RETIREMENT SAVINGS AND PUBLIC PENSIONS STUART J. WILSON

Transcription

1 UNIVERSITY OF REGINA ISSN DEPARTMENT OF ECONOMICS RETIREMENT SAVINGS AND PUBLIC PENSIONS STUART J. WILSON Deparen o Econocs Unversy o Regna Regna, Saskachewan Canada S4S A2 [email protected] Deceber 21 DISCUSSION PAPER #99

2 Rereen Savngs and Publc Pensons Suar J. Wlson * Unversy o Regna Deceber 21 Absrac An overlappng generaons general equlbru odel s presened o quany he pac o nroducng a publc penson progra on he rereen savngs ove o ndvduals n le-cycle econoes. Aggregae savngs raes are calculaed and copared or odel econoes or cases o varyng levels o benes. Model econoy resuls sugges ha, or odes pensons progras lke he Canada Penson Plan, aggregae savngs and doesc asse holdngs are reduced by weny percen. For ore generous plans, lke US Socal Secury, aggregae savngs and doesc asse holdngs are reduced by ory percen. Keywords: rereen savng, publc pensons, overlappng generaons. JEL Classcaon: E21, C68, H55 * Deparen o Econocs, Unversy o Regna, Regna, SK S4S A2. Tel: Eal: [email protected]. URL: hp:// The auhor would lke o hank Allen Head or helpul coens, Maxlan Scheser or research asssance, and acknowledges nancal asssance ro he Unversy o Regna n he or o a Specal Projecs Gran. None oher han he auhor can be held accounable or errors or oversghs. 1

3 I. Inroducon Ths paper presens an overlappng generaons general equlbru odel o quany he pac o nroducng a publc pay-as-you-go penson progra on aggregae savngs n le-cycle econoes. Aggregae savngs raes are calculaed and copared or odel econoes wh varyng rereen bene levels. Model resuls show ha he personal rereen savngs ove s sgncanly reduced wh he nroducon o a very odes penson progra. In he odel econoes nvesgaed, a penson progra, wh a replaceen rao o 14% o pre-rereen earnngs, reduces he aoun o savngs and doesc asse holdngs by ore han weny percen. A ore generous progra, wh a replaceen rao o 28% o pre-rereen earnngs, reduces he aoun o doesc asse holdngs by ore han ory percen, and he ne doesc savngs rae alls by alos a hal. In he ajor ndusralzed naons, savngs raes have generally declned snce he 197s. In he US, he household savngs rae has allen ro egh percen n he 197s, o nl n 1999 (Gordon (2:511)). 1 The Uned Saes wen ro beng a ne suppler o capal o he res o he world, o a ne debor (Berhe and Shoven, 1991:9). Prvae savngs raes n Japan ell ro 19.3% over , o 12.1% over (Bosworh, 1991:32). In Canada, personal ne savngs raes ell ro 9.2% n 1975 o 2.3% n 1999 (CANSIM arces 8614, 8629). Durng hs perod, ndusralzed naons have nsued and/or resrucured saey-ne progras o varous ypes, ncludng he expanson o uneployen nsurance progras, socal secury and publc penson progras. Research by Gokhale, Kolko and Sabelhaus (1996) has poned ou ha he nroducon o Socal Secury n he US has reduced povery o he elderly consderably. In he early 196s, he ypcal seveny year-old was consung wo-hrds he aoun o consupon o he ypcal hry year-old. Thry years laer, he ypcal seveny year-old consued one-h ore han a hry year-old. The redsrbuon o ncoe ro he young o he old has resuled n ncreased raes o consupon and has depressed savngs raes. Econoerc nvesgaons on he eec o penson syses on savngs have no 1 Adjusens or sock arke gans n he 198s and early 199s lead o he concluson ha he gansnclusve savngs rae declned soewha n he years leadng up o he d-199s, wh a surge durng he arke boo o he 199s (Gale and Sabelhaus (1999)). However, n lgh o recen econoc evens n 21, s unclear wha general paern wll eerge or personal savngs. 2

4 been able o deerne conclusvely he reducon n savngs as a resul o he nroducon o pay-as-you-go plans. Feldsen (1976) concluded ha ncreases n socal secury wealh n he US reduced personal savngs by ory percen. Subsequen research by oher auhors, usng deren econoerc speccaons, has reduced hs gure (or exaple, Munnell (1977) ncluded he eec o changes n he uneployen rae on savngs). Perhaps pensons ncrease savng by proong a rereen age and educang he publc abou he need o save or he uure (Cagan (1965), Kaona (1964), Leer and Lesnoy (1982)). In Canada, he aggregae ne savngs rae ell ro a hgh o 16.1% n 1974, o a low o 4.4% n The coponens o he aggregae savngs rae n Canada ro are depced n Fgure 1. To wha exen can he nroducon o he Canada Penson Plan n 1966 explan he declne n he savngs rae? A clear ajory o Canadans beleve ha an essenal governen acvy s he provson o a socal saeyne and he pleenaon o easures o ensure a basc sandard o lvng (Peers, 1995: 15). The Canadan Publc Penson progra was developed n 1966 o asss he elderly durng her rereen years, and o suppleen he Old Age Secury progra, rs nroduced n The Guaraneed Incoe Suppleen and he Spouse s Allowance were added n 1967 and 1975 respecvely. These progras provde subsanal help o he elderly and have helped o reduce he ncdence o povery aong he aged ro 41% n 1969 o 7% n The curren polcy debae ocuses on he ac ha, or he publc penson syse, whaever he nal nenons, he syse s largely an underunded one (Banng and Boadway, 1996:2). Whle he underunded naure o publc pensons has polcy plcaons or he uure susanably o he progra, also has plcaons regardng he ncoplee ranser o savngs ro he prvae secor, o he governen secor. The CPP s nanced by progra preus hrough payroll axes. Surpluses or decs o hs progra are ncluded n he annual operang dec or surplus o he governen and wll aec he level o governen savngs. The publc penson progra wll aec he ndvdual s rereen savngs ove, reducng he need o personally save o nance consupon when no longer n he workorce. To wha exen has he nroducon o publc pensons reduced he aggregae savngs rae? Ths work s nended o copleen he curren polcy debae on polcy reor, n lgh o he 3

5 assve publc expendures, boh curren and expeced, on socal progras, and he debae over he eecveness o new naves desgned o ncrease prvae savng. Ths paper presens an overlappng generaons general equlbru odel o lecycle econoes o nvesgae he pac o a publc pay-as-you-go penson progra on personal savngs n he aggregae. The odel econoes are populaed by agens o overlappng generaons. Agens have led and unceran lees and ace earnngs uncerany. Model resuls ndcae ha publc pensons progras sgncanly reduce he prvae rereen savngs ove o ndvduals. In he odel econoes nvesgaed, a odes penson progra, lke he Canada Penson Plan, wh a replaceen rao o 14% o pre-rereen earnngs, reduces he ne personal savngs rae and doesc asse holdngs by abou weny percen. A ore generous progra, wh a replaceen rao o 28%, ore lke ha o US Socal Secury, reduces he ne personal savngs rae and he aoun o doesc asse holdngs by ore han ory percen. As a consequence, n a sall open econoy, oregn ndebedness ncreases, and n a closed econoy, he equlbru neres rae ncreases and wages all.. II. Overlappng Generaons Le-Cycle Econoes The overlappng generaons raework has been used o exane socal secury, savng and capal accuulaon, and publc penson reor (or exaple, Hubbard and Judd (1987), Hubbard, Sknner and Zeldes (1995), Bohn (1999), Hugge and Venura (1999), Eery and Rongve (1999)). I has been ound ha, n odel econoes, socal secury and pensons can have a consderable pac on welare and dsor savngs ncenves. Ths raework s rch enough o ncorporae unceran ne lees, heerogeney n age and eployen saus, and oher changng characerscs over he le cycle. The Envronen The odelng envronen s slar o ha used by Hugge (1996), and Wlson (21b). The odel econoes o be exaned are populaed by overlappng generaons o raonal, orward-lookng agens. Agens are heerogeneous n age and eployen hsory. Agens lve o a axu o I perods, sar work a I w, and rere a I r. The odel akes as gven ha agens rere a age 65, wheher a penson progra exss or 4

6 no. 2 The populaon dsrbuon by age cohor a a pon n e s descrbed by he vecor µ, where µ =[ µ 1 µ 2 µ I ] T. The age cohor consss o µ agens. To dscrnae beween agens wh deren eployen hsory, agens whn a cohor are ndexed by h, where h (1, µ ). Agens ace unceran lees, bu know agedependen survval probables. The probably o survvng o ro age o age +1 s s. The uncondonal probably o survvng o age k s s( k) = Π s. In a seady-sae, k 1 j= 1 j age agens wll ake up a consan racon o he populaon a any pon n e, and he populaon growh rae wll be n. A he aggregae level, here s no uncerany. Producon s deernsc and s governed by a consan reurns o scale echnology o he ollowng or: Y = F. (1) α 1 α ( K, L ) = ΒK ( A L ) Labour-augenng echnologcal progress, A, grows a a consan rae g. Β s a scale paraeer. Capal deprecaes a a consan rae δ. The odel econoes o be nvesgaed wll be sall open econoes, where he neres rae wll be se exogenously, and wll be se o a consan. Agens axze expeced uly over a sandard copose good, wh eseparable preerences and dscoun acor β. The copose good can be used as capal, and earns a rsk-ree one perod reurn per un, R. Agens axze expeced lee uly, gven by: I I w j ( U ( ci ) + s( j + I w 1) U ( c j I )) 1 σ c ax EI β w w j= 1 +, where U ( c) = w 1 σ. (2) Agens are endowed wh labour ecency uns ha are dependen on age, denoed by e. Aduls o workng age ace he probably e π o beng eployed, and u π = 1- o beng uneployed n any gven perod. The probably o beng eployed n a gven perod or an ndvdual s ndependen o beng eployed n any oher e perod. I eployed, l(h ) = 1. I uneployed, l(h ) =. In hese econoes, whle here s no aggregae uncerany, here exss uncerany a he ndvdual level. e π 2 The labour orce parcpaon rae o ales aged 65 and older ell seadly ro 3% n 196 o 2% n 197, and has lucuaed around 1% n he las decade. The nduced rereen eec o pensons s explored n Feldsen (1974), and wll be le o be exaned n uure work n he odelng raework descrbed heren. 5

7 The governen provdes rereen benes and eployen nsurance o agens n he econoy. Indvduals who survve pas he age o I r-1 receve rereen benes a a rae equal o he bene rae, b,, es a level e ndcave o he eployen hsory o he average ndvdual o ha cohor when I r. 3 Uneployed agens receve a bene equal o a proporon, b,, o her expeced earnngs eployed. The governen nances he eployen nsurance and he penson progras by levyng payroll axes equal o a proporon, p, on labour earnngs. An agen o age chooses consupon, c,, and asse holdngs, perod, ha are carred no he nex perod, wh he ollowng consrans: a, c + = a +1,+1, n, + a, W = R a, + ( 1 p ) wl ( h ) e + b, w (1 l( h )) e T, and c,, and a, or all, and. (3) In hs conex, he value o T s deerned by he aoun o accdenal bequess le by hose who de n perod, beore he age o I. Accdenal bequess have been reaed several deren ways. Ros-Rull (1994) nroduces a arke ha has agens wre conracs wh ebers o her own age cohor o share wealh or debs o hose ebers who de beore age I. Soresleen (2) has accdenal bequess donaed o newborns n a lup-su ranser. Hugge (1996) reas accdenal bequess as ully axed and redsrbued aongs survvng agens n he econoy. The os approprae odelng sraegy would be ha o Hugge, as nherances end n pracce o be dsrbued aongs aly ebers o varyng ages. The reaen here ollows Hugge; he value o hese bequess s dsrbued equally aongs he adul populaon (hose o age I w or older). Agens are lqudy consraned and canno hold negave ne asses. Agens are no capable o borrowng whou collaeral greaer han or equal o he aoun borrowed, bu are allowed o orgage capal. In hs case agens are unable o borrow agans he prose o uure ncoe o nance consupon, and canno hold negave ne asse levels. In he le-cycle odel econoy wh survval uncerany, hs assupon resrcs agens borrowng so ha hey do no accuulae debs and de beore repayen. 3 Ths s done or splcy, nsead o keepng rack o each ndvdual s eployen hsory and havng 6

8 The governen leves a payroll ax equal o a rae p o eployen earnngs o nance he eployen nsurance and penson progras. In he seady sae, he governen budge us be balanced. Toal revenues ro he payroll ax wll be equal o he expendures n provdng eployen nsurance benes o he uneployed and pensons o hose who are rered. The governen budge consran s:, h e u ( pπ µ we ) ( b π µ we ) =. 4 (4) Seady-Sae Equlbru In order o descrbe a seady-sae equlbru n odel econoes n whch here s boh populaon and producvy growh, he varables us be ransored as ollows: L /, /, /, /, /, = L L K = K L A T = T A a = a A c = c A ω = ω / A, µ = µ / L, N = N / L. In he seady sae, he ransored varables are consan over e, and he unransored varables grow a consan raes. Denon: A seady-sae open econoy equlbru s {{ c, h, a, h }, h, ω, R, K, K, K, L, T } such ha: d (1) c, h, a, h are opal decson rules, h ; (2) Inpu arkes are copeve: ω = F (, 2 K L) and R = 1+ F ( K 1, L ) δ, wh R se on nernaonal arkes, and here assued consan; (3) The allocaons are easble: () Doesc asse holdngs equal doesc capal K = Σ µ a /(1 ) ; d, h,, n h h + () Foregn capal s he derence beween oal capal and doesc capal: K = K K ; d benes dependen on an ndvdual s eployen hsory. 4 The odel econoes n any cases have raes o neres n excess o he raes o populaon growh, eanng ha seady-sae decs wll cause a connually rsng deb o oupu rao. 7

9 () Toal aggregae wealh equals oal consupon and nex perod doesc asse holdngs: ω + Σ µ a R /(1 + n) = Σ µ c + Σ (1 + g) µ a ; L, h, h, h, h, h, h, h, h, h e (4) The nuber o eployed s E = Σ π µ, he nuber o uneployed u e su = Σ π µ. Eecve labour supply, L = Σ µ π e ; (5) Transers o he adul populaon equal accdenal bequess: T = Σ (1 ), h µ, h s Ra, h / N a(1 n), where N a denoes he nuber o aduls + n he seady-sae populaon. (6) The governen budge s balanced - he oal aoun o preus receved s equal o oal benes pad, ( p π b π ) µ we =. e u The ehod o copung he seady sae s slar o he ehod descrbed n Wlson (21b). Frs, he expeced oal labour supply n he econoy s calculaed. Then gven bene raes, b, he expeced oal aoun o penson and eployen nsurance benes s calculaed. The preu rae, p, s hen se and a guess o he ranser, T, s ade. The level o opal asse holdngs o agens n he econoy can be copued recursvely, gven he level o ransers. Then, he values o accdenal bequess (ransers) are calculaed and copared o he guessed level o ransers. I he wo values are equal he procedure s copleed, oherwse, he guessed level o ransers s updaed and he copuaonal procedure s repeaed unl convergence s acheved. 5 III. Model Calbraon In he odel econoes nvesgaed, each perod corresponds o one year. Agens have unceran lespan bu coonly know age-specc survval raes. The axu lespan s se a 95 years, and all agens de beore her 95 h brhday. Agens begn supplyng labour and akng decsons regardng consupon and asse holdngs a 2 years o age. Agens ully whdraw ro he labour orce a 65. There s no aggregae uncerany, bu here exss eployen uncerany a he ndvdual level. Agens save 8

10 o suppleen ncoe receved ro he governen eployen nsurance and penson progras, o sooh consupon over he le cycle. Populaon In he odel econoes exaned, a no-graon scenaro was assued or splcy. 6 Survval raes were derved ro he rao o he populaon o he populaon plus deahs a each age. Ths rao was calculaed usng he 1987 sascs or Canada, ro he CANSIM daabase (Sascs Canada). Age-specc raes can be calculaed or sngle ages ro brh o 69 years o age. Age-specc survval raes or agens n he cohor groups, 7-74, 75-79, 8-84, and 9 and older, were assued o be consan or each age over he age caegory. The survval rae o 94 year-olds s se o. Ferly raes were consruced usng he 1987 age-specc erly raes o eales ro Sascs Canada (1993) n ve-year cohors ro years o age, o years o age. Ferly raes were assued consan over all ages n each cohor group. Over 196-2, he sex rao o brhs n Canada averaged 1.55 ales or every eale. For he odel econoes, he ale-eale spl aong newborns s se o 1.55:1. For splcy, he seady-sae populaon dsrbuon or ales was hen used or he odel econoy. Ths was done o avod odelng eale erly decsons, and labour orce parcpaon decsons durng chld-rearng years. Gven he Canadan populaon paraeers, and a no-graon process, he populaon growh rae n he seady-sae was calculaed o be.79%. Anoher odel econoy was calculaed usng he hgher erly raes o Canadan eales n 197, whch resuls n a seady-sae populaon growh rae o.43%. 7 These populaon dsrbuons are copared wh he dsrbuons o he Canadan populaon n 1987 and 2 n Fgure 2. 5 A ore dealed descrpon s ncluded n he appendx. 6 Ths s done o elnae coplcaons ha arse n ryng o odel derences n gran wealh holdngs upon arrval and labour arke characerscs n econoes wh eployen uncerany. See Soresleen (2) or an llusraon o odelng hese derences n econoes whou eployen uncerany. 7 The seady-sae populaon calculaon procedure s descrbed n he appendx. 9

11 Earnngs and Eployen Uncerany The age-specc labour endowen prole s consruced usng he average earnngs levels o CPP Male conrbuors n 1987, ro Healh and Welare Canada (1989:Table 13), or agens beween he ages o 2 and 64 (nclusve). The eployen nsurance bene rae s se a 45% o earnngs or = 2 o Eployen uncerany was odeled by usng he age-specc uneployen raes or ales beween he ages o weny and sxy-our or Agens n he odel econoy are eher eployed or uneployed. All agens are wllng o work, bu hose who are uneployed canno work due o a shorage o deand, and wages do no adjus o clear he arke. The probably o beng uneployed n a gven perod or an agen s unrelaed o he probably o beng uneployed n any oher perod. The oral hazard proble resulng ro he exsence o an nsurance progra s no odeled n he exercse (see Hansen and Irohoroglu (1992)). Penson Progra The odel akes as gven ha agens rere a he age o 65, wheher or no a penson progra exss. The penson progra s o he pay-as-you-go ype where curren conrbuons are used o und curren benes. In he seady sae, oal benes wll equal oal conrbuons n each perod. The penson bene prole s derved ro he average aoun o onhly benes pu no play or ales, n 1987, o $35, an annual aoun o $3,66 (Healh and Welare Canada (1987)). Each successve generaon earns an average lee wage (1+g) hgher han he precedng generaon, so he bene prole s se o declne a a rae o (1+g) -1 aer he age o The endowen level upon rereen, e 65, s se o he annual aoun $3,66, and he bene rae, b, s se o 1 or = 65 o 94. The earnngs and penson bene prole s depced n Fgure 3. A second scenaro, where he penson bene rae s se o 2 (so ha he annual aoun corresponds o $7,32 n 1987), was exaned n order o quany he pac o ore 8 The average weekly bene was approxaely 45% o he average weekly earnngs over (Sascs Canada (1995: 5)). 9 Fgures ro CANSIM daabase. 1

12 generous benes on he odel econoes, benes ore n lne wh US Socal Secury. 11 Preerences and Technology The dscoun rae, β, and he consan relave rsk averson paraeer, σ, were se o 1.11 and 1.12, ollowng he esaes esablshed by Hurd (1989). The producon uncon s a sandard Cobb-Douglas wh he share o capal, α, se o.3. Deprecaon s se a.6. The scale paraeer, Β, s se o.4, o keep he opal asse holdngs whn he grd speced n he appendx. In he sall open-econoy seng, he real neres rae s exogenously gven, and s se o.2 or he odel econoes. The value or g, echnologcal progress s also se a.2. Table 1 presens odel paraeers ha are xed n he analyss. IV. Model Econoy Resuls The resuls presened n Tables 2 and 3 ndcae ha he publc provson o rereen benes can reduce he aggregae savngs rae and ncrease he relance on oregn capal n open econoes (or ncrease he equlbru neres rae n closed econoes). The enleen o odes benes aounng o 14% o age 64 average labour earnngs reduce he rereen savngs ove and reduce he aggregae savngs rae n odel econoy 1 by ore han one percenage pon, and reduce aggregae savngs rae n odel econoy 2 by wo percenage pons. The aoun o doesc savngs and asse holdngs s reduced by 23.1% and 21.7% respecvely. In he case o ore generous benes, equal o 28% o age 64 average labour ncoe, he aggregae savngs rae s reduced ro 6.3% o 3.7% n odel econoy 1, and ro 11.% o 6.8% n odel econoy 2. In such cases, he aoun o doesc savngs and asse holdngs s reduced by over ory percen. 1 Penson benes n Canada are ndexed wh he CPI, and so, wll rean consan n real ers over an ndvdual agen s rereen years. 11 The US Socal Secury progra replaces a larger poron o pre-rereen ncoe, abou double he replaceen rao o he Canada Penson Plan (Sabelhaus (1997)). 11

13 Sabelhaus (1997) shows ha ndvduals n Canada us save a hgher raes han her US counerpars because he US Socal Secury syse s uch ore generous han Canadan progras or rerees. For an ndvdual wh average annual earnngs o $5,, he US Socal Secury syse would replace 3% o hs or her earnngs n rereen. In Canada, he replaceen rae s 13%. Thus, one would expec he Canadan savngs rae o be hgher han ha o he US. The resuls or he odel econoes wh he bene level se o 1 are ndcave o he eec o Canadan rereen ncoe polcy on he aggregae savngs rae, whereas he resuls wh he bene level se o 2 are ndcave o he eec o US rereen ncoe polcy. Ths paper has deonsraed ha a publc pay-as-you-go penson syse can reduce he savngs rae and doesc capal holdngs, and ncrease he curren accoun dec and oregn ndebedness n sple le-cycle econoes o overlappng generaons. In a closed econoy, he rae o reurn on capal would ncrease and wages would all. Ths paper does no presen a odel ha nvesgaes he nduceen eec o pensons on rereen as dscussed n Feldsen (1974). Sabelhaus (1997) presens evdence ha he Canadan savngs rae ay also have been hgher durng he 197s and 198s as he labour orce parcpaon rae o Canadan ales aged 65 and older ell uch ore draacally han ha n he US. An nvesgaon no hese ssues wll be le or uure work. V. Concluson In he ajor ndusralzed naons, he declne n aggregae savngs raes has concded wh he nroducon and ncreased generosy o publc nsurance progras o help allevae povery. One resul o hs proved socal conscousness has been he draac ncrease n he ncoes o he elderly. The provson o socal secury and penson benes has lowered povery levels o he aged. In he US, prvae savngs raes ncreased n he 195s as he relave econoc saus o he elderly ell. The savngs declne n he pas hry years has concded wh a perod when he relave ncoes o he elderly have ncreased (Suers and Carroll (1987: 626)). The ypcal 7 year-old n he US oday s consung one-h ore han 12

14 he ypcal 3 year-old. Ths s a draac change ro he 196s when he average 7 year-old consued wo-hrds o he average consupon o a 3 year-old (Gokhale, Kolko and Sabelhaus (1996)). Socal secury and rereen polcy has played an nsruenal role n ncreasng he ncoes and allevang povery o he elderly. As he sple odel econoes nvesgaed n hs paper have shown, pay-as-you-go socal secury progras reduce prvae savng, and can help explan par o he savngs declne experenced by os naons. I s no he nen o hs paper o encourage he reducon o benes o encourage aggregae savngs, bu raher o show how penson progras reduce savngs ncenves. Oher ehods o proong doesc raes o savng have and should be pursued. The elnaon o governen decs s a ghy sep owards ncreasng he aggregae savngs rae o he US and Canada. Proong labour producvy growh s anoher (see Wlson (21c)). Reerences Banng, K.G., and Boadway, R. (1996), Reor o Rereen Incoe Polcy. Kngson: School o Polcy Sudes, Queen s Unversy a Kngson, Onaro. Bernhe, B.D. and Shoven, J.B. (1991), Naonal Savng and Econoc Perorance. NBER, Chcago. Bohn, H. (1999), Should he Socal Secury Trus Fund Hold Eques? An Inergeneraonal Welare Analyss, Revew o Econoc Dynacs 2: Bosworh, B. (1991), The Global Declne n Savng: Soe Inernaonal Coparsons. In Savng and Polcy, Cenre or Econoc Polcy Research, Ausralan Naonal Unversy, Canberra. Cagan, P. (1965), The Eec o Penson Plans on Aggregae Savngs. Naonal Bureau o Econoc Research, New York. Eery, J.H. and Rongve, I (1999), Much Ado Abou Nohng? Deographc Bulges, he Producvy Puzzle and CPP Reor, Coneporary Econoc Polcy 17(1): Feldsen, M.S. (1974), Socal Secury, Induced Rereen, and Aggregae Capal Accuulaon, Journal o Polcal Econoy 82: Gale, W.G., and Sabelhaus, J. (1999), Perspecves on he Household Savng Rae. Brookngs Papers on Econoc Acvy, no.1. 13

15 Gokhale, J., Kolko, L.J., and Sabelhaus, J. (1996), Undersandng he Poswar Declne n US Savng: A Cohor Analyss. NBER Workng Paper Seres No Gordon, R.J. (2), Macroeconocs, Eghh Edon. Addson-Wesley, Massachuses. Hansen, G.D., and Irohoroglu, A. (1992), The Role o Uneployen Insurance n an Econoy wh Lqudy Consrans and Moral Hazard. Journal o Polcal Econoy 1 (1): Healh and Welare Canada (1987), Monhly Sascs, Incoe Secury Progras. Oawa. Healh and Welare Canada (1989), Canada Penson Plan Conrbuors, Oawa. Hubbard, R.G., and Judd, K.L. (1987), Socal Secury and Indvdual Welare: Precauonary Savng, Borrowng Consrans, and he Payroll Tax. The Aercan Econoc Revew 77 (4): Hubbard, R.G., Sknner, J. and Zeldes, S.P. (1995), Precauonary Savng and Socal Insurance. Journal o Polcal Econoy 13 (2): Hugge, M. (1996), Wealh dsrbuon n le-cycle econoes, Journal o Moneary Econocs 38: Hugge, M. and Venura, G. (1999), On he Dsrbuonal Eecs o Socal Secury Reor, Revew o Econoc Dynacs 2: Hurd, M.D. (1989), Moraly Rsk and Bequess, Econoerca 57, 4: Kaona, G. (1964), Prvae Pensons and Indvdual Savngs. Survey Research Cener, Insue or Socal Research, Unversy o Mchgan, Ann Arbor. Munnell, A.H. (1977), The Fuure o Socal Secury. Brookngs Insuon, Washngon. Peers, S. (1995), Explorng Canadan Values: Foundaons or Well-Beng. CPRN Sudy No.F1, rev. ed. Canadan Polcy Research Nework, Oawa. Ros-Rull, J.V. (1994), Populaon Changes and Capal Accuulaon: The Agng o he Baby Boo, anuscrp, Unversy o Pennsylvana. Sabelhaus, J. (1997), Publc polcy and savng n he Uned Saes and Canada, Canadan Journal o Econocs 3: Sascs Canada (1993), Seleced Brh and Ferly Sascs, Canada, Oawa, Caalogue Sascs Canada (1995), Uneployen Insurance Sascs. Oawa, Caalogue 73-22S. Soresleen, K. (2), Susanng Fscal Polcy Through Igraon, Journal o Polcal Econoy 18: Suers, L. and Carroll, C. (1987), Why s U.S. Naonal Savng So Low? Brookngs Papers on Econoc Acvy, Volue 1987, Issue 2: Wlson, S.J. (21a), A Dynac General Equlbru Analyss o Mgraon and Capal Accuulaon: The Case o Canada. Dscusson Paper No. 86, Deparen o Econocs, Unversy o Regna. Wlson, S.J. (21b), The Quanave Sgncance o Precauonary Savngs n Le- Cycle Econoes. Dscusson Paper No. 98, Deparen o Econocs, Unversy o Regna. Wlson, S.J. (21c), The Declne n Savngs: Should We Be Surprsed? Dscusson Paper No. 1, Deparen o Econocs, Unversy o Regna. 14

16 Appendx A: Seady-Sae Populaon Dsrbuon The age dsrbuon o he populaon a a pon n e s denoed by he (2I x 1) vecor µ, where µ = [ µ 1, µ 2, µ I, µ 1, µ 2, µ I, ] T. Agens o age, and gender h ( or eales and or ales), ace a probably s,h o survvng ro he age o o he age o +1 ha s consan over e. The uncondonal probably o survvng o age k s s( k) = Π s. The vecor o age and gender specc erly raes s φ, and s assued k 1 j= 1 j consan over e. The nuber o gender newborns a e s: µ k 1, k, = φ, h, h µ, h, 1 where k denoes he gender o he newborn, and h denoes he gender o he agen (brhparen). The populaon o age agens (where > 1) a e s: µ,h, = s -1,h µ -1,h,-1. The law o oon o he populaon s represened by he arx Γ, where, Γ = φ 1, φ 2, s1, ( 1 + θ1, ) s2, ( 1+ θ φ 1, φ 2, so ha µ = Γµ -1. 2, ) φ I 1, si 1, ( 1+ θ I 1, ) φ I 1, φ I, φ I, φ 1, φ 1, s1, ( 1+ θ1, ) φ I 1, φ I 1, si 1, ( 1 + θ I 1, ) φ I, φ I, In order o copue he seady-sae o he odel econoy, he seady-sae age dsrbuon o hs econoy us be derved. To do hs, he egenvalues and egenvecors o he arx descrbng he law o oon o he populaon are copued. 15

17 The larges egenvalue o he arx Γ s equal o he seady-sae growh rae o he populaon. The seady-sae age dsrbuon o he populaon s dened by he produc µ* = Γ b µ, where each eleen o Γ s equal o he correspondng eleen o Γ scaled by s larges egenvalue, and where b s sucenly large so ha Γ b+1 µ - Γ b µ (). Appendx B: Soluon Mehod In he sall open econoy raework he reurn on capal s deerned on nernaonal arkes. Gven he seady-sae age dsrbuon, he aggregae seady-sae capal sock s calculaed by solvng he equaon ha denes he reurn on capal. Wages are se o he argnal producvy o labour. Seady-sae equlbra are copued usng he ollowng algorh: (1) Gven here s no aggregae uncerany, calculae he expeced value o he aggregae labour supply, he expeced value o he capal sock, oal oupu, and he wage rae. Then, gven he nsurance bene rae, and he expeced nuber o uneployed agens and he nuber o pensoners o each age cohor, calculae he preu rae. (2) Guess he value or he ranser o accdenal bequess, T. (3) Calculae he opal decson rules, c, a, o all agens aged Iw (15) o I (94), wh he values o a I w 1 and a I +1 se o zero, and aggregae over he odel econoy. To do hs, he ndvdual s dynac prograng proble us be solved: (a) ( ( 1 σ V a, l, ) = ax u c) + β (1 + g) s( ) E[ V ( a, l, + 1) ( a, l, )], ( c, a ) subjec o, c + a (1 + g ) Ra + (1 p) wl ( ) e( ) + bw (1 l( )) e( ) + T (b) c, a, a = = I w-1 or I. (c) l() = 1 wh prob = e e p and wh prob 1- p. 16

18 The decson rules are calculaed by axzng he value uncon on grdpons dened over he sae space. 2 evenly spaced grdpons were used or he asse varables a and a, and wo grdpons were used or l. For each perod o an ndvdual s le, he value uncon was calculaed on egh llon grdpons. The opal value o a or a gven value o a and l was ha value where he value uncon was axzed. (4) Consruc populaon saples wh rando labour characerscs usng he age-specc labour endowens and eployen probables. Calculae he asse holdngs o each agen o he saple, gven hs eployen hsory. For each populaon saple, calculae he value o accdenal bequess, T, ro a rando saple o agens ro each cohor who de whn n a gven perod, or each populaon saple, and nd he average over saples. (5) I he average value o T calculaed n sep (4) ders ro he nal guess n sep (1), repea he procedure usng he resul ro sep (4) as he nal guess unl convergence s acheved. The populaon saples were consruced usng he seady-sae populaon dsrbuon or he odel econoy. Thry saples o y housand agens were used o nd he average values n sep (4). 17

19 Table 1: Fxed Model Paraeers α β δ σ r g I w I w I b 2-64 s raes, Canada Table 2: Model Econoy 1 Resuls 1987 erly raes, n = -.79 (all raes n percenages) EI Preu Rae 3.4 Penson Bene Rae (b ) 1 2 Penson Preu Rae Ne Savngs Rae Foregn Capal Inlow Rae Percenage o doesc asse holdngs reduced due o publc pensons Noe: The oal preu rae (p s he su o he EI preu rae and he penson preu rae. Table 3: Model Econoy 2 Resuls 197 erly raes, n =.4 (all gures n percenages) EI Preu Rae 3.5 Penson Bene Rae (b ) 1 2 Penson Preu Rae Ne Savngs Rae Foregn Capal Inlow Rae Percenage o doesc asse holdngs reduced due o publc pensons Noe: The oal preu rae (p s he su o he EI preu rae and he penson preu rae. 18

20 Fgure 1: Canadan Ne Savngs Raes, Source: CANSIM Marces 8614, Ne Savng Rae Personal Savng Rae Busness Savng Rae Governen Savng Rae Foregn Savng Rae Fgure 2: Seady-Sae Populaon Dsrbuons Model Econoy 1 Model Econoy Dsrbuon 2 Dsrbuon Noe: The age cohors are grouped n one year age cohors unl 7, and are hen grouped n ve-year age cohors ro 7 o 89, and he nal age cohor consss o hose aged 9 and older. 19

21 Fgure 3: Model Econoy Earnngs and Penson Bene Prole Average Earnngs o Male CPP Conrbuors, 1987 Esaed Penson Bene Prole,