Financial Integration, intra-emu and Global External Imbalances in a Three-Country OLG Model

Transcription

1 bsrac Fnancal Inegraon, nra-em and Global Exernal Imbalances n a Three-Counry OLG Model EM s curren accoun mbalances durng he pre-crss perod up o 2008 are radonally explaned by ( fnancal negraon and convergence expecaons and ( by overopmsm and excessve real apprecaon n he perphery. Whle no quesonng hese radonal explanaons, Chen e al. (203 presen new sylzed facs regardng he rade lnkages beween euro zone s perphery (and core and he res of he world, n parcular Chna, he CEECs and ol exporers. cknowledgng hese emprcal facs hs paper uses a Damond (965-Buer (98 hree-counry (EM, sa,, wo-regon (EM core, EM perphery OLG model o show whch dfferences n economc fundamenals beween norhern and souhern EM counres and beween he laer and he res of he world were ransformed no he observed exernal mbalances (curren and fnancal accoun when fnancal negraon afer he ncepon of he common currency occurred. Keywords: Curren ccoun Imbalances, European Economc and Moneary non, Overlappng Generaons, Three-Counry Model JEL Code: F34, F36

2 Inroducon and Movaon The curren accoun mbalances of he European Economc and Moneary non (EM durng he pre-crss perod up o 2008 are emprcally well documened (e.g. Lane and Pels 202. The huge exernal defcs n souhern (ncludng Ireland (= perphery EM counres are radonally explaned by ( fnancal negraon and expecaon of convergence whn he common currency area and ( by over-opmsm and excessve real apprecaon n he perphery (e.g. Lane 2006, Coeurdacer and Marn 2009, Lane and Mles- Fere Whle no denyng he relevance of hese radonal explanaons, Chen e al. (203 presen new sylzed facs regardng nra-em curren accoun mbalances and he res of he world. mong hem he rade lnkages beween he EM subareas and he res of he world, n parcular Chna, he CEECs and ol exporers fgure promnenly, he rough balance of he whole euro area curren accoun nowhsandng. Perphery s curren accoun defc whle fnanced mosly by capal nflows from he core ncreased no vs-à-vs he core bu vs-à-vs he res of world, and smlarly for he curren accoun surpluses of he core. cknowledgng hese new sylzed facs s naural o ask wheher he curren accoun mbalances wh respec o he res of he world and he nra-em fnancal accoun mbalances can be explaned by an neremporal curren accoun model (Ca Zorz and Rubaszek 202 for he EM and he res of he world. s s well-known, afer he ncepon of he euro n 999, norhern and cener euro counres (usra, Belgum, Fnland, Germany, eherlands, France, n parcular Germany, sared o run curren accoun surpluses whle he souhern and wesern perphery (= PIIG: Porugal, Ireland, Ialy, Greece and pan accumulaed huge exernal defcs accompaned by a dramac loss of nernaonal compeveness due o srkng ncreases n her wages and prces compared o he norhern counres. Moreover, here was a sgnfcan dvergence n he dynamcs of prvae deb beween norhern and souhern counres (Psany-Ferry 202, Fgure 4: p o he ouburs of he global fnancal crss souhern deb boomed, manly n order o fnance housng nvesmen whle n he afermah of he crss governmen deb was subsued for prvae deb. Whle he conrbuon of fnancal negraon o he emergence of nra-em exernal mbalances s emprcally largely undspued, remans an open heorecal queson how dvergen curren accoun mbalances can be relaed o fnancal negraon n an neremporal general equlbrum model of a heerogeneous currency area. mong he few who address hs queson are Fagan and Gaspar (2008 who use a wo-good, wo-counry 2

3 overlappng generaons pure exchange model whou publc deb à la Yaar (965 and Blanchard (985 o compare he pre-euro fnancal auarky seady sae o euro-relaed fnancal negraon beween souhern and norhern euro counres. Fagan and Gaspar (2008 fnd ha he evoluon of nra-em exernal mbalances can be raced back o orh-ouh dfferences n me preference. However, Fagan and Gaspar (2008 neglec boh producon and capal accumulaon and he rade lnkages beween euro core respecve perphery and he res of he world. In vew of he euro-relaed dynamcs of housng nvesmen n pan and Ireland Farmer (203, 204 models producon and capal accumulaon whn Buer s (98 wo-counry overlappng generaons (OLG economy, one of he wo semnal conrbuons o he neremporal equlbrum approach o exernal mbalances. In vew of he raher modes nra- EM rade of goods and servces (Chen e al. 203, Buer s one-good seng s approprae o model he fnancal accoun mbalances across EM s core and perphery n he run up owards he global fnancal crss. Farmer (204 fnds ha he fnancal accoun defcs of EM perphery and he fnancal accoun surpluses of EM core can be raced back no only o core-perphery dfferences n me preference bu also o dfferences n he producon echnology (capal producon share and governmen expendure shares. Whle he one-good approach s conducve o model nra-em fnancal accoun mbalances n lne wh he radonal explanaon of euro-relaed fnancal negraon, s no approprae o model nra-em curren accoun mbalances whch can be arbued o rade lnkages beween EM s subareas and he res of he world. Moreover, snce he EM s a large open economy wh poenal mpacs of nra-em developmens on he oher large radng areas and vce versa, he nernaonal nerdependences among EM, sa and canno be negleced. To hs end, a leas a hree-good, hree-counry neremporal equlbrum model s needed. To he bes of hs auhor s knowledge of he leraure, hs hree-counry, wo-regon verson of he semnal Buer OLG model does no exs so far. Thus, here are wo man objecves of he paper: Frs, o presen sylzed macro facs regardng curren and fnancal accoun mbalances beween EM s core and perphery and he res of he world n order o movae he model se-up. econdly, o develop a hreecounry (EM, sa,, wo-regon (EM core and perphery OLG model n order o fgure ou how EM s core-perphery exernal mbalances can be arbued boh o fnancal negraon due o he common currency and o core s respecve perphery s evolvng rade lnkages o he res of he world. 3

4 The new model specfcaon feaures roughly man sylzed macroeconomc facs of norhern and souhern EM counres before he adven and afer he nroducon of he common currency unl he ouburs of he global fnancal crss. mong hem looms promnenly he fac ha he publc deb-o-gdp raos of several counres n souhern euro area dd no rse bu declned (Lane 202, p. 5. cknowledgng moreover he fac ha he deb o GDP raos of norhern EM counres ncreased only slghly, he modelng exercse assumes for smplcy ha boh norhern and souhern deb o GDP raos say consan over me. The mos obvous manfesaon of he creaon of he EM was he convergence of hgh nomnal (shor- and long-erm neres raes n souhern Europe owards he relavely low norhern (German raes. The man research queson addressed by he followng model analyss s wheher and how he emprcally observed nernaonal macroeconomc dvergence beween boh norhern and souhern EM counres and sa and n he begnnng 2000s can be arbued o he convergence of dfferen pre-em neres raes (fnancal auarky. We sugges ha dfferences n economc fundamenals lke savng raes and capal producon shares exsng beween norhern and souhern pre-em counres and beween sa and were ransformed no he emprcal observed macroeconomc dvergences durng he course of EM neres rae convergence. The paper s organzed as follows. In he nex secon, man sylzed macroeconomc facs, exsng boh before fnancal negraon and durng he EM negraon up o he ouburs of he fnancal crss n 2008 are assembled. In he followng secon, he frs-order condons (FOC for consraned neremporal uly and emporal prof maxma and he markeclearng condons are separaely specfed for pre-euro fnancal auarky and fnancal negraon afer euro ncepon. fer dervng he respecve equlbrum dynamcs, he exsence and dynamc sably of seady-sae soluons before and afer fnancal negraon are nvesgaed. Wh hese resuls a hand, s hen shown how he souhern EM and curren accoun defc hrough EM s fnancal negraon can be raced back o he lower savng rae n EM s ouh and n he and he relavely large capal producon share n EM s ouh and n sa. Concludng remarks n he fnal secon summarze key resuls of he modelng approach. ylzed Macroeconomc Facs: Fnancal uarky versus EM s Fnancal Inegraon In order o gude he desgn of he hree-good, hree-counry and wo-regon OLG model, some sylzed facs wh respec o he macroeconomc performance of he EM members, 4

5 sa and he and he evoluon of he curren accoun and he ne foregn asse poson n he EM, sa and he before he launch of he euro n 999 and up o 2008 are gahered n hs secon. Followng Fagan and Gaspar (2008, p. 9, he EM counres are separaed no wo groups based on he crera of relave shor-erm real neres raes n he lae 990s,.e. before he euro launch. The frs group, usually denoed as he core counres, comprses low neres rae counres: usra, Belgum, France, Germany and he eherlands. The second group denoed as perphery or convergng counres, consss of counres whch had relavely hgh neres raes before he nroducon of he euro (see fgure. Fg. Real shor-erm neres raes Legend: perphery, core. ource: Fagan and Gaspar (2008, p. 34 and own calculaons usng MECO. Fgure reveals ha n conras o he pre-em suaon (before 999, here s a szeable convergence of real neres raes beween EM core and perphery hereafer. 2 Fg. 2 Personal savngs raos n EM core and perphery owadays Fnland s ncluded whn core counres. Fagan and Gaspar (2008 exclude Fnland from core counres snce n he 990s he Fnnsh economy was dsored by specal facors afer he collapse of he ove non. We follow Fagan and Gaspar ( Remanng dfferences n he real neres raes are due o nflaon rae dfferences across EM core and perphery. 5

6 Legend: perphery, core. ource: Fagan and Gaspar (2008, p. 34 and own calculaons usng MECO. Regardng dfferences n economc fundamenals, fgure 2 porrays a subsanally lower personal savng rao (= household savngs as percen of dsposable ncome n EM s perphery han n he core. mlarly, fgures 3 and 4 reveal ha personal savng raes are subsanally lower han san raes, parcularly n he 990s and 2000s. Fg. 3 personal savng raes ource: FRED Daa. Fg. 4 san personal savng raes ource: CEIC Daa and auhor s own calculaons. Fg. 5 Housng nvesmen (as percen of GDP n euro perphery and core Legend: perphery, core. ource: Fagan and Gaspar (2008, p. 34 6

7 Fgure 5 porrays housng nvesmen (as percen of GDP n EM perphery and core. Whle housng nvesmen rose sgnfcanly n he perphery declned n EM s core. arng from a sgnfcanly lower personal savng rao n EM perphery relave o he core, housng nvesmen expendures n he perphery experenced a boom, whle housng nvesmen declned n he core counres. In vew of he sharp ncrease n prvae domesc expendures n he perphery and he mued response of oupu (Fagan and Gaspar 2008, macroeconomc equlbrum had o be esablshed hrough changes n he exernal balances of hese counres. s fgure 6 shows, hs resuled n sgnfcan curren accoun defcs n he perphery. Fg. 6 Curren accoun balances (as percen of GDP n EM perphery and core Legend: perphery, core. ource: Fagan and Gaspar (2008, p. 35 and IMF World Economc Oulook Daabase o surprsngly, EM perphery s curren accoun defcs led o he accumulaon of a sgnfcan ne foregn debor poson as shown n fgure 7 below. Fg. 7 e foregn asses (as percen of GDP n EM core and perphery Legend: perphery, core. ource: Fagan and Gaspar (2008, p. 35 and IMF Prncpal Global Indcaors. 7

8 gan, here s a smlarly dfferen evoluon of curren accoun and ne foregn asse poson raos of major san counres and of he as fgures 8 und 9 show. Fg. 8 Curren accoun o GDP raos n Chna, Japan, and K ource: OD Fg. 9 ne foregn asse poson (absolue and n percen o GDP ource: Wkmeda Commons Basc Model Consder an nfne-horzon model economy conssng of hree areas ( counres of he world economy, namely ( he EM, comprsng wo regons, named orh (ndexed by represenng EM s core and ouh (ndexed by represenng EM s perphery counres, ( he counres characerzed by a curren accoun surplus ousde he EM (ndexed by 8

9 represenng sa and ol-exporng counres, and ( he advanced curren-accoun defc counres (ndexed by represenng manly he. In each counry one commody, represenng he aggregae of housands of goods and servces s produced. Ths can be used for he purpose of consumpon as well as for nvesmen. The EM specalzes compleely n he producon of good X, sa n he producon of good Y, and he n he producon of good Z. Perfecly compeve frms n EM s ouh and orh, n sa and n he employ n every perod 2,,... labor servces,,,, and capal servces K,,,, usng he Cobb-Douglas (CD producon funcon ( (,,,, M a K o produce souhern (norhern EM aggregae oupu X ( X, sa s aggregae oupu Y and aggregae oupu Z where M 0,,,, denoe oal facor producvy n EM s ouh (orh, n sa and n he, respecvely. a s he common labor producvy and 0,,,, wh are he capal producon shares n EM s ouh (orh, n sa and n he.. One-perod prof maxmzaon by frms n EM s ouh (orh, n sa and n he mples he followng FOCs: K w M a,,,,, a ( K q M,,,,. a (2 whereby w denoes he real wage rae n regon respecve counry,,,. q,,,, denoes real un capal user coss n regon respecve counry,,,. 3 s usual n a Damond (965 ype OLG framework, wo generaons of homogeneous ndvduals overlap n each perod. dae, a new generaon of sze L eners he economy of counry (regon,,,. For smplcy we assume ha L L L for 3 In vew of sylzed facs presened n prevous secon a purely real model s clearly unable o explan all relevan emprcal facs regardng EM, sa s and mbalances. 9

10 all 2,,... and ha he populaon growh facors of all counres (regons are dencal and equal o L G. In vew of he emprcally raher smlar GDP growh raes n souhern and norhern EM counres (Fagan and Gaspar 2008 we assume moreover ha he respecve growh facors of labor producves a G and a G are equal n EM s ouh and orh, an assumpon whch apples raher well also o he bu lesser so o curren-accoun surplus counres lke Chna, Inda and oher san counres. However, acknowledgng he cach-up growh componen n emergng counres GDP growh raes he smplfyng assumpon a a a a a G G G G G seems o be less premaure. Ths mples ha he naural growh facor G G G s he same n all counres. n a L Each generaon lves for wo perods, workng durng he frs when young, and rerng n he second when old. The choce varables of each generaon, when young, are denoed by superscrp, and, when old, hey are denoed by superscrp 2. Each member of he generaon enerng he economy n perod supples one un of labor n-elascally o frms snce households arbue no value o lesure. In order o descrbe he opmzaon problems of households more specfcally he nsuonal framework regardng nernaonal ransacons across he hree counres and across EM core and perphery s now addressed. Regardng he hree counres, we assume ha each counry has s own currency and before he ncepon of he EM ouh and orh had her own currency, oo. To mmc he nroducon of he common currency n 999 we follow Gournchas and Jeanne (2006 as well as Fagan and Gaspar (2008, and assume ha before 999 EM s ouh and orh were fnancally auarkc whle afer he launch of he common currency EM s ouh and orh became fully fnancally negraed. In conras, he fnancal negraon across he EM and he oher wo counres remans ncomplee: n spe of nernaonal mobly of governmens bonds emed by EM s souhern and norhern, by he san and he governmens EM s and foregn real neres raes do no converge along he neremporal equlbrum pah. Wh regard o he rade lnkages we assume ha afer he ncepon of he common currency he rade lnkages beween EM s orh (ouh and he res of he world srenghened whle before he euro he EM and he foregn counres were auarkc. Ths srong assumpon mmcs he fac ha n he decade afer he launch of he euro Germany developed a sgnfcan rade surplus vs-à-vs sa, n parcular vs-à-vs Chna and ol exporers whle he rade balance of Greece, Ialy and pan worsened vs-à-vs hese 0

11 counres, Cenral and Easern European counres (CEECs ncluded (see Chen e al. 203 for emprcal deals. o surprsngly, boh fnancal negraon whn he EM and he evolvng rade lnkages beween he EM and sa mpac on he choce ses and consrans of younger households as well as on marke clearng condons. In order o work ou he consequences of nra-em fnancal negraon and he rade developmens wh non-euro counres as clearly as possble, he opmzaon problems of (younger households and frms as well as he marke clearng condons are now descrbed separaely for he wo cases of real and fnancal auarky and nra-euro fnancal negraon and ROW-rade of EM core and perphery. Pre-Euro Real and Fnancal uarky In order o faclae he modelng of he pre-euro suaon as real and fnancal auarky, we frs recall ha large real neres rae dfferences exsed beween he core (orh and he perphery (ouh of he laer EM. s fgure shows, souhern real neres raes were szeable larger han he correspondng norhern raes. econd, n conras o he laer fnancal negraon n he EM, n he 990s ouh (wh he excepon of Porugal dd no run large curren accoun defcs (as percen of GDP. Hence, when modelng he perod before he euro sar s no unrealsc o assume ha boh he curren accoun and he ne foregn asse poson of ouh and orh were zero. In conras, n he 990s sa (ncludng ol exporers ran a curren accoun surplus (as percen of GDP roughly equvalen n sze o he curren accoun defc of he (Engler 2009, p. 2. However, snce a hs me he ne foregn asse poson was only moderaely negave and Chna and oher emergng san counres dd no conrbue much o he mbalance, we assume for he sake of analyc smplcy ha he and sa were fnancally auarkc as ouh and orh were. Thrd, n conras o he curren pos-crss suaon where huge dfferences n governmen deb o GDP raos exs beween EM perphery and core, n he lae 990s he un-weghed average deb o GDP rao of EM perphery was no ha dfferen from he correspondng EM core value whch s also rue for he federal deb o GDP rao. In conras, he san publc deb o GDP rao was and s far below he EM and raos. Moreover, he EM orh-ouh deb o GDP dfferences dd no wden unl he ouburs of he global fnancal crss whch s also rue for he and sa s deb o GDP raos. nce he objecve of he modelng s o explan he effecs of he nra-em evoluon before he fnancal crss s approprae o assume ha he governmen deb o GDP raos n all counres of he model economy reman

12 consan over me. ddonally, as fgure 2 above shows he personal savng rae n ouh was perssenly lower han n orh. From fgure 4 we know ha sa s personal savng rae s sgnfcanly hgher han he correspondng norhern EM rae, whle he personal savng rae s slghly below he souhern EM personal savng rae (see fgure 3 and 2. Fnally, n vew of he dfferenal developmen of labor compensaons coss across EM core and perphery, s naural o assume 4 correspondng dfferences n souhern and norhern producon echnologes. Whle wage compensaon cos develop smlarly o norhern EM and hence smlar producon echnologes can be appled, sa s producon echnology feaures a much hgher capal producon share han n he or souhern EM (Ba and Qan 200. gans hs emprcal background of sylzed facs he neremporal uly maxmzaon problem n laer EM s ouh (orh before euro ncepon reads as follows: max ln x ln x s..: j, j j, 2 K B x s w, s, j,j j,j j, j j j j j j L L ( j, j j x s, j, 2 (, j where 0, j, denoes he me dscoun facor of (laer EM s regon j younger generaon, x, j, s he consumpon per capa of he commody produced j, n EM s regon j, s, j, s EM s regon j per-capa savngs, j, j, j denoes regon j fla wage ax rae 5, x, j, s old-age consumpon per capa of he j, 2 j, j commody produced n regon j, / j K,, L j s he real capal produced n regon j whch he regon j younger household wans o hold a he begnnng of he reremen j perod,, j, denoes he real neres rae on regon j governmen bonds and 4 Ths s anamoun o assume ha he labor compensaon cos dfferenals are no solely due o dfferences n oupu prces and naonal fscal nsrumens. 5 The assumpon of fla wage axes clearly clashes wh European ax code realy. However, snce hs paper does no focus on axaon for he sake of analycal smplcy a consan wage ax rae s assumed. 2

13 j,j j B / L, j, sands for he regon j governmen bonds he regon j younger household wans o hold a he begnnng of s reremen perod. Consran ( depcs he workng perod budge consran whle consran ( represens he reremen perod budge consran. fer havng descrbed he neremporal opmzaon problem of laer EM young households, we urn now o he neremporal choce problems of san and young households. By denfyng sa n he 990s wh Japan and ol exporng counres, we are no enled o assume rade auarky wh respec o sa and he. Conssen wh emprcal facs, sa and he ned aes exchanged before euro launch producon goods n addon o he consumpon of domesc producs and nvesmen n domesc producs and domesc governmen bonds. The san young household before euro launch solves he followng neremporal opmzaon problem: Max ln y ln z ln y ln z y, z, y,2 z,2 z K B s.. : ( y s w, s,,,,, e L L,2,,,2 z K B ( y, e L L y z where agan 0 denoes he san me dscoun facor, 0 (0 s he uly elascy of consumng he san ( produc, y ( z represens consumpon,, of he domesc (foregn good by he san young household durng he workng perod, e denoes he erms of rade of he san produc (= uns of he good per un of he san good, s represens household real savngs,.e. n erms of he san produc, w s he san real wage rae and s he san wage ax rae. Household s savngs are nvesed n san real capal K, / L and n san governmen bonds B, / L whch he san young household plans o hold a he begnnng of perod. Obvously, domesc real capal and domesc governmen bonds are perfecly subsuable from he perspecve of he san young household. In he reremen perod, he hen old san household uses he proceeds from he reurn on nvesmen n domesc real capal and domesc governmen bonds, ( ( / /,, K L B L wh represenng he real san neres rae n perod rae, n order fnance he reremen consumpon of he domesc good, y, and he good, z. 3

14 Fnally, he young household before euro launch solves he followng neremporal opmzaon problem: Max ln y ln z ln y ln z y, z, y,2 z,2 K B s.. : ( e y z s w, s,,,,, L L,,,2,2 K B ( e y z, L L where all parameers and varables have an analogous nerpreaon as n he opmzaon problem of he san young household. The governmen of each counry (regon,,, axes labor ncome and uses he proceeds from addonal borrowng o fnance he neres coss on exsng governmen deb and governmen expendures. The governmen budge consran of counry (regon reads as follows: where B B w L B,,,,, (3 denoes real governmen expendures and B s he level of real governmen deb n counry (regon,,, a he begnnng of perod. In lne wh Damond (965, we assume ha governmen expendures are unproducve. In addon o he resrcons mposed by household and frm opmzaon and by he above governmen budge consrans, markes for labor have o clear n all counres (regons and n all perods. L,,,,, 0,,2,... (4 nce he marke for fnancal asses s compeve, ransacon and adjusmen coss do no occur, no rsk (averson prevals, he followng no-arbrage condon (= naonal Fsher equaon holds n all counres (regons: q,,,,, 0,,2,..., (5 whereby 0 depcs he common fxed deprecaon rae of prvae capal (perod by perod n counry (regon. Regardng clearng of produc and asse markes we have o dsngush he wo regons of he laer EM from sa and. The asse marke clearng condons n he laer EM regons read as follows: 4

15 j j j j L,,, 0,,2,... s K B j, (6 B B, K K, j,, 0,,2,... (7 j j, j j j, j In accordance wh Walras Law, he clearng condon for he produc marke s rrelevan n regon j,. Clearng of governmen bond and real capal markes n sa and requres: B B, K K, 0,,2,..., (8,, B B, K K, 0,,2,... (9,, Fnally, we have he condons for he clearng of he produc markes:,,2,,2 Y, 0,,2,... L y L y L y L y K, (0,,2,,2 Z, 0,,2,... L z L z L z L z K. ( In order o be able o model he fac of me-saonary of counry (regon s publc deb o GDP raos beween 999 and 2008 we ransform oal ousandng governmen deb n counry (regon s governmen budge consran no deb o GDP raos. Ths s acheved by dvdng boh sdes of (3 by X for,, by Y for, by Z for and by defnng he deb o GDP raos as b B X,,, b B / Y, b B / Z and we oban for counry (regon : X w L G b b, wh G,,,,, (2 X, X, X X X Y Y Y w L G b b, wh G,,, (3 Y Y Y Z Z Z w L G b b, wh G,,. (4 Z Z Z Dvdng he asse marke clearng condon (6 on boh sdes by X,, and usng he defnon of he capal oupu rao v K X,,, (6 can be rewren as follows: 5

16 wl X, X, Ls X X G b G v, (5,,. In vew of he C-D producon funcon and nong X, G K a L K a L a L a L K a L K a L,,, X, n urns ou ha ( G G v v. cknowledgng he emprcal fac ha he pre-crss publc deb o GDP raos n all counres (regons remaned roughly consan over me we assume me-saonary publc deb o GDP raos: B B B B B B b, b 0,,, b, b 0, b, b 0,. (6 X X Y Y Z Z Moreover, we assume me-saonary governmen expendure shares:,, 0,,,,. (7 The governmen budge consrans (2-4 ogeher wh (6 and (7 yeld as follows: b X, b Y G,,, G, (8 b Z G. sng he Cobb-Douglas producon funcon s easly seen ha (/ [ / ( ],,, (/ [ / ( ], K X v M K a K Y v M K a (/ [ / ( ]. K Y v M K a Thus, he FOC for prof maxmzng capal servce npu (2 can be equvalenly wren as follows: q,,,,. (9 v 6

17 In order o smplfy he algebra, we assume. Then, acknowledgng (9 n (8 and, X n Y n Z n consderng G G v v G G v v G G v v yelds:,, (, b G v v n b n G v v v b,,. v. (20 The neremporal equlbrum dynamcs of he capal-oupu rao n laer EM ouh (orh s obaned by nserng (20 no (5: or: n n b v G v v v b [ b G v v ],,. (2 b v b v v,, G v n (22 s usual, a seady-sae neremporal equlbrum s defned as a fxed pon of he dfference equaon n (22: v v v,,. Evaluang (22 a a seady sae yelds: n 2 G b ( b ( v v 0,,. (23 n n G ( G ( Proposon (Exsence of seady soluons n ouh and orh uppose ha 0 b b G n,, whle b solves Gb 2 n seady sae soluons as follows: Gb n. Then, here are exacly wo srcly posve 7

18 v n n 2 n ( b G ( b G 4 ( b G n 2( G n n 2 n ( b G ( b G 4 ( b G v2,,. n 2( G, (24 Proof. ee Farmer (203, p. nce here are wo seady-sae soluons (local dynamc sably needs o be nvesgaed whch s done n proposon 2. Proposon 2 (Dynamc sably of seady soluons n ouh and orh uppose ha 0 b b,,. Then, he seady-sae soluon v n (24 s asympocally unsable whle he seady-sae soluon v 2 n (24 s asympocally sable. Proof. ee Farmer (203, p.. Knowng ha he larger seady sae soluon n (24 s asympocally sable we use o arbue he emprcally observed pre-euro orh-ouh dfferences wh respec o he real neres raes (and real wage raes o orh-ouh dfferences regardng fundamenals ncludng prvae savng raes, governmens expendure raos and capal producon shares. To hs end, we frs ry o fnd ou how he fundamenal parameers mpac he seady-sae value of he capal-oupu rao n (24. econd, we need nformaon abou he relave magnudes of he savng raes and capal producon shares n pre-euro orh and ouh. Dong he frs sep, s helpful o re-wre he larger seady-sae soluon n (24 by usng he defnon of he savng raes (,, as follows: v G b G b G b G,(25a 2 2 (2 n {( ( n [( ( n ] 4 n } v G b G b G b G.(25b 2 2 (2 n {( ( n [( ( n ] 4 n } Comparng he rgh-hand sde of (25a o ha of (25b we are led o he followng proposon 3. Proposon 3. uppose for smplcy ha b b. Moreover, assume ha,, b b. If, and, hen v2 v2 mplyng and w w. Proof. ee Farmer (203, p. 2 The second sep s o ensure ha he assumpons of proposon 3 are emprcally warraned wh respec o norhern and souhern canddae counres for EM n he lae 8

19 990s. The smplfyng assumpon b b s no warraned (Lane 202, p. 5, however, he beer fng assumpon numercally verfed. b b would only enforce he clam n proposon 3 as can be s emprcally warraned snce he souhern EM counres were (are less developed (lower GDP per capa han he norhern counres and here are promnen emprcal examples for he fac ha he capal producon share s hgher n cachng-up han n advanced counres (see Ba and Quan (200 for he hgh Chnese capal producon share of nearly 50% and Casell and Feyrer (2007 for he much lower capal producon share of 30%. The oppose holds wh respec o he governmen expendure quoa: less developed counres exhb lesser expendure quoas han hghly developed counres. nce, however, large-economy Ialy belongs o he souhern bloc s raher close o realy whch mples ha proposon 3 remans relevan. Fnally, n vew of he emprcal evdence provded by fgure 2 above s naural o assume ha,.e. he savng rae of he souhern EM counres s less han ha of norhern counres. Proposon 3 says ha he relavely hgh capal producon share and he low savng rae n ouh mply under fnancal auarky ha he seady-sae capal oupu rao n ouh s lower han n orh, and s assocaed wh a hgher real neres and a relavely low real wage rae. Ths clam s nuvely plausble. low savng rae mples for a gven capal oupu rao low savngs hus drvng he capal oupu rao down o ensure asse marke clearng. The capal oupu rao s also depressed by a relavely hgh capal ncome share snce hs mples a relavely low labor ncome share assocaed wh low per capa savngs. Due o decreasng margnal producvy of capal he lower capal oupu rao s assocaed wh a hgher neres rae and a lower real wage rae. o surprsngly, under fnancal auarky boh he souhern (norhern curren accoun C ( X K L x L x,, and he respecve ne foregn asse poson,,2 ( ( L s a L ( M ( v ( v b,, are zero,.e. no nernaonal borrowng and lendng akes place n spe of he neres rae dfferenal across counres. Obvously, he coss assocaed wh shfng capal from low-yeldng orh o profable ouh are prohbvely large. When modelng he adven of he common currency we assume ha hese nernaonal capal mobly coss are compleely removed over ngh whle he srucural parameers of boh economes reman as assumed n proposon 3. Before explorng he consequences of compleely removng nernaonal capal ransacon coss n he nex 9

20 secon, we check he exsence and dynamc sably of seady-sae soluons of he neremporal equlbrum dynamcs n he san- economy. The neremporal equlbrum dynamcs of he san respecve capal-oupu rao s obaned as n orh and ouh: j j j j j j j b j v b v v, j, G v. (26 j j j j j j j n j In order o deermne he san erms of rade we form he rao of he produc marke clearng condon (3 o he san produc marke clearng (2: ( Z K L z L z L z L z (,,2,,2,,2,,2 Y K L y L y L y L y. (27 From he soluon of he san respecve neremporal uly maxmzaon problem we oban under he smplfyng assumpon y z he followng consumpon funcons: y, w ( y, ( (28 z, w ( e z, ( (29,2 y ( (, y w, (30 (,2 z ( (, z e w, (3 ( y, w ( y, (32 e ( z, w ( z, (33 ( y ( w (,, (34 ( y,2 e,2 z ( (, z w. (35 ( 20

21 sng san and producon funcons, he rao of o san GDP urns ou o be as follows: u ( (, ( Z L M v v. (36 Y L ( M Inserng (28-(35 no equaon (27, dvdng he denomnaor of (27 on boh sdes by Z, dvdng he numeraor on boh sdes of (27 by rearrangng: e y n ( ( L [ v G ( v v ]( v z n ( ( L [ v G ( v v ]( v Y, we oban afer smplfyng and. (37 seady sae neremporal equlbrum s now defned as: v v v, v v v, e e e. Evaluang (26 and (37 a a non-rval seady sae yelds: n j j j j j j j j 2 G b ( j b ( v v 0, j,, (38 n j n j G ( G ( y n L [ v G ]( v e L [ v G ]( v ( z n (. (39 I s mmedae ha proposons analogous o proposons and 2 above can be formed ha ensure he exsence and dynamc sably of seady-sae soluons for he san- economy. lso proposon 3 can be analogously appled o he san- economy. Inernaonal Equlbrum under nra-euro Fnancal Inegraon and rade wh ROW To mmc fnancal negraon arsng hrough he se-up of he EM we assume n lne wh Buer (98 and Ln (994 ha boh physcal capal 6 and governmen bonds can be freely raded across souhern and norhern Home whou ncurrng any ransacon coss. In vew of he hgher neres rae n ouh, norhern younger households wll use her savngs o nves n souhern physcal capal and buy he bonds emed by he souhern governmen unl he souhern real neres rae declnes as much as here s no longer an ncenve o shf norhern savngs owards he ouh. nce he same compose commody s produced n orh and ouh, fnancal negraon does no nduce any commody rade beween EM core and perphery. Thus, whle younger households n ouh canno choose beween consumpon of he domesc and 6 To mmc he facs presened n Fgure 5 above we assume ha physcal capal s manly accumulaed by housng nvesmen. 2

22 of he norhern commody, hey can afer euro launch choose beween nvesng her savngs n domesc or norhern real capal and domesc or norhern governmen bonds. Moreover, rade n goods and servces beween EM core and perphery and ROW s now possble, snce sa respecve he specalzes on oher compose goods han EM. ow, souhern households can buy foregn good n addon o he domesc commody. The budge consran (n real and per-capa erms of he household lvng n ouh, when young s: K B x e y e z s w s. (40,,,,, (/ (/ (, wh L L ow he souhern EM young household buys / e and z from he a he relave prce of / e. ow, san good per un of EM good, whle, y from sa a he relave prce of e denoes he uns of he e porrays he uns of he good per un of EM good. In lne wh pre-crss emprcal realy, he souhern EM young household nvess s savngs only n domesc real capal and governmen bonds. When old he budge consran of perod- young household n souhern EM s:,,,2,2,2 K B x (/ e y (/ e z q. (4 L L In lne wh he new sylzed facs abou euro area mbalances (Chen e al. 203, souhern EM households arbue uly no only o consumpon of he domesc good bu hey also benef from consumng san and goods. Thus, each younger household n souhern EM maxmzes s uly funcon z ( ln x ln y ln z wh x,2 y,2 z,2 defned by equaons (40 and (4. ln x ln y ln z x, y, z, x y subjec o he budge consrans nalogously, he neremporal uly maxmzaon problem of he ypcal norhern EM household reads as follows: Max ln x ln y ln z ( ln x ln y ln z x, y, z, x,2 y,2 z,2 s.. : y z K K B B ( x s w (, s, ( x,,,,,,, e e L L L L y z,2,2,2 e e,,,, K K B B. L L L L q q (42 Here, y ( z,, sands for he purchases of san ( goods by he norhern EM,, young household, whle K L and B L denoe he respecve socks of souhern real capal and governmen bonds whch he norhern EM young household wans o hold a he 22

23 begnnng of perod. nce physcal capal and governmen bonds n each EM regon are perfecly subsuable, and snce whn he moneary unon boh asses can be assumed o be perfecly moble across ouh and orh, he followng nernaonal Fsher equaon (= real nernaonal neres pary condon holds n addon o he naonal Fsher equaons (5:. (43 The ypcal san young household solves he followng opmzaon problem: Max ln x ln y ln z ( ln x ln y ln z x, y, z, x,2 y,2 z,2 s.. : e z K B e B ( e x y s w (, s,,,,,,, e L L e L,2,,,,2,2 2 q e L L e L ( e x y e z K B e B. (44 Here, x sands for he purchases of EM goods by he san young household a he, relave prce of e, whle he purchase of he produc by he san young household occurs a he relave prce e / e,.e. uns of he san produc per un of he good., L denoes he sock of governmen bonds whch he san young household wans B o hold a he begnnng of perod. In lne wh pre-crss realy he san young household does no hold EM governmen bonds. Fnally, he ypcal young household solves he followng opmzaon problem: Max ln x ln y ln z ( ln x ln y ln z x, y, z, x,2 y,2 z,2 s.. : e y K B B ( e x z s w (, s e,,,,,,, e L L L e y ( e x z,2,2 e K B B.,,,,2 q e L L L (45 Here x sands for young household s purchases of he EM produc whle e / e, ndcaes now he uns of he produc per un of he san produc. gan n lne wh pre-crss emprcal realy, he young household does hold only norhern EM governmen bonds. In order o ensure arbrage-free erms of rade, he followng nernaonal real neres pary condons n addon o (43 ough o hold: 23

24 e (, 0,,2,..., (46 e e (, 0,,2,.... (47 e The markes for souhern and norhern EM and san and real capal clear accordng o: K K K, K K, K K, K K, 0,,2.... (48,,,,, The markes for souhern and norhern EM, san and governmen bonds clear accordng o: B B B, B B B,B B,B B B, 0,, (49,,,,,,, The nernaonal real neres pary condons (43, (46 and (47 ensure ha he worldwde amoun of savngs equals he worldwde supply of asses from souhern and norhern EM, sa and he : L s L s K B K B L s L s K K B B. (50, 0,,2,... e e e e Fnally, he produc markes n EM, sa and clear for all 0,,2,... accordng o he followng condons: X X L x L x K L x L x K L x L x,,2,,2,,2 L x L x,,2, (5 Y L y L y K L y L y L y L y L y L y (52,,2,,2,,2,,2, Z L z L z K L z L z L z L z L z L z (53,,2,,2,,2,,2. Havng descrbed he opmzaon problems of households and frms as well as he marke clearng condons, he neremporal equlbrum dynamcs can now be derved. From (9 and from he nernaonal Fsher equaons (43, (46 and (47 he followng relaonshps beween souhern EM, san, and norhern EM capal oupu raos and he erms of rade resul: v, 0,,2,... v, (54 24

25 v e e, 0,,2,..., (55 v v e e, 0,,2,.... (56 v Dvdng (50 on boh sdes by X and nroducng he defnons of he capal oupu raos as well as he deb oupu raos, he asse marke clearng condon (50 can be rewren as follows: L s X L s L s Y L s Z X X X X e Y X e Z X X X X ( v ( b G v b G v b Y v b Z G G, 0,,2,... Y Z e X e X (57 sng he producon funcons, he raos of souhern EM s, sa s and s o norhern EM s GDP urn ou o be as follows: ( X L ( M ( X L ( M ( v ( ( (, (58 ( Y ( L M ( ( ( v ( ( v, (59 X L ( M ( Z ( L M ( ( ( v ( ( v. (60 X L ( M cknowledgng (57-(60, he defnons of he GDP growh raes, he opmal savngs funcons resulng from household s uly maxmzaon problems (40-(42, (44-(45 and (8 n (57 yeld: ( b n v L ( M G v ( ( b v v v L { [ ] [ ( ]} ( M b v b n [ ] G [ ( ]} { [ ] v b v v e v 25

26 ( ( n v L M ( b ( v L ( M e v G [ v b ( ]} ( v ( v { [ ] ( n v L ( M ( v L ( M G [ v b ( ]} ( v ( v (. (6 Equaon (6 represens he fourh equaon of he neremporal equlbrum dynamcs of he capal-oupu raos, v, v, v, v, and he erms of rade hree-counry OLG model under EM fnancal negraon. e and e of he hree-good, The wo remanng dynamc equaon we oban by dvdng sa s good respecve he good marke clearng condon (52 respecve (53 by he combned EM good marke clearng condon (5: ( Y K L y L y L y L y L y L y ( (,,2,,2,,2,,2,,2,,2 X K X K L x L x L x L x L x L x L y L y L x,,2,,2, L x (62 ( Z K L z L z L z L z L z L z ( (,,2,,2,,2,,2,,2,,2 X K X K L x L x L x L x L x L x L z L y L x.,2,,2, L x (63 pon nserng he uly maxmzng consumpon funcons resulng from household s uly maxmzaon problems (40-(42, (44-(45 no he rgh hand sde of equaon (62 and (63, forunaely urns ou ha (62 respecve (63 can be rewren as follows: y ( Y K e, (64 x ( X K ( X K ( Z K e ( ( z x X K X K. (65 Dvdng he numeraor on boh sdes of (64 by Y and he denomnaor on boh sdes of (64 by X and akng accoun of (58 and (59, we oban he ffh equaon of he neremporal equlbrum dynamcs: 26

27 y ( ( n v L M ( n v G v e x v ( v G v v L ( M v ( ( {[ ] ( ( L M ( ( n v v G L v ( M v }. (66 Dvdng he numeraor on boh sdes of (65 by Z and he denomnaor on boh sdes of X and akng accoun of (58 and (60, we oban he sxh equaon of he (65 by neremporal equlbrum dynamcs: z ( ( n v L M ( n v G v e x v ( v G v v L ( M v ( ( {[ ] ( ( L M ( ( n v v G L v ( M In a seady sae wh v v v, v v v, v v v, v v v, e e e and e e e, he sysem of frs-order dfference equaons collapses on he followng sysem of seady sae equaons: v ( v, (68 v v v }. (67 ( v, (69 ( v, (70,,,,,, ( v ( e ( v ( e ( v, (7,,, n y x n, n G v v e G v v G v, (72 ( ( ( [( ( ],,, n z x n, n G v v e G v v G v. (73 ( ( ( [( ( ] Inserng (68-(70 no (7-(73, hen solvng (73 for (7, we oban wo equaons of e as funcon of condons non-rval seady sae soluons exs. e and nserng he resul no v. Proposon 4 ells us under whch Proposon 4 (Exsence of non-rval seady saes under EM fnancal negraon Le (,,,,,,,,,,,, x, y, L, L, L, L, M, M, n M, M, b, b, b, b, G be he parameer vecor and = 4 3 0, be he parameer space n he EM-sa- seady-sae marke equlbrum wh EM fnancal negraon. For any admssble parameer combnaon,, here exs some b (0,, b (0,, 27

28 b (0, and b (0, such ha for b (0, b, b (0, b, b (0, b and b (0, b, here are wo nonrval seady sae soluons ( e, e, v, v, v, v 0 and L L L L L L ( e, e, v, v, v, v 0. For b b b b 0, here s only one non-rval seady H H H H H H sae. Proof. ee he appendx 4 n Farmer (203, pp nce here are n general wo seady sae soluons, we had o nvesgae he local dynamc sably of each seady sae by calculang he egenvalues of he Jacoban marx of he neremporal equlbrum dynamcs (54-(56, (6 and (66-(67 n a small neghborhood of he seady saes. Due o he analycal complexy of he sx-dmensonal dynamcal sysem we are no able o prove dynamc sably n general bu can only show saddle-pon sably of he larger seady sae soluon for ceran numercally specfed parameer ses. Proposon 5 (addle-pon sably of he larger seady sae soluon uppose ha he condons n proposon 4 hold. Moreover, assume ha he followng n numercal values are arbued o model parameers menoned n proposon 4: G.6, x / 3, y / 3, z / 3, s 0.45, 0.55, 0.8, 0.4, 0.26, 0.2, 0.3, 0.2, 0.4, 0.23, 0.5, 0.2, M 2, M 2.5, M 2, M 3.5, L 75, L 300, L 40, b 0.027, b 0.023, b 0.02, b Gven hs parameer se, he seady sae ( e, e, v, v, v, v s saddle-pon sable whle ( e, e, v, v, v, v s saddle-pon unsable. L L L L L L H H H H H H Fnancally Inegraed versus Fnancally uarkc eady ae On knowng from posons 4 and 5 ha he larger seady-sae soluon under fnancal negraon s unque and dynamcally sable, proposon 6 below provdes an answer o he man queson wheher fnancal negraon across souhern and norhern EM,.e. he convergence of norhern and souhern EM real neres raes, conrbue o he dvergence of souhern and norhern EM curren accoun and ne foregn asse posons. Proposon 6 provdes he answer o hs queson. Proposon 6 (EM curren accoun and ne foregn asse poson effecs of EM fnancal negraon uppose ha he assumpons of proposon 3 hold,.e. he souhern EM fnancal auarky (F neres rae, ( rae, ( F F, s larger han he norhern EM fnancal auarky neres. Then, afer fnancal negraon (FI, he rao of he souhern curren accoun and 28

29 he ne foregn asse poson o souhern GDP s negave whle he respecve norhern raos become larger han zero,.e. ( ca FI 0 and ( FI 0 and ( ca FI 0 and ( FI 0. Proof. By assumpon, we have ( F ( F. Thus, ( ( v ( ( v F F F F. Fnancal negraon means ha he posve dfferenal beween souhern and norhern EM auarky neres raes dmnshes as he souhern neres rae declnes and he norhern neres rae rses. Due o decreasng margnal producvy of capal he declne n souhern neres rae s assocaed wh a rse n souhern capal oupu rao and vce versa n orh. ex, noe ha he souhern curren accoun o GDP rao akng no accoun souhern rade wh sa and reads as follows: ( ca FI G n v [ ( ( G n v [ b ( G n v ] ( ( v G n. I s easy FI o o see ha ( ca decreases as F v. nce under rade auarky ( 0 ca follows ha FI ( ca 0. Rememberng he defnon of he souhern EM ne foregn asse poson n seady sae as ( v ( b v G n [ v b ( ], dfferenaon of wh respec o v yelds ( v b ( v G. From he proof of proposon 2 we 2 n know ha here s a small neghborhood of he souhern EM auarky seady sae wh he larger capal oupu rao n whch v F H ( 0 holds. Hence, he souhern EM ne foregn asse poson deeroraes wh rsng souhern capal oupu rao. nce a he auarky value of v he souhern EM ne foregn asse poson s zero, and snce he H FI souhern EM ne foregn asse poson declnes wh rsng capal oupu rao, a ( v he souhern EM ne foregn asse poson s smaller han zero,.e. v FI H H ( 0. On he oher hand, snce norhern EM real neres rae rses durng fnancal negraon and he hgher neres rae s assocaed wh lower capal oupu rao, he norhern EM curren accoun and ne foregn asse o GDP rao becomes larger han zero n response o he lower norhern capal oupu rao. Proposon 7 (san and curren accoun and ne foregn asse poson effecs of EM fnancal negraon uppose ha fnancal auarky (F neres rae, ( fnancal auarky neres rae, ( F F, s larger han he san. Then, afer worldwde fnancal negraon (FI, he rao of curren accoun and ne foregn asse poson o GDP s negave whle he respecve san raos become larger han zero,.e. ( ca FI 0 and ( FI 0 and FI FI ( ca 0 and ( 0. Proof. In general, he proof of proposon 7 s smlar o ha of proposon 6. However, noce ha hrough seady-sae neres pary condons (68-(70 EM fnancal negraon mpacs san and curren accoun and ne foregn asse posons. 29

30 Concludng Remarks Ths paper explores, whn a hree-good, hree-counry OLG model wh producon, capal accumulaon and publc deb, he emergence of exernal mbalances (curren and fnancal accoun boh among EM core and EM perphery and sa respecve afer he ncepon of he common currency and before he ouburs of he global fnancal crss n I models he pre-euro suaon as real and fnancal auarky and he EM before he onse of he global fnancal crss as fnancal negraon characerzed by complee convergence of real neres raes. The fnancal negraon across he ROW,.e. sa and and he EM afer euro launch s ncomplee due o dfferen currences. fer assurng he exsence and dynamc sably of fnancal auarky seady saes, a lower savng rae, an equal governmen expendure quoa and a hgher capal producon share n ouh were shown o mply he emprcally observed souhern hgh real neres rae and low real wage rae assocaed wh no exernal mbalances beween ouh and orh before he adven of he common currency. ymmercally, he hgher savng rae and governmen expendure quoa and he lower capal producon share n orh mpled a norhern low real neres rae and a hgh real wage. fer he ncepon of he common currency, free capal mobly beween ouh and orh nduced mmedae nernaonal real neres pary leadng o a quck fall n souhern neres raes and o rsng norhern neres raes. mulaneously, relavely hgh nal souhern neres raes led he norhern core o nves her wealh n souhern housng and resdenal objecs. Thus, boh norhern and souhern exernal balances wden: EM perphery s curren accoun relave o sa and becomes negave whle smulaneously ncurs a ne foregn debor poson vs-à-vs EM core. On he oher hand, EM core runs a curren accoun surplus vs-à-vs ROW and smulaneously becomes a ne foregn credor for EM perphery. Moreover, nra-em real neres convergence conrbues also o he wdenng of san and exernal mbalances measured by curren and fnancal accoun mbalances. We may hus conclude ha he hree-good, hree-counry OLG model s capable of reproducng qualavely, he man sylzed facs presened above: a convergng real neres rae across souhern and norhern EM counres, rsng souhern EM and curren accoun defcs and norhern EM and san curren accoun surpluses assocaed wh larger exernal deb of he former and larger exernal cred of he laer. Proposon 3, 6 and 7 corroborae he clam ha he emergence of exernal mbalances beween boh norhern and souhern EM and he san and exernal mbalances afer EM fnancal negraon can 30

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