RESTORING FISCAL SUSTAINABILITY IN THE EURO AREA: RAISE TAXES OR CURB SPENDING? Boris Cournède and Frédéric Gonand *

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1 RESTORING FISCAL SUSTAINABILITY IN THE EURO AREA: RAISE TAXES OR CURB SPENDING? Boris Cournède nd Frédéric Gonnd Wih populion geing fiscl consolidion hs become of prmoun impornce for euro re counries. Consolidion cn be pursued in vrious wys wih differen effecs on poenil growh which iself will be drgged down by geing. A dynmic generl equilibrium model wih overlpping generions nd public finnce block (including py-s-you-go pension regime helh cre sysem non-geing-reled public spending nd sock of deb o be repid) is used o compre he mcroeconomic impc of four scenrios: ) incresing xes o finnce unchnged pensions nd repy public deb b) lowering fuure pension replcemen res nd repying public deb hrough lower rio of non-geing-reled oulys o GDP c) rising he reiremen ge by.25 yers per decde nd incresing xes only o py off deb nd d) incresing he reiremen ge by.25 yers per decde nd pying off deb hrough lower rio of non-geing-reled expendiure o GDP. This ls scenrio is he one where growh is sronges: wih grdul increses in he reiremen ge nd spending resrin verge GDP growh in he 200s would be 0.34 percenge poin sronger hn in scenrio where fiscl consolidion is chieved exclusively hrough x hikes. The pproprie conclusion from he model is no h public spending is bd per se bu h cus o lower-prioriy spending iems cn deliver surprisingly lrge income gins compred wih he lernive of rising xes. Inroducion nd min resuls. In coming decdes lrge fiscl dusmens in he euro re cnno be voided. In period when bby boomers were in heir prime working ge nd could hve been expeced o pre-fund les pr of he fiscl cos of heir reiremen by building ne sse posiion he opposie occurred nd public deb more hn doubled s shre of GDP over he ls 30 yers (Figure ). Unless curren policy seings chnge he fiscl pressures from helh nd pension coss men h public deb is on n explosive ph. To bring down he deb-o-gdp rio public ccouns will hve o move from ody s deficis ( 2.4 per cen of GDP in ) o emporry surpluses before seling blnced long-erm posiion. 2. A wide body of lierure cknowledges he mgniude of he chllenge nd provides esimes of he required dusmens ofen referred o s x gps. Mos pplied sudies of x gps rely on n ccouning frmework o esime by how much xes hve o rise o repy or sbilise public deb usully over severl decdes. While simple his mehod hs some drwbcks. I ignores he feedbck effecs of chnges in xes nd public expendiure progrmmes on he behviour of economic gens (nobly heir lbour supply nd sving decisions) nd ulimely growh. As resul he x gp pproch presens x increses nd expendiure cus s The uhors re members of he OECD Economics Deprmen nd cn be conced : boris.cournede@oecd.org nd frederic.gonnd@oecd.org The uhors re indebed o Michel P. Feiner Peer Hoeller Vincen Koen nd Dve Re for helpful discussions nd suggesions on erlier drfs. The uhors lso wish o hnk Dvid de l Croix Romin Duvl Jørgen Elmeskov Joquim Oliveir Mrins Rober Price Jen-Pierre Vidl nd Luks Vogel for useful commens s well s Celi Rukoski for echnicl preprion. All views expressed re heirs nd should no be ribued o he OECD or is member counries. This pper hs been previously published s Working Pper No. 520 by he Economics Deprmen of OECD. See EU Commission (2006) for recen survey of he vilble evidence.

2 258 Boris Cournède nd Frédéric Gonnd 90 The Irresisible Rise of he Public Deb-o-GDP Rio in he Euro Are Figure 80 Gross deb Ne deb Noe: Gross deb refers o generl governmen finncil libiliies. Ne deb is defined s gross deb minus he finncil sses of he generl governmen secor. Gross nd ne deb re mesured on nionl ccouns bsis i.e. mrke prices. These mesures generlly differ from he vlues used for he purpose of ssessing complince wih he crieri derived from he Msrich Trey which re esimed fce vlue. Source: OECD Economic Oulook No. 79 dbse. symmericl equivlen mens of chieving fiscl consolidion. The x gp erminology my even convey he impression h incresing xes is he nurl wy of consoliding public ccouns nd pying bck governmen deb. In conrs wih sic mehods his pper models severl chnnels hrough which differen policy opions for finncing geing-reled spending pressures nd repying public deb will ffec growh. A sylised dynmic generl-equilibrium model hs been buil nd clibred on euro re d. Akin o he pproch by Oliveir Mrins e l. () i is bsed on overlpping generions nd n endogenous cpil mrke. An imporn exension however is h here he lbour mrke is lso endogenised: chnges in x res ffec ne wges hus impcing lbour supply decisions nd in urn ll oher vribles hrough feedbck effecs. The model lso expnds on Oliveir Mrins e l. () by including spending on helh cre non-geing-reled iems nd deb service in he governmen block. In conrs wih Oliveir Mrins e l. () which focuses on he effecs of geing on growh he presen model hs been designed for nd concenres on compring differen policy opions o resore fiscl susinbiliy. 3. Four scenrios of fiscl consolidion hve been modelled (Tble ). The reiremen ge is unchnged in firs pir of scenrios where he uhoriies consolide he fiscl posiion eiher by rising x res (scenrio TU) or by lowering he pension replcemen re nd reducing he rio of non-geing-reled public spending o GDP (scenrio SU). A second pir of scenrios

3 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? 259 The Four Scenrios Tble Tx hikes Spending resrin Unchnged Reiremen Age TU: x hikes nd unchnged reiremen ge SU: spending resrin nd unchnged reiremen ge Rising Reiremen Age TR: x hikes nd rising reiremen ge SR: spending resrin nd rising reiremen ge incorpores increses in he reiremen ge by.25 yers every decde coupled wih x increses (scenrio TR) or reducions in he rio of non-geing-reled spending o GDP (scenrio SR). For he ske of relism ll four scenrios ssume h increses in public helh cre spending (which he model proecs endogenously) re finnced by rising xes. In ll scenrios fiscl consolidion is defined s pying off deb by so s o bring he fiscl ccouns ino shpe us before he geing pressures kick in in full force. There is srong cse bsed on inergenerionl equiy grounds for going furher nd building ne sse posiion so s o pre-fund spending pressures ssocied wih he demogrphic rnsiion. 2 However given he difficuly of qunifying he desirble ne sse posiion iming zero deb is resonble if conservive ssumpion. The model confirms h x increses hve cosly economic consequences. This is no surprising given he ssumpions buil ino he model. Wh is more ineresing is h hese coss re priculrly lrge. Resuls from he model sugges h x increses re much more cosly wy o chieve fiscl susinbiliy when compred wih spending resrin. In model simulions nnul consumpion per cpi is 5 per cen higher in if fiscl consolidion is chieved hrough expendiure resrin nd increses in he reiremen ge (scenrio SR) hn hrough cross he bord x hikes (scenrio TU). Tx-bsed sregies depress svings cpil ccumulion he cpil/lbour rio nd ulimely rel wges. The resuls re obined wih conservive ssumpions mos of which end o underesime he disorive effecs of xion (see he concluding secion below). 4. Resuls from he model lso highligh he benefi of combining expendiure resrin wih pproprie srucurl reform (here in he form of increses in he reiremen ge). If expendiure resrin includes grdul increses in he reiremen ge in line wih longeviy (scenrio SR) consumpion per cpi is 5 per cen higher hn in he purely x-bsed scenrio TU nd 8 per cen higher hn in scenrio SU where spending is curbed wihou dusing he reiremen ge. The min forces driving srong growh in scenrio SR re h rising reiremen ge booss lbour supply while moderion in public spending encourges household svings nd bolsers cpil ccumulion. The model resuls re consisen wih inuiion nd empiricl evidence h fiscl consolidion nd srucurl reform re o lrge exen muully reinforcing (see lso vn den Noord nd Cournède 2006). 2 This is priculrly rue for cegories of public expendiure such s helh cre where providing he services is difficul o refuse nd he coss cn hrdly be fully recovered hrough user chrges. Working generions should pre-fund o finnce heir higher demnd for helh-cre services ler in heir lives (see for insnce OECD for more deils).

4 260 Boris Cournède nd Frédéric Gonnd The model 5. The shorcomings of he x gp nlysis menioned in he inroducion cn be overcome using generl equilibrium model wih overlpping generions prmeerised on euro re d. This nlyicl frmework models he combined effecs of public deb reimbursemen nd geing-reled reforms of public finnces on lbour nd cpil mrkes nd hus growh in he long run. Appendix fully describes he model is nlyicl soluion nd he corresponding numericl mehod of resoluion. 6. The dynmics of he model re exclusively driven by demogrphics public finnce reforms he reimbursemen of public deb nd he behviourl responses of economic gens in he euro re. In line wih mos of he lierure on dynmic generl equilibrium models wih overlpping generions for lrge counries his model does no ccoun explicily for effecs semming from he exernl side of he economy. Accouning for exernl linkges would smooh he dynmics of he model bu only o limied exen. Euro re households my wn o inves in younger counries o push up he re of reurn on heir sses. Ler in he dissving phse ny domesic svings shorge is likely o be less binding if euro re governmens cn borrow on inernionl finncil mrkes. Bu such shif in he counerpr of governmen deb would do nohing o solve he ulime susinbiliy problem. Moreover he res of he world including much of he developing world is lso rpidly geing nd is herefore compeing for he sme limied pool of cpil. Home bis (he Feldsein-Horiok puzzle ) exchnge re risks nd finncil sysemic risk lso sugges h he possible overesimion of he impc of geing on cpil mrkes due o he closed economy ssumpion is very smll. Demogrphics 7. The model embodies 79 cohors ech yer hus cpuring in deiled wy chnges in he populion srucure. Demogrphic proecions for he euro re ggrege he nionl proecions compued by Gonnd () using officil demogrphic ssumpions. These proecions re close o member counries officil demogrphic forecss. Pricipion nd unemploymen res by ge groups re frozen from onwrds in scenrios wih unchnged reiremen ges. Scenrios wih rising reiremen ges include corresponding chnges in he pricipion re of older workers. The yer is used s sring poin for pricipion nd unemploymen res becuse he unemploymen gp ws hen close o nil in he euro re. Households mximising behviour 8. The household secor is modelled by sndrd seprble ime-ddiive consn relive-risk version (CRRA) uiliy funcion nd n iner-emporl budge consrin. The insnneous uiliy funcion hs wo rgumens consumpion nd leisure. The verge individul of given cohor decides how much o work consume nd sve so s o mximise he discouned vlue of heir lifeime uiliy correced for risk version subec o heir iner-emporl budge consrin. Households endogenously choose how long hey work bu heir decision o pricipe in he lbour force is exogenous. In oher words he inensive mrgin of lbour supply is endogenous in he model while he exensive mrgin is exogenous.

5 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? Households receive wge nd pension income longside governmen-provided goods nd services h re no reled o geing nd hey lso benefi from public spending on helh cre. 3 In he model public helh spending does no ener he revenue side of household ccouns bu i dds o uiliy by keeping hem live longer. 4 Households py proporionl xes on lbour income o finnce he reimbursemen of public deb he PAYG pension regime n lwys blnced helh cre regime nd non-geing-reled public expendiure. 5 The households opimision progrmme is fully solved in n nlyic fshion (see Appendix for deils). 0. An imporn feure of his life-cycle frmework is h i inroduces relionship beween sving nd demogrphics. The ggrege sving re is posiively linked o he shre of older employees in he ol populion nd negively o he shre of reirees. When bby-boom cohors ge older bu remin cive geing increses he sving re. When hese lrge cohors reire he sving re declines. Producion funcion. Producion is modelled hrough sndrd consn elsiciy of subsiuion (CES) funcion wih wo inpus: cpil nd efficien lbour. Exogenous echnicl progress drives he vriion of muli-fcor produciviy (MFP) over ime. As menioned bove working ime is endogenous nd resuls from households opimising behviour. 2. In he long-run equilibrium he growh re of he gross wge per uni of efficien lbour equls MFP gins becuse boh ol lbour force nd he cpil/lbour rio (in efficiency unis) re consn. There is no depreciion of cpil. Including his prmeer would no chnge he dynmics of he model since equilibrium condiions sem from sving behviour ne of cpil depreciion. The price of he good produced by firms is normlised o (numérire). Inflion is bsrced from since his is long-run model. Four scenrios of public finnce reforms chieving susinbiliy in he fce of geing 3. Four differen scenrios of public finnce reform re considered (Tble ). Appendix 2 provides complee descripion of he four scenrios nd he corresponding nlyic formuls. As menioned bove ll scenrios chieve fiscl consolidion defined s repying deb by. Alernive scenrios where geing-reled cos pressures re finnced hrough deb ccumulion Public spending on helh cre includes expendiure on long-erm cre hroughou he pper (see Appendix 2 for more deils). In he model demogrphic chnge is he only driving force behind proeced increses in public spending on helh cre. OECD (2006) shows h his ssumpion errs on he conservive side s income- nd echnology-reled effecs re lrge nd my even domine he impc of demogrphic fcors. However s he focus of his pper is on fiscl policy nd no on helh-cre reform delibere choice hs been mde of reining conservive ssumpions for he helh secor. The choice of his ssumpion hs lile impc on he resuls of he simulions for wo resons. Firs he dynmics of public helh spending in he model simulions repored here is consisen wih he resuls in OECD (2006) despie smll difference in he size of he increse. Second he choice of differen ssumpion for increses in helh expendiure would shif he resuls in ll scenrios bu would no ler heir relive posiions becuse he rise in public helh expendiure is finnced similrly in ll scenrios (by incresing he ssocied x). Tx revenues re rised only on lbour income nd pensions in he model. A vrin of he model incorporing proporionl x on cpil income hs been buil. The resuls sugges h he receips from he cpil income x were very smll compred wih he revenues from xes on lbour income nd pensions. This vrin ws no used furher becuse dding cpil xion seriously complices he nlysis of he opimision behviour of households wihou improving he modelling of public secor ccouns much.

6 262 Boris Cournède nd Frédéric Gonnd hve no been considered becuse hey imply unsusinble dynmics while he presen sudy focuses on compring differen wys o resore susinbiliy. 6 Scenrio TU: higher pension nd helh x deb reimbursed by xes 4. In scenrio TU he PAYG pension regime is blnced ech yer hrough higher conribuion res. The replcemen re nd reiremen ge remin unchnged. Cohors perfecly forecs fuure increses in he conribuion re. 5. The sock of public deb ccumuled in 2004 is equl o 7 per cen of GDP nd srs being pid bck (service included) from unil when public deb reches zero. The rionle for zero deb by is h governmen ges is fiscl house in order us before he geing pressures relly merilise. Aiming sock of deb of 60 per cen of GDP in would probbly no be susinble in his conex nd my hus no provide helpful bseline. The ineres re on he deb is equl o he equilibrium long-erm ineres re clculed endogenously by he model. 6. In his scenrio n ddiionl proporionl x is levied on lbour income nd pensions o py bck governmen deb beween nd. As from he ime he fiscl consolidion progrmme is nnounced () households re fully wre h hey will hve o py his specific deb reimbursemen x supplemen on heir lbour income or pensions beween nd. 7. Non-geing-reled public expendiure is finnced by proporionl x on lbour income. Households receive rnsfer income for n overll moun equl o he revenues of his x. This non-geing-reled public expendiure regime inroduces degree of income redisribuion wihin cohors becuse he moun of xes (in bsolue erms) is no consn cross individuls while he corresponding rnsfer pymen is. 8. Assumpions for he public helh cre regime re he sme in ll scenrios. I is finnced by proporionl x on lbour nd pension income h blnces is revenues wih expendiure ech yer. The x re rises in ll scenrios s public helh cre expendiure increses in he fce of geing. As menioned bove helh expendiure is no modelled s rnsfer dding o household income. Helh expendiure does however conribue o he uiliy of households in he model becuse i is necessry iem of spending o deliver he longeviy profile underlying he simulions. In oher words he uiliy households derive from helh expendiure is no erning more bu living longer. Scenrio SU: lower replcemen re of pensions deb reimbursed by lower non-geing-reled public spending higher helh x 9. In scenrio SU he x re finncing pensions is frozen from on nd he PAYG sysem is blnced herefer by grdully decresing replcemen res for new reirees. As households nicipe fuure cus in he replcemen re hey rehink heir lbour supply consumpion nd sving plns ccordingly. 20. While he helh regime is he sme s in scenrio TU he min feures of scenrio SU re wofold: he pension replcemen re becomes endogenous fer 6 See Europen Commission (2006) for long-erm proecions of deb levels on unchnged policy seings. For recen sudy of he implicions of unsusinble deb dynmics for long-erm economic growh see Gonnd (b).

7 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? 263 he reimbursemen of he public deb ccumuled up o 2004 is finnced by lowering non-geing-reled public expendiures. 2. Boh reforms re nnounced in nd households respond immediely. For ech cohor consumpion before is he sme s in he incresing conribuion re scenrio where households nicipe h PAYG sysem reforms nd public deb reimbursemen rely on x hikes. When nnounced in households dus heir opiml consumpion nd leisure ph over heir lifeime. Thus he reform promps ech cohor o devise new opiml iner-emporl phs for consumpion nd lbour supply over is remining lifeime. Scenrio TR: higher ge of reiremen slighly higher pension x deb reimbursed by xes higher helh x 22. In scenrio TR he effecive verge ge of reiremen rises by one yer nd qurer every en yers from unil in line wih forecss of fuure life expecncy increses while replcemen res re unchnged. Age-specific pricipion res of workers bove 50 re ssumed o increse in line wih he chnges in he reiremen ge. The (smll) residul imblnces of he PAYG regime re covered by chnges in he pension x re. 23. As in bse scenrio TU public deb is pid bck by n ddiionl proporionl x levied on lbour income nd pensions beween nd. The helh regime nd he non-geing-reled public spending re unchnged compred o scenrio TU. As bove households respond immediely o ll chnges in by deriving new iner-emporl opiml consumpion nd lbour supply phs for ll cohors. Scenrio SR: higher ge of reiremen slighly lower replcemen re of pensions deb reimbursed by lower non-geing-reled public spending higher helh x 24. In scenrio SR he verge effecive reiremen ge increses by one yer nd qurer every en yers s in scenrio TR from o. One difference wih scenrio TR is h he residul imblnces of he PAYG regime re covered by reducions in he replcemen re for new reirees. The pension x re is kep unchnged is level. 25. Consisen wih he focus on spending cus public deb is pid bck by lowering non-geing-reled public spending nd keeping he corresponding x is re. As in ll scenrios he helh regime is unchnged compred o scenrio TU. 26. As bove households respond immediely o ll chnges in by deriving new iner-emporl opiml consumpion nd lbour supply phs for ll cohors. Summry of he four scenrios 27. Tble 2 summrises he min chrcerisics of he reform scenrios simuled in he model. Resuls 28. The simulion resuls which re robus cross vriions in he prmeers (see Box ) show h he choices mde o resore he susinbiliy of public finnces cn hve lsing

8 264 Boris Cournède nd Frédéric Gonnd Min Feures of he Four Modelled Scenrios of Fiscl Consolidion Tble 2 The PAYG pension regime is finnced by: The public deb is reimbursed beween nd by: Non-geing-reled public expendiure is finnced by: Public helh cre spending is finnced by: Scenrio TU Scenrio SU Scenrio TR Scenrio SR higher xes on lbour income higher xes on lbour income nd pensions consn x re on lbour income nd pensions higher xes on lbour income lower replcemen res for new reirees lower non-geing-reled expendiure consn x re on lbour income nd pensions. higher xes on lbour income rising reiremen ge residul increses in pension xes higher xes on lbour income nd pensions consn x re on lbour income nd pensions higher xes on lbour income rising reiremen ge residul cus in replcemen res lower non-geing-reled expendiure consn x re on lbour income nd pensions higher xes on lbour income Box Prmeerision Clibrion nd Sensiiviy Anlysis The min exogenous vribles in he model re he demogrphic d. A se of demogrphic d hs been consruced for he period Hisoricl vlues were ghered from nionl sources. Gonnd s () proecions hve been used for he period o 258. The model is bck o is long-run sedy-se in In his siuion GDP per cpi growh is exclusively deermined by he exogenous growh in MFP nd cpil deepening grows in line wih MFP 0.45 per cen per nnum. By conrs during he demogrphic rnsiion he dynmic equilibrium is driven by geing nd public finnce reforms. The model is clibred on n ineres re of 3.5 per cen in he bse yer corresponding o he sum of MFP gins nd he discoun re s suggesed by life-cycle heory. In conrs wih oher sudies he model is no clibred on echnicl prmeers such s he relive version o risk o mimic observed vriions in he sock of cpil round he bse yer s procedures of his nure cn bis he long-run resuls. The level of he verge replcemen re is compued s he rio of pensions received per cpi over gross wges received per cpi in. The weighed verge replcemen re for compulsory pension regimes is round 62 per cen in he euro re (OECD b). While oher vlues for replcemen res would modify bseline levels sensiiviy nlysis indices h differences cross simulions would no be subsnilly ffeced. The vlues of he x res finncing he pension regime he blnced helh cre sysem nd he non-geing-reled public expendiure regime re se in 2004 (he yer preceding he implemenion of he reforms in he model) in line wih he nionl ccouns for he euro re. In order o es he robusness of model resuls o lernive specificions nd prmeer vlues exensive sensiiviy nlysis hs been crried ou (see Appendix 3). Overll he dynmics of he resuls proves o be resonbly robus o chnges in key prmeers. Source: Appendix 3 covers hese opics in more deil.

9 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? 265 implicions for developmens in oupu per cpi nd oher mcroeconomic vribles (Figures 2 3 nd 4). Scenrios wih unchnged reiremen ges Scenrio TU: srong increses in xes nd mrked fll in he sving re 29. Blncing PAYG sysems in he conex of geing requires very sizeble increse in x res on verge from 0 per cen in o round 24 per cen in. The proporionl x levied on lbour income nd pension o reimburse deb by would be round 6 per cen in. Ageing would lso mechniclly rnsle ino higher x res for finncing helh expendiure. Overll he x burden increses very subsnilly in his scenrio from 50 per cen of he GDP in he model in o 66 per cen in (nd 73 per cen in ). While mssive his increse is nurl reflecion of he chnge in he dependency rio over he period. 30. The chnges in he x-o-gdp rio in his scenrio cnno be compred wih sndrd x gp esimes. Tx gp esimes such s in EU Commission (2006) reflec dusmens h will hve o be mde over nd bove chnges in enilemen progrmmes nd in he x-o-gdp rio h re embedded in curren nd plnned policies. Anoher obscle o comprbiliy is he dynmic nure of he model simulions which incorpore he negive feedbck of higher xes on oupu growh. 3. The dynmics of he cpil/lbour rio reflec he relive speed of he declines in sving nd lbour supply boh riggered by geing over he simulion period. I is downwrd sloping over he proecion period minly becuse of he oin impcs of he deb reimbursemen x on sving nd cpil ccumulion up o nd of incresing xes on opiml working ime over he whole period. Overll from he s on boh cpil nd lbour re scrcer hn in in his scenrio while xes re much higher. 32. The dynmics of he verge working ime in scenrio TU which is componen of he dynmics of he lbour force mirrors minly he vriions of he wge ne of xes. The inremporl firs-order condiion in households mximision progrmme requires h ne wges nd working ime move in ndem. Since households smooh heir opiml ineremporl phs for consumpion nd lbour supply i is no meningful o compue n insnneous elsiciy of working ime o xes from he oucomes of he model. Scenrio SU: public spending resrin more svings nd higher wges 33. The increse in he overll x burden is fr more limied hn in scenrio TU: he x-o-gdp rio evolves from 50 in o nerly 52 per cen in. In his scenrio public helh expendiure which is incresing grdully in line wih geing is he only iem of governmen spending h drives xes higher. Non-geing-reled public spending lso flls beween nd o reimburse he deb. Overll he level of ol public expendiure is 7 per cen lower in in scenrio SU hn in scenrio TU. 34. Wih replcemen res of he PAYG pension regime declining o round 30 per cen from onwrds here re srong incenives for working households o increse heir svings relively o scenrio TU in order o void shrp reducion of heir income nd consumpion when reired. As resul he sving re is round 2 percenge poins higher in scenrio SU hn in scenrio TU nd cpil deepening is ccordingly much sronger.

10 266 Boris Cournède nd Frédéric Gonnd Rel GDP Growh Re nd Level Figure 2 2.5% Averge Annul Rel GDP Growh Reforms implemened from on; perfec forecs ssumpion for households 2.0% Scenrio TU Scenrio SU Scenrio TR Scenrio SR.5%.0% 0.5% 0.0% Consumpion Per Cpi.20 GDP Per Cpi Scenrio SU relive o scenrio TU Scenrio SU relive o scenrio TU Scenrio TR relive o scenrio TU Scenrio TR relive o scenrio TU.5 Scenrio SR relive o scenrio TU.5 Scenrio SR relive o scenrio TU Noes: Scenrio TU: higher pension x deb reimbursed by xes higher helh x. Scenrio SU: lower replcemen re of pensions deb reimbursed by lower non-geing-reled public spending higher helh x. Scenrio TR: higher ge of reiremen slighly higher pension x deb reimbursed by xes higher helh x. Scenrio SR: higher ge of reiremen slighly lower replcemen re of pensions deb reimbursed by lower non-geing-reled public spending higher helh x.

11 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? 267 Simulion Resuls for Public Finnce Regimes Figure 3 30% 25% Re of he Pension Tx on Lbour Income Scenrio TU Scenrio SU Scenrio TR Scenrio SR 30% 25% Re of he Deb Reimbursemen Tx on Lbour Income nd Pensions Scenrio TU Scenrio SU Scenrio TR Scenrio SR 20% 20% 5% \ 5% 0% 0% 5% 5% 0% 0% % 25% 20% Re of he Helh Tx on Lbour Income Scenrio TU Scenrio SU Scenrio TR Scenrio SR 40% 35% Re of he Tx on Lbour Income nd Pensions Finncing Public Non-geing-reled Expendiures Scenrio TU Scenrio SU Scenrio TR Scenrio SR 5% 30% 0% 5% 25% 0% 20% % Non-geing-reled Public Spending Per Cpi (percen of verge gross lbour income) Scenrio TU Scenrio SU Scenrio TR Scenrio SR 70% Replcemen Re of he Pension Regime for New Reirees Scenrio TU Scenrio SU Scenrio TR Scenrio SR 60% 22.5% 50% 40% 20.0% 30% 7.5% % Relive Level of Tol Public Expendiures (Pension Helh Non-geing-reled Spendings excl. Deb Service) = Level of Non-geing-reled Public Expendiures = Scenrio SU relive o scenrio TU Scenrio TR relive o scenrio TU Scenrio SR relive o scenrio TU Scenrio SU relive o scenrio TU Scenrio TR relive o scenrio TU Scenrio SR relive o scenrio TU

12 268 Boris Cournède nd Frédéric Gonnd Simulion Resuls for Mcroeconomic Vribles Aggrege Sving Re Sock of Cpil.4 Scenrio TU Scenrio SU Scenrio TR Scenrio SR Scenrio SU relive o scenrio TU.3 Scenrio TR relive o scenrio TU Scenrio SR relive o scenrio TU =.2 =..0 Figure Growh Re of he Equilibrium Rel Gross Wge 2.5% 2.0%.5%.0% % 4.5% Rel Ineres Re 4.0% 3.5% Cpil / Efficien Lbour Rio Scenrio TU Scenrio SU Scenrio TR Scenrio SR = Scenrio TU Scenrio SU Scenrio TR Scenrio SR Averge Working Time Scenrio TU Scenrio SU Scenrio TR Scenrio SR.02 Scenrio TU Scenrio SU Scenrio TR Scenrio SR TFP ssumpion:.5% per yer.0.00 = Oupu per Uni of Efficien Lbour Scenrio TU Scenrio SU Scenrio TR Scenrio SR 80% 70% Dependency Rio ().05 = 60%.00 50% 40% Scenrio TU Scenrio SU Scenrio TR Scenrio SR % () Reired populion/lbour force.

13 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? In scenrio SU he gross wge is higher over he proecion period hn in scenrio TU becuse he cpil/lbour rio in scenrio SU is brodly sble while i declines seeply in scenrio TU. As resul he cpil/lbour rio remins fr higher levels over he proecion period implying higher gross wges. Since xes re lower ne wges re much higher hn in scenrio TU bu here is no s much rnsfer income s in scenrio TU. 36. In scenrio SU he opiml working ime diminishes by round 2.5 per cen in when he reform is nnounced. This derives from he chnge in households informion se in nd n ssocied srong income effec. Aniciping h fuure overll xes will be lower hn previously expeced nd h sronger cpil deepening will boos fuure wges households relise h he reform in scenrio SU rises heir permnen income compred o scenrio TU. As resul hey increse boh heir curren consumpion nd he opiml level of leisure. From onwrds he opiml working ime slowly rises becuse of he grdul rise in verge produciviy resuling from geing. Scenrios wih grdully rising reiremen ges 37. Scenrios TR nd SR involve grdul increses in reiremen ges in line wih longeviy. Rising he reiremen ge by.25 yer per decde significnly booss lbour supply (long he exensive mrgin) nd slows down he increse in he old-ge dependency rio. Scenrio TR: limied x increses nd much improved lbour supply 38. The rise in conribuion res required o blnce PAYG sysems is much smller hn in scenrio TU becuse increses in reiremen ge limi he fll in he dependency rio. From 50 per cen of GDP in he shre of xes in GDP rises o 58 in gins 66 per cen in scenrio TU. Despie he much lower x burden scenrio TR delivers level of governmen spending h is only slighly (8 per cen in ) below h in scenrio TU. 39. The fvourble impc of grdully rising reiremen ge on lbour supply leds he cpil/lbour rio o be slighly lower hn in scenrio TU. The endency for individuls o sve less becuse heir reiremen period will be shorer hn in scenrio TU is roughly compensed by he longer working life period during which hey sve. As resul he chrcerisics of he equilibrium on he cpil mrke in scenrio TR re very similr o hose in scenrio TU. 40. As concerns he dusmen of he working ime in in scenrio TR wo opposie mechnisms re work. On he one hnd fuure cpil/lbour rios re now niciped by households o be lower hn previously hough (wih ps expecions in line wih scenrio TU). This implies h he fuure growh re of wges is lower nd he cos of leisure declines. On he oher hnd he rise in he x re finncing he PAYG pension regime is now fr more limied hn niciped before. This pushes up he verge cos of leisure ceeris pribus. Overll he ne impc on working ime urns ou o be negive suggesing sronger impc of lower lbour xes on leisure nd hus uiliy. Scenrio SR: x burden in check nd high levels of income 4. Scenrio SR incorpores n incresing reiremen ge (s in scenrio TR) nd fll in non-geing-reled public expendiure o reimburse he deb (s in scenrio SU):

14 270 Boris Cournède nd Frédéric Gonnd compred wih scenrio SU he grdul increse in he reiremen ge limis he rise in he dependency rio nd leds o higher replcemen re. The reducion of he replcemen re needed o blnce he PAYG sysem is 2 percenge poins insed of 34 percenge poins in scenrio SU in ; he rio of public spending o GDP is 5 percenge poins lower in in scenrio SR compred wih scenrio TU; he x burden lmos sbilises (52 per cen of GDP in insed of 66 per cen in scenrio TU); s in scenrio TR he cpil/lbour rio remins relively close o he one simuled in scenrio TU. Consequenly i is lower hn in scenrio SU in line wih more fvourble dynmics of he lbour force over he proecion period due o he increse in he reiremen ge. 42. The growh re of he economy would be on verge 0.2 per cen of GDP higher in he 200s in scenrio SU hn in scenrio TU due o sronger cpil ccumulion nd fr lower x burden. This would rnsle ino level of rel GDP per cpi 5 per cen higher in in scenrio SU hn in scenrio TU. 43. GDP growh would be even sronger in scenrio SR illusring he fvourble impc on growh of blncing he PAYG sysem in n geing conex by incresing he reiremen ge nd conining public spending rher hn rising xes or srongly diminishing replcemen res. The verge GDP growh re during he 200 s would be 0. per cen higher in scenrio SR hn in scenrio TR which relies more on x hikes nd 0.34 per cen higher hn in scenrio TU. The cumulive impc of such differences is lrge: he end of he simulion period () income per hed in scenrio SR is 7 per cen higher hn in scenrio TU. Concluding remrks 44. Model resuls indice h if he lrge dusmens needed o resore fiscl susinbiliy were mde by rising xes he induced disorions could enil lrge coss for economic growh wih mos of he negive feedbck coming hrough cpil mrkes. The mechnism is h if xes re incresed o finnce n unchnged pension replcemen re households hve much less incenive o sve nd inves hn if he replcemen re is reduced nd xes kep in check. Lower svings hold bck cpil deepening nd ulimely depress oupu per worker. Even hough he effec of x increses on cpil formion is lrge in simulion resuls i my sill be underesimed becuse cpil income is no xed in he model. 45. The negive impc of xion on lbour supply is relively modes in simulion resuls bu is likely o be sronger in prcice becuse o remin rcble he model does no embody some poenilly powerful chnnels: In he model he sme x re pplies o ll lbour inpus. In euro re counries x schedules re progressive. A consequence is h in prcice he income effec will be weker hn in he model nd he subsiuion effec will be sronger. The simulions re herefore likely o underesime he negive feedbck from higher xes on he number of hours worked (he inensive mrgin of lbour supply). While exogenous in he model pricipion (he exensive mrgin of lbour supply) is negively ffeced by xes in prcice. A lrge body of evidence indices h higher lbour x wedge reduces pricipion especilly hrough is disincenive effec on second erners (OECD 2006b nd Jumoe 2003).

15 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? In ddiion o he effecs cpured in he model x-bsed consolidion sregies cn lso enil ddiionl disorions vi he impc of xion on muli-fcor produciviy (MFP). Becuse muli-fcor produciviy is exogenous in he model he simulions do no incorpore he effec of xes on invesmen in humn cpil nd reserch nd developmen civiies. Mos sudies conclude h he effec is negive nd srong (Feldsein 2006). Humn cpil ccumulion nd reserch nd developmen effors re he min drivers of muli-fcor produciviy growh which iself is he dominn deerminn of long-erm growh. 47. On he oher hnd he ssumpion h MFP is exogenous is only vlid insofr s ny cus in expendiure fll on low-prioriy iems nd hose h hve no or lile effec on MFP. Erly reiremen schemes re good exmple wheres high-reurn infrsrucure proecs nd efficien educion progrmmes re wo exmples of res h expendiure-bsed fiscl consolidion sregies should lrgely preserve. In oher words he model implicily ssumes h of public expendiure is worh of income o households in he form of public services received bu i kes more hn of xes o fund his becuse xes hve disorionry effecs. In reliy here clerly re welfre benefis from funding number of socil progrmmes collecively indeed his is he rison d êre for public expendiure in he firs plce. The problem is h he coss of xion rise shrply wih he x re wheres he mrginl benefis of public expendiure progrmmes fll (he bes progrmmes re implemened firs). Thus he pproprie conclusion from he model is no h public spending is bd per se bu h cus o lower-prioriy spending iems cn deliver surprisingly lrge income gins compred wih he lernive of rising xes. 48. The model could be exended o inegre feedbcks from he composiion of public expendiure on MFP growh. Such n pproch would enble qunifying he implicions of differen expendiure reform scenrios for long-erm economic growh while king ccoun of feedbck effecs hnks o he generl-equilibrium nure of he model. In ddiion n exended model of his nure would shed some ligh on how much inefficien public spending is cosing in erms of los fuure growh. An imporn chllenge before implemening his pproch is o derive relible esimes for he impc of vrious componens of public spending on MFP. 49. The model could lso be used in normive nlysis perspecive o compre scenrios in erms of heir implicions for iner-generionl firness. The foundion of he model on he opimising behviour of households opens he possibiliy of compuing he lifeime uiliy of ech cohor under he considered scenrios. The heory of socil choice could hen be used o exmine how differen opions compre depending on he degree of version o iner-generionl inequliy.

16 272 Boris Cournède nd Frédéric Gonnd Demogrphics APPENDIX DESCRIPTION OF THE MODEL AND ITS SOLUTION 50. The model embodies 79 cohors ech yer hus cpuring in deiled wy chnges in he populion srucure. Ech cohor is chrcerised by is ge yer hs N members nd is represened by one verge individul. The verge individul s economic life begins 20 ( =0) nd ends wih cerin deh Ψ 0 (= Ψ 0 20 ) where Ψ 0 snds for he verge life expecncy birh of cohor born in yer. 5. In ech cohor proporion υ of individuls re working while µ re unemployed nd receive no income. The incive populion is divided ino wo componens. A firs componen corresponds o individuls who never receive ny conribuory pension during heir lifeime. They my ge socil ssisnce which he model ccouns for s pr of governmen spending. A proxy for he shre of he incive populion h never receives conribuory pension is found in he rio of incive people ged o incive people ged (in ). 7 Disinguishing beween pensioners nd incive people who never receive ny pension is no only relisic bu lso imporn o ge resonble levels for he conribuion re blncing he PAYG regime. The proporion π of pensioners in he populion is hen compued s residul. 52. Demogrphic proecions for he euro re ggrege he nionl proecions compued by Gonnd () using officil demogrphic hypoheses. These proecions re close o member counries officil demogrphic forecss. They re rnsformed from five-yer periods ( 200 ) nd ge groups (20-24 yers yers ) ino nnul d (20 2 yers in 200 ) using liner inerpolion. The implici nnul survivl probbiliies re close o UN proecions (Unied Nions 2002). 53. As fr s lbour force nd working populion proecions re concerned unemploymen nd pricipion res by ge groups re frozen from onwrds unless oherwise sed. The yer is probbly resonble sring poin becuse he oupu gp ws hen close o 0 in mos OECD counries. More deil on ssumpions bou pricipion res is provided when policy scenrios re nlysed (see below). Households secor s mximizing behviour 54. The household secor is modelled by sndrd seprble ime-ddiive consn relive-risk version (CRRA) uiliy funcion nd n iner-emporl budge consrin. This uiliy funcion hs wo rgumens consumpion nd leisure. 55. Inroducing n endogenous lbour mrke in generl equilibrium models wih OLG rises severl chllenges. Among ohers mny models compue he households opiml behviour using shdow wges during he reiremen period (see for insnce Auerbch nd Kolikoff 987; Broer e l. 994; Chuveu nd Loufir 997; Docquier e l. 2002). The use of numericlly 7 The ssumpion here is h he individuls no in he lbour force will never receive pension fer 65 nd remin ouside of he PAYG regime. The inuiion is he following: incive individuls ged beween 40 nd 44 re mos probbly neiher sudens nor reirees. Their number is compred o he number of incive people beween who in re lmos ll reired nd sill live. In mos counries round 20 per cen of old incive people do no receive pension. This is he ssumpion in he model. This mehod yields relisic conribuion res.

17 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? 273 compued shdow wges llows for meeing emporl consrin during he reiremen period i.e. when he frcion of ime devoed o leisure is equl o. These shdow wges re proxies for Kuhn-Tucker mulipliers. While in principle mhemiclly correc his mehod my no be very inuiive from n economic poin of view since i ssumes h gens keep opimising beween work nd leisure even during he reiremen period. One prcicl issue wih he shdow wge pproch s implemened in his lierure is h he mehod chosen o derive he shdow wges hs n impc on he overll generl equilibrium nd herefore on ll vribles vi he inremporl firs-order condiion. Furhermore his pproch mkes i prciclly impossible o derive n nlyicl soluion o he model nd seriously complices is numericl soluion. 56. These problems cn be overcome by specifying he model in wy where he households mximision problem cn be solved in wo seps. The specificion sepres ech cohor ino working individuls who decide on heir opiml consumpion nd lbour supply nd non-working individuls whose lbour supply is zero by definiion. 57. The lbour supply of he represenive individul of whole cohor ( l [ 0; ] h: l = ν ( l ) ( ν ) = ν l ) is such where ν is he frcion of working individuls in cohor ged in yer nd l is he opiml frcion of ime devoed o work by he working sub-cohor. 8 The model compues he opiml l s firs hen he opiml l s nd he c s (more deils follow below). This wo-sep mehod is no possible in models which do no brek down ech cohor ino sub-groups wih differen lbour supply. 58. The obecive funcion over he lifeime of he verge working individul of cohor of born in yer is: U Ψ 0 0 = σ ( ρ) = 0 / ( c ) η( H ( l ) where c snds for he consumpion level of he verge individul of he working sub-cohor of ge in ρ is he subecive re of ime preference (lso clled psychologicl discoun re) σ / / is he relive-risk version coefficien 9 / / / ( c ) η( H ( ) V l is he CES insnneous uiliy funcion yer η is he preference for leisure relive o consumpion he elsiciy of subsiuion beween consumpion nd leisure in he insnneous uiliy funcion σ = 8 9 ν For insnce if =70% of cohor ge yer re working nd devoe verge individul of he sme cohor devoes l of heir vilble ime o lbour hen he l = 35% of is vilble ime o lbour nd 65 per cen o leisure. For CRRA funcion his coefficien is equl o he inverse of he ineremporl subsiuion coefficien.

18 274 Boris Cournède nd Frédéric Gonnd nd H prmeer whose vlue depends on he ge of n individul nd whose nnul growh re is equl o he nnul TFP growh re (wih H = 0 ) The ineremporl budge consrin for he working sub-cohor of ge 20 (i.e. =0) in yer is: where: l 0 ω 0 Ψ 0 l ω = i= r i = c 0 Ψ 0 c = i= r ω is he fer-x income of working individul per hour worked such h = w ε ( τ D τ P τ H τ NA ) d NA ω ; w snds for he gross wge per efficien uni of lbour; he prmeer ε links he ge of cohor o is produciviy. Following Miles (999) ( ) ( ) qudric funcion is used: ε ( ) = e which displys n invered U-shpe pern wih pek 42 yers; he x re τ D snds for proporionl x on lbour income nd pensions finncing he reimbursemen of he public deb; τ P snds for he proporionl x re finncing he PAYG pension regime (see infr) pid by households on heir lbour income; τ H snds for he re of proporionl x on lbour income which finnces n lwys blnced helh cre regime (see infr). Helh expendiure hs fvourble impc on he uiliy of individuls becuse i underpins longeviy gins. To void double couning he model herefore does no ccoun for helh expendiure s income rnsfers received by households (in conrs o oher cegories of public spending); τ NA snds for he re of proporionl x levied on lbour income nd pensions o finnce public non-geing-reled public expendiure d ; 2 d NA snds for he non-geing-reled public spending h one individul consumes irrespecive of ge nd income. This vrible is used s monery proxy for goods nd services in kind bough by he public secor nd consumed by households. NA i 0 Inroducing his prmeer sbilises he rio of he conribuions of consumpion nd leisure o uiliy when echnicl progress is sricly posiive. The Euler equion (infr) suggess h he nnul growh re of consumpion is equl he sedy-se o he difference beween he ineres re nd he discoun re which in urn is equl o nnul TFP growh. See Broer e l. 994; Chuveu nd Loufir 995; Docquier e l The Ingenue em (200) uses he sme funcion. Ye more recen economeric sudies (Auber nd Crepon 2003) do no confirm he decrese of individul produciviy for older workers. However sensiiviy nlysis shows h he impc on mcroeconomic vribles especilly growh of he choice beween hese wo ssumpions is negligible. Tx revenues re rised only on lbour income nd pensions in he model. A scenrio incorporing proporionl x on cpil income hs been buil. The resuls suggesed h he receips from he cpil income x were very smll compred wih he revenues from xes on lbour income nd pensions. This vrin ws no used furher becuse dding cpil xion seriously complices he nlysis of he opimision behviour of households for lile benefi in erms of improving he modelling of public secor ccouns.

19 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? In such specificion he working sub-cohor lwys chooses sricly posiive opiml working ime hroughou is life. In oher erms he represenive individul ssocied wih he working sub-cohor never reires. This propery of he model does no led o unrelisic resuls becuse ech enire cohor is mde of working sub-cohor nd non-working sub-cohors wih weighs h vry wih he ge of he cohor. De fco for he represenive individul ssocied wih he whole cohor he reiremen ge is defined exogenously hrough he ν s which become equl o zero beween 65 nd 75 yers. Since l = ν l he represenive individul ssocied wih he whole cohor reires in he model when he exogenous prmeer ν reches zero The firs-order condiion for he inremporl opimizion problem derives from equlizing he rio beween he mrginl uiliies of consumpion nd leisure wih he rio of consumpion nd leisure prices. In he model he price of he goods produced is. The price of leisure (e.g. is opporuniy cos) is equl o he ne wge per uni of efficien lbour for cohor ( ) e.g. ω. Some lgebr yields he opiml relion beween c nd l 0 : > ( ) η c l = > 0 ω H The inr-emporl opimliy equion is conform o inuiion: higher fer-x work income per hour worked ( ω ) promps less leisure ( ) nd more work ( l ). l 62. The firs-order condiion for he iner-emporl opimizion problem derives from mximizing he iner-emporl uiliy funcion under he budge consrin. Solving wih Lgrngin nd fer some lgebr he following Euler equion is obined (where κ = / σ ): c c = κ κ r η ω ρ η ω The iner-emporl opimliy equion is lso consisen wih inuiion: if fer-x income per hour worked ( ω ) is sedy nd he rel re of reurn ( r ) is higher hn he psychologicl discoun re ( ρ ) consumpion will rise over ime; 3 Endogenising he reiremen decision wih he l would bring bou serious problems. The yer when l becomes equl o 0.05( ) ( ) zero is closely reled o he funcion ε ( ) = e linking he ge nd individul produciviy nd is decline fer some hreshold yer. Indeed he firs-order condiion suggess h l =0 only if ε declines sufficienly so h ( η ω ) c ( l ) = / equls. The ssocied reiremen ge cn be very high wih such specificion (more hn 90). Moreover here is lively debe bou he form of he funcion ε () which my no decline fer some hreshold-yer. For hese resons endogenising he reiremen decision using he l s does no pper o be good ide in his conex. Auerbch nd Kolikoff (987) for insnce impose n exogenous reiremen ge of 66 in heir model. 2

20 276 Boris Cournède nd Frédéric Gonnd if fer-x work income per hour worked ( ω ) rises over ime nd he rel re of reurn ( r ) is sedy nd no lower hn he psychologicl discoun re ( ρ ) consumpion ( c ) will rise over ime; nd lower risk version (lower σ hence higher κ ) implies lrger iner-emporl chnges in consumpion (in he nurl cse where he rel re of reurn r is higher hn he psychologicl discoun re ρ ). 63. Plugging his expression bck ino he budge consrin yields he iniil level of consumpion for he working cohor ged 0 = yer : [ ] Ξ = Ψ = Ψ = = ( / i i H r c ω η ω η ω ω where ( ) ( ) = = Ξ i i r 0 κ κ κ ω η ω η ρ. 64. The opiml consumpion ph for ech working sub-cohor is derived from he opiml vlue of 0 c nd he Euler equion. The phs of he lbour supplies of he working cohors ( l ) re hen derived from he vlues ( c ) using he inr-emporl firs-order condiion. Evenully one cn derive he opiml lbour supply of he verge individul of whole cohor (i.e. l such h l l ν = ). 65. Knowing he opiml phs ( l ) simplifies he compuion of he opiml level of consumpion of he verge individul of whole cohor. The vlues ( c ) re obined by mximising he uiliy funcion of he verge individul of whole cohor where he lbour supply 0 = > l l ν is lredy known i.e.: ( ) ( ) ( ) Ψ = = 0 0 / / / 0 ) ( H c U σ η ρ σ l under he iner-emporl budge consrin: Ψ = = Ψ = = = i i i i r c c r y y where y snds for he ol income ne of xes of he verge individul represenive of whole cohor such h : NA NA H P D NA NA H P D d w d w y ) ( ) ( Φ = Φ = τ τ τ τ ε τ τ τ τ ν ε l l

21 Resoring Fiscl Susinbiliy in he Euro Are: Rise Txes or Curb Spending? In he bove expression Φ snds for he pension income received by he reirees of cohor. I is proporionl o heir ps lbour income depends on he ge of he individul nd on he ge ψ which n individul is eniled o obin full pension. Three cses my occur in he model: ) No pension cn be received before he ge of 50: If ( 20) < 50 Φ = 0. 2) If n individul is bove 50 bu below he full-righ reiremen ge ς he or she cn receive pension reduced by penly. This penly ws ssumed o be equl o 6 per cen per yer 4 which corresponds pproximely o curil neurliy for curren PAYG regimes. Thus: ς 20 If 50 ( 20) < ς Φ = mx l p wεψ π ; 0 00 / 6 where p is he verge replcemen re of he regime when reiring ge ς. 3) Finlly n individul will obin full pension if his or her ge is bove or equl o ς. π If ( 20) ς Φ = Φ π This implies h he pension of he verge represenive individul is fl over ime (i.e. no wge-indexed) bu is dused ech yer by he chnge in he number of pensioners in ech cohor. 67. The opiml ph for consumpion sems from he Euler equion using Lgrngin: κ c r ρ = where he ineremporl subsiuion coefficien is equl o he inverse of he c risk version ( κ = σ ) prmeer. The iniil level of consumpion c 0 (i.e. he level of consumpion of cohor of ge 20 yer ) is obined by plugging he Euler equion ino he budge consrin: c Ψ 0 = Ψ 0 y0 y / r = i= i = i= κ ( ρ ) ( r ) This life-cycle frmework lso inroduces link beween sving nd demogrphics. In such seing he ggrege sving re is posiively correled wih he frcion of older employees in ol populion nd negively wih he frcion of reirees. When bby-boom cohors ge older bu remin cive geing increses he sving re. When hese lrge cohors reire he sving re declines. 69. Hving compued he opiml ph of consumpion for ll he cohors of he model verge individul sving ( s = y c ) nd individul welh ( Ω = ( r ) Ω s ) cn be compued. The nnul sving is invesed in he cpil mrke yielding n ineres re r. The ineres pymens re cpilised ino individul welh. i κ 4 This benchmrk corresponds roughly o n curilly fir penly re (see for insnce Csey e l. 2003).