The Impact of Introducing a Minimum Wage on Business Cycle Volatility: A Structural Analysis for Hong Kong SAR

Transcription

1 W/08/85 he Impac o Iroducig a iimum Wage o Buie ycle Volailiy: A Srucural Aalyi or Hog Kog SAR Naha orer ad Fraci Viek

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3 008 Ieraioal oeary Fud W/08/85 IF Workig aper Aia ad aciic Deparme he Impac o Iroducig a iimum Wage o Buie ycle Volailiy: A Srucural Aalyi or Hog Kog SAR repared by Naha orer ad Fraci Viek Auhoried or diribuio by Nigel halk December 008 Abrac hi Workig aper hould o be repored a repreeig he view o he IF. he view expreed i hi Workig aper are hoe o he auhor() ad do o ecearily repree hoe o he IF or IF policy. Workig aper decribe reearch i progre by he auhor() ad are publihed o elici comme ad o urher debae. We udy he impac o a miimum wage o buie cycle volailiy depedig upo i coverage ad adjume mechaim. A wih oher mall ope ecoomie Hog Kog SAR i vulerable o exeral hock wih i exchage rae regime precludig acive moeary policy. Adjume o pa hock ha relied o lexible domeic price. We id ha a miimum wage aecig 0 perce o employee would ampliy oupu volailiy by 0. perce o 9. perce ad employme volailiy by. perce o 7.8 perce. A ixed wage or idexaio o coumpio price ilaio icreae volailiy mo. Idexaio o wage ilaio or ui labor co growh i preerable largely preervig labor marke lexibiliy. JE laiicaio Number: 3 3 E4 E7 F4 Keyword: iimum wage idexaio mechaim buie cycle volailiy dyamic ochaic geeral equilibrium model uoberved compoe model marke lexibiliy mall ope ecoomy Auhor E-ail Addre: [email protected]; [email protected] he auhor graeully ackowledge comme ad uggeio received rom Nigel halk Hog Kog SAR abor Deparme ad emiar paricipa a he Hog Kog oeary Auhoriy.

4 oe age I. Iroducio...3 II. hagig Iequaliy ad he Wage roecio oveme...4 III. he heoreical ad Empirical Framework...5 IV. Wha Impac Will a iimum Wage Have o acroecoomic Adjume?...7 V. ocluio...4 Reerece...54 Figure. Noparameric Eimae o he abor Icome Diribuio...5. Icreae i Buie ycle Volailiy aued by Iroducig a iimum Wage Impule Repoe o a Domeic Supply Shock Impule Repoe o a Foreig Supply Shock Impule Repoe o a Domeic Demad Shock Impule Repoe o a Foreig Demad Shock Impule Repoe o a Domeic oeary odiio Shock Impule Repoe o a Foreig oeary odiio Shock...4 able. Hog Kog SAR: Gii oeicie or Icome Iequaliy Icreae i Buie ycle Volailiy aued by Iroducig a iimum Wage...8 Appedice. odel Developme Eimaio rocedure ad Eimaio Reul...6. Decripio o he Daa Se...53 Appedix able I. Deermiiic Seady Sae Equilibrium Value o Grea Raio...48 I. arameer Eimaio Reul...5

5 3 I. INRODUION wo year ago amid cocer over growig icome iequaliy i Hog Kog SAR he goverme iroduced a voluary miimum wage or eleced low wage occupaio. A review o hi voluary cheme recely cocluded ha i had bee raher ieecive i providig icome uppor o he workig poor. Give he ieecivee o he voluary cheme he goverme o Hog Kog ow pla o iroduce a uiveral auory miimum wage. While hi will provide wage proecio he goverme realie he eed o balace everal acor icludig he impac o he miimum wage o iequaliy employme buie operaio ilaio ad overall compeiivee whe deigig he miimum wage. A a relaively mall ad ope ecoomy ervig a a iermediaig hub or ieraioal rade ad iveme low Hog Kog SAR i coiderably expoed o hock ramied via rade ad iacial chael. Adjume o hee hock ha hiorically relied heavily o he lexibiliy o domeic good labor ad ae price give ha i rigid exchage rae arrageme (he iked Exchage Rae Syem) preclude a abiliaio role or moeary policy ad wih ical policy coraied by lag ad coiuioal limi. I oher word he moeary ad ical arrageme i Hog Kog place a premium o hi marke lexibiliy. oequely he iroducio o he miimum wage hould be doe i a way which preerve Hog Kog domeic price lexibiliy. hi paper aalye he impac o iroducig a auory miimum wage o buie cycle volailiy ad adjume o hock or diere level o coverage ad variou ype o adjume mechaim. hi aalyi i coduced wihi he ramework o a dyamic ochaic geeral equilibrium (DSGE) model o a mall ope ecoomy eimaed o i daa or Hog Kog SAR ad i mo ilueial radig parer he Uied Sae. hi model i imilar o ha ued by orer ad Viek (008) o uderad he driver o Hog Kog avig ad iveme low. However relecig he challege o uderadig he impac o a miimum wage we have augmeed he labor marke o ha model. I paricular houehold dier wih a ixed meaure upplyig ukilled labor ad paid he bidig legilaed miimum wage wih he remaiig houehold upplyig killed labor ad permied o opimally ree heir wage whe (radomly) able o do o. oequely killed idividual paricipae i he (relaively more) lexible labor marke while ukilled idividual paricipae i a eparae ad highly regulaed labor marke where wage are e accordig o he rule goverig he miimum wage. odiioal o a curre miimum wage he wage i aumed o adju ollowig ome e idexaio rule. I paricular we compare ive aleraive mechaim or adjuig he miimum wage: o idexaio (ixed miimum wage) idexaio o aggregae wage ilaio idexaio o ui labor co growh idexaio o coumpio price ilaio ad idexaio o he um o coumpio price ilaio ad average labor produciviy growh.

6 4 We id ha iroducig a miimum wage i Hog Kog SAR ha he poeial o elevae macroecoomic volailiy ad dior he dyamic repoe o he ecoomy o hock. Ideed iroducig a miimum wage which bid or 0 perce o houehold i eimaed o ampliy he volailiy o oupu over he buie cycle by 0. perce o 9. perce ad o employme by. perce o 7.8 perce. hee wide rage reveal he eiiviy o he eec o iroducig a miimum wage o he mechaim or adjuig i over ime. We alo id ha he reiliece o he ecoomy o Hog Kog o hock aecig i exeral price compeiivee ca be largely preerved hrough judiciou choice o he mechaim or adjuig he miimum wage over ime. I paricular idexaio o he miimum wage o aggregae wage ilaio i oud o domiae aleraive adjume mechaim wih o idexaio or idexaio o coumpio price ilaio paricularly booig volailiy. hi reul i robu o variaio i he coverage o he miimum wage ad he ource o buie cycle lucuaio. he orgaiaio o hi paper i a ollow. he ex ecio decribe he chagig paer o icome iequaliy over ime a well a he broad parameer o he voluary miimum wage cheme rialed by he goverme bewee 006 ad 008. he DSGE model o Hog Kog SAR he eimaio echique ad he eimaio reul are oulied i ecio hree. Ierece o he eec o iroducig a miimum wage i Hog Kog o he bai o ucodiioal adard deviaio ad impule repoe ucio i coduced i ecio our. Fially ecio ive oer cocluio ad recommedaio or urher reearch. II. HANGING INEQUAI AND HE WAGE ROEION OVEEN Riig iequaliy ha become a igiica policy iue i Hog Kog SAR i rece year. Alhough he exe o iequaliy i hard o meaure here are clear ig ha iequaliy ha icreaed over he pa decade. Uig daa rom ucceive populaio ceue he goverme ha eimaed gii coeicie which how ha iequaliy baed o houehold (raher ha idividual) icome icreaed bewee 996 ad 006. ax ad raer payme have eded o miigae he icreae i icome iequaliy bu iequaliy remai high. able. Hog Kog SAR: Gii oeicie or Icome Iequaliy Origial houehold mohly icome o ax o ax ad raer er capia ad po ax ad raer Source: 006 opulaio By-eu hemaic Repor: Houehold Icome Diribuio i Hog Kog. A imilar paer o riig iequaliy i idicaed by lookig a average mohly icome daa. Uig daa o employme ad average wage by occupaio (ad kerel deiy eimaio) Figure how ha o oly ha here bee ubaial cro-ecoral iequaliy or ome ime bu ha i ha icreaed over he pa decade. I paricular relecig appare egmeaio o Hog Kog SAR labor marke bewee killed ad ukilled worker he icome diribuio i bimodal. he diace bewee hee mode i large relaive o he uppor o he labor icome diribuio

7 5 (aroud hal o he uppor) ad mo o i ma i coceraed uder he lower mode. A meaured by he adard deviaio o labor icome iequaliy icreaed by.6 perce rom 997 o 007. o provide urher iormaio o he exe o iequaliy ad iorm he eig o he miimum wage he goverme i plaig o ehace he exe o available labor marke ad icome daa. Figure. Noparameric Eimae o he abor Icome Diribuio / perce quaile 0 perce quaile 30 perce quaile ohly labor icome (HK$ houad) perce quaile 0 perce quaile 30 perce quaile ohly labor icome (HK$ houad) Sadard deviaio=6.77 Skewe= Sadard deviaio=8.30 Skewe= / robabiliy deiy ucio are eimaed wih a ormal kerel employig a badwidh o.5. Relecig cocer over he appare rie i iequaliy he goverme lauched a voluary miimum wage he Wage roecio oveme i Ocober 006. I mai aim wa o provide a livig icome o worker i wo low wage occupaio: cleaer ad ecuriy guard. ompaie ha paricipaed i he cheme agreed o oer heir cleaig worker ad ecuriy guard wage a lea equal o he releva average marke wage prevailig a he ime (a meaured by he eu ad Saiic Deparme). hey were alo o eer io a wrie corac wih hoe worker hey direcly employed a well a heir coracor ad ubcoracor providig cleaig ad ecuriy ervice. A review o he cheme compleed i Ocober 008 oud ha alhough here had bee a icreae i he umber o worker beeiig rom he cheme over he wo year he perormace o he cheme had bee uaiacory. A a reul he goverme i ow commied o movig orward wih he legilaive work or a auory miimum wage. he heoreical Framework III. HE HEOREIA AND EIRIA FRAEWORKS hi paper aalye he impac o iroducig a auory miimum wage o buie cycle volailiy ad adjume o hock a i coverage ad adjume mechaim varie. hi aalyi i coduced wihi he ramework o a DSGE model o a mall ope ecoomy eimaed o i daa or Hog Kog SAR ad i mo ilueial radig parer he Uied Sae. Wih he model much he ame a ha i orer ad Viek (008) i hi ecio we oly provide a brie ummary o i ocuig o i ovel eaure. omplee decripio o he model eimaio procedure ad eimaio reul are laid ou i Appedix I.

8 6 he rucure o he DSGE model i airly adard alhough he labor marke ha bee ehaced o diereiae ype o labor (hoe wih low kill who are ubjec o he miimum wage ad hoe wih high kill who are o) ad give Hog Kog SAR aure a a radig hub here i a deailed erepô rade ecor. Followig Sme ad Wouer (003) hi DSGE model eaure hor ru omial price ad wage rigidiie geeraed by moopoliic compeiio aggered reopimiaio ad parial idexaio i oupu ad labor marke. hi aggered wage eig i applicable o high killed idividual who have moopoly power i he labor marke while hoe wih low kill are ubjec o he miimum wage. Followig hriiao Eichebaum ad Eva (005) ilaio ieria ad oupu periece are ehaced wih habi periece i coumpio ad employme adjume co i iveme ad variable capial uiliaio. Followig oacelli (005) icomplee exchage rae pa hrough i geeraed by hor ru omial price rigidiie i he impor ad expor marke. hi heoreical ramework i exeded o allow or erepô rade. he pricipal ovely o he model developed here i egmeaio o he labor marke bewee hoe wih low icome ha are proeced by he miimum wage ad hoe wih higher icome ubjec o ypical wage rigidiie. For racabiliy we aume ha a here are u a ixed proporio o houehold ϕ ha are ubjec o miimum wage W ad ha hi wage bid i all ae o he ecoomy or hee idividual. he remaiig killed idividual e heir wage W ubjec o radomly arrivig reopimiaio opporuiie. Give hi rucure he aggregae wage (i deviaio rom eady ae ad relaive o heir produciviy A ) i give by: ˆ ˆ u ˆ W W W l = ϕ l + ( ϕ ) l. () ˆ ˆu ˆ A A A he miimum wage i aumed o adju over he buie cycle i a imple rapare ad auomaic way. Speciically i i aumed o be poeially idexed o up o hree variable: aggregae wage W ilaio average labor produciviy y growh ad coumpio price ilaio. he idexed miimum wage hereore aiie W y u u W l l y l l l l u W = γ + γ l W + γ + W y () where 0 l W γ 0 l l / γ ad 0 γ are he weigh aached o he variou 5 idexaio variable. We deoe our ive experime by { m( ϕ )} m= 0 where ϕ meaure he proporio o houehold ubjec o a bidig miimum wage ad m i he ype o idexaio. Uder 0 here doe o exi a miimum wage repreeed by ϕ = 0. Uder () he miimum wage i o idexed repreeed by u W γ = 0 u γ = 0 ad u y γ = 0.

9 7 I cora uder () he miimum wage i ully idexed o pa aggregae wage u W ilaio repreeed by γ = u γ = 0 ad u y γ = 0. Uder () 3 he miimum wage i ully idexed o pa aggregae wage ilaio le average labor produciviy growh u W repreeed by γ = u γ = 0 ad u y γ =. Uder () 4 he miimum wage i ully u W u idexed o pa coumpio price ilaio repreeed by γ = 0 γ = ad u y γ = 0. Fially uder () 5 he miimum wage i ully idexed o he um o pa coumpio u W u price ilaio ad average labor produciviy growh repreeed by γ = 0 γ = ad u y γ =. he Empirical Framework Followig Viek (008a 008b) eimaio ad ierece i baed o a approximae liear uoberved compoe repreeaio o hi DSGE model o a mall ope ecoomy. arameer ad uoberved compoe are joily eimaed over he rece iked Exchage Rae Syem period wih a Bayeia procedure codiioal o prior iormaio cocerig he value o parameer ad judgme cocerig he pah o red compoe. For a deailed decripio o hi empirical ramework pleae reer o Appedix I. IV. WHA IA WI A INIU WAGE HAVE ON AROEONOI ADJUSEN? We aalye he eec o iroducig a auory miimum wage o buie cycle volailiy i Hog Kog SAR a i coverage ad adjume proce varie uig ucodiioal adard deviaio ad impule repoe ucio. I a ope ecoomy buie cycle are maieaio o he cumulaive eec o a variey o omial ad real hock origiaig domeically ad abroad ad ucodiioal adard deviaio ummarie heir average volailiy. I cora impule repoe ucio reveal he dyamic repoe o he ecoomy o iolaed hock. I our experime we aume or illuraive purpoe ha he proporio o houehold ubjec o he miimum wage i a icreaig ucio o he level o he miimum wage bu i ceered aroud 0 perce. Ucodiioal Sadard Deviaio orai o he coduc o moeary ad ical policy i Hog Kog SAR have hiorically bee couerbalaced by relaively lexible oupu ad labor marke which uderpi he reiliece o he ecoomy o hock impigig o i exeral price compeiivee. Give i rog rade ad iacial likage wih he re o he world he expoure o he ecoomy o Hog Kog o uch hock i prooud. he eimaed eec o iroducig a miimum wage o he buie cycle volailiy o key oupu ad labor marke variable i Hog Kog are depiced i Figure. We compare he icreae i he ucodiioal adard deviaio o oupu price ilaio oupu wage ilaio ad employme acro wo dimeio o he miimum wage: i coverage ad he proce by which i i adjued over ime.

10 8 Eimaed ucodiioal adard deviaio idicae ha iroducig a miimum wage i Hog Kog SAR which bid or 0 perce o houehold will ampliy he volailiy o oupu over he buie cycle by 0. perce o 9. perce ad o employme by. perce o 7.8 perce. hee wide rage reveal he eiiviy o he eec o iroducig a miimum wage o he mechaim or adjuig i over ime. Iroducig a miimum wage wihou idexig i i eimaed o ilae he buie cycle volailiy o oupu by 9. perce a he 0 perce coverage level ad o employme by 6.6 perce. Neverhele iroducig a miimum wage idexed o aggregae wage ilaio i eimaed o ampliy he volailiy o oupu over he buie cycle by oly 0. perce a hi coverage level ad o employme by oly 0. perce. Iroducig a miimum wage idexed o oher variable i eimaed o ilae buie cycle volailiy o iermediae degree. able. Icreae i Buie ycle Volailiy aued by Iroducig a iimum Wage / echaim (0.) (0.) (0.) 3 (0.) 4 (0.) 5 Oupu price ilaio Oupu Wage ilaio Employme / Repor he icreae i he ucodiioal adard deviaio o cyclical compoe caued by iroducig miimum wage mechaim m (0.). Ucodiioal adard deviaio are calculaed wih a oe arlo imulaio wih 999 replicaio or period dicardig he ir imulaed obervaio o elimiae depedece o iiial codiio where deoe he oberved ample ie. Idexaio o he miimum wage o aggregae wage ilaio reore oupu ad labor marke eiciecy more rapidly i repoe o hock ha aleraive adjume mechaim. I repoe o a hock which aec exeral price compeiivee reorig labor marke eiciecy require realigig he margial rae o ubiuio o houehold bewee leiure ad coumpio wih heir aer ax real wage. A ube o he killed houehold are able o adju heir wage opimally i a give period (doig o o equae he expeced pree value o heir margial rae o ubiuio bewee leiure ad coumpio wih he expeced pree value o heir aer ax real wage). hi implie ha he wage received by killed houehold adju relaively quickly o reore heir labor marke eiciecy codiio. Sice i hi oe ecor model he margial rae o ubiuio bewee leiure ad coumpio are highly poiively correlaed acro killed ad ukilled houehold i he miimum wage received by ukilled houehold i ully idexed o pa aggregae wage ilaio he i alo adju relaively quickly o reore heir labor marke eiciecy codiio. For a mall ope ecoomy wih a ixed exchage rae regime o idexaio or idexaio o he miimum wage o coumpio price ilaio ampliie diorio i he oupu ad labor marke. Wihou idexaio (or ome oher adjume) here i o way or real wage o adju aer a hock. Depedig o he hock idexaio o coumpio price ilaio

11 9 ca lead real wage o adju i he wrog direcio i repoe o a erm o rade hock which aec he price o impor real wage mu adju i he oppoie direcio o maiai he exeral price compeiivee o he labor marke. Idexaio o he miimum wage o coumpio price ilaio impede hi adjume a he price o coumpio move i adem wih he price o impor. Figure. Icreae i Buie ycle Volailiy aued by Iroducig a iimum Wage / Oupu rice Ilaio = 0. = 0. = Oupu = 0. = 0. = 0.3 erce erce () () 3() 4() 5() - () () 3() 4() 5() erce Wage Ilaio erce Employme = 0. = 0. = = 0. = 0. = 0.3 () () 3() 4() 5() 0 - () () 3() 4() 5() / Depic he icreae i he ucodiioal adard deviaio o cyclical compoe caued by iroducig miimum wage mechaim m(). Ucodiioal adard deviaio are calculaed wih a oe arlo imulaio wih 999 replicaio or period dicardig he ir imulaed obervaio o elimiae depedece o iiial codiio where deoe he oberved ample ie. Impule Repoe Fucio By reducig labor marke lexibiliy iroducig a miimum wage impede he reoraio o exeral price compeiivee ollowig hock. However he ie o hee impedime may be expeced o vary depedig o he ource o buie cycle lucuaio. Eimaed impule repoe o key oupu ad labor marke variable i Hog Kog SAR o a variey o omial ad real hock origiaig domeically ad abroad are compared i Figure 3 8 acro aleraive mechaim or adjuig he miimum wage over ime. I paricular we coider he impule repoe o oupu price ilaio oupu wage ilaio ad employme o he ollowig hock: domeic ad oreig upply hock domeic ad oreig demad hock ad domeic ad oreig moeary codiio hock.

12 0 Eimaed impule repoe idicae ha iroducig a miimum wage ha he poeial o dior he dyamic repoe o he oupu ad labor marke o hock. Relaive o aleraive adjume mechaim idexaio o he miimum wage o aggregae wage ilaio lea dior he impule repoe o oupu ad employme irrepecive o he ource o buie cycle lucuaio or imilar reao o hoe give above. Uder aleraive adjume mechaim he peak repoe o oupu ad employme o domeic ad oreig upply ad moeary codiio hock are geerally ampliied. Neverhele he peak repoe o oupu ad employme o domeic ad oreig demad hock are eeially ivaria o he iroducio o a miimum wage. Figure 3. Impule Repoe o a Domeic Supply Shock / 0.0 Oupu rice Ilaio 0.5 Oupu Aual perce rae I perce (0.) 4(0.) (0.) 3(0.) 5(0.) (0.) 4(0.) (0.) 3(0.) 5(0.) Aual perce rae (0.) 4(0.) Wage Ilaio (0.) 3(0.) 5(0.) erce (0.) 4(0.) Employme (0.) 3(0.) 5(0.) / Impule repoe o a ui adard deviaio domeic labor produciviy hock uder miimum wage mechaim m(0.). I repoe o a domeic upply hock i he orm o a icreae i labor produciviy i Hog Kog SAR oupu rie ad employme all. Ule idexed o aggregae wage ilaio a miimum wage dior he repoe o he oupu ad labor marke.

13 Figure 4. Impule Repoe o a Foreig Supply Shock / Oupu rice Ilaio Oupu Aual perce rae erce (0.) (0.) 3(0.) 4(0.) 5(0.) (0.) (0.) 3(0.) 4(0.) 5(0.) Wage Ilaio Employme Aual perce rae erce (0.) (0.) 3(0.) 4(0.) 5(0.) (0.) (0.) 3(0.) 4(0.) 5(0.) / Impule repoe o a ui adard deviaio oreig labor produciviy hock uder miimum wage mechaim (0.) m. I repoe o a oreig upply hock i he orm o a icreae i labor produciviy i he Uied Sae price ad wage boh declie o reore he exeral price compeiivee o he oupu ad labor marke. Durig hi period o adjume exce capaciy i he oupu ad labor marke arie. I hi cae he ype o idexaio doe o maer bu a miimum wage which i o idexed igiicaly ampliie hi uderuiliaio o reource. Figure 5. Impule Repoe o a Domeic Demad Shock / Oupu rice Ilaio 0.05 Oupu Aual perce rae erce (0.) 4(0.) (0.) 3(0.) 5(0.) (0.) (0.) (0.) 4(0.) 5(0.)

14 0.04 Wage Ilaio 0.05 Employme Aual perce rae erce (0.) 4(0.) (0.) 3(0.) 5(0.) (0.) (0.) 3(0.) 4(0.) 5(0.) / Impule repoe o a ui adard deviaio domeic ical expediure hock uder miimum wage mechaim m(0.). A domeic demad hock i he orm o a icreae i goverme expediure i Hog Kog SAR geerae capaciy preure i he oupu ad labor marke. A miimum wage doe o exacerbae hee capaciy preure bu doe dior he ubeque adjume o he oupu ad labor marke. Figure 6. Impule Repoe o a Foreig Demad Shock / Oupu rice Ilaio Oupu Aual perce rae (0.) (0.) 3(0.) erce (0.) 4(0.) (0.) 3(0.) 5(0.) (0.) 5(0.) Wage Ilaio Employme Aual perce rae (0.) 4(0.) (0.) 3(0.) 5(0.) erce (0.) 4(0.) (0.) 3(0.) 5(0.) / Impule repoe o a ui adard deviaio oreig ical expediure hock uder miimum wage mechaim m(0.).

15 3 A oreig demad hock i he orm o a icreae i goverme expediure i he Uied Sae geerae capaciy preure i he oupu ad labor marke. A miimum wage doe o exacerbae hee capaciy preure bu doe caue exceive ubeque dowward adjume o oupu ad employme ule idexed alhough he orm o idexaio doe o maer. Figure 7. Impule Repoe o a Domeic oeary odiio Shock / Oupu rice Ilaio Oupu Aual perce rae (0.) 4(0.) (0.) 3(0.) 5(0.) erce (0.) (0.) 3(0.) (0.) 5(0.) Wage Ilaio Employme Aual perce rae (0.) (0.) 3(0.) 4(0.) 5(0.) erce (0.) (0.) 3(0.) 4(0.) 5(0.) / Impule repoe o a ui adard deviaio oreig exchage raacio co hock uder miimum wage mechaim m(0.). Uder i iked Exchage Rae Syem deviaio rom ucovered iere pariy which exer omial depreciaio preure i Hog Kog SAR eceiae oeig moeary igheig o abilie he omial exchage rae. I repoe o hi igheig o moeary codiio price ad wage boh declie while exce capaciy i he oupu ad labor marke arie. Ule idexed o aggregae wage ilaio or ui labor co growh a miimum wage ampliie hi uderuiliaio o reource.

16 4 Figure 8. Impule Repoe o a Foreig oeary odiio Shock / Oupu rice Ilaio Oupu Aual perce rae (0.) (0.) 3(0.) 4(0.) 5(0.) erce (0.) (0.) 3(0.) 4(0.) 5(0.) Wage Ilaio 0.05 Employme Aual perce rae (0.) 4(0.) (0.) 3(0.) 5(0.) erce (0.) 4(0.) (0.) 3(0.) 5(0.) / Impule repoe o a ui adard deviaio oreig moeary policy hock uder miimum wage mechaim m(0.). I repoe o a igheig o moeary codiio i he Uied Sae price ad wage boh declie while exce capaciy i he oupu ad labor marke arie. hee repoe relec he correpodig igheig o moeary codiio i Hog Kog SAR uder i iked Exchage Rae Syem. Ule idexed o aggregae wage ilaio a miimum wage ampliie hi uderuiliaio o reource alhough dierece i he adjume uder he variou idexaio cheme are mall. V. ONUSION By leeig icome iequaliy iroducig a miimum wage may be expeced o promoe ocial abiliy. However by reducig labor marke lexibiliy i alo ha he poeial o elevae macroecoomic volailiy ad dior he dyamic repoe o he ecoomy o hock. hi paper eimae ha iroducig a miimum wage i Hog Kog SAR which bid or 0 perce o houehold will ampliy he volailiy o oupu over he buie cycle by 0. perce o 9. perce ad o employme by. perce o 7.8 perce depedig o he proce by which i i adjued over ime. he choice o 0 perce coverage o he miimum wage i purely or illuraive purpoe wih he ulimae coverage a ocial choice ye o be made by he goverme o Hog Kog. Idexaio o he miimum wage o aggregae wage ilaio i oud o domiae aleraive adjume mechaim alhough

17 5 idexaio o ui labor co growh alo perorm well. I cora a ixed miimum wage or idexaio o coumpio price ilaio ed o boo oupu ad employme volailiy by wide margi irrepecive o he coverage o he miimum wage ad he ource o buie cycle lucuaio. he domiace o idexaio o aggregae wage idexaio relec ha i our model ecoomy wage or killed worker are relaively lexible repod o he ame hock a hoe impigig o he low killed labor marke ad are relaively uaeced by diorio hereby allowig killed wage o move i a way ha allow he ecoomy o quickly adju o hock. I killed wage were urher diored i ome way or i he low killed labor marke wa uiciely egmeed (i.e. drive by diere acor) he low killed ui labor co growh may be preerable or idexaio. Noehele idexaio o ome meaure o labor co icreae (aggregae wage ilaio or ui labor co growh) will alway domiae a ixed miimum wage or idexaio o coumpio price ilaio. While hi paper provide a umber o broad leo or chooig he parameer ha gover a miimum wage give i model baed aure i ecearily gloe over ome impora pracical implemeaio iue. hee iclude he eig o he iiial miimum wage (ad hereore i coverage) he meaureme o labor marke idicaor a well a peciic ecoral eec. he level o he miimum wage i a ocial choice wih variou radeo havig o be made. Alhough we do o have cocluio o hi chooig a coervaive level iiially aeig he reulig ocial ad ecoomic coequece ad i eceary he adjuig i level would eem a eible approach. he miimum wage could alo be upplemeed wih ocial welare payme o provide poor amilie wih addiioal uppor. o he exe ha Hog Kog SAR labor marke i egmeed wih employme ad wage drive by diere acor he eig o he miimum wage ad choice o a adjume cheme become eve rickier. Ulimaely however hi i a empirical iue ad a uch we welcome he goverme pla o uppleme he available labor marke ad icome daabae o ha hee deciio ca be well iormed. Noehele meaureme o idicaor uch a aggregae wage average produciviy (oupu per worker) ad ui labor co growh (wage growh le produciviy growh) hould be baed o available macroecoomic daa o keep he exercie rapare. I addiio our aalyi o he eec o iroducig a miimum wage i Hog Kog SAR could be exeded alog everal dimeio. he e o mechaim or adjuig he miimum wage over ime could be augmeed o ecompa diere adjume requecie parial idexaio addiioal idexaio variable ad aymmeric idexaio. Furhermore he ecoral impac o a miimum wage (wih idexaio) could be udied i a model wih a highly egmeed labor marke a could he iroducio o a miimum wage complemeed wih direc icome uppor or he workig poor. hee exeio remai objecive or uure reearch.

18 6 AENDI I. ODE DEVEOEN ESIAION ROEDURE AND ESIAION RESUS oider wo ope ecoomie which are rucurally iomorphic excep where aed oherwie. he domeic ecoomy i mall relaive o he oreig ecoomy. Each o hee ecoomie coi o houehold irm ad a goverme which i ur coi o a moeary auhoriy ad a ical auhoriy. he Houehold Secor here exi a coiuum o houehold idexed by i [0]. Fracio ϕ o houehold are o ype u ad upply diereiaed iermediae ukilled labor ervice. he remaiig racio ϕ o houehold are o ype ad upply diereiaed iermediae killed labor ervice. Houehold o a give ype l {} u are oherwie ideical. oumpio ad Savig he repreeaive iiiely lived houehold o a give ype ha preerece deied over l l coumpio i ad labor upply i repreeed by ieremporal uiliy ucio l l l i β i i = U = E u( ) (3) where ubjecive dicou acor β aiie 0< β <. he iraemporal uiliy ucio i addiively eparable ad repree exeral habi ormaio preerece i coumpio ad labor upply l l / σ l l / + η ( i α ) ( ) l l i α u ( i i ) = ν ν / σ + / η (4) where 0 α < ad 0 α <. hi iraemporal uiliy ucio i ricly icreaig wih repec o coumpio i ad oly i ν > 0 ad give hi parameer rericio i ricly decreaig wih repec o labor upply i ad oly i ν > 0. Give hee parameer rericio hi iraemporal uiliy ucio i ricly cocave i σ > 0 ad η > 0. he repreeaive houehold o a give ype eer period i poeio o previouly hl purchaed domeic currecy deomiaed bod B i which yield iere a rik ree rae i ad oreig currecy deomiaed bod l B i which yield iere a rik ree rae i. here exi a repreeaive perecly compeiive iacial iermediary which aciliae i oreig exchage raacio or coolidaed ee geeraig reveue equal o i ixed l co. he repreeaive houehold alo hold a diveriied porolio o hare { x i j } j= 0i domeic iermediae good irm which pay divided { Π } = ad diveriied porolio j j 0

19 7 l o hare { x ik } i domeic iermediae good rader which pay divided k= 0 { Π k } k= 0 l where { } ad {} e. I upplie diereiaed iermediae labor ervice i l earig labor icome a omial wage W i. Houehold pool heir labor icome ad he goverme levie a ax o pooled labor icome a rae τ. hee ource o privae wealh are ummed i houehold dyamic budge corai: hl l l l hl l i + + E i + + j i j + + k ik + = ( + ) i + E( )( + ) i j= 0 k= 0 B B V x dj V x dk i B i B l l l l l ( Π j Vj ) xi j dj ( Π k Vk ) xik dk ( τ) Wh h dh i j= 0 k= 0 h= (5) Accordig o hi dyamic budge corai a he ed o period he repreeaive hl houehold purchae domeic bod B i + ad oreig bod B l i + a price E. I alo l purchae a diveriied porolio o hare { x i j + } j= 0i iermediae good irm a price l { V j } j= 0 ad diveriied porolio o hare { x ik + } k= 0i iermediae good rader a price { V k }. Fially he repreeaive houehold purchae ial coumpio good l k= 0 i a price. I period he repreeaive houehold o a give ype chooe ae coige equece l or coumpio { i } hl = domeic bod holdig { B i + } = oreig bod holdig l l { B i + } = hare holdig i iermediae good irm {{ x i j + } j = 0} = ad hare holdig i l iermediae good rader {{ x ik + } k = 0} = o maximie ieremporal uiliy ucio (3) hl ubjec o dyamic budge corai (5) ad ermial oegaiviy corai B i + 0 l l l B i + 0 x i j + 0 ad x ik + 0 or. I equilibrium eleced eceary ir order codiio aociaed wih hi uiliy maximiaio problem may be aed a u ( ) = λ (6) l i λ = β( + i)e λ + (7) Eλ = β( + i )E ( ) E λ (8) V λ = βe( Π + V ) λ (9) j j + j + + V k λ β Π k + Vk + λ+ = E( + ) (0) l where λ i deoe he agrage muliplier aociaed wih he period houehold dyamic budge corai. rovided ha he ieremporal uiliy ucio i bouded ad ricly cocave ogeher wih oher eceary ir order codiio ad raveraliy codiio

20 8 derived rom eceary complemeary lacke codiio aociaed wih he ermial oegaiviy corai hee eceary ir order codiio are uicie or he uique uiliy maximiig ae coige ieremporal houehold allocaio. ombiaio o eceary ir order codiio (6) ad (7) yield ieremporal opimaliy codiio u ( ) = E ( + i ) u ( ) () l l i β + i + + which eure ha a a uiliy maximum he repreeaive houehold o a give ype cao beei rom eaible ieremporal coumpio reallocaio. Fially combiaio o eceary ir order codiio (6) (7) ad (8) yield iraemporal opimaliy codiio βu ( ) βu ( ) l l + i + + i + E+ E ( + i) = E ( )( ) l l + + i u( i ) + u( i ) + E () which equae he expeced pree value o he gro real reur o domeic ad oreig bod. abor Supply ad Wage Seig here exi a large umber o perecly compeiive irm which combie he ial ukilled u u labor ervice havig produciviy coeicie A wih he ial killed labor ervice havig produciviy coeicie A o produce a ial labor ervice havig produciviy coeicie A accordig o coa elaiciy o ubiuio producio ucio ϑ ϑ ϑ u u ϑ ϑ ϑ ϑ ϑ = ϕ + ϕ A ( ) ( A ) ( ) ( A ) (3) u where 0 < ϕ ϑ > 0 ad A A A > 0. he repreeaive ial labor ervice irm maximie proi derived rom producio o he ial labor ervice wih repec o ipu o he ial ukilled ad killed labor ervice implyig ial ukilled ad killed eecive labor ervice demad ucio: A u u W / A = ϕ W / A ϑ A u u (4)

21 9 ϑ W / A A = ( ϕ ) A. W / A (5) Sice he producio ucio exhibi coa reur o cale i equilibrium he repreeaive ial labor ervice irm ear ero proi implyig aggregae eecive wage idex: ϑ ϑ u ϑ = ϕ ϕ u + W W W ( ). A A A (6) hi aggregae eecive wage idex equal he miimum co o producig oe ui o he ial eecive labor ervice give he eecive wage or he ial ukilled ad killed labor ervice. here exi a large umber o perecly compeiive irm which combie diereiaed l iermediae labor ervice i upplied by houehold o a give ype i a moopoliically l compeiive labor marke o produce ial labor ervice accordig o coa elaiciy o ubiuio producio ucio θ θ θ l l θ = i i= 0 ( ) di (7) where θ >. he repreeaive ial labor ervice irm maximie proi derived rom producio o he ial labor ervice wih repec o ipu o iermediae labor ervice implyig iermediae labor ervice demad ucio: l θ l W i l i =. l W (8) Sice he producio ucio exhibi coa reur o cale i equilibrium he repreeaive ial labor ervice irm ear ero proi implyig aggregae wage idex: θ l θ ( i ). i= 0 l W = W di (9)

22 0 A he wage elaiciy o demad or iermediae labor ervice θ icreae hey become cloer ubiue ad idividual houehold have le marke power. I a exeio o he model o omial wage rigidiy propoed by Erceg Hedero ad evi (000) alog he lie o Sme ad Wouer (003) each period a radomly eleced l racio ω o houehold o a give ype adju heir wage opimally. he remaiig l racio ω o houehold adju heir wage accordig o idexaio rule: W W =. (0) Il l l i W I i l W l he idexed wage or houehold o a give ype W I i adjued o accou or pa aggregae wage ilaio coumpio price ilaio ad average labor produciviy growh W Il W y γ l γ l γ l W y = W y W Il () where 0 l W γ 0 l l / γ ad 0 γ. Uder hi peciicaio alhough houehold adju heir wage every period hey irequely adju heir wage opimally ad he ierval bewee opimal wage adjume i a radom variable. I he repreeaive houehold o a give ype ca adju i wage opimally i period he i doe o o maximie ieremporal uiliy ucio (3) ubjec o dyamic budge corai (5) iermediae labor ervice demad ucio (8) ad he aumed orm o omial wage rigidiy. Sice all houehold o a give ype ha adju heir wage opimally i period olve a ideical uiliy maximiaio problem i equilibrium hey all chooe a commo wage W give by eceary ir order codiio: l* l l I θ θ * l l l ( ) ( ) l β u i u i W W W l ω θ l l Il l l = u( i ) u( i ) W W W E ( ) l* W W = l l I l l l ( ) l E ( ) u i ( )( ) W W W θ l* β W ω θ τ l Il l l = u( i ) W W W θ l. () hi eceary ir order codiio equae he expeced pree value o he coumpio beei geeraed by a addiioal ui o labor upply o he expeced pree value o i leiure co. Aggregae wage idex (9) equal a average o he wage e by he racio l ω o houehold o a give ype ha adju heir wage opimally i period ad he l average o he wage e by he remaiig racio ω o houehold ha adju heir wage accordig o idexaio rule (0):

23 θ I l l l l* W θ θ l l = ( ω )( ) + ω. I l W W W W (3) Sice hoe houehold o a give ype able o adju heir wage opimally i period are eleced radomly rom amog all houehold o ha ype he average wage e by he remaiig houehold equal he value o he aggregae wage idex ha prevailed durig period recaled o accou or pa wage ilaio coumpio price ilaio ad labor produciviy growh. he roducio Secor here exi a coiuum o iermediae good irm idexed by j [0]. Iermediae good irm upply diereiaed iermediae oupu good bu are oherwie ideical. Ery io ad exi rom he moopoliically compeiive iermediae oupu good ecor i prohibied. abor Demad ad Iveme l he repreeaive iermediae good irm ell hare { x i j + } i= 0o domeic houehold a price V j. Recurive orward ubiuio or V j + wih > 0 i eceary ir order codiio (9) applyig he law o ieraed expecaio reveal ha he po-divided ock marke value o he repreeaive iermediae good irm equal he expeced pree value o uure divided payme: V β λ = E Π. (4) j j =+ λ Acig i he iere o i hareholder he repreeaive iermediae good irm maximie i pre-divided ock marke value equal o he expeced pree value o curre ad uure divided payme: Π β λ + = E. (5) j V j Π j = λ he derivaio o reul (4) impoe a raveraliy codiio which rule ou el-ulillig peculaive ae price bubble. Share eile houehold o divided payme equal o e proi Π j deied a aer ax earig le iveme expediure: Π = ( τ )( W ) I. (6) I j j j j

24 Earig are deied a reveue derived rom ale o diereiaed iermediae oupu good j a price j le expediure o ial labor ervice j. he goverme levie a ax o earig a rae τ. he repreeaive iermediae good irm uilie capial K a rae u j ad re ial labor ervice j give produciviy coeicie A o produce diereiaed iermediae oupu good j accordig o coa elaiciy o ubiuio producio ucio ϑ ϑ ϑ K K ϑ ϑ ϑ ϑ ϑ j j = ϕ j + ϕ j F ( u K A ) ( ) ( u K ) ( ) ( A ) (7) K where 0 < ϕ < ϑ > 0 ad A > 0. hi coa elaiciy o ubiuio producio ucio exhibi coa reur o cale. I uiliig capial o produce oupu he repreeaive iermediae good irm icur a co G ( u K ) deomiaed i erm o oupu: j = F( u K A ) G ( u K ). (8) j j j j Followig hriiao Eichebaum ad Eva (005) hi capial uiliaio co i icreaig i he rae o capial uiliaio a a icreaig rae G κ ( ) ( ) u u j j K = μ e K (9) where μ > 0 ad κ > 0. I deermiiic eady ae equilibrium he rae o capial uiliaio i ormalied o oe ad he co o uiliig capial equal ero. apial i edogeou bu o irm-peciic ad he repreeaive iermediae good irm eer period wih acce o previouly accumulaed capial ock K which ubequely evolve accordig o accumulaio ucio K = ( δ ) K +H ( I I ) (30) + κ ( u ) j arial diereiaio o hi capial uiliaio co ucio yield G u( uj K) = μκe K > 0 ad κ ( ) ( ) u G u K = μκ e j K > 0. uu j

25 3 where depreciaio rae parameer δ aiie 0 δ. Followig hriiao Eichebaum ad Eva (005) eecive iveme ucio H ( I I ) icorporae covex adjume co I χ I I H ( I I ) = ν I (3) I I where χ > 0 ad ν > 0. I deermiiic eady ae equilibrium hee adjume co equal ero ad eecive iveme equal acual iveme. I period he repreeaive iermediae good irm chooe ae coige equece or employme { i } = capial uiliaio { u j } = iveme { I } = ad he capial ock { K + } = o maximie pre-divided ock marke value (5) ubjec o e producio ucio (8) capial accumulaio ucio (30) ad ermial oegaiviy corai K + 0 or. I equilibrium demad or he ial labor ervice aiie eceary ir order codiio W F ( u K A ) Φ = ( τ ) (3) A j j j A where Φ j deoe he agrage muliplier aociaed wih he period producio echology corai. hi eceary ir order codiio equae real margial co Φ j o he raio o he aer ax real wage o he margial produc o labor. I equilibrium he rae o capial uiliaio aiie eceary ir order codiio ( u K ) F = G (33) u j uk ( uj K A j ) K which equae he margial produc o uilied capial o i margial co. I equilibrium demad or he ial iveme good aiie eceary ir order codiio βλ QH( I I ) + E Q H ( I I ) = (34) + I + + λ which equae he expeced pree value o a addiioal ui o iveme i capial o i price where Q j deoe he agrage muliplier aociaed wih he period capial accumulaio ucio. I equilibrium hi hadow price o capial aiie eceary ir order codiio

26 4 { Φ δ + } βλ Q = u F u K A G u K + Q (35) + E j j uk( j j ) K( j ) ( ) λ which equae i o he expeced pree value o he um o he uure margial co o capial ad he uure hadow price o capial e o depreciaio. rovided ha he pre-divided ock marke value o he repreeaive iermediae good irm i bouded ad ricly cocave ogeher wih oher eceary ir order codiio ad a raveraliy codiio derived rom he eceary complemeary lacke codiio aociaed wih he ermial oegaiviy corai hee eceary ir order codiio are uicie or he uique value maximiig ae coige ieremporal irm allocaio. Oupu Supply ad rice Seig here exi a large umber o perecly compeiive irm which combie diereiaed iermediae oupu good j upplied by iermediae good irm o produce ial oupu good accordig o coa elaiciy o ubiuio producio ucio θ θ θ θ = j j= 0 ( ) dj (36) where θ >. he repreeaive ial oupu good irm maximie proi derived rom producio o he ial oupu good wih repec o ipu o iermediae oupu good implyig iermediae oupu good demad ucio: θ j j =. (37) Sice he producio ucio exhibi coa reur o cale i equilibrium he repreeaive ial oupu good irm ear ero proi implyig aggregae oupu price idex: θ θ j j= 0 = ( ) dj. (38) A he price elaiciy o demad or iermediae oupu good θ icreae hey become cloer ubiue ad idividual iermediae good irm have le marke power.

27 5 I a exeio o he model o omial oupu price rigidiy propoed by alvo (983) alog he lie o Sme ad Wouer (003) each period a radomly eleced racio ω o iermediae good irm adju heir price opimally. he remaiig racio ω o iermediae good irm adju heir price o accou or pa aggregae oupu price ilaio accordig o parial idexaio rule γ j = j (39) where 0 γ. Uder hi peciicaio opimal price adjume opporuiie arrive radomly ad he ierval bewee opimal price adjume i a radom variable. I he repreeaive iermediae good irm ca adju i price opimally i period he i doe o o maximie pre-divided ock marke value (5) ubjec o e producio ucio (8) capial accumulaio ucio (30) iermediae oupu good demad ucio (37) ad he aumed orm o omial oupu price rigidiy. Sice all iermediae good irm ha adju heir price opimally i period olve a ideical value maximiaio problem i equilibrium hey all chooe a commo price give by eceary ir order codiio: * θ γ θ * β λ E ( ω ) θφ j * = λ = θ γ θ * β λ E ( ω ) ( θ )( τ) = λ. (40) hi eceary ir order codiio equae he expeced pree value o he aer ax reveue beei geeraed by a addiioal ui o oupu upply o he expeced pree value o i producio co. Aggregae oupu price idex (38) equal a average o he price e by he racio ω o iermediae good irm ha adju heir price opimally i period ad he average o he price e by he remaiig racio ω o iermediae good irm ha adju heir price accordig o parial idexaio rule (39): θ θ γ * θ ( )( ) = ω + ω. (4) Sice hoe iermediae good irm able o adju heir price opimally i period are eleced radomly rom amog all iermediae good irm he average price e by he

28 6 remaiig iermediae good irm equal he value o he aggregae oupu price idex ha prevailed durig period recaled o accou or pa oupu price ilaio. he Impor ad Expor Secor he domeic ecoomy impor he oreig ial oupu good which i procee or purpoe o aborpio ad exporaio. he oreig ecoomy impor he domeic ial oupu ad proceed oreig ial oupu good which i procee or purpoe o aborpio. here exi a large umber o perecly compeiive irm which combie he ial e oerepô rade good wih he ial erepô rade good o produce ial rade good accordig o coa elaiciy o ubiuio producio ucio ψ ψ ψ ψ e ψ ψ ψ ψ = φ + φ ( ) ( ) ( ) ( ) (4) where 0 < φ < ad ψ >. he repreeaive ial rade good irm maximie proi derived rom producio o he ial rade good wih repec o ipu o he ial oerepô ad erepô rade good implyig ial oerepô ad erepô rade good demad ucio: = φ ψ (43) e = ( φ ). e ψ (44) Sice he producio ucio exhibi coa reur o cale i equilibrium he repreeaive ial rade good irm ear ero proi implyig aggregae rade price idex: ψ e ψ ψ = φ + φ ( ) ( )( ). (45) hi aggregae rade price idex equal he miimum co o producig oe ui o he ial rade good give he price o he ial oerepô ad erepô rade good.

29 7 he Real Exchage Rae ad he erm o rade he real exchage rae ad he erm o rade are meaure o he exeral price compeiivee o he oupu marke. Deie he real exchage rae Q = E (46) which meaure he price o oreig oupu i erm o domeic oupu. Alo deie he erm o rade = (47) which meaure he price o impor i erm o expor. he domeic currecy price o oerepô expor aiie =. here exi a large umber o perecly compeiive irm which combie he ial oupu good Z h { h h h I G } wih he ial oerepô impor good Z { I G } o produce ial domeic good Z { I G} accordig o coa elaiciy o ubiuio producio ucio ψ ψ ψ ψ Z ψ h ψ Z ψ ψ = φ + φ ν Z ( ) ( Z ) ( ) ( Z ) (48) Z where 0 < φ < ψ > ad ν > 0. he repreeaive ial domeic good irm maximie proi derived rom producio o he ial domeic good wih repec o ipu o he ial oupu ad oerepô impor good implyig ial oupu ad oerepô impor good demad ucio: Z = h Z φ Z ψ Z (49) Z ψ Z = ( φ ). ν ν Z Z (50) Sice he producio ucio exhibi coa reur o cale i equilibrium he repreeaive ial domeic good irm ear ero proi implyig aggregae domeic price idex:

30 8 ψ ψ Z Z Z ψ = φ ( ) + ( φ ). ν (5) ombiaio o hi aggregae domeic price idex wih ial oupu ad oerepô impor good demad ucio (49) ad (50) yield: Z ψ ψ ψ = φ φ + ( φ ) Z ν h Z Z Z (5) Z ψ ψ ψ Z Z Z Z = φ φ + φ ν ν ( ) ( ). (53) hee demad ucio or he ial oupu ad oerepô impor good are direcly proporioal o ial domeic good demad wih a proporioaliy coeicie ha varie wih he erm o rade. Impor Supply Expor Supply ad rice Seig here exi a large umber o perecly compeiive irm which combie diereiaed iermediae rade good k upplied by iermediae good rader o produce ial rade good accordig o coa elaiciy o ubiuio producio ucio θ θ θ θ k k = 0 = ( ) dk (54) where θ >. he repreeaive ial rade good irm maximie proi derived rom producio o he ial rade good wih repec o ipu o iermediae rade good implyig iermediae rade good demad ucio: θ k k =. (55) Sice he producio ucio exhibi coa reur o cale i equilibrium he repreeaive ial rade good irm ear ero proi implyig aggregae rade price idex:

31 9 θ θ = ( k ) dk. (56) k = 0 A he price elaiciy o demad or iermediae rade good θ icreae hey become cloer ubiue ad idividual iermediae good rader have le marke power. here exi coiuum o iermediae oerepô ad erepô good rader idexed by k [0]. Iermediae good rader upply diereiaed iermediae rade good bu are oherwie ideical. Ery io ad exi rom he moopoliically compeiive iermediae rade good ecor i prohibied. l he repreeaive iermediae good rader ell hare { x ik + } i= 0o domeic houehold a price V k. Recurive orward ubiuio or V k + wih > 0 i eceary ir order codiio (0) applyig he law o ieraed expecaio reveal ha he po-divided ock marke value o he repreeaive iermediae good rader equal he expeced pree value o uure divided payme: V β λ = E Π. (57) k k =+ λ Acig i he iere o i hareholder he repreeaive iermediae good rader maximie i pre-divided ock marke value equal o he expeced pree value o curre ad uure divided payme: Π β λ + = E. (58) k Vk Π k = λ he derivaio o reul (57) impoe a raveraliy codiio which rule ou el-ulillig peculaive ae price bubble. Share eile houehold o divided payme equal o gro proi Π deied a earig le ixed co F : k e e e e e k k k k Π = (59) k k k k F. Π = E (60)

32 30 Earig are deied a reveue derived rom ale o diereiaed iermediae rade good e e k a price k le purchae o domeic ial erepô impor good k a price or oreig ial oupu good k a price E. Where applicable ixed co equal average earig implyig ero average gro proi. I a exeio o he model o omial impor price rigidiy propoed by oacelli (005) alog he lie o Sme ad Wouer (003) each period a radomly eleced racio ω o iermediae good rader adju heir price opimally. he remaiig racio ω o iermediae good rader adju heir price o accou or pa aggregae rade price ilaio accordig o parial idexaio rule γ k = k (6) where 0 γ. Uder hi peciicaio he probabiliy ha a iermediae good rader ha adjued i price opimally i ime depede bu ae idepede. I he repreeaive iermediae good rader ca adju i price opimally i period he i doe o o maximie pre-divided ock marke value (58) ubjec o iermediae rade good demad ucio (55) ad he aumed orm o omial rade price rigidiy. Sice all iermediae good rader ha adju heir price opimally i period olve a ideical value maximiaio problem i equilibrium hey all chooe a commo price give by eceary ir order codiio * θ γ β λ E ( ω ) Ψ * = λ θ = θ θ γ β λ E ( ω ) = λ (6) e e e where Ψ = / ad Ψ = E / meaure real margial co. hi eceary ir order codiio equae he expeced pree value o he reveue beei geeraed by a addiioal ui o rade upply o he expeced pree value o i producio co. Aggregae rade price idex (56) equal a average o he price e by he racio ω o iermediae good rader ha adju heir price opimally i period ad he average o he price e by he remaiig racio ω o iermediae good rader ha adju heir price accordig o parial idexaio rule (6):

33 3 θ θ γ * θ = ( ω )( ) + ω. (63) Sice hoe iermediae good rader able o adju heir price opimally i period are eleced radomly rom amog all iermediae good rader he average price e by he remaiig iermediae good rader equal he value o he aggregae rade price idex ha prevailed durig period recaled o accou or pa rade price ilaio. oeary ad Fical olicy he goverme coi o a moeary auhoriy ad a ical auhoriy. he moeary auhoriy impleme moeary policy while he ical auhoriy impleme ical policy. he oeary Auhoriy he moeary auhoriy impleme moeary policy hrough corol o he hor erm omial iere rae accordig o a moeary policy rule exhibiig parial adjume dyamic o he orm i i = ρ ( i i ) i π i E i + ( ρ ) i ξ ( π π ) + ξ (l l ) + ξ ( i i ) + ξ (l E l E) + ν (64) π i E where 0 ρ i < ξ 0 ξ 0 ξ 0 ad ξ 0. A peciied he deviaio o he omial iere rae rom i deermiiic eady ae equilibrium value deped o a average o i pa deviaio ad i deired deviaio which i ur deped o he coemporaeou deviaio o coumpio price ilaio oupu he oreig omial iere rae ad he omial exchage rae rom heir deermiiic eady ae equilibrium value. he domeic moeary auhoriy impleme a ixed exchage rae regime π i repreeed by ρ i = 0 ξ = 0 ξ = 0 ξ = ad ξ E > 0. he oreig moeary auhoriy π impleme a lexible ilaio argeig regime repreeed by 0 ρ i < ξ > i E ξ 0 ξ = 0 ad ξ = 0. raiory deparure rom hi moeary policy rule are capured by erially ucorrelaed moeary policy hock ν. he Fical Auhoriy he ical auhoriy impleme ical policy hrough corol o omial goverme coumpio ad he ax rae applicable o he pooled labor icome o houehold ad he earig o iermediae good irm. I equilibrium hi diorioary ax collecio ramework correpod o proporioal oupu axaio. i

34 3 he raio o omial goverme coumpio o omial oupu aiie a ical expediure rule exhibiig parial adjume dyamic o he orm G G G G B B G G G G G + + G l l = ρg l l ( G) l l + ρ ζ ν + (65) where 0 ρ G <. A peciied he deviaio o he raio o omial goverme coumpio o omial oupu rom i deermiiic eady ae equilibrium value deped o a average o i pa deviaio ad i deired deviaio which i ur deped o he coemporaeou deviaio o he raio o he e oreig ae poiio o omial oupu rom i arge value. hi ical expediure rule uppor a deermiae raioal expecaio equilibrium oly i he e oreig ae poiio doe o chage ig. I he e oreig ae G G poiio i poiive he ζ > 0 while i i i egaive he ζ < 0. raiory deparure rom hi ical expediure rule are capured by erially ucorrelaed ical expediure hock ν. G he ax rae applicable o he pooled labor icome o houehold ad he earig o iermediae good irm aiie a ical reveue rule exhibiig parial adjume dyamic o he orm G G τ + + τ lτ l τ = ρτ(lτ l τ ) + ( ρτ) ζ l l ν + B B (66) where 0 ρ τ <. A peciied he deviaio o he ax rae rom i deermiiic eady ae equilibrium value deped o i pa deviaio ad i deired deviaio which i ur deped o he coemporaeou deviaio o he raio o he e goverme ae poiio o omial oupu rom i arge value. hi ical reveue rule uppor a deermiae raioal expecaio equilibrium oly i he e goverme ae poiio doe o chage τ ig. I he e goverme ae poiio i poiive he ζ < 0 while i i i egaive he τ ζ > 0. raiory deparure rom hi ical reveue rule are capured by erially τ ucorrelaed ical reveue hock ν. he ical auhoriy eer period holdig previouly purchaed domeic currecy deomiaed bod B Gh which yield iere a rik ree rae i ad oreig currecy deomiaed bod G B which yield iere a rik ree rae i. I oreig exchage raacio are ubjec o coolidaed ee. he ical auhoriy alo levie axe o he pooled labor icome o houehold ad he earig o iermediae good irm. hee ource o public wealh are ummed i goverme dyamic budge corai:

35 33 B + EB = ( + i ) B + E ( )( + i ) B Gh G Gh G + + l l G Wh h dhdi τ j j W j dj G i= 0 h= 0 j= 0 + τ + ( ). (67) Accordig o hi dyamic budge corai a he ed o period he ical auhoriy Gh purchae domeic bod B + ad oreig bod B G + a price E. I alo purchae ial goverme coumpio good G a price. arke learig odiio G A raioal expecaio equilibrium i hi DSGE model o a mall ope ecoomy coi o ae coige ieremporal allocaio or domeic ad oreig houehold ad irm which olve heir coraied opimiaio problem give price ad policy ogeher wih ae coige ieremporal allocaio or domeic ad oreig goverme which aiy heir policy rule ad corai give price wih upporig price uch ha all marke clear. Sice he domeic ecoomy i mall relaive o he oreig ecoomy i e e I G equilibrium ad e B+ 0. learig o he ial oupu good marke require ha oerepô expor equal producio o he domeic ial oupu good le he cumulaive demad o domeic houehold irm ad he goverme = I G (68) h h h e e where = ad =. learig o he ial oerepô impor good marke require ha oerepô impor aiy he cumulaive demad o domeic houehold irm ad he goverme or he oreig ial oupu good = + I + G (69) e e where = ad =. I equilibrium combiaio o hee ial oupu ad oerepô impor good marke clearig codiio yield aggregae reource corai: I G = + I + G +. (70) he rade balace equal expor reveue e e = +. e e = + le impor expediure

36 34 e B + deoe he e oreig ae poiio o he ecoomy which i equilibrium equal h he um o he domeic currecy value o privae ecor bod holdig B+ = B+ +E B+ G G h G ad public ecor bod holdig B = B +E B : B = B + B (7) G he impoiio o equilibrium codiio o houehold dyamic budge corai (5) reveal ha he e icreae i privae ecor ae holdig equal privae avig le iveme: e e e e I + τ B = ( + i ) B + ( ) + I. (7) he impoiio o equilibrium codiio o goverme dyamic budge corai (67) reveal ha he e icreae i public ecor ae holdig equal public avig: G G G G B+ B = i B + τ G. (73) ombiaio o hee houehold ad goverme dyamic budge corai wih aggregae reource corai (70) reveal ha he e icreae i oreig ae holdig equal he um o e ieraioal iveme icome ad he rade balace or equivalely avig le iveme: B+ B = i B +. (74) I equilibrium he curre accou balace i deermied by boh iraemporal ad ieremporal opimiaio. he Empirical Framework Eimaio i baed o a approximae liear uoberved compoe repreeaio o hi DSGE model o a mall ope ecoomy uder he rericio ha all houehold upply diereiaed iermediae killed labor ervice repreeed by ϕ = 0. Ierece i baed o he approximae mulivariae liear raioal expecaio repreeaio o hi DSGE model while relaxig hi rericio or he domeic ecoomy. I wha ollow E x + deoe he raioal expecaio o variable x + codiioal o iormaio available a ime. Alo x ˆ deoe he cyclical compoe o variable x while x deoe he red compoe o variable x. yclical compoe are modeled by lieariig equilibrium codiio aroud a aioary deermiiic eady ae equilibrium which abrac rom log ru balaced growh while red compoe are modeled a radom walk while eurig he exiece o a well deied balaced growh pah alog

37 35 which grea raio ad red growh rae are ime idepede bu ae depede. yclical ad red compoe are addiively eparable ha i x = xˆ + x. yclical ompoe he cyclical compoe o oupu price ilaio deped o a liear combiaio o i pa ad expeced uure cyclical compoe drive by he coemporaeou cyclical compoe o real margial co ad he ax rae accordig o oupu price hillip curve γ β ( ω )( ω β) ˆ τ ˆ ˆ ˆ ˆ ˆ π = π E l l l + π + + Φ + τ θ + γ β + γ β ω ( + γ β) τ θ (75) θ where Φ = ( τ). he periece o he cyclical compoe o oupu price ilaio i θ icreaig i idexaio parameer γ while he eiiviy o he cyclical compoe o oupu price ilaio o chage i he cyclical compoe o real margial co ad he ax rae i decreaig i omial rigidiy parameer ω ad idexaio parameer γ. hi oupu price hillip curve i ubjec o oupu price markup hock. he cyclical compoe o oupu deped o he coemporaeou cyclical compoe o uilied capial ad eecive labor accordig o approximae liear e producio ucio K β( τ) θ W where ( )( β δ θ ) ˆ θ W l l( ˆ ˆ θ W ) l( ˆ ˆ = uk A ) + θ θ =. hi approximae liear e producio ucio i ubjec o labor produciviy hock. he cyclical compoe o he rae o capial uiliaio deped o he coemporaeou cyclical compoe o he raio o capial o eecive labor accordig o approximae liear implici capial uiliaio ucio: (76) θ W θ W Kˆ l uˆ = l. κϑ + θ θ A ˆ ˆ (77) he eiiviy o he cyclical compoe o he rae o capial uiliaio o chage i he cyclical compoe o he raio o capial o eecive labor i decreaig i capial uiliaio co parameer κ ad elaiciy o ubiuio parameer ϑ. hi approximae liear implici capial uiliaio ucio i ubjec o labor produciviy hock. he cyclical compoe o coumpio iveme or goverme coumpio price ilaio deped o a liear combiaio o i pa ad expeced uure cyclical compoe

38 36 drive by he coemporaeou cyclical compoe o real margial co ad he ax rae accordig o hillip curve: Z γ Z β Z ( ω )( ω β) ˆ τ ˆ ˆ ˆ ˆ ˆ π = π E l l l + π + + Φ + τ θ + γ β + γ β ω ( + γ β) τ θ γ ( φ ) ˆ ˆ β( φ ) ˆ Δ + Δ Δ Z Z Z + l ( φ ) l E l. + γ β ˆ ν ˆ ˆ ν + γ β ν+ (78) Relecig he ery o he price o oerepô impor io he aggregae coumpio iveme or goverme coumpio price idex he cyclical compoe o coumpio iveme or goverme coumpio price ilaio alo deped o pa coemporaeou ad expeced uure chage i he cyclical compoe o he erm o rade. hee hillip curve are ubjec o oupu price markup ad impor produciviy hock. he cyclical compoe o coumpio deped o a average o i pa ad expeced uure cyclical compoe drive by he coemporaeou cyclical compoe o he coumpio baed real iere rae accordig o approximae liear coumpio Euler equaio: α α ˆ ν ˆ ˆ ˆ + l l ˆ = E l E l. + + σ r + α α α ˆ ν (79) he periece o he cyclical compoe o coumpio i icreaig i habi periece parameer α while he eiiviy o he cyclical compoe o coumpio o chage i he cyclical compoe o he coumpio baed real iere rae i icreaig i ieremporal elaiciy o ubiuio parameer σ ad decreaig i habi periece parameer α. hi approximae liear coumpio Euler equaio i ubjec o preerece hock. he cyclical compoe o iveme deped o a average o i pa ad expeced uure cyclical compoe drive by he coemporaeou cyclical compoe o he relaive hadow price o capial accordig o approximae liear iveme demad ucio: ˆ ˆ ˆ β ˆ I Q l I l ˆ = I + E l I+ + l ν. ( ) ˆ I + β + β χ + β (80) he eiiviy o he cyclical compoe o iveme o chage i he cyclical compoe o he relaive hadow price o capial i decreaig i capial iveme adjume co

39 37 parameer χ. hi approximae liear iveme demad ucio i ubjec o iveme produciviy hock. he cyclical compoe o he relaive hadow price o capial deped o i expeced uure cyclical compoe he coemporaeou cyclical compoe o he oupu baed real iere rae he expeced uure cyclical compoe o real margial co ad he expeced uure cyclical compoe o he margial produc o capial accordig o approximae liear iveme Euler equaio: Qˆ ˆ Q l = β( δ)e l ˆ ˆ + + β( δ) θ + W [ ] ˆ + + rˆ β( δ) E lφ+ E l. ϑ θ Aˆ ˆ + + uˆ Kˆ (8) he eiiviy o he cyclical compoe o he relaive hadow price o capial o chage i he cyclical compoe o he raio o uilied capial o eecive labor i decreaig i elaiciy o ubiuio parameer ϑ. hi approximae liear iveme Euler equaio i ubjec o labor produciviy hock. he cyclical compoe o he capial ock deped o i pa cyclical compoe ad he coemporaeou cyclical compoe o iveme accordig o approximae liear capial accumulaio ucio ˆ ˆ I l K = ˆ ˆ ( δ) l K + + δ l( ν I) (8) where I = δ. hi approximae liear capial accumulaio ucio i ubjec o iveme K produciviy hock. he cyclical compoe o he raio o omial goverme coumpio o omial oupu deped o i pa cyclical compoe ad he coemporaeou cyclical compoe o he raio o he e oreig ae poiio o omial oupu accordig o ical expediure rule: G ˆ ˆ G ˆ ˆ Bˆ = + + (83) G G G G l ρ l ( ) l ˆ. ˆ ˆ ˆ ˆ G ρg ζ ˆ + ν ˆ hi ical expediure rule eure covergece o he level o he raio o he e oreig ae poiio o omial oupu o i arge value i deermiiic eady ae equilibrium ad i ubjec o ical expediure hock.

40 38 he cyclical compoe o he ax rae deped o i pa cyclical compoe ad he coemporaeou cyclical compoe o he raio o he e goverme ae poiio o omial oupu accordig o ical reveue rule: Bˆ = + + (84) G τ + τ l ˆ τ l ˆ ˆ ρτ τ ( ρτ) ζ l ν. ˆ ˆ hi ical reveue rule eure covergece o he level o he raio o he e goverme ae poiio o omial oupu o i arge value i deermiiic eady ae equilibrium ad i ubjec o ical reveue hock. he cyclical compoe o expor price ilaio deped o a average o he coemporaeou cyclical compoe o oerepô ad erepô expor price ilaio: e ˆ π = φ ˆ π + ( φ ) ˆ π. (85) he cyclical compoe o expor reveue aiie ˆ l( ˆ ) l( ˆ ˆ = ) + e e e l( ˆ ˆ e ) where = +. he cyclical compoe o erepô expor price ilaio deped o a liear combiaio o i pa ad expeced uure cyclical compoe drive by he coemporaeou cyclical compoe o he deviaio o he domeic currecy price o erepô impor rom he price o erepô expor accordig o expor price hillip curve: e ( )( ) ˆ e e e γ β ω ω β ˆ ˆ ˆ ˆ π = π E l e l. + π + + θ ( ) ˆ + γ β + γ β ω + γ β θ (86) he periece o he cyclical compoe o erepô expor price ilaio i icreaig i idexaio parameer γ while he eiiviy o he cyclical compoe o erepô expor price ilaio o chage i he cyclical compoe o real margial co i decreaig i omial rigidiy parameer ω ad idexaio parameer γ. hi expor price hillip curve i ubjec o expor price markup hock. he cyclical compoe o expor deped o he coemporaeou cyclical compoe o oreig coumpio iveme goverme coumpio ad he erm o rade accordig o approximae liear expor demad ucio

41 39 ˆ I Iˆ G Gˆ ˆ I G l = ( φ ) l + ( φ ) l + ( φ ) l ˆ ν ˆ ˆ ν ν ψ φ φ + φ φ I + φ φ G I I G G ( ) ( ) ( ) l ˆ ν ˆ (87) I G I G where = ( φ ) + ( φ ) + ( φ ). he cyclical compoe o erepô ˆ e e expor aiie l ˆ e l ˆ = ψ l ˆ where = ( φ ). he eiiviy o he cyclical compoe o expor o chage i he cyclical compoe o he oreig erm o rade i icreaig i elaiciy o ubiuio parameer ψ. hi approximae liear expor demad ucio i ubjec o oreig impor produciviy hock. he cyclical compoe o impor price ilaio deped o a average o he coemporaeou cyclical compoe o oerepô ad erepô impor price ilaio: e ˆ π = φ ˆ π + ( φ ) ˆ π. (88) he cyclical compoe o impor expediure aiie ˆ l( ˆ ) l( ˆ ˆ = ) + e e e l( ˆ ˆ e ) where = +. he cyclical compoe o oerepô or erepô impor price ilaio deped o a liear combiaio o i pa ad expeced uure cyclical compoe drive by he coemporaeou cyclical compoe o he deviaio o he domeic currecy price o oreig oupu rom he price o oerepô or erepô impor accordig o impor price hillip curve: ˆ ˆ γ β ( ω )( ω β) E ˆ ˆ ˆ ˆ π = π E l l. + π + + θ ( ) ˆ + γ β + γ β ω + γ β θ (89) he periece o he cyclical compoe o oerepô or erepô impor price ilaio i icreaig i idexaio parameer γ while he eiiviy o he cyclical compoe o oerepô or erepô impor price ilaio o chage i he cyclical compoe o real margial co i decreaig i omial rigidiy parameer ω ad idexaio parameer γ. hee impor price hillip curve are ubjec o impor price markup hock. he cyclical compoe o oerepô impor deped o he coemporaeou cyclical compoe o coumpio iveme goverme coumpio ad he erm o rade accordig o approximae liear impor demad ucio

42 40 ˆ ˆ ˆ l ˆ I I I G G G = ( φ ) l + ( φ ) l + ( φ ) l ˆ ν ˆ ν ˆ ν ˆ I I I G G G ψ φ ( φ ) + φ ( φ ) + φ ( φ ) l ˆ ν (90) I G I G where = ( φ ) + ( φ ) + ( φ ). he cyclical compoe o erepô impor ˆ e e aiie l ˆ e l ˆ = ψ l ˆ where = ( φ ). he eiiviy o he cyclical compoe o oerepô impor o chage i he cyclical compoe o he erm o rade i icreaig i elaiciy o ubiuio parameer ψ. hi approximae liear oerepô impor demad ucio i ubjec o impor produciviy hock. he cyclical compoe o he eecive wage deped o a average o he coemporaeou cyclical compoe o he ukilled ad killed eecive wage: ˆ ˆ u ˆ W W W l = ϕ l + ( ϕ ) l. (9) ˆ ˆu ˆ A A A he cyclical compoe o ukilled ad killed employme aiy ˆl ˆl l( A) l( ˆ ˆ = A ) ϑ l Wˆ l / ˆ l A. Wˆ / Aˆ he cyclical compoe o he killed or ukilled wage deped o a average o i pa ad expeced uure cyclical compoe drive by he coemporaeou cyclical compoe o he deviaio o he margial rae o ubiuio bewee leiure ad coumpio rom he aer ax real wage accordig o wage hillip curve: ˆ l ˆ l ˆ l W W β W+ l = l + E l ˆ Il ˆ I l ˆ Il W + β W + β W+ (9) l l ( )( ) l ˆl l ˆl ˆ ˆ ˆ l ω ω β α l α l τ W l ˆ l l ˆ + τ. + + l θ ( ) ˆ ω + β η α σ α τ θ Relecig he exiece o wage idexaio he cyclical compoe o he killed or ukilled wage alo deped o pa coemporaeou ad expeced uure cyclical compoe o he idexed wage. he eiiviy o he cyclical compoe o he killed or ukilled wage o chage i he cyclical compoe o he deviaio o he margial rae o ubiuio bewee leiure ad coumpio rom he aer ax real wage i decreaig i l omial rigidiy parameer ω ad o chage i he cyclical compoe o adjued employme i decreaig i elaiciy o ubiuio parameer η. hee wage hillip curve are ubjec o wage markup hock.

43 4 he cyclical compoe o killed or ukilled idexed wage ilaio deped o pa aggregae wage ilaio coumpio price ilaio ad average labor produciviy growh accordig o idexaio rule: Wˆ ˆ yˆ = (93) ˆ Il l W l l y l l l l l ˆ Il W γ γ γ W. ˆ ˆ W yˆ he eiiviy o he cyclical compoe o killed or ukilled idexed wage ilaio o chage i he cyclical compoe o wage ilaio i icreaig i idexaio parameer l W γ o chage i he cyclical compoe o coumpio price ilaio i icreaig i l idexaio parameer γ ad o chage i he cyclical compoe o labor produciviy l y growh i icreaig i idexaio parameer γ. he cyclical compoe o average labor produciviy aiie l yˆ = lˆ l ˆ. he cyclical compoe o real margial co deped o he coemporaeou cyclical compoe o he deviaio o he aer ax real wage rom he margial produc o labor accordig o approximae liear implici labor demad ucio: ˆ ˆ ˆ l ˆ W τ θ W uk Φ l l ˆ = τ l. ˆ ˆ A τ ϑ θ A ˆ ˆ (94) he eiiviy o he cyclical compoe o real margial co o chage i he cyclical compoe o he raio o uilied capial o eecive labor i decreaig i elaiciy o ubiuio parameer ϑ. hi approximae liear implici labor demad ucio i ubjec o labor produciviy hock. he cyclical compoe o he omial iere rae deped o i pa cyclical compoe ad he coemporaeou cyclical compoe o coumpio price ilaio oupu he oreig omial iere rae ad he omial exchage rae accordig o moeary policy rule: iˆ = ρ iˆ + ( ρ )( ξ ˆ π + ξ lˆ + ξ iˆ + ξ l E ˆ ) + ν. (95) π i E i i i hi moeary policy rule e hoe ollowed by he domeic ad oreig moeary auhoriie uder parameer rericio ad i ubjec o moeary policy hock. he cyclical compoe o he oupu baed real iere rae aiie ˆ ˆ r E ˆ = i π + while he cyclical compoe o he coumpio baed real iere rae aiie ˆ ˆ r E ˆ = i π +. he cyclical compoe o he omial exchage rae deped o i expeced uure cyclical compoe ad he coemporaeou cyclical compoe o he omial iere rae diereial accordig o approximae liear ucovered iere pariy codiio:

44 4 l Eˆ = E l E ˆ ( iˆ iˆ ) E ˆ. (96) + + hi approximae liear ucovered iere pariy codiio i ubjec o oreig exchage raacio co hock. he cyclical compoe o he real exchage rae aiie ˆ ˆ ˆ l l l l ˆ Q = E + while he cyclical compoe o he erm o rade aiie l ˆ l ˆ l ˆ = where l ˆ l ˆ =. he cyclical compoe o omial oupu deped o he coemporaeou cyclical compoe o omial coumpio iveme goverme coumpio oerepô expor ad oerepô impor accordig o approximae liear aggregae reource corai: ˆ ˆ ˆ ˆ I l( ) l( ) l( ˆI ˆ G ) l( ˆG ˆ ) l( ˆ ˆ ) l( ˆ ˆ = + I + G + ). (97) I equilibrium he cyclical compoe o oupu i deermied by he cumulaive demad o domeic ad oreig houehold irm ad goverme. he cyclical compoe o he e goverme ae poiio deped o i pa cyclical compoe he pa cyclical compoe o he omial iere rae he coemporaeou cyclical compoe o ax reveue ad he coemporaeou cyclical compoe o omial goverme coumpio accordig o approximae liear goverme dyamic budge corai G G G ˆ B G G ˆ ˆ + = + + τ τ ˆ ˆ l B l B i l( ˆ ˆ) l( ˆ G ) β where B G β G ( ) = τ. hi approximae liear goverme dyamic budge corai β uppor deermiacy oly i he level o he e goverme ae poiio doe o chage ig. (98) he cyclical compoe o he e oreig ae poiio deped o i pa cyclical compoe he pa cyclical compoe o he omial iere rae he coemporaeou cyclical compoe o expor reveue ad he coemporaeou cyclical compoe o impor expediure accordig o approximae liear aioal dyamic budge corai ˆ B + = + + ˆ ˆ l B l B i l( ˆ ˆ ) l( ˆ ˆ ) β (99)

45 B β where ( ) 43 =. hi approximae liear aioal dyamic budge corai β uppor deermiacy oly i he level o he e oreig ae poiio doe o chage ig. Variaio i cyclical compoe i drive by welve exogeou ochaic procee oe o which i commo o he domeic ad oreig ecoomie. he cyclical compoe o he preerece labor produciviy iveme produciviy impor produciviy oupu price markup expor price markup impor price markup ad wage markup hock ollow aioary ir order auoregreive procee: ˆ = ˆ + N (00) l ν ρ l ν ε ν ε ν ~ iid (0 σ ) ν ν Aˆ = ρ Aˆ + ε ε N σ (0) A A l Al ~ iid (0 A) ˆ = ˆ + N (0) l ν I I I ρ l ν I ε ν I ε ν ~ iid (0 σ I) ν ν ˆ = ˆ + N (03) l ν ρ l ν ε ν ε ν ~ iid (0 σ ) ν ν ˆ = ˆ + N (04) l θ ρ l θ ε θ ε θ ~ iid (0 σ ) θ θ ˆ = ˆ + N (05) l θ ρ l θ ε θ ε θ ~ iid (0 σ ) θ θ ˆ = ˆ + N (06) l θ ρ l θ ε θ ε θ ~ iid (0 σ ) θ θ ˆ = ˆ + N (07) l θ ρ l θ ε θ ε θ ~ iid (0 σ ). θ θ he cyclical compoe o he ukilled ad killed labor produciviy hock aiy ˆl l A l ˆ = A. he cyclical compoe o he moeary policy ical expediure ad ical reveue hock ollow whie oie procee: i i i ˆ ν ν ~ iid (0 i ) ν = ε ε N σ ν (08) G G G ˆ ν ν ~iid (0 G ) ν = ε ε N σ ν (09) τ τ τ ν ν ˆ ~ iid (0 τ ). ν = ε ε N σ ν (0) he cyclical compoe o he oreig exchage raacio co hock ollow a aioary ir order auoregreive proce:

46 44 ˆ ˆ ρ ε ε ~ iid (0 σ ). = + N () he iovaio drivig hee exogeou ochaic procee are aumed o be idepede which combied wih our diribuioal aumpio implie mulivariae ormaliy. I I deermiiic eady ae equilibrium ν = ν = ν = ad σ = σ A = σ I = σ = σ = ν ν ν θ σ = σ = σ = σ = σ = σ = σ = 0. i G τ θ θ θ ν ν ν red ompoe he red compoe o he price o oupu coumpio iveme goverme coumpio expor erepô expor impor ad oerepô impor ollow radom walk wih ime varyig dri π : l l π ε ε ~ iid (0 σ ) = + + N () l l π ε ε ~ iid (0 σ ) = + + N (3) l l I I I I π ε ε ~ iid (0 σ I ) = + + N (4) l l G G G G π ε ε ~ iid (0 σ G ) = + + N (5) l l π ε ε ~ iid (0 σ ) = + + N (6) e e l l e e π ε ε ~ iid (0 σ e ) = + + N (7) l l π ε ε ~ iid (0 σ ) = + + N (8) l l π ε ε ~ iid (0 σ ). = + + N (9) I ollow ha he red compoe o he relaive price o coumpio iveme goverme coumpio expor erepô expor impor ad oerepô impor ollow radom walk wihou dri. hi implie ha alog a balaced growh pah he level o hee relaive price are ime idepede bu ae depede. he red compoe o he price o oerepô expor aiie l = l while he red compoe o he price e o erepô impor aiie l = l.

47 45 he red compoe o oupu coumpio iveme goverme coumpio expor erepô expor impor ad oerepô impor ollow radom walk wih ime varyig dri g + : = g ε ε N σ (0) l l ~ iid (0 ) = g ε ε N σ () l l ~ iid (0 ) I = g + + I + ε ε N σ () I I l l ~ iid (0 ) I G = g + + G + ε ε N σ (3) G G l l ~ iid (0 ) G = g ε ε N σ (4) l l ~ iid (0 ) l l e e e e g ε ε ~ iid (0 σ e ) = N (5) = g ε ε N σ (6) l l ~ iid (0 ) l l g ε ε ~ iid (0 σ ). = N (7) I ollow ha he red compoe o he raio o coumpio iveme goverme coumpio expor erepô expor impor ad oerepô impor o oupu ollow radom walk wihou dri. hi implie ha alog a balaced growh pah he level o hee grea raio are ime idepede bu ae depede. he red compoe o oerepô expor reveue aiie l = l while he red compoe o e e e erepô impor expediure aiie l = l. he red compoe o he omial wage ollow a radom walk wih ime varyig dri π + g while he red compoe o employme ollow a radom walk wih ime varyig dri : W = π + g + W + ε ε N σ (8) W W l l ~ iid (0 ) W = + + ε ε N σ (9) l l ~ iid (0 ). I ollow ha he red compoe o he icome hare o labor ollow a radom walk wihou dri. hi implie ha alog a balaced growh pah he level o he icome hare o labor i ime idepede bu ae depede. he red compoe o he idexed wage

48 46 I aiie lw = lw while he red compoe o average labor produciviy aiie l y = l l. he red compoe o real margial co aiie lφ = lφ while he red compoe o he rae o capial uiliaio aiie l u = 0. he red compoe o he hadow price o capial aiie l Q l I = while he red compoe o he capial K + K ock aiie l = l. he red compoe o he omial iere rae ax rae ad omial exchage rae ollow radom walk wihou dri: i = i + ε ε N σ (30) i i ~ iid (0 i ) τ τ lτ l τ ε ε ~ iid (0 σ τ ) = + N (3) E = E + ε E ε E N σ (3) E l l ~ iid (0 ). I ollow ha alog a balaced growh pah he level o he omial iere rae ax rae ad omial exchage rae are ime idepede bu ae depede. he red compoe o he oupu baed real iere rae aiie r = i Eπ + while he red compoe o he coumpio baed real iere rae aiie r = i Eπ +. he red compoe o he real exchage rae aiie lq = l E + l l while he red compoe o he erm o rade aiie l = l l. he red compoe o he e goverme G G B + B ae poiio aiie l = l while he red compoe o he e oreig ae B + B poiio aiie l = l. og ru balaced growh i drive by hree commo ochaic red. red ilaio produciviy growh ad populaio growh ollow radom walk wihou dri: π = π + ε ε N σ π (33) π π ~iid (0 ) g = g + ε ε N σ (34) g g ~iid (0 g) = + ε ε N σ (35) ~ iid (0 ). I ollow ha alog a balaced growh pah growh rae are ime idepede bu ae depede. A a ideiyig rericio all iovaio are aumed o be idepede which combied wih our diribuioal aumpio implie mulivariae ormaliy.

49 47 Eimaio he radiioal ecoomeric ierpreaio o macroecoomeric model regard hem a repreeaio o he joi probabiliy diribuio o he daa. We employ a Bayeia eimaio procedure which repec hi radiioal ecoomeric ierpreaio. Eimaio rocedure he parameer ad uoberved compoe o our rucural uoberved compoe model o a mall ope ecoomy are joily eimaed wih a Bayeia procedure codiioal o prior iormaio cocerig he value o parameer ad judgme cocerig he pah o red compoe. Ierece o he parameer i baed o a aympoic ormal approximaio o he poerior diribuio aroud i mode which i calculaed by umerically maximiig he logarihm o he poerior deiy kerel. Followig Egle ad Wao (98) we employ a eimaor o he Heia which deped oly o ir derivaive ad i egaive emideiie. Evaluaio o he logarihm o he poerior deiy kerel ivolve ir corucig a mulivariae liear raioal expecaio repreeaio o hoe equaio goverig he evoluio o cyclical compoe he olvig or he uique aioary oluio o hi mulivariae liear raioal expecaio model wih he algorihm due o Klei (000). he reula ir order vecor auoregreive repreeaio o hoe equaio goverig he evoluio o cyclical compoe i he combied wih a dyamic acor repreeaio o hoe equaio goverig he evoluio o red compoe o orm a liear ae pace model expreig he level o all oberved opredeermied edogeou variable a a ucio o a uoberved ae vecor which i ur evolve accordig o a ir order vecor auoregreive proce. hi liear ae pace model i he augmeed wih a e o ochaic rericio o eleced uoberved ae variable ummariig judgme cocerig he pah o he red compoe o all oberved opredeermied edogeou variable. he logarihm o he predicive deiy ucio i he evaluaed codiioal o he parameer aociaed wih hi liear ae pace model wih he iler derived i Viek (008a 008b) which adap he iler due o Kalma (960) o icorporae judgme. Fially he logarihm o hi codiioal deiy ucio i combied wih he logarihm o a mulivariae ormal deiy ucio ummariig prior iormaio cocerig he value o parameer. For a deailed dicuio o hi eimaio procedure pleae reer o Viek (008a 008b). Eimaio Reul he e o parameer aociaed wih our rucural uoberved compoe model i pariioed io wo ube. he ir ube i calibraed o approximaely mach ample average o ucio o he level o oberved edogeou variable where poible or eimae repored i he exiig empirical lieraure where eceary. he ecod ube i

50 48 eimaed wih he Bayeia procedure decribed above codiioal o he level o hiry oe edogeou variable or Hog Kog SAR ad he Uied Sae oberved over he rece iked Exchage Rae Syem period paig 983Q4 hrough 008Q. Subjecive dicou acor β i rericed o equal 0.99 implyig a aualied deermiiic eady ae equilibrium real iere rae o approximaely I deermiiic eady ae θ equilibrium he oupu price markup expor price markup θ ad impor price θ θ θ markup are rericed o equal.5 while he wage markup θ i rericed o equal θ θ.50. Depreciaio rae parameer δ i rericed o equal 0.05 implyig a aualied deermiiic eady ae equilibrium depreciaio rae o approximaely 0.0. I deermiiic eady ae equilibrium he coumpio impor hare φ iveme I G impor hare φ ad goverme coumpio impor hare φ are rericed o equal 0.65 domeically ad 0.0 abroad. he deermiiic eady ae equilibrium raio o coumpio o oupu i rericed o equal 0.60 while he deermiiic eady ae equilibrium raio o domeic oupu o oreig oupu i rericed o equal I deermiiic eady ae equilibrium he erepô expor hare φ i rericed o equal 0.65 while he erepô impor hare i rericed o equal he deermiiic eady ae equilibrium icome hare o labor W i rericed o equal 0.45 domeically ad 0.55 abroad. I deermiiic eady ae equilibrium he raio o goverme coumpio o oupu G i rericed o equal 0.0 domeically ad 0.0 abroad while he ax rae τ i rericed o equal 0.08 domeically ad 0. abroad. able I.. Deermiiic Seady Sae Equilibrium Value o Grea Raio / Raio Hog Kog SAR Uied Sae / I / G/ / e / / / W / K / G B / B / / Deermiiic eady ae equilibrium value are repored a a aual requecy baed o calibraed parameer value. Bayeia eimaio o he remaiig parameer o our rucural uoberved compoe model o a mall ope ecoomy i baed o he level o hiry oe oberved edogeou variable or Hog Kog SAR ad he Uied Sae decribed i Appedix II. hoe parameer aociaed wih he codiioal mea ucio are eimaed codiioal o

51 49 iormaive idepede prior while hoe parameer aociaed excluively wih he codiioal variace ucio are eimaed codiioal o diue prior. Iiial codiio or he cyclical compoe o exogeou variable are give by heir ucodiioal mea ad variace while he iiial value o all oher ae variable are reaed a parameer ad are calibraed o mach ucio o iiial realiaio o he level o oberved edogeou variable or prelimiary eimae o heir red compoe calculaed wih he iler decribed i Hodrick ad reco (997). he poerior mode i calculaed by umerically maximiig he logarihm o he poerior deiy kerel wih a modiied eepe ace algorihm. arameer eimaio reul peraiig o he period 983Q4 hrough 008Q are repored i able I.. he uicie codiio or he exiece o a uique aioary raioal expecaio equilibrium due o Klei (000) i aiied i a eighborhood aroud he poerior mode while our eimaor o he Heia i o early igular a he poerior mode uggeig ha he approximae liear ae pace repreeaio o our rucural uoberved compoe model i locally ideiied. hoe parameer aociaed wih he codiioal mea ucio are eimaed codiioal o idepede margial prior diribuio ceered wihi he rage o eimae repored i relaed empirical paper uch a hriiao Eichebaum ad Eva (005) ad Sme ad Wouer (003). he prior mea o idexaio parameer γ i 0.50 domeically ad 0.75 abroad implyig coiderable oupu price ilaio ieria while he prior mea o omial rigidiy parameer ω implie a average duraio o oupu price corac o ix quarer domeically ad eigh quarer abroad durig which ime oupu price are adjued ubopimally every quarer. he prior mea o capial uiliaio co parameer κ i 0.0 while he prior mea o elaiciy o ubiuio parameer ϑ i 0.50 implyig ha uilied capial ad eecive labor are moderaely cloe compleme i producio. he prior mea o habi periece parameer α i 0.95 while he prior mea o ieremporal elaiciy o ubiuio parameer σ i.75 implyig ha coumpio exhibi coiderable periece ad moderae eiiviy o real iere rae chage. he prior mea o iveme adjume co parameer χ i 5.75 implyig moderae eiiviy o iveme o chage i he relaive hadow price o capial. he prior mea o idexaio parameer γ i 0.50 domeically ad 0.75 abroad implyig moderae impor price ilaio ieria while he prior mea o omial rigidiy parameer ω implie a average duraio o impor price corac o ix quarer domeically ad eigh quarer abroad durig which ime impor price are adjued ubopimally every quarer. he prior mea o elaiciy o ubiuio parameer ψ i.50 implyig ha domeic ad oreig good are moderaely cloe ubiue i coumpio iveme ad goverme coumpio. he prior mea o idexaio parameer γ i 0.75 implyig moderae expor price ilaio ieria while he prior mea o omial rigidiy parameer ω implie a average duraio o expor price corac o ix quarer durig which ime expor price are adjued ubopimally every quarer. he prior mea o elaiciy o ubiuio parameer ψ i.50 implyig ha oerepô ad erepô expor are moderaely cloe ubiue i expor while he prior mea o elaiciy o ubiuio parameer ψ i.50 implyig ha oerepô ad erepô impor are moderaely cloe ubiue i impor. he prior mea o idexaio

52 50 parameer γ i 0.50 domeically ad 0.75 abroad implyig coiderable eiiviy o he real wage o chage i coumpio price ilaio while he prior mea o omial rigidiy parameer ω implie a average duraio o wage corac o ix quarer domeically ad eigh quarer abroad durig which ime wage are adjued ubopimally every quarer. he prior mea o habi periece parameer α i 0.95 while he prior mea o elaiciy o ubiuio parameer η i 0.50 implyig coiderable ieiiviy o he real wage o chage i employme. he prior mea o he omial exchage rae repoe coeicie ξ E i he domeic moeary policy rule i.00 implyig covergece o he level o he omial exchage rae o i arge value. he prior mea o he coumpio price ilaio π repoe coeicie ξ i he oreig moeary policy rule i.50 while he prior mea o he oupu repoe coeicie ξ i 0.5 implyig covergece o he level o coumpio price ilaio o i arge value. he prior mea o he e oreig ae G repoe coeicie ζ i he ical expediure rule i 0.0 while he prior mea o he e τ goverme ae repoe coeicie ζ i he ical reveue rule i.00 domeically ad.00 abroad implyig covergece o he level o he raio o e oreig ae ad e goverme ae o omial oupu o heir arge value. All auoregreive parameer ρ have prior mea o 0.85 implyig coiderable periece o hock drivig variaio i cyclical compoe. Judgme cocerig he pah o red compoe i geeraed by paig he level o all oberved edogeou variable hrough he iler decribed i Hodrick ad reco (997). 3 Sochaic rericio o he red compoe o all oberved edogeou variable are derived rom hee prelimiary eimae wih iovaio variace e proporioal o he ample variace o cyclical deviaio rom hem. All ochaic rericio are idepede repreeed by a diagoal covariace marix ad are harmoied repreeed by a commo acor o proporioaliy. Relecig lile coidece i hee prelimiary red compoe eimae hi commo acor o proporioaliy i e equal o oe. he poerior mode o all rucural parameer are cloe o heir prior mea relecig he impoiio o igh idepede prior o preerve ecoomically plauible impule repoe dyamic. he eimaed variace o hock drivig variaio i cyclical compoe are all well wihi he rage o eimae repored i he exiig empirical lieraure aer accouig or daa recalig. he eimaed variace o hock drivig variaio i red compoe are relaively high idicaig ha much o he variaio i he level o oberved edogeou variable i accoued or by variaio i heir red compoe. 3 Followig heir recommedaio he moohe parameer i e o 600.

53 5 able I.. arameer Eimaio Reul / Hog Kog SAR Uied Sae rior oerior rior oerior arameer ea SE ode SE ea SE ode SE α α χ η κ σ ϑ γ γ γ W γ γ y γ ω ω ω ω ψ ψ ψ π ξ ξ ξ E ρ i G ζ τ ζ ρ G ρ τ ρ ν ρ A ρ I ν ρ ν ρ θ ρ θ ρ θ ρ θ ρ ν A I ν ν θ θ θ θ i ν G ν τ ν σ σ σ σ σ σ σ σ σ σ σ

54 5 able I.. arameer Eimaio Reul / Hog Kog SAR Uied Sae rior oerior rior oerior arameer ea SE ode SE ea SE ode SE σ I I G G e e W i τ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ σ E σ π g σ σ / All oberved edogeou variable are recaled by a acor o 00.

55 53 AENDI II. DESRIION OF HE DAA SE he daa e coi o quarerly eaoally adjued obervaio o hiry oe macroecoomic variable or Hog Kog SAR ad he Uied Sae over he period 983Q4 hrough 008Q. All aggregae price ad quaiie are expediure baed. he omial iere rae i meaured by he hree moh moey marke rae expreed a a period average while he omial exchage rae i quoed a a ed o period value. Daa or Hog Kog wa obaied rom he EI daabae maiaied by Iere Securiie Icorporaed while daa or he Uied Sae wa exraced rom he FRED daabae maiaied by he Federal Reerve Bak o Sai oui.

56 54 Reerece alvo G. 983 Saggered rice i a Uiliy-aximiig Framework Joural o oeary Ecoomic Vol. pp hriiao.. Eichebaum ad. Eva 005 Nomial Rigidiie ad he Dyamic Eec o a Shock o oeary olicy Joural o oliical Ecoomy Vol. 3 pp. 45. Egle R. ad. Wao 98 A Oe-Facor ulivariae ime Serie odel o eropolia Wage Rae Joural o he America Saiical Aociaio Vol. 76 pp Erceg. D. Hedero ad A. evi 000 Opimal oeary olicy wih Saggered Wage ad rice orac Joural o oeary Ecoomic Vol. 46 pp Hodrick R. ad E. reco 997 o-war U.S. Buie ycle: A Decripive Empirical Iveigaio Joural o oey redi ad Bakig Vol. 9 pp. 6. Kalma R. 960 A New Approach o iear Filerig ad redicio roblem raacio ASE Joural o Baic Egieerig Vol. 8 pp Klei. 000 Uig he Geeralied Schur Form o Solve a ulivariae iear Raioal Expecaio odel Joural o Ecoomic Dyamic ad orol Vol. 4 pp oacelli. 005 oeary olicy i a ow a-hrough Evirome Joural o oey redi ad Bakig Vol. 37 pp orer N. ad F. Viek 008 A Srucural Aalyi o Savig ad Iveme Dyamic i Hog Kog SAR IF Workig aper (orhcomig) (Wahigo: Ieraioal oeary Fud). Sme F. ad R. Wouer 003 A Eimaed Dyamic Sochaic Geeral Equilibrium odel o he Euro Area Joural o he Europea Ecoomic Aociaio Vol. pp Viek F. 008a oeary olicy Aalyi: Developme ad Evaluaio o Quaiaive ool (Hyderabad Idia: IFAI Uiveriy re). 008b oeary olicy Aalyi i a Small Ope Ecoomy: Developme ad Evaluaio o Quaiaive ool (Germay: Vdm Verlag).