TCER WORKING PAPER SERIES INFLATION DIFFERENTIALS AND THE DIFFERENCES OF MONETARY POLICY EFFECTS AMONG EURO AREA COUNTRIES EIJI OGAWA MASAO KUMAMOTO

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1 TCER WORKING PAPER SERIES INFLATION DIFFERENTIALS AND THE DIFFERENCES OF MONETARY POLICY EFFECTS AMONG EURO AREA COUNTRIES EIJI OGAWA MASAO KUMAMOTO July 28 Workng Paper E-9 hp:// TOKYO CENTER FOR ECONOMIC RESEARCH -4-6 Maruno-uch, Chyoda Tokyo, Japan c 28 by EIJI OGAWA and MASAO KUMAMOTO. All rghs reserved. Shor secons of ex, no o exceed wo paragraphs, may be quoed whou explc permsson provded ha full cred, ncludng c noce, s gven o he source.

2 Absrac The purpose of hs paper s o nvesgae () a frs, wheher here exss perssen nflaon dfferenals among euro area counres, namely, wheher nflaon raes among euro area courers have converged or no, () nex, f here exs perssen nflaon dfferenals among euro area counres, we wll nvesgae he causes of he nflaon dfferenals, especally, we focus on he nflaon perssence componens (backward-lookng prce seng behavor) or cyclcal componens (oupu gap), () a las, f he causes of nflaon are dfferen among counres, wheher hese dfferences lead o dfferen effecs of moneary polcy has. We fnd ha () overall euro area nflaon raes are n a process of convergence, bu cross-counry dsperson n nflaon raes across counres has no been elmnaed, () he dfferences n he nflaon perssence and he sensvy of nflaon o cyclcal componens would conrbue o he nflaon dfferenals among euro area counres, () here exs he dfferences n moneary polcy effecs among hese counres, whch are conssen wh he dfferences of nflaon perssence and sensvy of nflaon o cyclcal componens across counres. EIJI OGAWA TCER and Graduae School of Commerce and Managemen Hosubash Unversy 2- Naka, Kunach, Tokyo, 86-86Japan ogawa.ej@srv.cc.h-u.ac.jp MASAO KUMAMOTO Faculy of Economcs Tokyo Keza Unversy -7-34, Mnam-cho, Kokubnj, Tokyo Japan kumamoo@ku.ac.jp

3 Inflaon Dfferenals and he Dfferences of Moneary Polcy Effecs among Euro Area Counres * Ej Ogawa Graduae School of Commerce and Managemen, Hosubash Unversy, 2-, Naka, Kunach, Tokyo Japan and Masao Kumamoo Faculy of Economcs, Tokyo Keza Unversy, -7-34, Mnam-cho, Kokubnj, Tokyo Japan Frs verson: May, 28 Ths verson: July 4, 28 Absrac The purpose of hs paper s o nvesgae () a frs, wheher here exss perssen nflaon dfferenals among euro area counres, namely, wheher nflaon raes among euro area courers have converged or no, () nex, f here exs perssen nflaon dfferenals among euro area counres, we wll nvesgae he causes of he nflaon dfferenals, especally, we focus on he nflaon perssence componens (backward-lookng prce seng behavor) or cyclcal componens (oupu gap), () a las, f he causes of nflaon are dfferen among counres, wheher hese dfferences lead o dfferen effecs of moneary polcy has. We fnd ha () overall euro area nflaon raes are n a process of convergence, bu cross-counry dsperson n nflaon raes across counres has no been elmnaed, () he dfferences n he nflaon perssence and he sensvy of nflaon o cyclcal componens would conrbue o he nflaon dfferenals among euro area counres, () here exs he dfferences n moneary polcy effecs among hese counres, whch are conssen wh he dfferences of nflaon perssence and sensvy of nflaon o cyclcal componens across counres. JEL classfcaon: E3, E32, E52 Keywords: Euro Area Counres, Inflaon Dfferenals, Hybrd Phllps Curve, Moneary Polcy * Ths paper s a revsed verson of paper ha was presened a he Zush Conference of he Tokyo Cener for Economc Research on May - n Shmoda. The auhors apprecae he parcpans for her useful commens. e-mal: ogawa.ej@srv.cc.h-u.ac.jp e-mal: kumamoo@ku.ac.jp

4 . Inroducon A unfed moneary polcy has been adoped among he euro area counres snce he hrd sage of Economc and Moneary Unon (EMU) sared on January 999. A sngle moneary polcy s conduced n he Eurosysem, whch composes of he European Cenral Bank (ECB) and he 5 naonal cenral banks of he euro area counres. A prmary objecve of he ECB s moneary polcy s o manan prce sably. The ECB ams a nflaon raes of below, bu close o, 2% over he medum erm. A smooh and effecve ransmsson of he sngle moneary polcy n he euro area counres s necessary for accomplshng he ECB s prmary objecve. Snce all counres face he same shor-erm nomnal neres rae se by Eurosysem under he money marke negraon, perssen nflaon dfferenals among euro area counres would cause he perssen shor-erm real neres rae dfferenals. Ths mples ha Eurosysem s polcy would be excessvely gh for low nflaon counres and loose for hgh nflaon counres, henceforh, unfed moneary polcy conduced by Eurosysem would have dfferen effecs n dfferen counres. Therefore, undersandng he causes of he nflaon dfferenal s mporan. However, s known ha perssen nflaon dfferenals connue o exs n he euro area counres. Accordng o a hybrd Phllps curve, whch s derved from he assumpon ha here exs backward-lookng frms whch use a smple rule-of-humb when seng her prce, ogeher wh he forward-lookng frms, nflaon rae oday depends on he pas nflaon rae (nflaon perssence), expecaon of nflaon rae and oupu gap (cyclcal componens). As poned ou by Hofmann and Remsperger (25), he frm s prce seng behavor would dffer dependng on dfferences n he pas moneary polcy regme. In counres where hgh nflaon and/or nera n nflaon were observed, consumers and frms would form expecaon for fuure nflaon raes dependng on he pas observaon, and would use ndexng pracce when seng prces and/or wages. These pracces would cause he nflaon perssence. Hence, he dfferences n degree of nflaon perssence among counres would be he source of he perssen nflaon dfferenals. In addon, he asymmery of cyclcal componens varaons among counres due o he asymmerc shocks causes he nflaon dfferenals among counres. Moreover, even f he cyclcal componens among euro area counres commoves wh each oher, he dfferences n he sensves of nflaon raes o he change n cyclcal componens would cause he nflaon dfferenals. In hese crcumsances, he unfed moneary polcy would have asymmerc effecs on nflaon. The purpose of hs paper s o nvesgae () a frs wheher here exss perssen nflaon dfferenals among euro area counres, namely, wheher nflaon raes among euro area courers have converged, () nex f here exss perssen nflaon dfferenals among euro area counres, we wll nvesgae whch facor causes he nflaon dfferenals, nflaon perssence componens (backward-lookng prce seng behavor) or cyclcal componens, () a las wheher moneary polcy has dfferen effecs. 2

5 The remander of hs paper s organzed as follows. In Secon 2, we nvesgae wheher here exs perssen nflaon dfferenals among euro area counres, namely, wheher nflaon raes among euro area courers have converged or no. We wll analyze he β - and σ -convergence proposed by Adam e al. (22) by usng panel un roo mehods. In Secon 3, we nroduce he Dynamc Sochasc General Equlbrum (DSGE) model wh a hybrd IS curve and a hybrd Phllps curve, followng Chrsano, Echenbaum and Evans (999), Erceg, Henderson and Levn (2) and Smes and Wouers (22), o consder he sources of nflaon dfferenals. In Secon 4, we wll esmae he hybrd Phllps curve usng Generalzed Mehods of Momens (GMM). In Secon 5, we conduc a Srucural VAR analyss o examne wheher he dfferences n he sources of nflaon among counres cause he dfferences n moneary polcy effecs among counres. Secon 6 s a concluson. 2. Inflaon Raes Convergence among Euro Area Counres In hs secon, we nvesgae wheher nflaon raes have converged among euro area counres usng β -convergence and σ -convergence approach proposed by Adam e al. (22). Adam e al. (22) propose β -convergence and σ -convergence measure, whch hey borrow from he economc growh leraure o nvesgae wheher nerbank neres rae among euro area counres relave o correspondng German rae have reduced or no. In he growh heory, β -convergence apples f a poor economy ends o grow faser han a rch, so ha he poor counry ends o cach up wh he rch one n erms of he level of per capa ncome. Therefore, β -convergence measure n Adam e al. (22) s based on he dea ha nomnal neres rae n counres wh relavely hgh have a endency o decrease more rapdly han n counres wh relavely low and examnes he speed of convergence. The second alernave concep of convergence n growh heory concerns cross-seconal dsperson. In hs concep, convergence occurs f he dsperson, whch s usually measured by he sandard devaon or varance of he logarhm of per capa ncome across a group of counres, declnes over me. Ths concep of convergence s called σ -convergence. Therefore, σ -convergence n Adam e al. (22) examnes he cross seconal dsperson n neres raes o measure he degree of fnancal negraon a any pon n me. In wha follows, we nroduce a model o measure he β - and σ - convergence of nflaon raes n euro area counres and hen, esmae he model usng panel un roo mehods. 2-. Mehodology β -convergence A frs, we assume ha he nflaon rae n counry, denoed π, ( =,, N ), follows AR( p ) process; π = μ + α π + α π + + α π + α π + ε (),, 2, 2 p, p+ p, p, 3

6 where μ reflecs dosyncrac facors n counry. Equaon () s rewren as where p p β = α j and γ j = αk. j= k= j,, j, j, j= p Δ π = μ + βπ + γ Δ π + ε (2) Snce β =Δ( Δπ, ) Δπ,, a negave β ndcaes ha he change of nflaon rae Δπ, nversely relaed o π d,, n oher word, nflaon rae n counres wh relavely hgh have a endency o decrease more rapdly han n counres wh relavely low. Then, he sze of s β s a drec measure of he speed of convergence n he overall marke. Snce a negave β s equvalen o he saonaly of π,. Therefore, equaon (2) can be esmaed by panel un roo es mehods. Panel un roo ess have been advanced by Levn and Ln (992, 993), Levn, Ln and Chu (22, LLC hereafer), Im, Pesaran and Shn (997, IPS). These ess are exenson of augmened Dckey and Fuller (979, 98, ADF) un roos es on ndvdual me seres o panel daa ses. In LLC es, we esmae equaon (2) and es for he null hypohess H : β = β =, agans he alernave hypohess H : β <. For our purpose o measure he speed of convergence n he overall marke assumpon of homogeney n β s s relevan, however, hs assumpon s resrcve and subjec o he possble heerogeney bas. Im, Pesaran and Shn (997) allow β o dffer across counres and devse a es for he null H : β = for all, agans he alernave H : β = for =, 2,, N bu β < for = N +, N + 2,, N. The deals of LLC es and IPS es are explaned n Appendx. σ -convergence Snce β -convergence measures wheher he neres rae converges o he same seady sae value and measures he speed of convergence, does no ndcae o wha exen markes are already negraed. On he oher hand, σ -convergence measures he degree of fnancal negraon a any pon n me. To undersand σ -convergence, assume ha π, follows AR () process wh fxed effecs erm for smplcy; π = μ + απ + ε (3),,, Equaon (3) can also be rewren as Δ π = μ + βπ + ε (4),,, See for Banerjee (999) and Smh and Fueres (24) for panel un roo es. 4

7 where β = α. By akng he mean of boh sdes of equaon (4) over N counres for me, we oban where N π N π and =, N = π μ απ = + (5) μ N μ 2. From equaon (3) and (5) and he sample analogue of he classcal regresson assumpons, we ge σπ, = ( σμ + 2 σμ, π + σε ) + ασ π, (6) where σ n 2 2 π, N ( π, π) =, n 2 μ N = 2 σ ( μ μ) are varance of nflaon rae across counres and varance of fxed effecs erms across counres respecvely. We assume ha varance of error erms, σ 2 ε, and a covarance beween μ and π, n μπ, N ( )(, ) = σ μ μ π π are boh consan over me 3. Equaon (6) mples ha he sequence of nflaon rae dfferenal π, follows saonary process, namely, < α <, he sequence of varance of neres rae 2 2 dfferenals among counres σ π,, also follows saonary process, snce < α <. Equaon (6) can also be wren as 2 2* 2 2 2* σ π, = σπ + α ( σπ, σπ ) (7) where σ 2 2 π ( σμ + 2 ασ u, π + σε )/( α ) denoes he seady sae value of σ 4 d,. 2 As dscussed n Barro and Sala--Mar n (995), equaon (7) mples ha σ π, rses or falls over 2 me dependng on wheher σ π, begns below or above he seady-sae value. Noe especally ha even f β -convergence holds, namely, < α < or β < n equaon (3) or (4), he dsperson 2 2* of nfla on raes would end o rse f σπ, < σπ holds a he nal perod. Thus, β -convergence s a necessary condon bu no a suffcen condon for σ -convergence. In wha follows, we esmae he augmened verson of equaon (4), σ = μ + ασ + α σ + + α σ + α σ ε (8) π, π, 2 π, 2 p π, p+ p π, p + p π,, π,, j π,,, j= Δ σ = μ + βσ + γ Δ σ + ε (9) 2 In dervaon o equaon (5), we use N 3 In dervaon of equaon (6), we use N N = ε =, because he mean of error erms s zero., N N ( μ μ) ε, = N ( π, π ) ε, = = =, because covarance beween ndependen varables and error erms s zero. Noe ha 4 2* * A he seady sae, σ = ( σ + 2 ασ + σ ) + α σ would hold. By subracng hs equaon π μ μ, π ε π from equaon (6), we oban he dfference equaon, σ σ α σ σ desrable equaon (7). 2 2* π, π = ( π, * π ), whch leads o 5

8 where consan erm μ ncludes σ 2 μ, σ μ, π and σ 2 ε, and p p β = α j and γ j = αk. j= k= j Equaon (9) can be esmaed by ADF un roo es mehods o nvesgae wheher he sequence of 2 σ π, would follow saonary process Daa A presen, euro area counres are consued by 5 counres; Ausra, Belgum, Cyprus, Fnland, France, Germany, Greece, Ialy, Ireland, Luxemburg, Mala, Neherlands, Slovena, Span and Porugal. We exclude Slovena whch nroduced euro January 27 and Cyprus and Mala whch nroduced euro January 28 from our sample counres. Daa are wh quarerly frequency and whole sample perod s 999Q o 27Q4, whch sars wh he nroducon of euro. Daa on nflaon rae are calculaed from Harmonzed Consume Prce Index (HCPI). All daa are from Eurosa. Fgure shows he averaged annual nflaon raes of area wde euro area and 3 counres from 999 o 27. From hs fgure, we can fnd ha nflaon raes vary around 2%, wh ranges from abou.5% n Fnland o abou 3.5 % n Ireland. From Fgure 2, whch shows he quarer o quarer nflaon rae, we can see ha nflaon rae n each counry vares whn some ranges, bu has no fully converged. <Inser Fgure., 2> 2-3. Emprcal Resuls β -convergence Table repors he resuls of LLC and IPS ess. Lag lengh s seleced based on SBIC. Sascs * for LLC es sands for a -sascs gven by equaon (A-) and sascs for IPS es sands for -sascs gven by (A-3) n Appendx. From Table, we can see ha he null hypohess W NT H : β = β = n LLC es and H : β = n IPS es can be rejeced, whch means ha overall euro area nflaon raes are n a process of convergence. σ -convergence Fgure 3 presens he sandard devaon of cross-counry dsperson n nflaon rae dfferenals. I seems ha here exss lle evdence of σ -convergence a frs glance. In realy, he las row of Table, whch dsplays he resuls of esmaon of equaon (9), hghlghs he fac ha sequence of { } T 2 σ π, = does no follow saonary process. These resuls mean ha cross-counry dsperson n nflaon rae has no declned, herefore σ -convergence does no occur. Lag lengh s se o 3 based accordng o SBIC. 6

9 <Inser Table and Fgure 3> 3. Model From he resuls n Secon 2, we can see ha here exs perssen nflaon dfferenals among euro area counres, namely, nflaon raes among euro area courers have no converged. The problem, hen, s o nvesgae he causes of he observed nflaon dfferenals. In hs secon, we derve he hybrd Phllps curve n whch nflaon rae oday depends on he pas nflaon rae, expecaon of nflaon rae and oupu gap. The model wll be esmaed n he nex secons. Our model s very smlar o recen dynamc sochasc general equlbrum model (DSGE) wh monopolscally compeve marke srucure and scky prce adjusmens, ncludng Chrsano, Echenbaum and Evans (999), Erceg, Henderson and Levn (2), Smes and Wouers (22) and Sensson, J. (23). We consder a closed economy whch s composed of households, frms. Infnely-lved households maxmze a uly funcon whch depends posvely on consumpon of goods relave o an exernal hab varable and negavely on labor supply. We assume he homogeney of labor servce of each household, for smplcy. Monopolscally compeve frms produce a dfferenaed good ha s solely consumed by households. They se her prces n saggered conracs wh mng lke ha of Calvo (983). In addon, we assume he exsence of backward-lookng frms whch uses a smple rule-of humb when seng prces. 3. Households There s a connuum of nfnely-lved households ndexed by [,]. Each of households has a uly funcon whch depends posvely on consumpon of goods relave o an exernal hab varable and negavely on labor supply. Each household maxmzes s uly funcon gven by E + σ C σ L ( C, H) ε L C,, L, β e + σ C σ = L e ε () where β s a dscoun facor, Dx-Sglz form C, s a household s consumpon ndex defned by famlar C, = C, ( j) dj () where C, ( j) s household s consumpon of good j [,]. Equaon () mples ha elascy of subsuon beween goods s consan and equals o. varables, L, s a household s labor supply, H s an exernal hab σ C and σ L are coeffcens of relave rsk 7

10 averson of household wh respec o consumpon and labor respecvely, and ε C, and ε, represen preference shocks and labor supply respecvely, whch follow a frs order auoregressve process wh an..d. normal error erm, εc, = ρcεc, + νc, (2) ε = ρε + ν (3) L, L L, L, The exernal hab s assumed o be proporonal o aggregae pas consumpon and s no affeced by any sngle household. H = hc (4) L where aggregae consumpon s defned as C C,. = d Household by maxmzes her uly funcon subjec o an neremporal budge consran gven B W C L I,,, + =, + +Ψ P P P where B, s household s bond holdng from o +, equaon (5), s a nomnal wage, B, (5) P s a prce ndex correspondng o W Ψ, s a prof of frm, and I ( ) s a nomnal neres rae on bonds beween and +. The prce ndex P s defned so as o equal o a mnmum expendure for whch a un of consumpon ndex can be purchased and can be derved as C, ( ) P = P j dj (6) In each perod, household faces wo uly-maxmzng problems, namely, () how much o consume he consumpon ndex C, under he neremporal budge consran (5), and () how much o consume each ndvdual dfferenaed goods C, ( j). As for he problem (), he demand for each ndvdual good s gven by P ( j) C, ( j) = C, (7) P and aggregang equaon (7) over households [,], oal demand for goods j by all consumers as where C( j) = C, ( j) d. As for he problem (), we form he Lagrangan, P ( j) C( j) = C P (8) σc + σ L (, ) C hc ε L C,, ε L, W B, B, L = E β e e + λ, L, + I + Ψ, C, + = σc + σl P P P and dfferenae wh respec o and B o ge frs order condons, C,, 8

11 σ εc ( ) C hc e = λ = λ (9) C,, λ βi λ E + P = P+ w here λ, s he Lagrangan mulpler. In dervng equaon (9) and (2), we use he fac ha he margnal uly of consumpon s dencal across households. Combnng he above wo frs order condons, we can oban he followng Euler equaon: σ ε C C, + C hc e I C+ hc) e = P+ σ ε C C, ( ) β ( E P Noe ha n hs case he neres elascy of oupu gap depends no only he neremporal elascy of subsuon, bu also on he hab formaon parameer. Nex we urn o he labor supply decsons of each household. We dfferenae he above Lagrangan wh respec o L ( ) o ge frs order condon ε e L, L, L (2) (2) W = λ (22) P σ and subsue equaon (22) no equaon (9), he labor supply equaon s derved as σ L σ W c ε L L = ( C hc ) e,. (23) P 3.2 Frms We ass ume a connuum of monopolscally compeve frms ndexed by j [,] produce a dfferenaed good. For smplcy, we gnore capal and defne he producon funcon of frm j as where consan reurn o scale s assumed. ε Y, Y( j) = e N j, (24) s a labor demand of frm j and ε represens N j, Y, producvy shock whch follows a frs order auoregressve process wh an..d. normal error erm, εy, = ρε Y Y, + νy, (25) Before analyzng he frm s prcng decson, consder s cos mnmzaon problem, whch s specfed as, W mn N j, + φ j, ( ε Y, N j, Y ( j )) (26) { N j, } P From he frs order condon, we can see ha margnal cos equals across frms and equals o Lagrangan mulpler, W / P = φ j, = φ (27) ε Y, 9

12 Snce aggregaed labor supply n equlbrum, equaon (23) can be w ren as L = L d mus equal o aggregaed labor demand, σ L σ W N C hc e P C L, = ( ) (28) We now urn o he prcng decsons. Followng Gal and Gerler (999), we assume ha a fracon of α of he frms can se a new prce n each perod. Namely, each frm s able o se a new prce wh probably α n each perod. The probably ha a frm wll be allowed o rese s prce n any perod does no depend on how long s exsng conrac has been n effec. Wh probably α, canno change prce so ha s prce s remaned o P. Moreover, here exs wo ypes of he frms n he economy when comes o prce decsons. A fracon ω of he frms, whch we refer o forward-lookng frms behave opmally, and remanng frms of fracon ω, whch we refer o backward-lookng frms, use a smple rule-of-humb when seng her prce. Therefore, prce ndex (6) can be rewren as = α ( α) ω ( ) ( α)( ω) ( ) + + P P P b P f (29) where P ( b ) and P ( f ) are he new prce se by forward-lookng frms and back-ward lookng frms respecvely. We assume ha backward-lookng frms se her prces accordng o he followng rule, n Pb ( ) = P Π (3) n where Π = P / P and we defne he ndex for newly se prces P by n ω ω P = P( b) P( f) (3) Snce producon funcon s homogeneous so ha average cos equals o margnal cos, presen dscouned value of forward-lookng frm s prof can be wren as P( f) E ( βα) l φ+ l Y+ l( f ) (32) l= P+ l where Y ( f ) s he oupu of represenave forward-lookng frms. As boh governmen and foregn secors are absen n our model, marke clearng condon mus sasfy, Y ( j) = C ( j) Y ε N j, dj (33) = C (34) and he oal demand for goods j by all consumers C ( j ) s gven by equaon (22), we can rewre equaon (36) as C P( f) ) E C P( f ( ) l βα φ+ l Y+ l l P l P l (35) = + +

13 Therefore, frs order condon of prof maxmzaon problem of forward-lookng frm s gven by C C ( ) l l l + + l E ( βα) Y+ l= E ( βα) φ+ l Y+ l P l= P l= P P f P P (36) 3.3 Log-lnear approxmaon We denoe he percenage devaon of varable X around he seady sae as X X xˆ log( X) log( X). X Log-lnearzng equaon (2) and usng he lnearzed marke clearng condons (33) and (34) resuls n hybrd IS curve, h yˆ = yˆ ˆ + E[ yˆ+ ] E[ ˆ π+ ] + E[ εc, εc, + ] (37) + h + h σ ( + h) σ ( + h) C When h =, hs equaon reduces o he radonal forward-lookng IS curve. Wh exernal hab formaon, oupu gap defned as he percenage devaon of real GDP from s seady sae value depends on a weghed average of pas and expeced fuure oupu gap. Nex, we log-lnearze equaon (29), (3), (3) and (36), C α ˆ π { ˆ ( ) ( ) ˆ = ωp b + ω p( f)} (38) α n pˆ( b) = pˆ ˆ π + ˆ π (39) n pˆ = ωpˆ( b) + ( ω) pˆ( f) (4) pˆ ˆ ˆ ( f) = ( βα) φ + βαe[ p+ ( f)] + βαe[ π+ ] (4) where pˆ ( b), ˆ n n p and pˆ ( f) denoe percen devaon of P( b)/ P, P( f)/ P and P / P, respec vely, from s seady sae value. Nex, we combne equaon (38) o (4) o elmnae pˆ ( b ) n and ˆp. Ths gves α + ( αω ) ω pˆ( f) = ˆ π ˆ π ( α)( ω) ( α)( ω) (42) Inserng equaon (42) o (4) leads o margnal cos-based hybrd Phllps curve, ω βα ( ω)( α)( βα) ˆ π ˆ π ˆ π ˆ ω( α + αβ ) + α ω( α + αβ ) + α ω( α + αβ ) + α = + E + + φ (43) Hybrd Phllps curve can be obaned as follows. We begn by log-lnearzng equaon (27), (24) and (28): ˆ φ = ( w ˆ p ˆ ) ε Y, (44) yˆ = ε + nˆ (45) Y, σlnˆ = εl, σc( yˆ hyˆ ) + ( wˆ p ˆ ) (46)

14 Nex, we combne equaons (45) and (46) and elmnae From equaons (44) and (47), we can see ha margnal co s s gven by n ˆ o oban he real wage as wˆ pˆ = ( σ + σ ) yˆ + σ hyˆ + ( ε σ ε (47) L c C L, L Y, ) ˆ φ = ( σl + σc) y ˆ + σchy ˆ + εl, ( + σl) εy, (48) Fnally, we combne equaons (43) and (48) o oban he followng hybrd Phllps curve: ω βα ( ω)( α)( βα)( σl + σc) ˆ π ˆ ˆ = π + Eπ+ + y ˆ ω( α + αβ) + α ω( α + αβ) + α ω( α + αβ) + α ( ω)( α)( βα) σch ( ω)( α)( βα) + y ˆ + { εl, ( + σl ) εy, } ω( α + αβ) + α ω( α + αβ) + α (49) From equaon (49), we can see ha nflaon a me forward-lookng erm Eπ + and cyclcal compone ns yˆ. depends on he backward-lookng erm π, 4. Esmaon of Hy brd Phllps Curve In hs secon, we esmae he hybrd Phllps curve as shown n equaon (49) for fve major euro area counres; France, Germany, Ialy, Neherlands and Span, whch ogeher accoun for over 8 percen of he euro area real GDP. 4. Emprcal Mehods Bengno and López-Saldo (22) used he generalzed mehod of momens (GMM) o esmae hybrd Phllps curve for fve major euro area counres over he perod 97Q o 997Q. von Hagen and Hofmann (24) focused on he mplcaon of nflaon dfferenals n euro area counres and esmae backward-lookng IS curve for euro counres over he perod 993Q o 24Q4 ncludng he domesc neres rae, he real exchange rae and euro area neres rae. Angelon and Ehrmann (24) used panel nsrumenal varables o esmae hybrd IS curve and hybrd Phllps curve separaely for 2 counres from 998Q o 23Q2. Smlarly, Hofman and Remsperger (25) used panel nsrumenal varables o esmae hybrd IS curve and hybrd Phllps curve separaely for counres over he perod 999Q o 24Q. Followng Bengno and López-Saldo (22), we esmae he IS curve and he Phllps curve for area wde euro area separaely usng GMM. We use expresson (37) and (53) as an orhogonaly condon, ˆ ˆ ˆ ˆ IS E [( y δ y δ E [ y ] + δ E [ ˆ π ]) z ] = (5) + +, b, f, r,,, P E[( ˆ π γ ˆ π γ E ˆ π γ yˆ ) z ] = (5), b,, f,, + y,,, IS P w here z, and, z denoe vecors of nsrumenal varables n esmaon for IS curve and Phllps 2

15 IS curve, respecvely. Our se of nsrumens z, s consued by he oupu gap wh lags of wo o fve, nomnal neres raes wh lags of one o four and nflaon rae wh lags of zero o hree, and z s consued by he combnaon of nflaon rae wh lags of wo o fve, oupu gap wh lags P, rw j of one o four and he logarhm of real wage, denoed by,, wh lags of one o wo. We nclude he logarhm of real wage n our nsrumens se, akng no accoun he margnal cos-based hybrd Phllps curve, equaon (43). 4.2 Daa Our sample counres are consued by fve major counres; France, Germany, Ialy, Neherlands and Span. Daa are wh quar erly frequency and our whole sample perod s 99Q o 26Q4, whch sars slghly afer he sar of he frs sage of EMU n July 99 and sars wh he negraon of Wesern and Easern Germany. Because, as menoned above, he frm s prce seng behavor would dffer dependng on dfferences n he pas moneary polcy regme, we exend he sample perod. Daa on nflaon rae are quarerly nflaon raes calculaed from GDP deflaor, snce daa on HCIP s avalable only from 998Q. Oupu gap s measured as he percen devaon beween logarhm of real GDP and poenal GDP, and calculaed by usng a sandard Hodrck-Presco fler wh smoohng parameer of,6. Daa on nomnal neres rae s nerbank marke raes wh hree monhly maures. Daa on GDP deflaor are from Inernaonal Fnancal Sascs, IMF, and daa on GDP are from Eurosa. Table 2 shows he correlaon marx of esmaed oupu gaps. From hs able, we can see ha busness cycle synchronzaon has no occurred, for example, he oupu gaps n France and Germany are posvely correlaed bu hey are negavely correlaed wh ha n Ialy. <Inser Table 2> 4.3 Emprcal Resuls Table 3 shows he resuls of our GMM esmaon of hybrd IS curves. The frs hree columns repor he esmaes of he parameers δ b,, δ f, and δr,, and her sandard errors, -value and p-value. The las column dsplays he Hansen s J-es of overdenfyng resrcons. From Table 3, we can see ha he all coeffcens of hybrd IS curves are well esmaed n correc sgns excep for Span where he coeffcen on real neres raes s esmaed n he oppose sgn. Moreover, he coeffcen on real neres rae n Ialy s no sgnfcan. Table 4 shows he resuls of our GMM esmaon of hybrd Phllps curves. The frs hree columns repor he esmaes of he parameers γ b,, γ f, and γ, y, and her sandard errors, -value and p-value. The las column dsplays he Hansen s J-es of overdenfyng resrcons. 3

16 From Table 3, we can see ha he all coeffcens of hybrd Phllps curves are well esmaed n correc sgns, bu her sgnfcance are dfferen n dfferen counres. The coeffcens of backward-lookng erms n Germany, Neherlands and Span are esmaed o be low and are no sgnfcan, on he oher hand, hose n France and Ialy are relavely hgh and sgnfcan. The magnudes of he esmaed coeffcens on cyclcal componens are almos he same n all counres, bu her sgnfcance are heerogeneous, namely, hey are sgnfcan n Ialy and Span bu no sgnfcan n France, Germany and Neherlands. These resuls mean ha he boh nflaon perssence and cyclcal componens would conrbue o he nflaon dfferenals among euro area counres. Therefore, we can classfy he fve counres no four groups as shown n Table 4. Group s composed of counres where backward-lookng erm s no sgnfcan (nflaon perssen s no observed) bu cyclcal componen s sgnfcan. In hese counres, when moneary polcy s ghened and nomnal neres rae rses, he nflaon rae would fall mmedaely and largely. Ths s because forward-lookng frms decrease her prces n expecaon ha nflaon raes would fall n he fuure, whch leads o a fall of nflaon rae oday. In addon, he rse of nflaon expecaon would rase he real neres rae, whch leads o a declne of oupu gap. Snce he cyclcal componen s sgnfcan, ha leads o a fall of nflaon rae oday. Ialy and Span are classfed n hs Group. Group 2 s composed of counres where boh nflaon perssen and cyclcal componens are no sgnfcan. In hese counres, nflaon rae falls mmedaely bu no larger han counres n Group. Ths s because as lke counres n Group, nflaon expecaon would fall mmedaely, whch leads o a fall of nflaon rae oday. However, snce he effecs of he declne of oupu gap on nflaon are no sgnfcan, he degree of nflaon fall s smaller han ha of Group. Germany s classfed no hs group. Group 3 s composed of counres where nflaon perssen s sgnfcan, bu cyclcal componen s no sgnfcan. In hese counres, he nflaon rae would no fall afer he rse of nomnal neres rae. Ths s because nflaon expecaon does no fall largely due o he backward-lookng expecaon, whch also does no decrease he nflaon raes oday. In addon, he scky nflaon expecaon would no rase he real neres rae herefore, would no decrease he oupu gap largely. Moreover, snce cyclcal componen s no sgnfcan, he effecs of oupu gap on nflaon would be neglgble. France and Neherlands are classfed n Group 3. Group 4 s composed of counres where boh nflaon perssen and cyclcal componens are sgnfcan. In hese counres, he effecs of nomnal neres rae rse on nflaon rae are no obvous. Ths s because as lke Group 3, nflaon expecaon does no fall largely, whch would no fall nflaon rae oday. In addon, he scky nflaon expecaon would no decrease he real neres rae largely, herefore, would no decrease he oupu gap largely. However, he change of 4

17 cyclcal componens affecs nflaon rae n hese counres. Therefore, f he degree of sensvy of nflaon rae o he change of cyclcal componen s large (small), nflaon would (no) fall. There are no counres classfed n hs group. In he nex secon, we consder wheher here exss he dfferences n moneary polcy ransmsson n hese counres, and wheher hese dfferences reflec above esmaed resuls. <Inser Table 3, 4> 5. Moneary Polcy Transmsson n he Euro Area Counres In hs secon, we nvesgae he moneary polcy ransmsson n he euro area. Especally, we focus on wheher here exs dfferences beween low nflaon counres and hgh nflaon counres n her mpulse response of prce level o moneary polcy shocks. To do hs, we employ srucural VAR (SVAR) model approach. When we use he SVAR model o nvesgae moneary polcy ransmsson, s necessary o denfy moneary shocks by mposng he denfyng resrcons. For he purpose, we employ he block recursve approach proposed by Chrsano, Echenbaum and Evans (999, 25) 5. I s a mer of he approach ha f we can denfy he moneary polcy shocks correcly, we can esmae he mpulse response funcons of each varable o moneary shocks correcly even hough we do no denfy all he economc srucure. 5. Model and Emprcal Mehod Le X denoe he k vecor of varables ncluded n he analyss and we assume ha he srucural VAR (SVAR) model of X s gven by AX = AX + AX AX p p + ε, ε~ d...(, D) (52) where p s a nonnegave neger w hch represens he lag order, A ( =,,2,, p) s a k k coeffcen marx and ε represens srucural shocks wh dagonal varance-covarance marx. The reduced form of SVAR mod el correspondng o equaon (52) s wren as X = BX + B2X BpX p + u, u~ d...(, Σu) (53) where ( =,2,, p) s a k k coeffcen marx. B Snce u B = A A, ( =,2,, p) (54) = A ε (55) Σ = A D( A ) (56) u are obaned from he above wo equaons, he problem, hen, s o ake he observed value of u 5 For he oher denfcaon, see Sms (992), Sms and Zha (996) and Bernanke and Mhov (998). 5

18 and resrc he sysem so as o recover ε as he varance-covarance marx ε = A u. Usng OLS n equaon (53), we can oban u Σ. Snce Σ s symmerc, conans only kk+ ( ) / 2 dsnc u elemens. Gven he dagonal elemens of A are all sandardzed o uny, A conans kk ( ) unknown parameers. In addon, here are k unknown values of dagonal varance-covarance marx D for a oal of k 2 unknown valu es n he srucural model. Therefore, o denfy he srucural model from an esmaed reduced form of SV AR model, s necessary o mpose kk ( )/ 2 denfyng resrcons on he srucural model. We now dscuss how we esmae he dynamc response of ke y macroeconomc varables o a moneary polcy followng Chrsano, Echenbaum and Evans (999, 25). A he sar, we assume ha he ECB conducs a moneary polcy so as o follow = f( Ω ) + ε (57) where s a money marke neres rae (MMR), f s a lnear funcon whch represens he feedback rule, o he elemens n Ω s an nformaon se, and Ω. We paron X no hree blocks as follows, ε s he moneary polcy shock whch s orhogonal X = [ X,, X ]. (58) 2 Here, we assume ha () he vecor X consss of k varables whose me values are conaned n Ω and ha are assumed no o respond conemporaneously o a moneary shock., n oher words, he mo neary polcy shock s orhogonal o he elemens n, and ha () he ECB does no see he vecor X 2, w hch s com posed of k2 ( k + + k 2 = k) varables of all he oher varables n Ω, when I s se. From hese recursveness assumpons, A can be wren as A A A The zero block n he f rs row of A ( k ) ( k k) ( k k ) k 2 = 2 22 ( k ) ( ) ( k2 ) A A A A 3 32 ( k k ) ( k ) 2 2 mddle row of hs marx reflecs he assumpon (). 33 ( k k ) slghly. We nclude logarhm of nernaonal commody prce ndex 2 2 X (59) reflecs he assumpon (), and he zero block n he In hs paper, we follow Chrsa no, Echenbaum and Evans (25), bu depar from hem ( y ), logarhm of prce ndex ( ( k 2 = ). p ) n X ( p c, ), logarhm of real GDP ( k = 3) and logarhm of money supply ( m ) n The reason for ncludng he nernaonal commody prce ndex n X s o solve or reduce he so-called prce puzzle problem. Here, prce puzzle sands for he phenomenon ha he mpulse response funcon of prce level such ha would rse raher han fall n response o a X 2 6

19 posve neres rae shock s observed n VAR-based analyss. Sms (992) proposed ha he one solu on o hs prce puzzle s o nclude he leadng ndcaor such as commody prce ndex. Ths s because when he leadng ndcaor would rse, he moneary auhory would expec he fuure rse n prce level and hen rse neres rae endogenously. However, f he leadng ndcaors would no ncluded n hese crcumsances, neres rae shock conans no only exogenous neres rae change bu also endogenous neres rae change whch corresponds o he expecaon of fuure rse n prce level. Unforunaely, he recursve assumpon s no suffcen o denfy all he elemens of A and o dsngush he frs k equaons from each oher, snce equaon (59) conans only k + ( k k ) + k = 5 resrcons, conrary o he requremens ha kk ( ) / 2 = resrcons are 2 2 needed. However, Chrsano, Echenbaum and Evans (999) show ha () here s lower rangular wh posve erms on dagonal, whch are conssen wh he recursveness assumpon, ha () each member of hs famly generaes precsely he same dynamc response funcon of he elemen of X o a moneary polcy shock, and ha () he dynamc response funcon of he elemen of X are nvaran o he orderng of varables n lower rangular and can apply he famlar Cholesky decomposon 6. X and X 2. Therefore, we can se A o be he In wha follows, we employ block recursve approach o denfy moneary polcy shocks and nvesgae he moneary polcy effecs. 5.2 Daa Our sample counres are consued by fve major counres analyzed n Secon 2; France, Germany, Ialy, Neherlands and Span. Daa are wh quarerly frequency and whole sample perod s from 999Q o 26Q4. Daa on real GDP s nomnal GDP deflaed by HCIP. Daa on prce ndex s HCIP. Daa on commody prce s IMF world commody prce ndex. Daa on MMR s 3-monh Eurbor. Daa on money supply s M3 n he 3 euro area counres because he growh of M3 s he Eurosysems reference value of moneary aggregae. Daa on commody prce ndex s from Inernaonal Fnancal Sascs, IMF and he oher daa are from. Eurosa. 5.3 Emprcal Resuls Snce our sample perods are small relave o our large VAR model (5 varables ncluded), we se lag lenghs p = n order o secure he degree of freedom. Fgure shows he mpulse response funcons of varables o a un srucural shock n neres rae over 2 perods (3 years). Boosrapped sandard errors wh 95% coverage for each mpulse response funcon are also calculaed. 6 Gven a posve-defne symmerc marx Σ u, here s one and only one decomposon no Σ = PP such ha P s lower rangular wh posve elemen of dagonal. u 7

20 When we focus on he resuls of mpulse response funcons of HCIP o neres rae shocks, he resuls are hghly conssen wh our expecaons n Secon 4. In Group counres; Ialy and Span, HCIP declnes sharply and mmedaely followng he ghenng of money marke neres rae. In Group 2 counres; Germany, HCIP responds gradually and n a hump-shaped fashon, boomng afer abou one and a half years and sarng o reurn o pres-shock levels. In Group 3 counres; France and Neherlands, HCIP rses raher han fall afer he Conraconary moneary polcy bu sars o declne gradually afer abou one year. These resuls show ha he combnaon of he degree of nflaon perssence and he degree of sensvy of nflaon rae o cyclcal componen s he source of perssen nflaon dfferenals 7. < Fgure 4> 6. Concluson In hs paper, a frs, we nvesgae wheher here exss perssen nflaon dfferenals among euro area counres, namely, wheher nflaon raes among euro area courers have converged by analyzng he β and σ -convergence by usng panel un roo echnques. From he emprcal resul, we can fnd ha he evdence of β -convergence, bu canno fnd ha of σ -convergence. Ths means ha overall euro area nflaon raes are n a process of convergence bu cross-counry dsperson n nflaon rae across counres has no been elmnaed. Nex, we nvesga e he causes of nflaon dfferenals. Followng Chrsano, Echenbaum and Evans (999), Erceg, Henderson and Levn (2), Smes and Wouers (22) and Sensson (23), we nroduce he DSGE model wh hybrd IS curve and hybrd Phllps curve. Accordng o hybrd Phllps curve, nflaon rae oday depends on he pas nflaon rae (nflaon perssence), expecaon of nflaon rae and oupu gap (cyclcal componens). And hen, we esmae he hybrd Phllps curve for France, Germany, Ialy, Neherlands and Span. The all coeffcens of hybrd Phllps curves are well esmaed n correc sgns, bu her sgnfcance are dfferen n dfferen counres. These resuls mean ha he boh nflaon perssence and cyclcal componens would conrbue o he nflaon dfferenals among euro area counres. In Ialy and Span, nflaon perssen s no sgnfcan bu cyclcal componen s sgnfcan. In hese counres, he nflaon rae would be expeced o fall mmedaely and largely afer he rse of neres rae. In Germany where boh nflaon perssen and cyclcal componens are no sgnfcan, nflaon rae would be expeced o fall bu smaller han Ialy and Span. In France and Neherlands, nflaon perssen s sgnfcan, bu cyclcal componen s no sgnfcan. In hese counres, he nflaon rae would be expeced no 7 However, when we see he mpulse response funcons of real GDP o neres rae shocks, he GDP ncreases bu raher decrease afer he gh moneary polcy n Ialy and Span. These resuls are conssen wh he esmaon of hybrd IS curves. In hese counres, he coeffcen on real neres rae s no sgnfcan or esmaed n oppose sgns. 8

21 o fall afer he rse of nomnal neres rae. A las, we consder wheher here exs he dfferences n moneary polcy effecs among hese counres, usng block-recursve SVAR model proposed by Chrsano, Echenbaum and Evans (999). The resuls obaned are conssen wh our expecaons saed above. In Ialy and Span, HCIP declnes sharply and mmedaely followng he ghenng of money marke neres rae. In Germany, HCIP responds gradually and n a hump-shaped fashon, boomng afer abou one and a half years and sarng o reurn o pres-shock levels. In France and Neherlands, HCIP rses mmedaely afer he rse of money bu sars o declne gradually afer abou one year. These resuls show ha he combnaon of he degree of nflaon perssence and he degree of sensvy of nflaon rae o cyclcal componen s he source of perssen nflaon dfferenals. 9

22 Appendx. Panel Un Roo Tes LLC es The LLC es s performed as follows. In he frs sage, we begn by esmang wo auxlary equaons for a gven se of lag orders; regressng Δ π and π, on he remanng varables (deermnsc and he lagged dfference) o oban he resduals ê, and vˆ,. In he second sage, we regress e ˆ on vˆ, eˆ ˆ, = βv, + ε, for ndvdual counry separaely and adjus eˆ and vˆ as e ˆ / ˆ = e σ ε and v, ˆ, / ˆ = v σ ε respecvely o accoun for heeroskedasy, where ˆ σ ( ) ˆ β ˆ ) ε = T p e = + T 2 ( ˆ, v 8 p 2,. In he fnal hrd sage, we esmae he panel regresson e, = βv, + ε, and compue he -sascs for ˆ β = as ˆ β β = RSE( ˆ β ) where RSE( ˆ β) = ˆ σ ε N T 2 2 v 2 N T = = p 2,, ˆ σ ˆ and + ε = ( NT 2 ) ( e 2, βv, ) = = p + N T = T N p. = If here are no deermnsc n he frs-sage regressons, he resulng -sascs s asympocally sandard normally dsrbued as T and N. However, f here s a consan or a me rend n he frs regressons, hen he resulng -sascs ends o nfny as T, even f he null s rue. Levn and Ln (993) sugges a correcon of -sascs called -sascs o remove he bas and o oban an asympoc sandard normal dsrbuon for he es sascs. -sascs s gven by ˆ 2 ( ) ˆ β NT SNT, σ ε RSE( β) μ T β = (A-) σt where μt and σ T are mean and sandard devaon adjusmen erms whch are compued by Mone Carlo smulaon and abulaed n her paper. -sascs s asympocally sandard 8 In hs sage, an esmae of he long-run varance of d, and he mean of he rao of T ( π ) K 2 T 2 π = T Δ 2, + w T = KL Δ = L+ 2, Δ, L L= 2 d, ˆ N S ( ˆ / ˆ NT = N σ π σ e ) = ˆ σ ( ) π 2 ( ) π σ o he nnovaon sandard devaon for each counry, are also calculaed, where K s he lag runcaon parameer and w s lag wndow. KL 2

23 normally dsrbued as T and N. IPS es IPS es s performed as follows. In he frs sage, he separae ADF regressons of equaon (4) are esmaed and he average of -sascs for β s calculaed as N NT = T where ( p ) denoes -sascs on β for counry T = N ( p ) (A-2) and represens he fac ha depends on he sample perod T and he lag lengh p. Im, Pesaran and Shn (997) show ha W NT = N N NT N E( T ( p )) = N N Var( ( p )) = T (A-3) s asympoc sandard normal dsrbued as N and T,where E ( ( p )) and Var( ( p )) are average and varance of ( p ) respecvely, whch Im, Pesaran and Shn (997) T T compued by smulaon as he average and varance over 5, Mone Carlo smulaons for dfferen values of T and p, and are repored n Table 3 (IPS able) n her paper. T Appendx 2. Dervaon of equaon (6) subjec o The prce ndex P solves he problem, { C, ( j)} mn Z ( ) ( ), = P j C, j dj We form he followng Lagrangan, and dfferenae wh respec o C, ( j) dj =. L= P() C, ( j) dj λ C, ( j) dj C, ( j) o ge frs order condon,, P ( j) = λc ( j). Therefore, we can see ha he mnmzed expendure over one un of C j, equals o Lagrangan mulpler λ. 2

24 P ( j) Snce C, ( j) = λ resuls Dervaon of equaon (7) * Z = P( ) j C, ( j) dj = λ C, ( j) dj and =, λ P ( j) C ( j) dj = dj = λ, we can oban he desred *, ( ) λ = Z = P j dj. The demand for each ndvdual good can be obaned by solvng he followng problem, subjec o { C, ( j)} max C ( ), = C, j dj P ( jc ) ( jdj ) = Z,, where Z, s any fxed oal nomnal expendure on goods. We form he followng Lagrangan, and dfferenae wh respec o any wo goods From above wo equaon,, λ, ( ) L= C ( j) dj Z P( j) C ( j) d j C C,, C, ( j ) and C, ( j ), o ge P ( j) ( j) = λ P ( j ) ( j ) = λ P ( j) C, ( j ) = C, ( j) P ( j ) s hold. Pluggng hs expresson no he precedng budge consran and usng equaon (5), P ( j) P ( j) ( ), ( ) =, ( ) ( ) ( ) =, ( ) ( ) =, ( ) p ( ) j P = P j C j dj C j P j P j dj C j P j P C j P Z, and usng CP= Z, show ha he represenave agen s demand for good j s gven by P( j) Z, P( j) C, ( j) = = C P P P 22

25 Dervaon of equaon (36) We dfferenae equaon (35) wh respec o P ( f ) o ge he frs order condon, l P( f) P( f) E ( βα) ( ) + φ+ l Y+ l = l= P+ l P+ l P+ l P + l Above equaon can be arranged as P ( f) l l E ( βα) P+ ( P P ) Y + = E ( βα) φ + P Y P whch leads o equaon (36). + + l l l l l l= l= Dervaon of equaon (37) From marke clearng condon, equaon (2) can be wren as εc, + σ C β I e ( Y+ hy) = E εc, σ C Π+ e ( Y hy ) Above equaon can be log-lnearzed as follows, β I = E [ ˆ + ˆ {( yˆ hyˆ ) ( yˆ hyˆ )} + ( Π π+ σc + εc, + εc, )] Noe ha β I / Π=n seady sae, hus, afer some arrangemens, he hybrd new IS curve s obaned. Dervaon of equaon (38) Dvdng boh sde of equaon (29) by P and afer some arrangemen, we ge = αp + ( α) ωp( b) + ( α)( ω) P( f) P = αp + ( α) ωp( b) + ( α)( ω) P f P ( ) P P( b) P( f) = α + ( α) ω + ( α)( ω) P P P Pb ( ) P( f) = α + ( α) ω + ( α)( ω) Π P P Then, we log-lnearze above equaon o ge, 23

26 P P( b) Pf = α { ( ) ˆ π } ( ) { ( ) ˆ + α ω + p( b)} + ( α)( ω) { + ( ) pˆ ( f )} P P P Snce n equlbrum, P = Pb ( ) = P( f), we can oban Dervaon of equaon (39) α ˆ π = { ωpˆ ( b) + ( ω) pˆ ( f) α } Dvdng boh sde of equaon (3) by P and afer some arrangemens, we ge n Pb ( ) P Π = P P Π Then, log-lnearnzng and usng he fac ha P = Pb ( ) = P( f) n equlbrum leads o equaon (39) Dervaon of equaon (4) Lef hand sde of equaon (36) can be log-lnearzed as follows, P( f) l P ( + pˆ ( )) ( ) { ( )( ˆ f E βα + p+ l pˆ)} Y( + yˆ+ l) P l = P l βα + l + l l = = ( + pˆ ( f)) E ( ) Y{ + ( )( pˆ pˆ ) + yˆ } Y = ( + pˆ ( f)) + E ( ) Y{( )( p p ) + y } l ˆ βα ˆ ˆ + l + l βα l = On he oher hand, rgh hand sde of equaon (36) can be log-lnearzed as follows l P ˆ ˆ ˆ βα φ + φ+ l + + l Y + y+ l l = P E ( ) ( ) { ( p p )} ( ) φ Y = + φ E ( βα ) Y{ + ˆ φ + ( pˆ pˆ ) + yˆ βα l + l + l l= Y = + E ( ) Y{ + + ( p p ) + Y } βα l ˆ ˆ ˆ ˆ βα φ+ l + l + l l = + l } Noe ha =. Combnng boh sdes of equaon (36) leads o φ 24

27 l ˆ = βα βα φ+ l+ + l l = pˆ ( f) ( ) E ( ) ( pˆ pˆ ) l E ++ l p++ l p l= = ( βα){ ˆ φ + βα ( βα) ( ˆ φ + ˆ ˆ )} l E ++ l p++ l p+ p+ p l= = ( βα)[ ˆ φ + βα ( βα) { ˆ φ + ˆ ˆ + ( ˆ ˆ )}] l E ++ l p++ l p+ } + ( βα) βαe l= l= = ( βα) ˆ φ + βα( βα) ( βα) { ˆ φ + ˆ ˆ = ( βα) ˆ φ + βαe[ pˆ ( f)] + βαe[ ˆ π ] + + ˆ π + Dervaon of equaon (42) Inserng equaon (4) o (38), we ge α = ˆ π α n pˆ and pluggng hs expresson o equaon (39), we ge ˆ π pˆ b ˆ ˆ ˆ α α α ( ) π π π = + = ˆ π We combne equaon (38) and above equaon o oban equaon (42). 25

28 References Adam, K., T. Jappel, A. Menchn, M. Padula and M. Pagano (22) Analyse, Compare, and Apply Alernave Indcaors and Monorng Mehodologes o Measure he Evoluon of Capal Marke Inegraon n he European Unon, Repor o European Commssons. Angelon, I. and M. Ehrmann (23), Moneary Polcy Transmsson n he Euro Area: Any Changes afer EMU?, European Cenral Bank Workng Paper No. 24. Angelon, I. and M. Ehrmann (24), Euro Area Inflaon Dfferenals, European Cenral Bank Workng Paper No Angelon, I., A. K. Kashyap, B.Mojon, and D. Terlzzese (22), Moneary Transmsson n he Euro Area: Where Do We Sand?, European Cenral Bank Workng Paper No. 4. Angelon, I., A. K. Kashyap, B.Mojon, and D. Terlzzese (23), The Oupu Composon Puzzle: A Dfference n he Moneary Transmsson Mechansm n he Euro Area and U.S., European Cenral Bank Workng Paper No Alssmo, F.,M. Ehrmann and F. Smes (26) Inflaon Perssence and Prce-Seng Behavor n he Euro Area: A Summary of he IPN Evdence, European Cenral Bank Occasonal Paper No. 46. Barro, R. and X. Sala--Marn (995) Economc Growh, McGraw-Hll. Benngo, P. and D. López-Saldo (22) Inflaon Perssence and Opmal Moneary Polcy n he Euro Area European Cenral Bank Workng Paper No. 78. Calvo, G.A. (983) Saggered Prces n a Uly Maxmzaon Framework, Journal of Moneary Economcs 2, pp Casares, M. (27), Moneary Polcy Rules n a New Keynesan Euro Area Model, Journal of Money, Cred and Bankng, Vol.n39, No. 4, pp: Chrsano, L. J., M. Echenbaum, and C. L. Evans (999), Moneary Polcy Shocks: Wha Have We Learned and o Wha End?, n Taylor, J. B. and M. Woodford (eds.), Handbook of Macroeconomcs Vol.A, Amsererdam: Elsever Scence, pp Chrsano, L. J., M. Echenbaum, and C. L. Evans (25), Nomnal Rgdes and he Dynamc Effecs of a Shock o Moneary Polcy, Journal of Polcal Economy, vol. 3 (), pp Erceg, C. J., D. W. Henderson and A.T. Levn (2), Opmal Moneary Polcy wh Saggered Wage and Prce Conracs, Journal of Moneary Economcs Vol. 46, pp Galí, J. and M. Gerler (999), Inflaon Dynamcs: A Srucural Economerc Analyss, Journal of Moneary Economcs Vol. 44, pp Hofmann, B. and Remsperger, H. (25), Inflaon Dfferenals among he Euro Area Counres: Poenal Causes and Consequences, Journal of Asan Economcs, 9, pp Im, K.S., M. H. Pesaran and Y. Shn (997) Tesng for Un Roos n Heerogenous Panels,, DAE Workng Papers Seres, No 9526, Unversy of Cambrdge 26

29 Levn, A. and C-F. A. Ln (992) Un Roo Tess n Panel Daa: Asympoc and Fne-Sample Properes, Deparmen of Economcs, Dscusson Paper No.92-93, Unversy of Calforna San Dego. Levn, A. and C-F. A.Ln (993) Un Roo Tess n Panel Daa: New Resuls, Dscusson Paper No.93-56, Unversy of Calforna San Dego. Levn, A. C-F. A. Ln and C-S. J. Chu (22) Un Roo Tess n Panel Daa: Asympoc and Fne-Sample Properes, Journal of Economercs, Vol. 8(), pp Mshkn, F.S. (995), Symposum on he Moneary Transmsson Mechansm, Journal of Economc Perspecves 9 (4), pp. 3-. Peersman, G. (24) The Transmsson of Moneary Polcy n he Euro Area: Are he Effecs Dfferen Across Counres?, Oxford Bullen of Economcs and Sascs, Vol. 66 (3), PP Roemberg, J.J. and M. Woodford (998), An Opmzaon-Based Economerc Framework for he Evaluaon of Moneary Polcy: Expanded Verson NBER Techncal Workng Paper 233. Sms, C. A. (992), Inerpreng he Macroeconomc Tme Seres Facs: The Effecs of Moneary Polcy, European Economc Revew 36 (5), pp Sms and Zha (998) Does Moneary Polcy Generae Recessons?, Workng Paper 98-2, Federal Reserve Bank of Alana Smes, F and R. Wouers (22), An Esmaed Dynamc Sochasc General Equlbrum Model of he Euro Area, Naonal Bank of Belgum Workng Papers-Reserch Seres Smh, R.P. and A-M. Fueres (24) Panel Tme-Seres, mmeo.(downloadable Smh s web se) Sensson, J. (23) Opmal Moneary Polcy n an Economy wh Inflaon Perssence, Journal of Moneary Economcs 5, pp Von Hagen, J. and Hofmann, B. (24), Macroeconomc Implcaons of Low Inflaon n he Euro Area, Norh Amercan Journal of Economcs and Fnance, Vol. 5, pp

30 Tables and Fgures Fgure. Averaged Inflaon Raes (Annual,999Q-27Q4) Fnland Germany Ausra France Belgum 3 Euro area Neherlands Ialy Porugal Luxembourg Greece Span Ireland (Source) Eurosa Fgure 2. Inflaon Raes (Quarer o Quarer, 999Q-27Q4) q 999q4 2q3 2q2 22q 22q4 23q3 24q2 25q 25q4 26q3 27q2 -.2 Belgum Germany Ireland Greece Span France Ialy Luxembourg Neherlands Ausra Porugal Fnland (Source) Eurosa 28