INTERNATIONAL MONETARY POLICY ANALYSIS WITH DURABLE GOODS

Transcription

1 INTERNATIONAL MONETARY POLICY ANALYSIS WIT DURABLE GOODS A Dsseraon by KANG KOO LEE Submed o he Offce of Graduae Sudes of Texas A&M Unversy n paral fulfllmen of he reuremens for he degree of DOCTOR O PILOSOPY Augus 9 Major Subjec: Economcs

2 INTERNATIONAL MONETARY POLICY ANALYSIS WIT DURABLE GOODS A Dsseraon by KANG KOO LEE Submed o he Offce of Graduae Sudes of Texas A&M Unversy n paral fulfllmen of he reuremens for he degree of DOCTOR O PILOSOPY Approved by: Char of Commee, Commee Members, ead of Deparmen, Denns W. Jansen Leonardo Auernhemer Davd Bessler agen Km Larry Olver Augus 9 Major Subjec: Economcs

3 ABSTRACT Inernaonal Moneary Polcy Analyss wh Durable Goods. (Augus 9) Kang Koo Lee, B.A., Sejong Unversy; M.A., Sejong Unversy Char of Advsory Commee: Dr. Denns W. Jansen The dsseraon sudes a model of an economy whch produces and expors durable goods. I analyzes he opmal moneary polcy for such a counry. Generally, moneary polcy has a bgger economc effec on durable goods relave o non-durable goods because durable goods can be sored and households ge uly from he sock of durable goods. Ths dsseraon shows ha, n Nash eulbrum, he cenral bank of a durable goods producng counry can conrol changes of he prce level wh smaller changes n he moneary polcy nsrumen. In he cooperave eulbrum, he moneary auhory of he counry whch mpors non-durable goods and expors durable goods should rase he neres rae by more, relave o he Nash case, n response o a rse n foregn nflaon. On he oher hand, he moneary auhory of he counry whch mpors durable goods and expors non-durable goods should rase he neres rae by less han he oher counry.

4 To my famly v

5 v TABLE O CONTENTS Page ABSTRACT... DEDICATION... TABLE O CONTENTS... LIST O IGURE... v v v CAPTER I INTRODUCTION... II TE MODEL Represenave ousehold rms and Prce Seng Governmen Polcy Uncovered Ineres Pary Marke Clearng Condons... 4 III EQUILIBRIUM Seady-Sae Eulbrum lexble-prce Eulbrum Scky-Prce Eulbrum... IV TE WELARE UNCTION AND OPTIMAL MONETARY POLICY The Welfare uncon and Opmal Subsdy Rae Opmal Moneary Polcy... 7 V CONCLUSIONS... REERENCES... 4 APPENDIX A... 6 VITA... 69

6 v LIST O IGURES gure low of durable goods n wo counres seng... 6 Page

7 CAPTER I INTRODUCTION A sgnfcan poron of measured consumpon spendng reflecs purchases of consumer durables long-lved ems such as furnure, auos, elevsons, and home compuers.. If all durables were rened n perfec renal markes, he durablenondurable dsncon would be unmporan. Emprcally, however, consumer purchases of durable ems are subsanal.. Many New Keynesan models neglec durable goods, such as Clarda, Gal and Gerler (999) and Woodford (). Ths may be due o he fac ha he share of he durable goods secor n he gross domesc produc (GDP) s ue a b smaller han he non-durables and servce secors. Accordng o Erceg and Levn (6), he share of he durable goods secor n U.S. GDP s only abou %. Some recen papers, however, pay aenon o he role played by durable goods. Erceg and Levn (6) and Monacell (8) show ha durable goods spendng s more sensve o moneary shocks han non-durable goods spendng. Barsky e al. (7) explan hese resuls as semmng from he specal properes of durables. They wre ha durable goods have neresng and unue properes ha are drecly relaed o her lengh of lfe. The neremporal elascy of subsuon for he consumpon of durable goods s naurally hgh for durables wh low deprecaon raes, such as housng and Ths dsseraon follows he syle and forma of he Journal of Inernaonal Economcs. Obsfeld and Rogoff (999) p. 96

8 busness srucures. Ths plays a much larger role n flucuaons of aggregae oupu and can play a large role n busness cycles. The unue feaure of durables and he dsncve feaure of long-lved durables wh scky prces lead o resuls ha are dfferen from resuls drawn from sudes lookng only a non-durables and comparng eulbra wh scky and flexble prces. Though here are recen sudes abou durables n closed economy, here are few papers focusng on durables and non-durables n an nernaonal seng. Ths sudy abou durable goods spendng n wo dfferen counres and he resulng polcy uesons wll, I hnk, prove o be a fruful area of research n he New Open Economy Macroeconomcs. Ths dsseraon works o provde answers o he followng uesons: Wha s he gan from moneary polcy cooperaon wh durables? ow does hs dffer from models wh only non-durables? Whch counry would have more benef from moneary polcy cooperaon, a counry producng only durable goods or a counry producng only nondurable goods? Several recen papers have nroduced durable goods no a closed-economy model. Barsky e al. (7) examne boh scky and flexble prce secors n a closed economy model wh durable and non-durable goods, and shows ha he presence of durable goods can aler he ransmsson of moneary shocks even hough durables have a small share n oal spendng. Parcularly, f durable prces are flexble, her work shows ha moneary polcy s neural. If durable prces are scky, he model works as a scky prce model even f non-durable prces are flexble.

9 Campbell and ercowz (5) sudy he role of collaeral deb n a busness cycle model and hey conclude ha lowerng he neres rae nduces an expandng labor supply by ncreasng he demand for durable goods, nsead of he sandard resul of a conracng labor supply by reducng he prce of curren lesure relave o fuure lesure. Monacell (8) sudes a New Keynesan model wh durable goods and argues ha assumpon on he degree of sckness of durables may become rrelevan when once a collaeral consran on borrowng s nroduced n he model. The reduced ably of borrowng also reduces he demand for non-durables when prces are scky n durable goods secor. Therefore, he collaeral consran makes a complemenary effec beween durable and non-durable demand, whle he moneary polcy ghenng produces a subsuon effec from durables o non-durables by rsng he user cos when prces are flexble. Erceg and Levn (6) compare he performance of several moneary polces n a scky prce model wh durable and non-durable goods, and hey show ha he opmal polcy rule can be approxmaed by a smple argeng rule for a weghed average of aggregae wage and prce nflaon when he socal welfare funcon consss of secorspecfc oupu gaps and nflaon raes. an (8) examnes he relaonshp among heerogeneous durably of consumpon goods, prce ndexes and moneary polcy n a scky prce model, and concludes ha he opmal polcy s o sablze core nflaon, gvng more wegh o he secor producng more durable goods.

10 4 A classc ssue n nernaonal moneary economcs s o ask wheher here s a gan from polcy coordnaon. Our goal s o examne hs ssue n an nernaonal economc model ha ncludes durable goods. Recen works n nernaonal moneary economcs area have nvolved he developmen of he dynamc sochasc general eulbrum models wh mperfec compeon and nomnal rgdes. Clarda e al. () examne nernaonal moneary polcy n a wo-counry scky prce model, where each counry faces a shor run rade off beween oupu and nflaon. They show ha, n he Nash eulbrum, each cenral bank needs o adjus s neres rae n response o only domesc nflaon, whle, n he coordnave eulbrum, here are gans when hey should respond o foregn nflaon. Gal and Moncell (5) analyze he properes and macroeconomc mplcaons of alernave moneary polcy regmes n a small open economy model wh saggered prce-seng, and show ha a domesc nflaon-based Taylor rule domnaes a CPIbased Taylor rule, and he laer domnaes an exchange rae peg. The res of he dsseraon s srucured as he followng. Chaper II presens he wocounry model nroducng durable goods. Chaper III descrbes eulbrum condons when prces are flexble and scky. Chaper IV sudes he welfare funcon and opmal moneary polcy n he Nash case and he case of cooperaon. Concludng remarks and fuure works are n Chaper V.

11 5 CAPTER II TE MODEL We follow he wo-counry model of Clarda e al. (). There are wo regons, labeled and. Whle he fnal goods producer n counry j supples a sngle dfferenaed durable good, he represenave household n counry j s a consumer of all he goods produced n boh counry and. Thus all goods produced are raded beween regons. The populaon of wo counres s a connuum of agens on he nerval [, ]. The populaon s dvded by (n, ] belongs o counry and [, n] belongs o counry. In hs economy, here are a large number of dencal and nfnely lved households. The represenave household derves uly from servces provded by wo durable goods and dsuly from supplyng labor. We nroduce durable consumpon goods as n an (8). The fnal durable goods are compose goods of dfferenaed non-durable nermedae goods. The producon of nermedae goods reures labor as he only npu. Inermedae goods are nroduced o provde an analycally convenen mean of havng scky prces, as s he nermedae goods producers who se prces n advance. The flow of fnal durable goods and nermedae goods s shown n gure.

12 6 K K, K, ( ) ( n) D ny () ( ny ) ( ) ( n) D ny ( n) D nd,, nd nd ( ny ) ( nd ) nd,, K K, K, ( ) gure. low of durable goods n wo counres seng. Represenave ousehold The represenave household of counry and seeks o maxmze a dscouned sum of per-perod ules of he form E u( K ) v( N ( )) d, E u( K ) v( N ( )) d (.) ere E s he expecaon operaor, s he dscoun facor, and N ( ) s he uany of labor of ype suppled n perod. Varables wh superscrp ndcae foregn counry values.

13 7 K s an argumen n he uly funcon, a Cobb-Douglas ndex of wo fnal durable goods socks : K K, K, K, K,, K ( ) ( ) (.) where denoes he nraemporal elascy of subsuon beween K, and K,. The sock per person of he fnal durable goods produced n each counry j a me s K j,, j,. K s he ndex of consumpon per person of durables n he home counry, and K s he ndex of durable goods consumpon per person n he foregn counry. The sock of he fnal durable goods produced n each counry j evolves accordng o a law of accumulaon: K ( ) K D, K ( ) K D (.) j, j j, j, j, j j, j, for j,, where D j, s he amoun of he purchased fnal durables produced n counry j per capa, and s he deprecaon raes of he fnal durable goods n counry j. Noe j j for j=,. j Le denoe he (random) payoffs n perod + of he fnancal asse porfolo held a he end of. Noe does no refer o he uany held of some sngle ype of bond. As assumng complee markes, households mus be able, a leas n prncple, o hold any of a wde selecon of nsrumens wh dfferen sae-conngen reurns. owever, we don need o nroduce any noaon for he parcular ypes of fnancal nsrumens ha are raded nernaonally. Snce any paern of fuure sae-conngen

14 8 payoffs ha a household may desre can be arranged for he approprae prce, we can wre he household s consumpon plannng and wealh-accumulaon problems whou any explc reference o he parcular asses uanes ha a household holds., denoes he correspondng sochasc dscoun facor for one-perod-ahead nomnal payoffs relevan o he domesc household. s The budge consran of he represenave household of counry and n perod E W () N () d () dp D P D T,,,,,, () () (),,,, E W N d d P D P D T (.4) where P j, s he prce of he fnal durable goods n counry j, N ( ) s he uany of labor of ype suppled, W ( ) s he nomnal wage of labor of ype, ( ) s he nomnal prof from sales of nermedae good, and T represen ne lump-sum ax collecons by he governmen. The frs-order condons are gven by u ( ) / ( ) k K K K P P u ( K ) K / K P ( ) P,,,, (.5) k,,,,, Le R denoe he gross nomnal yeld on a one-perod dscoun bond. Then by akng he expecaon of each sde of (.5), we have he Euler euaon : u ( K ) Q k RE uk( K) Q (.6) Woodford () Ch.

15 9 K, K, (.7) for [,], where Q / Q Q / Q vn( N( )) W( ) (.8) u ( K ) Q k, R E,,,,, s he expeced prce of he dscoun bonds payng off one un of domesc currency n +, and he user cos of durable goods consumpon n counry j Qj, s defned as Qj, Pj, E ( j) Pj, / R Qj, Pj, E ( j) Pj, / R (.9) The cos of lvng ndex (COLI) Q s defned as Q Q Q, Q Q Q (.),,,, Accordng o Cobb-Douglas preferences, he demand funcons are gven by K ( )( Q / Q ) K, K ( )( Q / Q ) K,,,, K ( Q / Q ) K, K ( Q / Q ) K,,,, (.). rms and Prce Seng. nal Goods Producers We assume fnal durables producers behave compevely. The echnology for producng he fnal goods n counry and from nermedae goods s ( ) ( ) (.) Y Y d Y Y d

16 where Y s oupu per person and θ> s he elascy of subsuon across goods produced whn a counry. Maxmzaon of profs yelds demand funcons for he ypcal nermedae good n counry and : ( ) ( ) /, ( ) ( ) / Y P P Y Y P P Y (.) The counry s prce ndex conssen wh he fnal goods producer n each counry earnng zero profs respecvely, s gven by, ( ), ( ) (.4) P P d P P d. Inermedae Goods Producers Inermedae goods producers behave as monopolsc compeors. Each of he dfferenaed nermedae goods uses a specalzed labor npu n s producon. The echnology for producng nermedae goods ype, s Y AN Y A N (.5) ( ) ( ), ( ) ( ) We assume ha me-varyng exogenous echnology facors across supplers whn a counry. A, A are dencal The varable cos of supplyng a uany Y Y of good s gven by (), () W () Y()/ A W () Y ()/ A (.6) Dfferenang (.6) wh respec o he nermedae good, we fnd ha he (nomnal) margnal cos of supplyng good s eual o

17 NMC () W ()/ A NMC () W ()/ A (.7) The relaonshp beween he real margnal cos and he uany suppled s gven by MC () NMC ()/ P, vn( Y( )/ A) Q u ( K ) AP k, v ( Y ( )/ A ) Q N () ()/, u ( K ) A k P, MC NMC P (.8) The Case of Perfecly lexble Prces As usual n a model of monopolsc compeon, s assumed ha each suppler undersands ha s sales depend upon he prce charged for s good, accordng o he demand funcon (.). If prces are perfecly flexble, opmzaon by he suppler of good n counry j nvolves seng a prce P () NMC(), P () NMC (), where /( ) s he seller s desred markup, deermned by he usual Lerner formula, and, s he subsdy o nermedae good producon n counry and. I follows ha each suppler wshes o charge a relave prce sasfyng P ( ) / P, MC( ), P ( ) / P, MC( ) (.9) The counry s naural raes are mplcly defned by v ( Y / A ) N N,, k( ),, ( ) k, P () v( Y / A) Q P() Q P u K AP P u K A P (.)

18 The Calvo Model of Prce Seng ollowng he Calvo syle s prce-seng, fracons, of nermedae goods prces n counry, reman unchanged each perod, whereas new prces are chosen for he oher, of he nermedae goods n counry,. or smplcy, he probably ha any gven prce wll be adjused n any gven perod s assumed o be,, ndependen of he lengh of me snce he prce was se and of wha he parcular good s curren prce may be. Then, he Dx-Sglz prce ndex of counry j n perod sasfes, ( ),, P P P, ( ),, P P P (.) An nermedae goods suppler n counry, ha changes s prce n perod and chooses s new prce P ( ) o maxmze k, k, k k k k E ( ) P( ) Y ( ) W ( ) N ( ) k W k() E, k( ) P( ) Y, k( ) k Aj, k (.) k where, k ( uk( Kk)/ Qj, k)/( uk( K)/ Qj, ), Y, k() P()/ Pk Yk. and The frs order condon for he opmal choce of P s k ( )( ) k ( ) N(, k( )/ k)/ k, k( ) (.) E P v Y A A Y k

19 where u ( K ) / Q. k k k k. Governmen Polcy The fscal auhory chooses a subsdy rae ha maxmzes he uly of he domesc household n a zero nflaon seady sae. Meanwhle, he cenral bank deermnes he shor-erm nomnal neres rae by a me-nvaran commmen rule. The moneary auhory supples bonds n amouns enough o mee bond demand a he arge nomnal-neres rae. Tha means he cenral bank, as ssuer of bonds ha promse o pay uns of s own bonds, can fx boh he nomnal neres rae on s bonds and he uany of bonds n exsence. In a cashless economy, he cenral bank sablzes he prce level around a desred level hrough adjusng he neres rae pad on cenral-bank balances. The home counry s governmen budge consran n me s gven by B T R B P () Y () d (.4) where B s governmen deb (he supply of bond) per person a end of perod. The foregn counry s governmen budge consran n me s gven by B T R B P () Y () d (.5) 4. Uncovered Ineres Pary We assume he complee nernaonal fnancal markes. Ths means ha real raes of reurn n he wo counres are eual. I mus sasfy ha

20 4 r E rr r E r r E E E where rr s real neres rae, log( P / P ) from he law of one prce and PPP and log( P / P ). We nroduce he nomnal exchange rae and he lnk beween prces for wo goods produced by he wo counres. We call he nomnal exchange rae, denoed he prce of foregn currency n erms of domesc currency. We have he law of one prce ha goods sell for he same prce n boh he home and foregn counres. Ths reures P P, P / P,,,, 5. Marke Clearng Condons Marke clearng condons Labor marke : N N N (.6) d s Inermedae goods marke : Y () Y, Y () Y (.7) nal goods marke : ( ny ) ( nd ) nd,, ny ( n) D nd,, (.8) Bond marke : ( nrb ) n RB ( nrb ) n RB d d ( n) n (.9)

21 5 Walras law holds n he economy. Suppose labor and nermedae goods markes are n eulbrum. Then combnng he household s budge consran and he prof funcons of nermedae supplers yelds he bond demand funcon n he form (.) E T PYd () () PYd () () P D P D,,,,, Rearrangng he governmen budge consran, one has he bond supply funcon gven by s B R B T P() Y() d (.) Combnng (.) and (.) gves E B R B P Y P D P D (.),,,,,, We can ge foregn counry s euaon along wh he same analogues. E B R B P Y P D P D (.),,,,,, Mulply economc scale and nomnal exchange rae for counry ( ne ) ( n) BR B P YP D P D,,,,,, n E n B R B P Y P D P D,,,,,, (.4) rom he bond marke clearng condon and he zero rade balance condon, TB n P D ( n) P D, (.4) can be rewren as,,,, The prof funcon of nermedae suppler of ype s gven by () ( ) P() Y() W () () n () ( ) P () Y () W () () n

22 6 ( ny ) ( nd ) nd,, ny ( n) D nd,, (.5) Euaon (.5) s he fnal good marke clearng condon. Thus, Walras law holds n he model.

23 7 CAPTER III EQUILIBRIUM or a real varable X, we defne x log( X / X), x log( X / X), and xˆ log( X / X ), where X and X are he seady sae value and he naural rae of X, respecvely. We defne : he aggregae sock of he fnal good produced n counry per capa and : he aggregae sock of he fnal good produced n counry per capa. ( n) ( n) K nk,, n ( n) K nk,, (.) Usng good marke clearng condons and defnon of K j,, Y ( ) Y ( ) (.) K K (.) 4 rom he demand funcons (.) ( nq ) ( ) QK nq, Q K, (.4) I hen follows he relaon of he aggregae sock of he fnal good produced n counry and 4 Proof s Appendx A..

24 8 K n ( ) K n n( ) ( n) K n ( n) n( ) (.5) where Q / Q Q / Q,,,,. Seady-Sae Eulbrum In he seady-sae (wh no nflaon), from he frs order necessary condons for he household s decson problem, we have: R / (.6) ( K / K )( / ) (.7) Laws of accumulaon of durable goods s vn ( Y / A) W (.8) u ( K ) Q k D K j j j Y, Y (.9) Marke clearng condons (fnal and nermedae goods markes, labor marke, bond marke) ( ny ) ( nd ) nd ny ( n) D nd (.) Y () Y, Y() Y (.)

25 9 Y () A N(), Y () A N () (.) ( n) n (.). lexble-prce Eulbrum When prces are fully flexble, prces are se as a mark-up over margnal coss, moneary polcy s neural, and hus, real varables are affeced by only real dsurbances (producvy shocks n our model). In flexble-prce eulbrum, uanes and prces of each dfferenaed good are eual: Y() Y, Y () Y (.4) and P () P, P() P (.5) The Domesc lexble Prce Eulbrum The flexble domesc prce eulbrum can be represened by he followng a lnearzed sysem: rom (.), rom (.5), y ( ) (.6) k h (.7) h (.8)

26 k ( ) (.9) Defne u / ( Ku ) s he neremporal elascy of subsuon of prvae k kk expendure, and Nv / v s he elascy of margnal dsuly of work. Noe ha NN N he upper bar means he domesc flexble prce eulbrum. C rr, E E (.) 5 where ( )( ), ( ) and Every fnal goods producng frm chooses he same prce under flexble prces. I follows P ()/ P, on (.8). Usng real margnal cos counry s naural raes from (.9) MC A, (), we have he y rr ( ) a (.) 6 where Q / P ( ). The relaonshp beween real neres raes by he acuson approach and he user cos approach s rr rr ( ) E rr (.) C A A,,, Assumng he echnology shocks are saonary, he naural rae of he durable good sock evolves he followng process 7 : E ( ) a ( ) Ea (.) 5 Appendx A.. 6 Appendx A.. 7 Appendx A.4.

27 , ( ) or, E ( ) a ( ) Ea where ( ) E ( ) a ( ) Ea E ( ) a ( ) Ea (.4) wh. ( ) The lexble Prce Eulbrum The double upper bar means he naural level when prces are flexble worldwde. rom (.5), y ( ) (.5) k ( ) h (.6) h (.7) k ( ) (.8) where ( )( ), ( ) C rr, E E (.9) where ( )( ), ( ) C rr, E E (.)

28 E ( ) a ( ) Ea (.), ( ) 4E ( ) a ( ) Ea (.) where ( ) where ( ), 4 ( ). Scky-Prce Eulbrum The log-lnearzaon of he Euler euaon and he euaons around he zeronflaon seady-sae, respecvely, are gven by C k Ek r E (.) y ( ) (.4) k h (.5) C where log Q / Q h (.6) s he COLI nflaon rae, and he real neres rae measured by he user cos can be rewren as C r E r E Eh h (.7) C, r E E r E r ( ) C A A,,, (.8) C A where, log Q, / Q,, and, log P, / P,.

29 Combnng above euaons, one obans E E rr (.9) C, Wh (.), Wh (.9), Wh (.), C C ˆ ˆ E r E, rr, (.4) ˆ ˆ ˆ ˆ C C E ˆ ˆ E ˆ ˆ rr rr (.4),, ˆ ˆ ˆ ˆ C C E ˆ ˆ ˆ ˆ E rr, rr, (.4) We have he Phllps curve euaon, as follows 8 ; ˆ ( ) ˆ E ( ) A A r E, rr, (.4) ( )( ) where. ( ) Usng (.) and (.4) o subsue for he oupu gap and neres rae erms n (.4), he supply euaon can be rewren euvalenly n he form E ( ) E ˆ ˆ ˆ ˆ E ( ) E (.44) 8 Appendx A.5.

30 4 or he worldwde flexble prce, we have he New Keynesan Phllps Curve of Counry, as follow; ˆ ( ) ˆ E ( ) A A ˆ rr, rr, (.45) As shown n he Appendx A.5., euaon (.45) can be smplfed as below; E ( ) E ( ) E ˆ ˆ ˆ ˆ ( ) ˆ E (.46) A smlar analogy s derved for he New Keynesan Phllps Curve of Counry : E ( ) E 4 ( ) E ˆ ˆ ˆ ˆ ( ) ˆ E (.47)

31 5 CAPTER IV TE WELARE UNCTION AND OPTIMAL MONETARY POLICY. The Welfare uncon and Opmal Subsdy Rae Case : Non-Cooperave Case (Nash Eulbrum) The domesc moneary polcy auhory seeks o maxmze he uly of he household, akng as gven he oher counry s polcy and oucomes. In open economy, he flexble prce economy s no he opmal, because he domesc cenral bank has an ncenve o make a surprse change of prce level for advanage of a household of he domesc counry. Therefore, he fscal auhory chooses a producon subsdy rae ha makes he naural level of oupu correspond o he effcen level n a zero nflaon seady sae, as follows 9 ; ( n) (5.) Noe ha subsdy depends only on he openness ( n ), no on he durably ( ). We can ge he moneary auhory s objecve funcon by akng second-order approxmaon of he uly funcon of he represenave household around he domesc flexble prce eulbrum. As shown n he Appendx A.7., we oban he followng uadrac objecve funcon: W ( ) Ku K E ˆ ˆ Nash k ( ) p.. O k, y, a (5.) 9 Appendx A.6.

32 6 ( )( ) where ( ) Case : Cooperave Case In hs secon, we analyze opmal polcy under cooperaon. We assume ha he wo moneary auhores maxmze a weghed sum of he objecve funcons of he home and foregn households. Lke he Nash eulbrum, we assume ha boh fscal auhores choose he subsdy rae ha maxmzes objecve funcon n he seady sae. The opmal subsdy rae for domesc good s, as follows ; (5.) We can ge a smlar euaon of he opmal subsdy rae for foregn good. (5.4) Ths means ha wo counres fscal auhores (, ) choose he common subsdy. (5.5) We can oban he moneary auhory s objecve funcon by akng second-order approxmaon of he uly funcon of a weghed average by he relave economc sze around he globally flexble prce eulbrum. As we show n he Appendx A.9., we oban he followng uadrac objecve funcon: Appendx A.8.

33 7 W ˆ ˆ 4 ˆ ˆ Cooperave ( ) uk KE n p.. O k, y, a ˆ ˆ n ˆ ˆ n n (5.6). Opmal Moneary Polcy Case : Non-Cooperave Case (Nash Eulbrum) An opmal moneary polcy n he Nash eulbrum seeks o mnmze he dscouned sum of losses (5.) subjec o he scky-prce eulbrum gven by euaons (.4) and (.44). The Lagrangan for hs problem s gven by by E E ( ) E, C C ˆ ˆ ˆ ˆ, E rr, rr, ˆ ˆ ˆ ˆ E ( ) E (5.7) C rs order necessary condons wh respec o rr,, ˆ ˆ, and are gven, (5.8) ˆ ˆ ( ),, (5.9) ( ) ( ) (5.),,,

34 8 for each. ollowng Woodford (999), he opmal polcy under a meless perspecve s ha he cenral bank mplemens condons (5.9) and (5.) for all perods. ence, he sysem of he economy under an opmal polcy can be represened by euaons (.44), (5.9), and (5.) gven nal condons, ˆ and,,. Combnng (5.9) and (5.), PPI nflaon and he oupu gap under he opmal polcy sasfy ( ) ( L)( ˆ ˆ ) ( ) (5.) where L s he lag operaor. Noe ha f here s no uncerany whch causes moneary polcy o devae from he opmal rule, euaon (5.) can be reduced o he opmal polcy rule n a sandard model gven by ( ) ˆ L ( ) (5.) whch mples ha he opmal polcy maxmzng socal welfare s o keep he (acuson) prce and he oupu gap a a consan rae ha does no depend on he durably of goods. We may combne he euaon (.4), wh he above soluons o oban an expresson for an neres rae rule ha mplemens he me-conssen polcy n he Nash eulbrum:

35 9 r r rr rr E E A A,, ( ) ( L) E (5.) The opmal rule may be expressed as he sum of hree componens; he domesc naural real neres rae, nex perod s expeced domesc nflaon gap, and a erm ndcang ha he cenral bank adjuss he nomnal rae wh respec o domesc nflaon gap. We oban a smlar euaon of he opmal neres rae rule for he foregn counry: r r rr rr E E A A,, ( ) ( L) E (5.4) Inuvely, he moneary auhory needs o change he nomnal neres rae less wh respec o durably, because he moneary polcy have more nfluence on durable goods han non-durable goods. The counry whch produces durable goods (e.g. ) may adjus he nomnal neres rae less n response o he domesc nflaon rae. Case : Cooperave Case An opmal moneary polcy n he Cooperaon case seeks o mnmze he dscouned sum of losses (5.6) subjec o he scky-prce eulbrum gven by euaons (.4), (.4) and (.46), (.47). The Lagrangan for hs problem s gven by

36 E ˆ ˆ ˆ ˆ n 4 n ˆ ˆ n n C C,,, ˆ ˆ ˆ ˆ rr rr E E C C,,, ˆ ˆ ˆ ˆ rr rr E E E ( ) E ˆ ˆ ˆ ˆ, ( ) E E ( ) ˆ E ( ) E 4 ˆ ˆ ˆ ˆ 4, ( ) E E ( ) ˆ C C rs order necessary condons wh respec o rr,, rr,, ˆ ˆ, (5.5) ˆ ˆ, and, are gven by, (5.6), (5.7) ˆ ˆ ( ),, ˆ ˆ (5.8) ˆ ˆ ( ) 4, 4, n 4 ˆ ˆ 4 n (5.9)

37 ( ) ( ) (5.),,, n 4, ( ) 4, ( ) 4, n (5.) for each. Combnng (5.8), (5.9), (5.), and (5.), PPI nflaon and he oupu gap under he opmal polcy n he cooperave eulbrum can be wren as follows ( ) ( L)( ˆ ˆ ) ( ) (5.) ( ) ( L)( ˆ ˆ ) ( ) (5.) where L s he lag operaor. We may combne he euaons of (.4) and (.4), wh he above soluons o oban an expresson for an neres rae rule ha mplemens he me-conssen polcy under he cooperave case: r r rr rr E E A A,, ( ) ( ) ( L) ( L) E E (5.4) A A A A If we consder he case of rr, rr, rr, rr,, so he real neres rae n he domesc flexble prce eulbrum s he same as n he globally flexble prce eulbrum, opmal polcy n he cooperave eulbrum can be wren as a lnear rule of opmal polcy n he Nash eulbrum and foregn nflaon gap. Ths suggess ha he cenral bank of he counry whch mpors non-durable goods should

38 rase he neres rae by more relave o he Nash case n response o a rse n foregn nflaon. A smlar analogy s derved for an neres rae rule of Counry : r r rr rr E E A A,, ( ) ( ) ( L) ( L) E E (5.5) Ths suggess ha he cenral bank of he counry whch mpors durable goods should rase he neres rae by less relave o he Nash case n response o a rse n nflaon of counry.

39 CAPTER V CONCLUSIONS Ths dsseraon sudes a model of an economy whch produces and expors durable goods. I analyzes he opmal moneary polcy for such a counry. Generally, moneary polcy has a bgger economc effec on durable goods relave o non-durable goods because durable goods can be sored and households ge uly from he sock of durable goods. Ths paper shows ha, n Nash eulbrum, he cenral bank of a durable goods producng counry can conrol changes of he prce level wh smaller changes n he moneary polcy nsrumen. In he cooperave eulbrum, he moneary auhory of he counry whch mpors non-durable goods and expors durable goods should rase he neres rae by more, relave o he Nash case, n response o a rse n foregn nflaon. On he oher hand, he moneary auhory of he counry whch mpors durable goods and expors non-durable goods should rase he neres rae by less han he oher counry. uure work mgh fnd neresng mplcaons from examnng dfferen values of, and hs wll probably reure numercal analyss. I mgh also be neresng o show he behavor of exchange raes from mperfec exchange rae pass-hrough sengs.

40 4 REERENCES Barsky, R., ouse, C., Kmball, M., 7. Scky prce models and durable goods. Amercan Economc Revew 97, Campbell, J. and ercowz, Z., 5. The role of collaeralzed household deb n macroeconomc sablzaon. Naonal Bureau of Economc Research Workng Paper. Clarda, R., Galí, J., Gerler, M., 999. The scence of moneary polcy: a New Keynesan perspecve. Journal of Economc Leraure 7, Clarda, R., Galí, J., Gerler, M.,. A smple framework for nernaonal moneary polcy analyss. Journal of Moneary Economcs 49, Erceg, C., Levn, A., 6. Opmal moneary polcy wh durable consumpon goods. Journal of Moneary Economcs 5, Gal, J., Monacell, T., 5. Moneary polcy and exchange rae volaly n a small open economy. Revew of Economc Sudes 7, an, K., 8. Durable goods, prce ndexes, and moneary polcy, Manuscrp, Texas A&M unversy. Monacell, T., 8. New Keynesan models, durable goods, and collaeral consrans. The Cener for Economc and Polcy Research Dscusson Paper 596. Obsfeld, M. and Rogoff, K., 999, oundaons of Inernaonal Macroeconomcs. The MIT Press.

41 5 Woodford, M.,. Ineres and Prces: oundaons of a Theory of Moneary Polcy. Prnceon Unversy Press.

42 6 APPENDIX A A.. Proof of K K (.) (pf) rom OC n u ( K ) Q RE u K Q k k( ) OC n u ( K ) Q u K Q k RE k( ) Gven he nernaonal radably of sae-conngen bond, he neremporal effcency condon s u ( K ) Q u K Q k RE k( ) The law of one prce, P P, P / P for all, and he defnon of he,,,, user cos (.9) and he cos of lvng ndex (.), and he uncovered neres pary r r E yelds K K A.. Dervng he euaon of (.) rom (.6), u ( K ) Q k RE uk( K) Q

43 7 u ( K ) K / K P ( ) P / R R u K K K P P R k,,, k( ), /, ( ), / K / K Q R K / K Q,,,, u ( K ) K / K Q R u K K K Q k,, k( ), /, K / K u ( K ) Q R K K u K Q, k,, / k( ), ( k k ) ( k k ) ( k k ) rr C,,, Usng (.9), k ( ), h log( K ) log( ) log( K Q / Q ),, log( K ) log( ) ( k k ) ( k k ) ( k k ) rr C,,, k k h h ( )( k k ) rr C, ( ) (( ) ) ( ) ( )(( ) (( ) )) rr C, ( )( ) ( ) ( ) rr C, rr E E where ( )( ), ( ) C,

44 8 A.. Dervng he counry s naural raes rom (.9) P () vn( Y / A) Q P u ( K ) AP, k, vn( Y / A) Q u ( K ) AP k, ( Y / A) Q ( K ) AP, Y A K ( ) Q P, ( ) n ( n) Q, Q n( ) P, Q, Y A ( ) n ( n) Q, n( ) P, Y A ( ) n ( n) ( n) Q, n( ) n( ) P, Y A ( ) ( ), n( ) n( ) P, Y A n ( n) ( n) Q y rr ( ) a A,

45 9 A.4. Analycal soluon o flexble-prce eulbrum Combnng y ( ) and y rr ( ) a, one ges A, ( ) rr ( ) a A, A ( ) rr, ( ) a o subsue for C A A Usng rr, rr, ( ) Err, (A.) C rr n C rr, E E, one ges E E rr ( ) Err (A.) A A,, Updang (A.) one perod and akng expecaons n perod, one obans A ( ) rr, ( ) a (A.) A Usng (A.) and (A.) o subsue for rr, n (A.), one ges A rr, E E ( ) ( ) E a A rr, ( ) ( ) a

46 4 E E ( ) ( ) a E E ( ) ( ) Ea ( ) E( ) E ( ) E E ( ) ( ) Ea ( ) ( ) a ( ) ( ) ( ) E ( ) ( ) Ea ( ) ( ) a ( ) ( ) ( ) E ( ) ( ) ( ) a ( ) Ea ( ) ( ) ( ) ( ) E ( ) ( ) a ( ) Ea E ( ) a ( ) Ea ( ) ( ) E ( ) a ( ) Ea

47 4 where ( ), ( ) A.5. Analycal soluon o flexble-prce eulbrum rom he opmal prce seng rule and he Dx-Sglz prce ndex, we can oban log-lnear approxmaon forms log P ( ) log P ( ) ( )log P ( ) (A.4) and T E log P ( ) log PT ( ) mc T (A.5) T Solvng hs euaon for log ( ) P, subracng log P ( ) from boh sdes, we ge T T p () E S mct T S T T E T ( ) mc T (A.6) where p ( ) log( P ( ) / P ( )) s he log relave prce chosen by supplers ha revse her prces n perod. If above euaon s expeced o hold n me + as well as me, follows ha p () E ( ) mc E p () (A.7) Euaon (A.4) mples ha he nflaon rae s proporonal (up o a log-lnear approxmaon) o he log relave prce chosen by supplers ha revse her prces, Woodford ()

48 4 p () p () (A.8) Usng hs relaon, o subsue for boh p () and p () n (A.7), we ge p () E ( ) mc E p () E ( ) mc E ( ) mc E mc E (A.9) rom he log-lnearzed form of he expresson for margnal cos vn( Y( )/ A) Q MC (), u ( K ) AP k, MC ( Y / A) Q ( ) K AP, ( ) K Y A Q P, Q ( ), Y A K P, Q, ( ), Y A K P, Q Q Log-lnearze, mc k y h, ( ) a where A ( ) a ( ) rr,

49 4 Then we have he Phllps curve euaon from (A.9), mc E (A.) ˆ ( ) ˆ E A A r E, rr, ˆ ( ) ˆ E ( ) A A r E, rr, (A.) (A.) ( )( ) where. ( ) rom (.) and (.4), A A A A ˆ E ˆ E rr rr rr rr,,,, A A ( rr ) ˆ ( ) ˆ rr ( ) A A ( rr ) ˆ ˆ rr ( ) ( ) ˆ ( ) ˆ ( ) ˆ ˆ E E ˆ ˆ ( ) ( )

50 44 ( ) ˆ ( ) ˆ ˆ E E ( ) E ( ) E ( ) ( ) ˆ ˆ ( ) ˆ ( ) ˆ ( ) E ( ) ˆ ˆ ( ) ( ) ( ) ˆ ˆ E ˆ E ( ) E ( ) ( ) ˆ ( ) E ( ) ˆ ˆ E ( ) E ( ) E ˆ ˆ ˆ ˆ E ( ) E (A.) or he worldwde flexble prce, ˆ ( ) ˆ E ( ) A A ˆ rr, rr, (A.4)

51 45 rom (.4) A A A A E ˆ ˆ ˆ ˆ E E rr rr rrrr E ˆ ˆ ˆ ˆ E ˆ ( ) ˆ ˆ ( ) E ˆ ˆ ˆ ( ) ( ) E ( ) E ( ) E E ( ) E ( ) E E ( ) E ˆ ˆ ˆ ( ) ( ) ˆ ˆ ( ) ( ) ( ) ˆ ( ) ˆ ˆ ˆ ˆ E E ( ) ( ) ˆ ( ) ˆ ˆ ˆ E ( ) (A.5) ( ) E ˆ ˆ ˆ ˆ ( ) ˆ E

52 46 A.6. The opmal rae of producon subsdy n Nash eulbrum max U u( K) v( N) n ( n) K s.. n( ) ( ) N uk ( j) j K j j vn ( ) K N N j j j K ( )( ) ( ) ( ) j j j uk K j vn N j j In seady saes, ( ) Kuk( K) NvN( N) NvN( N) ( ) Kuk( K) vn ( N) Q P NMC u ( K) A ( ) QK Q K N N Q ( n) k, whch gves he opmal subsdy rae n hs economy, ( n) ( n) K, A P P P, Q / P ( )

53 47 A.7. Second-order approxmaon of he welfare funcon n Nash eulbrum The second order approxmaon of he uly of consumpon uk ( ) uk ( ) uk K K ukk K K O K (A.6) Usng obans K K k k, and ukk / uk K, where k log( K / K) K, we uk ( ) uk k k ( ) k p.. O k (A.7) Usng k ( ) uk ( ) uk k ( ) ( ) ( ) p.. O k uk k ( ) ( ) ( ) ( ) p.. O k (A.8) The second order approxmaon of he dsuly of labor ( Y( )/ A) Y( ) Y( ) A A Y A YY AY AA A A O Y, A where v v/ Y( ), Y Y () Y () A AY () Y () YY v/ Y( ), and AY v/ Aj Y( ) Usng Y Y Y( y y ), A A A( a a ).

54 48 ( Y( )/ A) YYy( ) y( ) AAa a YYY y() y() AY AY a a y() y() AAA a a O y, a ( Y( )/ A) Y y ( ) y ( ) Y y ( ) Y YY AYa y ().. po y, a AY ( Y( )/ A) YY y( ) ( ) y( ) ( ) y( ) a p.. O y, a YvYY where represens he elascy of he margnal dsuly of work wh v Y respec o oupu, and usng AY A Y YY Ey () ( ) Ey () var y() ( Y( )/ A) d YY ( ) aey ( ) p.. O y, a where Ey( ) s he mean value of y ( ) across all dffenaed goods a me, and var y ( ) s he correspondng varance. We use he Taylor seres approxmaon o he CES producon funcon, Then y Ey () ( )var y() O y o elmnae Ey ( ).

55 49 ( ) ( ) y y a y ( Y( )/ ).., A d YY po y a (A.9) ( )var y ( ) Usng NvN( N) ( ) Kuk( K), ( ) ( ) y y a y ( ( )/ ) ( ) ( ) Y A d Kuk K ( )var y ( ) p.. O y, a (A.) W Nash uk KE ( ) ( ) ( ) ( ) ( ) ( ) y y a y ( ) ( ) Kuk K E.. p O k, y, a ( )var y ( ) ( ) Kuk ( K) E p.. O k, y, a ( ) ( ) y ( ) y ( ) a y ( )var y ( ) (A.) By he defnon of he durable good sock, YY ( Y) ( )( ) (A.)

56 5 Combnng he formula X X X x x wh (A.), one obans ( /) / y y / ( ) / (A.) no (A.), we ge Pluggng y ( ) y ( ) ( ) ( ) ( ) W Ku K E (A.4) ( ) ( ) ( ) a ( ) ( )var y ( ) ( ) Nash ( ) k ( ) ( ) ( ) p.. O k, y, a Assume ha he nal value of he sock of durables s eual o s seady sae value. Then we ge he formula ( ( ) ).

57 5 W Ku K E ( ) ( ) ( ) a ( ) a ( )var y ( ) ( ) Nash ( ) k ( ) ( ) ( ) p.. O k, y, a W Ku K E ( ) ( ) ( ) ( ) Nash ( ) k ( ) ( ) ( ) p.. O k, y, a ( ) a ( ) a ( )var y ( ), rom E ( ) a ( ) Ea

58 5 W Ku K E ( ) ( ) ( ) ( ) E ( )var y ( ) Nash ( ) k ( ) ( ) ( ) p.. O k, y, a Wh ( ) ( ) W Ku K E ( ) ( ) ( ) Nash ( ) k ( ) ( ) ( ) p.. O k, ya, E ( )var y ( )

59 5 W Ku K E Nash ( ) k ( ) p.. O k, ya, ( ) ( ) ( )( / ) ( ( )( )) E ( )var y ( ) ( ( )( ))/ ( )( / ) W ( ) ( ) Nash Kuk K E E ( )var y ( ) p.. O k, y, a

60 54 ( ( ) ) ( )( / ) ( ) ( ) ( )var ( )..,, Nash k W Ku K E E y p O k y a ( ) ( ) ( )var ( )..,, Nash k E E W Ku K E y p O k y a ( ) ( ) ( )var ( )..,, Nash k E W Ku K E E y p O k y a ( ) ( ) ( )var ( )..,, Nash k E W Ku K E E y p O k y a where s he smaller roo of uadrac euaon

61 55 ( ), Usng.. p. ( ) ( ) ( ) ( ) ( ) k ( ) ( ) ( ) ( ) k ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) WNash ( ) Kuk ( K) E ( )var y ( ).. po k, y, a var y( ) ( )( ) ( ) ( ) WNash ( ) Kuk ( K) E ( ) ( )( ).. po k, y, a

62 56 ˆ ˆ WNash ( ) Kuk ( K) E ( ) ( )( ).. po k, y, a ( )( ) where ( ) A.8. The opmal rae of producon subsdy n he cooperaon eulbrum max U u( K) ( n) v( N) nv( N ) n ( n) K n( ) s.. ( ) N ( ) N uk ( ) j j K j j vn ( ) ( n) K N N j j j K ( )( ) ( ) ( ) ( ) j j j uk K j n vn N j j uk ( ) j j K j j vn ( ) n j K j j N N K ( ) ( ) ( ) j j j uk K j nv N N j j In seady saes,

63 57 ( ) Kuk( K) ( n) NvN( N) ( ) NvN( N) Kuk( K) ( n) (A.5) Kuk ( K) nn v ( N ) N Nv ( N) Kuk ( K) N n (A.6) ( ) NvN( N) N v ( N ) Kuk( K) N ( n) n ( ) ( n) vn ( N) Q P NMC u ( K) A ( ) QK QK ( n) N ( n) N Q k, whch gves he opmal subsdy rae for domesc good n hs economy, ( n) K, A P P P, Q / P ( ) We can ge a smlar euaon of he opmal subsdy rae for foregn good by above way.

64 58 P v ( N ) Q N NMC u ( K ) A k QK QK Q nn nn, whch gves he opmal subsdy rae for foregn good, n K, A P P P, Q / P ( ) Ths means ha wo counres fscal auhores (,) choose he common subsdy. A.9. Second-order approxmaon of he welfare funcon n he cooperaon eulbrum The second order approxmaon of he uly of consumpon uk ( ) uk ( ) uk K K ukk K K O K (A.7) Usng obans K K k k, and ukk / uk K, where k log( K / K) K, we uk ( ) uk k k ( ) k p.. O k (A.8) Usng k ( )

65 59 uk ( ) uk k ( ) ( ) ( ) p.. O k uk( ) ( ) ( ) ( ) k p.. O k (A.9) The second order approxmaon of he dsuly of labor rom (A.9), ( ) ( ) y y a y ( Y( )/ ) A d YY.. po y, a ( )var y ( ) Usng ( ) NvN( N) Kuk( K) ( n) from (A.5), ( ) ( ) y y a y ( ) ( ( ) / ) ( ) ( ) n Y A d Kuk K ( )var y ( ) p.. O y, a (A.) y ( ) y ( ) a y ( Y ( )/ ).., A d Y po y a Y ( )var y ( ) Usng Nv ( N) Kuk ( K) from (A.6), N n

66 6 y ( ) y ( ) a y ( ( )/ ) ( ) n Y A d Kuk K ( )var y ( ).. po y, a (A.) W Cooperave uk KE ( ) ( ) ( ) ( ) ( ) ( ) y y a y ( ) ( ) Kuk K E ( )var y ( ) ( ) y y ( ) a y Kuk ( K) E ( )var y ( ) p.. O k, y, a (A.) y y ( ) ( ) var y( ) ( )( ) var y ( ) ( )( )

67 6 ( ) n ( n) Usng he condon n( ) ( n) WCooperave ( ) ( ) ( ) ( ) y y ( ) a y ( ) uke k ( )var y ( ) ( ) ( ) y y a y n n ( )var y ( ) p.. O k, y, a

68 6 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( Cooperave k W uke a )var ( ) ( ) ( ) ( ) ( ) ( ) ( ) var ( ) y n n a y..,, p O k y a

69 6 W Cooperave ( ) ( ) ( ) ( ) ( ) ( ) ( ) uke k ( )( ) ( ) a ( ) ( )var y( ) ( ) ( ) n ( ) ( )( ) n ( ) a ( ) ( ) var y ( ) p.. O k, y, a

70 64 W Cooperave ( )( ) ( ) ( ) ( )( ) ( ) a ( ) ( ) var y( ) n ( ) uke k ( ) n ( ) n ( ) n n ( ) n ( ) ( )( ) n n n n ( ) a ( ) ( ) var y ( ) n n p.. O k, y, a

71 65 W Cooperave ( ( )( ))/ ( )( / ) ( ) a ( ) a ( ) var y( ) n ( ) uke k ( ) n ( ) n () n n ( ) n ( ) ( )( ) n n n n ( ) a ( ) ( ) var y ( ) n n p.. O k, ya, ( ) n ( n) Usng he condon n ( ) ( n)

72 66 ( ( ) ) ( )( / ) ( )var ( ) ( ) ( ) ( ) ( ) Cooperave k W E y uke n n n n n n ( ) ( )( ) ( ) ( ) ( ) var ( )..,, n n n n a y n n p O k y a ( )var ( ) ( ) ( ( )( ))/ ( ) ( ) Cooperave k E E y n W u KE n n a n ( )var ( )..,, a n y n p O k y a

73 67 W Cooperave ( ) p.. O k, y, a u KE k E E ( )var y ( ) n 4E n E n ( )var y () n where s he smaller roo of uadrac euaon ( ) and s he smaller roo of uadrac euaon ( ) 4 W Cooperave ( ) p.. O k, y, a u KE k E E ( )var y ( ) 4 E n n 4 E n ( )var y ( ) n

74 68 W Cooperave ( ) p.. O k, y, a u KE k ( ) ( ) ( ) ( )( ) n 4 n ( ) ( ) n ( ) n ( )( ) W Cooperave ( ) p.. O k, y, a u KE k ˆ ˆ n 4 n ˆ ˆ n n ( )( ) where ( ) W ˆ ˆ 4 ˆ ˆ Cooperave ( ) uk KE n p.. O k, y, a ˆ ˆ n ˆ ˆ n n (A.)

75 69 VITA Name: Address: Emal Address: Kang Koo Lee 9-76 Jugong APT, Chang4Dong, Dobonggu, Seoul, Korea, -789 Educaon: B.A., Economcs, Sejong Unversy(Seoul, Korea), M.A., Economcs, Sejong Unversy(Seoul, Korea), Ph.D., Economcs, Texas A&M Unversy, Augus 9