What Do New Keynesian Phillips Curves Imply for Price Level Targeting? Robert Dittmar and William T. Gavin

Transcription

1 WORKING PAPER SERIES Wha Do New Keynesian Phillips Curves Imply for Price Level Targeing? Rober Dimar and William T. Gavin Working Paper 999-A hp://research.slouisfed.org/wp/999/99-.pdf PUBLISHED: Federal Reserve Bank of S. Louis Review, 8(), March/April, pp. -3. FEDERAL RESERVE BANK OF ST. LOUIS Research Division 4 Locus Sree S. Louis, MO 63 The views expressed are hose of he individual auhors and do no necessarily reflec official posiions of he Federal Reserve Bank of S. Louis, he Federal Reserve Sysem, or he Board of Governors. Federal Reserve Bank of S. Louis Working Papers are preliminary maerials circulaed o simulae discussion and criical commen. References in publicaions o Federal Reserve Bank of S. Louis Working Papers (oher han an acknowledgmen ha he wrier has had access o unpublished maerial) should be cleared wih he auhor or auhors. Phoo couresy of The Gaeway Arch, S. Louis, MO.

2 Wha Do New Keynesian Phillips Curves Imply for Price Level Targeing? ABSTRACT This paper exends he analysis of price level argeing o a model including he New- Keynesian Phillips Curve. We examine he inflaion-oupu variabiliy radeoffs implied by opimal inflaion and price level rules. In previous work wih he Neoclassical Phillips Curve, we found ha he choice beween inflaion argeing and price level argeing depended on he amoun of persisence in he oupu gap. Tha is, if he oupu gap was no oo persisen, or if lagged oupu did no ener he aggregae supply funcion, hen inflaion arges were preferred o price level arges. When we sar wih a New Keynesian Phillips Curve, he amoun of persisence in he oupu gap sill affecs he relaive placemen of he inflaion-oupu variabiliy radeoff. Bu, conrary o he Neoclassical case, even where he persisence of he oupu gap in he aggregae supply funcion is small or nonexisen, he price level argeing regime sill resuls in a more favorable radeoff beween oupu and inflaion variabiliy han does an inflaion-argeing regime. Original Dae: Augus 3, 999 Keywords: New Keynesian, Phillips Curve, Price Level Targeing JEL Classificaion: E3, E4, E5, E6 Rober Dimar Mahemaician Research Deparmen Federal Reserve Bank of S. Louis P.O. Box 44 P.O. Box 44 S. Louis, MO 6366 S. Louis, MO 6366 William T. Gavin Vice Presiden Research Deparmen Federal Reserve Bank of S. Louis (34) (34) dimar@sls.frb.org gavin@sls.frb.org Rober Dimar is a mahemaician and William T. Gavin is a vice presiden and economis a he Federal Reserve Bank of S. Louis. We hank Jim Bullard, Finn Kydland, Michael Kiley, Ahanasios Orphanides, Michael Pakko, Bob Rasche, Joe Rier, Dan Thornon and Chris Waller for helpful discussions.

3 In a previous paper, Dimar e al. (999a) used a simple Phillips Curve model and evidence abou he persisence in oupu gaps o show ha a price-level argeing regime would likely resul in a beer inflaion-oupu variabiliy radeoff han an inflaionargeing regime. Tha was an exension of work by Svensson (997). The Phillips Curve specificaion was consisen wih one derived from a Lucas Island model wih persisen supply shocks or a Fischer wage-conracing model. McCallum (994) refers o his as a Neoclassical Phillip Curve because i is consisen wih he Naural Rae Hypohesis (NRH) moneary policy canno keep oupu permanenly above is naural rae because only unanicipaed moneary policy affecs real oupu. Kiley (998) argues ha he Neoclassical specificaion is inconsisen wih U.S. daa because he believes here is hisorical evidence ha anicipaed moneary policy has had real effecs. He aribues Svensson s (997) favorable finding for price-level argeing o his choice of Phillips Curve specificaion. Kiley concludes ha, compared o he case wih inflaion argeing, price-level argeing would have been found o resul in a worse inflaion-oupu variabiliy radeoff if Svensson had sared wih a New Keynesian version of he Phillips Curve. Kiley derives he expecaion for he mean of oupu in a New Keynesian model, shows ha he expecaion depends on he lagged price level, and infers from his ha rying o sabilize he price level would raise he variabiliy of oupu. He does no derive he inflaion-oupu variabiliy radeoff implied by he model nor does he experimen wih alernaive policy rules using his New Keynesian specificaion. In his paper we exend he analysis of price level argeing of Dimar e al. (999) o a model including he New-Keynesian Phillips curve recommended by Kiley.

4 We examine he inflaion-oupu variabiliy radeoffs implied by opimal inflaion and price level rules. To be consisen wih our earlier work and ha of Svensson (997), we assume ha lagged oupu eners he aggregae supply funcion. The inroducion of lags is consisen wih boh he heoreical model of Taylor (98) who includes boh leads and lags of unemploymen in he Phillips Curve and he empirical work of Robers (995), who finds serial correlaion in he error erms of his esimaed Phillips Curves. Our inuiion is ha price level argeing should be preferable in a sicky-price world where prices are cosly o adjus. If prices were perfecly flexible, alernaive moneary policy rules would have almos no effec on real oupu. Bu in world where i is cosly o adjus prices, a policy ha reduces price flucuaions would seem o be appropriae. Indeed, we find ha he New Keynesian Phillips Curve provides even sronger suppor for price level argeing han did he model wih he neoclassical Phillips Curve. In previous work wih he Neoclassical Phillips Curve, we found ha he choice beween inflaion argeing and price level argeing depended on he amoun of persisence in he oupu gap. Tha is, if he oupu gap was no oo persisen, or if lagged oupu did no ener he aggregae supply funcion, hen inflaion arges were preferred o price level arges. However, empirical evidence showed a very high level of persisence in he oupu gap, suggesing ha price level arges offer he policymaker a beer menu of radeoffs beween oupu and inflaion variabiliy. To preview he resuls in his aricle, we show ha when we sar wih a New Keynesian Phillips Curve, he amoun of persisence in he oupu gap sill affecs he relaive placemen of he inflaion-oupu variabiliy radeoff. Bu, conrary o he

5 Neoclassical case, even where he persisence of he oupu gap in he aggregae supply funcion is small or nonexisen, he price level argeing regime sill resuls in a more favorable radeoff beween oupu and inflaion variabiliy han does an inflaionargeing regime. In he firs secion we briefly describe he New Keynesian model and compare i o he Neoclassical specificaion. In he second secion, we consruc he inflaion-oupu variabiliy curves implied by alernaive parameerizaions of he model. In conclusion, we discuss he assumpions ha are apparenly needed o find ha price level argeing would desabilize oupu. A NEW KEYNESIAN PHILLIPS CURVE Robers (995) shows ha he sicky price models of Taylor (98), Roemberg (98), and Calvo (983) all imply he same Phillips Curve srucure which has been called New Keynesian. We begin wih he same infinie-horizon, quadraic loss funcion used in our earlier work. The cenral bank wih an inflaion arge minimizes L A * = β λy ( π π ), = 3 8 where he superscrip A refers o he loss funcion of an inflaion argeing cenral bank, b is he cenral bank s discoun rae, (y ) is he deviaion of oupu from he arge level and ( * ) is he deviaion of inflaion from he cenral bank's inflaion arge. The erm,, gives he weigh on oupu gap relaive o he weigh on inflaion in he cenral bank's loss funcion. The Neoclassical Phillips Curve used in our earlier paper is given by 3

6 y e = ρ y α( π π ) ε, where deermines he persisence in he oupu gap, deermines he response of he oupu gap o unanicipaed inflaion, and is an i.i.d. echnology shock wih mean zero and variance σ ε. We are making no disincion beween he aggregae supply funcion and he Phillips Curve. Kiley (999) uses he Calvo (983) model o derive he following New Keynesian Phillips Curve: y e = ρ y α( π π ) ε. This is decepively similar o he Neoclassical version where he anicipaed inflaion ha eners he funcion is he expecaion for period raher han. Kiley includes a discussion of he empirical suppor for his specificaion and a discussion of he research ha has developed microeconomic foundaions for his aggregae relaionship. A comprehensive survey of he implicaions for moneary policy implied by New Keynesian heories can be found in Clarida e al. (999). To solve his model, we mus decide wha o assume abou how he cenral bank akes accoun of is effec on inflaion expecaions. Kydland and Presco (977) showed ha he presence of forward-looking expecaions in he cenral bank s Phillips curve consrain causes a problem of ime inconsisency if he bank ries o manipulae hose expecaions. To avoid his ime-consisency problem, we assume ha he cenral bank akes inflaion expecaions as given. Recen discussion of his issue can be found in Woodford (999) and Clarida e al. (999). To explain our decision o rea expecaions as Some would call our equaion an aggregae supply funcion because he dependen variable is he oupu gap. If he equaion were rearranged wih inflaion on he lef-hand side, hey would call i a Phillips 4

7 given, consider wha happens if we do no. We review he ime-consisency issue wihin he opimizaion problem faced by our inflaion-argeing cenral bank. To solve he consrained opimizaion problem a ime, we form he Lagrangian as: % & 3 i i 8 i3 i i i i i8 = ' * E β λ y ( π π ) µ y ρy α( π π ) ε, where he m s are a sequence of random mulipliers and he erm π i has replaced e π i in he Phillips Curve consrain because he cenral bank reas he expecaions of he fuure inflaion as a choice variable. Noe ha he firs order condiion when aken ( ) * wih respec o is given by 7 * π π αµ =. Since he bank is rying o opimize by influencing expecaions, he firs order condiion aken wih respec o akes he form, 7 * βe π π αµ βα E µ =, which is differen from ha for. If he bank were o re-opimize a ime, i will rederive a firs order condiion for ha mirrors he one derived for a ime, ye is disinc from ha derived for a ime. Since he firs order condiions derived a any ime characerize he bank's opimal policy, he bank's chosen policy a ime will be found sub-opimal a ime, hence he ime inconsisency. As is well undersood, wihou some mechanism o commi a ime, he bank will be emped o re-opimize, renege on any decisions made a ime, and derive a new policy a ime. Curve. King and Wason (994) show ha his disincion can be imporan when esimaing he parameers from hisorical daa, bu i does no maer in our analyical work. 5

8 Inuiively, he problem of ime inconsisency here resuls from he abiliy of a bank facing a New Keynesian Phillips Curve o derive rewards oday by creaing expecaions for omorrow. When a new period arrives, he empaion is o confound expecaions wih new policy since he gains from he previously announced policy have already been aken. In equilibrium, he cenral bank canno benefi from reneging on announced policies. If he bank re-opimizes each period, or even only occasionally, hen privae agens will learn ha he bank s announced fuure policy will no necessarily be implemened. When his occurs, he bank s abiliy o conrol expecaions will be los. To avoid his ime inconsisency problem, we assume ha he cenral bank akes privae secor expecaions as given. Under his assumpion, he bank, recognizing ha i may be unable o commi o policy announcemens, forgoes any aemp o manipulae privae expecaions. When he bank regards expecaions as given, he bank s opimizaion problem becomes a sandard one, wih a quadraic objecive and linear consrains. Furhermore, firs order condiions ake a sandard form for all ime periods, assuring policy rules are ime consisen. Linear decision rules can be conjecured for he bank s opimal policy. Upon subsiuing he conjecured linear rules ino he firs order condiions for he bank s opimizaion problem, we equae coefficiens on he variables in he decision rules and derive he bank s policy funcion. We assume ha he bank, in aking expecaions as given, bases is ime decisions on curren saes, y - and, in boh regimes and p - in he case of a price-level-argeing regime. Expecaions are hen assumed o be formed as a raional consequence of he bank s policy rule. I is much simpler o derive policy rules under an inflaion argeing regime. The derivaion of hese rules closely follows he derivaion in he appendix of Dimar e al. 6

9 (999). The bank s opimizaion problem is he same as shown above excep he inflaion expecaions are no longer reaed as a decision variable by he cenral bank. The Lagrangian is given as: % & = ' ( ) * * e E β λ y i ( π i π ) µ i y i ρy i α( π i iπ i) ε i, e ZLWKWKH s being a sequence of random mulipliers and i i denoes he privae secor s inflaion expecaions. Firs-order condiions for he bank ake he form: λ y µ βρ E µ = when aken wih respec o he sequence of y s, and he form: 7 * π π αµ = when aken wih respec o he sequence of s. Eliminaing he mulipliers from hese expressions gives he following Euler equaion: λy 7 7 α π π βρ * E π π * =. α Here he cenral bank wans o smooh inflaion deviaions from arge wih an adjusmen for he curren oupu gap. If here is no persisence in he oupu gap, hen he desired inflaion deviaions oday depend only on he oupu gap. We now seek a linear decision rule for inflaion of he form: π = A A y Aε 3. Expecaions of he privae secor are assumed o be raional, so a ime we have: e π = A A y. Subsiuing hese expressions ino he Phillips curve equaion and solving he resuling equaion for y yields a decision rule for y direcly of he form: 7

10 y = ρ αa A y α A α α A ε. 3 Decision rules are invarian so we can deermine by ieraing on he rule for o yield he following expression: = A A π = A A y Aε 3 ρ αa A y A α A α α A ε A ε. 3 3 Taking ime expecaions hen yields a linear expression for E. If we now subsiue he expressions for y, and ino he firs order condiion and equae consan erms and coefficiens on y - and, we obain hree equaions ha can be solved for he unknown A, A, and A 3. To obain our soluion, we assume ha he cenral bank akes inflaion expecaions as given. Under his assumpion, he Euler equaions for he inflaion argeing case are of he same form for boh he New Keynesian and Neoclassical specificaions of he Phillips Curve. However, he differen Phillips Curve specificaions lead o differen moneary policy rules. In he New Keynesian case, agens inflaion expecaions a ime are for inflaion a ime and involve y, whereas in he Neoclassical case, inflaion expecaions a ime are for inflaion a ime and involve only y -. Figure shows he inflaion-oupu variabiliy radeoffs for he Neoclassical and New Keynesian cases when he cenral bank has an inflaion arge. We graphically display he inflaion/oupu variabiliy radeoffs in he wo specificaions by firs expressing he oupu gap variance and he inflaion variance as funcions of he preference parameer λ while holding he parameers of he Phillips curve consan. For a given λ, he bank s 8

11 decision rules can be used o calculae an uncondiional variance for boh inflaion and he oupu gap (a single poin in Figure ). Varying he bank s preferences by varying λ will deermine he locaion of he curve represening he rade off beween σ π and σ y. The parameerizaions used here are he same as he ones used by Dimar e al. (999a): a =.5, b =.99, and r =.9. These assumpions imply a Phillips Curve slope of. when he Phillips Curve is wrien in erms of he inflaion rae. Using his form, Rudebusch and Svensson (998) esimae he slope o be.4, and Orphanides (998) esimaes he slope o be.8 wih a sandard error of.7. We assume ha he ineres rae is 4 percen a an annual rae, so he quarerly discoun facor is approximaely.99. As he Figure shows, he radeoff is similar across he wo model specificaions excep for exreme cases where he cenral bank pus lile weigh on he deviaion of inflaion from arge. In he Neoclassical case, he variance of inflaion rises monoonically wih l, he relaive weigh he cenral bank pus on he oupu gap in is loss funcion. In he New Keynesian case, wih his parameerizaion, he curve bends back; ha is, inflaion variabiliy begins o decline afer l goes above 3. I changes direcion again a very high values of l. We do no have any inuiion abou why his curve is oddly shaped when he cenral bank pus high weigh on reducing variabiliy of he oupu gap. Noe, however, Cecchei, McConnell and Quiros (999) esimaed l o be less han.33 (by our definiion of l) for he counries in he European Moneary Union. The ineresing quesion is wha happens when he cenral bank arges he price level insead of he inflaion rae. Now, he problem becomes more complicaed. We revise he loss funcion o reflec he cenral banks preference for a price level objecive: 9

12 B * L = Í β λ y ( p - p), = 3 8 where he price level, p, has replaced he inflaion rae and he superscrip B denoes a Loss funcion in he price level raher han he inflaion rae. Deermining decision rules for he bank in he case of price-level argeing proceeds in a similar manner as in he case of inflaion argeing, bu is complicaed by he presence of wo lagged sae variables in he banks Phillips curve, y - and p -. The bank s firs order condiion in his case will involve infinie sums of fuure price levels and oupu gaps. To simplify he derivaion of hese condiions, we firs define he new variable ~ * p = p p. The New Keynesian Phillips curve will ake he form: e y = ρ y α( ~ p ~ p ~ p ) ε, in he ransformed price variable. We can now form he bank s Lagrangian as: % & = e E β λ y i ( ~ p i) µ i y i ρy i α( ~ p i ~ p ~ i p i) ε i, ' 7 7 ( ) * wih, once again, he s being a sequence of random mulipliers. Firs order condiions now ake he form λ y µ βρ E µ = when aken wih respec o he sequence of y s and ~ p αµ βα E µ = when aken wih respec o he sequence of p s. We have found he simples way o eliminae mulipliers from he bank s firs order condiions is o regard boh sequences above as linear sysems in he unknown mulipliers. The sequence of firs order condiions derived as a resul of differeniaing he Lagrangian wih respec o he sequence of y s can be wrien as he linear sysem

13 βρ L µ λy βρ L E µ = λey βρ L E µ λey M M M M O M M while he oher sequence of firs order condiions can be wrien as he linear sysem α βα L µ ~ p α βα L E µ α βα µ = Ep ~ L E Ep ~ M M M M O M M These sysems can be solved for he unknown mulipliers by noing ha βρ βρ L L βρ L M M M M O = 3 βρ βρ βρ βρ βρ 6 6 βρ L L L M M M M O and α βα L α βα L = α βα L α M M M M O 3 β β β L β β L. β L M M M M O Thus, we can conclude from he firs se of firs order condiions ha j Eµ i = λ ( βρ) Ey j i, j= for i =,...,, and we can conclude from he second se ha Eµ i β j = ( ) E ~ p j i, α j=

14 for i =,...,. Equaing he wo expressions for he unknown mulipliers gives he following sequence of firs order condiions expressed solely in erms of sae variables: λ j β j ( βρ) Ey ( ) ~ j i = Ep j i. α j= j= Calculaing decision rules for he bank now proceeds in a similar manner o he calculaion of decision rules for a inflaion argeing cenral bank. When decisions are made a ime, he bank s sae variables are y, ~ p, and ε. We conjecure linear decision rules of he form Bp ~ By Bε for y and Ap ~ Ay Aε for ~. 3 3 Using he raional expecaions condiion, ~ e p A ~ p A y and he Phillips curve = equaion allows us o relae he coefficiens of he decision rule for y o hose in he rule for ~ p. Ieraing hese decision rules forward and aking expecaions allows us o wrie boh Ep ~ and Ey as a linear funcion of y, ~ p, and ε. In general, we have n n Ep ~ n n n = A6~ p A6y A6 ε, and n 3 n n n Ey = B6~ p B6y B6ε, n 3 wih he coefficiens A6 n n and B6, for i =,, 3, deermined ieraively as: i i An n A A i Ai n B B B i = B6 n i. Since his is a linear difference equaion in A6 n n and B6we explicily solve i in he form i A6 n i n n v v n i i B6 i = α θ α θ,,, where, v, and v are he eigenvalues and eigenvecors respecively of he marix i p

15 A B A B expressed as algebraic funcions of he unknown decision rule parameers A, A, B, and B. Wih his represenaion we can subsiue ino he firs order condiion, explicily sum he resuling geomeric series on he supposiion ha boh and are less han in absolue value, and finally equae coefficiens on sae variables. We have found he resuling equaions for he coefficiens in he decision rules o be oo algebraically complex o admi a closed form soluion. However, we have solved hem numerically for a range of parameers. We found ha boh roos, and, were real and inside he uni circle. We hen calculaed he inflaion-oupu radeoff implied by varying l, he bank s relaive preference for oupu sabiliy, beween zero and infiniy. Figure shows ha he inflaion-oupu variabiliy radeoffs are almos idenical for he wo versions of he Phillips Curve when here is a high degree of persisence in he oupu gap. We are no really ineresed in disinguishing beween hese alernaive views of he Phillips Curve. We wan o respond o he suggesion ha price level argeing would no work well under he New Keynesian Specificaion. Figures 3 hrough 5 show he inflaion-oupu variabiliy radeoffs implied by he New Keynesian specificaion for hree alernaive values of r, our measure of persisence in he oupu gap. The firs case compares inflaion argeing wih price level argeing for wha we believe is a realisic amoun of persisence, r =.9 (see Figure 3). The price level arge resuls in a beer inflaion-oupu variabiliy radeoff han does an inflaion arge. Figure 4 shows ha price level argeing sill dominaes inflaion argeing when r =.5. In he Neoclassical case, he radeoffs were idenical in his case. As r falls below.5, he 3

16 inflaion arge dominaed he price level arge in our earlier analysis. In conras, Figure 5 shows ha, under he New Keynesian specificaion, inflaion argeing resuls in a worse radeoff beween inflaion and oupu variabiliy even when r =. In summary, Dimar e al. (999), assuming a Neoclassical Phillips Curve, found ha price level argeing dominaed inflaion argeing for cases where he oupu gap was relaively persisen; ha is, when r >.5. In his aricle, we find ha when we use a New Keynesian Phillips Curve, price level argeing always dominaes inflaion argeing, even if we omi he lagged oupu gap from he aggregae supply funcion. IT S NOT THE PHILLIPS CURVE, IT S EXPECTATIONS FORMATION This raises an imporan issue. Simulaions of economeric models ypically find ha argeing he price level is a bad idea. Economiss have aribued his resul o he presence of nominal rigidiies such as wage conracs or price adjusmen coss. Ye in hese economeric experimens, i is also rue ha inflaion expecaions are almos always considered o be formed adapively. For example, Haldane and Salmon (995) use a small economeric model wih adapive inflaion expecaions o examine wheher moneary policy arges for price sabiliy should be expressed in levels or raes of change. They find ha price level argeing resuls in higher shor-run variabiliy for boh inflaion and oupu growh. These resuls are ypical of economeric model simulaions wih backward-looking expecaions (See Haldane and Salmon for references). There are a leas wo examples where cenral bank economiss conduced experimens wih price level arges using economeric models modified o include some forward-looking behavior. Black, Macklem, and Rose (997) look a combinaion rules 4

17 ha combine a long-erm price level objecive wih a shor-erm inflaion argeing rule. The presence of an error-correcion erm guaranees he evenual reurn of he price level o is long-run arge pah. For some values of he error correcion parameer beween. and.5, hey derive an inflaion-oupu variabiliy radeoff ha is beer han wih he inflaion rule alone. Using a policy model esimaed a he Board of Governors of he Federal Reserve Sysem, Williams (999) finds iineresingly, argeing he price level raher han he inflaion rae generaes lile addiional cos in erms of oupu and inflaion variabiliy. Under price level argeing, he expecaions channel helps sabilize inflaion, hereby eliminaing much of he oupu sabilizaion coss ha would oherwise be associaed wih reversing deviaions of he price level from is arge. Williams confirms our view ha he reason ha price level argeing fares so badly in economeric simulaions is ha his is exacly he ype of exercise for which he Lucas Criique is likely o be mos relevan. The policy rules ha were mos efficien in reducing inflaion and oupu variabiliy when he model assumes forward-looking expecaions, urn ou o be he wors when fixed adapive expecaions are assumed. And vice-versa, policies ha are efficien when expecaions are assumed o be adapive do poorly when expecaions are forward looking. Assumpions abou expecaions are criical for he analysis. We focus on an exreme comparison in our analysis, inflaion argeing versus price level argeing. Our resuls sugges ha argeing he price level in he shor run may work beer han previously hough. Bu hese resuls should be pu ino perspecive. We do no have enough confidence in he shor-run dynamics of economy o recommend ha any cenral bank adop a policy rule ha would represen a sharp break wih curren pracice. Raher, he role of he price level arge is o provide a long-erm 5

18 anchor for he moneary sysem. Dimar e al. (999b) showed ha a cenral bank can dramaically reduce he uncerainy abou inflaion inheren in an inflaion-argeing regime by ) adoping a long-erm price level objecive, and ) using i in an errorcorrecion framework o modify he shor-run inflaion arges. Tha analysis was based on an aggregae model including he Neoclassical Phillips Curve. Bu as we have shown here, he resuls would no be subsanially differen if we had sared wih a New Keynesian specificaion. 6

19 References Black, Richard, Tiff Macklem, and David Rose. "On Policy Rules for Price Sabiliy," Presened a a Bank of Canada Conference, Price Sabiliy, Inflaion Targes and Moneary Policy on May 3-4, 997. Calvo, Guillermo A. Saggered Prices in a Uiliy Maximizing Framework, Journal of Moneary Economics, (983), pp Cecchei, Sephen G., Margare M. McConnell, and Gabriel Perez Quiros. Policymakers Revealed Preferences and he Oupu-Inflaion Variabiliy Tradeoff: Implicaions for he European Sysem of Cenral Banks, Manuscrip, Federal Reserve Bank of New York (February 999). Clarida, Richard, Jordi Gali, and Mark Gerler. The Science of Moneary Policy: A New Keynesian Perspecive, NBER working paper 747, May 999, Forhcoming in he Journal of Economic Lieraure. Dimar, Rober, William T. Gavin and Finn E. Kydland. The Inflaion-Oupu Variabiliy Tradeoff and Price Level Targes, Review, Federal Reserve Bank of S. Louis (January/February 999), pp. 3-3.,, and. Price-Level Uncerainy and Inflaion Targeing, Review, Federal Reserve Bank of S. Louis (July/Augus 999), forhcoming. Fischer, Sanley. Long Term Conracs, Raional Expecaions, and he Opimal Money Supply Rule, Journal of Poliical Economy, 85 (977), pp Kiley, Michael T. Moneary Policy under Neoclassical and New-Keynesian Phillips Curves, wih an Applicaion o Price Level and Inflaion Targeing, Board of Governors of he Federal Reserve Sysem, Working Paper 998-7, May, 998 King, Rober G., and Mark W. Wason. The Pos-War U.S. Phillips Curve: A Revisionis Economeric Hisory, Carnegie-Rocheser Conference Series on Public Policy 4 (994), pp57-9. Orphanides, Ahanasios. Moneary Policy Evaluaion Wih Noisy Informaion, Finance and Economics Discussion Series (December 998). Robers, John. (995) New-Keynesian Economics and he Phillips Curve. Journal of Money, Credi, and Banking 7: Rudebusch, Glenn D. and Lars E. O. Svensson. "Policy Rules for Inflaion Targeing," in John B. Taylor, ed., Moneary Policy Rules, Chicago: Universiy of Chicago Press, 999 (see also NBER Working Paper 65, April 998). 7

20 Svensson, Lars. "Price Level Targeing vs. Inflaion Targeing: A Free Lunch?" Insiue for Inernaional Economic Sudies, Sockholm Universiy, Augus 997. An earlier version was published in Augus 996 as Naional Bureau of Economic Research Working Paper 579. Taylor, John B. Aggregae Dynamics and Saggered Conracs, Journal of Poliical Economy, 88 (98) pp.-3. Williams, John C. Simple Rules for Moneary Policy, Finance and Economics Discussion Series #999-, February 999. Woodford, Michael. Opimal Moneary Policy Ineria, manuscrip presened a he 6h annual conference on moneary economics and moneary policy joinly sponsored by he Federal Reserve Bank of San Francisco and he Sanford Insiue for Economic Policy Research (SIEPR), March 5 and 6, 999. An elecronic version of he paper is available a hp://www-siepr.sanford.edu/. 8

21 Figure : Inflaion-Oupu Variabiliy Tradeoffs wih Inflaion Targeing (r =.9) 6 5 Oupu Variabiliy 4 3 New Keynesian Phillips Curve Neoclassical Phillips Curve Inflaion Variabiliy 9

22 Figure : Inflaion-Oupu Variabiliy Tradeoffs wih Price Level Targeing (r =.9) 6 5 Oupu Variabiliy 4 3 Neoclassical Phillips Curve New Keynesian Phillips Curve Inflaion Variabiliy

23 Figure 3: Inflaion-Oupu Variabiliy Tradeoffs in a New Keynesian Model: r =.9 6 Oupu Variabiliy Inflaion Targeing Price Level Targeing Inflaion Variabiliy

24 Figure 4: Inflaion-Oupu Variabiliy Tradeoffs in a New Keynesian Model: r =.5.4. Oupu Variabiliy Inflaion Targeing Price Level Targeing Inflaion Variabiliy

25 Figure 5: Inflaion-Oupu Variabiliy Tradeoffs in a New Keynesian Model: r =. Oupu Variabiliy Inflaion Targeing Price Level Targeing Inflaion Variabiliy 3