Title: Long-Term Fiscal Indicators: Sustainability versus Terminal Debt Constraints. 1

Transcription

1 Workng Par no.: 14/2005 l: Long-rm Fcal Indcaor: uanably vru rmnal Db Conran. 1 Auhor: Nl Kl Frdrkn nkf@fm.dk Abrac: h ar rovd an amn of h concual and quanav dffrnc bwn hr alrnav way of drvng long-rm ndcaor of fcal anc, wo of whch nvolv runcaon of h m horzon whl h hrd on bad on h govrnmn nrmoral conran only and hu nvolv an ffcly nfn horzon. I urn ou ha, for h OECD counr, h wo fn-horzon alrnav nd o mly oo ll fcal conoldaon comard o wha rqurd for ru fcal uanably. In ohr word, h moon of a fxd horzon ycally lad o an xcvly omc cur of currn fcal anc and may furhrmor comlca cro-counry comaron. 1 h vw and analy rnd n h workng ar ar h ol ronbly of h auhor. h ar may hrfor nclud vw, whch ar no ncarly hard by h Mnry of Fnanc.

2 2 1. Alrnav aroach o long-rm fcal arg 2 In h lraur and among raconr a numbr of alrnav way of drvng forward-lookng conran on currn fcal olcy hav bn rood. h ky roblm ha h varou conrbuon k o ovrcom how o dal wh h nfn horzon of h govrnmn' nrmoral budg conran. h dffrnc hu rla o h chncal aumon ha ar nvokd n ordr o drv an ndx of fcal anc n a long-rm rcv ha lnd lf o numrcal alcaon. h uro of h ar o clarfy and xamn h naur of h dffrnc and a how hy nflunc h quanav amn of fcal uanably. o h ag, condr h connuou m quaon of moon for govrnmn db, 1 b b whr h m rmary urlu, b govrnmn db, whl dno h nomnal ra of nr and h growh ra of nomnal GDP. W aum ha h ra of growh and nr rman conan hrough m. W wh o drv and comar arora xron for h rqurd rmary urlu a m <. Ingraon of boh d of quaon 1 from o roduc 2 b b Rarrangng rm, and lng go o nfny, hn yld d 3 d b lm { b } By mong h aumon ha h lm rm qual o zro, w oban from quaon 3 h famlar nrmoral olvncy condon mlyng ha h n rn valu of fuur rmary urlu and hnc h xc of ax rc ovr non-nr govrnmn ndng mu qual nal n ublc db b. Ung quaon 2 and 3 w now condr h rqurd rmary urlu a m gvn hr dffrn way of rndrng h amn of fcal anc comuaonally fabl. In h fr wo aroach, a fn horzon mod hrough h rqurmn ha rmnal govrnmn db,.. b, b qual o om r-cfd valu. W fr condr h andard aroach buldng on h rqurmn ha rmnal db b b qual o nal db b. W call h h Unchangd rmnal Db, or UD, rul. Nx, w xamn wha 2 E-mal: nkf@fm.dk, hon drc: Commn and uggon from Hkk Okann ar grafully acknowldgd.

3 3 han whn h rmnal db lvl oband by aumng ha, n h rod from o, govrnmn budg balanc hold on avrag. h aumon rmd h Clo o Balanc, or CB, rul. Fnally, w condr h conqunc of ranng h nfn horzon whl mong conran on h m ah of h rmary urlu n ordr o uor comuaonal fably. On way of dong h o aum ha, from rod onward, h rmary urlu conan and qual o valu n rod. An alrnav way, whch w wll u blow, o mo a arcular funconal form on h m ah of h rmary urlu. cfcally, f w nvok h aumon of an xonnal adjumn ah, h ngral on h lf-hand d of quaon 3 may b olvd analycally. W call h aroach h uanably, or, rul. Ung h hr alrnav w oban h followng xron for h rqurd rmary urlu a m : Unchangd rmnal db UD [Blanchard. al 1990] ng rmnal db qual o nal db n quaon 2 and olvng ou yld 4 UD b 1 d Clo o balanc rul CB [EPC and EU Common 2003] In h ca, rmnal db b qual o nal db b dvdd by h comound nomnal ncom growh facor from rod o. Inrng n quaon 2 and rarrangng gv 5 CB 1 1 b 1 d uanably [Frdrkn 2001a,b] h aroach buld on h rqurmn ha ax ra and r caa govrnmn ndng.., h fcal nrumn ar manand ndfnly. In h ca, fcal olcy uanabl bcau no fuur chang n fcal nrumn ar rqurd. Ung quaon 3 w hu fnd 6 b d Noc how quaon 6 a ha h m rqurd rmary urlu qual o h annuy valu of oal govrnmn.., xlc lu mlc db, whr mlc db dfnd a h rn valu of h fuur chang n n govrnmn ndng mbodd n currn ax and xndur olc. 3 Comaron of h hr alrnav aroach 3 ha, mlc db rlad o h addonal fuur n govrnmn ndng gnrad by h currn ng of fcal olcy nrumn. Alrnavly, on mgh dfn mlc db a h rn valu of h oal n labl of h govrnmn v-à-v currnly lvng gnraon, bu uch a dfnon narora gvn h, nally, nfn horzon macro- aroach adod n h ar and h focu on h ncary adjumn of fcal olcy a m n ordr o afy h rlvan rmnal conran on govrnmn db or, undr h aroach, govrnmn olvncy.

4 4 h rmandr of h ar dvod o an amn of h concual a wll a quanav dffrnc bwn h maur of fcal anc drvd abov. A wll bcom vdn, h rul o cran ky characrc ha mak an aracv bnchmark agan whch o a h ba caud by mong a fn horzon undr h UD and CB rul. Clarly, a quaon 4 hrough 6 rval, whn go o nfny, h UD and CB rul convrg o h rul. Hnc, n h n hy ar dncal n h lm. Bu ha lm may b o dan ha h jufcaon for ung hr alrnav o h rul unfoundd. Blow, w rovd ma of h quanav xn of h aroxmaon rror. Bfor dong o, howvr, uful o focu on cran concual dffrnc bwn h UD, CB and aroach n rm of h way fcal olcy xlcly or mlcly aumd o volv ovr m. Undr h aroach, nal fcal nrumn ng may b manand ndfnly. Hnc, no chang n ax ra or xndur andard, vn n h xrmly dan fuur, ar ncary. In conra, quaon 4 and 5 how ha rn valu budg balanc hold only u unl h rmnal rod undr h UD and CB mhod. Accordngly, bcau h voluon of h rmary urlu afr h rmnal rod ffcvly gnord, oonr or lar fcal olcy wll hav o b adjud n ordr o nur ha h nrmoral budg conran of h govrnmn afd. Furhrmor, whl h UD mhod calcula h adjumn of fcal olcy ha mu b undrakn mmdaly a m and manand unl m, rc adhrnc o h CB rul would mly gradual chang n fcal olcy n ordr o manan budg balanc. Howvr, h magnud of h fcal ndcaor n quaon 5 ffcvly aum a on-off adjumn ha carrd ou a m and manand unl m. Accordngly, h oraonal conn of h CB rul n rm of h mld olcy rcron rman omwha unclar. A mhazd abov, h conc of uanably undr h rul drcly rlad o fcal olcy nrumn. In conra o h UD and CB rul, and bcau of h nfn horzon, h aroach by conrucon rqur no ubqun chang n fcal olcy. A uful way of rang h rory o no ha undr a fcal olcy afyng quaon 6, h dcronary comonn a dnguhd from h auonomou comonn.., h chang n h rmary urlu du o agng and ohr facor rman conan ovr m. h dcronary comonn mly qual o h nal, rqurd rmary urlu n quaon 6. h aroach hu ml ha oal govrnmn n db rvc conan and qual o h annuy valu of govrnmn n labl a h ou. h mrror mag of h rul ha undr a uanabl fcal olcy, oal govrnmn db lkw rman conan ovr m. 4 In h ycal agng cnaro, h rmary balanc dcln gradually durng h ranon. hrfor, undr a fcal olcy afyng h rul, xlc govrnmn db rducd n ordr o off h ncra n mlc govrnmn db ha occur a h aag of m convr h fuur labl mbodd n currn ax ra and xndur andard no currn labl wh corrondngly hghr n rn valu. 4 h rory ond ou by Bur rcly akng, conancy of oal db hold only whn h growhadjud ra of rurn conan.

5 5 No mlarly aracv nrraon of h voluon of govrnmn db al undr h UD and CB aroach. And, a nod abov, h dcronary comonn of h rmary urlu wll oonr or lar hav o adju n ordr o m h govrnmn olvncy conran. In h fnal ar of h ar, w rn quanav ma of h magnud of h rqurd addonal chang n dcronary fcal olcy. In ordr o quanfy h ba mld by h UD aroach, condr h amoun by whch h uanabl rmary urlu xcd UD, UD d d 1 7 A ov valu of h xron on h rgh-hand d of quaon 7 ndca ha h rmary urlu gvn by h UD mhod fall hor of wha rqurd for fcal uanably. h horfall, n urn, rflc h fac ha, by gnorng mlc db afr m, h UD aroach undrma h fcal burdn of agng. On h ohr hand, h fn horzon aumon gv oo much wgh o mlc db oblgaon n h nrm rod,.. from o. mlarly, h ba undr h CB rul may b xrd a { } UD CB b 1 8 h CB ba accordngly qual o UD ba lu a rm caurng h mor rngn fcal conoldaon rulng from forcng h db-o-gdp rao o dcln along wh nomnal ncom growh. Equaon 7 and 8 nclud nfn ngral ha w can olv by mong h xonnal adjumn aumon mloyd n Frdrkn 2001b. W hu dcomo mlc db no h comonn rlad o h rod u unl m d λ λ whr h long-rm droraon of h rmary urlu and λ dno h xonnal d of adjumn. mlarly, w fnd for h rod afr d λ λ 10

6 6 Inrng 9 and 10 n quaon 7 and 8, and mlfyng h rulng xron, yld 11 and 12 UD CB 1 λ λ λ λ b Equaon 11 and 12 may b ud o comu h ba mld by h UD and CB aroach by mly nrng arora valu for nal govrnmn db, h long-rm budg mac of agng c., and h nomnal ra of nr and ncom growh, a wll a h d of adjumn of h rmary urlu. Blow w do h for 19 OECD counr ung h aumon and daa of Frdrkn 2001b, bu bfor rocdng nrucv o condr om gnral ror of h aroxmaon rror and how hy rla o h concual dffrnc bwn h hr aroach. Fr, h UD ba alway ov a long a h rmary balanc drora n h long run. ha, h rmary urlu rqurd o afy h condon ha rmnal db qual o nal db wll lad o an undrmaon of fcal uanably. Prha omwha urrngly, h UD ba ndndn of nal govrnmn db d h fac ha h rmnal conran al drcly o h ock of formal govrnmn db oblgaon. In h n, h ramn of xlc govrnmn db quvaln undr h and UD aroach. h raon rlad o h conancy of oal govrnmn db undr a uanabl fcal olcy ond ou abov. Hnc, abn auonomou chang n h rmary urlu, h aroach wll dca conan govrnmn db and, hnc, a conan rmary urlu. h db ah mld by h mhod accordngly dncal o h ah ha mod whn h UD mhod ud. Inal xlc db hrfor do no gv r o any ba n h ca. h CB ba qual o UD ba bcau h horzon, and hnc h way fuur chang n h rmary urlu ar dal wh, runcad n h am way lu a rm rrnng ovrmaon of h burdn of nal govrnmn db. Accordngly, dndng on h comoon of oal govrnmn db, h clo-o-balanc rul may hr ovr- or undrma h rqurd ra of fcal conoldaon. On moran roblm wh h CB aroach hn ha dca xcv fcal conoldaon for counr wh hgh formal db nally, bu ll mlc db. Avalabl long-rm rojcon of h fcal mac of agng ycally covr h rod unl Aumng ha h nomnal nr ra 6 r cn, ha aggrga nomnal ncom grow a a ra of 4 r cn, and ha h annual d of adjumn of h rmary urlu qual 6 r cn, quaon 11 and 12 hn mly ha h ba arbuabl o mlc db amoun o 0,14 r cn of GDP for ach 1 rcnag on of GDP long-rm dcln n n ax rc. Accordngly, for a counry facng a 5 r cn of GDP ady-a agng burdn, h rqurd ra of fcal conoldaon hu undrmad by 0,7 r cn of GDP whn h UD aroach ud.

7 7 h ba du o nal govrnmn db arng undr h CB aroach qual 0,01 mulld by nal govrnmn fnancal n db. Ung h CB aroach, h rqurd ra of fcal conoldaon hrfor bad uward by ½ r cn of GDP whn nal govrnmn db qual 50 rcn. abl 1 blow how h wo ba for 19 OECD counr. A alrady nod, runcang h horzon ml ha govrnmn mlc db rlad o h rod afr 2050 gnord. A h fr hr column rval, h ffcvly amoun o undrmang govrnmn mlc db by abou onhalf. For h avrag OECD conomy, h ranla no an undrmaon of h rqurd ra of fcal conoldaon qual o 0,69 r cn of GDP whn h UD aroach ud, bu n a numbr of ca Canada, Fnland, Grc, Norway and an h ba xcd 1 r cn of GDP. abl 1. Ba Undr rmnal Db Conran n 2050 Rlav o Fcal uanably. Pr Cn of GDP n Govrnmn db Ba du o Ba oal ba Imlc db mlc db du o Exlc oal UD 2 CB 3 oa xlc o > db db o > oal rul rul l db Aurala , 32 2,14 0,81-0,05 0,81 0,76 Aura ,19 1,92 0,73-0,51 0,73 0,23 Blgum ,24 2,01 0,76-0,99 0,76-0,22 Canada ,25 3,64 1,39-0,44 1,39 0,95 Dnmark ,93 1,50 0,57-0,23 0,57 0,34 Fnland ,70 2,74 1,04 0,42 1,04 1,46 Franc ,16 1,87 0,71-0,38 0,71 0,33 Grmany ,94 1,52 0,58-0,45 0,58 0,13 Grc ,94 4,74 1,80-1,08 1,80 0,73 Irland ,56 2,52 0,96-0,37 0,96 0,59 Ialy ,32 0,51 0,19-0,98 0,19-0,79 Jaan ,47 0,75 0,29-0,59 0,29-0,30 Nhrland ,52 2,46 0,93-0,42 0,93 0,52 Norway ,39 8,70 3,31 0,74 3,31 4,05 Porugal ,07 1,72 0,65-0,56 0,65 0,10 an ,87 3,03 1,15-0,42 1,15 0,73 wdn ,10 1,77 0,67 0,01 0,67 0,68 Und Kngdom ,45 0,73 0,28-0,29 0,28-0,02 Und a ,34 2,16 0,82-0,43 0,82 0,39 Unwd. avrag ,51 2,44 0,93-0,37 0,93 0,56 GPD-wd. avg ,12 1,81 0,69-0,47 0,69 0,22 GPD-wd. EU avg ,98 1,58 0,60-0,50 0,60 0,10 GPD-wd. EMU avg ,08 1,74 0,66-0,56 0,66 0,10 N 1 h rul ar bad on h am bac aumon and ourc a Frdrkn 2001b xc for nal o govrnmn n db whch from OECD Economc Ou look no. 72, Dcmbr h nomnal ra of : nr and growh ar 6 and 4 r cn, r cvly, w hl h xonnal adjumn d u d o co mu mlc db oblgaon 6 r cn. 2 Unchangd rmnal Db,.. govrnmn fnancal n db n 2050 conrand o b qual o govrnmn fnancal n db n Clo o Balanc;.. h rao of govrnmn fnancal n db o GDP conrand o dcln wh nomnal ncom growh from 2002 o 2050.

8 8 A quaon 6 dmonra, h uanabl rmary urlu qual o h growh-adjud nr ra m oal govrnmn db. Wh h formr qual o 2 r cn and h lar a 2,3 m GDP on avrag for h 19 counr covrd n h abl, fcal uanably nca a rmary urlu of 4,7 r cn of GDP n h nal yar. Ung h aumon of unchangd rmnal db hn lad o an undrmaon of h rqurd rmary urlu by abou on-vnh. h CB mhod ml lowr ba on avrag bcau h wo ourc of rror nd o off ach ohr. For h avrag OECD counry, h CB ba abou 0,2 r cn of GDP. Hnc, whl h CB aroach alo nd o undrma h fcal challng facd by OECD govrnmn, h magnud omwha mallr. h abl alo llura how h CB ba may b hr ov or ngav dndng on h comoon of oal govrnmn db. For xaml, h Duch and Blgan govrnmn fac roughly dncal oal db burdn of aroxmaly 3 m GDP. Howvr, xlc db much hghr n Blgum, whra h agng burdn mor vr n h Nhrland. Alyng h CB mhod hn lad o an undrmaon of h rqurd rmary urlu n h Nhrland by abou 0,5 r cn of GDP, whl for Blgum ovrmad by 0,2 r cn GDP. On cular ac of h CB aroach ha counr wh ov nal n fnancal a ar ffcvly aumd o lquda ho a, n urn mlyng an addonal ourc of undrmaon of h rqurd ra of fcal conoldaon. h h ca for Fnland, Norway and wdn. hu, for Fnland, h horfall undr h CB mhod amoun o 1½ r cn of GDP comard o a olcy of ru fcal uanably. h xaml hu ndca ha h wo analycal hor-cu nvolvng runcaon of h m horzon nd o comlca h cro-counry comaron of fcal anc. A mnond rvouly, h ba arbuabl o runcaon dcln whn h horzon xndd. abl 2 how h conqunc of varyng h rmnal yar bwn 2025 and abl 2. m Horzon and Avrag Ba Undr rmnal Db Conran Rul. Pr Cn of GDP n 2002 Ba: Horzon rmnal yar of UD and CB rul Imlc db 1,4 9 0,69 0,19 0,07 0,02 - Exlc db 0,9-0,47-0,14-0,05-0,02 1 UD rul 1,4 9 0,69 0,19 0,07 0, 02 CB rul man 0,5 8 0,22 0,05 0,02 0,01 CB rul man abolu 0,9 3 0,42 0,12 0,04 0,01

9 9 Alo hown h avrag abolu ba undr h CB rul. Comaron of h man and man abolu ba rval ha abou half of h rducon n avrag ba rla v o h UD aroach d u o h fac ha h gn of h CB ba may b hr ov or ngav. h avrag abolu rror whn h CB mhod ud hu qual 0,4 r cn of GDP a a 50-yar horzon. h abl alo how ha a vry long horzon mu b mloyd n ordr for h ba o aum ngnfcan rooron. In ohr word, h UD and CB aroach rovd a rlabl amn of fcal uanably only a horzon of 150 yar or mor. h oucom h drc rul of h fac ha, a alrady nod, a vry ubanal oron of govrnmn mlc db rlad o h rod afr Concluon h ar rovd an amn of h concual and quanav dffrnc bwn hr alrnav way of drvng long-rm ndcaor of fcal anc. h concually mo aalng on fcal uanably, whr an nfn horzon manand and h uanably conran mod drcly and, n conra o h u of nally arbrary rmnal valu for govrnmn db, only on fcal nrumn. W u ha aroach a a bnchmark and comar wh wo alrnav on whr h m horzon runcad, hrby mlyng ha rmnal valu for govrnmn db n fn m ar ndd n ordr o rndr h quanav amn of fcal uanably comuaonally fabl. Whn h ycal m fram of long-rm fcal rojcon,.. abou 50 yar, rqurng rmnal govrnmn db o qual nal db hown o undrma h rqurd rmary urlu n h OECD counr by abou 0,7 r cn of GDP on avrag. And h m horzon of h rojcon would hav o b xndd gnfcanly o mor han 150 yar n ordr o rduc h ba o a rval magnud. An alrnav, fn horzon mhod bad on h conran ha rmnal govrnmn db qual nal db dlud by nomnal ncom growh. Gvn h rqurmn avrag ba rducd o abou 0,2 r cn of GDP. Howvr, cro-counry comarably hamrd by h fac ha h comoon of oal govrnmn db.., h l bwn xlc and mlc labl affc boh h gn and h magnud of h aroxmaon rror. W may hrfor conclud ha, for h OECD counr, h wo fn-horzon alrnav nd o mly oo ll fcal conoldaon comard o wha rqurd for ru fcal uanably. ha, a a by-roduc, h chncally movad moon of a fxd horzon ycally lad o an xcvly omc cur of currn fcal anc.

10 10 Rfrnc Blanchard, Olvr, Jan-Claud Chouraqu, Robr P. Hagmann and Ncola aror, h uanably of Fcal Polcy: Nw Anwr o an Old Quon, OECD Economc ud 15, Bur, Wllm H., A Gud o Publc cor Db and Dfc, Economc Polcy, Novmbr Euroan Common, Ovrvw of h 2002 uda of h ably and Convrgnc Pro gramm, ECFIN/045/03-EN, Fbruary Frdrkn, Nl Kl, Fcal uanably and ax moohng: A Prlmnary Analy of h Ca of Dnmark, n Balaon, Fabrzo and Danl Franco d.: Fcal uanably, Banca d'iala, 2001a. Frdrkn, Nl Kl, Fcal uanably n h OECD: A ml Mhod and om Prlmnary Rul, Workng Par 3/2001, Mnry of Fnanc, Arl 2001b. h://