EXTERNAL DEBT, GROWTH AND SUSTAINABILITY. Abstract. Introduction

Transcription

1 ETERNAL EBT, GROWTH AN SUSTAINABILIT Absrac Robro Frnkl * Th papr prsns a odl inndd o dfin and discuss h susainabili of rnal dbs in rgn arks. Th firs susainabili condiion is h isnc of a aiu in h dboupu raio. Wih so sipl bhavior hpohss i is shown ha susainabili dpnds on h iniial db-pors raio, h ra of growh of pors and h counr-risk priu. An ndognous counr-risk priu givs roo for ulipl quilibriu. Th odl allows h discussion of vulnrabili vis-à-vis financial shocks and h propnsi of h cono o jup o unsusainabl pahs. Two addiional susainabili condiions ar addd: a posiiv ra of growh and a iniu in h dosic absorpion-oupu raio. Th discussion of ulipl quilibriu, vulnrabili and h ponial insabili of susainabili is hn ndd o hs susainabili condiions. Inroducion In a prvious ssa Frnkl, 21 w analsd h siuaion of h Lain Arican counris in h con of financial globalizaion in h la 199s. This papr ss ou a or foral analical approach o his subjc. In paricular, w ain h dnaics of rnal db fro a balanc-of-pans prspciv, using h concp of susainabili. 1 Ernal db a b dscribd as susainabl whn hr ar no forsabl ajor difficulis in ing conracs in a il and propr annr. Obviousl, his dos no acuall guaran ha hos conracs will b. Susainabili is a judgn wih rspc o uncrain fuur vns, basd on prsn inforaion and probabl conjcurs. Th condiions of susainabili aind in his papr ar rasonabl a priori. Th counr s inrs ra, which is drind b h inrnaional ra and h counr risk priu, plas an iporan rol in our analsis. Th odl w s forh rflcs crain faurs of h rging ark conois, ha is o sa dvloping conois ha wr involvd in hr aspcs of h financial globalizaion procss: h opning of h local financial ark and is ingraion wih h inrnaional ark, h absorpion of n capial flows and h rsuling accuulaion of a significan sock of rnal obligaions. L us suppos ha h counris w ar aining hav issud a crain aoun of sovrign db dnoinad in * Snior Rsarchr, Cnro d Esudios d Esado Socidad CEES, Bunos Airs, Argnina and Profssor of h Univrsi of Bunos Airs. Th auhor prsss hanks o José Anonio Ocapo, Lanc Talor and Sbasián Kaz for hir cons on a prliinar vrsion. Marín Rapi assisd wih h odl siulaions. Alhough fw of hos rciss ar rflcd in h prsn vrsion, his collaboraion was iporan for h final rsul. 1 S Sionsn 1985 and Bhaduri 21.

2 2 forign currnc dollars which has bn placd on h inrnaional financial ark and h local ark. Inforaion abou h prics of bonds is frl availabl and an local or forign agn can acquir sovrign bonds a ark prics. 1. Sgnd ingraion. Th ral inrs ra and h counr risk priu 2 Inrs ras displa significan diffrncs bwn dvlopd and rging conois, dspi h ingraion ha iss aong financial arks. Hr w will considr how inrs ras ar drind in an rging ark. W hav said ha h counr issud dollar-dnoinad sovrign bonds, which wr radd on h scondar arks. Th pric of hos bonds drins hir ild, which w will call i. ild is convnionall brokn down ino wo rs: i r* + k 1 whr r* is h ild on a Unid Sas sovrign bond wih h sa auri and idnical characrisics, and k is h counr risk priu. Firsl, i rprsns h opporuni cos of an forign invsn in h counr, o h n ha h ass in qusion, ral or financial, is subjc o counr risk. So, h cos of inrnaional crdi o local banks or o ohr priva agns will gnrall hav o b qual o or grar han i. To facilia a discussion on how h ral inrs ra is drind wihou losing gnrali, l us suppos ha h naional financial ss is pariall dollarizd. This ans ha asss and liabiliis dnoinad in dollars ar issud b h financial ss oghr wih asss and liabiliis in local currnc. Sinc local banks can acquir sovrign bonds ilding i, his ra is h opporuni cos of local bank lnding in dollars. Consqunl, i is h floor pric of dollar bank loans, vn if h crdi has no bn fundd in h inrnaional ark. Th inrs ra on dollar loans us b qual o or grar han i. L us assu ha i is qual o i. To drin h ra in local currnc w nd o ak ino accoun h pcd rnd of h chang ra: j i + E + π 2 π > whr j is h noinal ra of inrs in local currnc, E is h pcd ra of noinal dvaluaion and π rprsns h chang risk priu. 2 On sgnd ingraion, s Frnkl 21.

3 L p and p* b h ras of local and inrnaional inflaion, rspcivl. W can subrac p fro boh brs of 2 and add and subrac p* in h scond br: j p i p* + [E p + p*] + π 3 3 This givs an prssion in which j p is h ral inrs ra in local currnc and E p + p* is h pcd ra of ral dvaluaion. I is as o s ha h ral inrs ra in local currnc us b grar han or qual o i p*, cp in h cas of an pcd ral apprciaion rnd srong nough o offs h chang risk priu π. W will disrgard his cas, howvr. W will hrfor assu ha: j p i p* 4 For h sak of siplici, l us suppos ha p* which is quivaln o considring p as h diffrnc bwn local and inrnaional inflaion and ha 4 holds as an quali: r j p i r* + k 5 2. Ernal financing Th counr has rcivd capial inco ha gnras an aoun of rnal db. Th capial inflows rsul fro a bond issu wih a auri L, which ild an inrnaional inrs ra r* and whos capial us b rdd in full a auri. Th currn-accoun balanc CC is: CC M r * whr rprsns pors, M ipors and r* is h inrs accrud on rnal db. W will assu a zro variaion in rsrvs and w will suppos for h i bing and for h sak of h prsnaion ha h currn accoun is in dfici. Financing nds NF ar: NF CC + λ + M + r * + λ. 6 whr λ 1/ L is h porion of h db ha aurs in i. As h bonds ar issud a a ra undr par k, o obain NF aoun of financing a volu Z of nw db us b issud so ha: Z NF and hrfor r* L r* + k L

4 kl Z NF 7 4 Th variaion in db is hrfor: d Z λ If w rplac wih 6 and 7 and rgroup, w obain: d kl r * + λ kl 1 kl + kl M 8 W calcula: kl, 1 sinc k r * + λ 1, r* > sinc 1 and quaion 8 is prssd as: d M 9 Th variaion in db can b brokn down ino a purl financial r, which dpnds on h aoun of db, and a r ha dpnds on h rad balanc. Th firs r rprsns h cos of financing h su of h inrs accrud on ising db plus rfinancing of capial auriis. If hr is a rad dfici <M, h scond r rprsns h cos of financing i. In boh rs h facor appars as a uliplir. Th highr h counr risk priu and consqunl h highr h inrs ra h counr us coi o paing in ordr o scur financing, h highr his facor. Noic ha quaion 9 is also valid in h cas of a rad surplus >M. In his cas h procds of h rad balanc ar usd o financ h inrs and auring capial of ising db, which is quivaln o supposing ha h rad balanc is usd o bu db bonds a ark prics. If h rad surplus is larg nough, h absolu valu of h scond r a b largr han h firs and h db conracs. I can hrfor b sn ha h currn-accoun dfici w assud abov for h purposs of h prsnaion is no ncssar, sinc quaion 9 is valid in ihr cas. If h risk priu is nil, quaion 9 is rducd o: d r * + M ha is, h variaion in db is h sa as h currn-accoun balanc wih h opposing sign. ivision of quaion 9 b givs h growh ra of h db:

5 5 d M ˆ 1 L b oupu and is ra of growh. Th ra of variaion of h db/oupu raio is: d M ˆ 11 which, uliplid and dividd b in h final r, can b prssd as: d M ˆ / 12 Th ra of variaion of h db/oupu raio in quaion 12 is prssd as a funcion of coonl sn acroconoic raios Growh ras of oupu and ipors W shall copl h odl b aking ndognous h growh ras of oupu and ipors. W will assu ha h ra of growh of pors is ognous. Th influnc of h counr risk priu on h ral cono is incorporad ino h odl b ans of h ral inrs ra. W will op for h sipls for, assuing ha h cono s growh ra is a funcion of h inrs ra: r + ρ r + ρ r * + ρ k, wih ρ < 13 whr ρ is h inrs ra lasici of oupu. W shall also ak ndognous h growh ra of ipors, assuing ha his ra is a funcion of h oupu growh ra: µ, wih µ > 14 whr µ is h ipor lasici of oupu. 3 For apl, if L 1 ars, r* 5% and h counr risk priu k.3 3 basis poins, hn.125. Wih rad in balanc, h growh ra of h db/oupu raio is zro onl if oupu grows a an annual ra of 1.25%. If h cono is growing a a ra of 7% and h db/oupu raio is 5% /.5, a rad surplus of 1.2% of oupu is ndd o sabiliz h db/oupu raio.

6 6 4. Th dnaics of db To rsolv diffrnial quaion 9 and obain db rajcor w us spcif h rajcoris of pors and ipors: M M whr and ar h growh ras of pors and ipors, rspcivl. Wih his spcificaion, quaion 9 bcos: d M 15 In h gnral cas ha and, h soluion o h diffrnial quaion is: M M + 16 Obviousl, h wa h db bhavs dpnds on h financial parars niond arlir, on h growh ras of pors and ipors and h condiions of rad dfici or surplus a. W will focus our analsis of h probl of db susainabili on h db/oupu raio. Th rajcor of oupu is: Consqunl, using 16, h db/oupu raio follows h rajcor: M [ ] + [ ] 17 Th voluion of h db/oupu raio, lik db islf, dpnds on h iniial posiion of h rad balanc. W wan o rov his ln o focus h analsis on h parars. In ordr o do his, w will assu hncforh ha h saring poin is a rad balanc. W will hrfor ak M and subsiu prssion of h of h db/oupu raio rajcor: in 17, which givs h following

7 This prssion clarl shows h iniial condiions ha influnc h voluion of h db/oupu raio: h dgr of opnnss of h cono / and h db/por raio /. Th firs of hs is a scal facor which dos no alr h characrisics of h db/oupu rajcor. This rajcor dpnds ssniall on h iniial db/por raio. A dvaluaion, for apl, brings abou an incras in h rlaiv pric of radabl goods, which incrass h dgr of opnnss of h cono and hrfor uliplis h whol curv of h db/oupu raio b his facor. This sa dvaluaion dos no affc h db/por raio, howvr, which hrfor dos no alr h for and characrisics of h db/oupu raio rajcor. Th dvaluaion affcs h shap of his curv onl hrough is ral ffcs, ha is, hrough is influnc on h ras of pors and ipors. Th inroducion of h hpohss for h ral cono 13 and 14 dfins a odl whos opraion can b plaind b obsrvaion of quaion 18. An incras in h counr risk priu nds o rais h db/oupu raio on h financial sid, bcaus parars and incras. Th incorporaion of h rcssionar ffc of a ris in h inrs ra adds anohr ln on h ral sid: an incras in h counr risk priu nds o lowr h oupu growh ra and, as a rsul, nds o rais h db/oupu raio. Bu a downurn in h growh ra of h cono causs a dip in h growh ra of ipors. Wih an por growh ra unalrd, h rad surplus pands or h dfici conracs and his ffc nds o lowr h db/oupu raio. 5. Financial dfici and rad surplus In ordr o anals h voluion of h db/oupu raio, w will sablish a nubr of rsricions on h odl parars. Th bs wa o do his is o sar wih quaion 11 and rwri i assuing iniial condiions of rad in balanc M. k ˆ k k k 19 Equaion 19 prsss h growh ra of h db/oupu raio. In his quaion w hav spcifid h parars ha dpnd on h counr risk priu. L us iagin ha in < h cono princs a counr risk priu which w will call k such ha h ra of growh is qual o h cos of rfinancing inrs and capial auriis on rnal db. Wih his growh ra, h ra of pansion in ipors is qual o h ra of pansion of pors, so ha h cono grows wih rad in balanc. In < quaion 19 would giv: ˆ

8 8 Th ra of growh of h db/oupu raio is nil and h cono is on a susainabl db rajcor wih a consan db/oupu raio. L us now iagin ha a conagion ffc pushs up h counr risk priu in k > k. In consqunc, riss, and a h sa i h ra of growh dclins >, < so ha >. Th growh ra of h db/oupu raio will urn posiiv hrough his ffc. Bu h downurn in h ra of conoic growh brings abou a fall in h growh ra of ipors < and hrfor > whn. In addiion, no wih quaion 19 ha in h growh ra of h db/oupu raio is posiiv: ˆ Th ffc of h incras in h counr risk priu is an upward rnd in h db/oupu raio. Bu fro a zro valu whn, h surplus bgins o pand whn >. In wha circusancs can a growing rad surplus offs h financial ffc of a ris in h counr risk priu and ak rnal db susainabl? In gnral rs, his probl iplis h following rsricions on h parars: > ; > L us anals h dnaics of h db/oupu raio wih hs supposiions. Indpndnl of h probl ha jusifis h, h supposiions w ar assuing appar o b h onl ons of inrs for analsing db susainabili. If > and h cono is no gnraing a rad surplus, h db/oupu raio is plosiv and h db is unqusionabl unsusainabl. If, w could discuss, for apl, how uch of a rad dfici h db rnd can olra wihou bcoing plosiv, bu his avnu of nquir dos no appar o b paricularl nicing.

9 9 6. Firs condiion of susainabili Th firs condiion of susainabili is ha h db/oupu raio us no bco plosiv. Th curv prssd b quaion 16 us hav a aiu. Th firs ordr condiion is: { + } 2 Th scond ordr condiion is: { } 2 2 < 21 4 Fro 2 i is clar ha h db/por raio is h onl iniial condiion rlvan for h isnc of a aiu. Sinc / >, h prssion wihin h squar bracks us cancl islf ou o vrif 2, and his dpnds clusivl on h iniial condiion /. Th isnc of a aiu of a valu > which saisfis 2 dpnds, firs of all, on h growh ra of pors. If >, hr will alwas b a aiu and h db will b susainabl whavr h valus of h growh ras of oupu and ipors wih h rsricions w hav alrad niond > ; >. Th ann o his docun conains a donsraion of his. In rs of h probl s ou abov, an cono would princ an incras in is risk priu such ha > >, bu h valu of would sill b lowr han h growh ra of pors <. In his cas h db/oupu raio would nd o grow bcaus of h ris, bu would rach a aiu poin. 4 In fac, vrificaion of h scond ordr condiion is rdundan bcaus w know ha >, so ha if 2 has a poin of inflion, i us b a aiu.

10 1 If <, h condiion o vrif 2 and 21 whn > is: > 22 This is donsrad in h ann. In rs of our probl, a ris in h risk priu aks h nw valu of highr han h growh ra of pors. In his cas, h db would b susainabl onl if 22 wr vrifid. Ohrwis h db/oupu raio would grow plosivl. Givn L and r*, an por growh ra and lasiciis ρ and µ, h lf-hand br of 22 is a dcrasing funcion of h counr risk priu: k [ k ] [ k ][ k k ] H k 23 Curv H is illusrad on h lf panl of figur 1. Th db/oupu raio has a aiu onl if h valu of H corrsponding o a givn k is grar han /. Th inrscion of curv H wih sraigh lin / drins criical risk priu k c such ha h db/oupu raio bcos plosiv for an k kc. Th wo panls of figur 1 illusra h abov probl in h cas ha h ris in h risk priu drins a valu >. Whn <, h counr risk priu was k and h growh of h cono was qual o h growh ra of h db. If h counr risk priu wr o ris b k1 k such ha H k 1 >, h db/oupu raio would nd o grow, bu i would rach a aiu, as shown in h scond panl. B conras, if h ris in h counr risk priu is k2 k, i would b larg nough for H k 2 <, and h db/oupu raio would nd o grow plosivl, as is also shown in h scond panl. W ar now in a posiion o su up h conclusions w hav drawn and prss h in rs of h probl s ou abov. In h vn of an incras in h counr risk priu, db susainabili dpnds firs of all on h growh ra of pors. If h cono is growing wih balancd rad, bu incrasing rad opnnss, h db is susainabl providd ha is sill lowr han h growh ra of pors afr h ris in h risk priu. In a diffrn scnario for apl if h cono is growing wih consan rnal rad/oupu cofficins, db susainabili dpnds on h db/por raio. Th lowr h db/por raio, h largr a ris in h risk priu h db/oupu raio can bar wihou bcoing plosiv.

11 11 L us now considr wo counris which hav h sa iniial condiions and bhaviour parars, cp for hir dgr of rad opnnss and, consqunl, hir db/por raios. Boh hav h sa iniial db/oupu raio, bu h firs cono has a significanl lowr por/oupu raio and hrfor ipor/oupu raio han h scond. W will call h firs cono Chil and h scond Brasarg. Boh hav h sa curv H k, as shown in figur 2. L us suppos ha boh princ an idnical variaion in counr risk priu k1 k such ha h nw valu of is highr han h growh ra of pors causd, sa, b an across-h-board drop in h prics of rging ark bonds. Wih h nw counr risk priu, h db/oupu raio grows plosivl in Brasarg, whil in Chil h db rains susainabl.

12 12 Figur 1 H / /k 2 /k 1 / / k k k 1 k c k 2 k Figur 2 H / Brasarg / Chil k k 1 k

13 13 Figur 3 H k k H k 7. Mulipl quilibria and slf-fulfilling prophcis L us iagin ha inrnaional invsors includ h db/por raio in hir counr risk assssn. Cris paribus, h highr h db/por raio, h highr h counr risk priu, sinc a highr db/por raio aks h counr or likl o nr ino an plosiv db rajcor in h vn of a slup in h pric of is bonds. Th rasoning bhind his assssn of risk is capabl of allowing for conoic polic racions. In h vn of a chang in inrnaional financial condiions ha hrans h susainabili of rnal db, h counr s govrnn can ipln asurs o incras h growh ra of pors and hus nsur susainabili. As can b sn in quaion 22, howvr, h highr h db/por raio, h largr h ndd incras in pors. Th odl consising of h condiion of susainabili and h funcion of h risk priu: k k H k k '<

14 14 can hav ulipl quilibria, as shown in figur 3. Curvs H k and k H, / inrsc a svral poins. In ohr words, h funcion is saisfid b diffrn risk prius, which drin crain db/oupu raio rajcoris. Cris paribus, h db is susainabl wih a sall counr risk priu. B conras, h db is unsusainabl for counr risk prius such ha H k. Figur 4 uss Chil and Brasarg o show h odl in which counris ha ar siilar bu hav diffrn rnal db/por raios prfor wih diffrn counr risk prius. In h figur, Chil s priu k Ch is lowr han Brasarg s priu k B bcaus Brasarg has a significanl highr db/por raio han Chil. Howvr, his assssn b h inrnaional financial ark has pushd Brasarg s counr risk priu clos o h criical valu ha would ak is db unsusainabl. As a rsul, Brasarg is or vulnrabl o alraions in inrnaional financial condiions han Chil, bcaus an incras of qual agniud in h wo counris risk prius aks Brasarg s db unsusainabl, whil ha of Chil coninus o b susainabl. For h sa rason, Brasarg s susainabili is or pron o slf-fulfilling prophcis. Whn h risk priu is such ha h valu of H k cos clos o h db/por raio as is h cas of Brasarg in figur 4, w a rasonabl assu ha inrnaional invsors will bco or pron o suddn changs of opinion in rspons o dosic or inrnaional signals, which can asil lad o incrass in h risk priu ha ak h counr s db unsusainabl. 8. Coplnar condiions of susainabili Th isnc of a aiu in h db/oupu raio is no a paricularl danding condiion. As wll as non-plosivnss, db susainabili ough o saisf ohr condiions, such as hos s forh blow. a Posiiv growh ra Th firs addiional condiion w will considr is h rquirn for h cono o ainain a posiiv growh ra. In h vn of an incras in h counr risk priu, h db a b susainabl in h sns ha i is no plosiv; vn so, his condiion a b vrifid in h con of a downurn in oupu. If h non-plosiv rajcor is basd on a prolongd conracion in oupu and ipors, soonr or lar i will bco ipossibl for h counr o is conracual obligaions. In consqunc, his condiion of susainabili is:

15 15 >, which in rs of our probl can b prssd as: + ρ k k 24 > whr ρ < is h inrs ra lasici of oupu and k k in h incras in h counr risk priu. Fro 24 i follows ha: k k < or ρ k < k 25 ρ

16 16 Figur 4 H / Brasarg / Chil k Ch k B Figur 5 H / k 1 k k k 1 k 2 k

17 17 Rsricion 25 is opraiv for a counr risk priu ha is lowr han ha which would ak h db unsusainabl fro h poin of viw of non-plosivnss. Figur 5 illusras his possibili. Th lowr panl of h figur shows wo curvs r * + k which prss h growh ras as a funcion of h inrs ra. Curv 2 cus sraigh lin a k k 2, a highr risk priu han ha which aks h db/oupu raio plosiv. In his cas, condiion 25 dos no opra: whn h risk priu riss h db bcos plosiv vn whn conoic growh ras ar posiiv. On h ohr hand, if h cono donsras curv 1, which cus sraigh lin a k k1, a lowr risk priu han would ak h db/oupu raio plosiv, h opraiv susainabili condiion is h on ha rquirs a posiiv growh ra. In his cas, h growh ra urns ngaiv for counr risk prius wih which h db would sill b susainabl fro h poin of viw of non-plosivnss. b Lowr lii o h absorpion/oupu raio Anohr condiion of susainabili can b drivd fro h isnc of an uppr lii on h proporion of oupu ha us b ransfrrd ou of h counr o db coins. L us suppos ha hr is an incras in h counr risk priu which is susainabl fro h prspciv of non-plosivnss. In h procss ha gnras h ris in h risk priu, h rad surplus rnds sadil upwards as a proporion of oupu. As a rsul, h absorpion/oupu raio dclins coninuousl. A h sa i, h db/oupu raio incrass unil i rachs a aiu a a givn poin in i. Fro hn on, providing hr is no alraion in h parars, h surplus will coninu o incras as a proporion of oupu and h db/oupu raio will rnd downwards. I a b supposd ha, onc h db/oupu raio has rachd is aiu lvl, cono polic will b dircd a incrasing h cono s growh ra and hnc h ra of growh of ipors, prsrving susainabili, sabilizing or rducing h downward rnd in h db/oupu raio and balancing or iigaing h conracion in h absorpion/oupu raio. This procss could no co abou if h absorpion/oupu raio wr o boo ou bfor h db/oupu raio rachd is aiu poin. This would ak h db unsusainabl. Th lii on h conracion of absorpion is drind ssniall b h isnc of an adissibl lvl in h cono s consupion ra, sinc h invsn ra canno drop blow a crain floor lvl wihou affcing h oupu growh ra and ipors. 5 12: W can approach his condiion of susainabili in a foral annr using prssion 5 This argun was coonl usd in h scond half of h 198s, whn h adjusn of h Lain Arican conois o pos-crisis condiions was on h agnda.

18 18 d M ˆ / This ra urns nil whn h db/oupu raio rachs is aiu lvl: M / a and hrfor: a M / 26 L s b h aiu adissibl valu of h rad surplus/oupu raio h absorpion/oupu raio is hrfor 1-s. Subsiuing in 26, h condiion of susainabili a b prssd as: a s Condiion 27 spcifis h ciling ha h cono s db/oupu raio a rach wihou cding h aiu adissibl ouward ransfr. For a givn counr risk priu, which drins a non-plosiv db rajcor, h db bcos unsusainabl if h db/oupu raio violas condiion L us no ha b dfining a aiu flow of adissibl rnal ransfr w arriv a a drinaion of a ciling on h db/oupu raio. Th condiion is forall analogous o h condiion ha ariss fro dircl supposing ha h counr is facing an rnal financing squz in proporion o is lvl of GP. 7 Clarl, in 27 h rsricion is no a chanical on, bu dpnds on h inrnaional inrs ra and h counr risk priu. Th highr h counr risk priu, h lowr h ciling on h db/oupu raio. Figur 6 illusras his condiion of susainabili. Th figur shows h rajcor of h db/oupu raio for a drind risk priu k. Th rajcor saisfis h non-plosivnss 6 Wih L 1 ars, r* 5%, k 5 hundrdhs of a prcnag poin and a aiu ouward ransfr ra s 3% of oupu, h db/oupu raio could no ris abov 51%. 7 Th rsricion is analogous o h isnc of a lii on h db/n worh raio in h cas of corpora financing. Bacha 1986 usd his argun as a basis for an rnal financing rsricion which liis h growh of an cono. 27

19 19 condiion. If h aiu adissibl proporion of ouward ransfr is s 1, h condiion is no opraiv and h db is susainabl. Wih a lowr aiu adissibl rnal ransfr, s 2, h sraigh lin of h rsricion cus h rajcor of h db/oupu raio bfor i rachs is aiu poin. In his cas h db is unsusainabl. 9. Mulipl quilibria II Each of h condiions of susainabili w hav considrd raiss h possibili of ulipl quilibria if i is akn ino accoun in h risk assssn conducd b inrnaional invsors. Such a possibili ariss fro h supposiion, for apl, ha h closr o ach of h rsricions iposd b h condiions, h highr h risk priu. This can b forall prssd b supposing ha h risk priu is drind b h following funcion: k K H k s ; ; K 1 < ; K 2 < ; K 3 < a This ans of drining risk priu can b usd o rapola ach of h condiions of susainabili fro h arguns s ou in poin 7 on ulipl quilibria and slffulfilling prophcis.

20 2 Figur 6 / s 1 s 2

21 21 Ann Th firs ordr condiion is h quaion 2: { + } Sinc >, h prssion in squar bracks us b canclld ou. ivision of h prssion bwn squar bracks b givs: i Th probl is how o show ha hr iss a > which saisfis quaion i wih h parars > and >. L us ak: A 1 and B 1 Eprssion i a hus b wrin as: 1 B A B A F + ii whr: B A No ha F and ' > F.

22 22 L us considr hr cass: 1 > > 2 > < 3 < < In cass 1 and 2 F. Thr is alwas a valu of > such ha 1 F o In cas 3 F A B. Thus, hr is onl on valu of > such ha 1 o 1 F, if o < A B. In consqunc, h condiion is: o <

23 23 Bibliograph Bacha, Edar 1986, Crciino con ofra liiada d divisas: una rvaluación dl odlo d dos brchas, El ilagro la crisis. Econoía Brasilña Lainoaricana, Edar Bacha d., Mico Ci, Fondo d Culura Econóica. Bhaduri, Ai 21, On h viabili of rnal db, Ernal Consrains on Susainabl Growh in Transiion Counris, Working Papr, No. 19, Kaziirz Laski d., Vinna, Insiu for Inrnaional Econoic Sudis, Spbr. Frnkl, Robro 21, Rflcions on dvlopn financing, CEPAL Rviw, No. 74 LC/G.2135-P, Saniago, Chil, Augus. Sionsn, Mario Hnriqu 1985, Th dvloping-counr db probl, Inrnaional b and h vloping Counris, Gordon W. Sih and John T. Cuddingon ds., Washingon,.C., World Bank.