Two-Tier Exchange Rates and Monetary Autonomy in a Portfolio-Balance Model

Ma ion, Nancy Pe eg im A icle Two-Tie Exchange Ra es and Mone a y Au onomy in a Po olio-Balance Model Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik P o ided in Coope a ion wi h: Duncke & Humblo , Be lin Sugges ed Ci a ion: Ma ion, Nancy Pe eg im (1979) : Two-Tie Exchange Ra es and Mone a y Au onomy in a Po olio-Balance Model, Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik, ISSN 0342-1783, Duncke & Humblo , Be lin, Vol. 99, Iss. 1-2, pp. 45-64, h ps://doi.o g/10.3790/schm.99.1-2.45 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/291423 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. 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I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ Two-Tie Exchange Ra es and Mone a y Au onomy in a Po olio-Balance Model By Nancy Pe eg im Ma ion* Small open economies ha wish o peg hei cu encies o hose o hei majo ading pa ne s o en ind hemsel es hampe ed by in- e es -sensi i e and specula i e capi al lows ha unde mine hei abili y bo h o main ain ixed exchange a es and o pu sue an in- dependen mone a y policy. Some coun ies, no ably he Belgo-Luxem- bou g Economic Union, F ance and I aly, ha e expe imen ed wi h he wo- ie exchange ma ke in he hopes o insula ing hei economies om in e na ional capi al lows and es o ing some au onomy o domes ic mone a y policy. Such an exchange egime in ol es he o mal es ablishmen o sepa a e exchange ma ke s o cu en and capi al ansac ions. The comme cial exchange a e, de e mined in he ma ke o cu en ansac ions, is equen ly pegged by he au ho i ies; he inancial exchange a e, de e mined in he ma ke o capi al ansac- ions, is usually ee o luc ua e. The pu pose o his pape is o examine he impac e ec s o ce ain dis u bances and changes in policies on a small open economy main- aining a wo- ie exchange ma ke . The ask a hand is eally wo old: i s , o de elop a po olio-balance model o a wo- ie exchange ma ke and second, o de e mine whe he he wo- ie exchange ma ke pe mi s a coun y o gain some au onomy o e i s mone a y policy when inancial asse s a e ei he impe ec ly o pe ec ly subs i u able. Fo he pu pose o his pape , mone a y au onomy is de ined o mean ha he au ho - i ies can egula e ne capi al lows independen ly o he ela i e a es o e u n a home and ab oad and hus ha e some con ol o e he domes ic in e es a e. The wo- ie exchange ma ke model is desc ibed below and is sol ed in Appendix I. A second e sion o he wo- ie exchange e- gime, one which in ol es a di e en segmen a ion o he exchange ma ke , is p esen ed and sol ed in Appendix II. In o de o compa e * Depa men o Economics, Da mou h College, Hano e , New Hampshi e 03755, USA. I am g a e ul o William B anson and Pe e B. Kenen o help ul dis- cussions. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 46 Nancy Pe eg ini Ma ion hese models wi h mo e amilia exchange- a e sys ems, he solu ions o bo h he uni a y lexible and uni a y ixed exchange a e a e p e- sen ed in Appendix III and IV; hey se e as backd ops o he discus- sion o wo- ie exchange a es. While he models can gene a e much ui ul analysis and compa i- son, bo h in espec o sho - un beha io and s eady s a e p ope ies, and can be ex ended in a numbe o ways,1 his pape will ocus on impac e ec s in he asse ma ke s o he wo- ie exchange sys em. I will examine he sho - un de e mina ion o he domes ic in e es a e and he inancial exchange a e and will hen examine hei e- sponses o a ious dis u bances. I will show ha he au ho i ies ha e some con ol o e he domes ic in e es a e, e en in he case o pe - ec subs i u abili y be ween domes ic and o eign bonds, when in e es income, a cu en -accoun i em, is epa ia ed a he comme cial ex- change a e, bu ha hey lose con ol o e he in e es a e when in e es income is channeled h ough he inancial exchange ma ke . Desc ip ion o he Model The model p esen ed below ex ends o he egime o wo- ie ex- change a es he po olio balance heo y de eloped by James Tobin (1969) e . al. in which weal h holde s decide how o dis ibu e ne wo h among a ailable asse s based on ela i e a es o e u n and he size o he o al po olio. I assumes ha demands o asse s a e s ock a he han low demands and a e ealized ins an aneously so ha ac ual holdings o asse s always e lec he desi ed composi ion o he po olio. Dis u bances o po olio equilib ium c ea e s ock adjus - men s as po olios a e ebalanced, causing ins an aneous changes in he domes ic in e es a e and he inancial exchange a e. In addi ion, dis u bances al e he a e o accumula ion o inancial asse s. In he model, he inancial exchange a e is ea ed as a ela i e asse p ice. I is among he a iables ha equilib a e asse ma ke s and i is de e mined in he sho un in hose asse ma ke s.2 1 Fo example, he inancial sec o o he wo- ie model can be ex ended by adding a domes ic asse which is aded, by adding expec a ions and by allowing o leakages be ween he wo exchange ma ke s. The comple e wo- ie exchange ma ke would include a goods sec o and one could as- sume a ixed comme cial exchange a e o a comme cial a e ha loa ed in i s own ie . One can a gue ha neglec ing he goods ma ke in his exe - cise is no a se ious omission since he model is cons uc ed so ha he inancial ma ke s a e una ec ed on impac by dis u bances in he goods ma ke . 2 When a Keynesian goods ma ke ( ixed p ices, adjus able ou pu ) is added o he inancial sec o and he s eady-s a e solu ions a e examined, one disco e s ha he inancial exchange a e is esponsi e o e en s in he goods ma ke as well as o inancial dis u bances. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 Two-Tie Exchange Ra es and Mone a y Au onomy 47 P i a e Weal h and Demands o Financial Asse s The model con ains h ee inancial asse s — a bond issued by he go e nmen o he small coun y and held only by i s own esiden s, a s ock o money issued by i s cen al bank and held in e nally, and a bond issued in he ou side wo ld and a ailable o he small coun y in pe ec ly elas ic supply. Fo eign money is no held domes ically bu i s exis ence is implied by he exchange a e. Assuming ixed p ices and no physical capi al s ock, he weal h o p i a e households can be w i en as he nominal (= eal) domes ic- cu ency alue o he money and bonds hey cu en ly hold: (1) wh = L* + B*> + eFh whe e Lh is he ac ual s ock o money held by households, Bh is he numbe o domes ic bonds held, Fh is he numbe o o eign bonds held and e is he spo inancial exchange a e ( he p ice o o eign cu ency in e ms o domes ic cu ency).3 Fo simplici y, i is assumed ha all bonds a e sho - e m, wi h ixed p ices in uni s o he cu ency o he issue and a iable in e es a es. The in e es a e on he o eign bond is de e mined in he wo ld ma ke and gi en exogenously o he small open economy ( ' = '). The in e es a e on he domes ic bond, , can a y independen ly o he o eign a e since p i a e weal h holde s in he small coun y ega d he wo ypes o bonds as impe ec subs i u es.4 Weal h holde s base hei nominal (= eal) demands o asse s in e ms o domes ic cu ency. The ac ion o he weal h hey wish o hold in each o he h ee asse s is assumed o depend on he e ec i e a es o e u n on domes ic and o eign bonds bu no on income.5 In a wo- ie exchange- a e sys em whe e he p incipal on bonds mus be acqui ed a he inancial exchange a e, e, bu he in e es income mus be epa ia ed a he ixed comme cial exchange a e, e, he e ec- i e a e o e u n on o eign bonds pe cei ed by domes ic weal h 3 While I am awa e o he a gumen ha domes ic bonds issued by he domes ic go e nmen a e no weal h (Ba o, 1974), I choose he e o ollow he o he adi ion. 4 Why a e he wo bonds conside ed impe ec subs i u es and why, i he e a e no ansac ions cos s, would anyone hold money? Weal h holde s would wan o hold bo h domes ic and o eign bonds because o exchange isks and hey would wan o hold money as well as sho - e m bonds, e en i he e we e no ansac ions cos s, i hey pe cei ed a de aul isk on bonds. 6 The a ionale o excluding income in a model ha assumes ins an aneous po olio adjus men can be ound in Allen, (1976), Hellwig (1975) and Allen- Kenen ( o hcoming). OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 48 Nancy Pe eg im Ma ion holde s is , which I shall call u.6 A change in he di e en ial be - ween he comme cial and inancial exchange a es can hus in luence capi al mo emen s di ec ly h ough a a e-o - e u n mo i e. The demand unc ions can be w i en as: (2) Bd = b ( , u) Wh (3) Ul = I ( , u) Wh (4) eF<* = ( , u) Wh W whe e u = — • The balance-shee cons ain o p i a e weal h holde s equi es ha he sum o hei demands o all asse s mus be equal o he weal h hey cu en ly hold. This cons ain means ha : b+l+j= 1 b + l + = 0 K + lu + = 0 I is assumed ha he h ee asse s a e g oss subs i u es, so ha desi ed holdings o a bond inc ease when he e u n on ha bond ises, while he desi ed holdings o he o he bond and o money decline: b > 0 , l < 0 u > 0 bu , lu < 0 I all pa ials a e non-ze o, i can be deduced ha each own pa ial mus be la ge in absolu e alue han ei he c oss pa ial: b > b > l whe e b , > l # 0 u> bu u> I lu whe e u, bu, lu 4= 0 Fu he mo e, wi h ins an aneous adjus men , he quan i ies demand- ed, Bd, Ld, Fd, a e equal o he amoun s ac ually held, Bh, Lh and Fh in (1). Fo his eason, any one o he demand equa ions is sa is ied when he o he wo a e sa is ied. 6 In he gene al case, he e ec i e a e o e u n on o eign bonds pe cei ed by domes ic esiden s would be: p?' (1 + a) — + whe e a is equal o he expec ed dep ecia ion in he ixed comme cial exchange a e and n is he expec ed dep ecia ion in he inancial a e. In his pape , i is assumed ha weal h holde s expec he comme cial a e o emain ixed {TZ= 0). I is also assumed ha he expec ed dep ecia ion o he inancial a e is he same o all weal h holde s and has a p obabili y dis ibu ion a ound mean ze o, so ha n — 0. In a mo e gene al model, expec a ions should be made explici . OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 Two-Tie Exchange Ra es and Mone a y Au onomy 49 The ma ke s o he h ee asse s a e assumed o be pe ec ly com- pe i i e and clea a all imes. The ma ke -clea ing equa ion o domes ic bonds is: (5) B — Bc — Bh = 0 whe e B is he ixed supply and Bc is he amoun held by he cen al bank. The ma ke -clea ing equa ion o domes ic money is: (6) L — Lh = 0 whe e L is he supply o money de e mined by he banking sys em. The ma ke -clea ing equa ion o o eign bonds is: (7) eF - eF* = 0 whe e F is he pe ec ly elas ic supply o o eign bonds a ailable o domes ic weal h holde s. (7) will be ue when (5) and (6) a e sa is ied. I should be s essed he e ha he omission o income om he asse demand unc ions has an impo an analy ical p ope y: i pe mi s he pa i ionabili y o he inancial ma ke s om he goods ma ke . I p o ides s ong jus i ica ion o s udying, in isola ion, he impac e - ec s o inancial dis u bances on he asse ma ke s. When income is excluded om he asse demand unc ions, he inancial sec o is un- a ec ed on impac by e en s in he goods ma ke . I one we e o con as he dynamics and long- un p ope ies o wo- ie and uni a y exchange a es in he ace o inancial dis u bances, che esul s would di e om he impac e ec s in pa because o eed- back e ec s om he goods ma ke . On impac , howe e , he e ec s o inancial dis u bances on he asse ma ke s a e he same whe he o no a goods ma ke is included. A sho - un analysis o jus he inan- cial ma ke s can be unde aken. Addi ionally, once he impac e ec o any inancial dis u bance on he domes ic in e es a e is de e mined, one can in e he change in ou pu , p o ided ha he change in he domes ic in e es a e is he dominan inancial dis u bance in he goods ma ke . The Banking Sec o * The banking sec o consis s o one cen al bank. The e a e no com- me cial banks. The liabili ies o he cen al bank a e equal o he s ock o money held by he p i a e sec o , Lh; i s asse s a e i s hold- ings o domes ic bonds, Bc, and he domes ic-cu ency alue o i s o eign-cu ency ese es, èR. The cen al bank balance shee is: 4 Zei sch i ii Wi scha s- und Sozialwissenscha en 1979/1/2 OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 50 Nancy Pe eg ini Ma ion (8) Lk = Bc - eR — Wc whe e Wc ep esen s he cen al bank's ne wo h; Wc changes o e lec capi al gains and losses esul ing om changes in he comme cial ex- change a e, by which he cen al bank is assumed o alue i s ese es. The cen al bank's holdings o domes ic bonds, Bc, is an exogenous policy ins umen . The in e es income o he cen al bank is Bc. Replacing L wi h (8) and Lh wi h (3), he ma ke -clea ing equa ion o domes ic money (6) can be ew i en as: (9) Be + eR - V/c - I ( , u) W* = 0 Replacing Bh wi h (2), he ma ke -clea ing equa ion o domes ic bonds (5) can be ew i en as: (10) B — Bc — b ( , u) Wh = 0 Sa ing Weal h can be al e ed in wo ways — by sa ing ou o cu en income and by capi al gains o losses due o changes in he inancial exchange a e. Following Allen-Kenen ( o hcoming), he o ali y o weal h ac- cumula ed h ough ime as a consequence o sa ing will be de ined as: T T (11) Whs = J Sd = J (i> + B>* + eFh) d o o whe e Lh, Bh and Fh ep esen ime a es o change. Subs i u ing (8) in o (11) and ecalling ha Bh = B - Bc yields: T T (12) W^ = Sd = (B + eR + eh) d o o Whs changes only g adually h ough ime. I is he e o e exogenous o he analysis o impac e ec s al hough impo an in he dynamics. To al weal h, a his o y o sa ing and o capi al gains and losses, can be w i en as: T (13) W7i = W/iS + J Fh e d o I s ime de i a i e is: (14) Wh = Whs + Fh e d The s ock o o al weal h can change ins an aneously since mo emen s in he inancial exchange a e b ing abou immedia e capi al gains o losses. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 Two-Tie Exchange Ra es and Mone a y Au onomy 51 Domes ic holdings o o eign bonds In his model, he small coun y canno accumula e o eign bonds ei he in he sho - un o o e ime. The cen al bank does no supply o eign cu ency o sa is y an excess demand o o eign bonds, so ha any excess demand me ely bids up he inancial exchange a e in he sho - un. The small coun y can accumula e o eign asse s ( ese es) o e ime by unning a cu en -accoun su plus. In ac , i he go e nmen bud- ge is balanced a all imes, which implies B = B, he only way he coun y can sa e is h ough a cu en -accoun su plus. Bu p i a e households canno use a cu en -accoun su plus o accumula e o eign bonds. They mus channel hei cu en -accoun ansac ions h ough he comme cial exchange ma ke and u n any ne p oceeds o e o he cen al bank in exchange o domes ic money.7 (The cen al bank, in u n, can use he p oceeds o acqui e ese es). I households now wan o acqui e o eign bonds, hey mus go h ough he inancial exchange ma ke . Doing so me ely bids up he inancial exchange a e. Thus he wo- ie exchange ma ke , as modeled abo e, p e en s households om accumula ing o eign bonds a any poin in ime o o e ime. The dynamic equa ion o he model can be exp essed as: (15) Whs = s = eR when he go e nmen budge is balanced and a wo- ie exchange- a e sys em is in e ec . The ma ke -clea ing equa ions o domes ic bonds and money (10) and (9) can be sol ed o changes in he domes ic in e es a e and he inancial exchange a e, gi en he exogenous a iable ', he policy- de e mined a iables Bc and e, and he his o y o household sa ing, V/hs. The s anda d wo- ie exchange- a e model, hence o h called Model I, is sol ed in Appendix I. In Appendix II, a pe mu a ion o he wo- ie exchange egime is p esen ed and sol ed (Model II). In ha pe mu- a ion, in e es income as well as all capi al accoun ansac ions a e channeled h ough he inancial exchange ma ke . As a esul , he e ec i e yield on domes ic esiden s' o eign bond holdings is equi a- len o a he han — . A change in he di e en ial be ween com- 7 Ins i u ionally, esiden s' ne o eign-exchange p oceeds may be held in a special non-in e es -bea ing accoun o be used solely o u u e pu chases o goods and se ices om he es o he wo ld. Fo simplici y, I igno e his op ion and assume ha all ne p oceeds mus be u ned o e o he cen al bank. 4* OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 52 Nancy Pe eg im Ma ion me cial and inancial exchange a es can no longe in luence capi al mo emen s di ec ly by a ec ing he a e o e u n. In addi ion, e- pa ia ion o in e es income canno al e ese e holdings o e ime. Finally, he mos in e es ing implica ion o his pe mu a ion is ha esiden s a e able — and indeed a e obliged — o accumula e o eign asse s o e ime using he in e es -income p oceeds ea ned om o eign holdings. As long as esiden s main ain some o eign asse s in hei po olios and ecei e a posi i e yield, in e es -income in lows o he inancial ma ke mus be ma ched by con inual capi al ou lows o e ime. The model canno con e ge on a s eady-s a e since he sys em canno each long- un s ock equilib ium in he asse ma ke s. In o de o compa e he s anda d wo- ie exchange sys em and i s pe mu a ion o mo e amilia exchange- a e egimes, he model is con- e ed o a uni a y lexible exchange a e and sol ed in Appendix III. I is hen con e ed o a uni a y ixed exchange a e and sol ed in Appendix IV. The signs o all impac e ec s con ained in all appendices a e dis- played below in Table I: Table I Table 1.1 Two-Tie Exchange Model (Model I) Table 1.2 Two-Tie Exchange Model (Model II) Dis u bance E ec 3 3 c Dis u bance E ec 3 3 c 3 Be — + dB* + 3 ' ? + 3 ? + 3 c ? + 3 c 0 0 Table 1.3 Table 1.4 Flexible Exchange Ha e Fixed Exchange Ra e Dis u bance E ec 3 3 c Dis u bance E ec 3 c 3 R 3BC — + 3 Be — — 3 7 + 3 ' + 3c 0 0 3c + Solu ion o Model I In a wo- ie exchange egime wi h in e es income epa ia ed a he comme cial exchange a e, an open-ma ke pu chase o bonds, 3 Bc OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 Two-Tie Exchange Ra es and Mone a y Au onomy 59 in e es a e. Since he subs i u ion e ec domina es he weal h e ec , he domes ic in e es a e will ise. This esul di e s om ha in low models which show ha wo- ie exchange a es o ally insula e he domes ic in e es a e om exoge- nous dis u bances in he o eign a e when domes ic and o eign bonds a e pe ec ly subs i u able.10 The di e en esul s he e should no be su p ising. The ac ha he small open economy canno insula e i sel comple ely i om ou side dis u bances is inhe en in he po olio-balance app oach o modeling he asse ma ke s. Diag amma ically, an inc ease in he o eign in e es a e can be shown as a igh wa d shi in he FF schedule. (See igu e 4). As a esul , weal h holde s swi ch hei demand om domes ic bonds and money o o eign bonds, pu ing upwa d p essu e on he in e es a e and upwa d p essu e on he inancial exchange a e: he excess sup- 10 See, o example, A gy-Po e (1972), p. 515. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 60 Nancy Pe eg ini Ma ion plies o domes ic bonds and money shi he BB cu e upwa ds and he LL cu e downwa ds. The p essu es s op only when he e ec i e e- u ns on bo h bonds a e equalized. The new equilib ium occu s a a poin like b in igu e 4, a a highe in e es a e and a dep ecia ed inancial exchange a e. As he inancial a e dep ecia es, weal h hol- de s expe ience capi al gains on hei o eign bond holdings so ha hey a e inclined o inc ease hei demands o domes ic bonds and money, pu ing downwa d p essu e on BB and some upwa d p essu e on LL. Bu again, hese shi s due o weal h e ec s a e mo e han o se by he shi s due o subs i u ion e ec s. Wi h pe ec subs i u abili y, an inc ease in he o eign in e es a e leads o an inc ease in he domes ic e u n on o eign bonds as well. Bu he e ec i e e u n on o eign bonds will now be lowe o do- mes ic esiden s han o o eigne s. A de alua ion o he comme cial exchange a e, like an inc ease in he o eign in e es a e, unambiguously inc eases he domes ic in e es a e, dep ecia es he inancial a e, and keeps he e ec i e a es o e u n on home and o eign bonds equalized o domes ic weal h hol- de s. A e he de alua ion, he e ec i e a e o e u n on o eign bonds is g ea e o domes ic esiden s han i is o o eigne s. Model II wi h Pe ec Subs i u abili y In Model II, one disco e s ha wi h pe ec subs i u abili y be ween domes ic and o eign bonds, an expansiona y mone a y policy dep e- cia es he inancial a e bu canno al e he domes ic in e es a e. Since e ec i e a es o e u n o bo h bonds mus emain equal a all imes, , he e ec i e e u n on domes ic bonds, canno di e ge om , he e ec i e e u n on o eign bonds. Diag amma ically, his s a e- men means ha he FF cu e is ho izon al a = ?'. No only a e he au ho i ies unable o al e he domes ic in e es a e h ough an open-ma ke ope a ion, bu hey a e unable o insula e he domes ic in e es a e, e en minimally, om ou side shocks, such as a change in he o eign in e es a e. By implica ion, a wo- ie ex- change egime segmen ed as in Model II does no g an in e es - a e au onomy when domes ic and o eign bonds a e pe ec subs i u es. Mo eo e , nei he a uni a y lexible exchange a e no a uni a y ixed exchange a e gi es any au onomy o e he domes ic in e es a e when domes ic and o eign bonds a e pe ec subs i u es. (In ac , he impac e ec s o Model II and he uni a y lexible exchange a e a e iden ical). OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 Two-Tie Exchange Ra es and Mone a y Au onomy 61 A wo- ie exchange ma ke which channels in e es income h ough he comme cial ma ke s ands ou as unique; i allows he au ho i ies o egula e ne capi al lows independen ly o he ela i e a es o e- u n a home and ab oad and hus allows he au ho i ies some sho - un in e es - a e au onomy, e en in he case o pe ec subs i u abili y be ween domes ic and o eign bonds. Appendix I Two-Tie Exchange Ma ke — Model I Impac E ec s Asse -Ma ke Equa ions: B — Bc — b ( , u) Wh = 0 Be + eR - Wc - I ( , u) Wh = 0 (1) (2) whe e T Wh = (B - Be) + (Be + eR- Wc) + eFh = Whs + Fh e d u = — ' e - b wh bu wh - bFh d - i wh iu wh - IFh de (a) (b) Di e en ia ed: 3 Be + Wh bu 3 + Wh bu 3 e + b 3 R -3 Be + Wh lud ' + Wh lu 'de - (1 - 1)3 R De e minan = D1 = - b Wh [lu ' Wh - IFh] + l Wh [bu ' Wh - bFh] > 0 T ace = - b Wh + lu ' Wh - IFh < 0 D 3 = 3 Be [lu Wh + bu ' Wh - IFh _ ^ph] + $ ' [Wh Fh (lu b - bu I)] + 3 e[ whFh (lub -bul)] + dR [- bFh + bu Wh (1 - I) + lu 'Whb] D1-de = dBc [(b + l ) Wh] + d [(l bu - lu b ) Wh Wh] + 3 e [(l bu - lu b ) Wh Wh '] + 3 R [(1 - Z) b Wh + l b W*] No e: 3 Whs = ¿3 R OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 62 Nancy Pe eg ini Ma ion Appendix II Two-Tie Exchange Ma ke — Model II Asse -Ma ke Equa ions: (1) (2) whe e (a) <b> Di e en ia ed: B - Be -b( , u) Wh = 0 Bc + èR-Wc -l ( , u) Wh = 0 T Wh = W^ + Fhèd o u = ' b Wh - bFh 3 l Wh - IFh 3 e dB* + buWhd ' + bdR + bdFh - 3 BC + lu Wh 3 + (- 1 + l) 3 R + l 3 Fh De e minan = D2 = (b l - l b) Fh W* > 0 T ace = -b Wh- IF* < 0 D2d = dBc[-{b + l) Fh] + 3 [(blM - lbu) Fh Wh] + 3 R[- bFh] + 3 Fh [0] D2 . 3 e = 3 Bc [(b + l ) Wh] + 3 [(Z bu - bT lu) Wh Wh] + 3 R [ + b) b Wh + bl Wh] + 3 Fh [(l b - b l) W No e: dWhs = èdR + ed Fh Appendix III Uni a y Flexible Exchange Ra e Asse -Ma ke Equa ions (1) b - Be -b ( , u) Wh = 0 (2) Bc + eR — Wc — I ( , u)Wh = 0 whe e (a) Wh = (B - Be) + (Bc + eR - Wc) + eFh (b) u = OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 Two-Tie Exchange Ra es and Mone a y Au onomy Di e en ia ed: b Wä - bFÄ 3 3 B^ + bu W* 3 ' + b 3 W* l W* - IF* 3 e - 3 R + lM W* 3 + I 3 W*» De e minan = D3 = (b I - l b) Fh Wh > 0 T ace = - bT W* - IFh < o D3 • 3 = 3 Be [- (b + i) F><] + 3 ' [(blM - lbM) F^ W*] + 3 [0] D3 • 3 c = 3 Be l(b + lT) W'<] + 3 [(l bu - b lu) W Wh] + 3 W e [(- b I + l b) W*>] No e: 3 Whs = ed Fh Appendix IV Uni a y Fixed Exchange Ra e Asse -Ma ke Equa ions (1) B — Bc — b ( , u) W* = 0 (2) Bc + eR — Wc — I ( , u) W* = 0 whe e (a) Wh = (B - Be) + (Bc + eR - W*) + eF>* (b) u = Di e en ia ed: 3 Be + bu W* 3 ' + b 3 W^ + bFh 3 - 3 Be + lu w* 3 ' + 3 W*« + IF* 3 < De e minan = D4 = b Wh > 0 T ace = - b W* - 1 < 0 D4 • 3 = 3 Bo [- 1] + 3 [ - bu Wh] + 3 e [- bF*] + 3 W*» [- b] D4 • e 3 R = 3 Be [- (b + l ) W*] + 3 [(b lu - bM l ) W* W*] + 3 e [(b I - l b) F^ W*] + [(b I - l b) W&] b W* 0 •l W* -1 3 — êd R No e: 3 W^ = ê 3 R OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44 64 Nancy Pe eg im Ma ion Re e ences Allen, P. 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(1976), The Theo y o Flexible Exchange Ra e Regimes and Mac oeconomic Policy, Scandina ian Jou nal o Economics, Vol. 78, No. 2. Fleming, J. M. (1971), Dual Exchange Ra es o Cu en and Capi al T ans- ac ions: A Theo e ical Examina ion, in: Essays in In e na ional Economics, London: Allan and Unwin. Gi on, L. and D. W. Hende son (1974), Cen al Bank Ope a ions in Fo eign and Domes ic Asse s Unde Fixed and Flexible Exchange Ra es, Boa d o Go e no s, unpublished. Hellwig, M. F. (1975), The Demand o Money and Bonds in Con inuous Time Models — A No e on a Pape by May, Jou nal o Economic Theo y, Decembe . Lanyi, A. (1975), Sepa a e Exchange Ma ke s o Capi al and Cu en T ans- ac ions, IMF S a Pape s, Vol. 22, No. 3. Salin, P. (1971), Un Double Ma ché des Changes es -il Jus i ié?, Re ue d'Éco- nomie Poli ique, Vol. 81, No. 6. Swoboda, A. K. (1974), The Dual Exchange Ra e Sys em and Mone a y In- dependence, in: R. Alibe (Ed.), Na ional Mone a y Policies and he In e - na ional Financial Sys em, Chicago: Uni e si y P ess. Tobin, J. (1969), A Gene al Equilib ium App oach o Mone a y Theo y, Jou - nal o Money, C edi and Banking, Feb ua y. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.99.1-2.45 | Gene a ed on 2023-04-04 11:56:44