.5] Inflaion coefficien in ineres rae rule φ Y [0,3] Oupu coefficien in ineres rae rule φ R [0,0.95] Ineres rae smoohing coefficien in ineres rae rule Table 4: Parameer range 3 Resuls under symmery Firs, I conduc he analysis under he assumpion ha he wo counries are symmeric excep for counry size n). In paricular, he degree of price sickiness is equal across counries. The world welfare loss funcion under symmery, equaion 2.25), is repeaed here for convenience: W = 1 2 ρ + η) varĉ C ) η)n1 n) var ˆT T ) α + σ1 + ση) 1 α)1 αβ) [ var π W + n1 n) var π R +.i.p. + O ξ 3 ). 3.1) I conains four componens: he variance of he consumpion gap Ĉ C ), he variance of he erms of rade gap ˆT T ), he variance of he world inflaion rae π W ), and he variance of he inflaion differenial π R ). ] ) 3.1 Analyical resuls The analyical resuls in his subsecion are crucial o undersanding he main finding of he paper. I derive he recursive law of moion RLOM) of he model equaions for each moneary regime using he mehod of undeermined coefficiens o obain he analyical expressions for he variances conained in he welfare loss funcion. The derivaions are based on he assumpion ha he degree of price sickiness and he persisence of produciviy shocks are idenical across counries α H = α F and ρ H = ρ F ) and ha moneary policy does no engage in ineres rae smoohing φ R = 0).

13 3.1 Analyical resuls 11 Forunaely, i is no necessary o derive he RLOM for he variables consumpion and world inflaion, since hey boh behave idenically across moneary regimes. To see his for he MU regime, subsiue ou he nominal ineres rae ˆR in he Euler equaion 2.7) by insering he ineres rae rule 2.13) and he equaions for aggregae demand 2.8) and 2.9): ρe Ĉ +1 = ρ + φ Y )Ĉ + φ π π W E π W ) The same equaion is obained compleely analogously for he FX regime. For world inflaion, insering he New Keynesian Phillips curves, which are idenical across regimes, ino he definiion of world inflaion π W = nπ H + 1 n)π F, where α H = α F = α due o symmery and herefore k H T = kf T = k T and k H C = kf C = k C, yields π W = k C Ĉ C ) + βe π W ) The reason why world inflaion is he same under boh he MU and he FX regimes is ha he erms of rade vanish from he equaion when he degree of price sickiness is equal across counries. The fac ha boh consumpion and world inflaion behave idenically across moneary regimes implies ha he variance of consumpion and he variance of world inflaion are idenical as well. As a resul, hey do no produce differences in welfare across he wo regimes. For he remaining wo variables, he erms of rade and he inflaion differenial, he reduced sysem of equaions under he MU regime is given by π R = k T ˆT T ) + βe π+1 R 3.4) ˆT = ˆT 1 + π R. 3.5) The reduced sysem of equaions under he FX regime is given by π R = k T ˆT T ) + βe π+1 R 3.6) ˆT = ˆT 1 + π R + Ŝ 3.7) E Ŝ +1 = φ π π R + φ Y ˆT. 3.8) Equaions 3.4) and 3.6) are obained by subracing he New Keynesian Phillips curve of counry H from ha of counry F. Equaions 3.5) and 3.7) are he ermsof-rade ideniies. Equaion 3.8) is obained by insering he ineres rae rules 2.22) and 2.23) and he equaions for aggregae demand 2.16) and 2.17) ino he uncovered ineres pariy condiion 2.21). The RLOM under he MU regime is, hen, given by see Appendix A for he enire derivaion) ˆT = b 1 ˆT 1 + c 1 T 3.9) π R = b 2 ˆT 1 + c 2 T, 3.10)

14 12 3 Resuls under symmery wih coefficiens b 1 = 1 + k T + β 1 + k T + β) 2 4β 2β b 2 = 1 + k T β 1 + k T + β) 2 4β 2β k c 1 = c 2 = c = T 1 + k T + β1 ρ H b 1 ). The RLOM under he FX regime is given by wih coefficiens b 1 = 0 b 2 = 0 b 3 = 1 ˆT = b 1 ˆT 1 + c 1 T 3.11) π R = b 2 ˆT 1 + c 2 T 3.12) Ŝ = b 3 ˆT 1 + c 3 T, 3.13) φ π ρ c 1 = H )k T φ π ρ H )k T + 1 ρ H + φ Y )1 βρ H ) 1 ρ c 2 = H + φ Y )k T φ π ρ H )k T + 1 ρ H + φ Y )1 βρ H ) φ π 1 φ c 3 = Y )k T φ π ρ H )k T + 1 ρ H + φ Y )1 βρ H ). Consequenly, he variances of he erms of rade gap and he variances of he inflaion differenial under each regime are given by [ ] 1 + ρ var MU ˆT T ) = H b 1 )c 2 1 b 2 1 )1 ρ Hb 1 ) 2c + 1 var T 3.14) 1 ρ H b 1 var FX ˆT T ) = c 1 1) 2 var T 3.15) var MU π R = 2c 2 1 ρ H ) 1 + b 1 )1 ρ H b 1 ) var T 3.16) var FX π R = c 2 2 var T 3.17) ) 1 η 2 [ ] var T = 1 ρ 2 var ν H + var ν F 2 covν H, ν F ). 3.18) 1 + η H Two imporan differences exis beween he MU and FX regime. Firs, in conras o he MU regime, here is no persisence in he erms of rade nor in he inflaion differenial under he FX regime b 1 = b 2 = 0). Hence, once he shock has vanished, boh variables reurn immediaely o heir seady sae. This is due o he nominal exchange rae. Inuiively, he coefficien b 3 = 1 implies ha, if he erms of rade were, for example, one percen below he seady sae in he previous period, he nominal ex-

15 3.2 Price sickiness 13 change rae would increase by one percen in he curren period, so ha he erms of rade are a seady sae. Naurally, his mechanism is absen under he MU regime, since he nominal exchange rae is fixed. Thus, boh he erms of rade and he inflaion differenial are inerial or hisory-dependen in he sense ha hey depend on he realizaion of he erms of rade in he previous period. While he ineria of he erms of rade in he conex of a moneary union has been recognized before e.g., Benigno, 2004; Pappa, 2004), i was regarded solely as a source of inefficiency in he economy. However, as will be shown below, he ineria of he erms of rade will also prove o be beneficial, namely from he perspecive of sabilizing inflaion expecaions. Second, in conras o he MU regime, moneary policy is able o influence he erms of rade gap and he inflaion differenial under he FX regime. Technically, he variance of he erms of rade gap and of he inflaion differenial depend on he ineres rae rule coefficiens φ π and φ Y. Moreover, if moneary policy is exremely aggressive owards inflaion under he FX regime φ π ), he variance of he erms of rade gap and of he inflaion differenial converge owards zero since c 1 1 and c 2 0). Thus, he efficien equilibrium can be approximaed arbirarily well, reducing he welfare loss o zero. In conras, he variance of he erms of rade gap and of he inflaion differenial under he MU regime canno be zero, and herefore he efficien equilibrium is no feasible Price sickiness The analyical expressions for he variances can be used o derive he condiion under which world welfare is larger in one or he oher moneary regime. Unforunaely, he resuling condiion is a complex inequaliy ha provides hardly any inuiion. In he following, I hus compue he welfare losses numerically and display he resuls graphically. The deep parameers are calibraed according o he baseline calibraion Table 3), excep for he parameers of ineres, which ake on a broad range of values Table 4). Wheher he world welfare loss is higher in one han in he oher moneary regime depends crucially on he Calvo parameer α, i.e., he degree of price sickiness in boh economies Figure 1). In boh regimes, he world welfare loss is increasing in he degree of price sickiness. 16 When he degree of price sickiness is raher low, he world welfare loss is higher under he MU regime han under he FX regime. The counries are beer off wih heir own currency and heir own independen moneary policy. However, beyond a cerain hreshold α 0.5), where he degree of price sickiness is raher high, he world welfare loss is higher under he FX regime han under he MU regime. The counries are beer off forming a moneary union wih one currency and one common moneary auhoriy. Quaniaively, he difference in welfare beween he wo moneary regimes can be subsanial. Under he baseline calibraion, he welfare loss under he MU regime is roughly 40 percen lower han under he FX regime 0.8/1.3). As described above, wo componens of he world welfare loss funcion 3.1) behave idenically across moneary regimes and, herefore, canno creae welfare differences 15 Thus, only he FX regime feaures he so-called divine coincidence see Corsei, Dedola, and Leduc 2011) for deails on he divine coincidence in open economies). 16 This feaure is common o he closed-economy seup of he basic New Keynesian model, as in Gali 2008).

16 14 3 Resuls under symmery MU FX Loss Calvo parameer α H =α F ) Figure 1: World welfare loss under various degrees of price sickiness α H = α F ) across regimes: he consumpion gap and he world inflaion rae Figure 2, upper and lower lef panel). However, his does no hold for he erms of rade gap and he inflaion differenial Figure 2, upper and lower righ panel). The conribuion of he erms of rade gap o he world welfare loss is higher under he MU regime han under he FX regime regardless of he degree of price sickiness. 17 This indicaes ha he MU regime enails coss. However, he conribuion of he erms of rade gap is much smaller han he conribuion of he inflaion differenial. This is due o he fac ha agens aach by far he highes weigh o inflaion, which is radiionally he case in microfounded welfare measures derived from New Keynesian models. Therefore, he inflaion differenial is he key o undersanding he above finding ha he MU regime yields higher world welfare when prices are relaively sicky. In fac, he paern in he lower righ panel of Figure 2 closely resembles he paern in Figure 1, wih a similar hreshold value of α 0.5. This indicaes ha he MU regime enails benefis. The conribuion of a componen o he world welfare loss is he produc of he variance of ha componen and is weigh. The weigh and variance of he inflaion differenial show opposie paerns wih respec o price sickiness. Whereas he variance decreases wih a rising degree of price sickiness Figure 3), he weigh increases Figure 4). Thus, alhough he variance decreases wih he degree of price sickiness, which per se enhances he agens welfare, he agens aach a higher weigh o inflaion as prices become sickier This holds for he conribuion of he counry-specific oupu gaps as well. The corresponding graphs are available upon reques. 18 The agens aach a higher weigh o inflaion as prices become sickier because he degree of inefficien price dispersion beween differeniaed goods is increasing in he degree of price sickiness for a given level of aggregae inflaion Woodford, 2003).

17 3.2 Price sickiness 15 Conribuion Consumpion Gap 0.8 MU 0.6 FX Calvo parameer α H =α F ) Conribuion World Inflaion MU FX Calvo parameer α H =α F ) Conribuion Terms of Trade Gap 0.4 MU 0.3 FX Calvo parameer α H =α F ) Conribuion Inflaion Differenial MU FX Calvo parameer α H =α F ) Figure 2: Conribuions o world welfare loss in Figure Variance Consumpion Gap MU FX Variance Terms of Trade Gap 2 MU 1.5 FX Calvo parameer α H =α F ) 1.5 x Variance World Inflaion MU FX Calvo parameer α H =α F ) Calvo parameer α H =α F ) Variance Inflaion Differenial MU FX Calvo parameer α H =α F ) Figure 3: Variances underlying he conribuions in Figure 2 Since he weigh of he inflaion differenial is idenical across he wo moneary regimes his holds for all componens), i is he variance ha causes he difference in welfare. Whereas he variance of he inflaion differenial is higher under he MU regime for lower degrees of price sickiness, i is higher under he FX regime for higher degrees of price sickiness. Tha is, inflaion raes are more sable under he MU regime

18 16 3 Resuls under symmery when prices are relaively sicky. 2 1 Weigh Consumpion Gap MU FX 2 1 Weigh Terms of Trade Gap MU FX Calvo parameer α H =α F ) Weigh World Inflaion MU FX Calvo parameer α H =α F ) Calvo parameer α H =α F ) Weigh Inflaion Differenial MU FX Calvo parameer α H =α F ) Figure 4: Weighs underlying he conribuions in Figure 2 The inflaion differenial in period can be expressed as he sum of curren and discouned expeced fuure erms of rade gaps. Solving equaion 3.4) forward, which holds under boh regimes, gives π R = k T E β k ˆT +k T +k ). 3.19) k=0 Accordingly, curren and expeced fuure erms of rade gaps are he only deerminan for he curren inflaion differenial. As shown nex, wo endogenous effecs ha boh influence he erms of rade gap explain why inflaion raes are more sable under he MU regime when prices are relaively sicky. Firs, he sabilizing propery of a flexible nominal exchange rae declines as prices become sickier "inheried sickiness of he nominal exchange rae"). Second, fixing he exchange rae enails he benefi of affecing inflaion expecaions in a favorable way by inducing hisory dependence ino he economy "inheren benefi of moneary unions") Inheried sickiness of he nominal exchange rae Wheher he nominal exchange rae sabilizes or desabilizes he erms of rade gap, hereby faciliaing an efficien allocaion across counries, depends on he way moneary policy is conduced. Recall he recursive law of moion for he nominal exchange rae, 3.13): Ŝ = b 3 ˆT 1 + c 3 T, wih c 3 = φ π 1 φ Y )k T φ π ρ H )k T + 1 ρ H + φ Y )1 βρ H ).

19 3.2 Price sickiness 17 Under he baseline calibraion, where moneary policy reacs o inflaion, bu no o oupu φ Y = 0), he coefficien c 3 is unambiguously posiive since φ π > 1) and smaller han one. Accordingly, in response o a shock ha leads o an increase in he flexible-price erms of rade, he nominal exchange rae will increase as well, pushing up he sicky-price erms of rade closer o he flexible-price erms of rade. Thus, he nominal exchange rae sabilizes he erms of rade gap. However, he sabilizing effec of he nominal exchange rae weakens as prices become sickier. The size of he response of he nominal exchange rae o a produciviy shock decreases wih he degree of price sickiness. Analyically, as he degree of price sickiness α increases, k T decreases and c 3 decreases. In he limi, when prices become fixed α 1), he nominal exchange rae is fixed as well k T 0, c 3 0). The reason for his is ha he expeced change in he nominal exchange rae depends on he ineres rae differenial across counries according o he uncovered ineres pariy condiion, 2.21): E Ŝ +1 = ˆR H ˆR F. Ineres raes, in urn, are se by moneary policy in response o inflaion according o he ineres rae rules. Therefore, an increase in price sickiness, which reduces inflaion variabiliy, reduces ineres rae variabiliy and, ulimaely, reduces he variabiliy of he nominal exchange rae. Thus, he nominal exchange rae inheris he sickiness of goods prices. This, in urn, hampers he sabilizaion of he erms of rade gap. Therefore, he sabilizing propery of he nominal exchange rae of faciliaing an efficien allocaion across counries declines wih he degree of price sickiness. Noably, for his effec o be effecive, he uncovered ineres pariy condiion need no hold exacly. I suffices for he ineres raes and he nominal exchange rae o be linked Inheren benefi of moneary unions The fac ha he benefi of a flexible nominal exchange rae declines wih he degree of price sickiness canno alone explain he finding ha he MU regime is welfareimproving over he FX regime. For even under relaively sicky prices, he nominal exchange rae sabilizes he erms of rade gap a leas o some exen compared o a siuaion wih a compleely fixed nominal exchange rae, as under he MU regime. This is also he reason why he variance of he erms of rade gap is lower under he FX regime regardless of he degree of price sickiness Figure 3, upper righ panel). Therefore, he MU regime mus also provide a benefi. The MU regime differs from he FX regime in one imporan respec, as he analyical resuls from Secion 3.1 have shown. In conras o he FX regime, he economy under he MU regime is inrinsically inerial. So, even in he presence of a one-off shock, he inflaion differenial and he erms of rade gap are persisen. As shown nex, his ineria will resul in a higher sabiliy of inflaion raes. The qualiaive difference beween he wo moneary regimes can be seen clearly by looking a he impulse response of he erms of rade gap o a posiive one-off produciviy shock in counry H Figure 5). 19 On impac, he erms of rade gap decreases under boh regimes because he sicky-price erms of rade do no increase as much as 19 The degree of price sickiness was chosen o be low α = 0.2), so as o make he differences in he impulse responses clearly visible. The differences are much smaller for higher degrees of price sickiness, bu are qualiaively he same.

20 18 3 Resuls under symmery he flexible-price erms of rade due o he sickiness of prices. However, in he following period, when he shock has vanished, he erms of rade gap has reurned o he seady sae under he FX regime, bu no under he MU regime. Under he FX regime, i is he nominal exchange rae ha brings he erms of rade gap auomaically back o he seady sae in he absence of shocks. 20 Under he MU regime, his mechanism is absen, since he nominal exchange rae is fixed. As a resul, he erms of rade gap is inrinsically inerial or hisory-dependen. Terms of Trade Gap MU FX Quarers Figure 5: Impulse response of he erms of rade gap o a posiive one-off produciviy shock in counry H ρ H = 0), wih α = 0.2 Imporanly, he hisory dependence of he erms of rade gap manifess iself in an overshooing paern. The erms of rade gap overshoos because he sicky-price erms of rade are sill elevaed above he seady sae afer he shock has vanished, whereas he flexible-price erms of rade are back a he seady sae. In subsequen periods, he erms of rade gap converges back o he seady sae. The qualiaive difference in he dynamics beween he wo moneary regimes prevails in siuaions in which he produciviy shock iself is persisen Figure 6, lef panel). 21 Whereas he erms of rade gap converges monoonically back o he seady sae under he FX regime, i overshoos he seady sae under he MU regime. Since he inflaion differenial is deermined by he erms of rade gap and is expeced fuure pah recall equaion 3.19), i exhibis he same qualiaive difference. Accordingly, under he FX regime he inflaion differenial increases on impac and converges monoonically back o he seady sae Figure 6, righ panel). In conras, 20 Ineresingly, his mechanism is independen of he ineres rae rule coefficiens φ π and φ Y recall he RLOM coefficien b 3 = 1). 21 The calibraion underlying he impulse responses in Figure 6 is now idenical o he calibraion underlying he welfare resuls in Figure 1 hrough 4.

21 3.2 Price sickiness 19 under he MU regime, price seers adjus heir prices less in he iniial period despie he sronger iniial change in he erms of rade gap because hey anicipae he fuure overshooing of he erms of rade gap. In subsequen periods, inflaion approaches he seady sae faser han under he FX regime and evenually overshoos he seady sae as well. 22 As a resul, he variance of he inflaion differenial, i.e., he sum of squared deviaions of he inflaion differenial from zero, is lower under he MU regime han under he FX regime Terms of Trade Gap Inflaion Differenial MU FX MU FX Quarers Quarers Figure 6: Impulse responses o a posiive produciviy shock in counry H wih ρ H = 0.9 and α = 0.75 To sum up: Since price seers are forward-looking, no only presen, bu also expeced fuure erms of rade gaps maer for curren inflaion. Since he nominal exchange rae is fixed under he MU regime, he erms of rade gap overshoos in response o a shock a some poin in ime, which would hen call for he opposie price adjusmens as in he presen. In anicipaion of his, curren price responses are smaller in magniude han under he FX regime. As a resul, inflaion is more sable under he MU regime. Thus, he inheren benefi of moneary union is ha i affecs inflaion expecaions in such a way as o lower he welfare-relevan variance of inflaion by inducing hisory dependence ino he economy. The srengh of his benefi increases as prices become sickier, since price seers aach higher weighs o fuure erms of rade gaps as he probabiliy of being able o rese prices decreases. The benefi of hisory dependence is well-known from he analysis of opimal moneary policy in a closed-economy environmen. Opimal moneary policy under discreion is inferior from a welfare perspecive o opimal policy under commimen because he former does no influence he inflaion expecaions of price seers in a favorable way. I suffers from he so-called sabilizaion bias. 23 In conras, opimal moneary policy under commimen induces hisory dependence ino he economy, herefore aking advanage of he fac ha price seers are forward-looking. This resuls in a higher sabiliy of inflaion. In exacly he same sense, forming a moneary union may be superior o mainaining a flexible exchange rae under cerain condiions because 22 Throughou he paper, I use he erm "overshooing" o describe boh "overshooing" and "undershooing". 23 For deails on he sabilizaion bias, see, e.g., Woodford 2003, Ch. 7), Gali 2008, Ch. 5), or Walsh 2010, Ch. 8).

22 20 3 Resuls under symmery fixing he nominal exchange rae affecs inflaion expecaions in a favorable way by inducing hisory dependence ino he economy. Noably, his benefi exiss despie he fac ha price levels are no saionary. 24 Thus, and in conras o Monacelli 2004), he benefi does no hinge upon saionariy of price levels. This is a paricular feaure of he small open economy assumpion and does no generally carry over o a wo-counry environmen. Insead, he benefi hinges upon he overshooing paern of he erms of rade, he anicipaion of which reduces he magniude of price changes, rendering he inflaion raes more sable. 3.3 Moneary policy The finding ha forming a moneary union is beneficial when prices are relaively sicky is very robus o he range of parameer values considered in Table The imporan excepion is he parameers ha govern he behavior of moneary policy, i.e., he coefficiens of he ineres rae rules. These will be considered nex Inflaion coefficien Wheher forming a moneary union urns ou o be beneficial depends crucially on he inflaion coefficien φ π in he ineres rae rules, i.e., on he aggressiveness of moneary policy owards inflaion Figure 7). 26 Saring ou a a very low response of moneary policy o inflaion φ π above, bu close o, one), he MU regime yields a lower world welfare loss for every degree of price sickiness. Increasing he aggressiveness of moneary policy a lile bi resuls in he FX regime being superior for very low degrees of price sickiness, bu inferior for higher degrees of price sickiness. As he aggressiveness of moneary policy increases furher, he hreshold value for α increases, beyond which he MU regime yields a lower world welfare loss. Evenually, beyond a cerain aggressiveness of moneary policy owards inflaion φ π 2.5), he MU regime is inferior o he FX regime regardless of he degree of price sickiness. The inuiion for his is as follows. Under he FX regime, when moneary policy reacs o inflaion only, he nominal exchange rae sabilizes he erms of rade gap in response o shocks see Secion 3.2.1). The srengh of his sabilizing propery increases wih he aggressiveness of moneary policy owards inflaion, since moneary policy direcly influences he nominal exchange rae via he uncovered ineres pariy condiion. As a resul, even when prices are relaively sicky, moneary policy can counerac by being more aggressive owards inflaion. In he limi φ π ), moneary policy perfecly sabilizes all welfare-relevan variables, reducing he welfare loss o zero divine coincidence). This is no he case under he MU regime because he common moneary policy has no influence on he erms of rade gap and he inflaion differenial when prices are equally sicky across counries see Secion 3.1). 24 Impulse responses for price levels are available upon reques. 25 The corresponding graphs are available upon reques. 26 The graph in he righ panel of Figure 7 is a roaion of he graph in he lef panel, in order o be able o see behind he seep surface area. Cuing hrough he wo surface areas along φ π = 1.5 produces Figure 1.

23 3.3 Moneary policy 21 Figure 7: World welfare loss under various degrees of price sickiness α H = α F ) and various values for he inflaion coefficien φ π ), from wo differen angles Oupu coefficien The welfare ranking beween he wo moneary regimes depends also on he oupu coefficien in he ineres rae rules φ Y, i.e., on he aggressiveness of moneary policy owards oupu Figure 8). For almos all he combinaions of φ Y and φ π considered, he FX regime yields a higher world welfare loss han he MU regime, alhough he degree of price sickiness was deliberaely chosen o favor he FX regime α = 0.2). Increasing he degree of price sickiness would favor he MU regime furher. In general, he sronger moneary policy reacs o oupu, he sronger i needs o reac o inflaion for he FX regime o remain superior. This relaionship is very seep; a small increase in φ Y e.g. from 0 o 0.25) requires a srong increase in φ π from roughly 1.5 o 2.3). Unlike in he case of he response o inflaion, he more aggressive moneary policy reacs o oupu, he smaller he impac response of he nominal exchange rae o shocks becomes see coefficien c 3 of he RLOM). When he aggressiveness of moneary policy owards oupu relaive o inflaion exceeds a cerain degree φ Y > φ π 1), he nominal exchange rae desabilizes he erms of rade gap in response o shocks c 3 < 0). The reason for his is ha from a welfare perspecive, a response o oupu by moneary policy is derimenal. I is no he deviaion of oupu from he seady sae ha is

24 22 3 Resuls under symmery Figure 8: World welfare loss under various values for he oupu coefficien φ Y ) and for he inflaion coefficien φ π ), wih α = 0.2, from wo differen angles welfare-relevan, i is he deviaion from he flexible-price counerpar oupu gap). 27 For example, a posiive produciviy shock in counry H induces an increase in oupu, bu a decrease in he oupu gap, since he increase in oupu is lower han he increase in flexible-price oupu. A welfare-oriened reacion of moneary policy would require a reducion in he ineres rae due o he negaive oupu gap. Insead, moneary policy raises he ineres rae due o he rise in oupu. As a resul, he variance of he inflaion differenial is higher when moneary policy reacs o oupu φ Y > 0) han when i does no reac o oupu φ Y = 0). 28 While a reacion o oupu is derimenal under boh regimes in Figure 8, he welfare loss is increasing in he oupu coefficien φ Y under boh regimes), he damage in erms of welfare is greaer under he FX regime. The reason for his is ha, in conras o he MU regime, moneary policy under he FX regime affecs every componen of he welfare loss funcion see Secion 3.1). Thus, conducing "bad" moneary policy is more harmful under he FX regime because moneary policy is more powerful in his regime. Essenially, he nominal exchange rae does no compensae for moneary 27 Recall ha he welfare loss funcion can be expressed alernaively in erms of counry-specific oupu gaps insead of he consumpion gap see equaion D.72). 28 This is common o he closed-economy seup of he basic New Keynesian model, as in Gali 2008).

25 3.3 Moneary policy 23 policy misakes; insead, i reinforces he qualiy of moneary policy. In his sense, a moneary union provides a hedging mechanism agains moneary policy misakes Ineres rae smoohing coefficien The welfare ranking beween he wo moneary regimes depends on he degree of ineres rae smoohing φ R as well Figure 9). 29 When moneary policy does no engage in ineres rae smoohing φ R = 0), he MU regime yields a lower welfare loss for relaively sicky prices. As he degree of ineres rae smoohing increases, he hreshold value for α, beyond which he MU regime is superior, increases as well. For very high degrees of ineres rae smoohing, he MU regime is welfare-improving only for exremely high degrees of price sickiness. Thus, ineres rae smoohing makes a beneficial moneary union less likely. Figure 9: World welfare loss under various degrees of price sickiness α H = α F ) and various values for he ineres rae smoohing coefficien φ R ), from wo differen angles The reason for his becomes clear by looking again a he impulse response of he erms of rade gap o a posiive one-off produciviy shock in counry H, bu now wih a relaively high degree of ineres rae smoohing Figure 10). The impulse response 29 Cuing hrough he wo surface areas along φ R = 0 produces Figure 1

26 24 3 Resuls under symmery under he MU regime is idenical o he siuaion wihou ineres rae smoohing Figure 5) because moneary policy coninues o exer no influence on he erms of rade when prices are equally sicky across counries. In conras, he impulse response under he FX regime now resembles he response under he MU regime. Alhough he produciviy shock is one-off, he erms of rade gap displays ineria in he form of overshooing. Terms of Trade Gap MU FX Quarers Figure 10: Impulse response of he erms of rade gap o a posiive one-off produciviy shock in counry H ρ H = 0), wih φ R = 0.9 and α = 0.2 As a resul, inflaion expecaions are affeced in he same favorable way as under he MU regime, namely by inducing hisory dependence ino he economy. Only he source of hisory dependence is differen. Under he FX regime, moneary policy has o engage in ineres rae smoohing o induce hisory dependence. Under he MU regime, hisory dependence is induced auomaically by he fac ha he nominal exchange rae is fixed. For he FX regime o be welfare-improving over he MU regime under relaively sicky prices, moneary policy has o implemen a sufficienly high degree of ineres rae smoohing. This renders he inflaion differenial more sable under he FX regime. The fac ha ineres rae smoohing under he FX regime reduces he welfare loss by sabilizing inflaion comes as no surprise. As shown by Woodford 1999), one way for moneary policy o implemen he kind of hisory dependence ha is desirable from he perspecive of opimal moneary policy is o engage in ineres rae smoohing by including a feedback of he curren nominal ineres rae o pas realizaions of he nominal ineres rae, as is he case in he ineres rae rules given by equaions 2.22) and 2.23).

27 4 Resuls under asymmery 25 4 Resuls under asymmery In he following, I check wheher asymmeries in counry size or in he degree of price sickiness maer for he welfare ranking beween he MU and FX regime. 4.1 Counry size If he wo counries differ only in populaion size, he analyical resuls from Secion 3.1 carry over. Accordingly, he RLOM under boh moneary regimes, equaions 3.9) hrough 3.13), are valid in his case. As one can see, he RLOMs are independen of he counry size n. Thus, he welfare-relevan inflaion differenial and he erms of rade gap are independen of n. As a consequence, he hreshold value for α, beyond which he MU regime yields a lower world welfare loss, is compleely insensiive wih respec o n. Therefore, he welfare ranking beween he MU and FX regime does no depend on counry size. 4.2 Price sickiness The world welfare loss funcion under differen degrees of price sickiness across he wo counries is given by equaion 2.24) and repeaed here for convenience: W = 1 2 ρ + η) varĉ C ) η)n1 n) var ˆT T ) α H + σ1 + ση)n 1 α H )1 α H β) var π H α + σ1 + ση)1 n) F ) 1 α F )1 α F β) var π F +.i.p. + O ξ 3 ). 4.1) I conains four componens: he variance of he consumpion gap Ĉ C ), he variance of he erms of rade gap ˆT T ), he variance of inflaion in counry H π H ), and he variance of inflaion in counry F π F ). Unless he degree of price sickiness is exremely high α 0.9, which corresponds o an average duraion of price conracs of a leas 10 quarers), asymmery in he degree of price sickiness does no maer for he welfare ranking beween he MU and FX regime Figure 11). Drawing from he analysis above, he inuiion is he following. Firs, he inheren benefi of moneary unions of inducing hisory dependence is independen of counry characerisics. I depends only on he fac ha he nominal exchange rae is fixed and ha price seers are forward-looking. Second, he nominal exchange rae inheris he sickiness of goods prices from boh counries. I does no maer if he sickiness is equally presen in boh counries or if he sickiness comes primarily from one counry. Thus, as long as he aggregae degree of price sickiness in he world as a whole is sufficienly high, he MU regime coninues o be beneficial.

28 26 5 Conras o radiional OCA heory Figure 11: World welfare loss under differen degrees of price sickiness across counries α H = α F ), from wo differen angles 5 Conras o radiional OCA heory This paper has shown ha in he sandard wo-counry New Keynesian DSGE model, counries benefi from forming a moneary union when prices are relaively sicky bu do no when prices are relaively flexible. This finding is clearly a odds wih Friedman 1953) s case for flexible exchange raes and wih he radiional OCA heory. 30 Firs, noe ha in he model employed in his paper he need for macroeconomic adjusmen is riggered by an asymmeric emporary change in produciviy, whereas he radiional OCA analysis usually assumes a permanen shif in demand from he producs of one counry o he producs of he oher. Second, and more imporanly, he role of expecaions differs quie subsanially beween he New Keynesian and he Old-Keynesian framework. In he Old-Keynesian framework, in which he key predicions of he radiional OCA heory were developed, expecaions of economic agens were reaed as exogenous. In conras, in New Keynesian models privae secor expecaions are reaed as endogenous. As shown, i is precisely he expecaions channel ha renders inflaion raes more sable under he 30 De Grauwe 2012) summarizes he key insighs from he radiional OCA heory.