A Computional General Equilibrium Model with Vintage Capital 1

Transcription

1 Cmul Geel Equlbum Mdel h Vge Cl Lïc Cdu Ce, Séhe Dée Ce d Je-Pee Lgue Ceem e em Iduc Cmul geel equlbum mdel uully ume uy uy echlgy: he cl ey he duc ce c be chged euly d hu c. hu, cmeve mek, he c duc ully d euly dju cue ecmc cd. h me h elc chge el ge he c cl led vey gc d quck mve demd lb d cl. Meve, he quck djume he cl ck huld cue huge v he l veme. Heve, cul emlyme d cl ck ehb much eke mveme h he edced bve. Hece, he eg h heecl mek elc mdel eque me mveme. Oe y decee he c-evy duc c c umg le djume c uully qudc c. h eul mhe dymc djume lb d cl. Heve, h ecc e u d hc um hu g emcl ud. Meve, vey ucvcg y mdel evebly, d g d hg c. lly, he uy uy mek uble gve mle d cceble el he medum em mveme he ge he vlue dded, hch e beved me Eue cue. lhugh djume c mh he dymc c demd he h u, hey e m uce duce medum em chge he cme dbu beee cl d lb. key eue he uy uy ecc, h cel emcl lue, h ll he vge cl hve he me cl ey. O he cy, e uld eec he cue echlgy meu be ly vlble he ely ceed u duc. h ecely h he uy cly ecc de. I h mek, cue ecmc cd ec he cl ey he e duc u he echlgcl chce d he umbe hee u ceed he veme he ecmy. he he duc u kee he echlgy hey ee gve he ce. Heve, cue ecmc cd ec he bly d led he cg -ble u. Hece, he ggege cl-lb chge gdully h he l veme d he cg ld blee duc u. Puy cly veme my hu vde medum em dymc he dbu cme. h ecc h me he dvge. he evebly veme embedded he mdel d g c c ely be duced. h gve cvcg ud he cke emlyme. he de develed hee ee ed by ee e by Cblle d Hmmu. We hve beeed vey ueul cmme by gè Béy, Pee-Yve Hé, Pul Zgmé, Pee Scc d Wee Rege. Séhe Guchd mde vluble ccm d ugge evu ve he e.

2 Dee ll dvge, he uy cly echlgy ue m eu dbck. I mleme mcecmc mdel cumbeme e., he mdel h lg memy ce kee ck ll he vge cl ceed he, h e ll kg de. hu he mdel h vble h lg lg. Secd, he lg hz ve eche he uue. Me ecely, he dec cceg he e duc u vlve d vble h cve he eeced leme hee u. he mdel h he vble h lg led. Heve, hee blem c be ely vecme dy. Mdel h vble eeg lg led d lg c be lved h eul lghm ce he mlemeed ll, d mul me deceg h he mveme el cmue. he ec ee mdel eeeg he duc gd d he demd c h uy cly echlgy. I he ecd ec e cle he mdel by cmleg demd de, by ducg ge cuve d by umg he equlbum he gd mke. he, e decbe he deem he equlbum. he hd ec ee he eul he mul he mdel., he clb uch h he edy e he mdel decl he vege u he ech ecmy ve he, e vege hehe he ee eece d uquee lu he mdel e ed. I cul, e llue he ueule he bly cd hghlghed Lgue. lly, he uh ec dcue he cequece he duc mey lcy d ml gde he mdel.

3 . echlgy d c demd I h ec, e duce he ecc he echlgy m d e deeme he dec. ech de, m buld umbe e duc u, hch ll duce e ed le. hey hve che he cl ey embded hee u. Sce h cl ey c chge he uue, he eeced leme he e duc u he dec-mkg. Bh cl ey d eeced leme e e mmze he eeced dcued ch l mu ll c. Meve, m ee he h ech lde u uld mke dug he cue ed ee ke cvy. Whe h egve he u e ced. he, e c ggege he dec m d ge he veme, he emlyme d he duc he cue ed. echlgy d veme c We cde eeeve m, eecly cmeve gd mke, hch mu mke chce me. h me, he m decde cque k e u cl. I l che he echlgy embded h cl. he echlgy meu chcezed by e e -de hmgeu duc uc: σ σ σ σ k, z[ αk α ], h:, σ >, < α < z. h equ deeme he mu gd duced by cmbg k u cl h u lb. eee he ececy he echlgy vlble me. σ he e e elcy c ubu. he cl ey che me he ee leme he cl u deed by: k. he duc uc c be ee :, z[ α σ α] σ σ I he uue, he vge cl ceed ll ehe be ued h cl ey be ced. We dee e u duc ceed me he cmb u lb d u cl. h u duc duce, u gd. he begg ed,.e.me, e u duc e ceed. he ed ech ed, c he m ge bku d ducg. c be ee he e hch he duc u de ll e bu mcecmc cd m e decl, he chce mde by y dvdul m l hld he ggege level. me eee he begg ed. 3

4 bd mgeme, mke echcl dcule he mleme duc. I h ee, equvle egeu deec e. evey u, duc he ed llg ll. he u ceed me e ducve m he begg ed,.e.me. he ggege veme mde me deed by he llg el: I he c e u cl, cludg he ll c, eeed u gd duced, egeu d equl c >. Cblle d Hmmu 994, 996 h h h h c um, eeced demd hck e eleced he cue chge he veme l ce, d hve eec he cg ge deuc. O cue, he umbe ced u chge h me ce he dee vge cl d hve he me ze 3. b Vlue e duc u We dee he ml ee e e h muy e ed, vlble me. We l dee he ml ge d ech ke he duc u he k de dug ed. By cve, e ume h h ge d he ed ed. Le u cde u duc ceed me. Whe cl ced, me, g he ke c hee he ce level me d he el g c ececy u 4. I he duc u ge bku, heve, g c cued. We dee by V, he ee vlue he ch l he duc u bul, meued he ed ed,.e. he vlue he duc u he m h hve ge bku ul h me. I ce bkucy, h vlue ze. We hve he llg bge cd: [, ] V V, c, 3 Cblle e Hmmu 994 l cde he ce me geel c uc: c > d c >. umg ve vlue I c c h c c led lucu he cg ge h eeced chge demd. e h h um dee m h mdel b q: Cblle d Hmmu he veme eg he c uc he ggeged vlue veme he ecmy, he dvdul m cde h c chge. 4 h me h he u duc h bee cve m he begg ed me,h ed. 4

5 hee c he ce e. he ed ed, he e duc u c ehe ell d ve he ceed he cl mke, hld. I he ce, hehe ll ge V, he ed ed. I he ecd ce, he u ll yeld e he ed ed equl : c [,, ]. Bede, he ed ed, he u ll ehe g bku, h bbly, ll be kg de, h bbly. I ble dee l cd d eml cd he deece equ bve., he um ee ey me h he cl vlue e duc u he ed he ed he bul equl buldg c kg ccu he bly bkucy: V c, he ve h decde cee e duc u y buldg c dug he ll ed : c. He e h h u h bbly g bku he ed ed, d bbly em kg de. I vlue he ed ed, eeced he begg ed he: V,. Secd, he he duc u ced, he e h y he g c. e h he eeced cg de he e u,, ecely ege umbe ye. We dee he ege he eeced leme 5 e duc u, d decml 6. he vlue he duc u, he de ced, equl he g c. h dee he eml cd. I he mdel, he duc u ceed me ll be ducve ull ed me,.e. m he begg ed ul he ed ed. I ll ll be kg de he begg ed, bu ll be ly ducve dug c ed equl. Hece, e d he eml cd, e mu mke ddl um he vlue ml ge ececy u, ce d g c he de. We ume h hee hee vble h 5 he eeced leme ced he ed me dug hch u kg de. 6 hu e hve. ll he u he me vge e decl. We vd cg chce be dcee: gve me, ll he u gve vge uld be ehe ced ke ue. Wh mdel ug he ye bc me u, h dcee chce uld hve duced g dcue he ee he mdel hck. bee um h gve vge my be ced d he e my be ke ue. he um, mde he e h vge ced emedy me de ed. h um lghly dee, bu lle me ccl. 5

6 6 de e equl he gemecl el beee he ed ed d he ed ed : We ume h he cme eled he c he ed g he begg ed d lg eceved d ed he ed he ed. We l ume h he bbly g bku deede he legh he c. lly, echcl ge umed be cuu uc me gve by:. We hve he eml cd: [ ],, c V he vlue he m he ceed he ee vlue uue eeced mu he g c he eeced cg ge. e h he ce e duc u he begg ed eble m ve c he g c cued by cg u he begg ed he he u ceed beg duce. We dee η he c ke e u cmg m ced u. h vg η he vlue he e u. he vlue e duc u bed by ummg he bge equ ul cg de: { },,, c c V η

7 c Chcec he e duc u Whe e u ceed, e mu che he echlgy embded he b led leme, d he mke cd hey eec dug h ed. he chce he led leme d he cl ey h e u eul m he mmz he vlue h u mu ll c:, V c Ψ., he -de cd elve he eeced leme c be bed decly ce he bjecve uc Ψ devble. Heve, Ψ deed he eleme h dee he eeced leme: hch ege, d hch el umbe beee d. he bjecve uc cully hee vble uc: Ψ,,. m deeme he cme he eeced leme d he cl ey he e duc u h Ψ mmzed. Eeced le me he ege he eeced leme,, he deed by: Ψ,, Ψ,, > 3 Ψ,, Ψ,, < h yem equ my hve me h e lu. I he ce, he hle mdel huld be lved ech hee lu. he eed lu uld he be he e ced h he hghe elh he e he u. Heve, e gve ed, e beleve h ude eble ecmc um, he yem equ h uque lu. he decml he eeced cg de he u deemed by he llg -de cd: Ψ,, 7

8 8 hu: 4 l l l,, l c c c c Cl ey he cl ey che by ve he e duc u he deved by he -de cd:,, Ψ. 5, ' c c c hee, ' he mgl ducvy cl. By cmbg h equ d he ee-ey cd, e ge ee ed : 6

9 9 { },, ' ' η c c Cl ey deemed by ee d uue ee e. uue eeced el ge e u deed by cl ey. hu, e hve c c e hch vlve he vege ee d uue c hee he dl c e deved m uy uy echlgy ly deed cue c. d Scg d ggeg We cde he dec cceg he duc u bul bee me. ech vge cl, cl ey beg ledy e, he ve check hehe ll ble. I, dcded. Ude u um, duc u bul dug ed hch ege umbe, bu c be ued he hle ed. Le u cll he ge he lde u hch ued he begg ed 7,.e.me, d hch ll be ced me <. h u bul ed. I vlue he ed h ed 8 : { },,, c c V η 7 S, he u h bee cve h de ed. 8 Wge, ce d g c h ed e gemecl el he vlue he ed ed d.

10 ,,, c V Ψ he ge he lde duc u ued he begg ed deed by: < Ψ Ψ > Ψ Ψ,,,,,,,, Le u dee,,,, U Ψ Ψ he, e hve: 7,,, c c c U he ed me dug hch he lde u e kg de h ed deed by:,, Ψ

11 8 l l l,, l c c c c I ble dee he ggege level emlyme d duc. de,he duc ucue vlble chcezed by he ee: { },,hee he ge he dee duc u kg de, d by. ggege emlyme d duc ccy e bed by ummg hee vge 9 : 9,, Y 9 I he bve gh e hve cmued d he ege d he decml he ge he lde u hch c geee ve. Heve e culd dd he um h ce ducve u ced, c be u ue g. I h ce, e huld duce he c u mz blem. he mmum umbe vlble u duc c be clled he hycl ducve ccy. I geel h ccy ll be ued, he ece beg g uced cee demd me.

12 . Clue d equlbum he mdel I h ec e cle he mdel he mle ble y. he, e vege h he cue equlbum he ecmy deemed he d eeced uue e k. ggege demd d lb uly he mdel cmleed by ddg hee equ: he equlbum he gd mke, he eeml bge equ eeeve cume d ge cuve. ggege uly mu be equl l demd, hch c el cum d veme. Y C I c Cum vee he llg Eule equ hch ume c elve k ve ρ d me eeece β huehld. Cue cum deed eeced level d he el ee e he llg ed. ρ β C C lly, lb uly deed ge cuve lkg he ml ge ececy u he ce level, he edge elecg he ed beee he uchg e ge he ke d he eecve lb c m d he emlyme e hee he vlble lb ce, hch ccu he eec lb mke cd ge bgg. 3 l ϕ l l l ϕ edge ϕ he geel equlbum he mdel de deemed by equ 3. Mey lcy eg he ml ee e d cl lcy e he edge We culd cde ggege uly he ecmc ducve ccy, d duce me cke duc ce. d h e c ume h demd eve ed, h eecve duc equl l demd bu my de m he ecmc ducve ccy. he ecc he mdel uld becme meh me cmlced ude h um d huld b hevly he hey dequlbum ecmc., e huld cmue he equlbum he mdel eeed h e. We ge he equlbum ce d he l demd d ule. he, e huld cmue he eecve ce cmb he ce he evu ed d he cue equlbum ce. lly, e huld cmue he eecve equlbum me ce h h eecve ce hch clude eecve umbe kg u, emlyme, ml ge, ec.. I ec 4 e ll duce yl mey ule.

13 edge. g c, he lb ce, d echcl ge, e egeu. b euly d l he mdel emk mu be mde h., e mully he ge e d he ce ll lg d led by y ve umbe, he equ he mdel e ll veed. hu, he mdel ee he ey euly. I c be ee el em. Secd, e u duce he llg ed, he el ee e h m ke ccu he dec-mkg deed by:. Le u dee he l e eeced e ed by:. ml ee e egeu, he he el ee e edgeu hugh. cully, u mdel h ucue hch vey ml he ucue he eclcl gh mdel. hu, e uld eec u mdel clude he el ee e edgeu vble. I mey lcy eg he ml ee e, he eeced l huld be deemed by he mdel. Heve, he l ce level d ll he llg ce huld be udeemed, hch uug mdel hu ml ch. e huld be edgeu vble. I he ecmy me, Heve, u mdel, cue d l e e he equ h deeme he ge he lde u kg de he begg ed, d he c me dug hch ll em ducve. I he cue l e deemed by he mdel, he l ce level uld be deemed by he ml ch uld be gve by he ce level. h ge, he ce me cecy, e ll cde egeu vble, d e ll check h he lcl cd eece d uquee, gve by Blchd d Kh 98, e ed by he mdel. hey uld be ed mde edgeu e uld ge y lu meezed by he l vlue he l e. h eul uld be chged he cue l e ee duced gume he ge equ 3, eul ggeed ge cc. Heve, e ll ee h yl mey ule c lve hee blem. he cmlee mdel gve d cmmeed ed 3. he equ, gve h ed, e he mlemeed ll gm. 3

14 c Equlbum he mdel Wh uy cly ecc, ggege uly dju ggege demd y., veme l vde e ddl duc cce. Secd, he bly vlble vge cmmd he mu duc u h hve be ced. Heve, he mdel eeed hee, he duc u ceed de beg ducve he begg ed. S hee veme l ccue dy demd bu m uly. hu, ech ed, uly c ly dju hugh he cg ld duc u. he echlgy hee vge e, he bly ly deed he cue el ge ececy u. Hece, he e cg ld duc u ceg uc he cue el ge. ggege emlyme deed by he mu lb ched ech vge duc ll kg de. I decee h he ge he lde ble duc u. hu ggege emlyme decee h el ge. lb uly eeeed by ge cuve ccdg hch cee emlyme gge cee ge clm, he equlbum he lb mke deeme el ge, ggege emlyme d he ge he lde u kg de. ggege uly bed by ummg ll he vge duc, ble cue el ge. Cue cum deed by he eeced level e ed cum d he el ee e. he ggege demd mee ggege uly hugh he veme l. y gve cl ey he e duc u, veme l dju hugh he umbe u ceed. he echlgcl chce he e u deed he cue d eeced vlue he el ee e d el ge. 4

15 3. Smul he mdel he edy e d he clb he mdel ed 4 gve he equ he blced gh h he mdel. he bc me u e ye. he clb uch h he edy e equlbum elce OECD l ccu vege d ve he ed ggege duc, emlyme d veme Y,, I, ell he ge e, he ce level d he ml ee e,,. he mee be evlued e he chcec he duc uc z d α, he cle c he ge equ ϕ, d he k emum µ, hch duced d hc y he deece beee he eu veme d he ee e. Vlue he ubeved edgeu vble mu l be cmued: he eeced leme he e u duc, he cl ey d he umbe:, d.cully,he mee d he ubeved vble ly deed he ge he vlue dded d he veme e ee ed 5. he clcul eeed ed 5 e u m h e ecey g deee he lycl ly. h eble u dcu he mc mcecmc d he vlue mee d ubeved vble, hu much l ccucy. Heve, he vlue eeed ble e ely cmued, ug he edy-e mdel eeed ed 4. ble h he eul ce, he Ued Se d J. he ge he d he veme e ced he vege vlue ve he ed e h l ccu veme l clude dellg, ucue, d dul buldg. Vlue-dded l clude hug evce. I m e h he eeced cg de he e u duc ced he de cg he duc u h hve ge bku bee. h de ced dec eled mcecmc cd echcl ge d ge. evehele, he bbly g bku y e bu ecmc cd equl ech ed. Hece, ech e duc u deece e ul de, he ced. he eecve leme e u c he be deed : D he edy-e. 5

16 ble : Clb he mdel vege ce Ued Se J She ge vlue dded Y Iveme e Y I..7.7 Leme he e duc u ye Eecve leme e duc u D ye: Cl ey Pduc uc mee σ.99 α z Reu veme % g c e cle ze hey mu.% el ge ccee he mc he he vble; ul d echcl ge cee eecvely he e.5% d % e um. he bbly g bku he ed ech ed equl % d he ll c e e. Suce: OECD l ccu. Cume e umed hve elve k ve d me eeece e eecvely.5 d 5%. he ge cuve chcezed by elcy el ge emlyme.3, d he cl edge.5. lly, e ume h m d ve g c h he ce e u η. b Blchd d Kh' cd d mul mehd 3 he mdel clbed ech d ee educed vble, d le m cmued ud he eeece edy e. mg he gl vble educed vble equvle gve cmm ed e ll vble. We c l dee eded vble uch h he cmm ed equl he hghe blced gh e ee he mdel. he egevlue he le m he mdel e eded vble e equl he egevlue he le m he mdel e educed vble, mulled by he hghe blced gh e lu e. he equeme he mdel cvege he lg u blced gh h evee he e cde eded vble bly he eded deece h he e cde educed vble bly he elve deece. he evey emede 3 he mehdlgy ued h gh develed Lgue. ll he cmu ee mde ude ll, h he cmmd Lk d Sck. 6

17 he e cde he gl vble he mdel hch hve dee lg u gh e, bu h ce, he cece he le m he mdel deed me, d he lcl cd he eece d he uquee lu, develed by Blchd d Kh 98, d ly. he mdel h 73 -edud led vble. Whe e cde he le m h educed vble, e hve 73 egevlue h mdulu lge h. S he Blchd d Kh cd e veed, d hee uque lu h he educed m mdel. Meve, he lge egevlue le h equl.95. Sce he hghe gh e he mdel he el GDP gh e, hch umed be equl.5%, he Blchd d Kh e l veed he eded m mdel.95*.5<. Hece, bly eded deece d bly elve deece e veed. hee cd e uce eue he eece d he uquee lu h he mdel gl vble. We mule he mdel h el ecd de mehd mlemeed ll Sck lghm. We ume h gl vble, hch ll dee ed, mu cvege he lg u he blced gh h. he mul he mdel ve 5 ed ke bu mue. he mdel c be ued llue he ueule he cce bly hghlghed Lgue. I he educed m mdel, he lge egevlue h mdulu le h eled he dymc cum. hgh elve k ve ρ, h egevlue cle, bu ll y bel uy. Hece bly elve deece ll ed. Heve, he Blchd d Kh cd e veed yme he eded m mdel, becue he evu egevlue me he lg u el gh e he ecmy lge h. emle, he ρ 5, he hghe egevlue h mdulu le h he educed m mdel equl.99. hu, he eded m mdel, h egevlue becme.99*.5>. h u, he he Blchd d Kh cd e veed he le m he mdel e educed vble bu eded vble, clled eud-hyee by Lgue. I h ce e d k he mdel e gl vble h uque lu. I u ce, he mul lghm dvege, hch ugge, ccdg Bucekke 995, h hee lu he mdel. c Shck he ge-eg el llue he ee he mdel, e cde eme chge he ge-eg el ce. h hck my em m ul lcl eve h emely h he ge cuve ud, uch cee he u e me geeu uemlyme bee hch mve he ude uy cumbe ke. I he edy-e, he el ee e deemed by cume eeece. Hece, he e eu d he cl ey he duc u e uchged. Cdeg he c c e, he ge e h m e ble y l uchged. hu, he ud h he ge cuve led decee l emlyme d cee uemlyme. Sce lb he budg duc c he lg u, uu decee 7

18 he me emlyme. hee eec he ge he vlue-dded he lg u. Heve, he h he e edy-e chcezed by chge he dbu cme beee duc c. ed 6 ee he eul h mul Ch 5. he ed, el ge dju ud Ch 4. he bly eg duc u deee. he ge he lde u kg de decee d emlyme d ggege uly ll Ch. he, ggege demd Ch dju dd h veme l me ecely h he umbe e u ceed. he chcec he e duc u hve chged ce ve eec y cee el ge: he e u e me cl eve d hve hghe eeced leme Ch 3. he llg ed, ee u ee ceed, ggege emlyme le. h mhe he mc he ud h he ge cuve cue el ge. he, he ge he lde u kg de decee le h he evu ed. Bede, he decee he ce e u he evu ed egvely ec cue uly, lhugh hee u e me ducve. E, he ll ggege uly ge h he evu ed, ce he le cg e ld u de cmee he le umbe ecely ceed u. he mdel ehb medum em dymc. Rel ge h ud he begg d eveully eu lly he l level, ve 3 decde. Sce he ll GDP d emlyme l vey gdul, he cee he ge he vlue-dded lg lg Ch 5. Hece, cy mdel umg uy uy echlgy, he uy cly mek vde medum em chge he cme dbu beee lb d cl. Smlly, he ll he veme e, elecg h he dd djume veme l ecede he ll uu, l l ud 3 decde. he ech eec 4, ml eue he uy cly ecc, ee he mdel. he chge he duc cce e u, llg hck, h mc ggege uly he me hee vge e ced. Hee, he ud h he ge cuve led decee he ducve ccy ll he u ceed e he hck. he duc u ceed bee he hck.e. me ducve e gdully ced d elced by he e e. h el he eve ll ggege uly. Ye e he cg he l e-hck vge ggege uly eced by ud hck, ce he vge ced h ed he le ducve u ceed e he hck. 4 mg he lge egevlue le h e, evel e cmle ee bve. he lge e h edcy 35 ye hch ced he ech eec decbed hee. u mdel clude l eec, h ech eec eeced bee he cg he u ceed e he hck d cee h mveme vble bee he 35 ye. We c ee uch mveme he ch ed 6. he cmle egevlue h edcy 7 d ye c el hee beved chge. Rel Imgy Mgude Ped 74: : : :

19 4. Mey lcy, ce deemcy d hyee he um mey ule h m c he ml ee e vey elc. he cce he cel bk he level he l e he ecmy c cveely be edeed by yl-ye mey ule, ccdg hch he ml ee e cee h he l e. Meve, e hve umed ul h he eeced l e edgeu, bu h he eecve l e egeu. h lgclly ce d e ll duce el beee bh e, hch ll be edgeu. I h ce, he cel bk eg he ml ee e, he Blchd d Kh cd e veed e egevlue lge h e mg. Heve, h yl mey ule h blem ll de. Mey lcy ule d l deemcy Wh egeu ml ee e, he mdel deeme he l e eeced e ed d he cue l e egeu., e ll ue h he ml ee e edgeu d ll bckd yl ule: * e d l e. * * α,hee * d * We ll duce he cecy equ: e he edy-e vlue he el ee Ude he cd α > 5, he eg he yl ule cee by e he umbe egevlue h mdulu lge h. e me -edud led vble h l be cluded he mdel, ce, he mdel, bh educed d eded m, y he Blchd d Kh cd 6. I e mule he mdel me, d e he equ he mdel. umed be gve by hy d cmued by he mdel., eee he ce level, e hve :. S, he cue ce level deemed by cue l d he ce level he evu ed. he ce level emely deed he ce level beved me :. 5 cully, α mu lghly eceed uy ce he dymc he l e ecluvely deemed by he yl ule. he l e dymc l ec he chce he m h egd he cg ld u d he eeced leme e e. Heve, hee α. uce cee by e he umbe egevlue h mdulu lge h.eue he bly he mdel. 6 hee e 9 egevlue h mdulu lge h. 9

20 h hyhe eled egevlue equl he he mdel e educed vble ee Lgue,. b Smulg mey lcy hck mdel h hyee he ml ee e, he cue l e d he ce level e dded he l edgeu vble he mdel he evu ec, gehe h hee equ: yl ule h α. 5, d. We c ke ccu ml gde, cmg m mul-ed ge cc by ddg l em equ 3, hch becme: l ϕ ϕ l Wedge ϕ l ϕ 3 l We ume ϕ h mdel ll e he Blchd d Kh cd. hee e 9 -edud led vble d 9 egevlue h mdulu lge h he educed m mdel ell he eded m mdel. Oe egevlue equl uy. he lge egevlue le h e equl.95. Hece, evuly, he mdel e he bly cd educed d eded m, d h uque lu h. llue he dymc he mdel h edgeu mey lcy, e mule eeced y hck he ml ee e 5 ye. ce, h y h he uul mey ule c em m he cel bk cce he u cl u. he eul he mul e eeed ed 6 Ch 6. he y dd h he mey ule gge cee he l e eeced e ed h he el ee e, deed h e, lm uchged Ch 9. he equlbum he ed bely eced by he hck. he ecd ed, heve, he cee he e l gge ll el ge ce ml ge e cky. he le lb c he led cee he ge he lde u kg de ell ggege uly d ggege emlyme Ch 7. m cee me duc u d veme l cee. he ve mc GDP ge dug he 5 ye he mey lcy h. Heve, GDP kee ck he cee he ze he vge ud 5 me ye.

21 Cclu h e ee mc-ecmc mdel umg uy cly veme d eec egh, he le he k by Cblle d Hmmu. Whe clbed ech d, he mdel h hve uque lu h eble vlue he mee. Me ecely, he mehdlgy eeed Lgue e h he bly mdel h vble h dee ed eued he he le m he mdel bh educed d eded m y he Blchd d Kh cd. hee cd e veed he mee eed hee. We h heve h hgh k-ve huehld, he bly he mdel he gl vble me ed, lhugh Blchd d Kh cd e ll veed he educed m mdel. h llue he elevce h mehdlgy. he mdel h vble h lg led d lg lg, bu c be muled ely ug he Sck lghm mlemeed ll. We mule eme h he ge cuve. he uy cly mek vde medum em dymc he dbu cme beee duc c h uy uy mdel lck. hghlghed by Cblle d Hmmu 998 he ce ce, uy cly veme my hu be he e y mdel c demd Eue cue.

22 ed : he uquee lu he yem equ 3 he mullcy lu he yem equ 3 deed he my he ee,,,, U Ψ Ψ elve. Me ecely, he chge he ve elh eulg m he legheg he u leme m h uque lu he g U chge ly ce. We hve:,,, c c c U Cde de eugh he uue h m eec he e c,he g c ececy u, d he ee e e c, ell he l e. h hz he el ge e ececy u l cdeed be c. he, he chge elh cmg m he cee he u leme by e ed becme:

23 3, c c U h ee deceg. hgh vlue, h he me g : c c hch egve ecmclly luble vlue he vble. I,h ee ke ve vlue, he g chge ly ce d hee uque lu yem equ. e h, h ee egve, e ge he lu. Sce he evu eg ume vlue eugh he uue, he eece he lu, le y, c be uled u. I culd be he ce he ve eec vey m chge he g c, he e d he el ee e. We ll eglec h bly h ll.

24 4 ed : he cmu he c c e equ 6 hmgeu de, e hve:,,, ' ', hee, ' he mgl ducvy lb, meued ececy uy 7. Hece, he mz cd 5 equvle : ], [ ], [ ' c c c c c he ee he duc u vlue ued elme h equ: } ] [ ], [, ' c c c V c c η I e cmbe h equ h he ee-ey cd, e ge equ 6. 7,, ' k.

25 5 ed 3: he cmu he equlbum he mdel ed 3 equ he llg equ deeme he equlbum he ecmy me, he he d he eeced uue e gve. he eml cd ce me e cmued by he edy e mdel ed 3. We dee he el ge ececy u, he l e eeced e ed, d he l e he cue ed. m chce e u, ell ggege uly d ggege emlyme, ee vble ve ed me de h edgeu. I ll, vble e el umbe. S ble de lg led by vble he mdel eve hugh h vble he ke ly ege vlue. I l mble um ve ed me h edgeu. Lly, he cmmd h yeld he ege vble ecgzed by he mdelg cedue ll cully c be deved. he lu e hve mlemeed e u he e g, hch equl ve, - egve d equl ze. he ck c ummg, ve ed h cve he de he me ed e e eeed, he ee he equ me cmb g e. h cmb equl he de e vd d he de e e. e h e c elcly ee he vble d he lgebc he mul. blck ] [, σ σ σ α α z 3 [ { [ ] [ ]]},,, c c c g

26 6 4 [ ] { } l l l,, l,5,5 c c c c g g 5 [,5,5,5, ' c c g g c g 6 { c g g c g ' ',,5,5,,5 η h yem 5 equ deeme,,,, d.

27 7 d blck 7 [ { [ ] ]},,, c c c g 8 { [ ] } l l l,, l.5.5 c c c c g g gve l vble, hee equ deeme d. { } g g g Y,.5.5,.5 h equ deeme Y.

28 C C ρ β h equ deeme C. Y C I c h equ deeme I. I h equ deeme. 9 { g.5 g.5 g.5 } h equ deeme. 3 l ϕ l l ϕ edge ϕ h equ deeme. Edgeu vble 3 : ge he lde duc u kg de he begg he cue ed : c he cue ed dug hch he lde duc u he begg he cue ed e eecvely kg de. C : cum he cue ed, : duc ccy duc u mlemeed he cue ed I : veme he ed, ducve m he e ed : educed cl ey he e duc u cl dvded by ececy d emlyme mlemeed dug he e ed : umbe duc u bul dug he cue ed d emlyme equed by hee u he llg ed. 8

29 : emlyme he cue ed : eeced l e he e ed : ege he leme he u mlemeed dug he cue ed : decml he leme he u mlemeed dug he cue ed : el ge e dvded by ececy Y : cue el GDP Egeu vble : ececy he ed; : vlble lb ce : ee e he ed edge : cl edge c : e : educed g c.e. deled by c : el c he veme mlemeed dug he cue ed : l e he cue ed 9

30 ed 4: he edy-e he mdel he gh e &: ul gh e : l e : echcl ge gh e g & : duc gh e Edgeu vble 3, d, gg e C I d Y, gg e g d, gg e & he ee ug he e g ed 3 mly hee, ce hee me eeece led lg vble he edy-e mdel. he level 3 equ blck, z[ α 3 { [ σ α] σ σ, [ c, ] 4 g c [ c, ]]} [ c, ] c, l l 5 ', c g,5 g,5 g,5 c c 3

31 3 6 [ ] { [ ] },,5,5,,5 ' ' c c g g g η d blck I ρ β g c I C Y. g Y & &.5, 9 g & &.5 7 [ { [ ] [ ]},,, c c c g 8 [ ] l,, l c c c l l l edge ϕ ϕ ϕ

32 e h m equ 3, 4, 7 d 8, e ge: 8. 8 Me ecely, ccdg equ 4 d 8, e hve:. Le u cde h. Equ 7 c be ee ug equ 3 : g X g X hee X c, [ c, ] [ c, ] By de, hgh eugh X be egve. Meve, he ll he duc u duce le c me, X ve. hu, e hve:. 3

33 ed 5: Clb he mdel Le u duce he e uly mee ξ, he g c yely ge, gve by: ξ. We dee R µ he el eu ve, hee he ml ee e, he l e eeced e ed d µ k emum. dcu he mc l ccu d he vlue he mee d he ubeved d, e eed lycl lu he edy-e mdel. h c be ely de lg he eeced leme dvded beee ege d decml. We che hee cmue he -de cd elve he eeced leme he mdel ee e cuu me. he, e ue he dcee me equvle h cd elcg equ 3 d 4 ed 4. he leme me vble umed be ege. hu e eglec he decml he ggeg equ. lhugh hee um e meh ce, e beleve hey led el beee vble h c be qulvely eeed. he vlue e u, cuu me mek, c be e : V e θ d e θ θ dθ θ θ c e d e,, η h e. he -de cd elve he eeced leme he e u he llg he edy-e ll:, e c he equvle dcee me mek:, c 3b h equ 3b elce equ 3 d 4 ed 4. Equ 7 d 8 h ed e l elced by ml mul. he he equ he edy-e mdel e he ed 4 h, d. We ee umbe hee equ ed 4 h ll. By de e hve,e ccee he eeced leme. he equ 3b bve cmbed h ggege duc d ggege emlyme equ d 9 gve he eeced leme he e u: h g h & Y ξ R 33

34 34 hee h Whu g c ξ, he evu equ deeme he eeced leme he duc u em he he ge vlue-dded d he gh e ul d echcl ge. e h g c ec vely he leme ce he le hee c e chged he le he ee vlue. he, he eeced leme l deed vely he el eu he g c e ke ccu. he cl ey d he duc ccy e u e deved m he eeced leme. I l he ce he umbe e u ceed ech ed,.e. he emlyme ched he e u: h I &, g h h Y & d h & he duc uc e he cle c z cece α :, σ σ σ σ α z z Equ 5 c he be ee ug he bve el: σ σ σ,, R h c c z Cmbg he evu equ d equ 6 led he llg el: c R h c c R h, η ξ hch c be ee :. h R h c R h R h c I c R h g h Y & η ξ h equ eee he dbu l cme beee cl d lb. I c be eged deed ly he ge he vlue dded Y d he veme e Y I.

35 35 he cle c he deed by:,., σ σ σ R h c c z I d mee α by:, σ σ α z

36 ed 6: Smul eul - Ud h he ge cuve Ch : ggege demd djume % chge m bele - Cum Iveme GDP Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y Ch : ggege uly % chge m bele chge m bele ye Iveme GDP ggege emlyme ge he lde u gh cle Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y 36

37 Ch 3 : echlgy chce he e u chge m bele,7,6,5 Cl ey e u,4 Eeced leme e u ye,3,, 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y Ch 4 : Rel ee e d ge e % chge m bele, chge m bele,,,8,8,6 Wge e Rel ee e gh cle,6,4,4,,, -, -, 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y 37

38 Ch 5 : Lb he vlue dded d veme e chge m bele,,8,6 Lbu he vlue dded Iveme e,4, -, -,4 -,6 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y - y hck ml ee e Ch 6 : ggege demd djume % chge m bele,5,5 Cum Iveme GDP -,5 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y 38

39 Ch 7 : ggege uly % chge m bele chge m bele ye,5 Iveme GDP ge he lde u gh cle ggege emlyme,5,5,5 -,5 -,5 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y Ch 8 : echlgy chce he e u chge m bele,5,,5 -,5 -, Cl ey e u -,5 Eeced leme e u ye -, -,5 -,3 -,35 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y 39

40 Ch 9 : Rel ee e d ge e % chge m bele, chge m bele, -, -, -,4 Wge e Rel ee e gh cle -,4 -,6 -,6 -,8 -, , -, 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y Ch : Lb he vlue dded d veme e chge m bele,4, -, -,4 Lbu he vlue dded Iveme e -,6 -,8 -, 45 Y 43 Y 4 Y 39 Y 37 Y 35 Y 33 Y 3 Y 9 Y 7 Y 5 Y 3 Y Y 9 Y 7 Y 5 Y 3 Y Y 9Y 7Y 5Y 3Y Y 4

41 Reeece Bucekke Ru 995 leve Mehdlgy Slvg le d- Lkg Mdel, Jul Ecmc Dymc d Cl, 9, Blchd Olve d Chle M. Kh 98 «he Slu Le Deece Mdel ude Rl Eec», Ecmec 48, Cblle Rcd J. e Mhmd L. Hmmu 998 Jble gh : bly, c ubu, d uemlyme, Cege-Rchee Ceece See Publc Plcy 48, Cblle Rcd J. e Mhmd L. Hmmu 996 O he mg d Ececy Ceve Deuc, Quely Jul Ecmc, Cblle Rcd J. e Mhmd L. Hmmu 994 he Cleg Eec Rece, he mec Ecmc Reve 84, Gvzz cec d Chle Wylz 985 «he Ze R Pblem : e he Dymc Deem he Sy Equlbum Le Mdel», Reve Ecmc Sude LII, Lgue Je-Pee he Blchd d Kh cd mcecmec mdel h eec egh, mmeghed Ceem. 4