Economic Papers Series

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1 Pape No. ( Ecooic Pape Seie Macoecooic Model of Public Deb Sevici Capaciy ad Deb Maaee Deb i o a ae of coce a lo a i i aaeable ad uaiable. Deb aaee i he poce by which he ovee acquie ad ue he deb effecively ad efficiely. Deb i aaeable a lo a he co of acquii deb i eaoably low ad deb obaied i ued efficiely i uch a way ha i help owh ad efficie allocaio of eouce i he lo u. Deb i ued efficiely if he aio of deb evice o oal eveue ad exeal deb evice o expo fall o eai coa. The udelyi aupio i ha he pojec fo which boowed oey i ued would eeae ufficie oupu ad expo fo deb epaye. D. Mohaad Ihfaq Lead Ecooi, Depae of Fiace, Govee of Dubai, UAE.ihfaq@dof.dubai.ov.ae 7/9/2 Pape No. (4

2 7/9/2 Macoecooic Model of Public Deb Sevici Capaciy ad Deb Maaee I: Ioducio Deb i o a ae of coce a lo a i i aaeable ad uaiable. Deb aaee i he poce by which he ovee acquie ad ue he deb effecively ad efficiely. Deb i aaeable a lo a he co of acquii deb i eaoably low ad deb obaied i ued efficiely i uch a way ha i help owh ad efficie allocaio of eouce i he lo u. Deb i ued efficiely if he aio of deb evice o oal eveue ad exeal deb evice o expo fall o eai coa. The udelyi aupio i ha he pojec fo which boowed oey i ued would eeae ufficie oupu ad expo fo deb epaye. Public deb aaee ypically ivolve aciviie ai fo he foulaio of a deb/boowi aey. Thi aey i eeally baed o couy deb iuaio, fiacial ae iuaio, eed of ew fiace, ue of boowed oey, eei of deb evice obliaio o ie ad aieace of ifoaio ye ad daabae. Thee aciviie eed o be oveed ude a explici ad clea leal adae ad oaized ude a faewo whee ole ad epoibiliie of he aecie ivolved ae well pecified. The objecive of hi udy i o pee oe ehod o evaluae he deb evici capaciy of a couy. I hi coex, a effo i ade o pee a acoecooic faewo fo deb eiee of a couy. The udy i oaized a follow. I ecio II, we pee he ehod o evaluae he deb evici capaciy of he couy. Secio III pee he deb eiee iple odel wih o evice paye. I ecio IV, we pee he odel of deb eiee i cae of iee paye. Secio V pee he uay ad cocluio. Ofe efeed o a he fo, iddle ad bac office fucio; fo oe deail ee Guidelie fo Public Deb Maaee, Wold Ba ad Ieaioal Moeay Fud (Febuay 2.

3 7/9/2 II: Mehod o Evaluae he Deb-Sevici Capaciy of a Couy Hih deb lead eeally o hih deb evice liabiliy. Howeve, he eveiy of he deb evice liabiliy of a couy deped o he elaiohip of i deb o i GDP ad o he level of deb i elaio o i deb evice obliaio. A uch, he abolue volue of deb of a couy i o pehap a uch a ae of coce a he exe of deb evice liabiliy. The level of deb evice liabiliy of a couy ay be hih o low depedi o i level of ecooic develope. The icidece of deb evice liabiliy of a boowi couy i eeally efleced fo deb idicao expeed a aio of deb o GNP (Deb-GNP, deb o deb-evice liabiliy (Deb-Sevice, deb-evice o foei exchae eai (Deb-FEE, ec. The deb evice paye ay be lae o all depedi o he value of uch deb idicao ad he codiio ude which loa ae ouh ad eceived. A uch, he value of hee aio ad heeby he eveiy of deb bude eep chai i epoe o chae i he e of boowi ad oveall ecooic codiio of a couy. 2 Deb evice liabiliy i aeed by ehod of peceae. Biefly, deb ad deb-evice chae ae expeed a peceae of aual value, fo exaple, of GNP, expo, foei exchae eai, ipo ec i diffee way. The ehodoloy of aei he lo-u deb-evici capaciy of a couy i baed o he copaio of co ad beefi of public deb ued i he poce of ecooic develope. Thee ae wo ehod of deeii he deb-evice capaciy of a couy. Fi ehod cooly ued o copae co ad beefi of public deb i he ciical iee ae (CIR appoach. The ecod appoach i he ideificaio of he lii value of he Deb-GDP aio. The CIR idicae he level of iee ae ha ae he owh ae of public deb equal o he owh ae of GDP. I i alo he axiu iee ae ha ca be paid o loa while aiaii a he ae ie a deiable deb-gdp aio. I piciple, if he aveae iee ae o loa exceed he CIR, 2 Avaovic e al. (964, Alibe (98, Nowzad & Willia (98 ad Lee (983 vey well hihlihed he deiabiliy ad appopiaee of uch idicao. 2

4 7/9/2 deb will iceae fae ha GDP leadi heeby o a eve-iceai deb bude. Alebaically, he CIR i calculaed a: CIR ( whee, i owh ae of GDP, aial avi ae, aveae avi ae a he beii of he peiod, ad i iceeal capial-oupu aio. Fo he pupoe of calculaio, he value of CIR, ad ca be calculaed fo diffee ie peiod o ow how he deb-evici capaciy of a couy ay have chaed. The opial boowi capaciy ca alo be foud cocepually by ui a iple odel. 3 Techically, opial exeal boowi i a fucio of i co ad beefi. The e a which public deb ca be obaied ae cucial i deeii he co-beefi aio. The objecive i o obai loa a uch a iee ae a ede deb/gdp aio able ove ie. A able deb/gdp aio ay deped o a paicula elaiohip ao eleva vaiable. The equaio eioed below coec he equied vaiable i a elaiohip, which deeie he coveece of exeal deb o a able aio i e of GDP. 4 D (2 i Whee, D,,, ad i deoe public deb, Go Doeic Poduc GDP, iceeal capial oupu aio, owh ae of GDP, aial avi ae ad iee ae o public deb. The equaio clealy how ha deb-gdp aio i a iceai fucio of he iee ae o public deb. To deeie he effec of a chae i GDP owh ae o he deb-gdp aio, coide he followi deivaive: 3 Avaovi (964, Soloo (977, Nowzad (98 ad Lee (983 hihlihed he ue of iple odel i hei udie. 4 Fo deail ee Lee (983. 3

5 7/9/2 D i i i 2 i 2 i 2 i if i i ad i 2 if i I follow ha deb-gdp aio will iceae o deceae wih he owh ae of GDP depedi o whehe he iee ae o public deb i le ha o eae ha he aio of avi ae o iceeal capial oupu aio. The value of diffee deb idicao ad CIR baically povide a fuue uidelie fo eoiaio of deb eucui o fuue loa eoiaio. Iep aaee of deb ad eulaly ii deb o GDP ae liely o iduce chae i he ai acoecooic idicao lie cowdi ou of ivee, fical iabiliy, iflaioay peue ad exchae ae flucuaio ec. Fuhe, ii deb bude ha alo ay udeiable iplicaio fo he couy. Thee i, heefoe, a eed o ae eiou aep a fidi a uaiable idieou oluio of he deb. Sice deb becoe a coce whe i coe aaeable ad uaiable lii, policy ae ae ueed o foulae a poce by which ovee i foced o ue loa effecively. Deb i ued efficiely a lo a he level of exeal deb-evice ad he aio of deb evice o oal eveue ae eihe falli o a lea eaii coa. Public deb ca be uaiable a lo he pojec fiaced wih boowed oey eeae ufficie oupu ad expo eai fo deb epaye. Fuhe, i i equied o aiai capial oupu aio ad hihe aial avi ae o avoid uuaiable ae of iee o boowed oey. 4

6 7/9/2 III: Macoecooic Model of Deb Reducio Thi ecio pee a acoecooic odel of deb eiee baed o Haod-Doa wo-ap odel of ecooic owh. We exed Haod-Doa owh odel o allow he ole of public deb i he poce of ecooic owh. We ioduce a eial ie i he odel a a policy deciio i ode o aalyze he ade-off bewee vaiou objecive of develope plai uch a he ade-off bewee he deie o becoe idepede of fuue boowi ad o achieve a hih owh ae of GDP. Oly afe a aee of hi ade-off, i ca be decided o udeae he a ad policie coie wih he oveall develope objecive. Peuably, he idepedece fo fuue boowi doe o ea ha he couy will be fee fo all id of deb liabiliie uch a foei pivae ivee, fud fo aoizaio ad iee paye o loa. All ha i ea by hi idepedece fo boowi i ha afe oe pecific ie hee hould be o iceae i deb liabiliy ad he couy hould be fee fo he eed of fuhe boowi. By ha ie doeic eouce hould exceed he ivee equied o eue oupu owh equivale a lea o he evice paye due fo all fo of public deb which wee obaied i he pa. To bei wih, we dicu oe eeal iue eleva o he queio of idepedece fo fuue boowi ad oe quaiaive aee of i iplicaio. The aalyi i he exeded o coide he iplicaio of public deb o he deb-evice obliaio, which ae aoizaio ad iee paye o boowed loa. 5

7 7/9/2 IV: The Siple Model wih No Sevice Paye Naioal icoe ideiy how ha a ay poi of ie, he oal aou of eouce available o a couy which i ca coue ad e aide fo (o ivee o ue fo expo i equal o he couy o aioal poduc plu i ipo. I follow fo aioal icoe ideiy ha a ay ie he diffeece bewee a couy o ivee ad o doeic avi i eceaily equal o he diffeece bewee i ipo ad expo. Theefoe a couy ca ive oe ha i ca ave, ad hu achieve a owh ae hihe ha ha deeied by i doeic avi ae, if i ca ipo oe ha i expo by he ae aou. Thi will aually deped upo how i fiace he ipo uplu. Whehe he couy elie o pivae e capial iflow o boow publicly, a e boowi eai he oly offei ie i he balace of paye o fiace he defici. Thu, he ole of public deb i a owi ecooy i quie obviou. A ive aou of public deb ca fiace a equal aou of ipo-uplu of he capial eceivi couy ad alo allow i ivee o exceed i doeic avi by he ae aou, ha i: I S M X F ( Whee I,S,M,,X ad F deoe o ivee, o doeic avi, ipo, expo ad e fudi (boowi, epecively. If o iceeal capial-oupu aio i deoed by, ad owh ae of GDP by, he: I (2 Whee i GNP a ie. The ae of avi i expeced o ie ove ie. Le be he aveae ae of avi a he iiial peiod, ha i peiod zeo, ad he iceeal avi ae bewee peiod zeo ad. We aue ha he avi fucio i of he followi fo. S (3 Subiui fo (2 ad (3, we ca wie ( a follow: 6

8 7/9/2 F (4 F (5 Equaio (5 ive u a uique elaiohip bewee he owh ae of GDP,, ad he e boowi a a popoio o GDP i.e F/. Give he iceeal capial-oupu aio, aial ae of avi, aveae avi ae a he iiial peiod ad he iiial ad he cue level of GDP; we ca obai eihe he e boowi equied by a ae ae of owh, o he ae of owh ha ca be achieved wih a ive aou of boowi. Sice / F >, a lae boowi ca achieve a hihe ae of GDP owh, eepi all ohe faco coa. The above foulaio ca alo be ued o eaue he capaciy of he couy o abob boowed fud. The popoiio o which he above aue i.e. he ae of owh ca be aied by iceai he ae of ivee fiaced by boowi i baed, iplicily aue ha capial, o labo, i he ai boleec fo aii he ae of owh. 5 Thi way of looi a he elaiohip bewee boowed oey ad he ae of owh of GDP iplie ha evey yea he ipo uplu oehow e adjued o he e iflow of public deb. Toal ipo adju auoaically o he wo exoeou vaiable i.e. X ad F ad he owh ae eiely deped o how fa F ca eliiae he boleec of he low ae of doeic avi. Bu ipo ay o be o feely adjuable i a udedeveloped couy ad hu a oe copeheive odel will ieviably coai addiioal coai. Fo 5 I cae of a udedeveloped ecooy, hi aupio ay be quie uealiic. Eve if hee i a uliied upply of capial ad labo, he ae of owh ay have a uppe boud deeied by he upply of copleeay faco lie illed labo, aae, eepeeu, ec. I ha cae hee i a opiu ae of eceip of boowed capial which i equal o he exce of ae of ivee, equied o ealize he axiu poible owh ae deeied by he ohe o-capial faco, ove he ae of avi. Thi exce equiee baically will deeie he abopive capaciy fo boowed fud. A lae aou of deb beyod he abopive capaciy of a couy will fail o aie he ae of owh (Haod,

9 7/9/2 ha pupoe, we aue ha hee i a iid elaiohip bewee he level of ipo equied ad he level of GDP. The aupio ha hee i a iiu ipo equiee coepodi o a level of GDP ca be iepeed i wo way: Fi, he ipo equiee i i fixed popoio o coupio, o ivee ad expo, which, a a fi appoxiaio ay be eaded a he ae. Such a aupio ay be queioable fo a udedeveloped ecooy a a ealy ae of develope whee ipo o coupio aio ay be uch hihe due o he ipo of oe baic eceiie fo uppoi i ubiece level of coupio. The cae ay be iila wih expo if hey ae o copleely ive exoeouly. Bu eve if hee exi coupio ad expo bae wih eliible iiu ipo equiee, i i quie poible ha o ivee equied fo aiaii ha level of coupio ad expo ove ie ay eed oe iiu level of ipo. The iiu level of ipo i equied iply becaue ceai ih ype of equipe, achiey, ec. ae o doeically poduced. I he cae whee oly a ive aou of loa i available o fiace he ap bewee avi ad ivee, he fudi ay o achieve he ae of owh ae of GDP a deeied by he capial oupu aio. Thi i becaue ipo ay iceae due o iceae i icoe ad hi iceae i ipo ay exceed he expo by oe ha he ive aou of boowed fud. I eihe cae, he codiio fo a ive aou of deb o achieve a ae of GDP owh deeied by he aou of avi- ivee ap i ca fiace, i ha M X+F, wih M accoui fo he iiu level of ipo. If hi codiio i o fulfilled, hee will be wo opeaive coai o he owh level of GDP, aely he eouce coai I-S F 8

10 7/9/2 ad he balace of paye coai M-X F. The oluio of he ye will deped upo which of he wo coai i oe eicive, i.e. whicheve ive he lowe oluio. 6 I i alo adoped ha hi uppe boud o GDP owh ae, deeied by he ipo coai becoe le ad le eicive wih ie a ii GDP i liely o be accopaied by iceai availabiliy of doeically poduced capial ood. Thu, i he lo u, he avi-ivee ap ha will deeie he effec of boowi capial o he owh ae of GDP, alhouh i he ealy phae of develope he ipo coai ay be oe ipoa. The followi aalyi i aily focued o he deb iflow filli he avi-ivee ap. Alhouh, hi ede he aalyi paial i aue, bu i ay be ill woh while aily fo wo eao: (a Eve if hee wee o ipo coai, he effec of public deb o owh ae will deped o how fa i ovecoe he avi coai; ad (b I ay be aiaied ha i he lo u i i he avi coai ha i oe eicive ha he ipo coai. Give he ucue of ou odel i i poible o calculae he ube of peiod afe which a couy will eeae eouh doeic avi o fiace he ivee equied o aai a ive GDP owh ae wihou depedi o public boowi. Thi i deived fo equaio (4 epoduced a follow: F (6 I he h yea whe F =, he equaio (6 ay be ewie a: Sei F = i he eial peiod ad e-aai (6, we obai: 6 Cheey ad Buo (962 ioduced a vaia of he fi id of ipo eicio eioed above ad eiaed ipo equiee fo he oluio of a ipu-oupu odel ude oe ic aupio. They obeved ha he ipo boleec a lowe level of GNP i oe eicive ha he avi boleec. 9

11 7/9/2 (7 Sice, we ca fuhe wie hi equaio a: (8 Equaio (8 pei he deeiaio of peiod ( o e idepedece fo public boowi wih a ive ae owh ae of GDP. 7 I i obviou ha he eeial codiio fo a couy o becoe idepede fo public deb a a fuue dae i ha., ha i, he aial ae of avi hould exceed he equied ae of ivee. Fuhe, he value of ( will be alle, i.e. he yea of elfufficiecy will be cloe, he lae he diffeece bewee he aial ae of avi ad he equied ivee ad he hihe he value of he iiial ae of avi (. Aui ha > ad >, i u be ephaized ha Equaio (4, (5 ad (8 efe all o he cae of public deb ai place puely i he fo of iee fee boowi. No iee paye obliaio i aached o he, ad afe he h yea, ha i, whe he yea of idepedece fo public deb i eached, he couy doeic avi will exceed i equied ivee ae. I ha cae, if he ae ae of owh i aiaied, he couy will be able o led oey iead of boowi fo diffee ouce. Ohewie he couy ae of owh will have o iceae evey yea o ha he ae of ivee 7 Thi aupio will be elaxed i Secio IV. Fo Equaio (7 we ca alo calculae he ube ( of yea eeded fo iiu-ipo equiee o be fully fiaced by he couy expo. The M = X o.. = X Aui a coa ae of owh ove ie i GDP ad expo, we e.. ( + = X ( + e (+ / (+e = [ /.] X / ; fo which he value of ca be obaied. Thi eed o be equal o he obaied fo equaio (8.

12 7/9/2 equied o achieve hihe ae of owh i equal o he iceai doeic avi. The odel he will loo lie a iple Haod-Doa ye. I S (9 Subiui fo he avi ad ivee fucio fo ( ad (2 ad e-aai, we obai: ( A ie pae, hi iceai ae of owh will appoach a he expeio will appoach owad zeo ove ie. To illuae how hi ehod ca be applied i pacice, we aue ha if couy eed o e idepedece fo boowi a oe pecific ie i fuue, ay afe 5 yea bewee 29- ad , i.e. o boowi aid will be equied by Hee we coceae oly o avi-ivee ap, aui iplicily ha ipo, expo ad ohe eleva vaiable e oehow o ohe coecly balaced. 9 Thu, if avi- ivee ap i eliiaed by he yea , he i i poible ha couy ay, houh o eceaily, will becoe idepede of boowi by ha ie. The ohe aupio of hi execie i ha he avi-ivee ap i coveed by foei aiace coi i he fo of a oly wih o epaye obliaio. Thi i obviouly uealiic, bu i i juified becaue hi ive he iiu ha will be equied fo aaii idepedece fo deb i fifee yea. 8 Thi execie i pefoed oly fo he ae of illuaio. We eely y o fid ou wha ae he coie value of diffee aiude if hi clai i boe ou i pacice. 9 I he followi aalyi, we icopoae ohe ap a well.

13 7/9/2 The followi Table ive o aui GDP owh of aoud 7 pece pe au, he coie value of o aial capial-oupu aio ad he aial ae of avi, which will eable he couy o becoe elf-uppoi afe fifee yea (= yea of idepedece fo foei aid=5. TABLE Diffee Value of Maial Rae of Savi ad Maial Capial-Oupu Raio o e idepedece i 5 yea wih ive = 7 % ad aveae avi ae =%. K S 2.5% 27.5% 32.4% 37.9% To e idepedece fo deb i 5 yea, able ive diffee value of he aial ae of avi ad aial capial-oupu aio, if he expeced 7 pece ae of GDP owh ad aveae avi ae of % i ae a he ae owh ae. Thi able how ha fo he couy o becoe idepede by 25 fo deb, ad o achieve he ae of owh of abou 7 pece would equie a low a aial capial oupu aio a 2.5 ad a iceeal avi ae of abou 22 pece. All hi ee o be oo abiiou, a he available epiical evidece would ue ha a aial capial oupu aio of 2.5 i oo low o a aial ae of avi of 22 pece i oo hih. I eeal, he fiue of he able idicae he aou of effo i e of aii he ae of avi o of poduciviy of ivee ivolved i ay aep o achieve idepedece fo boowi a a ealy dae. Ui foula [+] = ( / - -. which ca be wie a = [. ( + - -] /[+] - We ca calculae aial ae of avi fo diffee owh ae ad diffee capial-oupu aio ive aveae avi ae ad ube of yea o e idepedece fo deb. Siilaly we ca calculae he equied capial-oupu aio fo ive aial, aveae avi ae ad GDP owh ae. Thi aalyi i oe valid if we icopoae he aoizaio peiod ad deb-evice obliaio i ou aalyi. We coplee hi aalyi i he followi ex whee we icopoae aoizaio ad deb-evice obliaio. 2

14 7/9/2 We ca ae ue of Equaio (9 ad fid he yea of idepedece fo iee fee loa ai io accou diffee value of GDP owh ae ad aial avi ae. Thi eiiviy aalyi i exeded o icopoae diffee value of capial oupu aio a well. The eul of ou execie ae peeed i Table 2, 3 ad 4. The eul how ha he ube of yea equied o achieve uch idepedece wih a ipulaed ae of owh i hihly eiive o vaiaio i aial capial-oupu aio ad aial ae of avi. The aalyi how ha he educio i he yea of depedece i oe epoive o a deceae i ha o a iceae i he value of, i.e. he ye i oe eiive o vaiaio i iceeal capia-oupu aio ( ha i iceeal avi ae(. If ie by 2 pece fo 2.5 o 3., he value of u ie by oe ha 25 pece i.e. fo 2.5 pece o 27 pece o achieve idepedece i he ive fifee yea. Table 2 ad able 3 how he eul obaied by ui diffee value of capialoupu aio, aial avi ae, GDP owh ae. We ue aveae avi ae a pece, i able 3, i ode o fid he vaiaio i he peiod o e idepedece fo boowi whe aveae avi ae i low. Table 2 Diffee Value of he ea of Idepedece fo Foei Boowi fo Diffee Value of GDP Gowh Rae ad Maial Rae of Savi (ive =2.5,3 & 3.5 ad aveae avi ae=2% K=2.5 K=3 K= Noe: Bla cell i he able how ha he eceay codiio. o e idepedece fo foei boowi i o fulfilled. 3

15 7/9/2 Table 3 Diffee Value of he ea of Idepedece fo Foei Boowi fo Diffee Value of GDP Gowh Rae ad Maial Rae of Savi (ive =2.5,3 & 3.5 ad aveae avi ae=% K=2.5 K=3 K= Noe: Bla cell i he able how ha he eceay codiio. o e idepedece fo foei boowi i o fulfilled. The eul how elaive eiiviy of he ye o vaiaio i he aial capial oupu aio ad aial avi ae oce we aue a ive level of GDP owh ae ad iiial level of doeic avi ae. Thi i of oe iee i elaio o he queio: how uch addiioal effo i equied i he fo of aii he aial ae of avi if he aial capial- oupu aio u ou o be hihe ha expeced o ha he ae yea of idepedece i acually ealized. O he bai of ou eul i able 2 ad able 3, we ca ay if he ube of yea o each idepedece fo deb (wihou iee paye i a ive objecive, ad if he aial capial-oupu aio exceed he pojeced value by x pece, he he aial ae of avi u be aied ove i pojeced value by oe ha x pece o ha he ive objecive i poible o ealize. Maial capial-oupu aio i a echoloical vaiable which i epoive o policy vaiaio. 4

16 7/9/2 5 We ca pove hi clai aheaically a: Coidei Equaio (8:, We ca fuhe e-wie a: c. l l ( whee, c = lo ( +, a coa fo a ive ae of owh. Sice,, ad ae uually idepede, ai paial deivaive wih epec o, we wie c. c.. (2 Sice, by aupio, hi how ha a ie i will educe (, he ube of yea ae o each idepedece. Siilaly, c. (3 which how ha a ie i will aie aai aui ha (. I ode ha he effec of a ie i i copeaed by a ie i o, we e d d (4 Subiui (2 ad (3 io (4, we obai: d c d c... d d. > ice Thi pove he popoiio ha ay iceae i will have o be copeaed by a popoioally lae iceae i, o ha he ae of he yea of idepedece i ealized.

17 7/9/2 IV: The Model wih Iee Paye Uil ow, i ou aalyi, o efeece ha bee ade o he poble of iee paye o boowi. Ule boowi flow puely i he fo of iee fee loa, fud will have o be paed evey yea fo iee paye i addiio o ad aoizaio paye. So hee will be a aual dai equal o he paye of iee ad aoizaio fo he couy doeic avi. Thi dai i doeic avi ha o be explicily ae io accou i he equaio of boowi equiee. The exac ie pofile of uch epaye deped upo he aaee fo aoizaio ad iee paye fo diffee id of loa. If boh iee ad aoizaio ae chaed o he e deb ouadi he loa ae o copleely liquidaed bu he uliquidaed balace of each loa becoe alle ad alle evey yea. Aleaively iee ay be chaed o he e deb ouadi, while he yealy aoizaio i fixed i equal ialle of he oiial value of each loa. e aohe poibiliy i o fix equal ialle ehod wheeby aoizaio ad iee o each loa ae paid off i a eie of equal ialle. Thee ay be eveal ohe way of chai iee ad aoizaio o diffee id of loa ubjec o diffee ehod of chai iee ad aoizaio ae i ay paicula yea. Quie ofe, oe id of ace peiod i aached o official loa o ha he paye of iee ad/o aoizaio do o a ill oe yea afe he loa ae aed. We fuhe aue ha all loa ae ive fo a peiod of T yea ad he ae of iee oveie i ae fo all loa. Howeve, he eiaio of deb equiee i hi cae i quie coplicaed. We coide explicily he fac ha afe evey (T+j yea, he jh yea loa i copleely liquidaed ad o oe epaye obliaio i ivolved fo i. I cae of public deb evici equiee, he elaiohip bewee ivee-avi ap ad he iflow of foei boowi, a ive by equaio (, eed o be eealized. 6

18 7/9/2 Deoi he oc of public deb a he ed of peiod by D ad he ae of iee o public deb by, he ie pah of e foei boowi ca be wie a follow. F D I S (5 I ode o obai a paaeeized oluio fo e boowi, we aue ha he oc of deb i he iiial peiod (peiod i zeo, he ae of iee i coa ad he ivee ad avi fucio ae ive by equaio (2 ad (3 epecively. Ude hee aupio equaio (5 ca be olved fo he equilibiu value of he public deb boowi. I i how i Appedix ha uch a oluio i ive by: Fo ( ( ( F (6 Fo ( ( F (7 The above equaio ca be ued o calculae he ube of yea ha ae equied o achieve idepedece fo boowi. Le he yea whe boowi becoe zeo be deoed by. The coidei fi he oe eeal cae of, ha i equaio (6, he codiio ha F ca be olved a follow. ( ( (8 Thi equaio ca be eaaed o olve fo a follow. 7

19 7/9/2 8 (9 O (2 Tai aual lo o boh ide ad olvi fo yield: lo lo (2 lo lo (22 The above equaio olve he ube of yea by which boowi becoe zeo, i e of all he ohe paaee of he ye. I ode o deeie whehe uch a codiio will exi i a paicula iuaio, we coide he hee poibiliie: >, < ad = oe by oe.

20 7/9/2 9 CASE A: R > G Whe >, we hall have lo. Theefoe fo a eaiful oluio fo (ha i >, he ueao i equaio (6.22 u alo be poiive ad hece we u have ( (23 O. (24 Thu i follow ha wih >, a couy ca aai idepedece fo boowi (i boowi becoe zeo i a fiie ie peiod if: ( (25 CASE B: R < G Wih < we have lo. Theefoe fo >, he ueao i equaio (22 u be eaive ad hece we u have

21 7/9/2 2 (26 O (27 I follow ha wih <, a couy ca aai idepedece fo boowi i a fiie ie peiod if: (28 CASE C: R = G I he bodelie cae = he oluio (6.8 i opeaive ad he codiio ha F ca be olved a follow. ( ( (29 Fuhe iplifyi ad eaai, we ed up wih he codiio: (3 To illuae he effec of ioduci epaye obliaio io ou odel, we calculae he yea of idepedece (epaye peiod of loa wih diffee ipulaed ae of owh

22 7/9/2 ad uifo ae of evice paye o he aupio of o ouadi deb a he iiial peiod ad he value of he aial ae of avi equal o 5 pece, he iiial aveae avi ae equal o pece, ad he aial capial-oupu aio equal o 3.5 ad 3. Ui equaio (5 ad (22, he yea of idepedece whe F= ca be calculaed. The Table 4 how ha he ube of yea o e idepedece fo public deb iceae a owh ae ad evice paye ae iceae. Fo exaple wih low owh ae of 3 pece ad evice paye of ju 3 pece, he yea o e idepedece i alo 4 oh. Howeve hihe owh ae of aoud 6 pece ad evice paye of 6 pece equie alo yea o e idepedece fo deb. Table 4 Diffee Value of Repaye Tie of Exeal Deb fo Diffee Value of ad (ive capial-oupu aio= 3.5; aial avi ae = 5 % ad aveae avi ae=% a Thee eul eify ou peviou aalyi of deb paye capaciy ha if we eed o pay a iee ae of hihe ha ciical iee ae he he deb i o uaiable. Table 5 i a exeio of he peviou able 4 wih he chae i capial oupu aio fo 3.5 o 3. 2

23 7/9/2 Table 5 Diffee Value of Repaye Tie of Exeal Deb fo Diffee Value of ad (ive capial-oupu aio= 3; aial avi ae = 5 % ad aveae avi ae=% The eul i Table 5 ad able 6 how ha wih lowe capial-oupu aio, he ube of yea o e idepedece iceae ad capial-oupu aio i a ipoa deeia of ei idepedece fo public deb. Wih hih owh ae ad hih evice paye, he ube of yea o e idepedece fo deb aid iceae ive capial-oupu aio, aial ad aveae avi ae fo diffee value of GDP owh ae ad evice paye aio. The Table 4 how he elaive eiiviy of he ye o vaiaio i he aial capial oupu aio. The elaive eiiviy of he ye o vaiaio i he abiiou owh ae wih hih evice paye i alo foud ui oe hihe owh ae wih hih evice paye ad eul ae how i Table 6 below. Table 6 Diffee Value of Repaye Tie of Exeal Deb fo Diffee Value of ad (ive capial-oupu aio= 3; aial avi ae = 25 % ad aveae avi ae=%

24 7/9/2 Nevehele hi execie clealy how he iplicaio of havi oe epaye obliaio aociaed wih public deb of a couy. If hee wee o epaye obliaio i he iiial peiod, he he couy wih a aial ae of avi equal o 25 pece, he iiial aveae avi ae of pece, ad a aial capial oupu aio of 3, would pay bac all deb ouadi afe 8.3 yea if he owh ae wee 5 pece. The exiece of oe ouadi deb i he beii will oly popoe fuhe he yea of idepedece fo public deb. Accodi o fiue i able 3, whe loa equied fo evice paye i 4 pece, i will ae a lea 9.5 o 6.4 yea o pay bac all deb if he ae owh ae i 5 pece pe yea. If he ae owh ae i 7 pece, i will ae 27 yea wih he equied ae of evice paye of 4 pece, ad 33.4 yea wih a equied evice ae of 6 pece. If he ae icoe owh ae i 8 pece, i will ae 54 yea o pay bac all loa wih a equied evici ae of oly 4 pece, ad 5 yea wih a equied ae of evici of 7 pece. Thi ea ha whe we equie oe loa fo evice paye ad fo iceaed owh ae, he he peiod o pay bac loa alo iceae. The fiue (able 5 ad able 6 how ha he ye i hihly eiive o ae of GDP owh i elaio o aial ae of avi. A he ae of owh iceae, he yea of paye of loa alo iceae. Whe i ae a he ae of evice paye o loa, i low value idicae a poloed peiod of aoizaio ad low ae of iee. I ealiy, oveall deb coe o couie i he fo of a, loa ad diec ivee. Thi udy ha povided oe ehod of calculai he yea of idepedece fo public deb ude oe pojeced o aued value of oe eleva paaee. We have explaied how difficul i i o becoe idepede of deb, eve ude codiio of equii o feh iflow of loa. 23

25 7/9/2 Refeece Wold Ba (2, Guidelie fo Public Deb Maaee, Opeaio Evaluaio Depae, Wahio DC: Wold Ba. Avaovic, Daolav, ad ohe (964, Ecooic Gowh ad Exeal Deb, Joh Hopi Pe, Balioe 964. Alibe, Robe Z. (98, A Cocepual Appoach o he Aalyi of Exeal Deb of Developi Couie, Wold Ba Saff Woi Pape No. 42 (Wahio, Ocobe 98. Nowzad, Baha ad Richad C. Willia (98, Exeal Idebede of Developi Couie, Occaioal Pape No. 3, Ieaioal Moeay Fud (Wahio, May 98. Lee, Juoo (983, The Exeal Debe-Sevici Capaciy of Aia Developi Couie, Aia Develope Review. Vol., No. 2. Soloo, Robe (977, A pepecive o he Deb of Developi Couie, Booi pape o Ecooic Aciviy: 2, pp Haod R. F. (963, Deiable Ieaioal Movee of Capial i Relaio o Gowh of Boowe ad Lede ad Gowh of Mae Ieaioal Tade Theoy i a Developi Wold, ed. By Haod ad Haue, Macilla. Chey, Holli ad M. Buo, (962, Develope Aleaive i a Ope Ecooy: The Cae of Iael, Ecooic Joual, Vol. 77, No. 285, pp

26 7/9/2 The ie pah of e boowi i ive by. APPENDIX DERIVATION OF EQUATION (5 F D I S (A I ode o obai a oluio fo deb F, we fi eed o ace he oluio fo he oc of foei D. Sice boowi i peiod i equal o he chae i deb i peiod ove peiod -, he ie pah of he oc of deb ca be expeed a a diffeece equaio: D D F (A2 Subiui fo F fo equaio (A, we obai: D D I S (A3 Subiui bacwad, ui he iiial value D ad aui ha he ae of iee i coa, we obai he followi educed fo equaio fo he above diffeece equaio: j D ( I S (A4 j j j Now ui he ivee ad avi fucio ive by (2 ad (3 he ivee-avi ap i peiod ca be wie a: 25

27 7/9/2 26 S I (A5 Now ubiui fo (A5, he ie pah of public deb ive by (A4 ca be expeed a follow. ( ( j j j j D (A6 Ui he oluio fo eoeic eie, we obai: D, ( (, ( ( ( ( (A7 To obai he oluio fo he e boowi, we ubiue fo (A5 ad (A7 io (A o yield F ( ( ( ( ( ( (A8

28 7/9/2 27 Fially colleci coo faco ad fuhe iplifyi he expeio, we obai he followi oluio fo he e boowi. F ( (, ( ( ( (A9