NBER WORKING PAPER SERIES MONETARY POLICY IN OPEN ECONOMIES: PRACTICAL PERSPECTIVES FOR PRAGMATIC CENTRAL BANKERS. Richard Clarida

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1 NBER WORKING PAPER SERIES MONETARY POLICY IN OPEN ECONOMIES: PRACTICAL PERSPECTIVES FOR PRAGMATIC CENTRAL BANKERS Richard Clarida Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA Ocober 2014 Paper prepared for he Hoover Insiuion Conference on Moneary Policy for he 21s Cenury. I would like o hank he conference organizers, paricipans, and especially my discussan Maurice Obsfeld as well as Ken Judd for insighful suggesions for fuure work. The views expressed herein are hose of he auhor and do no necessarily reflec he views of he Naional Bureau of Economic Research. The auhor has disclosed a financial relaionship of poenial relevance for his research. Furher informaion is available online a hp:// NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions by Richard Clarida. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Moneary Policy in Open Economies: Pracical Perspecives for Pragmaic Cenral Bankers Richard Clarida NBER Working Paper No Ocober 2014 JEL No. E52,E58,F3 ABSTRACT This paper reviews and inerpres some of he key policy implicaions ha flow from a class of DSGE models for opimal moneary policy in he open economy. The framework suggess ha good macroeconomic oucomes in open economies are possible by focusing inflaion argeing ha is implemened by a Taylor ype rule, a rule ha in equilibrium is refleced in he exchange rae as an asse price. Opimal moneary policy will no be able deliver a saionary ( sable ) nominal exchange rae le alone a fixed exchange rae or one ha remains inside a arge zone because, absen a commimen device, opimal moneary can deliver a saionary domesic price level. Anoher feaure in he daa for inflaion argeing counries ha is consisen wih moneary policy via Taylor ype rule is ha i will end push he nominal exchange rae in he opposie direcion from PPP in response o an inflaion shock he bad news god news resul of Clarida Waldman (2008;2014). This is so even hough in he long run of hese models he nominal exchange rae mus in expecaion obey PPP. Richard Clarida Columbia Universiy 420 Wes 118h Sree Room 1111, IAB New York, NY and NBER rhc2@columbia.edu

3 Moneary Policy in Open Economies: Pracical Perspecives for Pragmaic Cenral Bankers Richard H. Clarida* C. Lowell Harriss Professor of Economics Columbia Universiy and NBER May 19, 2014 Inroducion The heory and pracice of conducing moneary policy in he global economy has evolved and, along many dimensions, converged over he pas weny years. In he fifeen years before he world financial crisis, his was eviden in he widespread adopion of inflaion argeing, flexible exchange raes, and of policy implemenaion well undersood and evaluaed wihin a Taylor Rule framework. Empirical research sugges ha he apparen convergence o a Taylor Rule framework did in fac occur during his period (Clarida and Gerler (1996); Clarida, Gali, Gerler (1998;2000); Clarida (1999;2001;2009); Lubik and Schorfheide (2003); Engel and Wes (2006); Molodsova and Papell (2009)). We believe his convergence was no coincidence. In fac, building on he research program inroduced in Taylor (1982;1993) and advanced by Obsfeld and Rogoff (1996;2000) and Svensson (2000), a number of papers (Clarida, Gali, Gerler (2001;2002); Obsfeld (2002); Corsei and Peseni (2005); Gali Monacelli (2005)); Engel (2009); Woodford (2010); Devereux and Hnakovska (2011)) among ohers show ha, in dynamic sochasic general equilibrium models wih nominal rigidiies, flexible exchange raes and inflaion argeing produce desirable macroeconomic oucomes in open economies. Indeed under cerain condiions and in paricular models, inflaion argeing implemened by a Taylor rule in a regime of flexible exchange raes characerizes he opimal moneary policy for a cenral 2

4 bank seeking o maximize a well specified social welfare funcion in an open economy This paper reviews several of he mos relevan findings from his lieraure, findings ha unil now have been and likely will, in he fuure be, of pracical ineres o pragmaic cenral bankers conducing moneary policy in he global economy of he 21 s cenury. The focus will be on implicaions from his research ha, in our opinion, are mos likely in he decades ahead o be robus in pracical, real world applicaion, no jus in he paricular heoreical models from which hey were originally derived. The plan of he paper is as follows. In Secion II we review he se up of he open economy DSGE model inroduced in Clarida, Gali, Gerler (2001;2002), Gali Monacelli (2005)) and Gali (2008) and exended by, among ohers, Engel (2009)); Woodford (2010), and Devereux and Hnakovska (2011). We provide inuiion for he isomorphism resul ighly linking opimal moneary policy in open and closed economies ha is a propery of a class of models discussed in Clarida, Gali, Gerler (2001;2002). In Secion III we solve for opimal moneary policy and highligh several key and we believe robus implicaions of he above cied DSGE lieraure for open economy moneary policy operaing away from he zero lower bound. We are moivaed by a belief ha as he world s major cenral banks begin o normalize policy raes and escape (finally!) from he zero bound, he Taylor Rule framework will re emerge as he preferred de faco if no de jure consruc for conducing, evaluaing, and ulimaely for communicaing moneary policy, wih he crucial undersanding ha. The neural real ineres rae, a key inpu o Taylor rule analysis, appears in pracice o be ime varying (Laubach and Williams (2001)), and his ime variaion is likely o be more imporan in he fuure han in he pas for calibraing moneary policy. In paricular, he neural real ineres rae in he open economy will in general be a funcion of global as well local facors such as he rae of poenial growh. 3

5 The exchange rae is an asse price will reflec expecaions of he fuure ime pah of he policy rae as summarized by he policy rule and hus he expeced fuure ime pah of inflaion and oupu under he policy rule. One imporan empirical implicaion of moneary policy by Taylor rule in he open economy is ha bad news abou inflaion can be good news for he nominal exchange rae (Clarida and Waldman 2008); see also he discussion in Krugman, Obsfeld, Meliz (2011) even hough wih inflaion argeing, bad news abou inflaion mus in expecaion be bad news for he long run level of he nominal exchange rae. Moreover,.. In he absence of a commimen device ha binds cenral banker and heir successors, opimal moneary policy in he open economy can a mos achieve a saionary rae of inflaion no a saionary price level. In oher words, price level argeing is no in general ime consisen in he class of DSGE models cied above, a direc consequence of Clarida, Gali, Gerler (1999); Woodford (2003); and he isomorphism resul in Clarida, Gali, Gerler (2001;2002) and Gali Monacelli (2005). As a resul, even if he equilibrium erms of rade are saionary, he equilibrium nominal exchange rae under an opimal policy will resemble a random walk. Technically i will possess a uni roo bu in fac will be co inegraed wih he price level. In oher words A regime of fixed exchange raes is a mirage (Obsfeld and Rogoff (1996)) in he sense ha in hese economies i is no ime consisen in he presence of nominal rigidiies for he policymaker who is maximizing household welfare o promise fix he exchange rae. Moreover, in general, while PPP may be expeced o hold in he long run 4

6 The persisence of PPP deviaions will in general depend direcly on he policy rule in economies in which inflaion ineria is endogenous. Theoreically (Clarida Waldman (2008;2014), he greaer is he relaive weigh he policy maker places on oupu sabilizaion relaive o inflaion sabilizaion, he greaer will be he equilibrium half life of PPP deviaions. Clarida and Waldman (2008) repor an empirical announcemen effec sudy (Table 1) ha documens he bad news good news correlaion in high frequency daa for G10 counries over he period. Clarida Waldman (2014) updae he original announcemen effec sudy o span period and show (Table 2) ha he bad news good news effec remains a robus feaure of he daa on days when here are inflaion announcemens.. In Secion IV we presen an analysis based on Clarida and Waldman (2014) who use a small open economy version of he Gali Monacelli (2005) model wih a hybrid Phillips curve o generalize and exend he findings of Clarida Waldman (2008) wih regards o he bad news good news resul as well as he endogenous persisence of PPP deviaions under opimal moneary policy. Secion V concludes. II. A Model Clarida, Gali, Gerler (2001;2002) and Gali Monacelli (2005) sudy a class of DSGE models wih nominal rigidiies ha can be used o analyze opimal moneary policy in open economies and he role of he nominal exchange rae in he ransmission mechanism. These models have been fruifully exended in subsequen work by Engel (2009); Woodford (2010); and Devereux and Hnakovska (2011) among ohers. Clarida, Gali, Gerler (2001) and Gali Monacelli (2005) are models of small open economies while Clarida, Gali, Gerler (2002) is a general equilibrium wo counry model. Focusing on he home economy, he basic se up of hese models is as follows. 5

7 The home economy produces a radable consumpion good from a CES coninuum of differeniaed inermediae inpus, each of which is produced wih a linear echnology over a CES bundle of differeniaed varieies of labor. The elasiciy of subsiuion among inermediae inpus is ξ > 1 and he elasiciy of subsiuion among varieies of labor is η > 1, wih η a saionary sochasic process. Nominal wages are flexible and each worker earns he same wage W(), bu he nominal price of each inpu can only be re se a random discree inervals as in Calvo (1983). As in Woodford (2003), here will be a welfare cos o domesic inflaion wih his Calvo pricing assumpion, because inflaion will change he relaive prices of inpus and hus cause final oupu o be inefficienly produced. This welfare cos will be decreasing in ξ. Households have Cobb Douglass preferences over a consumpion index C comprised of he home produced final good and a differeniaed consumpion good produced abroad. A key parameer is γ which is he share of home spending on he foreign good. The larger is γ, he more open is he home economy. The law of one price holds and here is producer currency pricing. The relaive price of he foreign produced consumpion good in erms of he home produced consumpion good, he erms of rade, is denoed by S = E(P* /P) where E is he nominal exchange rae and P and P* are producer currency prices of goods for expor in home and foreign. Uiliy akes he sandard form 1 1 C N U ( C) V ( N) 1 1 Where 1/σ is he ineremporal elasiciy of subsiuion of consumpion, and N is labor supply. We will focus on he benchmark case wih σ 1 bu derive many of our resuls for he general σ > 0 case as well. 6

8 Households maximizes a discouned sum of expeced uiliy wih a discoun rae β subjec o a sequence of budge consrains P cpi C E { M, 1D 1} W N D T where M,+1 is a nominal sochasic discoun facor, D is he disribuion paid on securiies brough ino dae, T is lump sum ax collecion, and Г is he disribuion of profis earned by producers of inermediae inpus. Firms will se prices as a mark up over marginal cos. Given he linear echnology, real marginal cos is jus he real produc wage scaled by produciviy MC = (1 τ){w /P }A 1 In our open economy his can be wrien as MC = (1 τ)k 1 {W /P cpi }S γ A 1 where P cpi k 1 PS is he CPI, P is he price of he consumpion good produced a home, τ is a wage ax or subsidy, and k =(1 γ) (1 γ) γ γ cpi w. The firs order condiion for labor supply implies W / P (1 ) N C where 1 + μ w = η /{η 1} is a wage mark up. They key hing o noe is he disincion beween he real produc wage W/P ha is relevan for he labor demand and he real CPI wage ha is relevan for labor supply. Unlike in he closed economy, hese differ in he open economy because of he erms of rade. This is crucial for undersanding he open economy Phillips curve o be derived below. Subsiuing for he real CPI wage we obain a srucural equaion for real marginal cos in he open economy MC (1 w 1 1 )(1 ) N C S k A. Price seing by inermediae goods producers is saggered as in Calvo (1983), resuling in an open economy Phillips curve for domesic inflaion as a funcion of he deviaion of log real marginal cos from is seady sae level of log(ξ/(ξ 1)) wih 1+μ p = ξ/(ξ 1) he desired markup over nominal marginal cos by inermediae goods producers. We have 7

9 E 1 mc where lower case leers denoe log deviaions from he non sochasic seady sae and δ=(1 F)(1 βf)/f wih (1 F) he fracion of firms ha rese prices each period. I is useful o wrie ou he open economy Phillips curve explicily in erms of endogenous variables and he produciviy and cos push realizaions E y c s (1 ) a 1) w 1 where we have used he fac ha n y a, wih he approximaion due o he omission of a second order erm ha capures he inefficien demand for labor resuling from he dispersion of domesic relaive prices in an economy saggered pricing and non zero inflaion. For households, an Euler equaion will characerize he equilibrium relaionship beween he log consumpion index, CPI inflaion, and he one period nominal ineres rae R 1 2) c E { c 1} ( R E 1 Es 1) where π+1 is he rae of inflaion in domesic goods prices. Again, recall ha in he open economy CPI inflaion is a funcion of he change in he equilibrium erms of rade as well as inflaion in he price of domesically produced goods. 8

10 An Isomorphism Resul Inspecion of equaions 1) and 2) reveals ha in he special case wih γ = 0 he sysem reduces o he sandard closed economy DSGE model (Clarida, Gali, Gerler (1999);Woodford (2003)). Tha model is closed wih a goods marke equilibrium condiion c = y and specificaion of a policy rule for R as a funcion of π and y (and perhaps oher, exogenous variables such as produciviy growh or governmen spending). Moreover, an opimal policy rule can be derived for he γ=0 version of he model for a loss funcion ha is quadraic in inflaion and he gap beween y and is level y under flexible prices. And indeed, Clarida, Gali, Gerler (1999) show ha he opimal moneary policy in he closed economy can be wrien as a version of a Taylor rule. Bu how does one close he open economy model skeched ou above? Alhough here are number of ways o do his (see Obsfeld (2002); Corsei and Peseni (2005) and Engel (2009) for alernaives), here are wo known cases consisen wih global general equilibrium ha will resul in a se of equilibrium condiions exacly isomorphic o he closed economy analysis in Clarida, Gali, Gerler (1999). These resuls are derived in Clarida, Gali, Gerler (2002) and Gali Monacelli (2005). Boh cases require ha preferences be Cobb Douglas, and each case is a direc implicaion of he insighful analysis of Cole and Obsfeld (1991). The isomorphism resul will obain for any σ > 0 if home and foreign Cobb Douglas uiliy funcions are idenical (Clarida, gali, Gerler (2002)). The isomorphism resul will also obain wih differing home and foreign Cobb Douglas uiliy funcions say feauring a bias for domesically produced goods if σ is idenically equal o 1 across counries (Gali and Monacelli (2005)). As shown by Cole Obsfeld (1991), in hese wo cases he erms of rade ha clears he markes for inernaionally raded goods will resul in balanced rade period by period and will replicae he period by period consumpion allocaions in he home and foreign counries ha would resul in a world wih a complee 9

11 se of coningen claims markes. In a Cole Obsfeld world, rade in goods is macro economically equivalen o rade in asses. Because in hese cases rade is balanced period by period, in equilibrium income will equal expendiure and here will be an exac linear relaionship beween c, y, and s each period given by c = y + γs. Subsiuing his consumpion index in 2), we obain an open economy IS equaion y = Ey+1+γs γe s+1 σ 1 (R E π+1 γ E s+1). As in saic models, a erms of rade worsening oday booss expors and increases demand for domesic oupu. Also noe ha an anicipaed erms of rade worsening in he fuure raises expeced CPI inflaion and lowers he consumpion real ineres rae for any given nominal ineres rae which will il consumpion demand oward he presen. Wih balanced rade and idenical preferences goods marke equilibrium will imply an exac linear relaionship beween s, y, and y* given by s = y y* which we can use o subsiue ou for s in he open economy IS curve. Afer some simplificaion we obain 3) ~ { ~ 1 y E y 1} [ R E{ 1 } rr] 0 where a ilde over a variable, which is indicaed wih an oversrike, flexible prices is given by y~, indicaes log deviaion from is flexible price equilibrium level y. The neural equilibrium real rae consisen wih rr 0E{ y 1 } k 0 E{ y * 1 } 10

12 where σ0 = σ γ(σ 1) > 0, κ0 = γ(σ 1), and Δy*+1 is growh in foreign oupu. In our benchmark case σ 1 and hus κ0 0. In oher worlds, unless σ = 1 he neural real ineres rae in he home counry will in general be proporional o an average of domesic poenial and world growh raes. Finally we noe ha he log of poenial oupu will be given by y 1 [(1 ) a y 0 * ] where κ = σ(1 γ) + γ + φ. As is he case for he Euler equaion, we can subsiue ou for consumpion and he erms of rade and obain he srucural Phillips curve ha will prevail in he open economy under condiions discussed above. We see ha mc = μ w + κ y + κ0y* (1+φ)a. However, 1 * using he equilibrium condiion for poenial oupu y [(1 ) a y ], i mus be he case 0 ha he equaion for real marginal cos simplifies o mc ~ from which we obain y w 4) E{ ~ 1} { (1 ) } y u wih λ = {σ(1 γ) + γ + φ}δ and u = δμ w. We noe ha in he baseline case. he more open is he economy he flaer is he Phillips curve relaionship beween he oupu gap and inflaion. 11

13 III. Opimal Moneary Policy in he Open Economy To solve for opimal moneary policy in he open economy we need o specify he cenral bank of objecive funcion. There are wo ways o do his. We can jus assume as in he closed economy analysis of Clarida, Gali and Gerler (1999) much of he pre Woodford inernaional moneary lieraure ha he objecive funcion is quadraic in inflaion and he oupu gap wih an arbirary relaive weigh α on sabilizing oupu a is naural level y. Or, as was derived in Clarida, Gali and Gerler (2002) and Gali Monacelli (2005), we can follow Woodford (2003) and solve for α and hus he opimal policy rule as a funcion of deep parameers. Under eiher approach, i is imporan o noe ha, absen a fiscal policy, even under flexible prices he economy will be disored away from he firs bes equilibrium. This is due o he marke power ha heerogeneous workers have in he labor marke and ha inpu producers have in he goods marke. A welfare maximizing policy will wan o offse hese disorions wih a wage subsidy ha is financed via a lump sum ax. As in Woodford (2003) we assume his is done. However, as was poined ou by Corsei and Peseni (2001), in an open economy here will be an incenive for policy o resric oupu below is compeiive flexible price level o ake advanage of he imperfec subsiuabiliy beween impored and expored consumpion goods. In order o avoid he ime consisency issues (Kydland Presco (1977)) ha would arise, we follow Clarida, Gali, Gerler (2002) and assume he employmen subsidy is se so ha he cenral bank has no incenive o engineer a surprise depreciaion or appreciaion of is exchange rae. This subsidy will saisfy (1 τ)(1+μ w )(1+ μ p )(1 γ) = 1. So for a policymaker ha wans o maximize an objecive funcion proporional o W H E [ ~ y 2 ] subjec o 3) and 4) and aking y* and Eπ+1 as given, he firs order condiion will be given by 12

14 y ~ which is of he same form as in Clarida, Gali and Gerler (1999). Since under opimal policy he oupu gap will be linear in inflaion, he equilibriums rae of inflaion under opimal policy will saisfy 2 E{ u 1 } ( / ). Solving forward and assuming u u we obain 1 π= (1 βρ + λ 2 /α) 1 u. Thus as is well known, for he case of an enirely forward looking Euler equaion and Phillips curve, here will be no endogenous dynamics and inflaion, he oupu gap, and he erms of rade of rade will inheri he exogenous dynamics of he cos push shock. In he nex secion we show how his model can easily be generalized via a hybrid Phillips curve o incorporae endogenous dynamics and work ou he implicaion for he nominal exchange rae. The opimal policy rule given α is obained by subsiuing he firs order condiion ino 3) and using equilibriums dynamics for inflaion. In erms of endogenous variables we see ha R rr (1 ) 1 0 E 1 wih again σ0 = σ γ(σ 1) and λ = {σ(1 γ) + γ + φ}δ. Thus opimal policy in he open economy can be wrien as a forward looking Taylor rule wih a ime varying neural real ineres rae given * by rr 0E{ y 1} k 0E{ y }. Unless σ=1, here will in general be spillovers from foreign 1 oupu growh o he home flexible price equilibrium and under opimal moneary policy his will be refleced in he neural real ineres rae. Of course he policy rule can also always be wrien as a linear funcion of he exogenous sae vecor [a,a*, u, u*]. 13

15 Wha are he implicaions of opimal policy for he nominal exchange rae? We noe ha e = e 1 + Δ s + π π* and ha s y ~ y y ~* y y. Using he fac ha * 1 [(1 ) a ( ~ y 0 * y * )] y * 1 * 0 [(1 ) a * * ( ~ y y )] we can solve for flexible price oupu levels under opimal policy in erms of exogenous produciviy and cos push shock erms. For he symmeric case γ = ½ his simplifies o 6) e e w ( w 1) ( u u * ) ( u 1 u * 1) ( a a * ) 1 1 where w = (1 ) and ψ= (1 βρ + λ / α) 1.There are five imporan implicaions of 6). Firs, opimal moneary in his class of models wih nominal rigidiies will feaure a flexible exchange rae. The exchange rae regime is no assumed or imposed on he analysis i arises endogenously from he environmen wih a policymaker who maximizes he welfare of domesic households. Second, no only does opimal moneary policy feaure a flexible exchange rae, he equilibrium exchange rae mus possess a uni roo even hough shocks are saionary and our Cole Obsfeld equilibrium replicaes he complee marke allocaion. Third, so long a relaive home and foreign produciviy levels a a* are saionary, hen so oo will be he equilibrium erms of rade s, and his will imply ha he nominal exchange rae is co inegraed wih relaive home and foreign price levels p p*. Thus he nominal exchange rae mus possess a uni roo because ime consisen moneary policy canno deliver a saionary price level, only a saionary rae of inflaion around a zero mean (C Clarida, Gali and Gerler (1999); Woodford (2003)). The uni roo in he nominal exchange rae is required o produce a saionary equilibrium erms of rade given ha opimal moneary policy produces uni roo price levels a home and abroad ha hemselves 14

16 are no co inegraed. Fourh, in he symmeric wo counry model presened here bad news abou inflaion will be good news for he nominal exchange rae under opimal moneary policy so long as α, he relaive weigh placed on sabilizing oupu, is no oo large. A cos push shock u will increase domesic inflaion and under opimal policy induce he cenral bank o raise he nominal ineres rae by more han expeced inflaion. The rise in he ex ane real ineres rae will cause s o fall and his, along wih he rise in he real ineres rae iself, will reduce demand for home oupu. In he bad news good news case he equilibrium decline in s is larger in absolue value han is he equilibrium rise in inflaion, and hus can only be accomplished via an appreciaion of he nominal exchange rae. This is so even hough, because of he uni roo in he home price level, he nominal exchange rae is expeced o depreciae in he long run in response o a cos push shock oday. As is eviden from inspecion of 6), a necessary and sufficien condiion for he bad news good news resul is simply ha α < wλ. In he baseline case wih σ 1 his will always be saisfied so long as α < λ; ha is if he relaive weigh on he oupu erm in he welfare funcion is less han he slope of he Phillips curve, hen bad news for inflaion mus be good news for he nominal exchange rae. Thus far, we have aken α o be a primiive. However, as confirmed in Clarida, Gali and Gerler (2002) and Gali Monacelli (2005), Woodford s (2003) derivaion of he quadraic approximaion o he welfare funcion of he represenaive agen acually pins down α as a funcion of deep parameers. And indeed as in Woodford s (2003) closed economy analysis Clarida, Gali and Gerler (2002) show ha α = λ/ξ wih ξ >1 in he open economy as in he closed. Thus for he baseline σ 1 case, wih α chosen opimally, bad news for inflaion mus be good news for he nominal exchange rae in he symmeric equilibrium. 15

17 Robusness In he wo counry model analyzed here, here will gains o inernaional policy cooperaion unless σ = 1. I is naural o ask if he key conclusions discussed above are robus in an equilibrium where moneary policy is chosen o maximize world welfare and incorporaes he gains from inernaional policy cooperaion ha are ignored in he Nash equilibrium. A leas in he model of Clarida, Gali and Gerler (2002) and he imporan exension in Engel (2009) who allows for currency mis alignmen, home bias in preferences, and local currency pricing (all of which are absen in Clarida, Gali and Gerler (2002)) he answer is yes. Under cooperaion, a regime of flexible exchange coninues o be opimal and he exchange rae will coninue o possess a uni roo because again, in he absence of he commimen device, home and foreign price levels are non saionary and imporanly are hemselves no co inegraed wih each oher. The mirage of fixed exchange raes coninues o be a mirage. And a leas for he symmeric equilibrium in he wo counry model, bad news abou inflaion will coninue o be good news for he nominal exchange rae under opimal cooperaive moneary policy. Moreover, under cooperaive policy a version of a Taylor rule coninues o characerize he opimal moneary policy in he open economy, wih he simple difference ha he moneary policy rule in each counry under cooperaion reacs o an average of foreign as well as home inflaion producer price inflaion in he case of Clarida, Gali and Gerler and CPI inflaion in Engel (2009) he wih he relaive weighs on he wo a funcion of he imporance of inernaional spillovers. In paricular, under cooperaion he policy rule is given by R rr (1 ) (1 ) 0 * 1 0 E 1 0E 1 16

18 IV. A Model wih Endogenous Dynamics Clarida Waldman (2014) work wih a version of he Gali Monacelli (2005) DSGE model ha can produce endogenous dynamics in oupu, inflaion, and deviaions from PPP. The model feaures a hybrid Phillips curve (Gali Gerler (1999)) and allows for home bias in consumpion, and hus ransiory deviaions of he CPI real exchange rae from long run PPP. We preserve he Cole Obsfeld srucure by assuming Cobb Douglas uiliy bu wih home bias and σ = 1, so here will be no cross counry spillovers impacing poenial oupu. We rea log foreign oupu, he foreign ineres rae, and foreign inflaion as exogenous, consan (as in Gali and Monacelli (2005) and De Paoli (2009)), and equal o zero. Goods marke equilibrium requires γny/s +(1 γ*)n*y* = N*Y* where N is populaion of home counry and Y* is per capia foreign oupu. This implies S N Y * * N * Y We assume he share of foreign spending on he home good saisfies γ* = γ(n/n*) so ha S = Y/Y* exacly for any (N/N*) so s = y y*. Noe also ha an appeal of his formulaion is ha he goods marke equilibrium condiion is invarian o (N/N*) while he share of foreign spending on home oupu converges o zero as does N/N*. The IS curve simplifies o 3 ) ~ y { ~ E y 1} [ R E{ 1 } rr] wih rr E{ a 1} and y a. 17

19 We assume a Gerler Gali (1999) hybrid Phillips curve emerges because a consan fracion of price re seers each period use a rule of humb based on lagged inflaion o se prices E f 1 b 1 mc where he parameers χf, χb, and δ χ are funcions of he fracion of rule of humb price seers as well as he Calvo parameers F and β. Under our assumpion on preferences and using he goods marke equilibrium condiion, we can subsiue for real marginal cos o obain 4 ) E } {1 } ~ y u f { 1 b 1 where we now have λ = (1+φ)δx. To focus on endogenous persisence, we now assume u is whie noise. Wih home bias, he CPI real exchange is given by Q = EP* cpi /P cpi = (k/k*)s 1 γ* γ where k =(1 γ) (1 γ) γ γ and similarly for k*. Recall γ is share of home spending on foreign good while 1 γ* is share of foreign spending on foreign good. Wih home bias, he CPI real exchange rae will reflec flucuaions in equilibrium erms of rade. The isomorphism resul is very useful because he policymaker ha wishes o maximize W H E [ ~ y 2 ] subjec o 3 ) and 4 ) as well as an assumed law of moion for inflaion 7) a auu 18

20 faces exacly he same problem as he policymaker in Clarida, Gali and Gerler (1999) Secion 6. Wha he policy maker akes as given, accordingly, is no he level of expeced inflaion, bu raher how privae secor expecaions of inflaion omorrow respond o movemens in inflaion oday. To solve for he equilibrium we assume ha privae secor forecas of π + 1 akes he form νππ + νuu, where νπ and νu are arbirary consans ha he policy maker akes as given. In he raional expecaions equilibrium νπ and νu equal he rue fundamenal parameers in he reduced form inflaion equaion, aπ and au. And of course aπ and au mus be consisen wih he inflaion dynamics implied by 3 ) 4 ) and he policy rule. The firs order condiion for his problem is ~ y (1 a ) where we noe ha opimal policy wih endogenous inflaion ineria calls for a more aggressive response o inflaion deviaions from arge han for he case of exogenous coss push persisence. Using he goods marke equilibrium condiion and recalling ha q = (1 γ* γ)s we see ha under opimal policy q { 1 * }( ) {1 * } a (1 a ) where q is he log deviaion of he CPI real exchange rae from he seady sae value of 0. We seek a fixed poin for aπ by subsiuing he firs order condiion ino 4 ) and imposing he law of moion 7) on expeced inflaion 2 f a b u 1 (1 a ) 19

21 Collecing erms we see ha 2 ( 1 f a ) b (1 a ) 1 u We see immediaely ha he fixed poin aπ mus saisfy 8) 2 (1 ) b a (1 a ) / a f Exisence of a fixed poin for aπ in he compac se [0,1] is insured for all admissible parameers so long as χf + χb 1 which is always he case in he Gali Gerler (1999) formulaions of he `hybrid Phillips curve. Moreover, for a sandard parameerizaion (ξ=10,φ=1,β=0.99,f=0.75) he Blanchard Kahn condiions (1979) for uniqueness (in his case, ha one roo of he cubic be sable and he oher wo have modulus greaer han uniy) are saisfied for all feasible choices for he share of backward looking price seers. Figure 1 depics he deerminaion of aπ as a funcion of α and is he DSGE model analogue o Figure 1 in Clarida Waldman (2008) paper which sudied a similar bu ad hoc model wih χf = 0. We see immediaely ha Resul One: Equilibrium inflaion ineria as well as he half life of deviaions from PPP in response o cos push shocks are monoonically increasing in α, he relaive weigh on oupu sabilizaion in he cenral bank welfare funcion. Under opimal policy he nominal exchange rae mus saisfy 9) e ( 1) a p 1 (1 a ) 20

22 where we have used he firs order condiion plus he equilibrium condiion for erms of rade and he definiion of he nominal exchange rae. The following resuls follows immediaely. Resul Two: Bad News for inflaion mus be Good News for he nominal exchange rae if α < λ. Resul Three: Bad news for inflaion mus be Good News for he nominal exchange rae if α is equal o is opimal value α = λ/ξ. We gain insigh ino hese resuls by deriving he opimal policy rule as before. I akes he form R E a 1 (1 a 1 E 1 (1 a ) a ) We noe ha in his σ = 1 case, while economies can differ in heir degree of openness, if heir policymakers share he same α and heir economies same srucure, hey will run he same opimal policy rule. This policy rule in urn will imply ha a shock o inflaion in ime will impac he enire expeced fuure ime pah of he ex ane real policy rae as of ime. I is sraighforward o show ha in equilibrium wih lim i E s i 0 we mus have e p p * E ( R ) p p * E i0 i i1 i0 i1 a (1 a ) E (1 a ) i0 i1 Thus he exchange rae is an asse price ha is he sum of hree erms: a purchasing power pariy erm (he source of he uni roo), a erm reflecing he pah of expeced fuure produciviy growh, and a erm reflecing he expeced ime pah of fuure inflaion. So via he Taylor rule he macro drivers of he opimal policy rae become he macro facors of he nominal exchange rae pinned down by he parameers of he opimal Taylor rule as well as he endogenous rae of inflaion ineria. 21

23 V. Concluding Remarks The models oulined above are simple bu solvable! and do omi a number of imporan consideraions such as endogenous capial accumulaion, curren accoun imbalances, and imperfec financial markes, he laer of which can open he door o nominal exchange rae volailiy unrelaed macro fundamenals. And in pracice, several inflaion argeing cenral banks do appear o allow he policy rae o reac direcly o exchange rae deviaions from PPP over and above any informaion ha said PPP deviaions provide for forecasing inflaion iself (Clarida, Gali, Gerler (1998); Lubik and Schorfheide (2003) Engel and Wes (2006); Engel, Mark, and Wes (2007)). Tha said, a leas o his auhor, he framework oulined above does provide a useful consruc for hinking abou moneary policy in he open economy and undersanding wha i can deliver and wha i can. The framework suggess ha good macroeconomic oucomes in open economies are possible by focusing inflaion argeing ha is implemened by a Taylor ype rule, a rule ha in equilibrium is refleced in he exchange rae as an asse price jus as i is refleced in long erm bond yields via he expecaion channel for he expeced fuure policy rae (Ang and Piazzesi (2003)). Opimal moneary policy will no be able deliver a saionary ( sable ) nominal exchange rae le alone a fixed exchange rae or one ha remains inside a arge zone because, absen a commimen device, opimal moneary can deliver a saionary domesic price level. Moreover, even under cooperaion, home and foreign domesic price levels will no be co inegraed so a uni roo in he nominal exchange rae is necessary o deliver a saionary erms of rade. Anoher feaure in he daa for inflaion argeing counries ha is consisen wih opimal moneary policy via Taylor ype rule is ha i will end push he nominal exchange rae in he opposie direcion from PPP in response o a cos push shock he bad news god news resul of Clarida Waldman (2008;2014). This is so even hough in he long run of hese models 22

24 he nominal exchange rae mus in expecaion obey PPP. So wha a firs glance migh appear o be an indicmen of moneary policy by Taylor rule in he open economy ha i pushes he exchange rae away from PPP in response o inflaion shocks is acually a propery of opimal policy! The model oulined in Secion IV also has implicaions for he Rogoff (1996) PPP puzzle: why are esimaed half lives of PPP deviaions on he order of welve o weny quarers while esimaed half lives of inflaion deviaions from arge are wo o four quarers? Recall ha in he model of Secion IV he log deviaion from PPP is given by q { 1 * }( ) {1 * } a (1 a ) Now for he special case of no produciviy shocks, PPP deviaions and inflaion deviaions from arge will have idenical half lives governed by he endogenous rae of inflaion persisence aπ. Bu, if here are saionary (relaive) produciviy shocks and home bias, he PPP deviaion is no longer an AR(1) bu he sum of wo AR(1) processes. And as is well known, he sum of wo differen AR(1) processes is an ARMA(2,1) process. Depending on he persisence of relaive produciviy shocks and heir variance, PPP deviaions can have a much longer esimaed halflife recovered from a mis specified AR(1) model for he real exchange rae han do inflaion deviaions from arge in he model of opimal moneary policy in Secion IV. As of his wriing many of he world s major cenral banks are operaing a or close o he zero lower bound for he policy rae. For many of hem, Taylor ype rules ha well accouned for he policy rae before he global financial crisis have implied negaive policy raes since Tha said as economies recover and oupu gaps close (afer adjusing for he impac of he crisis on poenial oupu), cenral banks will begin o normalize he policy rae. As hey do a Taylor rule wih suiable inpus for he expeced pah of he neural real ineres rae, inflaion, and he 23

25 oupu gap can be a relevan benchmark for assessing he expeced normalizaion pah for he policy rae communicaed by he cenral bank and priced ino financial markes (Clarida Parikh (2014)). *Paper prepared for he Hoover Insiuion Conference on Moneary Policy for he 21s Cenury. I would like o hank he conference organizers, paricipans, and especially my discussan Maurice Obsfeld as well as Ken Judd for insighful suggesions for fuure work. 24

26 References Ang, A., and M. Piazzesi. ʺA no arbirage vecor auoregression of erm srucure dynamics wih macroeconomic and laen variables.ʺ Journal of Moneary economics 50.4 (2003): Blanchard, O J, and C. M. Kahn. ʺThe soluion of linear difference models under raional expecaions.ʺ Economerica (1980): Calvo, G., Saggered Prices in a Uiliy Maximizing Framework,ʺ Journal of Moneary Economics 12: (1983). Clarida, R. H. G3 exchange rae relaionships: A recap of he record and a review of proposals for change No. w7434. Naional bureau of economic research, Clarida, R H. ʺThe empirics of moneary policy rules in open economies.ʺ Inernaional Journal of Finance & Economics 6.4 (2001): Clarida, R., J Gali, and Gerler, Moneary Policy Rules in Pracice: Some Inernaional Evidence, European Economic Review, (1998)., The Science of Moneary Policy, Journal of Economic Perspecives, (1999)., Opimal Moneary Policy in Closed versus Open Economies: an Inegraed Approach, No. w8604. Naional Bureau of Economic Research, 2001, A Simple Framework for Inernaional Moneary Policy Analysis,ʺ Journal of Moneary Economics 49: (2002). Clarida, R H., and M Gerler. ʺHow he Bundesbank conducs moneary policy.ʺ Reducing Inflaion: Moivaion and Sraegy. Universiy of Chicago Press, Clarida, R. and S. Parikh: Guidance Counselors The Inernaional Economy, Spring 2014 Clarida, R and D Waldman, Is Bad News abou Inflaion Good News for he Exchange Rae in John Campbell, Edior, Asse Prices and Moneary Policy, Chicago: Universiy of Chicago Press, 2008., Bad News Abou Inflaion is Good News for he Nominal Exchange Rae Under Opimal Moneary Policy: DSGE Theory and a Decade of Empirical Evidence, in process, 2014 Cole, H L., and M Obsfeld, Commodiy Trade and Inernaional Risk Sharing: How Much Do Financial Markes Maer?ʺ Journal of Moneary Economics 28: 3 24 (1991). Corsei, G. and P. Peseni, Welfare and Macroeconomic Independence, Quarerly Journal of Economics,

27 , ʺInernaional dimensions of opimal moneary policy.ʺ Journal of Moneary economics 52.2 (2005): De Paoli, B. ʺMoneary policy and welfare in a small open economy.ʺjournal of Inernaional Economics 77.1 (2009): Devereux, M B., and V Hnakovska. Consumpion Risk Sharing and he Real Exchange Rae: Why does he Nominal Exchange Rae Make Such a Difference?. No. w Naional Bureau of Economic Research, Engel, C, and K Wes, Taylor rules and he deuschmark dollar real exchange rae.ʺ Journal of Money, Credi and Banking38.5: , 2006 Engel, C., N. Mark, and K. Wes, Exchange Models are No As Bad As You Think?, NBER Macro Annual Engel, C. Currency misalignmens and opimal moneary policy: a reexaminaion. No. w Naional Bureau of Economic Research, Galí, J. Moneary Policy, inflaion, and he Business Cycle: An inroducion o he new Keynesian Framework. Princeon Universiy Press, Galı, J, and M Gerler. ʺInflaion dynamics: A srucural economeric analysis.ʺ Journal of moneary Economics 44.2 (1999): Gali, J, and T Monacelli, Moneary Policy and Exchange Rae Volailiy in a Small Open Economy,ʺ Review of Economic Sudies 72: (2005) Krugman, P. M. Obsfeld, M. Meliz, Inernaional Economics Prenice Hall Page 2011 Kydland, F E., and E C. Presco. ʺRules raher han discreion: The inconsisency of opimal plans.ʺ The Journal of Poliical Economy (1977): Laubach, T, and J. C. Williams. ʺMeasuring he naural rae of ineres.ʺ Review of Economics and Saisics 85.4 (2003): Lubik, T A., and F Schorfheide. ʺDo cenral banks respond o exchange raes? A srucural invesigaion.ʺ Journal of Moneary Economics Molodsova, T, and D H. Papell. ʺOu of sample exchange rae predicabiliy wih Taylor rule fundamenals.ʺ Journal of Inernaional Economics77.2 (2009): Obsfeld, M. and K. Rogoff, Foundaions of Inernaional Macroeconomics, MIT Press, 1997., ʺNew direcions for sochasic open economy models.ʺ Journal of inernaional economics 50.1 (2000):

28 Obsfeld, M. ʺInflaion argeing, exchange rae pass hrough, and volailiy.ʺ American Economic Review (2002): Svensson, L. E.O., Open Economy Inflaion Targeing,ʺ Journal of Inernaional Economics 50: (2000). Taylor, J, B., 1982, Macroeconomic radeoffs in an inernaional economy wih raional expecaions, in: Hildebrand, ed., Advances in economic heory (Cambridge Universiy Press, Cambridge)., Macroeconomic Policy in a World Economy: From Economeric Design o Pracical Operaion, W.W. Noron, New York, 1993., Discreion Versus Policy Rules in Pracice, Carnegie Rocheser Series on Public Policy, Norh Holland, 39, 1993, pp Whie, W., Globalizaion and he Deerminans of Domesic Inflaion, BIS Working Paper No. 250, March Woodford, M, Ineres and Prices: Foundaions of a Theory of Moneary Policy, Princeon: Princeon Universiy Press, 2003., Globalizaion and Moneary Conrol, in Galí, Jordi, and Mark Gerler, eds. Inernaional Dimensions of Moneary Policy. Universiy of Chicago Press,

29 TABLE 1 The Original Clarida Waldman (2008) Resul for he July 2001 December 2005 Sample Regression of Exchange Rae Change on Inflaion Surprise in 10 Minue Window Before and Afer Announcemen Bad News Abou Inflaion is Good News for The Exchange Rae for IT Counries Headline Core MoM YoY MoM YoY Coefficien T- Saisic R-Squared # Observaions Regression mehod: sacked OLS. Percenage change in exchange rae resuling from a one percenage poin upward surprise in inflaion. Posiive coefficien indicaes appreciaion of domesic currency. Counries: Ausralia, Canada, Euro area, Japan, New Zealand, Norway, Sweden, Swizerland, UK, and US. Daa: July December Some counries missing observaions. Clarida Waldman Is Bad News Abou Inflaion Good News for he Exchange Rae, NBER Working Paper

30 TABLE 2 Updaed Clarida Waldman (2014) Resul for July 2001 December 2013 Sample 29

31 FIGURE 1 Fixed Poin Soluion for aπ as funcion of λ/α 30