CAPITAL MOBILITY, REAL EXCHANGE RATE APRECIATION AND ASSET PRICE BUBBLES IN EMERGING ECONOMIES

Transcription

1 CAPITAL MOBILITY, REAL EXCHANGE RATE APRECIATION AND ASSET PRICE BUBBLES IN EMERGING ECONOMIES A post kynsan macoconomc modl fo a small opn conomy José Luís Oo Abstact: Th objctv of ths pap s to show that opn conoms that () hav (shot-tm) captal moblty and () a low dg of oganzaton n fnancal makts may hav bubbls n asst pcs f th s an xognous shock to ths conoms that poducs a al xchang at appcaton. In od to do that, w wll psnt a post kynsan macoconomc modl fo small opn conoms basd n Taylo (98) and Taylo and O Connll (985). Ou modl dffs fom modls dvlopd by ths authos n sval aspcts. Fst of all, w wll consd a boad lst of assts ( 9 assts). Scond, w wll consd th fulfllmnt of Mashall-Ln condton, so that a al xchang appcaton wll poduc a ducton n nt xpots. Thd, w wll suppos, contay to Taylo and O Connll, that pofts a xpctd to ncas f cunt at of ntst s bgg than nomal o saf at of ntst. Fnally, w wll suppos that th s mpfct captal moblty n th sns of Mundll and Flmng so that ntst at dfncal s a majo facto dtmnng captal nflows to mgng counts. Ky-Wods: Asst Pc Bubbls, captal moblty and Mashall-Ln Condton Rsumo: O objtvo do psnt atgo é mosta qu conomas abtas caactzadas po () mobldad d captas d cuto tmo () baxo nívl d oganzação dos mcados fnancos podm xb bolhas nos pços dos atvos fnancos s oco um choqu xógno à ssas conomas qu poduza uma apcação da taxa d câmbo al. Paa dmonsta a valdad dss ponto, mos apsnta um modlo macoconômco pós-kynsano paa uma pquna conoma abta basado m Taylo (98) Taylo O Connll (985). O modlo apsntado nst atgo df dos modlos dsnvolvdos po sss autos m váos aspctos. Em pmo luga, consda-s uma lsta mas ampla d atvos ( 9 atvos). Em sgundo luga, mos supo qu a condção d Mashall-Ln é atndda d foma qu uma apcação da taxa d câmbo á poduz uma dução das xpotaçõs líqudas. Fnalmnt, mos supo a xstênca d mobldad d captas mpfta a la Mundll-Flmng d foma qu o dfncal d taxa d juos é um dtmnant fundamntal dos fluxos d captas d cuto pazo paa os paíss mgnts. Palavas Chav: Bolhas d pços d atvos, mobldad d captas, condção d Mahall- Ln. Códgo do JEL: F4 ÁREA DA ANPEC : ÁREA 0 Ths atcl s a modfd vson of th pap dlvd at VI Intnatonal Wokshop n Post Kynsan Economcs hld at Unvsty of Tnnss, Knoxvll, fom to 8 of Jun, 000.

2 . Intoducton On of th most fa-achng conomc dvlopmnt of th lat dcads s th xplosv gowth of ntnatonal fnancal tansactons and captal flows. Powful focs hav dvn th apd gowth of ntnatonal captal flows, lk volutonay changs n nfomaton and communcatons tchnologs n fnancal svcs ndusty wold-wd and th tnd n both ndustal and dvlopng counts towad conomc lbalzaton and th globalzaton of tad. Th lbalzaton of captal account has contbutd to hgh nvstmnt n many counts and ncass th volum and volatlty of ntnatonal captal flows. So fnancal lbalzaton has bn assocatd wth costly fnancal css n sval counts. Th agumnts about potntal sk of opn captal makts asng fom poblms of ncomplt nfomaton and oth dstotons. Thy pont out that th a nfomaton gaps n fnancal makts. Such mpfctons gv s to sval poblms that hav potntal to lad to nffcnt and unstabl fnancal makts. Ctcs of th ffcnt makts vw agu that btwn sval poblms affct fnancal makts on of th most mpotant s hdng bhavo. Hdng can mak sns whn th pvat tun of adoptng a patcula cous of acton s an ncasng functon n th numb of agnts that adopt th sam cous of acton. Agnts may ty to follow th lad of somon thy blv to b btt nfomd (cf. Banj, 99) o hdng can occu whn nvsto lack nfomaton about th qualty of thos who manag th funds (cf. Shafstn & Stn, 990). It s not dffcult to s that n th psnc of asymmtc o ncomplt nfomaton, nvsto wll qut atonally tak actons that can amplfy pc movmnts and pcptat suddn css. In oth wods, hdng bhavo can lad to shap nvsto actons, and bubbls n fnancal makts. Fnancal lbalzaton and hdng bhavo can pomot bubbls n captal makts, and vn fnancal css wth potntally damagng consquncs. A consqunc of ths statmnt s that fnancal lbalzaton unambguously mpovs th ffcncy of souc whn t s not accompand by polcs to lmt nffcnt and unstablty of captal makts, spcally hdng bhavo. Ths suggsts that th thotcal psumpton n favo of th lbalzaton of captal account, lk popos th classc cas fo captal moblty, s not coct by th psnc of ncomplt nfomaton. Dvlopng counts hav adoptd polcs to ncas ntnatonal captal flows. In patcula, stctons on captal account tansactons bgan to dcln n Latn Amca at th nd of th 980s whn hghly ndbtd counts put th wost aspct of th dbt css bhnd thm and th ndustal counts vncd a nwd wllngnss to undtak Phd n Economcs at Fdal Unvsty of Ro d Jano (UFRJ) and Assocat Pofsso n Economcs at Mstado m Economa Empsaal (UCAM). E-mal : joo@canddomnds.b. Echngn t al (998) xamns sval aspcts of captal account lbalzaton.

3 lndng to dvlopng counts. Nvthlss, pxstng nffcncs ld to th mgnc of fnancal nstablty unlatd to fundamntals. Fnancal makts of ths counts, howv, hav som patcula fatus that mak thn mo susctbl to th ocunc of bubbls n asst pcs than fnancal makts n dvlopd counts n th fac of fnancal lbalzaton. In fact, fnancal makts n mgng counts lk Bazl o South Coa hav a low dg of oganzaton whch poducs a gat volatlty n asst pcs whn compad to th fluctuatons n asst pcs obsvd n th fnancal makts of dvlopd counts. Th low dg of oganzaton that pvals n fnancal makts of mgng counts tnds to ncas th possblty of ocunc of hdng bhavou, makng assts dmand mo snsbl (mo lastc) to changs n cunt condtons. Ths ncasd snsblty n assts dmand sults n gat volatlty of asst pcs. Th objctv of ths pap s to show that opn conoms that () hav (shot-tm) captal moblty and () a low dg of oganzaton n fnancal makts may hav bubbls n asst pcs whch a dfnd by Dymsk (998) as cumulatv ncas n quty pcs n laton to supply pc of captal goods - f th s an xognous shock to ths conoms that poducs a al xchang at appcaton. In fact, almost all mgng counts hav xpncd a a al xchang at appcaton n th 990 s (cf. Mshkn, 999, p.). Ths suggsts that xchang at appcaton can b th tggng vnt of asst pc bubbls obsvd n som of ths counts n th last dcad pap s to show that opn conoms that () hav (shot-tm) captal moblty and () a low dg of oganzaton n fnancal makts may hav bubbls n asst pcs f th s an xognous shock to ths conoms that poducs a al xchang at appcaton In od to do that, w wll psnt a post kynsan macoconomc modl fo opn conoms basd n Taylo (98) and Taylo and O Connll (985). Ou modl dffs fom modls dvlopd by ths authos n sval aspcts. Fst of all, w wll consd a boad lst of assts ( 9 assts). Scond, w wll consd th fulfllmnt of Mashall-Ln condton, so a al xchang appcaton wll poduc a ducton n nt xpots. Thd, w wll suppos, contay to Taylo and O Connll, that pofts a xpctd to ncas f cunt at of ntst s bgg than nomal o saf at of ntst. Fnally, w wll suppos that th s mpfct captal moblty n th sns of Mundll and Flmng so that nts at dfncal s a majo facto dtmnng captal nflows to mgng counts. Th psnt atcl s oganzd n 6 sctons. Scton, psnts th basc stuctu of th conomy und dscusson. Scton shows th bhavo of th conomy n th shot un,. n th ntval of (logcal) tm wh asst stocks and xpctatons a hld constant. Scton 4 psnts th bhavo of ou modl conomy n th long un, showng th xstnc of a saddl-path tajctoy to th stady-stat poston of th modl. Scton 5, dscusss th spons of th conomy to a patcula xognous shock : a al xchang S Echngn t al (998).

4 at appcaton. As a sult of ths shock, a bubbl n asst pcs may occu. Scton 6 psnts th conclusons of th atcl. - Th Basc Buldng Blocks Lt us consd a small opn conomy that poducs a sngl good wth th assstanc of labou and an mpotd nput. Th tchnology mployd by fms of ths conomy s lontff typ, that s tchncal cofcnts of poducton. labou-output ato and mpots-output ato a constant. W wll also suppos that pc of th sngl good poducd n ths conomy s dtmnd by a fxd mak-up ov unt costs. In ths cas, pc dtmnaton can b psntd by th followng quaton : p ( + τ )[ wb + p 0a0 ] () Wh : p s th mony pc of th sngl domstc good, w s th mony wag at, s th nomnal xchag at, p 0 s th pc of th mpotd nput n fogn cuncy, b s th labou-output ato and a 0 s th mpot nput-output ato. Snc th mak-up s constant thn all vaatons n th at of poft com fom vaatons n th dg of capacty utlzaton. Th at of poft can b xpssd by th followng quaton : τ u () + τ In th dmand sd of th conomy, w wll suppos, lk Kalck, that woks spnd all th ncom n consumpton goods and that captalsts sav a constant facton of pofts. In ths cas, th consumpton n nomnal tms can b xpssd by th followng quaton : pc wbx + ( s) pk () Wh : C s th al consumpton xpndtu, X s th quantty of output poducd n th conomy, s s th popnsty to sav out of pofts, K s th captal stock n al tms. mt: Th goods makt wll b n qulbum f and only f th followng condton s pc + pi + p (G-T) + p E p X (4) wh : I s th al nvstmnt spndng, G-T s th al fscal dfct and E s th al nt xpots. Usng () n (4) w found aft all algbcal manpulatons that :

5 4 g s + γ + ε φτ wh : I& G T g ; γ ; K K 0 ε E K ; (5) φ p a wb + p a 0 In quaton (5), g s th gowth at of th captal stock dsd by ntpnus, γ s th fscal dfct as a popoton of th conomy s captal stock, ε s th nt xpots as a popoton of th captal stock and φ s th facton of mpotd nput costs n unt costs. In od to dtmn th qulbum loc of th goods makt, w wll suppos fst that th at of gowth of th captal stock whch s dsd by th ntpnus s gvn by th followng quaton : g g + h( + ) (6) 0 Wh : s th xpctd futu at of poft and s th cunt at of ntst. Equaton (6) stablshs that gowth at of captal stock s a functon of th dffnc btwn xpctd at of poft () and th cunt at of ntst (). Ths s a smpl fomalzaton of th thoy of nvstmnt bhavo that Kyns psntd n chapt lvn of th Gnal Thoy. Th stat of long tm spctatons whch, accodng to Kyns, s a majo dtmnant of nvstmnt spndng, s psntd by n quaton (6). Th cunt at of poft ( ) s also addd to th nvstmnt quaton n od to psnt th nflunc of changs n th lvl of capacty utlzaton on nvstmnt dmand. Mo pcsly, w a supposng that an ncas n th dg of capacty utlzaton, cots pabus, wll ncas nvstmnt spndng. W wll also consd that ε s dtmnd by th followng quaton : ε ε + ε q (7) 0 p wh : q p In quaton (7), nt xpots as a facton of conomy s captal stock s a postv functon of al xchang-at (q). In oth wods, w a supposng that Mashall-Ln condton s bng fulflld. Th nomnal xchang-at () s fxd, that s, montay authots th Cntal Bank mploy th stock of fogn svs to sustan a fxd paty wth fogn cuncs. In ths sttng, all vaatons n al xchang at com fom changs n domstc pc lvl o n fogn pcs. Usng (6) and (7) n (5), w obtan th loc of combnatons btwn th cunt at of poft and th cunt at of ntst fo whch th goods makt s n qulbum,. agggat dmand s qual to agggat supply. So w hav th followng quaton : 4

6 5 g + ε ε q + γ + h( ) s + φτ h (8) In od to dtmn th slop of th loc of goods makt qulbum whch wll b lablld as GG loc lt us tak th total dvatv of (8). Aft all mathmatcal manpulatons w hav : h (8a) s + φτ h Equaton (8 a ) shows that n od to th GG loc to b downwad slopng s ncssay that ( s +φτ - h) b postv, that s th sum of popnsty to sav out of pofts and popnsty to mpot b bgg than th popnsty to nvst. Ths condton s, n gnal, assumd by all macoconomc modls, so th s no loss of gnalty f t s also assumd by th psnt modl. Th GG loc s shown n fgu. GG Th nxt stp s to consd th asst makts and th fnancal scto of ths conomy. W wll suppos that th s 9 dffnt assts n th conomy : fogn svs (R), domstc bonds (B), fogn bonds (B ), quts (P E), loans (L), bank svs (H), dmand dposts (D), captal goods (P k K) and scuts (F). Ths assts a hold by fou dffnt agnts : Cntal Bank, comcal banks, fms and nts. Equatons (9)-() dscb th balanc shts of all agnts of ths conomy : F + R H (9) H + L D (0) Fgu 5

7 6 P k K L + P E + N () D + B + B + P E W () Wh : P k s th dmand pc of captal goods, P s th pc of quts, N s fm s nt woth, W s nts s total walth. Fo smplcty, w wll assum that comcal banks a focd by law o convnton to hold a constant facton of dmand dposts n th fom of bank svs, that s : H θ D ; 0 < θ < () W wll also suppos that nts dcd about what popoton of th fnancal walth that wll b hold n dmand dposts, domstc and fogn bonds and quts. Ths assts a supposd to b mpfct substtuts so that dmand fo ach asst s nfluncd not only by ts own at of tun but also by th at of tun of oth assts. Th sam assumpton s also mployd by Tobn (969) and Taylo and O Connll (985). In ths sttng, nts s potfolo dcson s dscbd by th followng systm of quatons : µ (, + d, + ) W D (4) β (, β (, ε (, + d + d + d, + ) W, + ) W, + ) W B B P E (5) (6) (7) W D + B + B + P E (8) Equatons (4)-(7) dscb th dmand of ach knd of asst by nts. As w can s, th facton of walth that nts wsh to hold n ach of th fou possbl assts s a functon of th vaabls : domstc ntst at, fogn ntst at plus xpctd dvaluaton of domstc cuncy and cunt at of poft plus xpctd at of poft. Th fst vaabl can b thought as th at of tun on domstc bonds whl th scond s claly th at of tun on fogn bonds calculatd n tms of domstc cuncy. Fnally, th thd vaabl s a (poo) poxy fo th at of tun on quts. Equaton (8) s th (stock) budgt constant of nts. It shows that total dmand of assts cannot b lag than total walth. But t s ncssay to obsv that, whl total walth s a datum n almost all IS-LM typ macoconomc modls, n th psnt modl total walth s an ndognous vaabl (cf. Taylo and O Connll, 985, p.87). In fact, total walth s a postv functon of quty pcs whch, n tun, a ndognously dtmnd. In fact, usng (4), (5) and (7) n (8) t can b shown that : 6

8 7 W B µ (.) β (.) ε(.) (9) Equaton (9) dtmns th valu of total walth as a functon of () th stock of fogn bonds valuatd n tms of domstc cuncy, () th domstc at of ntst; () th fogn at of ntst plus th xpctd at of dpcaton n domstc cuncy and (v) th cunt and xpctd at of poft. Usng () and (9) n (4), t can also b shown that : µ (, + d, + ) θ µ (, + d, + ) β (, + d, + ) ε(, + d, + ) ( ) (0) Equaton (0) can b thought as th qulbum loc of fnancal makts. Such loc wll b lablld as loc FF. In od to dtmn th slop of FF loc, t s ncssay to mad som assumptons about th sgn of patal dvatvs n th systm pstd by quatons (4)-(7). Mo spcfcally, w wll suppos that : µ < 0, µ < 0, µ > 0 (a) ε < 0, ε β > 0, β < 0, β < 0, ε < 0 (b) > 0 (c) Gvn th condtons statd n ( a ) to (c), w can b shown that : ( + ) µ + β + ε () ; θ ( + ) µ + β + ε In quaton (), both numato and dnomnato hav ambguous sgn. In od to solv ths ambguty, t s ncssay to mpos adtonal stctons to th paamts of (). Fo such, w wll fst calculat th ffct of an ncas n ntnatonal at of ntst ov domstc at of ntst. It s a stlyzd fact about macoconomc pfomanc of small opn conoms und fxd xchang-at gm that an ncas n fogn at of ntst wll poduc a shap ncas n domstc ats. So w can analys what stctons should b mposd to th paamts of th modl n od to poduc ths stlyzd fact. Thus w obtan th followng xpsson : ( + ) µ + β + ε () + d ) ( + ) µ + β + ε ( In od to th sgn of () b postv, dnomnato must hav a postv sgn. But th dnomnato n () s qual to th dnomnato n (), so ths on has also a postv sgn. But what about th sgn of numato n ()? In od to dtmn t s sgn, w hav to mpos adtonal stctons to th laton btwn µ, β and ε. It s a stlyzd fact about fnancal makts n mgng conoms lk Bazl o South Coa that stock makts hav a low dg of oganzaton,. thy hav low lqudty and show wd 7

9 fluctuatons n quty pcs. Ths spcal fatus of stock makts n mgng conoms mpls that dmand lastcty of quts n laton to ts own at of tun s vy hgh. On th oth hand, t can b asly dmonstatd that a hgh lastcty of dmand fo quts can sult fom a postv sgn n th numato of () 4. Und ths assumptons, th FF loc wll b downwad slopng (s fgu ). 8 FF Fgu Shot Run Equlbum and Compaatv Statcs W a now abl to analys th shot un qulbum of ths conomy, that s th smultanous qulbum of all makts whn asst stocks and xpctatons about futu poftablty of captal goods a kpt constant. Fom (8) and (0), w know that : (, q, γ, ) ; < 0, > 0, > 0, (, d,, ) ; < 0, > 0, 4 > 0, 4 > 0 > 0 (4) (5) Equatons (4) and (5) a smpl psntatons of th GG and FF loc, spctvly. Cavalho (99) dfns an oganzd makt as on n (...) whch avods xcssv potntally dsuptv fluctuatons n th pc of assts, avodng thby solvncy css that could b thatn th pfomanc of that makt. To contan th fluctuatons n asst pcs s th functon of makt maks (...) sdual buys o slls that absob xcss suppls o dmands whn thy xcd som accptabl magm (p.87). 4 S apndx fo a fomal poof of ths statmnt. 8

10 Gnal qulbum of goods and fnancal makts qus a pa of valus fo and such that quatons (4) and (5) a solvd smultanously. Ths wll happn n th pont wh GG cuv ntcpt FF cuv, as shown by fgus a and b. 9 GG FF FF GG Fgu a Fgu b Fgus a and b show two possbl shot un qulbum confguatons. In th fst on shown by fgu a FF cuv s lss nclnd than GG cuv. In th scond psntd by fgu b GG cuv s lss nclnd than FF cuv. Fo shot un analyss w wll not consd th ssu of qulbum stablty; n oth wods, w wll suppos that th conomy s always n shot un qulbum. In ths cas, th latv nclnatons of GG and FF cuvs s mpotant only fo compaatv statcs. 9

11 0 0 Fo analyss of compaatv statcs, w wll suppos that GG s stp than FF cuv. So, usng (5) n (4) and takng total dvatv of th sultng quaton, w can asly dmonstat that : Expssons (6) and (7) sumazs th ffcts of changs n () xpctd dvaluaton of domstc cuncy, () xpctd at of poft, () al xhang at, (v) fscal dfct as a facton of conomy s captal stock and (v) ato of bank svs and fogn bonds valuatd n tms of domstc cuncy ov qulbum lvls of cunt ats of ntst and poft. Ths sults allow us to wt th followng quatons : 4 Long Run Equlbum and Dynamcs Now w must tun ou attnton to th bhavo of th systm n th long un. As alady bn told, n th long un asst stocks and xpctatons wll b changng as a sult of th ndognous opaton of th conomy. In patcula, montay bas whch, n th psnt modl, s qual to bank svs may chang as a sult of balanc of paymnts dfcts o suplusus, and xpctd at of poft may chang as a sult of changs n th cunt stuaton of th conomy. Takng th fst dvatv of n laton to tm, w obtan th followng xpsson : Equaton (0) shows that at of gowth of th ato btwn montay bas and fogn bonds s qual to th dffnc btwn th at of gowth of montay bas and th at of gowth of th stock of fogn bonds. Fo smplcty, w wll assum that stock of fogn bonds s kpt constant though tm, so all changs n coms fom changs n montay bas. In th absnc of stlzaton, changs n th stock of hgh powd mony wll b qual to changs n fogn svs (cf. McCallun, 996, p.8). Snc th s a fxd xchang at gm, all vaatons n th stock of fogn svs com fom suplusus o dfcts n th balanc of paymnts. ( ) (7) 0 0 0; 0; 0; (6) 0 0; 0; ; 0 0; 4 4 < > + < < + + > + > > < > + < q d q d γ γ (9) ),,,, ( (8) ),,,, ( γ γ q d q d (0) ˆ B B H H & & &

12 W wll suppos that balanc of paymnts dfcts o suplusus a dtmnd by th followng quaton : BPA ε + ε q φτ K + ϕ d K ;0 < ϕ < ( [ ] ( ) ) 0 Th fst tm n () s th cunt account suplus whch s a postv functon of al xhang at. Mashall-Ln condton s satsfd and a ngatv functon of cunt at of poft. Th scond tm s th captal account suplus whch s a postv funton of th dffnc btwn domstc at of ntst and ntnatonal at of ntst plus xpctd at of dvaluaton n domstc cuncy. Th cofcnt ϕ psnts th snsblty of captal account suplusus to th dfnc btwn domstc and ntnatonal at of ntst. Snc ϕ <, ths conomy s not und a systm of pfct captal moblty. Mo pcsly, w a supposng, lk Mundll (96, 96) and Flmng (96), that th s mpfct captal moblty btwn counts (cf. McCallun, 996, p.45). Ths mpfcton on moblty of captal can, n tun, b th sult of govnmntal stctons on captal movmnts, lk thos that pvald n most counts dung th post wa pod. Dvdng both sds of () by K, and mmbng that BPA s qual to tm dvatv of montay bas, w obtan th followng xpsson : H& H h [ ε 0 + εq φτ + ϕ( d )] ; h () H K ˆ h Usng () n (0), w hav th followng dffncal quaton : [ ε + ε q φτ (, ) + ϕ( (, ) d )] () 0 Fom () w can obtan th loc of all combnatons n and fo whch th ato btwn montay bas and th stock of fogn bonds s kpt constant though tm. Th slop of ths loc s gvn by : φτ ϕ > 0 (4) ϕ φτ wh : ; ; ; Now w must tun ou attnton to th voluton of xpctd at of poft though tm. W wll suppos, lk Taylo and O Connll (985), that : & ψ (, ) ; ψ > 0 (5) wh : s ( ) th " saf" at of nt st Equaton (5) stablshs that f cunt at of ntst s bgg than saf at of ntst than th wll b a contnous ncas n xpctd at of poft. Th aconal fo ths assumpton s that, n ths cas, ntpnus wll xpct a futu ducton n th

13 domstc at of ntst and thus a futu ncas n agggat dmand and n th dg of capacty utlzaton 5. Fom (5) w can obtan th loc of all combnatons n and fo whch xpctd at of poft s constant though tm. Th slop of ths loc s gvn by : > 0 (6) Ths conomy wll b n stady-stat whn valus of and a such that () and (4) a both st qual to zo. Gafcally, ths wll occu n th pont wh cuv 0 ntcpts th cuv 0. A possbl stady-stat confguaton of ths conomy s psntd n Fgu Fgu 4 Wh : and a th stady-stat valus of and. Now w hav to analys th stablty of stady-stat qulbum. In od to do that, s ncssay to calculat th matx M of patal dvatvs of th dynamc systm composd by quatons () and (5) [ cf. Lma, 999, p. 644]. Th lmnts of ths matx a gvn by : 5 In Taylo and O Connll (985), xpctd pofts a supposd to fall whn cunt at of ntst s bgg than saf o nomal at of ntst. Howv, th atonal fo ths assumpton s not cla. If cunt at of ntst s bgg than nomal at of ntst than s asonabl to assum that ntpnus wll xpct a futu dducton n th at of ntst. Snc agggat dmand and th dg of capacty utlzaton wll ncas f ntst at falls, so ntpnus should xpct a futu ncas n at of poft. In ths cas, th s no cla ason to assum that xpctd at of poft wll fall.

14 M M M M ψ ψ φτ φτ p + ϕ + ϕ p (6a) (6b) (6c) (6d) Th stady-stat qulbum of ths conomy wll b unstabl f and only f th tac of Matx M s ngatv (cf. Takayama, 99, p. 408). Ths wll occu, n tun, f th followng condton s satsfd : φτ c ϕ < ϕ (7) Expsson (7) stats that stady-stat qulbum wll b unstabl f ϕ s lss than a ctcal valu ϕ c. In oth wods, fo stady-stat qulbum b unstabl, captal moblty cannot b vy hgh. Ths conomy wll hav a saddl-path f and only f th dtmnant of matx M s also ngatv (Ibd, p. 408). Ths wll occu f and only f th followng condton s satsfd : > (8) It can b asly dmonstatd that (8) mpls that 0 cuv s stp than 0 cuv, as t s shown n fgu 4. 5 Ral xchang at apcaton and dynamcs of gowth and quty pcs : booms and bubbls. Now, w wll tun ou attnton to th ffcts of al xchang at appcaton ov a st of vaabls, n patcula : () th cunt at of poft, () th cunt at of ntst and () quty pcs. In th famwok dvlopd n sctons -4, w wll b abl to show that a al xchang at appcaton may caus an tmpoay ncs n gowth at of captal stock and a bubbl n quty pcs,. a cumulatv ncas n quty pcs dung a fnt lnght of tm. Fst of all, w wll analys th ffct of al xchang at appcaton ov 0 cuv. Sttng (5) qual to zo, and takng th total dvatv of th sultng quaton, w obtan th followng xpsson : q < 0 (9) q Expsson (9) stats that a ducton n al xchang-at. a al xchang at appcaton wll poduc an ncas n xpctd at of poft. Gafcally, ths ffct s psntd by a ghwad shft n 0 cuv, as t s shown n fgu 5.

15 4 0 0 Fgu 5 In od to dtmn th ffct of a al xchang at appcaton ov 0 cuv, w hav to st () qual to zo and tak total dvatv of th sultng quaton. Aft all ncssay algbcal manpulatons, w av at th followng xpsson : ξ φτ q φτ q + ϕ ϕ q (40) Expsson (40) has an ambguous sgn bcaus t s not possbl to dtmn th sgn of numato. Claly, ambguty s causd by th psnc of ξ. th snsvty of nt xpots as a facton of conomy s captal stock to changs n al xchang at. Howv, t s a stlyzd fact about sm-ndustalzd conoms that nt xpots a not vy snstv to changs n al xhang ats. So, w can assum that ξ s na zo. In ths cas, th sgn of (9) wll b ngatv, manng that al xchang at appcaton wll poduc an ncas n xpctd at of poft. Ths ffct s psntd gafcally by a ghtwad shft n 0 cuv, as shown n fgu 6. 4

16 5 0 0 Fgu 6 Th fnal ffct of a al xchang at appcaton ov stady-stat valus of and wll dpnd on th latv shft of both cuvs. If th ghtwad shft n 0 cuv s sufcnt stong, so th wll b a a ducton n stady-stat valu of and an ncas n stady-stat valu of (s Fgu 7). Snc qulbum at of poft s a postv functon of and a ngatv functon of, than cunt at of poft wll ctanly ncas. On th oth hand, qulbum at of ntst s a ngatv funton of and a postv funton of, so th wll b a cla ducton n th at of ntst. An ncas n qulbum at of poft and a ducton n qulbum at of ntst wll nduc nts to substtut domstc bonds fo quts n th potfolos. Thus th wll b a shap ncas n dmand fo quts whch wll poduc an ncas n quty pcs

17 6 0 Fgu 7 Tabl I sumazs th ffcts of a al xchang at appcaton ov stady-stat valus of,,, and P. Tabl I R P Ral xchang at apcaton So fa w hav only analysd th ffcts of al xchang at appcaton ov stady-stat valus of and. Howv, out of stady-stat dynamcs s much mo ntstnng. In fact, lt us consd th stuaton dsplayd n Fgu 8. Pont A psnts th ntal stady-stat poston of th conomy,. bfo th occunc of a shock ov al nchang-at. Aft th appcaton n al xchang-at, conomy stats to mov n DD path. As w can s, fom pont A to pont B th s () a contnuous ducton n th valu of ; and () a contnuous ncas n. Fom pont B on, xpctd at of poft contnu to ncas, but th ato btwn bank svs and fogn bonds bgns to s. A B DD 6

18 7 Fgu 8 Th bhavou of and fom A to B poducs th followng ffcts :. Fst of all, snc s a postv funton of and a ngatv functon of th wll b a cumulatv ncas n th cunt at of poft. Ths ncas s accompand by a contnuous ducton n th at of ntst, snc t s a ngatv functon of and a postv functon of. Th combnd ffct of () ncas n cunt and xpctd at of poft; and () ducton n th at of ntst wll sult n a ncas n th dsd at of captal accumulaton,. an ncas n th at of gowth of captal stock.. Snc conomy s und a fxd (nomnal) xchang-at gm, a contnuous ducton n th ato btwn bank svs and fogn bonds s followd, und no-stlzaton assumpton, by a contnuous ducton n th stock of fogn svs.. As a sult of () a contnuous ncas n cunt and xpctd ats of poft; and () a contnuous ducton n th at of ntst, th s a cumulatv ncas n pc of quts as soon as nts substtut domstc bonds fo quts n th potfolos. In oth wods, a bubbl n quty pcs dfnd as a cumulatv ncas n asst pcs latv to pcs of captal goods - s poducd as a sult of th dynamc path of and. 4. Snc th dg of capacty utlzaton s ncasng ov tm, and domstc at of ntst s bng ducd; th wll b a contnuous ncas n mpots of aw matals and a outflow of captal. In oth wods, ths conomy wll hav a cunt account and a captal account dfcts, whch wll b fnancd by a contnuous loss of fogn svs. Fom pont B on, th bhavou of man macoconomc vaabls s ambguous. Fo xampl, f th contnuous ncas n th xpctd at of poft has th ffct of ncasng cunt at of poft; th contnuous ncas n th ato btwn bank svs and stock of fogn bonds wll hav just th oppost ffct. Snc th bhavou of s undtmnd, w can t say anythng about th bhavo of quty pcs and th at of gowth of captal stock. Th only statamnt that can b mad s about th bhavou of fogn svs. >Fom pont B on, th s a cla ncas n bank svs and, und nostlzaton assumpton, n th stock of fogn svs. Th tm path of cunt at of poft, cunt at of ntst, stock of fogn svs and quty pcs a dsplayd n fgu 9. 7

19 8 P R T 0 (A) T (B) Tm Fgu 9 6 Concluson Though out ths atcl, w hav shown that a asst pc bubbl dfnd as a cumulatv ncas n asst pcs latv to pcs of captal goods can sult fom a al xchang at appcaton n conoms that hav () (mpfct) captal moblty and () a low dg of oganzaton n fnancal makts. Ths a common fatus of mgng counts lk Bazl o South Coa, so that th possblty of ocunc of asst pc bubbls n ths conoms s not small. Apndx : Th Slop of FF locus and dmand lastcty of quts. If th numato n () s postv thn : 8

20 9 ( + ) β > µ ε ( A) Multplyng both sds of (A) by [ (+)/εw], w hav : β ( + ) ( + ) µ ( + ) ε ( + ) > ( A) εw εw εw But th last tm n (A) s th lastcty of quts dmand n laton to th xpctd at of poft, whch w wll dfn as η ε, +. It s asy to show that : β + µ η β, + > η m, + ηε, + ( A) ε ε Wh : η β, + s th dmand lastcty of domstc bonds n laton to xpctd at of poft and η µ, + s th dmand lastcty of mony n laton to xpctd at of poft. Manpulatng (A) w av at th followng xpsson : β + η ε, + > ηβ, + p + η µ, + η ε, ( A4) ε + Expsson (A4) shows that numato n () wll b postv f and only f dmand lastcty of quts n laton to xpctd at of poft s bgg than som ctcal valu η ε, +. Rfncs Avy, C. and Zmsky, P. (998), Multdmnsonal Unctanty and Hd Bhavo n Fnancal Makts, Th Amcan Economc Rvw, vol. 88, n 4, Sptmb: Banj, A (99). A Smpl Modl of Hd Bhavou. Th Quatly Jounal of Economcs, Vol. CVII, N.. Calvo, G. (998), Vats of Captal Makt Css, n G.A. Calvo and M. Kng (dtos), Th Dbt Budn and ts Consquncs fo Montay Polcy, Chapt 7; London: Macmllan Pss Ltd. Calvo, G. (999), Contagon n Emgng Makts: whn Wall Stt s a ca, Unvsty of Mayland, ( Calvo, G. and Rnhat, C. (999), Whn Captal Inflows Com to a Suddn Stop: Consquncs and Polcy Optons, Unvsty of Mayland Cavalho, F.C (99). M. Kyns and th Post Kynsans. Edwad Elga : Aldshot. Dymsk, G (998). Bubbl Economy and Fnancal Css n East Asa and Calfona : a spatalzd Mnsky Pspctv. Unvsty of Calfona at Rvsd. 9

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