Default Risk on Government Bonds, Deflation, and Inflation

Transcription

1 Defaul Ris on Governmen Bonds, Deflaion, and Inflaion Kazumasa Oguro Moohiro Sao Hiosubashi Universiy Hiosubashi Universiy This version: November 5, 202 Absrac This paper analyzes how deflaion and inflaion influences he real ineres raes of governmen bonds by using an overlapping generaions model. We find ha deflaion may lower he real ineres rae of governmen bonds o he same level of public deb o capial, even if he fiscal consolidaion rule is he same, as opposed o he convenional view ha he real ineres rae of governmen bonds is deermined independen of deflaion if he classical dichoomy holds. Our resuls are consisen wih how he real ineres raes of Japanese governmen bonds reac in periods of deflaion. This paper also addresses he impac of fiscal inflaion i.e., moneizing all pars of he GB s defaul using moneary policy. We calculae he expeced fiscal inflaion when he defaul rae in he even of fiscal consolidaion is raised. The fiscal inflaion may be high if he exen of he required ax increase in fiscal consolidaion is low. Key words: Overlapping generaions model, real ineres rae, fiscal consolidaion rule, defaul ris, fiscal inflaion JEL codes: E7, H30, H5, H60, E62, H63 Corresponding auhor: Kazumasa Oguro, Insiue of Economic Research, Hiosubashi Universiy, 2- Naa, Kuniachi, Toyo , Japan. ZVU07057@nify.com. We would lie o express our graiude o he many people who advised us during he wriing of he firs draf of his paper, paricularly Prof. Toru Naazao, Sophia Univ.; Prof. Taashi Oshio, Hiosubashi Univ.; Prof. Keiichiro Kobayashi, Hiosubashi Univ.; Prof. Yasushi Iwamoo, Toyo Univ. The views expressed herein are hose of he auhors. The responsibiliy for all errors is solely ha of he auhors.

2 2. Inroducion Alhough he fiscal burden has been increasing in all indusrialized counries, Japan s deb-o-gdp raio is he highes among developed naions, even beyond hose of Ialy and Greece, which have recenly faced serious fiscal crises. The susainabiliy of he Japanese fiscal sysem is declining because of is low feriliy rae and aging populaion, wih he Inernaional Moneary Fund 2009 esimaing ha he gross public deb of Japan could reach 277% of GDP by 206. FY200 was he firs year in he pos-war era ha ax revenues declined below governmen bond GB issues in he iniial budge. As he cumulaive ousanding governmen deb coninues o expand, here are growing concerns abou a significan increase in ineres paymens should ineres raes rise in he fuure. The Japanese governmen, herefore, is aiming o raise consumpion ax in wo sages: o 8% in April 204 and o 0% in Ocober 205. The Cabine Office 202 prudenly analyzed Japan s economic and fiscal projecions for he medium o long-erm and suggesed ha even if he consumpion ax rae increases by 205, he primary balance defici of he cenral and local governmens combined in 2020 will reach approximaely 7 rillion yen, which is 3% of GDP. However, Japan s governmen is now facing a so-called Deadloc Die because i lacs sufficien suppor in boh he upper and he lower houses o pass and implemen fiscal reform. Thus, if he ax rae remains a he curren level i.e., 5%, he primary balance defici of he cenral and local governmens combined in 2020 will amoun o 4.5% of GDP. These figures indicae ha furher balance improvemen is necessary o mainain fiscal susainabiliy. In a counry wih such huge public deb, he ineres rae on GBs would hen rise o reflec his defaul ris. Manganelli and Wolswij 2009 poined ou ha wihin he GBs of EU counries, a well-esablished empirical paern shows ha ineres rae spreads are expanding because of increasing public deb-o-gdp raios and ha hese spreads could be inerpreed as reflecing he ris

3 3 of governmens defauling on heir deb obligaions. Codogno e al. 2003, Bernoh e al. 2004, and Aiobi and Sramann 2008 also found he exisence of spreads ha may be inerpreed as a ris premium. Consequenly, IMF 20 warned ha mare concerns over Japanese fiscal susainabiliy may provide a sudden spie in Japanese GB yields ha quicly renders he public deb unsusainable. By conras, he ineres rae on Japanese GBs is currenly lower han hose of oher developed counries and i is declining even hough Japanese public deb coninues o increase. In order o solve his paradox, Oguro and Sao 20 consruced an overlapping generaions model wihin an endogenous and sochasic growh seing. They analyzed he relaionship beween he ineres rae of GBs and he consolidaion fiscal rule and made hree ey findings. Firs, he ineres rae of GBs may be declining because public deb is accumulaed relaive o privae capial where he former crowds ou he laer as opposed o he convenional view ha public deb accompanies a rise in he ineres rae. Second, he fiscal consolidaion rule plays a ey role in deermining he ineres rae in equilibrium. According o his view, he ineres rae of Japanese GBs coninues o remain relaively low because he governmen is promoing fiscal reform and because domesic invesors may believe ha he Japanese governmen will no defaul on is deb obligaions. Third, depopulaion also lowers he ineres rae of GBs o he same level as public deb o capial, even if he fiscal consolidaion rule is he same. However, economic changes imply ha he relaively low ineres rae of GBs may no coninue in he fuure. << Inser Figure abou here. >> Furhermore, Oguro and Sao 20 absraced he role of moneary policy e.g., he effec of deflaion and inflaion on he real ineres rae of GBs. If he classical dichoomy holds, he real

4 4 ineres rae of GBs would be deermined independen of deflaion, by using he Fisher equaion proposed by Fisher 930. However, according o he recen view of he New Keynesian model developed by Maniw and Romer 99, Walsh 2003, and Woodford 2003, inflaion argeing policy affecs real economic growh and he real ineres rae. Therefore, if price dynamics is involved in he model proposed by Oguro and Sao 20, new findings may be shown. As presened in Figure, he long-erm real ineres rae is sable, even hough Japanese public deb coninues o increase. In his mechanism, deflaion may suppress he real ineres rae of GBs because of he arbirage beween privae capial and GBs, hereby pulling down he real reurn on capial. Therefore, in he presen sudy we provide a macroeconomic model in order o analyze he effec of deflaion and inflaion on he real ineres rae of GBs by inegraing price dynamics ino he model of Oguro and Sao 20. We find ha deflaion may lower he real ineres rae of GBs o he same level of public deb o capial, even if he fiscal consolidaion rule is he same, as opposed o he convenional view ha he real ineres rae of GBs is deermined independen of deflaion if he classical dichoomy holds. Our resuls are consisen wih how he real ineres rae of Japanese GBs reacs in periods of deflaion. This paper also addresses he impac of fiscal inflaion i.e., moneizing all pars of he GB s defaul using moneary policy. We calculae expeced fiscal inflaion when he defaul rae in he even of fiscal consolidaion is raised. Fiscal inflaion may be exremely high if he exen of he required ax increase in fiscal consolidaion is low. The remainder of he presen paper is organized as follows. Secion 2 describes he model. In secion 3, we consider fiscal consolidaion and esablish he equilibrium of he real ineres rae of GBs and he expeced fiscal inflaion. In secion 4, we describe he parameers and scenarios for he presened simulaion and discuss he implicaions of he resuls. Secion 5 concludes.

5 5 2. Model Seing 2. Basic Seing Based on he seing proposed by Oguro and Sao 20, we use an overlapping generaions model wih price dynamics e.g., deflaion and inflaion. Specifically, we suppose ha each generaion conains a represenaive household who lives for wo periods. Each period is composed of several sages. In sage, producion shoc is shown. The household of he young generaion supplies labor in sage 2. Then, in sage 3, oupu is realized, wages are paid o he young and he reurn on capial is disribued o he old. The governmen collecs axes and repays public deb in sage 4. In sage 5, young and old households consume he former bu also save by choosing a porfolio. Public deb and privae capial are carried over ino he nex period. Our analysis has wo seps. Firs, we esablish he inra-period or saic equilibrium given he degree of public deb and capial carried over from he previous period. We hen urn o heir dynamics in which economic growh is endogenous and sochasic. 2.2 Producion We use Y o denoe he aggregae real oupu a period ha is produced by a represenaive privae firm. The producion funcion of he economy is given as l Y AK where A >0 is consan, μ>0, and 0<α<. is he produciviy shoc. For he sae of simpliciy, we assume ha he shoc is disribued according o he disribuion funcion F over he inerval [, ] wih E. refers o privae real capial ha is invesed in he previous period and l is labor supply per worer a period. Given ha he populaion of each generaion

6 6 is normalized o one, L l becomes he oal labor supply. K refers o he average real capial invesmen, which represens he exernal effec of capial accumulaion. Following he lieraure on endogenous growh, his may be inerpreed as nowledge spillover ha generaes a scale economy. In equilibrium, we have K We denoe he price level as P in period. Le P / P be he inflaion rae. We rea he inflaion rae as a policy insrumen in he presen model. Anoher ey assumpion is ha he afer ax disposal nominal wage W is deermined prior o period and is sicy. Specifically, his is defined by W P w, where w Y w is he real wage given as where capures he noion of he bargaining power of worers or of he labor union relaive o ha of employers. The wage ax rae is added o accruing o employers and hus heir labor demand. w in order o deermine he labor cos The wage rigidiy is a source of influence ofinflaion on he real economy.in addiion, he assumpion ha he afer ax wage is predeermined highlighs he degree o which he wage ax rae disors he economy. In a more general conex, may imply ha nominal wage rae is parially adjused o inflaion beween periods wih Insead we can regard i as he degree o which he wage ax burden is spli beween worers and employers. Admiedly he presen model lacs micro-foundaion of deermining. We leave i for he fuure research bu ae is as parameer for analyical convenience. Le Y A K be average oupu evaluaed a a full employmen l. In his regard, worers i.e., he labor union do no incorporae he feedbac effec of heir nominal wage seing wihin labor demand. We nex urn o he demand for labor and capial. Given ha w is he ax-inclusive

7 7 labor cos in real erms and ha K is consan, we have: P w P Y / l r Y / 2 ; Throughou he model, we resric parameers so ha l, namely unemploymen exiss. 2.3 Household Problem The household s lifeime uiliy is assumed o ae he following form: y o U c c 3 where θ>0. y c denoes he young period real consumpion, whereas o c is he old period one. Eq. 3 implies ha he household s preference is neural o hese riss. One may find i odd ha ris and ime preferences are separaely defined. Our specificaion deviaes from he sandard seing, which assumes ha he lifeime uiliy is addiive over periods and over differen saes of he economy. The iner-emporal elasiciy is herefore no ied o he inverse of he ris aversion in he presen conex. Eq. 3 is useful o isolae he household s porfolio choice beween privae capial and GB from he decision abou oal real saving s. We now urn o he household s budge consrains. Denoing he price level a period as P, he household s budge consrains for he young and old periods are given by Pc y o Ps P w l P w l 4. P c q Ps R q P s r 4.2 where R is he nominal ineres rae of GBs one plus and q represens he share of GBs in he household s saving. is he defaul rae, aing a value beween zero and uniy. The variables wih ilde sae ha hey are no nown when saving a period. R is deermined a

8 8 period bu wih a defaul ris, he ne reurn on GBs is no cerain. 2 In 4.2, he firs erm of he righ-hand side P s R is inerpreed as he ne reurn on GBs of he nominal saving P s and he second erm of he righ-hand side P s r as he reurn on capial of he nominal saving P s, where P r / P represens one plus capial gain per saving. Based on he hypohesis of he Fiscal Theory of Price Level developed by Leeper 99, Woodford 994, 995, Sims 994, and Cochrane 998, 200, we can inerpre he defaul rae as he effec of fiscal inflaion. 3 If he governmen chooses o moneize all pars of he defaul using moneary policy, / and P holds. 4 P In he young period, he household decides real saving s and chooses porfolio q in order o maximize E U y o c E[ c ] subjec o Eq. 4, where he expecaion is aen over and r. The household s opimizaion yields he following: s * R wl E Er where l / 5.3 Owing o he Cobb Douglas specificaion, he real saving is a fixed share of real wage income afer ax. The income effec and subsiuion effec offse one anoher as given in 5..

9 9 5.2 gives he arbirage condiion beween privae capial and GBs. Given ha he household is ris-neural, he arbirage leads he expeced reurn of boh asses o be equaed, which should be inuiive. 2.4 Mare Equilibrium This subsecion considers he mare equilibrium given he prevailing fiscal policy. In every period, boh labor and capial mares are cleared. Given and, he equilibrium values of real wage and real reurn on privae capial a period are deermined by subsiuing and 5. ino 2 so ha w A K 6. / r AK 6.2 Consider he exernal effec. In equilibrium, we have K, he capial invesmen in mare being exacly equal o he average in he economy. In addiion, we se he parameer associaed wih he exernaliy so ha he equilibrium real oupu is proporional o privae capial. The following assumpion provided by Romer 986 is imposed: Assumpion Then, real oupu urns ou o be A / Y 7 The above is familiar in he endogenous growh model, which yields consan real growh rae as a funcion of policy parameers. The real wage rae is linear wih respec o as well, whereas he real reurn on privae capial urns ou o be independen of :

10 0 w 6. A A / r 6.2 Lasly, we urn o he capial mare. Because of he closed economy, household savings mus mee he demand of privae firms and he governmen. Denoed by b is he real value of GBs issued a period and repaid a +. 5 Given ha he oal real saving a period is s, which is allocaed beween and b, he equilibrium condiion is expressed by b s * A / / 8 Manipulaing he above esablishes he dynamics of privae capial accumulaion as he following: b / A / Governmen Budge The governmen raises revenue by issuing GBs and axing wage income. I hen spends on deb repaymen and he real value of public expendiure, he laer being denoed by G. G is assumed no o conribue o producion or direcly ener he household s uiliy 3. This assumpion is moivaed o simplify our analysis, bu i may be plausible when he governmen spending comprises mosly poliical rens or por divered o special ineres groups. The fund flow of he governmen budge a period is wrien as P b P Rb P { T G } 0

11 where Y and Y is given in 7. P b T denoes he nominal value of GBs issued a period. In he oher wo erms, P is muliplied o conver hem o nominal variables. A his poin, we disinguish he fiscal rule beween he pre-fiscal consolidaion and he fiscal consolidaion regimes. This is denoed by,, }, which conains ax rae, governmen expendiure raio {, and defaul rae /, and may be sae coningen in he consolidaion regime. The fiscal rules are assumed o be public informaion, implying ha hey are incorporaed ino he pricing of GBs as discussed below. In he presen mode, we insead ae he pragmaic view ha governmen policy is largely poliically consrained, so i does no aim o opimize social welfare. 0 Le {,, } wih 0. In he pre-consolidaion regime, he governmen axes wage income a he rae of and spends a given porion of he poenial real oupu ha calculaes Y a he mean of, i.e., and a, so ha G Y where / Y A G remains proporional o Y defined above in he consolidaion regime as illusraed laer. Wih and 2, he real value of he primary surplus a period is defined by PS T G A /,, 2 where,, / / / Subsiuing 2 ino 0 and manipulaing i esablishes he dynamics of he public deb over

12 2 periods: b R b A /,, 3 where / is as given in 8. Noe ha in he presen economy, b / as well as serve as sae variables ha are deermined a period and carried over o period +. This affecs he ris of fiscal consolidaion a +, as discussed in secion Equilibrium 3. Fiscal Susainabiliy 0 The fiscal rule {,, } in he pre-consolidaion regime does no ensure ha public deb remains a a fiscally susainable level. The ax rae may be oo low and/or he expendiure raio oo high, which srucurally generaes a primary defici, i.e.,,, 0 for mos of. Then, public deb may reach a level a which he saus quo fiscal rule canno be susained. Given he use of he overlapping generaions model in his sudy, he capial mare may no discipline governmen financing because households are no necessarily concerned abou long-run fiscal susainabiliy. Unless = for sure, wih ris-neural preferences, households are willing o purchase GBs as long as 5.3 holds, wih he defaul ris compensaed by a higher ex ane promised nominal ineres rae. In he presen conex, herefore, he governmen can access credi as long as he GB level does no exceed domesic saving wih he ineres rae fulfilling 5.3. Suppose, however, ha he economy reaches b 2 s, ha is, he domesic saving a period + is fully absorbed by

13 3 governmen borrowing. Given ha he economy is closed, no privae invesmen can ae place, which implies ha here is no producion in he subsequen period or Y 2 0 for all 2. Once his occurs, he governmen can find no resource for repaymen. I hen has o defaul on he deb so ha 2 = is cerain and ha here is no reurn on GBs. 6 This in urn implies ha he household ceases o lend o he governmen. The governmen is hen forced o underae fiscal consolidaion wihou furher borrowing. This enails ax increases, expendiure reducions, and he defaul on GBs. Lemma : Full defaul is ineviable a period + irrespecive of 2 when b 2 s. 3.2 Threshold Wih b 2 s or 2 0, we have b / 2 a period +. Insering his ino 3 and manipulaing i yields he following condiion of he hreshold level of, which he regime change arises: R b / A / / ˆ 4 ˆ The above defines he hreshold implicily as he funcion of he ineres rae charged on b as well as he deb-o-capial raio and demography: ˆ R, Z ˆ, where Z b /,. Wih R and b /, ˆ increases so ha fiscal consolidaion is more liely o be in place, whereas i is lowered wih.

14 4 Lemma 2: Fiscal consolidaion mus occur a period + when ˆ The fiscal consolidaion rule involves ax increases, expendiure reducions, and he defaul on GBs. We denoe he sae of he economy a period + by, b /,. The fiscal rule is hen expressed as wih b 0 ha conains 2,, 0 where he defaul rae / fulfills 7 R b A /,, 5 The governmen canno fully mee is obligaion bu repays is ousanding deb as much as possible ou of he primary surplus, as illusraed in 5. Under he consolidaion rule, ax rae, expendiure raio, or defaul rae deviaes from he iniial levels. The fiscal rule can ae he general form. In he simulaion shown in secion 4, we specify he fiscal consolidaion rule. Noe ha i aes only one period o resrucure governmen finance. Given ha no GBs are issued, he economy will reurn o he iniial regime in he nex period wih no deb liabiliy being carried over. 3.3 Nominal Ineres Rae Le us now urn o he nominal ineres rae of GBs R ha is seled a period, accouning for he fiscal consolidaion in he even of ˆ. Recall he arbirae condiion 5.3 ha equaes reurn on GB and capial in he expeced erm. Manipulaing his using 6.2 and 5 esablishes he following:

15 5,,, ˆ ˆ ˆ / df b A R F 6 where ˆ / ˆ / ˆ df df / / /,,, Noe ha reflecs he expeced reurn on privae capial. I is clear o see ha his is non-increasing wih he hreshold level given ha. Eq. 6 yields he nominal ineres rae of GBs as a funcion of he hreshold, he deb-o-capial raio, and he populaion:, ˆ Z R R. 3.4 Ineracion There exiss ineracion beween he hreshold of fiscal consolidaion ˆ and he nominal ineres rae of GBs R defined by 4 and 6, respecively. By solving hese equaions, heir equilibrium values can be obained. Noe ha hese are assessed from period or an ex ane perspecive when is no nown and fiscal consolidaion is no ye in place. Proposiion : Denoed by * R and * ˆ are he equilibrium levels of he nominal ineres rae of GBs and he hreshold of fiscal consolidaion condiional upon / b and he consolidaion rule. These are given as soluions o he following equaions:

16 6 ˆ / / / A b R,,, ˆ ˆ ˆ / df b A R F In he above proposiion, we do no preclude he case ha here arise muliple equilibria, he wo equaions inersecing more han wice or he equilibrium diverges, * ˆ reaching as shown by Oguro and Sao 20. In addiion, by insering he soluion ino 5 and aing he expecaion, we can obain he following proposiion: Proposiion 2: Wih he deb-o-capial raio / b and he consolidaion rule, fiscal inflaion ha is calculaed in he expeced erm is given as follows:,, ] [ ˆ / F df A b R E 7 4 Simulaion 4. Parameer Seing and Scenarios By using he simulaion developed in secion 3, he aim of his secion is o analyze he impacs of deflaion and inflaion on he real ineres rae of GBs and he hreshold ha he consolidaion occurs given b / a period. Moreover, we calculae he fiscal inflaion of 7 and he hreshold ha he consolidaion occurs given b / a period. Our quaniaive analysis does no inend o replicae any pracice of economy. Raher, i aims o supplemen our heoreical model, resolve he ambiguiy of is resuls, and clarify is policy implicaions. The parameers are specified in Table. disribues over [0.5.5] according o he inverse

17 7 U-shaped densiy funcion wih a mean of one. We se he ax rae o be relaively low 0% and he expendiure rae a 0% of poenial oupu as well. This implies ha a primary defici is liely o resul unless is larger han he mean of one, so here exiss he possibiliy ha public deb is accumulaed as consolidaion ris is enhanced. The fiscal consolidaion rule demands ha expendiure be cu o The wage ax rae under consolidaion is assumed o be increasing in, whereas i increases wih b /. This is specified as in Table. The consolidaion rule relies on more ax increases for large deb-o-capial raios, whereas he defaul rae / is raised when is small and so he economy is depressed. Such a presumpion should be plausible. The parameer g in he ax funcion refers o he exen of he required ax increase. The simulaion ses wo values for g: g=2 and g=5. A higher g value implies larger ax increases in fiscal consolidaion, which in urn implies lower fiscal inflaion. This is defined as residual by 7. By comparing he resuls of differen levels of g, we can assess he effec of he fiscal rule on R * and * ˆ as well as he ransiion of he deb-o-capial raio. In order o examine he impacs of deflaion and inflaion, we consider hree cases: zero inflaion 0, 2 0.5% deflaion per annum , and 3 0.5% inflaion per annum Here, we ae one period in our model o represen 30 years. Disinguished by he parameer g and he price dynamics, six scenarios are presened in Table 2. << Inser Tables and 2 abou here. >> 4.2 Resuls In his secion, we focus on he inerior equilibrium in he simulaion. The real ineres rae of

18 8 GBs for he six scenarios are shown as in Figures 2 and 3, where b / is reaed paramerically on horizonal axis. 8 Figure 2 is relaed o Scenarios o 3 wih g=2 and Figure 3 relaed o Scenarios 4 o 6 wih g=5. In Figure 2 wih g=2, we ae Scenario wih zero inflaion 0. The real ineres rae of GBs is gradually increasing wih b /. A b / =0.65, he sable inerior level of he real ineres rae of GBs disappears. Scenario is compared wih Scenarios 2 and 3 in order o assess he impacs of deflaion and inflaion. The real ineres rae of GBs in Scenario 2 wih 0.39and ha in Scenario 3 wih 0. 6 differ from ha in Scenario. A he same level of b /, he real ineres rae of GBs in Scenario 2 is lower and ha in Scenario 3 higher han ha in Scenario. In Scenario 2, he sable inerior level of he real ineres rae of GBs disappears a b / =0.585 and in Scenario 3 i disappears a b / = We now urn o Figure 3 wih g=5. In Scenarios 4 o 6, here exiss a range in which he real ineres rae of GBs shows downward sloping, confirming he heoreical hypohesis of Oguro and Sao 20. Figure 3 has wo verical scales. The lef-hand scale of he figure shows he level of he real ineres rae of GBs and he righ-hand scale he difference beween he real ineres rae of GBs a b / and ha a b /. Tae Scenario 4 wih zero inflaion 0. The real ineres rae of GBs iniially declines wih b /. Is moderae downward rend coninues unil b / =.32 where he real ineres rae of GBs aes is minimum value. The slope is hen reversed, furher increasing he deb-o-capial raio and rapidly raising he real ineres rae. A b / =.44, he sable inerior level of he real ineres rae of GBs disappears. Scenario 4 is also compared wih Scenarios 5 and 6 in order o assess he impacs of deflaion and inflaion. A he same level of b /, he real ineres rae of GBs in Scenario 5 is lower and ha in Scenario 6 higher han ha in Scenario 4. In Scenario 5, he sable inerior level of he real ineres rae of GBs disappears a b / =.335, and in Scenario 6 a b / =.485. Inflaion can susain he

19 9 inerior equilibrium for larger b / compared wih deflaion. I can be hus concluded ha deflaion lowers he real ineres rae of GBs, bu does no susain he inerior equilibrium. << Inser Figures 2 and 3 abou here. >> Consider he hreshold of he regime change * ˆ. In all scenarios, his monoonically increases in b / as shown in Figures 4 and 5. By comparing hese figures wih differen consolidaion rules, * ˆ says lower when he ax increase in he consideraion is larger i.e., g is high, reflecing a lower ineres rae. The prospec for large ax increases in he even of fiscal resrucuring, which conribues o lowering he defaul rae, only serves o miigae consolidaion ris, which should be inuiive. The ris is refleced in he GB premium, which is defined as he difference beween he real ineres rae of GBs and he expeced real reurn on capial. The premium remains negligible when ris is low: according o consolidaion ris, he revenue deficiency is largely filled by ax increases and expendiure reducions. The defaul rae in he even of consolidaion is raised as he deb-o-capial raio increases, which in urn augmens he premium. To see he effec of deflaion and inflaion on * ˆ, we compare Scenario Scenario 4 wih Scenarios 2 and 3 Scenarios 5 and 6. The simulaion esablishes ha he hreshold is lowered in he case of inflaion and rises in he case of deflaion. << Inser Figures 4 and 5 abou here. >> We now urn o fiscal inflaion, which is calculaed in he expeced erm as in 7. The expeced fiscal inflaion is lowered as he ax increase in he consolidaion grows i.e., g is high.

20 20 Figures 6 and 7 show fiscal inflaion from he perspecive of period +. 9 In Figure 6, for b / <0.35, fiscal inflaion is low in Scenarios o 3. However, afer ha, i monoonically increases in b / as shown in he figure. A he near poins of b / =0.60 in Scenario, i reaches over 20%. A he near poins of b / =0.57 in Scenario 2, i reaches over 24%. This indicaes he impac of fiscal inflaion i.e., moneizing all pars of he defaul using moneary policy. In Figure 7, he expeced fiscal inflaion also monoonically increases in b /. A he same level of b /, i is lower han ha in Figure 6 because of he larger ax increase in he consolidaion i.e., higher g. For b / >0.375, he dispariy becomes prominen. A he same level of b /, fiscal inflaion in Scenario 6 wih 0. 6says lower han ha in Scenario 4 wih zero inflaion and ha in Scenario 5 wih is higher han in Scenario 4. I can be hus concluded ha iniial inflaion reduces he expeced fiscal inflaion when he defaul rae in he even of consolidaion is raised. In addiion, he fiscal inflaion in Scenario 4 reaches 27.7% a b / =.425, ha in Scenario % a b / =.32, and ha in Scenario 6 24.% a b / =.485. << Inser Figures 6 and 7 abou here. >> 5 Conclusion In his paper, we analyze he impac of deflaion and inflaion on he real ineres rae of GBs, using an overlapping generaions model wih he relaionship beween he real ineres rae of GBs and he fiscal consolidaion rule. Our ey findings are summarized as follows. Deflaion may lower he real ineres rae of GBs o he same level of public deb o capial, even if he fiscal consolidaion rule is same, as opposed o he convenional view ha he real ineres rae of GBs is

21 2 deermined independen of deflaion if he classical dichoomy equaion holds. Our resuls are consisen wih how he real ineres rae of Japanese GBs reacs in siuaions of deflaion. This paper also addresses he impac of fiscal inflaion i.e., moneizing all pars of he GB s defaul using moneary policy. We calculae he expeced fiscal inflaion when he defaul rae in he even of fiscal consolidaion is raised. The fiscal inflaion may be high if he exen of he required ax increase in fiscal consolidaion is low. Our model is highly sylized and highlighs cerain issues ha should be examined in fuure research. These issues include he search for he acual hreshold of regime change and he limiaion of using he public deb-o-gdp raio in he Japanese economy, 2 he effec on our model of he financial crisis, especially he ban runs Diamond & Dybvig 983; Diamond & Rajan 200; Allen & Gale 998; Uhlig 200 caused by he defaul of GBs, and 3 he analysis of he hreshold of regime change and he limiaion of he public deb-o-gdp raio in an open economy.

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23 23 Inernaional Moneary Fund 20. Japan Susainabiliy Repor. Manuscrip, Saff of he IMF. Leeper E. M. 99. Equilibria under acive and passive moneary policies. Journal of Moneary Economics, 27, Manganelli S. & Wolswij G Wha drives spreads in he Euro area governmen bond mare? Economic Policy, 58, Maniw N. G. & Romer D. 99. New Keynesian Economics, and 2. MIT Press. Oguro K. & Sao M. 20. Public deb accumulaion and fiscal consolidaion. Cener for Inergeneraional Sudies, Insiue of Economic Research, Hiosubashi Universiy, Discussion Paper Series 57. Romer P Increasing reurns and long-run growh. Journal of Poliical Economy, 94, Sims C A simple model for he sudy of he deerminaion of he price level and he ineracion of moneary and fiscal policy. Economic Theory, 4, Uhlig H A model of a sysemic ban run. Journal of Moneary Economics, 57, Walsh C. E Moneary Theory and Policy, 2 nd edn. MIT Press. Woodford M Moneary policy and price level deerminacy in a cash in advance economy. Economic Theory, 4, Woodford M Price level deerminacy wihou conrol of a moneary aggregae. Carnegie-Rocheser Conference Series on Public Policy, 43, 46. Woodford M Ineres and Prices: Foundaions of a Theory of Moneary Policy. Princeon Universiy Press.

24 24 If he labor mare is in full employmen, l. 2 In 4.2, we absrac idiosyncraic ris including he banrupcy of he privae capial. This presumes ha he household can fully diversify such ris and ha only he aggregae shoc remains. 3 In his paper, we assume ha alhough moneary policy deermines price level, i passively follows acive fiscal policy. 4 In he case, we obain o P c q Ps R q P s r from We consider only a single period bond in order o absrac issues of bond mauriy composiion. 6 However, reurn on privae capial remains posiive wih he revenue maximizing ax rae being bounded by less han 00%. 7 Noe ha wih fiscal inflaion P P P P 8 The real ineres rae of GBs is calculaed from he nominal ineres rae of GBs R and price dynamics. 9 In his paper, alhough one period in our model is 30 years, we assume ha fiscal inflaion finishes afer hree years. Therefore, he expeced fiscal inflaion in Figures 6 and 7 are calculaed as 3 E [ ] /. *

25 25 Table Parameers Parameers Values A {,, } τ=0. λ=0. b, b / Min g, 3. 8, b / Scenarios Table 2 Scenarios The exen of he required ax increase Price dynamics g g g g g g

26 Figure : Public deb o GDP, Long-erm Real Ineres Rae and Deflaion % Inflaion as measured by he growh rae of GDP deflaor General governmen gross financial liabiliies percen of GDP Long-erm real ineres rae Year

27 Figure 2: The Real Ineres Rae of GBs in Scenarios o 3 g Scenario Scenario 2 Scenario The public deb o capial raio Figure 3: The Real Ineres Rae of GBs in Scenarios 4 o 6 g The public deb o capial raio Scenario 4 Scenario 5 Scenario 6 Difference of Scenario 4 Difference of Scenario 5 Difference of Scenario 6

28 Figure 4: Threshold in Scenarios o 3 g 2 Scenario Scenario 2 Scenario 3 The public deb o capial raio Figure 5: Threshold in Scenarios 4 o 6 g 5 Scenario 4 Scenario 5 Scenario 6 The public deb o capial raio

29 Figure 6: Fiscal inflaion in Scenarios o 3 g % 25.0% 20.0% Scenario Scenario 2 Scenario 3 5.0% 0.0% 5.0% 0.0% The public deb o capial raio Figure 7: Fiscal inflaion in Scenarios 4 o 6 g % 30.0% 25.0% Scenario 4 Scenario 5 Scenario % 5.0% 0.0% 5.0% 0.0% The public deb o capial raio