Public Debt Accumulation and Fiscal Consolidation

Transcription

1 Puic De Accumuaion and Fisca Consoidaion Kazumasa Oguro Hiosuashi Universiy Moohiro Sao Hiosuashi Universiy Asrac In his sudy we anayze he reaionship eween he ineres raes of governmen onds GB and he fisca consoidaion rue y using an overapping generaion mode wih endogenous and sochasic growh seings Our ey findings are summarized as foows Firs he ineres raes of GB may e decining as puic de accumuaes reaive o privae capia as opposed o he conveniona view ha he uidup of puic de accompanies a rise in ineres raes Second he fisca consoidaion rue pays a ey roe in deermining ineres raes in equiirium Third he economy may exhii discree changes wih divergen ineres raes impying ha our oservaion of reaivey ow GB ineres raes does no ensure he coninuaion of ha rend in he fuure Fourh a prevenive ax increase o conain puic de a susainae eves wi no gain he poiica suppor of exising generaions whose ife-span is imied Ciizens prefer o shif he uimae urden of puic de o fuure generaions JEL cassificaions: E7; H3; H5; H6; E62; H63 Keywords: Overapping generaion mode; ineres rae on governmen onds; fisca consoidaion rue; defau ris

2 Inroducion Puic de as a percenage of gross domesic produc GDP has receny een increasing in deveoped counries Japan s gross puic de GDP raio was especiay high in 2 compared o hose of oher deveoped counries The Inernaiona Moneary Fund 29 esimaes ha Japan s gross puic de coud reach 277% of GDP y 26 In addiion Japan s ne puic de GDP raio was aso higher han ha of oher deveoped counries in 2 In such circumsances he ineres raes of governmen onds GB heoreicay rise as a refecion of defau ris as shown y Manganei and Woswi 29 Codogno e a 23 Bernoh e a 24 and Aioi and Sramann 28 have each aso found he exisence of spreads ha may e inerpreed as ris premiums On he oher hand he ineres raes of Japanese Governmen Bonds JGB have een ower han hose of oher deveoped counries governmen onds In addiion we can oserve ha he ineres raes of JGB are curreny decining even hough Japanese puic de coninues o increase see Figure Ahough einhar e a 22 found ha in of he 26 high-de overhang cases in advanced economies ineres raes on governmen onds were eiher ower or aou he same as during he years of ower puic de GDP raios he driving mechanism is uncear A reevan mode and mechanism are required o iusrae a seemingy paradoxica confuence of rends The foowing possiiiies are considered as faces of he mechanism: he refecion of defau ris for JGB is wea ecause 95% of JGB are hed y domesic invesors; 2 domesic invesors may eieve ha he Japanese governmen wi no defau on is de oigaions ecause here are severa fisca reform opporuniies eg consumpion ax increases ha coud hep mainain fisca susainaiiy; 2 and 3 domesic and foreign invesors eieve ha he ineres raes on JGB are ow ecause economic growh whie he counry s popuaion is oh aging and decining is aso expeced o e ow Despie hese possie drivers he mechanism ehind he curren decine in ineres raes on JGB remains uncear and here is no mode ha expains i One compicaion is ha GB ineres raes aso depend on fisca poicy: in paricuar he fisca consoidaion rue which invoves eg ax increases expendiure cus and defauing on onds is imporan as governmens canno aways According o he OECD Economic Ouoo 9 daaase he genera governmen ne financia iaiiies GDP raio of Japan in 2 was 276%; ha of he Unied Saes 738%; Unied Kingdom 67%; Ausraia 49%; Canada 336%; France 627%; Germany 55%; Iay 2%; and Greece 33% 2 Braun and Naaima 22 examine he case of puic ond ue in which differen invesors possess differen prospecs for de crisis wih imperfec capia mare They esaish ha ond price does no immediaey respond o he possiiiy of he crisis and hus is ineres rae remains ow Their mode is ased upon exchange economy however asracing producion 2

3 ro over puic de o fuure adminisraions and generaions Gae and Orszag 22 and Lauach 29 have poined ou ha he response of GB ineres raes o fisca poicy depends on expecaions aou he fuure course of fisca poicy Peroi 27 and Favero and Giavazzi 27 aso have found evidence of a change in he reaionship eween macro-eve variaes and fisca poicy; his change has een inerpreed as evidence of a change in reacions of fisca poicy o a saiizaion of he puic de GDP raio Urie 26 and Juessen e a 29 have anayzed governmen defau ris and is refecion on GB ineres raes each y using a quaniaive macroeconomic mode However Urie 26 focuses on exerna de wihin an open economy In he case of exerna de defauing is considered a deierae sraegic decision of he governmen ha refecs he oucome of an opimizaion proem eg Eaon and Gersoviz 98; Areano 28 Ahough Juessen e a 29 focus on inerna de using a mode and a cosed economy hese heoreica sudies never examine he poenia effecs of he fisca consoidaion rue on ineres raes Therefore we provide a macroeconomic mode o expain he imporance of he fisca consoidaion rue and his mode carifies he reaionship eween decreasing GB ineres raes and increasing puic de Figure Japan governmen ond ineres raes vs puic de % Genera governmen ne financia iaiiies percen of GDP Long-erm ineres rae Year Source: OECD Sas Exracs There are a numer of assumpions inheren in his sudy We consider overapping generaion modes ha use endogenous and sochasic growh seings Producion echnoogy conains spiover associaed wih privae capia and produciviy shoc Each generaion comprises a represenaive househod ha ives for wo periods; we aso accoun for demographic changes in he economy Popuaion growh is assumed o e nown u can vary over ime In he young period he 3

4 househod suppies aor in an easic manner Taxes are evied on wages and par of afer-ax wage income is saved We aso assume ha here are wo ypes of asses ha are ax-free: privae capia and GB The former yieds uncerain reurns due o he produciviy shoc of he susequen period and he aer promises a fixed reurn u aso a ris of defau Unie Juessen e a 29 we consider ha defau may e paria In he od period he househod is reired and receives reurns on privae capia and GBs The ey findings of his sudy can e summarized as foows The ineres rae of GB may decine as puic de accumuaes reaive o privae capia as found y einhar e a 22 so he former may crowd ou he aer; his scenario conrass wih he conveniona view ha an accumuaion of puic de accompanies an increase in ineres rae The prospec of fuure ax increases due o he fac ha he fisca consoidaion rue serves o ower expeced reurns on privae capia which in urn decreases hrough arirage ineres raes charged on GB We esaish ha he fisca consoidaion rue pays a ey roe in deermining equiirium ineres raes In addiion he economy may exhii discree changes and divergen ineres raes impying ha a rend wherein here is a decine in GB ineres raes may no coninue as puic de coninues o accumuae We aso show ha any prevenive ax increases o conain puic de wi no gain he poiica suppor of exising generaions whose ife-span and herefore heir period of sef-ineres is imied; insead ciizens prefer o shif he uimae urden of puic de o fuure generaions who canno curreny voe This finding aigns wih he commony hed eief ha puic de is expoiaive of fuure generaions The res of his paper is organized as foows Secion 2 descries he mode and Secion 3 considers he fisca consoidaion rue and esaishes equiirium GB ineres raes Secion 4 uses he equiirium in he anaysis of comparaive saics In Secion 5 we carify our heoreica argumen y simuaion and discuss he impicaions of he resus and Secion 6 concudes 2 Mode Seings 2 Basic seing In his sudy we empoy a sochasic overapping generaion mode wih endogenous growh seing Foowing he ieraure we consider oh human and physica capia as driving force for economic growh The former aes form of educaiona expense ha enhances effecive aor u is disored y wage axaion whereas he aer generaing spiover is crowded ou y puic de The mode is 4

5 highy syized and does no inend o repicae he reaiies of economy aher i is consruced in a way o highigh he essence of fisca consoidaion ris In his mode each generaion conains a represenaive househod ha ives for wo periods; in each period a singe good is produced y aor and capia and he producion is sochasic due o echnoogy shoc In he presen mode producion shoc feaures economic saes ha in urn affec he accumuaion of puic de We suppose ha he saes are argey divided ino norma and high-performance regimes The aer is an uniey even u i coud resove de overhangs as he governmen can raise sufficien ax revenue o mee de iaiiy wihou overy reying on a new de issuance I incorporaes he opimisic view ha a fisca consoidaion wi no e required once high economic growh can e achieved eaed o his Imrohorogu and Sudo 2 esimae ha unprecedenedy high growh of oa facor produciviy a an average of 6% for one decade mus e in pace for Japan o eiminae he ousanding de Such opimisic view for growh mirace seems o e impici in he argumen agains ax hie and massive expendiure cu o resrucure puic finance ofen capuring popuariy among peope even when accumuaing puic de is ceary unsusainae Each period is divided ino severa sages A Sage producion shoc is reveaed The househod of he young generaion suppies effecive aor a Sage 2 Then oupu is reaized a Sage 3 whereupon a wage is paid o he young and a reurn on capia is disriued o he od The governmen coecs axes and repays puic de a Sage 4 A Sage 5 he young and he od househods consume whie aso saving and choosing a porfoio Puic de and privae capia are hen carried forward o he nex period In he foowing o carify our anaysis foows wo seps Firs we esaish an inra-period or saic equiirium given puic de and capia carried over from he previous period We hen urn o dynamics Economic growh is endogenous and sochasic due o produciviy shoc 22 Producion Y denoes he aggregae oupu a period ha is produced y a represenaive privae firm The producion funcion of he economy is given as Y A K ne a A K where he dynamic of he echnoogica progress is represened as a and A > is consan μ > 5

6 and < α < denoes produciviy shoc is a consan parameer ha is defined aer represens privae physica capia ha is invesed in he previous period and e represens human effecive aor suppy per worer a period The popuaion of generaion is denoed y 2 Then E n e gives he oa size of aor as an effecive erm K n = refers o he average capia invesmen and represens he exerna effec of capia accumuaion; foowing he ieraure on endogenous growh i may e inerpreed as nowedge spiover ha serves as pure puic generaing an economy of scae omer 986 In he equiirium we have K We assume ha he shoc is disriued according o he disriuion funcion F f d over [ ] wih E Is suppor can e divided ino wo ranges Assumpion [ ] [ ] { } wih eing sufficieny arge and is sma wih f d eing infiniesima [ ] refers o he norma regime of he economy whereas { } corresponds o he uniey even of high performance; in he aer he fisca consoidaion ris is removed Suppose ha producion is perfecy compeiive The price of oupu eing normaized o uniy we can wrie he wage and reurn on capia as 2 w Y / E ; r Y / As is cusomary in he ieraure he mare ransacion fais o accoun for he spiover effec in deermining he reurn on capia 23 The househod proem Consider he househod proem The househod iving for wo periods choose consumpion and hus saving as we as effecive aor suppy In he presen conex we assume ha he effecive aor is enhanced y educaiona expense Is udge consrains a he young and he od periods are respecivey given y where 3 rae and / y e c s e / ~ o ~ c s q q ~ r 32 is wage income ax w is afer ax wages is he GB s one pus ineres q represens he share of he GB in oa savings represens he defau rae as a vaue eween and uniy The variaes wih ide address unnown quaniies when saving a period is deermined a period wih defau ris; he ne reurn on GB is no cerain 3 The 3 In Secion 32 we asrac idiosyncraic ris incuding he anrupcy of privae capia This presumes ha he househod can fuy diversify such ris and ha ony aggregae shoc wi remain 6

7 househod is confroned wih riss of oh produciviy shoc and governmen defau in he susequen period when maing saving decisions The second erm in 3 designaes he cos of educaion which serves o increase effecive aor suppy e whie aor hours are aen as uniy capures he decreasing margina reurn on educaion We suppose ha such a cos aes he form of pecuniary expenses and for he sae of simpiciy i is conemporary expense Tha is educaiona invesmen occurs in he same period as aor eing suppied Admiedy his asracs dynamic characerisics of human capia invesmen u is convenien way o formuae he essence See for insance Bovenerg and Jacos 25 In addiion we aow e o e unounded The effecive aor suppy is decided ony afer ecomes nown and eners he udge consrain so ha i responds o afer-ax wage hus asracing income effec This simpificaion aigns wih he ieraure on opima income axaion Given ha each generaion wors ony in one period he human capia is no accumuaed and carried over o he nex period Le us urn o he househod s ifeime uiiy I is assumed o ae he foowing form: y o 4 c c where θ > U y c denoes he young period of consumpion whereas o c is he oder period Eq 4 impies ha is preference is neura o hese riss Given he Co Dougas form of he uiiy funcion however he iner-empora easiciy of susiuion urns ou o e uniy One may find i odd ha ris and ime preferences are defined separaey; our specificaion deviaes from he sandard seing ha assumes ha ifeime uiiy is addiive over periods and over differen economic saes In he presen conex iner-empora easiciy is no ied o he inverse of ris aversion Admiedy ad hoc Eq 4 heps isoae he househod s porfoio choice eween privae capia and GB from he decision on oa savings s Le us susiue 3 ino he uiiy funcion In he young period he househod decides effecive aor suppy e saves E U s and chooses porfoio e / q o maximize reurns: / ~ e s s E q q r where he expecaion is cacuaed over and r The househod s opimizaion yieds he foowing: 5 52 e z s ~ 7

8 and ~ 6 ~ E Er where z e / e / By 5 he wage easiciy of effecive aor suppy is consan a δ Wage axaion ecomes disorive as easiciy increases Admiedy he endogenous educaion expense capures ony a par of he ax-induced inefficiency In a more genera conex he disorion wi e ariuae o choices vis-à-vis ris-aing occupaiona choice and aor hours as we as ax-avoidance aciviies ha diver some resources from producion δ may e hen regarded as a parameer ha represens a syized noion of he perverse effec of ax on economic growh Due o he Co Dougas specificaion savings is a fixed share of he wage income ne of he aor disuiiy z wih he income effec and susiuion effec offseing one anoher as given in 52 Finay 6 gives he arirage condiion eween privae capia and he GB Given ha he househod is ris-neura arirage eads o he equaion of expeced reurn of oh asses which shoud e inuiive 24 Mare equiirium This susecion considers mare equiirium given fisca poicy A every period oh he aor and capia mares are ceared Given and he equiirium vaues of wage and reurn on privae capia a period are deermined y susiuing 5 ino 2 such ha 7 w A K / n / / / / 72 r A K The oupu a period ecomes / n / / / 8 Y A Consider he exerna effec: in he equiirium we have K / / n K wih he capia invesmen in mare eing exacy equa o he average in he economy In addiion we se he parameer associaed wih exernaiy such ha he equiirium oupu is proporiona o privae capia The foowing assumpion is imposed: Noe ha Assumpion 2 if δ = or if he effecive aor suppy is compeey ineasic as assumed y 8

9 omer 986 We aso e / for exposiiona convenience Then 8 urns ou o e / / 8 Y A n The aove is famiiar in he endogenous growh mode which yieds consan growh raes as a funcion of poicy parameers The wage rae is inear wih respec o on privae capia urns ou o e independen of : / / 7 w n A / / 72 r A n as we whereas he reurn Finay we urn o he capia mare Because of he cosed economy househod savings mus mee he demand of privae firms and he governmen denoes GBs issued a period and repaid a + 4 Given ha oa savings a period is n s as aocaed eween and equiirium condiion is expressed y 9 n s / n / A Manipuaing he aove esaishes he dynamics of privae capia accumuaion as he foowing: / / 9 n A he Now e us consider he growh rae This economy grows a he rae of which is sochasic and defined as ~ / / Y ~ ~ n ~ Y n Compared o he growh mode conaining agens earing an infinie ife he OLG may exhii dynamic inefficiency in which he growh rae ecomes more han he ineres rae The foowing emma yieds he condiion ha he economy remains dynamicay efficien: Lemma : The economy is dynamic efficien or r if Proof of his is shown in Appendix A Throughou he paper we assume ha he aove inequaiy hods 25 Governmen udge The governmen raises revenue y issuing GB and axing wage income; hen spends his revenue on de repaymen and puic expendiure he aer of which is denoed y G G is assumed no 4 We consider ony a singe-period ond and hus we asrac issues of ond mauriy composiion 9

10 o conriue o producion or direcy ener ino househod uiiy 3 This assumpion is moivaed o simpify our anaysis u may e pausie when governmen spending comprises poiica rens or so-caed por divered o specia ineres groups The funding fow of he governmen udge a period is wrien as where { T G } T w L Y and Y is given in 8 is puic de carried over o he nex period The governmen may hod financia asses such as pension funds Eq incorporaes such a circumsance y inerpreing in erms of ne de For he aer use he foowing emma esaishes he revenue-maximizing ax rae ha deermines he upper ounds for ax raes in he case of fisca consoidaion: Lemma 2: Tax revenue is maximized a Max A his poin we disinguish fisca rue eween pre-fisca consoidaion and fisca consoidaion regimes This is denoed y { } which conains ax rae governmen expendiure raio and defau rae and i may e sae-coningen for consoidaion regimes Fisca rues are assumed o e puic informaion; his assumpion impies ha hese rues are incorporaed in he pricing of GB as discussed eow The presen mode does no suppose opimizaion ehavior on he par of he governmen in he pursui of socia wefare We insead ae he pragmaic view ha governmen poicy is argey poiicay consrained as opposed o eing designed on he asis of economic raionae Le { } wih In he pre-consoidaion regime he governmen axes wage income a he rae of I spends a given porion of poenia oupu ha cacuaes Y a he mean of ; ha is and such ha G Y where / / Y An 2 This may capure he siciness of governmen spending; i is neiher pro nor couner-cycica We can hen inerpre G as neura o economic fucuaion For anayica convenience we suppose ha he expendiure remains proporiona o Y in he consoidaion regime as we ahough may e owered Wih and 2 he primary surpus a period is defined y where / / 3 PS T G An

11 / / Susiuing 3 ino and manipuaing i esaishes he dynamics of puic de over muipe periods; we arrive a where / / 4 A n / is as given in 9 Noe ha in he presen economy / and serve as sae variaes ha are deermined a period and carried over o period + They hen affec he ris of fisca consoidaion a + as discussed in he nex secion 3 Equiirium 3 Fisca susainaiiy The fisca rue { } in he pre-consoidaion regime does no ensure ha puic de remains a fiscay susainae eves Tax raes may e oo ow and/or expendiure raio may e oo high o srucuray generae a primary defici; ha is for mos of The puic de may reach a eve a which he saus quo fisca rue canno e susained We do no suppose ha he governmen underaes precauionary measures o preven such circumsances Poiica economy consideraions on such measure wi e discussed aer The ieraure of fisca susainaiiy discusses he ransversaiy condiion of he presen vaue of he primary fisca surpus in he infinie fuure Indeed Juessen e a 29 using infiniey iving agens considers ha he governmen is forced o defau on is de once he condiion fais o hod In he OLG seing however he capia mare may no wor o discipine governmen financing ecause he finie-ife househod may no e concerned wih ong-erm fisca susainaiiy The househod is wiing o purchase GB in is young period as ong as he arirage condiion 6 is fufied The consoidaion ris is compensaed wih a higher GB ineres rae 5 In he presen conex herefore he ransversaiy condiion does no necessariy guide he hreshod 5 I is arguae ha ransversaiy condiion does no represen raiona decision maing u is raher normaive crierion o assure fisca discipine Such discipine mus e enforced y invesors In he OLG seing no invesors are moivaed in such a way

12 ha riggers he fisca consoidaion or maximum / under which he governmen can susain saus quo Such a hreshod may e deermined in erms of he oerance or confidence of he mare in he governmen s capaciy o remain soven which in urn coud e dependen on is hisorica record of fisca consoidaion and/or invesors eiefs; however i may insead emerge as a sor of opima defau sraegy se y he governmen On a reaed noe we iusrae in secion 6 he poiica economy of deciding upon fisca consoidaion We eave deerminans of he consoidaion hreshod o fuure research u do define i as exogenous Moreover we aow he scope of governmen sovency o e maxima To e specific we assume ha he governmen can access credi insofar as he GB eve does no exceed domesic savings 6 Indeed he arirage condiion 6 is fufied even for arge / since here exiss sma proaiiy ha he high economic performance wih eiminaes puic de In he foowing consider he governmen sovency a period + Suppose ha he economy reaches 2 n s ha is he domesic savings a + is fuy asored y governmen orrowing given ha he economy is cosed and no privae invesmen can ae pace which impies ha here is no producion in he susequen period or Y 2 for a 2 Once his occurs he governmen can find no resource for repaymen whereupon i mus hen defau on he de so ha 2 = is cerain and herefore here wi e no reurn on GB 7 This in urn impies ha househods cease o end o he governmen The governmen is hen forced o underae fisca consoidaion wih no furher orrowing; his enais ax increases expendiure cus and furher defauing on GB Lemma 3: Fu defau 2 = is ineviae a period + 2 irrespecive of 2 n s a + 2 when Wih 2 n s or we have 2 / 2 2 condiion is no fufied See Appendix B In he foowing we suppose ha he fisca consoidaion and we presen he equiirium compaie wih i a period + Oviousy he ransversaiy riggers 2 / 2 32 The hreshod 6 This may represen he noion ha ris of fisca crisis remains ow when domesic invesors are dominan in purchasing GB as is he case in Japan ahough we mode cosed economy asracing inernaiona ransacions 7 On he oher hand reurn on privae capia remains posiive wih he revenue-maximizing ax rae eing ounded y ess han % 2

13 Insering ino 4 and manipuaing i yieds he foowing condiion of he hreshod 2 / 2 eve of eow which regime change occurs: 8 / / 5 An This defines he hreshod as he funcion of he ineres rae charged on as we as he de capia raio and demography: where / n Wih and / whereas i is owered wih n increases such ha fisca consoidaion is more iey o e in pace Figure 2 / Fisca consoidaion a Lemma 4: Fisca consoidaion mus occur a period + when Fisca consoidaion invoves ax increases expendiure cus and defauing on GB wih no new de issuance In he presen conex we use he erm defau raher oosey: he defau may e paria or refer o a resrucuring ha reconracs he condiions of repaymen The sae of he economy a period + is denoed y The fisca rue is hen expressed as wih 2 which conains 8 In a more genera conex if we denoe he de oerance y 2 / 2 he hreshod 5 can e re-expressed as / / An Excep ha parameer γ is added he feaure of he hreshod does no change 3

14 Max where he defau rae fufis 9 / / 6 A n The governmen canno fuy mee is oigaion u repays is ousanding de as much as possie ou of he primary surpus as iusraed in 6 Under he consoidaion rue eiher he ax rae expendiure raio or defau rae deviaes from iniia eves The fisca rue can ae a genera form u may e pausiy evied according o he foowing resricions: Assumpion 3 i / ii / iii / In he simuaion wihin secion 5 we specify he fisca consoidaion rue Noe ha i aes ony one period o resrucure governmen finance Given ha no GB is issued he economy wi reurn o he iniia regime in he nex period wihou de iaiiy eing carried over 33 Ineres rae Le us urn o he GB ineres rae which is seed a period and accouns for fisca consoidaion in he even of eca he arirage condiion 6 which equaes reurn on GB wih capia in he expeced erm Manipuaing i wih he use of 6 and 6 esaishes he foowing: 7 F Min[ n / ] / A Min[ ] ~ ~ ~ df ~ where / / / / df df and in refers o he vecor of ax raes Noe ha refecs he expeced reurn on privae capia We can ceary see ha i is nonincreasing wih he hreshod eve given ha This represens he perverse effec of wage ax increases under fisca consoidaion ha woud discourage an effecive aor suppy and in urn ower he produciviy of privae capia 9 The consoidaion rue can e inerpreed in a reduced form ha incorporaes he dependence of he equiirium vaues of and on / n / / E r n A 4

15 In 7 is reaed as a conro variae For a sufficieny arge he defau rae according o 6 may urn ou o e negaive which canno occur To resric 2 o e nonnegaive we cu he hreshod a which is impiciy defined y: / / 6 An Noe ha for he fisca consoidaion does no invove defau 7 yieds he GB ineres rae as a funcion of he hreshod he de capia raio and he popuaion: Consider he comparaive saics: is increasing wih n since he produciviy of privae capia is enhanced as effecive aor suppy expands / direcy appearing in 6 serves o raise whereas according o Assumpion 2 he induced ax increase under consoidaion wors in he opposie direcion given ha / To furher address feaures of he GB gross ineres rae differeniae wih respec o he hreshod ha esaishes: 8 f F Min[ ] Z d n / / A d M M where d d aes a vaue of if and oherwise Then he effec of is descried in he foowing emma: Lemma 5: Denoing and where / n we have n / / A / / where This emma impies ha he ineres rae is increasing resp decreasing in when fisca consoidaion enais no ax increase resp no defau and hus revenue oss is compensaed for y defauing on ousanding de resp y raising ax a he hreshod eve I may e counerinuiive for o e owered as increases To see his poin noe ha in he presen mode fisca consoidaion invoves oh he defau and he ax increase The former adds he ris premium of GB reaive o privae capia herey raising is ineres rae; he aer on he oher hand reduces 5

16 he reurn on privae capia which wors o ower he GB ineres rae hrough arirage We hen have he case of when ax increases dominae he defau ris / Figure 3 depics he shape of ineres as he hreshod changes M refers o he as wo erms on he arge race on he righ-hand side of 8 Given ha i ocaes he upper ound of Z ha corresponds o he as erm in he aove equaion When is a a ow eve 8 ecomes posiive wih exceeding M A he poin where M he sign of 8 is reversed and ou o e hus enhancing he asoue vaue of / inersecs wih decines wih Once reaches d urns Figure 3 M E [ r ] To furher carify he feaure of he GB gross ineres rae we consider differen rues of fisca consoidaion No Tax Increase: Le for a such ha here is no need for a ax increase Consoidaion enais defauing on ousanding de as we as cuing governmen expenses The defau rae fufis / / 7 A n According o Lemma 5 he funcion of shoud e upward wih respec o Lemma 6 Consider fisca rue wih no ax increase; aso assume ha F is uniform Then Z is 6

17 increasing and goay convex in wih / / if 9 A / / / Z n 2 Eq 9 ensures ha is ocaed aove M M in Figure 2 The ef-hand side of 9 is increasing in / given ha / / and M / / is defined in 8 whereas he righ-hand side is decreasing wih i This in urn impies ha he inequaiy hods for a sufficieny arge puic de capia raio No Defau: Suppose insead ha no defau is aowed or for a u he ousanding de mus e fuy repaid hrough ax increases and expendiure cus wih eing impiciy deermined y 6 wih / / 7 n A = Then 7 reduces o which is decreasing wih is aso decreasing in he de capia raio if is raised which in urn reduces he righ-hand side of 7 34 Ineracion There exiss ineracion eween he hreshod of he fisca consoidaion and he GB ineres rae which are defined y 5 and 7 respecivey Soving hese equaions yieds heir equiirium vaues Noe ha hese are assessed from period or he ex ane perspecive when is no nown and fisca consoidaion is no ye in pace Proposiion : Denoe y and he equiirium eves of he GB ineres rae and he hreshod of fisca consoidaion condiiona upon / and he consoidaion rue If he equiirium vaues exis hese are given as souions o he foowing equaions: / / n A F Min[ n / ] / A Min[ ] ~ ~ ~ df ~ In he aove proposiion we do no precude he case ha here arise muipe equiiria wih he The sufficien condiion needed for his o exis is given y: / / / 7

18 wo equaions inersecing more han wice or wih he equiirium diverging ha is reaching In he aove proposiion we do no precude he case ha here arise muipe equiiria wih he wo equaions inersecing more han wice or wih he corner equiirium wih diverging To e specific we can esaish: Coroary o Proposiion : In he corner equiirium wih we can define he GB ineres rae a defined as 7 a if 2 / / An 2 ensures ha where where is he souion o and cacuaed from In he corner equiirium he GB ineres rae is so high ha he fisca consoidaion is ineviae uness { } ie he growh mirace occurs as iusraed in Figure 4 eca ha aes an exremey high vaue ha in urn assures he arirage condiion 6 o hod is is Figure 4 C B A 4 Comparaive Saics 4 De accumuaion 8

19 Le us focus on he inerior souion egarding comparaive saics fuy differeniaing equaion 5 of hreshod and equaion 7 of he GB ineres rae esaishes / d / / / n 2 d dn / n / / / d Meanwhie we focus on he inerior and sae equiirium where he equiirium ineres rae is finie wih H / / case of here eing no demographic change > Then we oain he foowing proposiion in he Proposiion 2: De capia raio i ii iii is increasing if / / is increasing if and / / / is decreasing if and / / / Figure 5 depics some possie scenarios Figure 5a gives he case of and / / / This appies o he consoidaion rue where here is no ax increase The iniia equiirium is ocaed a poin A Increasing he de capia raio moves righward and upward The inersecion of he wo funcions is hen shifed up and o he righ such ha oh he ineres rae and he hreshod are raised In Figure 5 sopes downward which is so if he consoidaion rue does no aow defau or if i is ocaed eow M M as in Figure 2 The iniia equiirium is again given y poin A moves in he same way as Figure 5a wih / Suppose / The hreshod is raised moving he new equiirium o poin B The / change in ineres rae is no cerain Le / / In a more genera conex a ax increase induced y a fisca resrucuring ha in urn owers ~ ~ ~ in 7 may e dominan is hen owered o poin C whereas change in As a consequence we have he circumsance in which is amiguous decreases as de accumuaes reaive o privae capia as depiced in Figure 5 This is iey o occur when he fisca consoidaion rue incudes arge ax increases whie eeping he defau rae ow a mos of as discussed earier In conras Figure 5a impies ha he defau ris is significan in he fisca rue I is ofen said ha as a consequence of crowding ou privae invesmen a uidup of puic de 9

20 eads o surges in ineres raes The raionae ehind such an argumen invoves he diminishing margina reurns on invesmen Decreased privae capia hen enhances is produciviy on margin which in urn raises he mare ineres rae The endogenous growh seing however does no ransae in a crowding ou ino such increases in he margina produc of as i is fixed and depends upon he wage ax rae and oher eemens of he economic environmen aher expecaions of fuure ax increases reduce he expeced reurn on privae capia which is in urn refeced in ower eves of To sae i differeny a ower signas a cauionary view of fuure governmen financing in he presen conex Figure 5a Figure 5 B A B A C A his poin i is worh poining ou ha he consoidaion rue pays a ey roe in deermining equiirium If consoidaion is done mosy y defauing on puic de in he exreme he case of Figure 5a ecomes iey increasing as puic finances deeriorae The conrasing rend shown in Figure 5 is oserved when consoidaion incudes a significan ax increase whie respecing he de oigaion I can e seen ha is ower under he aer fisca rue han under he former given ha / The differen fisca rues are compared in he simuaion as we 42 Discree change In Figure 5 we assume a unique and inerior souion o equaions 5 and 7 However we may have muipe equiiria or he inerior equiirium souion may cease o exi As an exampe consider he consoidaion rue wih no ax increase Suppose ha F is uniform in he norma 2

21 regime; aso assume ha 9 hods which in urn yieds / wih / and / / Figure 6 iusraes such o e he case Tha figure depics hree differen eves o he raio wih 2 / / / 3 A / he GB ineres rae and he hreshod funcions inersec ony once; a poin A; his yieds a unique equiirium For he midde eve of he raio he wo funcions urn o cross wice a poins B and C; poin B provides a sae equiirium whereas C is unsae In he case of muipe equiiria he oucome depends upon he eiefs or percepions of he househod ha purchases GB In a more genera conex in which househods of one generaion are heerogeneous some coordinaion of eiefs is needed o deermine which equiirium is achieved Noe ha furher increasing / shifs he wo curves so ha poins B and C are oo cose; hey ouch a poin D in he case of / 3 eyond which he inerior souion disappears Then he economy umps o he corner souion wih and as iusraed in he Coroary o Proposiion hus yieding higher ineres raes and a higher hreshod For exposiiona simpiciy he corner souion is no depiced in Figure 5 Generay speaing he consoidaion ris ecomes maxima when he GB ineres rae aes an exremey high eve In he presen conex a high ineres rae enhances he proaiiy of fisca consoidaion he aer serving o increase GB ineres rae I shoud e noed ha he case in Figure 6 can appy o a wider range of consoidaion rue scenarios insofar as hey are confirmed in he simuaion Figure 6 3 / / 2 / C 2 / 3 / / D B A In summary we have addressed he circumsances in which a uidup of puic de migh ead o ower GB ineres raes owing o he prospec of fuure ax increases ha reae o fisca 2

22 consoidaion as iusraed in Figure 5 and in which here migh hus e a sudden rise of ineres raes ie as seen in Figure 6 hus increasing he fisca consoidaion ris Therefore he oservaion ha he GB ineres rae has remained reaivey ow does no ensure ha he same rend wi coninue in he fuure as puic de accumuaes We confirm hese scenarios in he simuaion in Secion 5 43 Demographic impac Nex we examine he effecs of demographic changes Noe ha in he endogenous growh mode he popuaion or aor force is a ey driving force ha enhances produciviy When he popuaion size decreases so oo does produciviy and hus he expeced reurn on capia is diminished; his in urn wors o reduce The hreshod of he regime swich is increased on he oher hand ecause he primary surpus is owered As hese eemens inerac he ne impac is as saed in he foowing proposiion: Proposiion 3: Consider a reducion in n Then i ii decreases if is enhanced if / is increasing In genera he equiirium effecs of he demographic change on and are amiguous In Secion 5 we conduc a simuaion o compare he scenarios of differen demographic changes 44 De accumuaion In he previous secion / was aen as fixed and he equiirium was esaished as condiiona upon i We now consider he accumuaion of puic de which is sochasic as i reies on he reaizaion of produciviy shoc Comining 9 and 4 and advancing he period y one we oain he ransiion process of he de capia raio as foows: 22 2 / / / / / ~ / ~ / n A where ~ saes ha is vaue is uncerain a period The immediaey higher / is ransied o a higher 2 / 2 in he nex period given ha accouns for he dependency of on / According o Proposiion 2 his impies 22

23 ha he ris of fisca consoidaion a period + increases aong wih he curren de capia raio if / / Figure 7 depics he shape of he ransiion funcion 22 wih he consan n a n has hree eves: ow midde and high Noe ha a smaer vaue of shifs 22 upward Aso noe ha he curve approaches infiniy if / goes o he criica eve such ha / n ha is ecomes coinciden wih he hreshod of fisca consoidaion Suppose ha / / / / L By 22 he de capia raio carried over o he nex period is given y M / eing ocaed a poin E if M In he figure we have which impies ha here arises a regime change a period + if L H whereas governmen financing is susainae when Figure 7 shows ha 2 / 2 approaches infiniy a L wihou consoidaion In he even L no puic de ha is 2 is issued under he consoidaion rue and hus he economy moves ac o is origin On he oher hand he raio is owered o 2 2 / 2 / or poin F when H Figure 7 2 / 2 L M H / E / 2 F 2 M 2 H 2 L / / 5 Numerica Exampe 5 Specificaion This secion aims o provide numerica exampes of he comparaive saics deveoped in Secion 3 Specificay we examine he heoreica hypoheses ha puic de accumuaion may ead o ower ineres raes and ha he equiirium ineres rae may exhii a discree change from a reaivey 23

24 ow o an exremey high eve In addiion we confirm wheher he equiirium in he preconsoidaion regime is affeced y he fisca consoidaion rue and demographic change Moreover we cacuae he hreshod a which consoidaion occurs given / a period Needess o say our quaniaive anaysis does no inend o repicae any rea-word economic pracice; raher i suppemens our heoreica mode resoving he amiguiy of is resus and carifying is poicy impicaions The parameers are specified in Tae U-shaped densiy funcion wih a mean of 2 disriues over [ 55 ] according o he inverse We se he ax rae a a reaivey ow % and we aso se he expendiure rae o % of poenia oupu This impies ha he primary defici is iey o resu uness is arger han he mean of ; hus here exiss he possiiiy ha puic de is accumuaed wih consoidaion ris hus eing enhanced The fisca consoidaion rue commands he expendiure o e cu in haf o 5 The wage ax rae under consoidaion is increasing in whereas i increases wih / as imposed y Assumpion 2 This is specified in Tae Consoidaion reies on more ax increases o miigae a arge de capia raio whereas he defau rae is raised when is sma and he economy is herefore depressed Such a presumpion shoud e pausie The parameer g in he ax funcion refers o he exen of he required ax increase The simuaion se hree vaues for g ie 5 75 and A higher g impies a arger ax increase in he consoidaion which in urn impies a ower defau rae aove ax funcion is consrained so ha differen vaues of g we can assess he effec of he fisca rue on ha is defined as residua y 5: he aes an inerior vaue By comparing he resus of and as we as changes in he de capia raio To examine he demographic change we consider he case ha he popuaion remains consan over ime and aso he case ha i is decining; in he aer we assume ha i annuay decreases y 3% Taing one period o sand for 3 years we e 3 n 3 n Disinc in erms of he parameer g and demographics four scenarios are presened as summarized in Tae 2 Scenario is aen as a enchmar in he foowing ae δ 5 α 3 θ 333 Tae : Parameers 2 More correcy form assumpion he range of is [ ] [55] { } Therefore in our 5 simuaion we aso considers he effec of { } as he possiiiy of { } and 5 24

25 A 7 { } τ = λ = / Min g Max 3 8 / Tae 2: Scenarios Scenario Benchmar g = 75 Scenario 2 g = 5 Scenario 3 g = n 3 Scenario 4 g = 75 n n 3 52 esus In he simuaion we focus ony on he inerior equiirium The GB ineres raes for differen scenarios are shown in Figure 8 where / is reaed paramericay and aen on he horizona axis In a scenarios here exiss a range in which exhiis a downward sope confirming our heoreica hypohesis Tae he enchmar scenario Scenario There he ineres rae is iniiay decining wih / Is moderae downward rend coninues uni = 78 where / aes he minimum vaue The sope is hen reversed furher increasing he de capia raio and rapidy raising he ineres rae A / = he sae inerior eve of disappears diverging o he corner equiirium which is no expiciy reaed here This is consisen wih wha is seen in Figure 6 The enchmar scenario is compared o Scenarios 2 and 3 o assess he impacs of a ax increase in Scenario 2 arey differs from he enchmar for ow eves of / Afer / = 3 however he former egins o exceed he aer and he difference eween hem widens quicy Once he raio exceeds 735 Scenario 2 oses is inerior equiirium whereas i remains in he enchmar scenario In he former scenario wih g = 5 he ax increase is ess significan han in he aer scenario when fisca consoidaion is impemened Given ha oh scenarios impose 5 in he even of he consoidaion his impies ha Scenario 2 experiences a higher defau rae and consequeny adds a ris premium o GB Now e us consider Scenario 3 wih g = Again is ineres rae moves aou he same as he enchmar when he puic de capia raio is no high For / > 5 he dispariy urns ou o e prominen wih in Scenario 3 saying ower han ha in he enchmar The former can hen susain he inerior equiirium for a arger / han he aer I can hen e concuded ha consoidaion invoving a greaer ax 25

26 increase eads o ower susaining he inerior equiirium 3 Figure 8: GB ineres rae GB Ineres rae Puic de o capia raio Scenario Scenario2 Scenario3 Scenario4 Consider he hreshod of regime change / In a scenarios i monoonicay increases in as in Figure 9 In comparing differen scenarios wih differen consoidaion rues says ower when he ax increase is arger ha is g is high refecing a ower ineres rae The prospec of arge ax increases in he even of a fisca resrucuring ha conriues o a ower defau rae serves o miigae consoidaion ris which shoud e inuiive The ris is refeced in a GB premium ha is defined as he difference eween he GB ineres rae and he expeced reurn on capia The premium remains negigie when ris is ow: according o he consoidaion ris he revenue deficiency is argey fied y ax increases and expendiure cus The defau rae in he even of consoidaion is raised as he de capia raio increases which in urn augmens he premium To see he effec of he demography we compare he enchmar scenario wih Scenario 4 The figure reveas ha overa he decining popuaion wors o diminish equiirium ineres raes The gap in ineres raes eween he wo scenarios firs decines wih / uni he raio reaches 72 whereupon i sars o increase sharpy In Scenario 4 he inerior equiirium is susained up o / = 67 and hus he fisca consoidaion ris is reduced reaive o he enchmar case eca ha in genera he demographic impac on was amiguous The simuaion esaishes ha he hreshod is owered in he case of smaer popuaion ha is he downward shif of due o a decrease in n dominaes he upward movemen of wih 3 The simuaion aso reveas ha an unsae equiirium appears when he de capia raio is very cose o he criica eve of he puic de capia raio in which he sae inerior souion disappears 26

27 he primary aance deerioraing as in Figure 5 Figure 9: Threshod Threashod Puic de o capia raio Scenario Scenario2 Scenario3 Scenario4 Consider he economic growh ha is cacuaed in he expeced erm as ~ / E ~ E ~ Growh decreases as privae capia is crowded ou y puic de which decreases / given 9 Figure gives he expeced growh rae from he perspecive of period + Tax increases ie a higher g in he consoidaion regime exer wo opposing impacs on growh As saed aove i serves o ower which increases / as accumuaed a period The ax urden on he oher hand reduces he oupu in he even of consoidaion a period + and his is refeced in he race of he expecaion in In comparing Scenarios and 2 he wo yied amos he same growh rae for a ower / and he aer experiences sighy higher growh afer = 4 han he former uni he criica raio in which he inerior souion disappears in / Scenario 2 The same can e seen when Scenario 3 is compared o Scenario u he difference herein is negigie Demography maes a considerae difference The expeced growh rae seen in Scenario 4 is iniiay ower han he enchmar scenario u as he de-o-capia raio increases he reaionship is reversed and he difference expands as puic de is ui up reaive o capia This chain of evens may e couner-inuiive u i occurs ecause he ower ris of fisca consoidaion serves o decrease he expeced ax rae from he perspecive of period In addiion as he GB ineres rae is owered privae capia accumuaion is ess crowded in Scenario 4 hus enhancing / 27

28 Figure : Expeced economic growh rae % Expeced growh rae% Puic de o capia raio Scenario Scenario2 Scenario3 Scenario4 53 De accumuaion Consider he dynamics of he puic de capia raio which was reaed as exogenous in he previous susecion We divide which is reaized a he + period in four casses and for each quarered group and he condiiona expeced eve of 2 / 2 is cacuaed given a / ha is deermined a period Noe ha he expecaion is aen from he perspecive of period Tae 3 shows he resus in he enchmar scenario / Tae 3: Changes in de capia raio 5~75 75~ ~25 25~ The expeced raio of 2 / 2 increases wih / and is higher for he ower quarer of 28

29 A he owes quarer ha is [575] he average of 2 / 2 exceeds he criica raio = a which inerior equiirium ceases o exis according o Figure 6 when he de 2 / 2 capia raio / is more han 6; his impies ha fisca consoidaion is ineviae a + 2 or 2 In higher-quarered groups of he expeced raio remains a a susainae eve for arger / For insance a he highes quarer ha is [255 ] he inerior equiirium survives a period + for a / vaue of ess han 72 6 Poiica Economy We have hus far assumed he process of puic de accumuaion o e exogenous One possie oecion is ha here shoud exis a sef-correcing mechanism o conain puic de a susainae eves y raising axes and/or cuing expendiures Indeed raiona voers may no aow he ris of fisca crisis o deepen over ime u may underae prevenive measures o curai such ris In our OLG seing however he represenaive househod of each generaion which nauray has a imied ife-span may no ac in such a manner To see his in effec consider simpe maoriy voing wih respec o ax increases in a preconsoidaion regime so as o decrease he puic defici Boh he young and he od generaions in each period exercise heir voing righs Wha are voers preferences wih respec o such prevenive measures? The consumpion of he od voers under he saus quo is equa o o 32 s q q r c where he ar impies ha heir choices are sun a he eginning of period Given ha he reurn on privae capia decines wih wage axes he oder group opposes any ax increase Le us now consider he young voers Their ifeime expeced uiiy in he equiirium reaizaion of where is expressed y 23 E U s s E r ~ r E ~ r ~ / A E and wihou a prevenive ax increase Differeniaing 23 wih respec o he ax rae yieds d de ~ r d 24 EU d E ~ r d d The firs erm represens he direc effec of raising I owers he afer-ax wage income ha 29

30 he young generaion earns a period ; his decreases uiiy The enhanced ax revenue on he oher hand improves he curren primary aance which reduces he ris of he fisca consoidaion Tha is d d d d / d d The aove in urn enhances he expeced reurn on capia This which is capured in he second erm of 24 serves o raise he young generaion s ifeime uiiy Therefore he comined effec of such ax increases is no cerain To resove his amiguiy we rey on simuaion In Figure we ae he enchmar scenario and depic changes in he ogarihm of he expeced uiiy as he wage ax rae increases from he iniia eve EU vaues correspond o differen eves of = % Differen og / ha are predeermined a period / aes a smaer vaue as he raio increases refecing he crowding effec ha in urn owers receiving wages For a / uiiy decreases wih he ax rae; his reveas ha he perverse effec of decreasing disposae wage income ie y imposing higher ax raes dominaes he gain derived from augmening he expeced reurn on capia whie he consoidaion ris is reduced Ineresingy he uiiy oss derived from increasing he wage ax is exaceraed wih he puic de capia raio eing raised as a resu Thus i ecomes increasingy difficu o raise axes as governmen finances worsen We oain mosy he same resus wih a he oher scenarios In shor he young househod wi voe agains ax increases in he preconsoidaion regime Figure : Expeced uiiy Expeced uiiy Wage ax rae /=5 /=3 /=45 /=6 /=75 /=9 Thus prevenive measures vis-à-vis fisca consoidaion ris wi never gain poiica suppor from exising generaions Puic de wi e hen ef o accumuae uni he regime swich ecomes ineviae when To sae i differeny he normaive crieria of fisca 3

31 susainaiiy such as he Dormer condiion or he ransversaiy condiion of a ong-erm governmen udge do no incenivize conemporary poiics o underae fisca resrucuring Of course he fuure generaion wi suffer from a arge puic de ha owers due o crowding ou and reduces heir wages and which can rigger wage ax increases in he even of a consoidaion Such wefare oss of he fuure generaion is no incorporaed y curren voers who are assumed o e sef-ineresed The poiica faiure o underae a resrucuring effor has een examined y Aesina and Drazen 99 who modeed deayed saiizaion as a war of ariion or a sor of game of chicen eween vesed ineress They address he fac ha he iming of acua fisca consoidaion urns ou o e oo ae reaive o he opima iming ha maximizes he oin payoff of saehoders eaed sudies y Veasco 2 and Ihori and Iaya 22 consider puic de accumuaion as a consequence of a noncooperaive sugame among specia ineres groups ha freey exrac resources from he governmen udge In heir conex fisca resrucuring is feaured as a vounary conriuion for he puic good ha suffers from he free-riding moive These modes assume he infinie ife of agens wihou cooperaion The presen paper wih is OLG seing addresses he moive of conemporary generaions o shif he urden of fisca consoidaion o fuure generaions ha canno ye voe or even do no ye exis The presen mode does no accoun for he poiica process of deermining ax and expendiure raes or τ and λ in he preconsoidaion regime aher hese vaues are aen as exogenous However we have esaished he condiions under which he iniia ax and expendiure poicies are no correced and he consoidaion ris is enhanced as curren generaions do no agree o accep a ax hie 6 Concuding remars In his paper we anayze he reaionship eween GB ineres raes and he fisca consoidaion rue using an overapping generaion mode wih endogenous and sochasic growh seings Our ey findings are summarized as foows GB ineres raes may decine as puic de accumuaes reaive o privae capia as suggesed y he findings of einhar e a 22 as opposed o he conveniona view ha a uidup of puic de accompanies a rise in ineres raes This is consisen wih he seemingy paradoxica circumsances surrounding GB ineres raes in Japan where raes remain ow despie a puic de GDP raio ha has een increasing over he as severa decades This paper aso addresses he fac ha fisca consoidaion rue pays a ey roe in 3

32 deermining equiirium ineres raes Moreover he reaivey sae inerior equiirium may disappear in a discree manner ha shifs he economy o a siuaion in which consoidaion is ineviae and GB ineres is quie high The normaive sandpoin suggess ha prevenive acion shoud e underaen o conain such fisca ris However precauionary ax increases mean o conain puic de o susainae eves wi no win he poiica suppor of exising generaions as heir ife-spans and periods of sef-ineres are imied Insead voers prefer o shif he uimae urden of puic de o fuure generaions ha canno curreny voe Admiedy our mode is highy syized and asracs some ey issues ha shoud e furher examined in fuure research These incude he search for he rea hreshod of regime change and he imis of puic de GDP raio underaen y cairaing our mode o rea economies eg he Japanese economy 2 he effec on our mode of infaion ased on he Fisca Theory of Price Leve as iusraed y Cochrane 2 and 3 he anaysis of anoher voing game eg eween ow and high income househods over ax increases in he preconsoidaion regime so as o decrease puic defici Nauray he resus of our sudy woud have greaer earing and impor if heir generaizaiiy coud e demonsraed 32

33 Appendix A From Eq 72 9 and he condiion of dynamic efficiency is represened as foows: ~ r ~ n / / ~ n n / / A ~ / A n ~ / 33

34 34 Appendix B Assume ha here is no defau Then 2 2 } { PS PS G T where G T PS / / n A Given ha here is no consoidaion ris he ransversaiy condiion is no fufied if he foowing hods: / / / / / / / / 2 / r E E E n A E n A n E A PS E PS E E Lim where / / n n Y Y By emma he righ-hand side aes a finie vaue whereas he ef side diverges as he puic de capia raio rises or / goes o infiniy

35 35 Appendix C We define ~ ~ ~ ~ / / df A n where / / / / df df / / F / F f / / f A n f B- maing use of / / n A B- / / / / A n f f A n f B-2 maing use of / / / / f f B-2 / / / / / f A n f / / / / / A n

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