Public Debt Accumulation and Fiscal Consolidation

Transcription

1 Puic De Accumuaio ad Fisca Cosoidaio Kazumasa Oguro Hiosuashi Uiversiy Moohiro Sao Hiosuashi Uiversiy Asrac I his paper we aayze he reaioship ewee ieres raes o goverme ods GB ad fisca cosoidaio rue y usig a overappig geeraio mode wih edogeous ad sochasic growh seigs. Our ey fidigs are summarized as foows. Firs ieres raes of GB may e deciig as puic de accumuaes reaive o privae capia as opposed o he coveioa view ha uidup of puic de accompaies a rise i ieres raes. Secod fisca cosoidaio rue pays a ey roe i deermiig ieres raes i equiirium. Third he ecoomy may exhii discree chages wih ieres raes divergig impyig ha our oservaio of reaivey ow GB ieres raes does o assure he coiuaio of ha red i he fuure. Fourh a preveive ax icrease o coai puic de a susaiae eves wi o gai he poiica suppor of exisig geeraios whose ife spa is imied. Ciizes prefer o shif he uimae urde of puic de o fuure geeraios. JL cassificaio: 7; H30; H5; H60; 6; H63 Keywords: Overappig geeraio mode; ieres rae o goverme od; fisca cosoidaio rue; defau ris

2 . Iroducio Puic de as a perceage of GDP has recey ee icreasig i deveoped couries. The gross puic de-o-gdp raio of Japa is especiay high compared o ha of oher deveoped couries i 0. The Ieraioa Moeary Fud 009 has esimaed ha Japa s gross puic de woud reach 77% of GDP y 06. I such circumsaces ieres raes o goverme ods GB woud heoreicay rise as a refecio of defau ris as show y Magaei ad Woswi 009. Codogo e a. 003 Beroh e a. 006 ad Aioi ad Srama 008 have aso foud he exisece of spreads ha may e ierpreed as ris premiums. O he oher had ieres raes of Japaese Goverme Bod JGB has ee ower ha ha of oher deveoped couries. I addiio we ca oserve ha he ieres raes of JGB are currey deciig eve hough Japaese puic de coiues o icrease See Figure. A reeva mode ad mechaism are required o iusrae he seemigy paradoxica cofuece of reds. The foowig possiiiies are cosidered as faces of he mechaism: he refecio of defau ris for JGB is wea ecause 95% of JGBs are hed y domesic ivesors; domesic ivesors may eieve ha he Japaese Goverme wi o defau o is de oigaios ecause here are severa fisca reform opporuiies e.g. cosumpio ax icreases ha coud hep maiai fisca susaiaiiy; ad 3 domesic ad foreig ivesors eieve ha he ieres rae o JGB is ow ecause ecoomic growh uder he coury s agig ad deciig popuaio is expeced o e ow as we. Despie hese possie moivaios he mechaism for he curre ieres rae decie remais ucear ad here is o mode o expai i. Oe compicaio is ha GB ieres raes aso deped o fisca poicy. I paricuar fisca cosoidaio rue e.g. ax icreases expediure cus ad defauig o ods is impora as govermes cao aways ro over puic de o fuure admiisraios ad geeraios. Gae ad Orszag 00 ad Lauach 009 have poied ou ha he respose of GB ieres raes o o fisca poicy depeds o expecaios aou he fuure course of fisca poicy. Peroi 007 ad Favero ad Giavazzi 007 aso have foud evidece of a chage i he reaio of macro variaes o fisca poicy. This chage has ee ierpreed as evidece of a chage i reacios of fisca poicy o saiizaio of de-o-gdp. Urie 006 ad Juesse e a. 009 have aayzed goverme defau ris ad is refecio o GB ieres raes y usig a quaiaive macroecoomic mode. However Urie 006 focuses o exera de wih ope ecoomy. I he case of exera de defauig is cosidered a deierae sraegic decisio of he goverme ha refecs he oucome of a opimizaio proem e.g. ao ad Gersoviz 98 or Areao 008. Ahough Juesse e a. 009 focus o iera de usig a mode wih cosed

3 ecoomy hese heoreica sudies ever provide examie he poeia effecs of fisca cosoidaio rue o ieres raes. Therefore we provide a macroecoomic mode o expai he imporace of fisca cosoidaio rue; his mode carifies he reaioship ewee decreasig GB ieres raes ad icreasig puic de. Figure % Geera goverme gross fiacia iaiiies perce of GDP Log-erm ieres rae Year Source: OCD Sas xracs I his paper we cosider overappig geeraio modes wih edogeous ad sochasic growh seigs. The producio echoogy coais spiover associaed wih privae capia ad produciviy shoc. ach geeraio comprises he represeaive househod ha ives for wo periods. We accou for demographic chages i he ecoomy. Popuaio growh is assumed o e ow u ca vary over ime. I he youg period he househod suppies aor i a easic maer. Taxes are evied o wages. Par of afer-ax wage icome is saved. We suppose ha here are wo ypes of asses ha are ax free. Oe is privae capia ad aoher is GB. The former yieds ucerai reurs due o he produciviy shoc of he suseque period. The aer promises a fixed reur u aso a ris of defau. As opposed o Juesse e a 009. we cosider ha defau may e paria. I he od period he househod is reired ad receives reurs o privae capia ad GBs. Key fidigs of his paper are summarized as foows: Ieres rae of GB may e deciig as puic de is accumuaed reaive o privae capia so he former crowdig ou he aer as opposed o coveioa view ha ui up of puic de accompaies rise of ieres rae. The prospec of fuure ax icreases due o as he fisca cosoidaio rue serves o ower expeced reur o privae capia which i ur decreases ieres raes charged o GB hrough arirage. We esaish ha fisca cosoidaio rue pays a ey roe i deermiig equiirium ieres raes. I addiio he ecoomy may exhii discree chages ad divergig ieres raes impyig ha he deciig GB ieres rae red may o coiue as puic de furher accumuaes. We aso show ha preveive 3

4 ax icreases o coai puic de wi o gai he poiica suppor of exisig geeraios whose ife spa is imied. Isead ciizes prefer o shif he uimae urde of puic de o fuure geeraios who cao currey voe. This cofirms he argume ha puic de is expoiive of fuure geeraios. The res of he paper is orgaized as foows: Secio descries he mode. I secio 3 we cosider fisca cosoidaio rue ad esaish equiirium GB ieres raes. Secio 4 uses he equiirium i aaysis of comparaive saics. We carify our heoreica argume y simuaio i secio 5. Secio 6 discusses he impicaios of he resus ad Secio 7 cocudes.. Mode Seig. Basic seig I his paper we empoy a sochasic overappig geeraio mode. ach geeraio coais a represeaive househod ha ives for wo periods. I each period a sige good is produced y aor ad capia u he producio is sochasic due o echoogy shoc. ach period is divided io severa sages. A Sage producio shoc is reveaed. The househod of he youg geeraio suppies aor a Sage. The oupu reaizes a Sage 3 wih wages eig paid o he youg ad reur o capia eig disriued o he od. The goverme coecs axes ad repays puic de a Sage 4. A Sage 5 he youg ad he od househods cosume he former aso savig ad choosig a porfoio. Puic de ad privae capia are carried over o he ex period. To carify our aaysis foows he wo seps. Firs we esaish ira-period or saic equiirium give puic de ad capia carried over from he previous period. We he ur o dyamics. The ecoomic growh is edogeous ad sochasic due o produciviy shoc.. Producio Y deoes aggregae oupu a period ha is produced y he represeaive privae firm. The producio fucio of he ecoomy is give as μ Y AK 4

5 where A >0 is cosa μ > 0 ad 0 < <. deoes produciviy shoc. For he sae of simpiciy we assume ha he shoc is disriued accordig o he disriuio fucio F over he ierva [ ] wih. represes privae capia ha is ivesed i he previous period ad represes aor suppy per worer a period. Popuaio of geeraio is deoed y. The L represes oa aor suppy. K refers o average capia ivesme ad represes he exera effec of capia accumuaio. Foowig he ieraure o edogeous growh i may e ierpreed as owedge spiover ha serves as a pure puic geeraig a ecoomy of scae omer 986. I he equiirium we have. K Suppose ha producio is perfecy compeiive. The price of oupu eig ormaized o uiy we ca wrie he wage ad reur o capia as w Y / L ; r Y / As is sadard i he ieraure mare rasacio fais o accou for he spiover effec i deermiig he reur o capia..3 The househod proem The househod s ifeime uiiy is assumed o ae he foowig form: / y o 3 θ c c / U y o where θ > 0 ad > 0. deoes he youg period of cosumpio whereas is he oder c period. The secod erm i he firs race is he disuiiy of aor suppy. I eers i he uiiy fucio so ha aor suppy respods o afer-ax wage asracig icome effec. This simpificaio foows he ieraure o opima icome axaio. For isace see F. The firs race erm of 3 ca e he ierpreed as a e gai of he youh period. c The househod of geeraio suppies aor oy afer ecomes ow. However i is cofroed wih riss of oh produciviy shoc ad goverme defau whe maig savig decisios. q. 3 impies ha is preferece is eura o hese riss. Give he Co Dougas form of he uiiy fucio however ier-empora easiciy of susiuio urs o e uiy. Oe may fid i odd ha ris ad ime prefereces are separaey defied; our specificaio deviaes from he sadard seig ha assumes ha ifeime uiiy is addiive over periods ad over differe saes of he ecoomy. Ier-empora easiciy is o ied o he iverse of ris aversio i he prese coex. Admiedy ad hoc q. 3 heps isoae he househod s porfoio choice ewee privae capia ad GB from he decisio o oa savigs. s 5

6 Househod udge cosrais a he youg ad he od periods are give y y 4. c s w ω 4. o c s q ζ q r where is wage icome ax ω is afer ax wages is he GB s oe pus ieres rae ad q represes he share of he GB i oa savigs. ζ represes he defau rae as a vaue ewee zero ad uiy. The variaes wih ide address uow quaiies whe savig a period. is deermied a period wih defau ris ; e reur o GB is o cerai. I he youg period he househod decides aor suppy ad savig s ad chooses porfoio o maximize reurs: q / y θ o c [ c ] / η U This is suec o q. 4 where he expecaio is cacuaed over ζ ad r. The househod s opimizaio yieds he foowig: 5. where ω Ψ 5. s θ 5.3 ζ r Ψ ω / ω / ω By 5. wage easiciy of aor is cosa a. Wage axaio ecomes disorive as easiciy icreases. Due o he Co-Dougas specificaio savigs is a fixed share of he wage icome e of he aor disuiiy wih icome effec ad susiuio effec offseig oe aoher as give i Ψ 5.. Fiay 5.3 gives he arirage codiio ewee privae capia ad he GB. Give ha he househod is ris-eura arirage eads o he equaio of expeced reur of oh asses which shoud e iuiive..4 Mare quiirium This susecio cosiders mare equiirium give fisca poicy. A every period oh aor ad capia mares are ceared. Give ad he equiirium vaues of wage ad reur o privae capia a period are deermied y susiuig 5. io such ha I 4. we asrac idiosycraic ris icudig arupcy of privae capia. This presumes ha he househod ca fuy diversify such ris ad ha oy aggregae shoc wi remai. 6

7 w μ / 6. ω AK / μ / / / 6. r AK / The oupu a period ecomes / / μ / / / 7 Y AK Cosider he exera effec: i he equiirium we have K he capia ivesme i mare eig exacy equa o he average i he ecoomy. I addiio we se he parameer associaed wih exeraiy such ha equiirium oupu is proporioa o privae capia. The foowig assumpio is imposed: Noe ha Assumpio μ μ if 0 or if aor suppy is compeey ieasic as assumed y omer 986. The 7 urs o e / / / / 7 Y A The aove is famiiar i he edogeous growh mode which yieds cosa growh raes as a fucio of poicy parameers. The wage rae is iear wih respec o as we whereas reur o privae capia urs ou o e idepede of : 6. ω A w / / / / 6. r A Lasy we ur o he capia mare. Because of he cosed ecoomy househod savigs mus mee demad of privae firms ad he goverme. deoes GBs issued a period ad repaid a. Give ha oa savigs a period is as aocaed ewee ad he equiirium codiio is expressed y 8 s / / s A θ Maipuaig he aove esaishes he dyamics of privae capia accumuaio as he foowig: / 8 / A θ Now cosider growh rae. This ecoomy grows a he rae of χ ha is sochasic ad defied as / Y / / 9 Y χ As opposed o he growh mode wih ages of ifiie ife he OLG may exhii dyamic iefficiecy i which growh rae ecomes ower ha ieres rae. The foowig emma yieds he codiio ha he ecoomy remais dyamicay efficie: We cosider oy a sige period od ad hus we asrac issues of od mauriy composiio. 7

8 Lemma : The ecoomy is dyamic efficie or χ r if θ Proof of his is show i Appedix A. Throughou he paper we assume ha he aove iequaiy hods..5 Goverme udge The goverme raises reveue y issuig GB ad axig wage icome. I he speds his o de repayme ad puic expediure he aer eig deoed y G. G is assumed o o coriue o producio or direcy eer io househod uiiy 3. This assumpio is moivaed o simpify our aaysis u may e pausie whe goverme spedig comprises poiica res or por divered o specia ieres groups. The fudig fow of he goverme udge a period is wrie as where 0 { T G } T w L Y ad is give i 7. For he aer he foowig emma Y esaishes he reveue-maximizig ax rae ha deermies he upper ouds for ax raes i he case of fisca cosoidaio: Lemma : Tax reveue is maximized a Max A his poi we disiguish fisca rue ewee pre-fisca cosoidaio ad fisca cosoidaio regimes. This is deoed y Ω { λ ζ } which coais ax rae goverme expediure raio λ ad defau rae ζ ad may e sae-coige for cosoidaio regimes. Fisca rues are assumed o e puic iformaio impyig ha hese rues are icorporaed i he pricig of GB as discussed eow. The prese mode does o suppose opimizaio ehavior of he goverme i he pursui of socia wefare. We isead ae he pragmaic view ha goverme poicy is argey poiicay cosraied as opposed o eig desiged ased o ecoomic raioae. 0 Le Ω { λ ζ } wih ζ 0. I he pre-cosoidaio regime he goverme axes wage icome a he rae of ad speds a give porio of poeia oupu λ λ ha cacuaes Y a he mea of ; ha is ad such ha G λy where / / / Y A G remais proporioa o Y defied aove i he cosoidaio regime ad iusraed aer. Wih 8

9 ad he primary surpus a period is defied y where / / PS T G A Δ λ Δ λ λ / / / Susiuig io 0 ad maipuaig i esaishes he dyamics of puic de over muipe periods we arrive a / / 3 A Δ λ where / is as give i 8. Noe ha i he prese ecoomy ad serve as sae variaes ha are deermied a / period ad carried over o period. They he affec he ris of fisca cosoidaio a as discussed i he ex secio. 3. quiirium 3. Fisca susaiaiiy 0 The fisca rue Ω { λ ζ } i he pre-cosoidaio regime does o assure ha puic de remais a fiscay susaiae eves. Tax raes may e oo ow ad/or expediure raio may e oo high o srucuray geerae primary defici; ha is Δ λ < 0 for mos of. The puic de may reached a eve a which he saus quo fisca rue cao e susaied. We do o suppose ha he goverme uderaes precauioary measures o preve such circumsaces. Poiica ecoomy cosideraios o such measure wi e discussed aer. Give he OLG seig a capia mare may o wor o discipie goverme fiacig ecause he fiie-ife househod may o e cocered wih og ru fisca susaiaiiy. Uess i is cerai ha ζ wih ris-eura preferece ad ha 5.3 hods a househod wi purchase GB wih he defau ris perceived as eig compesaed y a higher ex ae promised ieres rae. I he prese coex herefore he goverme ca access credi isofar as he GB eve does o exceed domesic savigs wih he ieres rae fufiig 5.3. Suppose however ha he ecoomy reaches s ha is he domesic savigs a period is fuy asored y goverme orrowig give ha he ecoomy is cosed ad o privae ivesme ca ae pace which impies 9

10 ha here is o producio i he suseque period or Y 0 for a. Oce his occurs he goverme ca fid o resource for repayme. I he has o defau o he de so ha ζ is cerai ad herefore here wi e o reur o GB. 3 This i ur impies ha he househods cease o ed o he goverme. The goverme is he forced o uderae fisca cosoidaio wihou furher orrowig. This eais ax icreases expediure cus ad furher defauig o GB. Lemma 3: Fu defau is ieviae a period irrespecive of whe s. Wih s or 0 we have / a period. The ieraure of fisca susaiaiiy discusses he rasversaiy codiio of he prese vaue of he puic de i he ifiie fuure. Ideed Juesse e a. 009 usig ifiiey ivig ages cosiders ha he goverme is forced o defau o is de oce he codiio fais o hod. I he OLG seig however he househod is wiig o purchase GB i is youg period whe de repayme occurs i he ex period or he cosoidaio ris is compesaed wih a higher GB ieres rae. To sae i differey he rasversaiy codiio does o defie goverme defau i he prese mode. See Appedix B. 3. The hreshod Iserig / io 3 ad maipuaig i yieds he foowig codiio of he hreshod eve of eow which regime chage occurs: / λ / 4 / / A θ This defies he hreshod impiciy as he fucio of he ieres rae charged o as we as de-o-capia raio ad demography: Z where. / 4 Wih ad / whereas i is owered wih. Z icreases such ha fisca cosoidaio is more iey o e i pace Lemma 4: Fisca cosoidaio mus occur a period whe Fisca cosoidaio ivoves ax icreases expediure cus ad defauig o GB. The sae of he ecoomy a period is deoed y Ξ /. The fisca rue is he expressed as Ω Ω wih which coais Ξ 0 3 O he oher had reur o privae capia remais posiive wih he reveue maximizig ax rae eig ouded y ess ha 00%. 4 We e whe he LHS exceeds he HS a. Noe ha he fac ha cosoidaio is ieviae wih does o mea fu defau ha is ξ give ha / remais a a fiie eve. 0

11 Ξ λ λ λ Ξ 0 ζ ζ Ξ where he defau rae fufis 5 / / 5 ζ A λ Δ The goverme cao fuy mee is oigaio u repays is ousadig de as much as possie ou of he primary surpus as iusraed i 5. Uder he cosoidaio rue eiher ax rae expediure raio or defau rae deviaes from he iiia eves. The fisca rue ca ae a geera form u may e pausiy evied accordig o he foowig resricios: Assumpio i / 0 ii ζ / 0 iii λ / 0 I he simuaio of secio 5 we specify fisca cosoidaio rue. Noe ha i aes oy oe period o resrucure goverme fiace. Give ha o GB is issued he ecoomy wi reur o he iiia regime i he ex period wihou de iaiiy eig carried over. 3.3 Ieres rae Le us ur o GB ieres rae which is seed a period accouig for fisca cosoidaio i he eve of. eca he arirage codiio 5.3 which equaes reur o GB ad capia i he expeced erm. Maipuaig i wih he use of 6. ad 5 esaishes he foowig: where 6 Φ F / A / Φ / / df / ad of Φ meas he vecor of / Δ df λ df Noe ha Φ refecs he expeced reur o privae capia. 6 We ca ceary see ha i is o-icreasig wih he hreshod eve give ha. This represes he perverse effec of wage ax icreases uder fisca cosoidaio ha discourage aor suppy ad i ur ower he produciviy of privae capia. 5 The cosoidaio rue ca e ierpreed i a reduced form ha icorporaes he depedecy of he equiirium vaues of ad o Z /. 6 / / r A Φ

12 6 yieds he GB ieres rae as a fucio of he hreshod he de-o-capia raio ad he popuaio: Z. The effec of is descried i he foowig emma: Lemma 5: Deoig Z ad ζ ζ Z where / we have > 0 < > ζ < / Z / A / / / The proof is show i Appedix C. This emma impies ha he ieres rae is icreasig resp. decreasig i whe fisca cosoidaio eais o ax icrease resp. o defau ad hus reveue oss is made up for y defauig o ousadig de resp. y raisig ax a he hreshod eve. I may e coueriuiive ha may e owered as icreases. To see he poi oe ha i he prese mode fisca cosoidaio ivoves oh he defau ad he ax icrease. The former adds he ris premium of GB reaive o privae capia herey raisig is ieres rae. The aer o he oher had reduces he reur o privae capia which wors o ower he GB ieres rae hrough arirage. We he have he case of / < 0 whe ax icreases domiae he defau ris. Cosider he icrease of. is icreasig wih i sice he produciviy of privae capia is ehaced as aor suppy is ehaced. O he oher had he impac of he de-o-capia raio is amiguous as we. direcy appearig i 6 serves o raise whereas y / Assumpio he iduced ax icrease uder cosoidaio wors i he opposie direcio. Tha is / 0. To carify our aaysis i wi e of hep o cosider exreme cosoidaio rues as foows: No Tax Icrease: Le Ξ for a such ha here is o eed for a ax icrease. Cosoidaio eais defauig o ousadig de as we as cuig goverme expeses. The defau rae fufis / / 5 ζ Ξ A Δ λ Ξ D D Ω Ω Ξ represes such fisca cosoidaio. Accordig o Lemma 5 he fucio of Z shoud e upward wih respec o.

13 No Defau: Suppose isead ha o defau is aowed or ζ 0 for a u he ousadig de mus e fuy repaid hrough ax icreases ad expediure cus wih eig Ξ ND impiciy deermied y 5 wih ζ ζ 0. Le Ω ND deoe fisca rue. The 6 reduces o 6 Ξ / A / Φ Ω which is decreasig wih. 7 is aso decreasig i he de-o-capia raio give ha he HS of 6 decreases as Ξ is raised. 8 Ξ 3.4 Ieracio There exiss ieracio ewee he hreshod of he fisca cosoidaio rae ad he GB ieres defied y 4 ad 6 respecivey. Sovig hese equaios yieds heir equiirium vaues. Noe ha hese are assessed from period or ex ae perspecive whe ad fisca cosoidaio is o ye i pace. is o ow Ω Ω. These are give as souios o he foowig equaios: Ξ Proposiio : Deoe y ad he equiirium eves of he GB ieres rae ad he hreshod of fisca cosoidaio codiioa upo ad he cosoidaio rue / / / F / λ / / A θ A / Φ Τ Δ λ df I he aove proposiio we do o precude he case ha here arise muipe equiiria wih he wo equaios iersecig more ha wice or wih he equiirium divergig ha is reachig as iusraed eow. Coroary o Proposiio : 7 ND ND The sufficie codiio for Ω Ω o exis is give y: Δ 0 Ξ / / λ θ / 8 Oe may oe ha goverme fiacig ca e regarded as susaiae i he prese coex eve for wihou defau. We ierpre fisca susaiaiiy i a sighy sric way i ha i refers o a circumsace i which saus quo fisca poicy icudig axaio ad expediure ca e susaied. 3

14 I he corer equiirium wih we ca defie he GB ieres rae cosoidaio rue Ω Ω ha fufis 9 Ξ Φ Τ Ξ Δ wih o defau a Z λ Z df so ha / / A Z λ Z Δ where > 0 ad are he souio o Z. if here exiss a I he coroary he defau rae is se o zero a. The cosoidaio rue a he corer equiirium may differ from he oe appied o he ierior oe. The presumpio is ha he represeaive househod forecass Ω whe i aicipaes. Aso oe ha > is o assure ha 4 yieds aig as give. 4. Comparaive Saics 4. De accumuaio egardig comparaive saics oay differeiaig he equaio 4 of hreshod Z ad he equaio 6 of he GB ieres rae Z esaishes / d / / / 7 d d / / / / d Meawhie we focus o he ierior ad sae equiirium where he equiirium ieres rae is fiie wih H / / > 0. The we oai he foowig proposiio i he case of o demographic chage. 9 The sufficie ad sric codiio for such fisca rue o e feasie is: Φ 0 Max < Δ Max df Give ha he LHS is deciig wih he wage ax rae. 0 This iequaiy is re-wrie as: Δ Z λ Z / / / λ > θ 4

15 Proposiio : The de-o-capia raio i is icreasig if / 0 / ii is icreasig if / > 0 ad / / 0 iii is decreasig if < 0 ad / 0 / / Figure depics possie scearios. Figure a gives he case of / > 0 ad / / 0. The iiia equiirium is ocaed a poi A. Icreasig he de-o-capia raio moves Z righward a d Z upward. The iersecio of he wo fucios is he shifed up ad righ such ha oh he ieres rae ad he hreshod are raised. I Figure Z is soped dowward. The iiia equiirium is agai give y poi A. Z moves i he same way as Figure a wih /. Suppose / 0. The hreshod is raised movig he ew equiirium o poi B. The chage i / > ieres rae is o cerai. Le chage i is amiguous. / / 0. is he owered o poi C whereas Figure a Figure Z B Z Z A A Z C 0 0 The upsho is ha we have he circumsace ha decreases wih de eig accumuaig reaive o privae capia as depiced i Figure. This is iey whe fisca cosoidaio rue icudes arge ax icreases whie eepig he defau rae ow a mos of such as Ω ND ND Ω Ξ as discussed earier. I coras Figure a impies ha he defau ris is 5

16 sigifica i he fisca rue. I is ofe addressed ha as cosequece of crowdig ou privae ivesme he uidup of puic de eads o surges i ieres raes. The presumpio of such a argume is dimiishig margia reurs o ivesme. Decreased privae capia he ehaces is produciviy o margi which i ur raises mare ieres rae. The edogeous growh seig however does o rasae he crowdig ou io such icreases of he margia produc of as i is fixed depedig upo he wage ax rae ad oher ecoomic evirome. aher expecaio of fuure ax icreases reduces he expeced reur o privae capia which is i ur refeced i ower eves of differey ower coex.. To sae i sigas a cauioary view of fuure goverme fiacig i he prese A his poi i is worh addressig ha cosoidaio rue pays a ey roe i deermiig D D equiirium. If cosoidaio is doe mosy y defauig he puic de as Ω Ω Ξ i he exreme he case of Figure a ecomes iey raisig as he puic fiace deerioraes. The corasig red show i Figure is oserved whe cosoidaio icudes a sigifica ax icrease whie respecig he de oigaio. I ca e perceivae ha is ower i he aer fisca rue ha he former give /. The differe fisca rues are compared i he simuaio as we. 4. Discree Chage I Figure we assume a uique ad ierior souio o equaios 4 ad 6. However we may have muipe or corer equiiria. Figure 3 iusraes such o e he case assumig 0 give he cosoidaio rue Ω Ξ appied o he ierior equiirium. Aso / > suppose / 0 such ha he curve of Z moves upward aog wih / he de-o-capia raio. 3 The figure depics hree differe eves of he raio wih / < / < /. A / he GB ieres rae ad he hreshod fucios iersec oy oce a poi A ha yieds uique equiirium. For he midde eve of he raio he wo fucios ur o cross wice a pois B ad C. Poi B gives sae equiirium whereas C is usae. I he case of muipe equiiria oucome depeds upo eief of he househod who purchases GB. Noe ha furher icreasig / I a more geera coex i which househods of oe geeraio are heerogeeous some coordiaio of eiefs is eeded o deermie which equiirium is achieved. 6

17 shifs he wo curves so ha pois B ad C come oo cose. They ouch oe aoher a D i he case of / 3 eyod which he ierior souio disappears. This impies ha he ecoomy movig aog he sae ierior equiirium may exhii a discree chage o he corer souio wih higher ieres raes ad hreshod. Thus he oservaio ha GB ieres rae has remaied reaivey ow does o assure ha he same red coiues i he fuure as puic de accumuaes. Figure 3 3 / / / C / 3 / / D B A 0 I he figures we address he circumsaces i which he uidup of puic de migh ead o ower GB ieres raes owig o he prospec of fuure ax icreases reaig o fisca cosoidaio ad i which here migh hus e a sudde rise of ieres raes from reaivey sae ad ow raes o exreme eves hus icreasig he fisca cosoidaio ris. We cofirm hese scearios y simuaio i secio Demographic Impac Lasy we examie he effecs of demographic chage. Noe ha i he edogeous growh mode he popuaio or aor force is a ey drivig force o ehace produciviy. Wih popuaio size owered produciviy decreases ad hus he expeced reur o capia is dimiished which i ur wors o reduce. The hreshod of he regime swich is icreased o he oher had ecause he primary surpus is owered. These ieracig he e impac is as saed i he foowig proposiio: 7

18 Proposiio 3: Cosider reducio i i. The decreases if < 0 / ii is ehaced if is icreasig I geera he equiirium effecs of he demographic chage o ad are amiguous. I secio 5 we coduc a simuaio o compare he scearios of differe demographic chages. 4.4 De accumuaio I he previous secio / was ae as fixed ad he equiirium was esaished as codiioa upo i. We ow cosider accumuaio of puic de. I is sochasic as i reies o reaizaio of he produciviy shoc. Comiig 8 ad 3 ad advacig he period y oe we oai he rasiio process of he de-o-capia raio as foows: 7 / / θ / / / / A / where addresses ha is vaue is ucerai a period. λ The immediaey higher is rasied o a higher i he ex period give / / accouig for he depedecy of o. Accordig o Proposiio his impies ha / he ris of fisca cosoidaio a period is raised wih he curre de-o-capia raio if / / 0. Figure 4 depics he shape of he rasiio fucio 7 wih cosa ha he curve approaches ifiiy if goes o he criica eve such ha / / ; ha is ecomes coicide wih he hreshod of fisca cosoidaio. 0 / / M give y / / eig ocaed a poi if. I he figure we have a. I shows hree eves of : ow midde ad high. Noe ha a smaer vaue of shifs 7 upward. Aso oe Suppose ha M < L < /. By 7 he de-o-capia raio carried over o he ex period is L which impies ha here arises a regime chage a period if whereas goverme fiacig is susaiae whe. Figure 4 shows ha H / L L approaches ifiiy a wihou cosoidaio. I he eve o puic de ha is 0 is issued uder he cosoidaio rue ad hus he ecoomy moves ac o is origi. O 8

19 H he oher had he raio is owered o / / or poi F whe. Figure 4 / L M H / / F M H 0 L / 0 / 5. Simuaio 5. Specificaio This secio aims o coduc a simuaio of he comparaive saics deveoped i secio 3. To e specific we examie he heoreica hypoheses ha puic de accumuaio may ead o ower ieres raes ad ha he equiirium ieres rae may exhii a discree chage from reaivey ow o a exreme high eve. I addiio we cofirm wheher he equiirium i he pre-cosoidaio regime is affeced y fisca cosoidaio rue ad demographic chage. Moreover we cacuae he hreshod a which cosoidaio occurs give / a period. Needess o say our quaiaive aaysis does o ied o repicae ay pracice of ecoomy. aher i is o suppeme our heoreica mode resovig amiguiy of is resus ad carifyig is poicy impicaios. The parameers are specified i Tae. disriues over [0.5.5] accordig o he iverse U-shaped desiy fucio wih mea of oe. We se he ax rae a a reaivey ow 0%. We se he expediure rae a 0% of poeia oupu as we. This impies ha primary defici is iey o resu uess is arger ha mea of oe so here exiss he possiiiy ha puic de is accumuaed wih cosoidaio ris hus eig ehaced. Fisca cosoidaio rue commads he 9

20 expediure o e cu i haf o λ The wage ax rae uder cosoidaio is icreasig i whereas i icreases wih as imposed y Assumpio. This is specified i Tae. / Cosoidaio reies o more ax icreases for arge de o capia raio whereas he defau rae is raised whe is sma ad he ecoomy is herefore depressed. Such presumpio shoud e pausie. The parameer g i he ax fucio refers o he exe of he required ax icrease. The simuaio se hree vaues of g ad.0. Higher g impies a arger ax icrease i he cosoidaio which i ur impies a ower defau rae ξ ha is defied as residua y 5: he ax fucio aove is cosraied so ha aes ierior vaue. By comparig resus of differe eves of g ξ we ca assess he effec of fisca rue o ad as we as he rasiio of he de-o-capia raio. To examie he demographic chage we cosider he case ha he popuaio remais cosa over ime ad aso he case ha i is deciig. I he aer we assume ha i auay decreases y 0.3%. Taig oe period o sad for 30 years we e Disic y he parameer g ad he demography four scearios are preseed as summarized i Tae. Sceario is ae as a echmar i he foowig ae. Tae : Parameers θ.333 A Ω { λζ } 0. λ 0. Ω Ω Ξ Mi g Max 3.8 / λ / 0. Tae : Scearios Sceario Bechmar g 0.75 Sceario g 0.5 Sceario 3 g.0 Sceario 4 g esus I simuaio we focus oy o he ierior equiirium. The GB ieres raes for differe scearios 0

21 are show i Figure 5 where / scearios here exiss a rage i which is reaed paramericay ae o horizoa axis. I a exhiis dowward sopig cofirmig our heoreica hypohesis. Tae he echmar sceario Sceario. The ieres rae is iiiay deciig wih. Is moderae dowward red coiues ui 0.78 where aes he / / miimum vaue. The sope is he reversed furher icreasig he de-o-capia raio ad rapidy raisig he ieres rae. A /. he sae ierior eve of disappears divergig o he corer equiirium which is o expiciy reaed here. This is cosise wih he iusraio of Figure 4. The echmar sceario is compared wih Sceario ad 3 o assess impacs of he ax icrease. i Sceario arey differs from he echmar for ow eves of /. Afer / 0.3 however he former egis o exceed he aer ad he differece ewee hem wides quicy. Oce he raio goes eyod Sceario oses is ierior equiirium whereas i remais i he echmar sceario. I he former wih g 0.5 he ax icrease is ess sigifica ha he aer whe fisca cosoidaio is impemeed. Give ha oh scearios impose λ 0.05 i he eve of he cosoidaio his impies ha Sceario experieces a higher defau rae ad cosequey adds a ris premium o GB. Now cosider Sceario 3 wih g. Agai is ieres rae moves aou he same as he echmar whe he puic de-o-capia raio is o high. For / >0.5 he dispariy urs ou o e promie wih i Sceario 3 sayig ower ha i he echmar. The former ca he susai he ierior equiirium for arger ha he aer. I ca he e cocuded ha cosoidaio ivovig more ax icreases eads o ower susaiig he ierior equiirium. Figure 5: GB Ieres ae / GB Ieres rae Puic de o capia raio Sceario Sceario Sceario3 Sceario4 The simuaio aso reveas ha a usae equiirium appears whe he de-o-capia raio is very cose o he criica eve of he puic de-o-capia raio i which he sae ierior souio disappears.

22 Cosider he hreshod of regime chage. I a scearios i is moooicay icreasig i / as i Figure 6. I comparig differe scearios wih differe cosoidaio rues says ower whe he ax icrease is arger; ha is g is high refecig a ower ieres rae. The prospec of arge ax icreases i he eve of fisca resrucurig ha coriues o a ower defau rae serves o miigae he cosoidaio ris which shoud e iuiive. The ris is refeced i a GB premium ha is defied as he differece ewee GB ieres rae ad expeced reur o capia. The premium remais egigie whe ris is ow: accordig o he cosoidaio ris he reveue deficiecy is argey fied y ax icreases ad expediure cu. The defau rae i he eve of cosoidaio is raised as he de-o-capia raio icreases which i ur augmes he premium. Figure 6: Threshod Threashod Puic de o capia raio Sceario Sceario Sceario3 Sceario4 To see he effec of he demography we compare he echmar sceario wih Sceario 4. The figure reveas ha overa he deciig popuaio serves o dimiish equiirium ieres raes. The gap of ieres raes ewee he wo scearios firs decies wih / ui he raio reaches 0.7 ad he sars o icrease sharpy. I Sceario 4 ierior equiirium is susaied up o /.67 ad hus he fisca cosoidaio ris is reduced reaive o he echmar case. eca ha i geera he demographic impac o was amiguous. The simuaio esaishes ha he hreshod is owered i he case of smaer popuaio. Tha is he dowward shif of Z due o decreasig domiaes he upward moveme of Z wih primary aace deerioraig as i Figure. Cosider he ecoomic growh ha is cacuaed i he expeced erm as

23 9 / / χ Growh decreases as privae capia is crowded ou y puic de which decreases / give 8. Figure 6 gives he expeced growh rae from he period perspecive. Tax icreases i.e. higher g i he cosoidaio regime exer wo opposig impacs o growh. As saed aove i serves o ower which icreases / as accumuaed a period. The ax urde o he oher had reduces he oupu i he eve of cosoidaio a period ha is refeced i he race of he expecaio i 9. I compariso ewee Scearios ad he wo yied amos he same growh rae for ower ad he aer experieces sighy higher growh afer / / 0.4 ha he former ui he criica raio i which he ierior souio disappears i Sceario. The same ca e see whe Sceario 3 is compared wih Sceario. However he differece is egigie. Demography maes a cosiderae differece. The expeced growh rae see i Sceario 4 is iiiay ower ha he echmar sceario u as he de-o-capia raio icreases he reaioship is reversed ad he differece expads as puic de is ui up reaive o capia. This may e couer-iuiive u i is ecause he ower ris of fisca cosoidaio serves o decrease he expeced ax rae from he period perspecive. I addiio wih GB ieres rae eig owered privae capia accumuaio is ess crowded i Sceario 4 ehacig /. Figure 7: coomic Growh xpeced growh rae% Puic de o capia raio Sceario Sceario Sceario3 Sceario4 5.3 De accumuaio 3

24 Cosider he dyamics of he puic de-o-capia raio which has ee reaed as exogeous i he previous susecio. I doig so we divide which is reaized a period io four casses ad for each quarered group ad he codiioa expeced eve of / is cacuaed give a / ha is deermied a period. Noe ha he expecaio is ae from he period perspecive. Tae shows he resus i he echmar sceario. Tae : Trasiio of De-o-capia aio / The expeced raio of / / is icreasig wih ad is higher for he ower quarer of. A he owes quarer ha is [ ] he average of / goes eyod he criica raio /. a which ierior equiirium ceases o exis accordig o Figure whe he de-o-capia raio / is more ha 0.06 impyig ha fisca cosoidaio is ieviae a or. I higher-quarered groups of he expeced raio remais a susaiae eve for arger /. For isace a he highes quarer ha is [.5.5] ierior equiirium survives a period for ess ha 0.7. / 6. Poiica coomy We have so far assumed he process of accumuaio of puic de as exogeous. Oe possie oecio is ha here shoud exis a sef-correcig mechaism o coai puic de a susaiae eves y raisig axes ad/or cuig expediures. Ideed raioa voers may o aow he ris of fisca crisis o deepe over ime u may uderae preveive measures o curai such ris. I our OLG seig however he represeaive househod of each geeraio wih imied ife spa may 4

25 o ac i such a maer. To see his i effec cosider simpe maoriy voig over ax icreases i he pre-cosoidaio regime so as o decrease puic defici. Boh he youg ad he od geeraios a each period exercise heir voig righ. Wha are voers prefereces for such preveive measures? The cosumpio of he od voers uder he saus quo is equa o 4. o r q q s c ξ where he ar impies ha heir choices are su a he egiig of period. Give ha he reur o privae capia decies wih wage ax he oder group opposes ay ax icrease. Now cosider he youg voers. Their ifeime expeced uiiy i he equiirium reaizaio of is expressed y 9 θ θ θ ψ θ θ ψ θ θ θ θ θ Ψ r r r s s U where A / ω Ψ ad wihou a preveive ax icrease. Differeiaig 9 wih respec o he ax rae yieds 0 d d d r d r U d d θ The firs erm represes he direc effec of raisig. I owers Ψ he afer-ax wage icome ha he youg geeraio ears a period which decreases uiiy. The ehaced ax reveue o he oher had improves he curre primary aace which reduces he ris of he fisca cosoidaio. Tha is 0 / d d d d d < d The aove i ur ehaces expeced reur o capia. This capured i he secod erm of 0 serves o raise he youg s ifeime uiiy. Therefore he comied effec of such ax icreases is o cerai. To resove his amiguiy we rey o simuaio. I Figure 8 we ae he echmar sceario ad depic chages i he ogarihm of he expeced uiiy as wage ax rae icreases from he iiia eve 0%. The differe og correspods o differe eves of ha are pre deermied a period. aes a smaer vaue as he raio icreases refecig he crowdig effec ha i ur owers receivig wages. For a uiiy is decreasig wih he ax rae. This reveas ha he perverse effec of decreasig disposae wage icome due o higher ax raes domiaes he gai from augmeig he expeced U / / / 5

26 reur o capia wih he cosoidaio ris eig reduced. Ieresigy he uiiy oss derived from icreasig wage ax is exaceraed wih puic de-o-capia raio eig raised as a resu. Thus i icreasigy ecomes difficu o raise axes as goverme fiaces worse. We oai mosy he same resus for a oher scearios. I shor he youg househod wi voe agais ax icreases i he pre-cosoidaio regime. Thus preveive measures of he fisca cosoidaio ris wi ever gai poiica suppor from exisig geeraios. The puic de wi e he ef o accumuae ui he regime swich ecomes ieviae whe. To sae i differey he ormaive crieria of fisca susaiaiiy such as he Dormer codiio ad he rasversaiy codiio of he og-erm goverme udge do o iceivize coemporary poiics o uderae fisca resrucurig. Of course he fuure geeraio wi suffer from arge puic de ha owers due o crowdig ou ad reduces heir wages ad ha ca rigger wage ax icreases i he eve of he cosoidaio. Such wefare oss of he fuure geeraio is o icorporaed y curre voers who are assumed o e sefish. Figure 8: xpeced Uiiy.000 xpeced uiiy Wage ax rae /0.5 /0.3 /0.45 /0.6 /0.75 /0.9 The poiica faiure o uderae a resrucurig effor has ee examied i Aesia ad Draze 99 which modeed deayed saiizaio as a war of ariio or a sor of game of chice ewee vesed ieress. They address he fac ha he imig of acua fisca cosoidaio urs ou o e oo ae reaive o he opima imig ha maximizes oi payoff of saehoders. eaed sudies y Veasco 000 ad Ihori ad Iaya 00 cosider puic de accumuaio as a cosequece of a o-cooperaive sugame amog specia ieres groups ha freey exrac resources from he goverme udge. I heir coex fisca resrucurig is feaured as a vouary coriuio for he puic good ha suffers from he free ridig moive. These modes assume 6

27 ifiie ife of ages wihou cooperaio. The prese paper wih is OLG seig addresses he moive of coemporary geeraios o shif he urde of fisca cosoidaio o he fuure uor geeraios ha cao ye voe. The prese mode does o accou for he poiica process of deermiig ax ad expediure raes or ad λ i he pre-cosoidaio regime. aher hese vaues are ae as exogeous. However we have esaished he codiios uder which he iiia ax ad expediure poicies are o correced ad he cosoidaio ris is ehaced as he curre geeraios do o agree o accep a ax hie. 7. Cocudig remar I his paper we aayze he reaioship ewee GB ieres raes ad he fisca cosoidaio rue usig a overappig geeraio mode wih edogeous ad sochasic growh seigs. Our ey fidigs are summarized as foows. GB ieres raes may decie as puic de accumuaes reaive o privae capia as opposed o he coveioa view ha uidup of puic de accompaies a rise of ieres raes. This is cosise wih he seemigy paradoxica circumsaces of GB ieres raes i Japa where raes remai ow despie a puic de raio o GDP ha has ee icreasig for he as severa decades. This paper aso addresses he fac ha fisca cosoidaio rue pays a ey roe i deermiig equiirium ieres raes. Moreover he reaivey sae ierior equiirium may disappear i a discree maer ha shifs he ecoomy o a siuaio i which cosoidaio is ieviae ad GB ieres is quie high. The ormaive sadpoi suggess ha preveive acio shoud e uderae o coai such fisca ris. However precauioary ax icreases o coai puic de o susaiae eves wi o gai he poiica suppor of exisig geeraios whose ife spa is imied. Isead voers prefer o shif he uimae urde of puic de o fuure geeraios ha cao currey voe. Admiedy our mode is highy syized ad asracs some ey issues ha shoud e furher examied i fuure research. These icude he search for he rea hreshod of regime chage ad he imiaio of puic de-o-gdp raio uderae y cairaig our mode o rea ecoomies e.g. he Japaese ecoomy he effec o our mode of ifaio ased o he Fisca Theory of Price Leve as iusraed y Cochrae 00 ad 3 aaysis of aoher voig game e.g. ewee ow ad high icome househods over ax icreases i he pre-cosoidaio regime so as o decrease puic defici. Our sudy woud e more worhwhie if i were possie o show hose resus more geeray. 7

28 Appedix A From he equaios 6. 8 ad 9 he codiio of dyamic efficiecy is represeed as foows: χ r / / / / / A θ / / A / θ θ 8

29 Appedix B Assume o defau. } { PS PS G T G T PS where / / Δ A λ Give o cosoidaio ris he rasversaiy codiio is o fufied if he foowig hods: / / / / / / 0 λ χ λ χ λ Δ Π Δ Π Δ Π Π Π r A A A PS PS Lim / / / Π Π Π where / / Y Y χ / By emma he HS aes a fiie vaue whereas he ef side diverges as he puic de-o-capia raio rises or goes o ifiiy. 9

30 Appedix C We defie df / / / df Δ Τ Φ / / A λ σ where df Τ Φ / 0 / / >< F σ 0 >< F f / σ 0 / / >< Δ Τ Φ f A f λ B- maig use of / / Δ A λ ζ B- 0 f f f ζ / / / / >< Τ Φ Τ Φ A A ζ B- maig use of / / / / Τ Φ f f B- 0 / / / / / >< f A f ζ / / / / / ζ >< A 30

31 efereces Aioi B. Srama T 008. Fisca Poicy ad Fiacia Mares. coomic Joura Aesia A. Draze A. 99. Why are Saiizaios Deayed?. America coomic eview Areao C Defau is ad Icome Fucuaios i mergig coomies. America coomic eview Beroh K. Schuech L. vo Hage J Sovereig is Premia i he uropea Bod Mare. CP Discussio Papers Cochrae J. H. 00. Udersadig Poicy i he Grea ecessio: Some Upeasa Fisca Arihmeic. NB Worig Paper Codogo L. Favero C. Missae A MU ad Goverme Bod Spreads. coomic Poicy ao J. Gersoviz M. 98. De wih Poeia epudiaio: Theoreica ad mpirica Aaysis. eview of coomic Sudies Favero C. Giavazzi F De ad he effecs of fisca poicy. NB Worig Paper. 8. Gae W. Orszag P. 00. The coomic ffecs of Log-Term Fisca Discipie. Tax Poicy Ceer Ura Isiue ad Brooigs Isiuio. Decemer. Ihori T. Iaya J. 00. A Dyamic Mode of Fisca ecosrucio. uropea Joura of Poiica coomy Ieraioa Moeary Fud 009. The Sae of Puic Fiaces: Ouoo ad Medium-Term Poicies Afer he 008 Crisis. Mauscrip IMF Fisca Affairs Deparme. Juesse F. Liema L. Schaer A Defau is Premia o Goverme Bods i a Quaiaive Macroecoomic Mode. Tierge Isiue Discussio Paper 009-0/. Lauach T New videce o he Ieres ae ffecs of Budge Deficis ad De. Joura of he uropea coomic Associaio Magaei S. Woswi G Wha Drives Spreads i he uro Area Goverme Bod Mare?. coomic Poicy Peroi I Search of he Trasmissio Mechaism of Fisca Poicy. NB Macroecoomics Aua omer P Icreasig eurs ad Log-u Growh. Joura of Poiica coomy Urie M A Fisca Theory of Sovereig is. Joura of Moeary coomics Veasco A Des ad Deficis wih Fragmeed Fisca Poicymaig. Joura of Puic coomics