PUBLIC PENSION SUSTAINABILITY OPTIONS: THE RELATIVE MERITS OF INCREASING CONTRIBUTION RATES OR SWITCHING TO A FULLY-FUNDED PENSION STUART J.

Transcription

1 UNIVERSITY OF REGINA ISSN (on-lne) DEPARTMENT OF ECONOMICS ISBN PUBLIC PENSION SUSTAINABILITY OPTIONS: THE RELATIVE MERITS OF INCREASING CONTRIBUTION RATES OR SWITCHING TO A FULLY-FUNDED PENSION STUART J. WILSON Deparmen of Economcs Unversy of Regna Regna, Saskachewan Canada S4S 0A econ@uregna.ca July 007 DISCUSSION PAPER #08

2 Publc Penson Susanably Opons: The Relave Mers of Increasng Conrbuon Raes or Swchng o a Fully-Funded Penson Suar J Wlson* Absrac Many naons are experencng populaon agng due o rsng lfe expecances and declnes n ferly. As a resul, polcymakers are srugglng wh he susanably of publc penson sysems. Ths paper uses an overlappng generaons dynamc equlbrum model o nvesgae he relave mers of wo penson susanably opons. The frs opon nvolves ncreasng he penson conrbuon raes of workers o ensure susanably of he ypcal pay-as-you-go penson sysem. The second opon s he swch o a fully-funded plan, n whch he governmen s requred o ncur deb o honour exsng penson lables, wh ndvduals makng conrbuons no he new fully-funded penson sysem when workng, bu also payng ncome axes o servce governmen deb. The mng of hs swch concdes wh he baby boom generaon enerng he old worker sage of lfe whch s conssen wh he mng of he curren penson reform debae. Smulaon resuls sugges ha economes facng no populaon growh n he fuure and whou echnologcal progress are no beer off swchng o a fully-funded penson sysem. JEL Classfcaon Codes: E, C68, H55, J6 The auhor graefully acknowledges fnancal asssance from he Socal Scences and Humanes Research Councl of Canada as par of he research program, Savngs and he welfare sae. A verson of hs paper was presened a he Inernaonal Symposum on Economc Theory, Polcy and Applcaons, Ahens, Greece -3 Augus 006. * Deparmen of Economcs Unversy Of Regna Regna, SK, Canada S4S 0A Tel: + (306) Emal: suar.wlson@uregna.ca URL:

3 . Inroducon Many naons are concerned wh he susanably of governmen-run penson sysems. For he mos par, he pay-as-you-go (PAYGO) penson sysem s he mos common ype of penson sysem, wh conrbuons by workers beng used o fund conemporaneous benefs o rerees. These sysems were generous o early generaons, when lfe expecances were relavely low, and as populaons and he labour force were growng. However, he susanably of hese sysems s n queson as a resul of he dramac fall n ferly raes snce he pos-wwii baby boom, and rsng lfe expecances. In Canada, susaned mmgraon has allevaed some of he mpac of hese demographc changes, bu Fgure sll shows he srkng effec of decreased ferly and populaon agng. In 97, almos half of he populaon of Canada was younger han 5 years of age, and less han en percen was older han 64 years of age. By he year 050, he Canadan populaon s expeced o conss of almos equal shares of hose aged less han 5, beween 5 and 44, beween 45 and 64, and older han 64. The rao of hose over 64 o hose beween he ages of 5 and 64 was less han weny percen n 97, and s expeced o be ffy percen n 050. Wh lower raes of mmgraon experenced by oher naons, he problem s more severe. The effec of populaon agng on penson sysems can be summarzed by he expeced change n penson payroll axes f here s no change n he benef formula for benefcares. The average conrbuon payroll ax rae n he European Unon was found o be 6% a he begnnng of he weny-frs cenury, and s expeced o rse o 7% by 050 whou any furher reform (European Unon Commsson, 00). Smlarly, n he Uned Saes, he conrbuon rae for Socal Secury would have o rse from.4% o 7.8% (Socal Secury Admnsraon, 00). Reform of he exsng PAYGO sysems could nvolve gradually decreasng fuure benef raes, gradually rasng he reremen age, usng general ax revenues o fund penson defcs, and also quckly rasng conrbuon raes o parally pre-fund fuure benefs. A promnen reform opon s o replace PAYGO sysems wh fully-funded or parally-funded sysems. Feldsen (995) and Feldsen and Samwck (996) examned a ranson from a PAYGO sysem o a fully-funded sysem ha provdes he same level of benefs. They found ha here would be posve gans o fuure

4 generaons from a deb-fnanced ranson under he condons ha he margnal produc of capal s hgher han he rae of aggregae wage growh, and hgher han he rae of me dscounng, and also ha he rae of aggregae wage growh s posve. Snce he US experence n he lae weneh cenury was one of low aggregae wage growh and hgh raes of reurn, he auhors conclude ha a polcy shf would be benefcal o he US. However, such a move mgh no be polcally possble snce hose alve durng he ranson may experence a welfare reducon, and hus no allow such a polcy shf. Boh of hese works used a paral equlbrum analyss and dd no accoun for he effecs of such polcy changes on he naon s capal sock, household savngs decsons, and neres raes. Kolkoff (995, 996) smulaed he ranson from a PAYGO o a prvazed sysem usng a general equlbrum overlappng generaons model, wh no demographc change (consan one percen annual populaon growh), no echnologcal progress, no nrageneraonal heerogeney, and no lfeme uncerany. He found ha effcency gans were sronges when he benefconrbuon lnkage n he PAYGO srucure s poor, and when a consumpon ax s used o fnance he ransonal socal secury benefs. Wh a poor benefconrbuon lnkage, he shf o personal accouns causes agens o supply more labour. When he benef-conrbuon lnkage s srong and he ranson s funded usng a proporonal ncome ax, fuure generaons may nsead suffer losses. Kolkoff, Smeers and Wallser (999) added nrageneraonal heerogeney n earnngs o he basc modelng framework, and found ha prvazaon can have sgnfcan gans n he long run, bu ha ransonal generaons can experence welfare losses. DeNard, Imrohoroglu and Sargen (999) commened ha demographc change was rarely modeled n general equlbrum models, bu could have very dramac effecs on smulaon resuls. They used a dynamc general equlbrum overlappng generaons model wh unceran lfemes, echnologcal progress, and US demographc projecons o examne he mpac of dfferen reform measures on macroeconomc varables and welfare across generaons. The expeced coss and fundng of Medcare and Medcad as a resul of demographc change were also added o he analyss. Ther resuls ndcaed ha o susan he socal suppor for he elderly, he payroll ax rae may have o rse as hgh as sxy percen, or consumpon axes may have o rse o hry-seven percen. A polcy ha focuses on ncreasng he reremen age and he payroll ax rae durng he demographc ranson s benefcal 3

5 for fuure generaons, wh a relavely small cos o ransonal generaons. They concluded ha he bes reform measure would be one whch smplfes and srenghens he lnkage beween an ndvdual s conrbuons and benefs. Fehr (000) exended he basc overlappng generaons general equlbrum model o sudy he mpac of a se of PAYGO reforms on he macroeconomy and he welfare of dfferen generaons. He ncorporaed nrageneraonal heerogeney, rsng lfe expecances, and declnng ferly no he modelng framework. The reform expermens examned he effec of ncreasng he reremen age, decreasng benefs, and gradual ncreases n general axes o fnance penson defcs. He found ha srenghenng he lnkage beween benefs and conrbuons led o effcency gans, and, s he baby-boom generaon (and n some cases, he followng generaon) ha experence welfare losses as a resul of he shf from he saus quo, whle laer generaons benef from he reforms ha reduce he burden of he unfunded sysem. Buler (000) examned penson reform of he PAYGO sysem n a small open economy envronmen, usng a model ha ncorporaed lfeme uncerany and deah bequess. Reform expermens o rean PAYGO feaures focused on he effecs on ransonal generaons of () reducng benefs, () ncreasng he reremen age, and () ncreasng he payroll ax, o rean he pay-as-you-go budge balance. In addon, he effecs of an ncrease n he consumpon ax o pay for penson defcs, keepng all feaures of he PAYGO srucure consan, was nvesgaed. Buler provded welfare comparsons across reform opons for agens of dfferen generaons. The resuls show ha consumpon axes provde fewer dsorons han payroll axes. In general, older generaons (boh curren older workers and rerees) prefer ax ncreases o susan he penson sysem nsead of benef reducons, and prefer ncome ax ncreases o consumpon ax ncreases, whle younger generaons a he me of projeced reforms have he oppose preferences. In addon, older workers a he me of projeced reforms prefer ncreases n payroll or consumpon axes o ncreases n he reremen age, whle younger workers have he oppose preferences. Cooley and Soares (996, 999) used an overlappng generaons model where agens lve four perods, and agens face he penson susanably ssue. Wll voers dump he PAYGO penson sysem n favour of a prvazed sysem, or suppor? The auhors concluded ha f voers beleved ha hey could abandon oblgaons o rerees, he PAYGO sysem would collapse because generaons followng he babyboomers wll elec o abandon he sysem because of he heavy coss assocaed wh 4

6 supporng he reremen of he baby-boom generaon. If voers canno abandon her oblgaons o rerees, he sysem does no collapse because voers wan o avod welfare losses ha resul from fundng benefs for pas generaons and pre-fundng her own penson benefs. If voers are gven he opon o gradually phase-ou he PAYGO sysem, he only opon ha s suppored by voers s one n whch he ranson s deb-fnanced, so ha fuure (non-vong) generaons bear a subsanal poron of he coss. Servcng he deb wh labour axes s also preferable han consumpon axes o voers. In addon, Conesa and Kruger (999) ndcaed ha ncome uncerany could reduce he suppor for penson reform from a PAYGO o a fully-funded sysem, and ha an mmedae ranson s preferable o a gradual ranson. Conssen wh dfferen smulaon sudy resuls, many auhors have argued ha s no possble o acheve a Pareo mprovemen by changng o a fully-funded penson sysem. Geanakoplos, Mchell and Zeldes (998), Snn (000), and Breyer (00) have dscouned he of-ced reasons for he move o fully-funded or parally funded pensons. The PAYGO sysem essenally ransfers ncome across generaons. Inroducory generaons receve benefs far greaer han her conrbuons, and o pay for hese excess benefs, fuure generaons pay an mplc ax as par of her penson conrbuons o fund he mplc PAYGO penson deb. A ranson from a PAYGO o a fully-funded penson sysem nvolves converng he mplc PAYGO penson deb no explc deb, hen deermnng how fuure generaons wll servce and pay off hs deb. Any benefs n movng o a fully-funded sysem ha arse due o a decrease n ax dsorons o he labour-lesure and consumpon-savng decsons may also be acheved by elmnang such dsorons n penson and ax polcy whle reanng he PAYGO sysem. The effcency of he PAYGO sysem may be mproved by drecly lnkng benefs o conrbuons. The focus of hs paper s on comparng he welfare of generaons under wo dfferen governmen penson polcy responses o demographc change. The frs opon s o ncrease PAYGO penson conrbuon raes, leavng he benef srucure unchanged. The second opon s o mmedaely shf o a fully-funded penson sysem, leavng he benef srucure unchanged, and by fnancng he PAYGO penson oblgaons a he me of he swch wh deb, whle he governmen leves ncome axes o cover he neres paymens of he deb. Ths alernave polcy opon s chosen gven he Cooley and Soares (999) concluson ha a deb-fnanced ranson o a fully-funded penson s preferable o voers, and gven he Conesa and 5

7 Kruger (999) asseron ha an mmedae ranson s preferable o a gradual one. The modelng expermens nclude economes wh consan and posve populaon growh o presen baselne smulaons o mrror he analyses by Kolkoff (995, 996) and Kolkoff, Smeers, and Wallser (999), bu also nclude economes wh demographc change as n DeNard, Imrohoroglou and Sargen (999), and Fehr (000), o reflec curren populaon projecons ha have movaed he penson susanably and reform debae. Agens n he model economes wll also supply labour nelascally, and penson benefs wll depend drecly on conrbuons. Ths s o absrac from ssues surroundng he labour-lesure dsoron of penson polcy ha have promped he crque ha governmens should reduce hese dsorons raher han enac a ranson from a PAYGO sysem o a fully-funded sysem.. Modelng Envronmen A smple overlappng generaons dynamc general equlbrum framework wll be used o examne he relave mers of he wo dfferen penson susanably opons. Agens lve for hree perods, wh each perod correspondng o 0 years. These hree perods are defned as follows: In he frs perod of lfe, agens are born no he economy as young aduls; n he second perod of lfe, agens are older workers; and n he hrd perod, agens are no longer workng, bu are rerees. When workng, agens pay mandaory conrbuons o a penson sysem as a percenage of wages, and when rered, agens receve benefs a a gven rae of her pror employmen earnngs.. Populaon Process The populaon of he model economy s defned as follows, where N denoes he populaon of ha cohor n he h perod of lfe n me : () N = N, + N, + N 3,. There s no lfeme uncerany, so ha agens lve for all hree perods. As such, N +,+ = N, for =,, and for all. The populaon wll evolve over me, a he mevaryng growh rae, n, so ha N, = (+n )N,- 6

8 Agens supply e uns, and e uns, of labour nelascally n he frs and second perods of lfe respecvely. A me, he oal labour supply n he model economy s defned as: () L = N e N., +, e. Technology Producon n he economy s deermnsc, and s defned by he consan reurns o scale producon funcon: α α (3) Y = A K L. As such, he reurns o he facors of producon, labour and capal, per un, are: α α (4) w ( α )A K L, and = α α (5) r = αa K L δ..3 Governmen Penson Sysem The governmen runs a pay-as-you-go penson sysem whereby benefs n any perod pad o rerees are funded by conrbuons by workers n ha same perod. The governmen mposes a penson conrbuon rae, p,, on labour earnngs a me, and pays ou benefs o rerees, he amoun of whch s denoed by b for rerees. These benef levels wll be deermned n advance and wll be se as a proporon (br) of wage earnngs when employed: (6) b = br w e w ). ( + e As such, he penson budge consran s: (7) N, p, we + N, p, we = b N 3,. Wh he PAYGO sysem, p, = p,. For he purpose of hs paper, ncome axes wll be rased solely for he purpose of managng neres paymens on deb followng he shf o a fully-funded penson sysem. Income axes wll be charged on neres ncome, wage earnngs ne of penson conrbuons, and penson benefs, a rae τ. 7

9 .4 Preferences Agens maxmze uly over a sandard compose good, whch can be used for consumpon, c, or used as a capal asse n producon, a, wh me separable preferences, subjec o a dscoun facor β, under he followng consrans: 3 ( = =, + (8) U c, ) β log c, subjec o (9) c, = we ( p, )( τ ) a,, (0) c, + = ( w + e ( p, + ) + r + a, )( τ + ) + a, a, +, () c3, + = ( r + a, + + b + )( τ + ) + a, + () 0. a,, The aggregae level of capal sock held by resdens s defned as: (3) K d, = N, a, + N, a, +. The oal amoun of capal sock used n producon, K s equal o he sum of capal held by resdens, K d,, and by foregners, K f,. In he case of a closed economy, K f s se o zero. Agens n he model economes have perfec foresgh. They perfecly predc he evoluon of he populaon, and of echnologcal progress (A ), whou uncerany. Tha s, hey can perfecly predc he evoluon of wages, he rae of reurn, premum raes, penson benefs, and oher economc varables..5 The Shf o Fully-Funded Pensons In an economy ha wshes o shf from a pay-as-you-go penson sysem o a fullyfunded one, he governmen wll sell new deb equvalen o he penson payou of he pay-as-you-go penson sysem for rerees who conrbued before he swch. Wh he swch, new penson conrbuons are nvesed n capal markes and conrbue o he sock of producve capal n he economy. As n he case of he PAYGO penson sysem, conrbuons are ax-shelered, and benefs are subjec o ncome ax when receved. If he swch occurs n perod T, hen he governmen wll rase funds by sellng bonds o pay he benefs o he rered n me T: (4) B T = bt N3, T = br( wt e + wt e ) N3, T 8

10 Those who were n he second perod of lfe a he me of he swch would have conrbued o he pay-as-you-go sysem when n he frs perod of lfe, as well as no he fully-fnanced sysem n he second perod of lfe, and hose conrbuons wll now be addressed. Le us assume ha hs cohor s promsed benefs under he prevous penson sysem accordng o her earnngs hsory whle under he pay-asyou-go sysem, along wh he marke value of her conrbuons whle under he fully-funded penson sysem: * (5) b = br( w e R p w e. T + T ) + T +, T Then he governmen needs o rase he frs poron of benefs by ssung new deb n me T+: (6) B br w e N. T + = ( T ) 3, T + In hs case, f agens n hs generaon connue o receve benefs se as a defned proporon of her lfeme earnngs, hen he premum rae for hs generaon n her second perod of lfe s: * * (7) br( wt e) = RT + p, T wt e, or p, T = br / RT +. Those who were n he frs perod of lfe, or as ye unborn, a he me of he swch o he fully-funded penson sysem n me T, wll pay conrbuons ha are nvesed n capal markes and add o he capal sock for producon. These conrbuons wll be se a an equal rae across earnngs n he wo work perods, and wll be defned by p * *, = p, + T for agens ha rere n perod +>T+. Le agens n hs generaon also receve benefs se as a defned proporon of her lfeme earnngs, so ha hese agens wll receve benefs as follows: * * (8) b = br w e + w e ) = R ( R p w e p w ), wh her premum rae se o: + ( + + +, +, + + e * * (9) p = p = br w e + w e ) / R ( R w e w ),, + ( e Governmen deb-servce s now addressed. Assume ha he governmen wans o servce only neres paymens on he wo bond ssues n perpeuy, so ha he level of governmen deb remans a DT + = BT + BT + for all >. In perod T+, leves axes on ncomes excludng penson conrbuons and ncludng penson benefs o pay neres paymens on he frs bond ssue. In perod T+, >, leves axes o pay neres paymens on boh bond ssues. In open economes, foregn capal earnngs are also axed a he same rae. 9

11 Snce he economes nvesgaed heren are all deermnsc whou uncerany, rae of reurn equaly mus exs beween he wo avalable asses, producve capal and governmen deb. The aggregae level of capal sock used n producon and held by resdens s now defned as: * * (0) K = N a + p w e ) + N ( a + p w e D, for T. d, +, (,,,,, ).6 Compuaon of Equlbra The mehod of compung equlbra for a closed economy s slghly dfferen han ha used for an open economy. The mehod for compung equlbra n he open economy s smpler, and wll be descrbed frs. In an open economy, he rae of reurn on asses s deermned exogenously n world capal markes. Capal s assumed o be perfecly moble. If he amoun of domescally-suppled capal s oo low (or oo hgh), funds wll flow n from abroad (or domesc capal wll flow ou), unl he reurn o capal equals he world neres rae. The amoun of labour s defned n each perod gven he populaon process. The seps for compung equlbra are as follows:. Eq. (5) s solved for K, gven he nernaonal rae of reurn, he level of labour, and he producon parameers, A, α, and δ, for all values of ;. The wage rae s calculaed usng Eq. (4), for all values of ; 3. The penson conrbuon rae n Eq. (7) s calculaed wh predefned values for he benef levels for rerees, for all values of ; 4. The agens opmzaon problem s solved recursvely as defned by Eqs. (8-), for all values of = o 3, and all values of ; 5. The opmal levels of asse holdngs over me are used o calculae he level of domesc capal sock holdngs over me, usng Eq. (3). 6. The dfference beween he level of capal used n producon and he level of domesc asse holdngs n he open economy s equal o foregn-held capal sock n any gven me perod. The mehod of solvng equlbra n he closed economy dffers slghly from ha descrbed above. In sep, nal guess values for K are defned, and are hen used o calculae he raes of reurn, r, n Eq. (5). Seps hrough 5 do no change. In sep 6, however, he value of foregn-held capal sock s zero for he closed economy. 0

12 If he values of domesc capal sock holdngs from sep 5 do no equal he guess values for he capal sock from sep, hen he guess values for he capal sock are updaed, and he procedural seps are repeaed unl he calculaed values of capal sock n sep 5 are equvalen o he prevous guess values n sep. To calculae he ranson o fully-funded penson sysems, he wo bond ssues n Eqs (4) and (6) are calculaed along wh he new penson conrbuon raes defned n Eqs (7) and (9), and he requred ncome ax raes o fnance neres paymens on he penson deb n sep 3. Sep 5 s adjused so ha he level of capal sock s calculaed usng Eq (0). 3. Model Calbraon In order o conduc he smulaon expermens, he model mus be calbraed for he populaon processes, echnology, preferences, and for he governmen penson sysem. 3. Populaon Processes Two separae populaon processes wll be examned n boh open and closed economy sengs. The frs wll be one wh a consan populaon growh rae, o serve as a baselne for comparson wh prevous work ha dd no model demographc change (Kolkoff, 995, 996, Kolkoff, Smeers and Wallser, 999). The second wll be one defned by a process nended o mrror ha experenced, and expeced o be experenced, n Canada: an nal seady sae wh consan growh, followed by a one-generaon declne n he brh rae correspondng o ha experenced over he perod, subsequenly followed by a one-generaon baby-boom over he perod, hen followed by no growh (baby bus). The populaon growh rae n he frs seady sae n boh populaon processes s se o 0.5, whch s approxmaely.0% on an annual bass. For he frs process, he populaon s always n hs seady sae of consan growh. For he second populaon process, he frs seady sae s followed by a one-generaon declne n he growh rae for he generaon born durng he nerwar perod: he growh rae for hs generaon s se o 0.35 (correspondng o.5% annually). Ths generaon eners he

13 labour force over he perod and s n he 5-44 age caegory as of 97. The baby-boom generaon (born over he perod) s.75 mes bgger han he precedng generaon, whch corresponds o an annual ncrease of almos hree percen, and s n he 5-44 age caegory a he 99 census. The baby boom generaon s all rered by he 03 census perod. Fgure shows he dfferences n he age-composon of he populaon gven hs second populaon process, and he Canadan populaon a census pons. Noe ha he model economes fal o replcae he smaller sze of he cohor of rerees n years before 0; hs s because he model economes do no ncorporae lfeme uncerany and rsng lfe expecances. The mplcaons of hs wll be dscussed laer. Agens are endowed wh age-dependen effcency uns. For young workers, e s normalzed o. For older workers, e s se o., so ha older workers earn wages ha are en percen hgher han hose of young workers. In 003, he average earnngs of Canadan male workers was $38,400 for hose aged 5 o 34, $50,500 for hose aged 35 o 44, $55,600 for hose aged 45 o 54, and $4,700 for hose aged 55 o 64 (Sascs Canada CANSIM Table ). The rao of earnngs of older workers o younger workers s abou.. In he US, he medan level of earnngs was $39,595 for males aged 5 o 44, and $47,978 for males aged 45 o 64 n 003 (US Census Bureau, 004). The rao of earnngs of older workers o younger workers n he US was.. 3. Technology, Preferences, and Penson Benefs The share of ncome o capal s se o 0.3, followng he esmae repored n Abel e al (006: 57) and Auerbach and Kolkoff (998: 7). The deprecaon rae s se o 0.7, whch corresponds o he annual esmae of 6% by Sokey and Rebelo (995). For he purpose of hs paper, oal facor producvy s held consan followng convenon n Kolkoff (995, 996), Kolkoff, Smeers and Wallser (999), Cooley and Soares (996, 999), Fehr (000) and Buler (000). The dscoun facor (β) s se o 0.785, o approxmae he annual fgure of (Cooley and Soares, 999). In Canada, he publc penson sysem payed a maxmum annual benef of $9,770 n 004, whch s approxmaely equal o 0% of average earnngs of workers aged 45 o 64 (OSFIC, 004: 50; Sascs Canada CANSIM Table ). Snce workers n he model economes work wo perods and receve benefs n one perod, he model

14 economy governmen operaes he penson sysem so ha benefs receved by rerees are equal o 0% of lfeme employmen earnngs (br = 0.). The neres rae n he open economy seng s se so ha he rae s whn he range of neres raes gven he closed economy resuls. In he nal seady sae, he open economy s operang under a capal accoun surplus (foregn capal flows n). In he fnal seady sae, he economy s operang under a capal accoun defc. The me of he mmedae ranson o a fully-funded penson s when generaon 33 (he frs baby-bus generaon) eners he workforce (T=33). Ths s also he perod when he baby-boom generaon s n he older worker sage of lfe, whch s conssen wh he curren phase of he demographc ranson. 4. Smulaon Resuls The resuls of he smulaon exercses under consan populaon growh n boh open and closed economy sengs are presened n Tables and. The resuls for he open economy wh demographc change are presened n Tables 3 and 4. The resuls under he closed economy seng wh demographc change are presened n Tables 5 and Economes wh Consan Populaon Growh The open economy resuls are examned frs because facor prces do no change over he demographc cycle, whch makes easer o pnpon and separae he benefcal effecs from negave effecs (he effec of changng wages and neres raes add anoher dmenson o he analyss of closed economy resuls). For an open economy wh consan populaon growh, ceran and unchangng lfemes, and no echnologcal change, here s no demographc change o aler he economy from he seady sae, so ha all generaons of he model economy under he mananed PAYGO sysem receve he same level of wages, neres raes, penson conrbuon raes, benef raes, and lfeme uly. Table shows he resuls for an open economy ranson from a PAYGO o a fully-funded penson sysem, wh consan populaon growh. The nal seady-sae resuls for generaons 6 hrough 3 are dencal o he resuls for subsequen generaons f here was no change from he PAYGO penson sysem. The shf o he fully-funded sysem begns a me 33, when 3

15 generaon 33 eners he labour force as young workers. The shf o a fully-funded sysem requres bond ssues o pay for he promsed benefs of he rered under he PAYGO sysem, wh neres paymens o be fnanced wh ncome axes. Generaons 3 hrough 36 are worse off wh he shf o full-fundng because of he penson deb axaon burden ha offses any benefcal effecs of lower conrbuon raes. Laer generaons are beer off under he fully funded sysem because of he lower conrbuon rae requred o provde equal benefs, and also due o he ever fallng axaon burden of he penson deb as he populaon connues o grow. Table presens he resuls for he smulaon exercse of a closed economy wh consan populaon growh and a ranson o a fully-funded penson sysem when generaon 33 eners he labour force. Noe agan ha whou any change o he PAYGO penson sysem, all generaons experence he same facor prces, penson premum raes and benefs, and lfeme uly so ha all generaons are equally well-off and n a seady sae equlbrum. In Table, Generaons 30 and earler are n hs frs seady sae. Generaon 3 s affeced by he swch snce he rae of reurn on her asses falls n he las perod of her lfemes, and leads o lower consumpon n ha fnal sage of lfe. Smlarly, Generaon 3 s adversely affeced by he drop n neres raes, bu also faces new ncome axes n he fnal perod of her lves. Ineresngly, Generaon 33 s beer off because benefs from lower penson conrbuon raes, hgher wage raes when workng, and hgher neres raes n he fnal perod of lfe, whch more han offse he effec of ncome axes durng her second and hrd perods of lfe. Generaons 34 hrough 37 are all adversely affeced by he shf o full-fundng due o he deb servcng burden, bu laer generaons are beer off wh he shf snce he penson deb burden decreases as he populaon connues o grow. These resuls confrm Kolkoff s fndngs ha, n model economes wh consan and posve populaon growh, a shf from a PAYGO sysem o a fullyfunded sysem can be welfare-mprovng for unborn generaons, and ha here may be ax-deferral polces for he ransonal generaons ha can make all generaons beer off. A convncng argumen may be made ha a shf o full-fundng can make all generaons beer off wh approprae ransonal polces under he scenaro of consan and posve populaon growh. However, hese expermens do no ackle he major problem ha naons are expeced o face as he dependency burden of he elderly on he labour force ncreases. The PAYGO sysem faces he susanably ssue because of demographc change. How would a shf o a fully-funded sysem 4

16 affec generaons n he presence of demographc change? Tables 3 hrough 6 presen he resuls of he smulaon expermens for economes ha experence demographc pressures smlar o hose currenly experenced by many naons, n parcular, a baby-boom followed by a baby-bus. 4. Open Economes wh Demographc Change Table 3 presens he resuls for an economy under he PAYGO sysem. Noce ha generaon 30 s worse off han precedng generaons snce hey pay a hgher premum rae n her second perod of work, because he labour force growh rae has declned wh he enry of generaon 3 no he labour force. Generaons 3 and 3 pay slghly hgher premum raes n boh work perods han generaons n he frs seady sae. Generaon 33 (he frs baby-bus generaon) pays a much hgher premum rae n he second perod of lfe as he baby-boom generaon exs he labour force and receves penson benefs. All fuure generaons pay penson premum raes under he PAYGO sysem of 0% of wages, whch causes a lower level of uly n he second seady sae han when compared o he frs, when he populaon was growng. In he second seady sae wh no populaon growh, consumpon n all hree perods s lower han for generaons n he frs seady sae wh posve and consan populaon growh. The resuls also show ha foregn capal dependency falls as he populaon growh rae slows. Savngs of generaons under no growh are much beer able o fund capal requremens han when he labour force s growng. Table 4 shows he resuls for he ranson o a fully-funded penson sysem. Agan, he penson sysem swch occurs when generaon 3, he baby-boomers, ener he second perod of work. Generaon 3 s worse off under he swch o a fullyfunded penson sysem han connung under he PAYGO sysem because hey now have o pay ncome axes n he hrd perod of lfe o fnance neres paymens on penson deb. The frs and second baby-bus generaons are beer off wh he swch han whou snce hey pay lower penson conrbuon raes under he new sysem, ha are more han enough o offse ncome axes ha are pad o servce penson deb durng her lfemes. However, subsequen generaons (35 and hgher) are worse off wh he swch o full-fundng han under he PAYGO sysem because he negave effec of ncome axes domnaes he posve effecs of lower penson conrbuon raes. Snce he populaon does no grow, he economy seles no a seady sae wh 5

17 an ncome ax rae of 6.3% o servce neres paymens on he penson deb n perpeuy. 4.3 Closed Economes wh Demographc Change Tables 5 and 6 presen he resuls when a closed economy s subjec o demographc change. In closed economes, generaons are affeced by changes n penson conrbuon raes and ncomes axes, as well as by changes n facor prces. The effec of he demographc ranson on he model economy ha reans he PAYGO penson sysem s shown n Table 5. Generaon 8 experences a small boos n uly due o hgher neres raes n he fnal perod of lfe (when = 30). Conversely, generaon 9 experences a declne n welfare prmarly due o much lower neres raes n her fnal perod of lfe. Generaon 30 receves a welfare mprovemen wh hgher wages n he second sage of lfe, and hgher neres raes n he hrd perod of lfe. Laer generaons experence declnes n welfare compared o earler generaons (numbered less han 8) n he frs seady sae, prmarly as he resul of ncreasng penson conrbuon raes and declnng raes of reurn on asses ha are only parally offse by ncreases n wages. In he closed economy smulaon, he demographc ranson causes agens o consume more n he frs perod of lfe, and less n he las wo perods of lfe, when compared o hose agens lvng n he frs seady sae equlbrum. The smulaon resuls for he model economy wh a shf o a fully-funded sysem durng he demographc ranson are presened n Table 6. The resuls for generaons up o 30 are unchanged from Table 5. Generaon 3 s worse off under he shf o a fully-funded plan because of he lower rae of reurn n he hrd perod of lfe under he shf han under a PAYGO sysem. Ths s due o he ncrease n savngs by baby-boomers n he frs perod of lfe wh he shf. Generaon 3 (he babyboom generaon) s also worse off wh a penson sysem shf. Consumpon s lower n all hree perods for baby-boomers f he penson sysem shfs o a fully-funded sysem n her second perod of lfe (when compared o a connung PAYGO sysem). The negave effec of lower neres raes and hgher penson conrbuon raes more han offses he posve effec of hgher wages for he baby-boom generaon. Generaons 33 and 34 are he wnners from he ranson polcy nvesgaed for hs paper. They experence he posve effecs of lower penson 6

18 conrbuon raes ha overshadow any effecs from changng facor prces and deb servcng coss when compared o he scenaro of mananng a PAYGO sysem. Generaons followng generaon 34 are worse off under a ranson han mananng he saus quo because he negave effecs of ncome axaon o servce he penson deb burden are greaer han any posve effecs from lower penson conrbuon raes. 4.4 Dscusson To summarze he smulaon resuls, has been show ha economes wh consan and posve populaon growh can mprove he welfare of unborn generaons wh a ranson o a fully-funded penson sysem. Generaons lvng durng and mmedaely followng he ranson are generally adversely affeced gven he ransonal polcy smulaed for hs paper, bu f fuure generaons are much beer off, may be possble o develop ransonal polces o compensae ransonal generaons and make all generaons beer off han under a PAYGO sysem. However, once demographc changes ha reflec curren demographc projecons are ncluded n he expermens, generaons may be beer off reanng he PAYGO srucure han aempng o shf o a fully-funded penson sysem, because of he coss of servcng a deb-fnanced penson shf. No populaon growh means ha he per capa coss of deb servcng wll no declne n he fuure, and hese coss overshadow he posve effecs of lower conrbuon raes. A comparson of he open economy and closed economy resuls for ransonal generaons (n parcular, he baby-boom and frs baby-bus generaons) reveals ha agens n he closed economy experence larger reducons n welfare han her open economy counerpars because of changng facor prces durng he demographc ranson. However, fuure generaons n closed economes are beer off han her open economy counerpars snce changng facor prces have bufferng effecs afer he compleon of he demographc ranson. The model economes nvesgaed heren offer benef raes ha may appear low o readers. These benef raes are nended o mrror replacemen raes n Canada. In comparson, Socal Secury pays abou wce he benefs o rerees n he US. Smulaons wh he benef rae ncreased do no sgnfcanly aler he comparave resuls for model economes under a connued PAYGO sysem versus a shf o full- 7

19 fnancng. However, when he replacemen rae s oo hgh (br = 0.4) n model economes, he ncenve o prvaely save s lower, and he penson deb upon he swch o full-fundng s so hgh, ha here s no enough savngs domescally o provde capal and also purchase he governmen bond ssues for ousandng PAYGO oblgaons n closed economes. The modelng resuls should be aken wh some cauon due o modelng smplfcaons. Mos mporanly, he model economes do no ncorporae: () changes n lfe expecances; () mprovemens n echnology or human capal; () earnngs heerogeney and uncerany; or (v) lfeme uncerany and bequess. Alhough hese are lmaons, her omsson does allow a smple comparson of he changes n welfare across generaons as a resul of he ferly ranson, and he proposed shf n penson polcy, all else equal. The mplcaons of hese omssons are brefly noed below, and are lef for a more horough examnaon n fuure work. Frs, he model economes do no ncorporae changes n lfe expecances. As a resul, he rao of rerees o workers and he PAYGO conrbuon rae are oversaed for perods before me perod 33 when he frs baby-bus generaon eners he workforce, as compared o acual Canadan populaon fgures and projecons up he year 0 (see Fgure ). Smlarly, he model economy PAYGO rae may be undersaed for fuure generaons f lfe expecances connue o rse. As a resul, early generaons n he model economes pay raes ha are hgher, and laer generaons may pay raes ha are lower, han her real lfe counerpars. Ths would mean ha he PAYGO penson burden s projeced o be somewha hgher han n he model economes nvesgaed heren. Ths s a consequence of he ncreasng rao of reremen years o workng years, as people lve longer, and n some cases, work fewer years (earler reremen and/or delayed enry no he workforce wh more years of schoolng). However, ncreasng lfe expecances would requre hgher conrbuon raes for boh he PAYGO and fully-funded penson plans f he reremen age s held consan. Second, he model economes do no ncorporae echnologcal progress or ncreases n human capal. DeNard, Imrohoroglou and Sargen (999) ncorporaed annual echncal progress of.6% n her projecons for he US economy. For Canada over he 98 o 00 perod, oal facor producvy grew a an average annual rae of.0% (Abel e al, 006: 58). However, earnngs of workers were sagnan over hs perod (Sascs Canada CANSIM Table ), and low-wage earners who are mos relan on publc penson sysems faced declnng real wages 8

20 over hs me. Incorporang echncal progress no he model would lower he PAYGO penson conrbuon rae, snce reree benefs are based on her lfeme earnngs, and conrbuon raes are based on workers earnngs whch would be hgher han hose of her predecessors. In addon, generaons would acheve hgher levels of welfare han he precedng generaon as a resul of hgher wages due o echnologcal progress. Fuure generaons would be beer able o deal wh hgher conrbuon raes n he PAYGO sysem wh demographc change, bu would also be beer able o deal wh ncome axes as a resul of he shf o a fully-funded penson sysem. Snce hgher raes of populaon growh would make he shf o a fullyfnanced penson sysem more aracve han connung a PAYGO sysem for fuure generaons, so oo would hgher raes of echnologcal progress. There may be hreshold raes of growh n populaon and/or echnologcal progress beyond whch a swch o full-fnancng s welfare-mprovng, and below whch economes should rean he PAYGO penson sysem. Thrd, he model economes do no ncorporae earnngs heerogeney and uncerany. Snce some PAYGO penson sysems (ncludng he Canada Penson Plan) have upper lms on oal annual conrbuons and benefs, low earnng agens would have hgh conrbuon and benef raes as a proporon of wage earnngs, and low levels of prvae wealh, whle hgh earnng agens would have low conrbuon and benef raes as a proporon of wage earnngs. Model economes wh earnngs heerogeney would have agens wh varyng penson conrbuon and benef raes. Incorporang earnngs heerogeney may no make a sgnfcan dfference n he smulaon resuls, snce model economes whou earnngs heerogeney, bu wh dfferen penson conrbuon and benef raes, yeld smlar resuls n boh open and closed economes for PAYGO pensons versus a penson shf o full-fundng. Fourh, model economes do no nclude lfeme uncerany and bequess. As a resul, here s no ransfer wealh across generaons. Lfeme uncerany alers he consumpon and savngs paern of agens as hey wegh he expeced probably of beng alve and needng o consume n he fuure agans consumng n earler perods. Bequess would ncrease he level of asses of nherors and also aler her consumpon paerns. There have been many dfferen reform opons dscussed by polcymakers o allevae he burden of he penson sysem for fuure generaons. In Canada, followng a revew of CPP program n he md-990s, he legslaed rae was seadly ncreased from 6.00% n 997 o 9.90% n 003 and held a ha rae hereafer, n order o buld 9

21 up he CPP rus accoun and preven fuure ncreases n he premum rae, gven populaon projecons no he mddle of he weny-frs cenury. Ths polcy change responds o hree dsnc ssues. Frs, allevaes he penson burden of he large baby-boom generaon on fuure generaons. Second, srenghens he conrbuonbenef lnkage wh ndvduals lvng longer lfemes and recevng penson benefs longer han her predecessors. Thrd, hs response s n lne wh he argumen made by Snn (000). If he baby-boom generaon and hose ha follow nves fewer resources no he nex generaon by rasng fewer chldren han her predecessors, hen hese generaons should be makng hgher conrbuons no her pensons whle workng. The savngs made hrough lower chld-rearng coss should be compensaed by hgher penson conrbuons n order o manan her expeced penson payou. If he model economes wh a connung PAYGO srucure were subjeced o early rses n conrbuon raes o pre-fund benefs, he baby-boom generaon and he frs baby-bus generaon would suffer welfare losses due o hgher conrbuon raes, o he benef of fuure generaons. Upon casual nspecon of he modelng resuls n Tables and 5, hs may mprove nergeneraonal equy n he open economy case, bu exacerbae nergeneraonal nequy n he closed economy case, furher harmng he relave poson of he baby-boom and he frs baby-bus generaon, relave o fuure generaons. A more horough analyss of hs ssue s also lef for fuure work. 5. Concluson Many naons are facng he publc penson susanably ssue as a resul of he dramac declne n ferly raes snce he 960s, and rsng lfe expecances. Conrbuon raes n he pay-as-you-go penson sysem wll have o ncrease f oher aspecs of he sysem are no reformed. One popular reform opon n polcy crcles s o shf o a fully-funded penson sysem. Ths paper has used an overlappng generaons dynamc general equlbrum model o evaluae wo compeng reform opons: rasng conrbuon raes whn he PAYGO srucure, and shfng o a fullyfunded sysem usng deb-fnance and ncome ax deb servce. Smulaon resuls sugges ha, n model economes wh populaon growh and no echnologcal progress, a shf o a fully-funded penson sysem mproves he welfare of fuure generaons when compared o a susaned PAYGO srucure as n Kolkoff (995, 996) and Kolkoff, Smeers and Wallser (999). However, n model economes ha 0

22 experence a demographc ranson o no populaon growh, and whou echnologcal progress, mananng a PAYGO penson sysem s preferable o a swch o full-fundng for fuure generaons. References Abel AB, Bernanke BS, Smh GW, Kneebone RD (006) Macroeconomcs, Fourh Canadan Edon. Pearson Educaon Canada, Torono. Auerbach AJ, Kolkoff LJ (998) Macroeconommcs: An Inegraed Approach, Second Edon. MIT Press, Cambrdge. Breyer F (00) Why fundng s no a soluon o he socal secury crss. Manuscrp, Unversy of Kansanz (hp:// calls_conferences/pensonref_pdf/panel_breyer.pdf). Buler M (000) The polcal feasbly of penson reform opons: he case of Swzerland. Journal of Publc Economcs 75: Cooley TF, Soares J (996) Wll socal secury survve he baby boom? Carnege- Rocheser Conference Seres on Publc Polcy 45: 89-. Cooley TF, Soares J (999) Prvazng socal secury. Revew of Economc Dynamcs : Conesa JC, Krueger D (999) Socal secury reform wh heerogeneous agens. Revew of Economcs Dynamcs : De Nard M, Imrohoroglu S, Sargen TJ (999) Projecd US demographcs and socal secury. Revew of Economc Dynamcs : European Unon Commsson (00) Reforms of penson sysems n he EU an analyss of he polcy opons. European Economcs 73: 7-. Fehr H (000) Penson reform durng he demographc ranson. Scandnavan Journal of Economcs 0(3): Feldsen M (995) Would prvazng socal secury rase economc welfare? NBER Workng Paper 58. Feldsen M, Samwck A (996) The ranson pah n prvazng socal secury. NBER Workng Paper No Geanakoplos J, Mchell OS, Zeldes SP (998) Would a prvazed socal secury sysem really pay a hgher rae of reurn? NBER Workng Paper No. 673.

23 Kolkoff LJ (995) Prvazaon of socal secury: how works and why maers. NBER Workng Paper No Kolkoff LJ (996) Smulang he prvazaon of socal secury n general equlbrum. NBER Workng Paper No Kolkoff LJ, Smeers K, Wallser J (999) Prvazng socal secury n he Uned Saes comparng he opons. Revew of Economc Dynamcs : OSFIC (004) s Acuaral Repor on he Canada Penson Plan. Offce of he Supernenden of Fnancal Insuons Canada, Oawa. Snn HW (000) Why a funded penson sysem s useful and why s no useful. Inernaonal Tax and Publc Fnance 7: Socal Secury Admnsraon (00) The 00 Annual Repor of he Board of Trusees of he Federal Old-Age and Survvors Insurance and Dsably Insurance rus Funds. Washngon DC. Sokey N, Rebelo S (995) Growh effecs of fla-rae axes. Journal of Polcal Economy 03: US Census Bureau (005) Curren Populaon Survey, 004 Annual Socal and Economc Supplemen.

24 Table : Smulaon Resuls for he Open Economy Shf o a Fully-Funded Penson Sysem wh Consan Populaon Growh Relave Generaon Cohor U c, c, + c 3, + p, p, + b 3, + a, a, + K d, / K τ w R Or Tme Sze * * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* * 0.04* Noes: The shf o full-fundng occurs a me 33, when Generaon 33 s n he frs perod of lfe. Penson conrbuon raes under he fully-funded sysem are denoed wh *. U denoes he lfeme value of uly relave o he seady-sae level, gven Eq (8): U = U U 6. The rao of deb o domesc wealh s 0.5% and 3.% n perods 33 and 34 respecvely. 3

25 Table : Smulaon Resuls for he Closed Economy Shf o a Fully-Funded Penson Sysem wh Consan Populaon Growh Relave * U c, c, + c 3, + p, p, + b 3, + a, a, + / K Generaon Cohor Or Tme Sze K τ * * * * 0.038* * * * * * * * 0.040* * 0.043* * 0.045* * 0.047* * 0.048* * 0.048* * 0.049* * 0.049* * 0.049* Noes: The shf o full-fundng occurs a me 33, when Generaon 33 s n he frs perod of lfe. Penson conrbuon raes under he fully-funded sysem are denoed wh *. U denoes he lfeme value of uly relave o he seady-sae level, gven Eq (8): U = U U 6. The rao of deb o he capal sock s 9.5% and.% n perods 33 and 34 respecvely. w R 4

26 Table 3: Smulaon Resuls for he Open Economy under a PAYGO Penson wh Demographc Change Relave * U c, c, + c 3, + p, p, + b 3, + a, Generaon Cohor Or Tme Sze a, + K d, / K Noe: U denoes he lfeme value of uly relave o he seady-sae level, gven Eq (8): U = U U 6. τ w R 5