Input-Output Interactions and Optimal Monetary Policy

Transcription

1 Inpu-Oupu Ineracion and Opimal Moneary Policy Ivan Perella Caholic Univeriy of Leuven Emiliano Sanoro Caholic Univeriy of Milan Univeriy of Copenhagen April, Abrac Thi paper deal wih he implicaion of facor demand linkage for moneary policy deign in a wo-ecor dynamic general equilibrium model. Par of he oupu of each ecor erve a a producion inpu in boh ecor, in accordance wih a realiic inpu-oupu rucure. Sraegic complemenariie induced by facor demand linkage ignificanly aler he ranmiion of hock and amplify he lo of ocial welfare under opimal moneary policy, compared o wha i oberved in andard wo-ecor model. The diincion beween value added and gro oupu ha naurally arie in hi conex i of key imporance o explore he welfare properie of he model economy. A flexible inflaion argeing regime i cloe o opimal only if he cenral bank balance inflaion and value added variabiliy. Oherwie, argeing gro oupu variabiliy enail a ubanial increae in he lo of welfare. JEL claificaion: E3; E3; E5 Keyword: Inpu-Oupu Ineracion, Muli-Secor Model, Opimal Moneary Policy We would like o hank Guido Acari, Aqib Alam, Tiago Cavalcani, Domenico Delli Gai, Han Dewacher, Sean Holly, Søren Hove Ravn, Henrik Jenen, Donald Roberon, Raffaele Roi, Demohene Tambaki, Karl Whelan, and oher paricipan in he Macroeconomic Workhop, Univeriy of Cambridge, he 9 Dynare Conference a he Norge Bank, he 4nd Annual MMF Conference in Limaol (Cypru) and he 3rd Conference on Economic Policy and he Buine Cycle a he Univeriy of Milan-Bicocca, for heir conrucive commen. All remaining error are our own. Addre: Cener for Economic Sudie, Faculy of Buine & Economic, Kaholieke Univeriei Leuven, Naameraa 69, 3 Leuven, Belgium. Ivan.Perella@econ.kuleuven.be. Addre: ITEMQ, Caholic Univeriy of Milan, I-3 Milan, Ialy. emiliano.anoro@unica.i.

2 Inroducion Thi paper deal wih he implicaion of facor demand linkage for moneary policy deign. We build a dynamic ochaic general equilibrium (DSGE) model wih wo ecor ha produce ervice and manufacured good. The gro oupu of each ecor erve eiher a a final conumpion good, or a an inermediae inpu in boh ecor, according o a realiic inpu-oupu rucure. Facor demand linkage are empirically relevan and heir imporance in he ranmiion of boh ecoral and aggregae hock ha long been recognized by he lieraure exploring he ource and channel of propagaion of he buine cycle. Horvah (998, ) how ha cro-indury flow of inpu maerial can reinforce he effec of ecoral hock, generaing aggregae flucuaion and co-movemen beween ecor, a originally hined by Long and Ploer (983). More recenly, Bouakez, Cardia, and Ruge-Murcia () and Sudo (8) have hown ha facor demand linkage help a generaing poiive co-movemen beween non-durable and durable pending in he face of a moneary innovaion, hu overcoming he limi of andard wo-ecor model ha feaure heerogeneou degree of price ickine acro ecor. 3 However, none of hee paper ha aken a normaive perpecive. The novel conribuion of he preen udy i o explore how moneary policy hould be purued in a model wih cro-indury flow of inpu maerial. In our framework he moneary auhoriy canno aain he Pareo opimal allocaion conien wih he full abilizaion of oupu and inflaion. Thu, we explore opimal moneary policy under he aumpion ha he policy maker can credibly commi o a policy rule derived from he minimizaion of a ocial welfare funcion. The lo funcion balance, along wih ecoral inflaion variabiliy, a preference o reduce flucuaion in aggregae conumpion (or, equivalenly, value added). Given he naural diincion beween conumpion and producion in he preence of inpu maerial, i i no longer irrelevan wheher he moneary auhoriy arge he oupu gap or he conumpion gap. Thi reul ha imporan implicaion for boh he ranmiion of exogenou hock and he elecion of policy regime a alernaive o he opimal policy under commimen. Inroducing facor demand linkage ino an oherwie andard wo-ecor model amplifie he lo of ocial welfare and aler he ranmiion of hock o he yem, compared o he benchmark economy wihou inpu maerial. A diincive feaure of he model i ha a echnology hock o eiher ecor alo affec poenial oupu in he oher ecor, even if preference over differen ype of conumpion good are eparable. Inpu-oupu rucure are a pervaive feaure of indurialized economie. Mo of he good in he economy are ued for boh conumpion purpoe and a inermediae in oher ecor, in accordance wih dene nework of facor demand linkage. Bouakez, Cardia, and Ruge-Murcia (9) and Holly and Perella () repor exenive evidence on he imporance of inpu-oupu ineracion. In hi repec, we hould noe ha he co of inermediae good correpond o he large hare in he oal co of producion. Dale Jorgenon daa on inpu expendiure by US indurie how ha inpu maerial (including energy) accoun for roughly 5% of oulay, while labor and capial accoun for 34% and 6%, repecively. Kim and Kim (6) how ha a imilar mechanim generae widepread co-movemen of economic aciviy acro ecor. In a imilar vein, Carvalho (9) explore he nework rucure of inerecoral rade. 3 Alhough he co-movemen puzzle ha been emphaized in connecion wih he dichoomy beween durable and non-durable (Barky e al., 7), ecoral co-movemen i an inheren feaure of he buine cycle (ee, e.g., Hornein and Prachnik, 997 and Chriiano and Fizgerald, 998) ha muliecor DSGE model need o be able o replicae.

3 Furhermore, facor demand linkage imply ha he relaive price of ervice no only affec he marginal rae of ubiuion beween manufacured good and ervice, bu alo exer a poiive (negaive) impac on he real marginal co in he manufacuring (ervice) ecor. The relaive magniude of he econd effec depend on he off-diagonal elemen in he inpu-oupu marix. Beyond reconciling convenional wo-ecor DSGE model wih a realiic rucure of he economy, hi paper deec imporan difference beween he way moneary policy hould be purued and wha i oherwie precribed by he exiing lieraure on muliecor model wihou facor demand linkage. We compare he welfare properie of he model under alernaive policy regime and how ha a flexible inflaion argeing regime deliver a welfare lo cloe o ha aained under he opimal policy. Mo imporanly, he cenral bank aain a maller lo when flucuaion in aggregae or core inflaion are balanced wih hoe in real value added, compared o he lo induced by argeing gro oupu. We alo conider he cae of aymmeric price ickine, which implie a naural divergence beween core and aggregae inflaion. Alhough uch a difference i ill relevan wihin our framework, argeing eiher core or aggregae inflaion make lile difference in erm of welfare lo. By conra, wha maer i he erm accouning for real volailiy: in hi repec, argeing he conumpion gap enail ubanial benefi compared o argeing he producion gap. Thee reul emphaize he diincion beween conumpion and producion ha naurally arie in hi cla of model. The remainder of he paper i laid ou a follow: Secion inroduce he heoreical eing; Secion dicue he calibraion of he model economy; Secion 3 explore he Pareo opimal oucome; Secion 4 udie he implemenaion of he opimal moneary policy under commimen and compare he reuling lo of ocial welfare wih ha aainable under a number of alernaive policy regime. Secion 5 conclude. The Model We develop a DSGE model wih wo ecor ha produce manufacured good and ervice, repecively. 4 The model economy i populaed by a large number of infiniely-lived houehold. Each of hee i endowed wih one uni of ime and derive uiliy from he conumpion of ervice, manufacured good and leiure. A in Bouakez, Cardia, and Ruge-Murcia () he wo ecor of producion are conneced hrough facor demand linkage. 5 Good produced in each ecor erve eiher a a final conumpion good, or a an inermediae producion inpu in boh ecor. The ne flow of inermediae good beween ecor depend on he inpu-oupu rucure of he upply ide. 4 Boh ype of conumpion good are non-durable. Perella and Sanoro () udy opimal moneary policy in a imilar eing, auming ha conumer have preference defined over boh durable and non-durable good. 5 Throughou he paper we will refer o facor demand linkage a indicaing cro-indury flow of inpu maerial. If a pecific feaure of he framework i excluively deermined by he ue of inermediae good in he producion proce (i.e., iner-ecoral relaionhip are no eenial) we will explicily refer o inpu maerial. 3

4 . Producer Conider an economy ha coni of wo diinc ecor producing ervice (ecor ) and manufacured good (ecor m). Each ecor i compoed of a coninuum of firm producing differeniaed produc. Le Y (Y m ) denoe gro oupu of he ervice (manufacuring) ecor: Y i = [ ( Y i i ) ε ε i f df ] εi ε i, i = {, m} () where ε i denoe he ime-varying elaiciy of ubiuion beween differeniaed good in he producion compoie of ecor i = {, m}. Each producion compoie i produced in he "aggregaor" ecor operaing under perfec compeiion. I i poible o how ha a generic firm f in ecor i face he following demand chedule: Y i f = ( P i f P i ) ε i Y i, i = {, m} () where P i i he price of he compoie good in he i h ecor. Uing () and (), he relaionhip beween he firm-pecific and he ecor-pecific price i: P i = [ ] ( ) P i ε i ε i f df, i = {, m}. (3) Secor are relaed by facor demand linkage. Par of he oupu of each ecor erve a an inermediae inpu in boh ecor. The allocaion of oupu produced in he i h ecor i uch ha: Y i = C i + M i + M im, i = {, m} (4) where C i denoe he amoun of conumpion good produced by ecor i, while M i (M im ) i he amoun of good produced in ecor i and ued a inpu maerial in ecor (m). The producion echnology of a generic firm f in ecor i i: Y i f = Z i [( M i f ) γi ( M mi f γ γ i i γγ mi mi ) γmi ] αi (L i f) αi, i = {, m} (5) where Z i (i = {, m}) i a ecor-pecific produciviy hock, L i f denoe he number of hour worked in he f h firm of ecor i, M ji f (j = {, m}) denoe maerial inpu produced in ecor j and upplied o firm f in ecor i. Moreover, γ ij (i, j = {, m}) denoe he generic elemen of he inpu-oupu marix, Γ, and correpond o he eady ae hare of oal inermediae good ued in he producion of ecor j and upplied by ecor i. The inpu-oupu marix i normalized, o ha he elemen of each column um up o one: j={,m} γ j = (and j={,m} γ jm = ). Maerial inpu are combined according o a CES aggregaor: M ji f = [ ] ( ε j ) M ji kf,)(ε j )/εj /(εj dk, (6) 4

5 where { } M ji kf, i a equence of inermediae inpu produced in ecor j by firm k, k [,] which are employed in he producion proce of firm f in ecor i. Firm in boh ecor e price given he demand funcion repored in (). They are alo aumed o adju heir price wih probabiliy θ i in each period. When hey are able o do o, hey e he price ha maximize expeced profi: max E Pf i n= [ ] (βθ i ) n Ω +n P i f+n ( + τ i ) MCf+n i Y i f+n, i = {, m} (7) where Ω i he ochaic dicoun facor (conien wih houehold maximizing behavior, which i decribed in he nex ubecion), τ i i a ubidy o producer in ecor i, while MCf i denoe he marginal co of producion of firm f in ecor i. The opimal pricing choice, given he equence {P, P m, Y, Y m }, read a: P i f = ε i (ε i ) ( + τ i ) E n= (βθ i) n Ω +n MC i f+n Y i E n= (βθ i) n Ω +n Y i f+n f+n, i = {, m}. (8) Noe ha auming ime-varying elaiciie of ubiuion ranlae ino ecoral copuh hock ha allow u o accoun for ecor-pecific hif parameer in he upply chedule. In every period each firm olve a co minimizaion problem o mee demand a i aed price. The fir order condiion from hi problem reul in he following relaionhip: MC i fy i f = W i L i f = P α i α i γ i M i f = P m Mf mi, i = {, m}. (9) α i γ mi I i ueful o expre he ecoral real marginal co a a funcion of he relaive price, Q = P, and he ecoral real wage: /P m MC P MC m P m = φ ( Q γ m = φm (Q γ m ) α (RW ) α Z ) αm (RW m Z m ) αm, (), () where, for i = {, m}, RW i = W i /P i i he real wage in ecor i and φ i i a convoluion of he producion parameer (φ i = α α i i ( α i ) α i ). From () and () i i clear ha he relaive price exer a direc effec on he real marginal co of each ecor, whoe magniude depend on he ize of he cro-indury flow of inpu maerial. 6 Specifically, for he i h ecor he abolue impac of Q on 6 Noe ha under a diagonal inpu-oupu marix, which raionalize a wo-ecor model wih a pure roundabou rucure, he relaive price doe no affec he real marginal co. In hi cae a higher hare of inermediae good dampen he impac of he real wage on he real marginal co, increaing raegic complemenariy in price-eing among firm in he ame ecor. In urn, hi may deermine large oupu effec in he face of a diurbance o nominal pending (ee Bau, 995 and Woodford, 3, pp. 7-73). Thi effec i ill a work wihin he general rucure we enviage. In addiion, cro-indury flow of inpu maerial induce raegic complemenariie beween ecor (Horvah, 998). 5

6 MC i /P i i relaed o he "imporance" of he oher ecor a inpu upplier, i.e. on he magniude of he off-diagonal elemen in he inpu-oupu marix (γ m and γ m ). Thi i a diincive feaure of he framework we deal wih. By conra, in radiional muli-ecor model wihou facor demand linkage (e.g., Aoki, ), he relaive price only affec he real marginal co indirecly, hrough he marginal rae of ubiuion beween differen conumpion good. 7. Conumer Houehold derive income from working in firm in he wo ecor, inveing in bond, and from he ream of profi generaed by he producion ecor. They have preference defined over a compoie of ervice (C ), manufacured good (C m ) and labor (L ). They maximize he expeced preen dicouned value of heir uiliy: E = [ H β σ ] σ ϱ L+v, () + v where H = (C ) µ (C m ) µ m, µ and µ m (= µ ) denoe he expendiure hare on ervice and manufacured good, β i he dicoun facor, σ i he invere of he ineremporal elaiciy of ubiuion, v i he invere of he Frich elaiciy of labor upply. The following equence of (nominal) budge conrain applie: i={,m} P i C i + B = R B + i={,m} W i L i + i={,m} Ψ i T, (3) where B denoe a one-period rik-free nominal bond remuneraed a he gro rik-free rae R, and T denoe a lump-um ax paid o he governmen. The erm Ψ + Ψ m capure he nominal flow of dividend from boh ecor of producion. We aume ha labor can be eiher upplied o ecor or m according o a CES aggregaor: L = ] [φ λ (L ) +λ λ + ( φ) λ (L m ) +λ λ +λ λ, (4) where λ denoe he elaiciy of ubiuion in labor upply, and φ i he eady ae raio of labor upply in he ervice ecor over he oal upply of labor (i.e., φ = L /L). Thi funcional form allow u o accoun for differen degree of labor mobiliy beween ecor, depending on λ. 8 To ee hi, we repor he following relaionhip, which can be rerieved from he fir order condiion of conumer uiliy maximizaion wih repec 7 Similarly, in a model wih verical inpu linkage he relaive price only exer a direc effec on he real marginal co of he final good ecor. Neverhele, i can ill be relaed o he real marginal co of he inermediae good ecor hrough he marginal rae of ubiuion beween conumpion and leiure (ee Huang and Liu, 5 and Srum, 9). 8 Empirical evidence ugge ha labor i no perfecly mobile acro ecor. Davi and Haliwanger () uppor hi view, finding limied labor mobiliy acro ecor in repone o moneary and oil hock. 6

7 o L and L m : 9 ( φ ) ) λ L λ φ L m W = W m. (5) For λ = labor i prevened from moving acro ecor and i relaive upply i conanly equal o he eady ae level. By conra, for λ = worker devoe all ime o he ecor paying he highe wage. Hence, a he margin, all ecor pay he ame hourly wage, o ha houehold are indifferen o allocaing heir ime o work for one ecor or he oher. Thu, perfec labor mobiliy i aained. For λ < hour worked are no perfec ubiue. An inerpreaion of hi i ha worker have a preference for diveriy of labor and would prefer working cloer o an equal number of hour in each ecor even in he preence of wage difference acro ecor..3 The Governmen and he Moneary Auhoriy The governmen erve wo purpoe in he economy. Fir, i delegae moneary policy o an independen cenral bank. We aume ha he hor-erm nominal inere rae i ued a he inrumen of moneary policy and ha he policy maker i able o precommi o a ime-invarian rule. In Secion 4 we udy moneary policy under alernaive policy regime characerized by differen lo funcion ha he cenral banker commi o minimize. The econd ak of he governmen coni of axing houehold and providing ubidie o firm o eliminae diorion ariing from monopoliic compeiion in he marke for boh clae of conumpion good. Thi ak i purued via lump-um axe ha mainain a balanced fical budge..4 Marke Clearing The allocaion of oupu produced by each ecor require ha ecoral gro oupu i parly old on he marke for conumpion good, while a proporion i old on he marke for inpu maerial. Therefore, (4) mu be me in each ecor. Conequenly, aggregae producion i greaer han aggregae conumpion, which in hi eing can be regarded a he empirically relevan definiion of real value added (or GDP). Soluion and Calibraion To olve he model, we log-linearize behavioral equaion and reource conrain around he non-ochaic eady ae and hen ake he deviaion from heir counerpar under flexible price. The difference beween log-variable under icky price and heir 9 The fir order condiion for he conumer problem are repored in Appendix A. Horvah () moivae a imilar pecificaion baed on he deire o capure ome degree of ecorpecificiy o labor while no deviaing from he repreenaive conumer/worker aumpion. However, an imporan difference beween (4) and he CES aggregaor ued by Horvah () i ha he former allow u o neuralize he impac of labor marke fricion in he eady ae. See alo Nakamura and Seinon (8b) on he diincion beween value added and gro oupu in muli-ecor model wih inpu maerial. 7

8 linearized eady ae i denoed by he ymbol "ˆ", while we ue " " o denoe percen deviaion of variable in he effi cien equilibrium (i.e., flexible price and conan elaiciie of ubiuion) from he correponding eady ae value. Finally, we ue " " o denoe he difference beween linearized variable under icky price and heir counerpar in he effi cien equilibrium. I i ueful o repor he yem of dynamic equaion decribing he log-linearized economy: c = γ ( r E π + rr ) + E c + + γ µ m ( σ) ( E c m + c m ), (6) c = c m q, rw = γ c ( σ) µ m c m + ϑ ( φ) l m + ( ϑφ + λ ) l, (8) l = λ ( rw rw m + q ) + l m, (9) ỹ = α γ m ỹ m = α m γ m m m (7) + α γ m m m + ( α ) l, () ỹ = (C /Y ) c + (M /Y ) m + α m γ mm m mm + ( α m ) l m, () ỹ m = (C m /Y m ) c m + (M m /Y m ) m m + (M m /Y ) m m, () + (M mm /Y m ) m mm, (3) rmc = rw + l ỹ, (4) rmc m = rw m + l m ỹ m, (5) rmc = m ỹ, rmc m (6) = m m + q ỹ m, (7) rmc = m m q ỹ, (8) rmc m = m mm ỹ m, π = βe π + + κ rmc + η, (3) π m = βe π m + + κ m rmc m + η m, (3) q = q + π π m q, (3) where γ = ( σ) µ, ϑ = ( ) v λ, κi = ( βθ i ) ( θ i ) θ i (i = {, m}) and η and η m are reduced-form expreion for he ime-varying co-hif parameer in he ecoral New Keyneian Phillip curve. In Secion 4 we will conider alernaive moneary policy rule o cloe he model. The model i calibraed a a quarerly frequency. We aume ha he dicoun facor β =.993. We e σ =, a value in line wih Ngai and Piaride (7), ha implie eparabiliy in he uiliy derived from differen conumpion good. Following Horvah (), we e he expendiure hare on ervice (µ ) o.6. He meaure he conumpion weigh a he average expendiure hare in he Naional Income and Produc Accoun (NIPA), from 959 o 995. The invere of he Frich elaiciy of The eady ae condiion are repored in Appendix B. We omi he ime ubcrip o denoe variable in he eady ae. Appendix C preen he economy under flexible price. (9) 8

9 labor upply (v) i e o 3, while λ =, which reflec limied labor mobiliy. 3 A o he parameer included in he producion echnologie of he wo ecor, we refer o Bouakez, Cardia, and Ruge-Murcia (9) and e α =.5 and α m =.75. The enrie of he inpu-oupu marix are e in accordance wih he inpu-ue able of he US economy: γ =.86 and γ m =.4. 4 Thee number are in line wih he enrie of he US inpu-ue able. Thee value imply a poiive ne flow of inpu maerial from he ervice ecor o he manufacuring ecor. 5 A differen age of he analyi we allow for boh ymmeric and aymmeric degree of nominal rigidiy acro ecor. In he ymmeric cae we e θ = θ m =.75. Finally, we aume ha ecoral elaiciie of ubiuion have a eady ae value equal o. A dicued above, he yem feaure wo ecor-pecific echnology hock, z and z m and wo co-puh hock, η and η m. Exogenou variable are aumed o follow a fir-order aionary VAR wih iid innovaion and diagonal covariance marix. We e he parameer capuring he perience and variance of he produciviy growh ochaic procee o ha ρ z = ρ zm =.95 and σ z = σ zm =., repecively. A o he co-puh hock, we follow Jenen (), Walh (3) and Srum (9), and aume ha hee are purely raniory, wih σ η = σ ηm =.. 3 The Pareo Opimum Removing ource of diorion in he labor marke (imperfec labor mobiliy) and he good marke (monopoliic compeiion) repreen a deirable iuaion for a benevolen cenral banker. A hi age of he analyi we are inereed in underanding wheher, afer removing hee diorion (in a varian economy wihou co-puh hock), he moneary auhoriy can aain a fir be allocaion where inflaion and he oupu gap in boh ecor are joinly abilized. The anwer o hi queion i negaive for general parameer value and hock procee. The following propoiion formalize our reul. Propoiion In he model wih icky price and perfec labor mobiliy acro ecor, here exi no moneary policy ha can aain he Pareo opimal allocaion unle he hock buffeing he ervice ecor equal he one buffeing he manufacuring ecor, caled by a facor ζ = ( α ) / ( α m ). 6 Proof. See Appendix D. Thi reul i in line wih Huang and Liu (5), who emphaize ha verical rade linkage caue boh aggregae oupu and he relaive price o flucuae in repone o produciviy hock, unle hee are idenical, in which cae only oupu would flucuae. 3 Thi value i in line wih he calibraion propoed by Horvah () and Bouakez, Cardia, and Ruge- Murcia (). The lieraure on wo-ecor model ha generally conidered eiher perfec mobiliy (e.g., Huang and Liu, 5 and Srum, 9) or immobiliy (e.g., Aoki, and Erceg and Levin, 6). A value of λ = allow u o capure low equalizaion of nominal wage, which i conien wih he empirical evidence (e.g., Davi and Haliwanger, ). 4 Thee hare have been compued uing he able "The Ue of Commodiie by Indurie" for 99, produced by he Bureau of Economic Aciviy (BEA). The inpu-ue able ha diplayed remarkable abiliy ince afer he 8. 5 Moreover, hey imply ha he marginal impac of change in he relaive price on he real ecoral marginal co i, in abolue value, higher for he manufacuring ecor, a α m > α and γ m γ m. 6 Allowing for imperfec labor mobiliy would only furher conrain he abiliy of he moneary auhoriy o neuralize echnology hock. 9

10 Therefore, he moneary auhoriy i faced wih a rade-off, a i can abilize eiher he oupu gap or he relaive price gap, bu no boh. I i inereing o noe ha more rericive condiion are required for he full abilizaion of he framework we enviage. Once we aume ha inpu maerial are ued by boh ecor and ha produciviy hock are Hick neural, 7 no only ecoral innovaion need o be perfecly correlaed, bu he producion echnologie need o be he ame acro ecor. 8 4 Opimal Moneary Policy A he cenral bank canno aain he Pareo opimal allocaion we urn our aenion o policy raegie capable of aaining econd be oucome. We explore equilibrium dynamic under he aumpion ha he policy maker can credibly commi o a rule derived from he minimizaion of hi objecive funcion. The opimal policy coni of maximizing he condiional expecaion of ineremporal houehold uiliy ubjec o privae ecor behavioral equaion and reource conrain, a dicued by Woodford (3). 9 To evaluae ocial welfare we ake a econd-order Taylor approximaion o he repreenaive houehold lifeime uiliy. Our procedure follow he andard analyi of Roemberg and Woodford (998), adaped o accoun for he preence of facor demand linkage. The reuling ineremporal ocial lo funcion read a: SW U H (H) H E = β { (σ + ν) (µ c + µ m c m ) + ς [ ϖ (π ) + ( ϖ) (π m ) ]} +.i.p. + O ( ξ 3), (33) where ϖ = φε (κ ς), ς = φε (κ ) + ( φ) ε m (κ m ),.i.p. collec he erm independen of policy abilizaion and O ( ξ 3) ummarize all erm of hird order or higher. According o (33) he welfare crierion aumed by he cenral bank balance, along wih ecoral inflaion variabiliy, flucuaion in aggregae conumpion (or, equivalenly, value added). Thi i a diincive feaure of he model under cruiny, a he preence of inpu maerial implie a non-rivial diincion beween oupu and con- 7 Inead, Huang and Liu (5) aume ha echnological progre i Harrod neural in he final good ecor. Under hi aumpion he Pareo opimum only require he ecoral echnology hock o be perfecly correlaed. 8 I i alo ueful o compare our reul o Aoki (). In hi eing, complee abilizaion of he wo-ecor economy i achieved whenever he cenral bank abilize core inflaion. Here, inead, facor demand linkage are uch ha he relaive price may differ from i level under flexible price even if he cenral bank abilize inflaion in he ickier ecor, unle α = α m and hock are perfecly correlaed. In hi cae ymmeric pa-hrough of he hock ono he wo ecor can be appreciaed and he relaive price i auhomaically abilized. 9 We purue a imele perpecive approach, a in Woodford (999). Thi involve ignoring he condiion ha prevail a he regime incepion, hu imagining ha he commimen o apply he rule deriving from he opimizaion problem had been made in he dian pa. In hi cae, here i no dynamic inconiency in erm of he cenral bank own deciion-making proce. The yem i olved for he evoluion of he endogenou variable by relying on he common pracice dicued, e.g., by Sim (). We aume ha hock ha hi he economy are no big enough o lead o pah of he endogenou variable dian from heir eady ae level. Thi mean ha hock do no drive he economy oo far from i approximaion poin and, herefore, a linear quadraic approximaion o he policy problem lead o reaonably accurae oluion. Appendix E repor he derivaion of he quadraic welfare funcion.

11 umpion. Therefore, i i no longer irrelevan wheher he cenral bank arge oupu or conumpion gap variabiliy. The weigh of he ime-varying erm in (33) can be inerpreed a follow: (i) ς indexe he oal degree of nominal ickine in he economy and i inverely relaed o boh κ m and κ ; (ii) ϖ accoun for he relaive degree of price ickine in he ervice ecor. Alo noe ha he relaive imporance of ecor-pecific inflaion variabiliy depend on he eady ae raio of labor upplied o he ervice ecor o he oal labor force (φ). How do facor demand linkage influence ocial welfare? Figure repor he lo defined over he ubpace of he producion parameer α and α m, for differen hock configuraion. The general paern ugge ha welfare lo increae monoonically in he hare of inermediae good ued o produce ervice, wherea change in he income hare of inpu maerial in he manufacuring ecor exer a negligible impac. Such an aymmeric impac can be acribed o he ervice good ecor being he large ecor and a ne upplier of inpu maerial. Iner Figure abou here To appreciae he acual conribuion of cro-indury inpu-oupu ineracion o he lo of ocial welfare, we compare he lo in he model wih facor demand linkage o ha obained in a model ha feaure a pure roundabou inpu-oupu rucure (i.e., γ = γ mm = ). 3 Figure repor he difference beween he wo loe over he producion parameer ubpace. When boh echnology and co puh hock are in place, facor demand linkage beween ecor induce an aenuaion in he welfare lo wih repec o he alernaive cae. Aenuaion increae in boh α and α m, hough he marginal effec of an increae in he income hare of inpu maerial ued by he manufacuring ecor on he lo of welfare i greaer han ha regiered for he ervice ecor. Thi reflec he role of he ervice ecor a he main inpu upplier of he economy. Imporanly, aenuaion i le eviden when only co puh hock are conidered. Thu, cro-indury flow of inpu maerial are effecive in aenuaing he lo of welfare (compared o he alernaive cae), o he exen ha echnology hock can be regarded a one of he driver of he buine cycle. In fac, facor demand linkage are uch ha ecoral producion under flexible price alway diplay poiive co-movemen, even in he preence of aymmeric echnology hock. Thi feaure implie an endogenou aenuaion of flucuaion in he ecoral conumpion gap ha will be appreciaed in furher deail in he impule-repone analyi of he nex ecion. Iner Figure abou here We are no only concerned wih he direc welfare implicaion of facor demand linkage, bu alo wih cenral bank poenial mipercepion abou heir role in he producion proce. Neglecing cro-indury flow of inpu maerial i likely o generae exce lo wih repec o he welfare crierion conien wih he correcly pecified When α = α m i follow ha φ = L L = Y Y +Y. m I could be noed ha increaing lo may imply emerge a he join oucome of increaing he imporance of he producion facor characerized by price ickine (i.e., inpu maerial), while decreaing he impac of labor, which i remunaraed a a flexible wage. However, noe ha limied labor mobiliy ill implie a real diorion in he labor marke. 3 Such a producion rucure would be imilar o ha employed by Bau (995).

12 model economy. To addre hi iue we implemen he opimal policy under he aumpion ha α = α m =. Figure 3 graph he (percenage) exce lo under mipercepion wih repec o ha aained under he "rue" producion rucure. Exce lo increae in he acual ineniy of ue of inpu maerial. Alo noe ha he marginal impac of miperceiving α i greaer han ha aociaed wih α m. Once again, accouning for he ervice ecor a he large ecor i he key for inerpreaion of hi reul. Iner Figure 3 abou here 4. Impule-repone Analyi under Opimal Moneary Policy To iolae he conribuion of facor demand linkage o he ranmiion of hock under he opimal policy, we compare our baeline eing wih boh model where no croindury flow of inpu maerial are in place and model ha rule ou inpu maerial. Figure 4 repor equilibrium dynamic following a one-andard-deviaion echnology hock in he ervice ecor, under differen aumpion abou he producion rucure. 4 All variable bu he inere rae are repored in deviaion from heir fricionle level. Symmeric nominal rigidiy i aumed, wih θ = θ m = Iner Figure 4 abou here A echnology hock in he ervice ecor caue he producion ervice o become relaively cheaper. However, heir price i prevened from reaching he level conien wih flexible price, hu inducing a negaive conumpion gap of ervice. Negaive comovemen beween he producion gap of he ervice and manufacuring ecor can be appreciaed in he model wihou cro-indury flow of inpu maerial. In hee framework change in he relaive price only affec relaive conumpion of he wo good hrough he marginal rae of ubiuion. Therefore, in he face of a ecoral echnology hock conumer ubiue away from he conumpion good produced by he ecor which ha no been direcly hi by he hock o conume more of he good ha ha become relaively cheaper. Even in he model wih cro-indury flow of inpu maerial negaive co-movemen beween he conumpion gap arie due o hi ubiuion effec. However, facor demand linkage induce poiive co-movemen in he producion gap of manufacured good and ervice hrough increaed demand of inpu maerial from boh ecor. Auming differen rucure of he producion economy ha imporan effec on he way opimal moneary policy hould be purued. In he model wihou facor demand linkage he real inere rae (meaured in uni of ervice) iniially rie, hu prevening oupu (and conumpion) in he ervice ecor from riing a much a i would do under flexible price. Concurrenly, he real rae of inere doe no rie enough o preven he oupu gap in he manufacuring ecor from riing oo much. By conra, in he model 4 The repone o a ecoral innovaion (i.e., a echnology or a co-puh hock) in he manufacuring ecor mirror in he oppoie direcion hoe induced by an analogou hock in he ervice ecor. For hi reaon, and for breviy of expoiion, we kip heir decripion. Thee reul are available upon reque from he auhor. 5 A in Srum (9) we op for hi choice o preven he cenral bank from focuing excluively on he ickier ecor in he formulaion of i opimal policy, a prediced by Aoki (). In he nex ubecion we draw implicaion from he model under aymmeric degree of nominal rigidiy acro ecor.

13 wih facor demand linkage he real inere rae iniially decreae, gradually converging o i equilibrium level hereafer. The reuling real inere rae gap i ignificanly maller han ha appreciaed in he model wihou facor demand linkage. Thi effec i inimaely relaed o he exience of cro-indury flow of inpu maerial ha induce he conumpion of manufacured good under flexible price o increae, hu helping o reduce heir conumpion gap. Such an endogenou mechanim i no a work in he model wihou facor demand linkage, where he conumpion of manufacured good under flexible price i no affeced by he hock, a a reul of eing σ = (which implie eparabiliy of houehold preference in he conumpion of differen good). A o he repone of price, he iner-ecoral inermediae inpu channel i reponible for aenuaing deflaionary preure in he ervice ecor while inducing higher inflaion in he manufacuring ecor, compared o he model wihou inpu maerial. I i worh recalling ha, in he preence of cro-indury flow of inpu maerial, he relaive price doe no only have a direc effec on he marginal rae of ubiuion beween manufacured good and ervice. A hown by equaion () and (), Q alo exer a poiive (negaive) effec on he real marginal co in he manufacuring (ervice) ecor. Thu, he poiive relaive price gap reinforce he convenional inflaionary effec on manufacuring inflaion hrough i influence on he real marginal co. Thi effec, combined wih he expanionary policy purued by he cenral bank, deermine ronger inflaionary preure a he aggregae level in he model wih facor demand linkage, compared o he economy wihou inermediae inpu. When comparing our benchmark economy o ha feauring roundabou producion, deflaion in he ervice ecor i ill aenuaed due o he direc impac of he relaive price on firm real co of producion. A o he manufacuring ecor, he model wih pure roundabou echnology produce much ronger inflaionary preure, which are driven by he ubanial increae in he producion gap. Figure 5 repor equilibrium dynamic following a co-puh hock in he ervice ecor. Boh he model wih facor demand linkage and ha wih roundabou producion diplay an aenuaion in he deflaionary repone of he inflaion rae of manufacured good, compared o he model wihou inpu maerial. However, wherea in he roundabou eing aenuaion i induced by a lower lope of he NKPC - a reul already oberved by Bau (995) - a diincive feaure of he model wih cro-indury flow of inpu maerial i he effec of he relaive price on he marginal co of firm producing manufacured good. A poiive q parially counerac he deflaionary effec ha operae hrough he convenional demand channel, compared o he model wihou inpu maerial. Concurrenly, conracion in he producion of manufacured good i magnified by he preence of facor demand linkage. Iner Figure 5 abou here I i worh drawing aenion o a uble difference in he ranmiion of echnology and co-puh hock in he model wih facor demand linkage. Secoral echnology hock caue he conumpion gap of he wo good o co-move negaively. The drop in he conumpion gap of he ecor ha experience he poiive echnology hock i compenaed by a rie in he demand gap of inermediae good from he oher ecor. Thu, each ecor experience oppoie demand effec on he marke for he conumpion and inermediae good. By conra, a ecoral co-puh hock deermine a conracion of final good conumpion in boh ecor, which caue a drop in he conumpion of boh ype of inermediae good, hu reuling in an even greaer lump in he gro 3

14 oupu. 6 Thee feaure of he ranmiion mechanim have imporan implicaion for he elecion of alernaive policy regime, a hown in he nex ecion. 4. Opimal Moneary Policy veru Alernaive Policy Regime We now ae he lo of welfare under he opimal policy and variou alernaive policie. 7 Alernaive regime admi imple lo funcion, which are eleced becaue of heir uiabiliy o be communicaed o and underood by he public. We ue he econd-order welfare approximaion (33) a a model-conien meric. In each cae we compue he expeced welfare lo a he percenage of eady ae aggregae conumpion (and muliply he reuling erm by ). The following period lo funcion are evaluaed: Sric inflaion argeing: Gap argeing: Flexible inflaion argeing: WIT WGT IT WF ) = ( π IT ) GT = ( x = (σ + ν) W GT IT + ς W Thu, we conider boh ric and flexible inflaion argeing regime, a well a conumpion and oupu gap argeing. Inflaion argeing regime may arge eiher core or aggregae inflaion (i.e., π IT = {π core, π agg }). In he fir cae he weigh aached o he ecoral rae of inflaion depend on he relaive degree of price rigidiy, a well a on he relaive ize of each ecor and he degree of ubiuabiliy among differeniaed good (π core = ϖπ + ( ϖ) π m ). In he econd cae he weigh aached o ecoral inflaion only depend on he relaive ize of each ecor (π agg = φπ +( φ) π m ). Flexible inflaion argeing regime balance flucuaion in core or aggregae inflaion ogeher wih a erm ha penalize flucuaion in aggregae conumpion or gro oupu (i.e., x GT = { x c, x p }, where x c = µ c +µ m c m and x p = φỹ +( φ) ỹ m ). The weigh aached o he erm capuring variabiliy in real aciviy ( W GT ) and inflaion variabiliy ( W IT ) are he ame a hoe appearing in he welfare crierion derived from he econd-order approximaion. 8 Noe ha boh ric or flexible inflaion argeing regime aim a abilizing he volailiy of aggregae (or core) inflaion and no he volailiy of ecoral inflaion eparaely. From a raegic viewpoin we are willing o underand wheher he cenral bank can approximae he opimal policy oucome wihou aking he ecoral rae of inflaion a eparae objecive, a uggeed by he welfare crierion we have derived. In principle, hi hould enable he moneary auhoriy o provide he public wih a more inelligible arge. Svenon (997) ree he imporance of auming inermediae arge which 6 Imporanly, imperfec labor mobiliy exacerbae hi effec, increaing he wedge beween conumpion and producion. When aggregae demand increae, a labor canno flow acro ecor wihou fricion, firm need o increae inermediae inpu by more han hey would do under he aumpion of perfec labor mobiliy o mee higher demand. Conequenly, flucuaion in producion and conumpion are wider in he preence of imperfec labor mobiliy. 7 In hi ecion we ill conider he opimal moneary policy from a imele perpecive. Neverhele, i i imporan o acknowledge ha i would alo be poible o conruc a dicreionary regime wih a differen lo funcion capable o ouperform commimen (Denni, ). 8 Aigning he ame weigh o producion and conumpion variabiliy in he flexible inflaion argeing regime hould help u a appreciaing he addiional lo induced by a cenral bank ha erroneouly conider producion gap variabiliy and conumpion gap variabiliy a inerchangeable from he perpecive of evaluaing he moneary policy rade-off. 4

15 are highly correlaed wih he goal, eay o conrol, and ranparen - o a o enhance communicaion o he public. In hi ene, meaure of overall inflaion are more uiable han ecoral rae of inflaion. 9 Table repor he welfare lo under he opimal rule and he alernaive regime. The overall lo i diaggregaed ino he variabiliy of each erm weighed in (33). In he fir inance boh echnology and co-puh hock are aumed o buffe he model economy. Moreover, we aume ha ecor are ymmeric in he degree of nominal rigidiy (θ m = θ =.75): in hi cae π core = π agg. Laer in hi ecion we will relax hi aumpion. Iner Table abou here A expeced on a priori ground, whenever co-puh hock are accouned for, a flexible inflaion argeing regime perform nearly a well a he opimal policy, while oher policie diplay a poor performance. Mo imporanly, he cenral bank aain a welfare lo cloer o ha under he opimal policy when flucuaion in aggregae (or core) inflaion are balanced wih hoe in he aggregae value added (i.e., conumpion), compared o he lo induced by conrolling flucuaion in he gro oupu (i.e., producion). Recall from Secion 4. ha ecoral hock ypically induce higher variabiliy in aggregae producion han conumpion. 3 Therefore, auming a welfare crierion ha balance flucuaion in he rae of inflaion wih gro oupu variabiliy mirepreen he acual rade-off faced by he cenral bank. Indeed, according o (33) inflaion variabiliy hould be balanced wih flucuaion in conumpion raher han gro oupu. Iner Table abou here Table repor he relaive performance of alernaive policy regime under differen ource of exogenou perurbaion. Once again, flexible inflaion argeing ouperform oher alernaive. Thi i alo he cae when hock o eiher ecor are conidered eparaely (ee Table, column 3 and 4). A noed by Woodford (3, pp ), ric inflaion argeing diplay a "compeiive" performance only when echnology hock are he unique ource of perurbaion o he yem, wherea accouning for co-puh hock enail a raher poor performance. In addiion, i i worh poining ou ha producion gap argeing ouperform conumpion gap argeing only when co-puh hock are accouned for. In hi cae, reducing conumpion gap volailiy allow he cenral bank o conrol ju par of he volailiy in he real marginal co, wherea argeing he producion gap parially accoun for he preence of he inermediae inpu channel. 3 9 Noe ha accouning for ecoral inflaion volailiie enail izeable advanage, compared o reducing he volailiy of an aggregae index of price change, whenever q ha a direc influence on he lo of welfare (a, e.g., Aoki,, Huang and Liu, 5 and Srum, 9). In hi cae, an explici repone o ecoral inflaion rae allow he cenral bank o indirecly conrol flucuaion in he relaive price. However, in our eing relaive price volailiy doe no appear a a direc objecive in he lo funcion. Thu, we hould no expec he cenral bank o incur ino greaer loe when implemening policie ha diregard ecoral inflaion volailiie. 3 A poiive co-puh hock conrac he demand for boh ype of conumpion good, hu depreing he demand of inpu maerial and cauing an even greaer lump in ecoral gro oupu. Oherwie, when a echnology hock ake place, inpu-oupu ineracion induce poiive co-movemen beween ecoral producion, wherea he conumpion gap move in oppoie direcion and end o offe each oher. 3 In urn, ecoral inflaion volailiy alo benefi from hi effec (ee Table, column and ). 5

16 Oherwie, when echnology hock are conidered, conumpion gap argeing ouperform producion gap argeing; he reaon being ha he producion and conumpion gap a he aggregae level end o co-move negaively and ha he ecoral conumpion gap are le volaile han heir producion counerpar, a hined in he analyi of Secion 4.. Iner Table 3 abou here Table 3 repor he lo of welfare under aymmeric price ickine, in he form of manufacured good price being more flexible han he price of ervice (θ =.75, θ m =.5). 3 In hi cae, core inflaion differ from aggregae inflaion, a dicued earlier. Conidering core inflaion argeing a an alernaive o aggregae inflaion argeing i omewha relaed o a long-anding debae concerning he informaion (in erm of relaive ecoral price ickine) ha he cenral bank can acce when formulaing i policy. Woodford (3) how ha, in a wo-ecor model wih no inpu maerial, opimal commimen policy i nearly replicaed by an inflaion argeing regime, whereby he weigh aached o ecoral inflaion depend on he relaive degree of nominal ickine. 33 A expeced, hi reul can only be replicaed if we rule ou ecoral co-puh hock. 34 Oherwie, when aeing alernaive flexible argeing regime in he model wih aymmeric price ickine, he dichoomy beween aggregae and core inflaion loe much of he uual appeal in erm of comparing welfare loe. Once again, wha eem relevan and inherenly conneced wih he preence of inpu maerial i he diincion beween oupu and conumpion. In fac, a flexible inflaion argeing regime ha balance conumpion and (eiher core or aggregae) inflaion variabiliy deliver a lo of welfare yemaically lower han ha aained under a lo funcion balancing oupu and (eiher core or aggregae) inflaion variabiliy, which mirepreen he acual rade-off faced by he cenral bank. 5 Concluion We have inegraed iner-ecoral facor demand linkage ino a dynamic general equilibrium model wih wo ecor ha produce ervice and manufacured good. Par of he oupu produced in each ecor i ued a an inermediae inpu of producion in boh ecor, according o a realiic inpu-oupu rucure of he economy. The reuling ecoral ineracion have non-negligible implicaion for he formulaion of policie aimed a reducing real and nominal flucuaion. A key role i played by he relaive price, which no only ac a an allocaive mechanim on he demand ide (hrough i influence on he marginal rae of ubiuion beween differen clae of conumpion good), bu alo on he upply ide (hrough i effec on he ecoral real marginal co of producion). 3 Bil and Klenow (4) and Nakamura and Seinon (8a) repor evidence of higher frequency of price adjumen for manufacured good han ervice. 33 Aoki () how ha he welfare-heoreic lo funcion conien wih a muli-ecor economy wih heerogeneou degree of price ickine aign higher weigh on he inflaion variabiliy of ecor characerized by higher nominal ickine. Thi provide a heoreical raionale for eeking o abilize an appropriaely defined meaure of "core" inflaion raher han an equally weighed price index. 34 Noe ha core inflaion argeing reurn he ame lo a ha oberved under he opimal policy. However, hi reul only hold when he difference in he ecoral degree of nominal rigidiy i very large, a in he paricular cae we conider (ee alo Aoki, ). 6

17 The preence of inpu maerial implie a non-rivial difference beween aggregae conumpion (or, equivalenly, value added) and gro oupu. Such a diincion prove o be of crucial imporance a differen age of he analyi. In fac, he welfare crierion conien wih he econd-order approximaion o houehold uiliy reveal ha he policy maker i faced wih he ak of abilizing flucuaion in he ecoral rae of inflaion and aggregae value added, raher han gro oupu. Moreover, raegic complemenariie induced by facor demand linkage aler he ranmiion of hock o he yem, compared o wha i commonly oberved in oherwie andard wo-ecor model. Thee reul how how accouning for a realiic feaure of muli-ecor economie enail non-negligible difference wih repec o he policy precripion rerievable for framework ha rule ou inpu-oupu ineracion or conider a verically inegraed producion rucure. The opimal policy can be cloely approximaed by a flexible inflaion argeing regime. However, i i of crucial imporance o arge conumpion gap variabiliy raher han oupu gap variabiliy. Thi raegy allow he cenral bank o avoid inducing addiional lo emanaing from iner-ecoral complemenariie. 7

18 Reference A, K. (): Opimal Moneary Policy Repone o Relaive Price Change, Journal of Moneary Economic, 48, B, R. B., C. L. H, M. S. K (7): Sicky-Price Model and Durable Good, American Economic Review, 97(3), B, S. (995): Inermediae Good and Buine Cycle: Implicaion for Produciviy and Welfare, American Economic Review, 85(3), 5 3. B, M., P. J. K (4): Some Evidence on he Imporance of Sicky Price, Journal of Poliical Economy, (5), B, H., E. C, F. J. R -M (9): The Tranmiion of Moneary Policy in a Muli-Secor Economy, Inernaional Economic Review, 5(4), (): Durable good, iner-ecoral linkage and moneary policy, Journal of Economic Dynamic and Conrol, 35(5), C, V. M. (9): Aggregae Flucuaion and he Nework Srucure of Inerecoral Trade, Mimeo, Univeria Pompeu Fabra. C, L. J., T. J. F (998): The buine cycle: i ill a puzzle, Economic Perpecive, (Q IV), D, S. J., J. H (): Secoral job creaion and derucion repone o oil price change, Journal of Moneary Economic, 48(3), D, R. (): When i dicreion uperior o imele perpecive policymaking?, Journal of Moneary Economic, 57(3), E, C., A. L (6): Opimal moneary policy wih durable conumpion good, Journal of Moneary Economic, 53(7), H, S., I. P (): Facor demand linkage, echnology hock and he buine cycle, Cener for Economic Sudie - Dicuion paper ce.6, Kaholieke Univeriei Leuven, Cenrum voor Economiche Sudiën. H, A., J. P (997): Inermediae inpu and ecoral comovemen in he buine cycle, Journal of Moneary Economic, 4(3), H, M. (998): Cyclicaliy and Secoral Linkage: Aggregae Flucuaion from Independen Secoral Shock, Review of Economic Dynamic, (4), (): Secoral hock and aggregae flucuaion, Journal of Moneary Economic, 45(), H, K. X. D., Z. L (5): Inflaion argeing: Wha inflaion rae o arge?, Journal of Moneary Economic, 5(8), J, H. (): Targeing Nominal Income Growh or Inflaion?, American Economic Review, 9(4),

19 K, Y. S., K. K (6): How Imporan i he Inermediae Inpu Channel in Explaining Secoral Employmen Comovemen over he Buine Cycle?, Review of Economic Dynamic, 9(4), L, J., C. P (983): Real buine cycle, Journal of Poliical Economy, 9, N, E., J. S (8a): Five Fac abou Price: A Reevaluaion of Menu Co Model, The Quarerly Journal of Economic, 3(4), N, E., J. S (8b): Moneary Non-Neuraliy in a Muli- Secor Menu Co Model, NBER Working Paper 4, Naional Bureau of Economic Reearch, Inc. N, L. R., C. A. P (7): Srucural Change in a Muliecor Model of Growh, American Economic Review, 97(), P, I., E. S (): Opimal Moneary Policy wih Durable Conumpion Good and Facor Demand Linkage, MPRA Paper 3, Univeriy Library of Munich, Germany. R, J. J., M. W (998): An Opimizaion-Baed Economeric Framework for he Evaluaion of Moneary Policy: Expanded Verion, NBER Technical Working Paper 33, Naional Bureau of Economic Reearch, Inc. S, C. A. (): Solving Linear Raional Expecaion Model, Compuaional Economic, (-),. S, B. E. (9): Moneary Policy in a Forward-Looking Inpu-Oupu Economy, Journal of Money, Credi and Banking, 4(4), S, N. (8): Secoral Co-Movemen, Moneary-Policy Shock, and Inpu-Oupu Srucure, IMES Dicuion Paper Serie 8-E-5, Iniue for Moneary and Economic Sudie, Bank of Japan. S, L. E. O. (997): Inflaion foreca argeing: Implemening and monioring inflaion arge, European Economic Review, 4(6), 46. W, C. (3): Speed Limi Policie: The Oupu Gap and Opimal Moneary Policy, American Economic Review, 93(), W, M. (999): Commenary on: how hould moneary policy be conduced in an era of price abiliy?, in New Challenge for Moneary Policy, A Sympoium Sponored by he Federal Reerve Bank of Kana Ciy, pp (3): Inere and Price: Foundaion of a Theory of Moneary Policy. Princeon Univeriy Pre. 9

20 Table and Figure TABLE : WELFARE UNDER ALTERNATIVE POLICIES Lo Componen π π m x Toal Opimal Policy Inflaion Targeing Conumpion Gap Targeing Producion Gap Targeing Flexible Inflaion Targeing (wih Conumpion) Flexible Inflaion Targeing (wih Oupu) Noe: x = µ c +µ m c m. The welfare lo i compued a a percenage of eady ae aggregae conumpion (muliplied by ). TABLE : W ELFARE UNDER ALTERNATIVE POLICIES AND DIFFERENT SHOCK CONFIGURATIONS Tech. Shock Co Puh Shock Ser. Sec. Shock M an. Sec. Shock Opimal Policy Inflaion Targeing C onum pion G ap Targeing P ro ducion G ap Targeing F lexible Inflaion Targeing (w ih C onum pion) F lexible Inflaion Targeing (w ih O upu) Noe: The fir wo column repor he lo aribuable o echnology hock and co-puh hock generaed in boh ecor, repecively. The la wo column repor he lo due o boh hock o eiher ecor. The welfare lo i compued a a percenage of eady ae aggregae conumpion (muliplied by ).