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1 econsor Make Your Publcaons Vsble. A Servce of Wrschaf Cenre zbwlebnz-informaonszenrum Economcs Lassla, Jukka; Valkonen, Tarmo Workng Paper Penson prefundng, ageng, and demographc uncerany ETLA Dscusson Papers, The Research Insue of he Fnnsh Economy (ETLA), No. 74 Provded n Cooperaon wh: Research Insue of he Fnnsh Economy (ETLA), Helsnk Suggesed Caon: Lassla, Jukka; Valkonen, Tarmo (2) : Penson prefundng, ageng, and demographc uncerany, ETLA Dscusson Papers, The Research Insue of he Fnnsh Economy (ETLA), No. 74 Ths Verson s avalable a: hp://hdl.handle.ne/49/6365 Sandard-Nuzungsbedngungen: De Dokumene auf EconSor dürfen zu egenen wssenschaflchen Zwecken und zum Prvagebrauch gespecher und koper werden. Se dürfen de Dokumene nch für öffenlche oder kommerzelle Zwecke vervelfälgen, öffenlch aussellen, öffenlch zugänglch machen, verreben oder anderweg nuzen. Sofern de Verfasser de Dokumene uner Open-Conen-Lzenzen (nsbesondere CC-Lzenzen) zur Verfügung gesell haben sollen, gelen abwechend von desen Nuzungsbedngungen de n der dor genannen Lzenz gewähren Nuzungsreche. Terms of use: Documens n EconSor may be saved and coped for your personal and scholarly purposes. You are no o copy documens for publc or commercal purposes, o exhb he documens publcly, o make hem publcly avalable on he nerne, or o dsrbue or oherwse use he documens n publc. If he documens have been made avalable under an Open Conen Lcence (especally Creave Commons Lcences), you may exercse furher usage rghs as specfed n he ndcaed lcence.

2 ETLA ELINKEINOELÄMÄN TUTKIMUSLAITOS THE RESEARCH INSTITUTE OF THE FINNISH ECONOMY Lönnronkau 4 B 2 Helsnk Fnland Tel Telefax World Wde Web: hp:// Keskuseluahea Dscusson papers No. 74 Jukka Lassla Tarmo Valkonen PENSION PREFUNDING, AGEING, AND DEMOGRAPHIC UNCERTAINTY Ths research was carred ou wh fnancal suppor from he Cenral Penson Secury Insue n Fnland and from he ageng programme of he Academy of Fnland. We have grealy benefed from dscussons wh he Insue's economss Mkael Forss, Lasse Kosknen, Bo Lundqvs, Ismo Rsku, Janne Salonen and Rejo Vanne. We also hank Juha Alho for provdng us wh hs smulaons, Eja Kaupp for he model programmng and Lans Bovenberg for commens. The paper was presened a he 56h Congress of he Inernaonal Insue of Publc Fnance, Sevlle, Span, Augus 28-3, 2. ISSN

3 LASSILA, Jukka VALKONEN, Tarmo, PENSION PREFUNDING, AGEING, AND DEMOGRAPHIC UNCERTAINTY. Helsnk: ETLA, Elnkenoelämän Tukmuslaos, The Research Insue of he Fnnsh Economy, 2, 2 p. (Keskuseluahea, Dscusson Papers, ISSN ; No. 74). ABSTRACT: Penson prefundng can be used o smoohe conrbuon raes n economes where ageng wll ncrease penson expendure. Bu how exensve should prefundng be, n a defned benef penson sysem, when here s consderable uncerany concernng fuure moraly, ferly, and mgraon? We sudy he prefundng rules n he Fnnsh earnngs-relaed penson sysem wh an OLG smulaon model. Increasng he degree of prefundng could yeld a more even nergeneraonal oucome and make fuure generaons poson beer, bu s que possble o overshoo and harm curren generaons oo much. Makng he degree of prefundng ferly-dependen seems a useful alernave. Wh declnng ferly, curren large cohors would pay modesly ncreased conrbuons. The accumulaed funds, however, wll be huge n relaon o he wage blls of smaller fuure cohors. Key Words: Pensons, paral prefundng, ageng, demographc uncerany LASSILA, Jukka VALKONEN, Tarmo, PENSION PREFUNDING, AGEING, AND DEMOGRAPHIC UNCERTAINTY. Helsnk: ETLA, Elnkenoelämän Tukmuslaos, The Research Insue of he Fnnsh Economy, 2, 2 s. (Keskuseluahea, Dscusson Papers, ISSN ; No. 74). TIIVISTELMÄ: Tavoeena on uka, men yöeläkkeden rahasonnlla ja rahasojen käyöllä vodaan vamenaa väesön käänymsen aheuamaa eläkemaksujen nousupanea. Lähökohana on nykynen Suomen yksysen sekorn yöeläkejärjeselmä. Rahasopolkan arvonkreerenä käyeään vakuuksa kansanaloudellsn muuujn, yönanajan ja yönekjän eläkemaksuhn, eläkejärjeselmän okeudenmukasuueen ja koalouksen hyvnvonn. Tulosen mukaan rahasonnn kasvaamnen ny, kun yövoman määrä on velä suur, ols hyvä apa asaa väesön käänymsen kusannuksa er sukupolven kesken. Erysen suoselavaa lsärahason on sllon, jos käänymnen on odoeua nopeampaa. Väesöepävarmuudela vodaan suojauua ehokkaas oamalla synyvyys huomoon rahasonsäännössä. Tuloksa on laajemmn esely julkasussa Eläkerahaso ja väesön käänymnen, Eläkeurvakeskuksen ukmuksa 999:2 ja ETLA B 58. Asasana: yöeläkejärjeselmä, rahason, käänymnen, väesöepävarmuus

4 . INTRODUCTION The debae concernng penson fundng has wo man branches. One, perhaps somewha passng, s ha beween PAYG and fully funded sysems, whch s also found under he headng of penson prvasaon. The oher, emergng branch concerns prefundng as a ool for preparng for he effecs of populaon ageng on penson expendures. The former branch relaes fundng more o defned-conrbuon sysems, whereas he laer nclude ssues relaed specfcally o prefundng n defned-benef penson sysems. Ths paper belongs o he laer caegory. Our paper makes he pon ha once he decson o prefund has been done, he rules for fundng have o be decded, and hese rules are crucal for he success of he prefundng polcy. The rules defne he amouns of new fundng and whdrawals from funds. We concenrae on rules ha relae prefundng o penson rghs and demographc developmens, and dscuss only shorly oher ypes of fundng. Our sarng pon s he curren Fnnsh prvae-secor earnngs-relaed penson sysem. I s based on a defned benef prncple, bu s a he same me parally funded wh forward-lookng fundng rules. We analyse he mpacs of changng he prefundng rules, keepng he deermnaon of he benefs nac and leng he conrbuon rae o adjus. The mehod we use s o smulae he polces wh a numercal overlappng-generaons model. The paper also characerses he mpacs of demographc uncerany on he penson sysem and he aggregae economy. Analyss of he prevous populaon forecas errors shows ha he uncerany s much larger han generally s recognsed consderng he me horzons used by penson sysems. Ths uncerany boh ncreases he need for preparng for fuure and makes he creaon of good fundng rules a demandng ask. The paper s organsed as follows. Secon 2 surveys recen relevan leraure and descrbes some exsng prefundng pracces, especally hose n Fnland. In Secon 3 we descrbe boh he sochasc populaon smulaons and he overlappng-generaons general equlbrum model ha uses hese smulaons as npus. Secon 4 analyses he effecs of ncreasng he degree of prefundng n he Fnnsh penson sysem, and Secon 5 dscusses he effecs of complemenng he curren rules wh a ferly-dependen componen. Secon 6 concludes. 2. PREFUNDING IN DEFINED BENEFIT SCHEMES 2.. Background Penson reform leraure s passng he sage n whch here was a vgorous fgh n favour and agans prvasaon of he penson sysem. Prvasaon, n s mos smple verson, means a shf from a publc defned benef pay-as-you-go sysem o a prvae fully funded defned conrbuon sysem. The consensus, f any, s based on he recognon of, on one hand, he effcency, nergeneraonal farness and ransparency of he prvae sysem, and on he oher, he low ndvdual rsks and admnsrave coss of he publc sysem. The role of pre-fundng polcy s, accordng o hs consensus, less mporan han he mos

5 2 enhusasc supporers of prvasaon clam, bu s seen more as means of smoohng he nergeneraonal ncdence of ageng coss (see e.g. Snn 998). Snn (2) saes ha, n presen value erms, here s nohng o be ganed from a ranson from PAYG o funded sysem, even hough he laer would offer a permanenly hgher rae of reurn. Bu he sees a paral ranson o a funded sysem as a way o overcome curren demographc crss. Funds would replace mssng human capal wh real capal, and hus help smoohng ax and chld rearng coss across he generaons. Changng crcumsances may warran a change n he degree of fundng whn he penson sysem. Orszag and Orszag (2) noe ha commng o he up-fron coss assocaed wh movng from a PAYG sysem o a prefunded sysem whou any assurance ha he coss could be recapured f he reform urns ou o be less benefcal han had been ancpaed may be unwse. Therefore fundng rules should be flexble. If he am s o sablze he conrbuon rae n a defned benef sysem, many knds of flexbly n prefundng mgh be warraned. Shor erm varaons n he ax base due o busness cycles can be addressed by buffer funds. Buffers are also used o allevae he nergeneraonal burden due o reremen of baby boom generaons. We consder he mos mporan long erm rsk o be devaons n demographc varables, perhaps gong beyond he known varaon n he sze of curren age cohors. Ferly and penson sysem have been conneced n many sudes. Snn (998a) emphasses he role of a PAYG sysem as an nsurance for ndvduals agans no beng able o have chldren, or havng ungraeful chldren who are no wllng o ake care of her parens. He noes ha he sysem unforunaely also faclaes free-rdng volunarly no havng chldren. The queson wheher penson benef should be relaed o he number of chldren he reree has had, has also been addressed, see e.g. Snn (998b) and he references heren. Many curren publc penson schemes have already feaures whch promoe ferly. The ofen used measure s o allow penson accrual o ake place also durng maerny leave. Penson prefundng s a fundamenal par of mos volunary penson schemes. Palacos and Pallares-Mrallès (2) classfy he mandaory schemes accordng o he fnancng prncples and fnd ha abou half of mandaory schemes are purely pay-as-you-go fnanced. Abou a hrd have some reserves, even hough hey are based on a defned benef (DB) prncple. In mos cases hese funds are, however, ransory and dsspae afer he schemes maure. The reasons gven for prefundng vary. In Sweden, he nal dea was o neuralze he negave effec of a PAYG scheme o prvae savng and o use he reserves as a buffer agans cyclcal varaons (Sundén 2). In Fnland, he offcal explanaon for paral fundng was he need o smoohe he expendure pressures due o populaon ageng, bu also oher nerpreaons have been gven. The Employees Pensons Ac (TEL) was creaed n negoaons beween rade unons and employers organsaons. Shor-erm barganng consderaons and he need for polcal suppor may well have been mporan facors (see Lassla and Valkonen 2a). The man pon s ha he deermnaon of penson rghs can be shfed n a DB scheme o be he same as n a DC scheme. Thereafer s only queson of he sze and mplcaons of he nergeneraonal ncome ransfer due o he fnancng mehod of he penson sysem.

6 3 2.2 Penson prefundng n Fnland: old-age pensons n he prvae secor The man prvae-secor earnngs-relaed penson sysem n Fnland, he so-called TEL scheme, s parally funded, bu fundng does no affec penson benefs. I only affecs he level and me pah of conrbuons. Fundng s collecve bu based on ndvdual penson rghs. Currenly he man prefundng rules are as follows. A par of old-age penson benefs, payable afer age 65, s funded for each employee. Fundng akes place beween ages 23 54, so only benefs accrued durng hose years are (parally) funded. The degree of nal fundng s below one hrd 2 : of he.5 (of wage ncome) penson rgh accrung every year,.5 s funded. The presen value of accrued rghs s calculaed usng a 3 dscoun rae and a moraly able. No fundng s done for benef ncreases due o ndexaon. Fundng of dsably and unemploymen penson akes place when he case occurs. The nal funded share s 8 and, agan, no fundng s done for benef ncreases due o ndexaon. The pensons are pad, and funded, only unl age 65. Afer ha he pensoner receves old-age penson. In he followng we concenrae on old-age pensons. We frs descrbe he prefundng of he average employee's fuure benefs, and how he fund s run down n he reremen age. Then we aggregae o oal populaon level, o be able o presen he dynamcs of oal funds, he mechansm of conrbuon deermnaon, and he use of he yeld of funds. Prefundng on he ndvdual level Every year, new penson rgh accrues for each worker, and a par of he presen value of he rgh s prefunded. For someone already rered, a par of he money prefunded n her workng years s used o pay a par of her penson. Equaons () and (2) below descrbe hese fundng rules for he average worker and pensoner n each age group n perod. The gross labour ncome of he average worker n age group s denoed by g. IN () h = a kg M h j,, S, j + r ) j= /( = 23,,54 ndvdual accumulaon rule OUT IN TEL j (2) h, = h + j, j ( + r ) = 65,,M ndvdual decumulaon rule j= 23 Accordng o equaon (), a share a of he presen value of he penson rgh accrung n perod o workers aged beween s pu o funds. The presen value ncludes all old-age penson years, from 65 o a maxmum age denoed by M. The labour ncome g 2 There s no specfed arge for he share ha s funded. Before 997 fundng beween ages was full, n he sense ha f here would have been no wage nflaon, he 5 nomnal yeld requremen of he funds would have resuled n funds suffcen o pay ou, whou any PAYG fnancng, exacly he benefs whose rghs had accrued beween ages Needless o say, here was nflaon boh n prces and n wages, and fundng was far from full. The changes made n 997, descrbed n Lassla and Valkonen (2a), were calbraed so ha he requred fundng would say a he prevalng level, and.5 s a resul of ha calbraon.

7 4 creaes a penson rgh for each year from age 65 onwards. For prefundng purposes, he magnude of hs rgh s evaluaed gnorng all fuure changes due o wage or prce developmens. Thus he value of he rgh s smply kg for each reremen year. Currenly, k s.5. The dscoun facor ncludes boh an neres rae and survval probables. The fund rae h of neres, used n hs calculaon, s admnsravely se. We denoe by r. The erm S n () descrbes he expeced effecs of moraly. Only a share S of hose n age group n perod s expeced o be alve n age j. Equaon (2) saes ha, for a rered person, he amoun prefunded earler (when he curren pensoner was beween ages 23-54) for perod 's penson, and he neres accrued o hose funds, s used o pay a par of he person's penson (he res comes from he PAYG par). The neres accrued s calculaed usng anoher admnsravely se neres rae, he so-called TEL-calculaed neres rae (assumed here consan for a smpler exposon). Equaons () and (2) are n pracse neresng only o penson companes, as hey are used n calculang her penson lables. Each company s responsble for he prefunded pars of he pensons of hose nsured n he company. The companes are jonly responsble for he res of pensons. Bu he equaons are mporan, of course, for he aggregae dynamcs of he penson sysem, especally for he level and me pah of he conrbuon rae. Aggregae penson funds and he conrbuon rae The oal amoun of new fundng n perod s obaned by mulplyng he average ndvdual fundng n age group, descrbed n equaon (), by he number of workers n n he age group, and summng over all age groups. Ths s done n equaon (3). The oal amoun whdrawn from funds s obaned analogously (equaon 4). Three oher aggregaes are defned n equaons (5) o (7): he oal wage bll, from whch he penson conrbuons are colleced, he oal amoun of old-age earnngs-relaed penson expendure, where he average ndvdual pensons are denoed by z, and he oal amoun of oher ransfers from he penson secor. 54 (3) A = n = 23, h IN, new fundng, oal M OUT (4) W = n, h, whdrawals from funds, oal = 65 (5) G = 64 = 8 (6) Z = M = 65 Z (7) S = M = 8 n n, n z g,, oal conrbuon base (wage bll), oal old-age penson expendure s Z,, oher pensons from he TEL sysem

8 5 The dynamcs of he oal amoun of funds, H, follow from equaon (8) and he conrbuon rae s deermned as a resdual from equaon (9). TEL (8) H = H ( + r ) + A W l Z TEL (9) τ G Z + S + A W H r r ) ( = Conrbuons mus be suffcen o cover ha par of penson expendure whch does no come from whdrawals from funds, plus new fundng and ransfers, mnus he dfference beween real yeld r on funds and he TEL-calculaed neres rae 3. To beer see he role of demographcs n he deermnaon of conrbuons, we nser equaons (3) - (7) no equaon (9) and reorder. () τ l M M 54 M OUT IN Z n, z, n, h, n, h, n, s, = 65 = 65 = 23 = 8 H ( r = = 8 n, g, = 8 n, g, = 8 n, g, = 8 n, g, = 8 n, r g TEL, ) The frs erm on he RHS s he rao of penson expendure o wage bll. The man demographc varable s he number of pensoners relave o wage-earners. The second erm s lke he frs one: he number of pensoners relave o wage-earners s he crucal demographc facor. The hrd erm, new fundng relave o wage bll, s demographcly raher nvaran: he numeraor depends on he number of people beween ages 23 and 54, and he denomnaor on hose beween ages 8 and 65. The overlap s 32 years, and n addon he labour force parcpaon raes for ages below 23 and above 54 are low. The fourh erm ncludes all aduls n he numeraor and workng-age people n he denomnaor. I vares wh demography, bu should be kep n mnd ha oher ransfers from he penson sysem are raher small compared o old-age pensons. The ffh erm, he neres accrual over he TEL-rae, shows ha he amoun of funds relave o he wage bll s mporan for he conrbuon rae f he acual yeld exceeds he admnsravely se rae. In he followng we assume he wo raes equal. If he goal s o smooh he me pah of conrbuons, equaon () shows hen roughly he effec of Fnnsh-ype prefundng. The frs par s he normal pure PAYG effec, whch s reduced by he second erm, n a way smlar o reducng he penson benef level. The cos of hs reducon s he hrd erm, whch s roughly consan n me. So he varably n he PAYG par s reduced by ransformng a par of o a consan. The queson we ask s: should we ncrease he role of hs smoohenng? The reasonng s smple: currenly he amoun whdrawn from he funds reflecs only he number of curren pensoners. I perhaps should reflec also he number of curren workers. The hrd erm wll hen also reflec he rao of curren workers o fuure workers. I becomes more responsve o demographc varaons. 3 The yeld dfferenal vares beween penson companes, and s he man facor n her compeon for cusomers, whch are employers provdng penson nsurance for her workers.

9 6 Besdes fundng, here are oher ways a penson sysem can prepare for dfferen elemens of demographc uncerany. Longevy could be deal wh by lnkng penson benefs o lfe expecancy. Ths has been done n Sweden (see Sherman, 999). Ne emgraon can be a very dffcul problem, because may leave very lle me o adjus. One possbly s ndexng he benefs o he developmens of he wage bll (see Dsney, 999). Paral raher han full ndexng may be called for, as he laer may make he benefs very unpredcable, whch should be avoded as rered persons have usually very lmed possbles o reac o benef cus. Ferly changes, on he oher hand, affec he penson sysem wh a longsh delay. Lassla and Valkonen (2b) compares longevy-adjusmen and ndexaon of he benefs o oal wages o he ferly adjusmen n prefundng as devces of nergeneraonal redsrbuon of demographc rsks. 3. THE MODEL Our man ool s an overlappng-generaons general equlbrum smulaon model. I uses as npus dfferen demographc scenaros, produced by sochasc populaon smulaons. Techncally hs s sraghforward. Inellecually here s a gap: here s no uncerany n OLG model. The households and frms n he model do no ake no accoun demographc uncerany n her decsons. They have perfec foresgh of he fuure populaon developmen n each alernave. Clearly would be more sasfacory o have uncerany ncluded; we feel, however, ha he resuls are neresng enough o fully jusfy our mehod, whle wang for more suable models. 3. Demographc uncerany Alho (998) has made sochasc populaon forecass for Fnland. Based on prevous forecas errors n ferly, longevy, and mgraon, he has modelled he uncerany n demographcs, and made 5 smulaons wh he model. He provded wo sample pahs for hs sudy. They are repored also n Lassla and Valkonen (999). The 5 smulaons were ordered wh respec o her age rao sasc n 23. The age rao s he number of people over 6 years dvded by he number of people beween ages From hs orderng, he wo samples closes o he lms of 8 confdence nerval n 23 were chosen. Fgure shows hese realsaons, and he base scenaro also. The 8 confdence nerval n he age rao n 23 s wde: he lms are.63 and.787. Ths can be roughly ranslaed no penson language: wh a probably Fnland wll have 8 pensoners or more for every workng-age persons, and wh a probably here wll be 6 pensoners or less for every workng-age persons n 23, provded ha he acual reremen age wll no ncrease subsanally. In any case, he ncrease wll be large, as he curren rao s 3.5 pensoners for workng-age persons.

10 7 Fgure. Rao of populaon n ages over 6 o he populaon n ages KELA-Eurosa Low age rao Hgh age rao ETLA Age rao: rao of populaon n ages over 6 o hose beween Hgh (low) age rao: neares realsaon o he upper (lower) lm of he 8 confdence nerval of he age rao n 23. Source: calculaons by J. Alho The hgh age rao s a resul of declnng ferly and ne emgraon, and he low age rao s manly he resul of declnng lfe expecancy. 3.2 OLG Model FOG s an Auerbach-Kolkoff-ype, perfec foresgh numercal overlappng generaons model. There are fve secors: households, enerprses, a governmen, a penson fund and a foregn secor. The labour, goods and capal markes are compeve and prces balance demand and supply perod-by-perod. There s no money or nflaon n he model. Households and frms are he forward-lookng decson makers. Household behavour Households maxmse he uly from consumpon and lesure n dfferen perods and he beques ha hey gve. The lfe-cycle plan for he household sarng s work lfe a me = s he soluon o he followng maxmsaon problem subjec o he perodc uly funcon (2), lfeme budge consran (3) as well as deermnaon of gross labour ncomes (4), reference penson (5), old-age pensons (6) and he dscoun facor (7): Max, () c l B T U γ B γ + µ T = ( + δ ) ( + δ ) γ, T,

11 8 (2) (3) U = ρ ρ c + αl ( ) ρ T W g = T w T w T T C C ( τ ) Z R + z ( τ ) R + R B + s + s = c p ( + τ ) R R T B T = T w+ (4) g = ( l ) e w = = = TW w ref T (5) z = θ g = w W λ p p C TW C λ (6) λ2 λ 2 C ref w p = z C w T p W TW z. (7) R = S, ( r + ) Households consder he possbly of early deah by dscounng fuure consumpon and ncomes by a facor whch ncludes boh he neres rae and he age-specfc survval probably. The varable c descrbes consumpon, p s prce, l s lesure, and of he consan parameers γ s he elascy of neremporal subsuon, δ s he rae of me preference and ρ s he elascy of subsuon beween consumpon and lesure. Households receve a beques B a he age of and gve a beques B before dyng. The parameer µ deermnes he srengh of he joy-of-gvng beques move. The aggregae amoun of he generaon specfc ransfers S s deermned o balance he revenues and expendures of he cenral governmen. A lfe-cycle plan s made a he age of 2, and people plan o rere a he age of T +. The budge consran (3) says ha dscouned w lfeme wage and penson ncome equals dscouned consumpon expendure. The erms w τ andτ C are ncome ax and value added ax parameers. The θ -parameers descrbe how he penson rghs are relaed o career earnngs. More wegh s gven o he las workng years, because n pracse he pensonable wage s aggregaed over he las years of each employmen conrac. As benefs depend on and conrbuons are pad from wages, here s an ndrec connecon beween conrbuons and benefs on ndvdual level. Ths connecon s no one-o-one, however, as all career earnngs are no weghed equally. The ndexng of accrued penson rghs s dfferen n workng-years and n reremen: λ s currenly.5 and λ s.2. 2 The acual equaons of he smulaon model are he frs-order condons derved from he opmsaon problem. C T

12 9 Decson problem of he frms Frms choose he opmal amoun of nvesmen and use of labour o maxmse he prce of her shares. The marke value of he frm s deermned as a dscouned sum of fuure dvdends. The problem can be presened as maxmsng n he begnnng of he perod he dvdends D dsrbued durng he perod plus he value of he frm V a he end of he perod, subjec o he amoun of nal capal sock, he cash-flow equaon of he frm (9), he CES producon funcon F (2), he accumulaon condon of he capal sock K (2), he deermnaon of he frm's deb funcon G (23). (8) Max L I, K, F (9) D = ( ) D + V. subjec o: F B (22) and he nvesmen adjusmen cos l F d F F F K [ ( + τ ) r B ] + B p I p F G w L B (2) ( ) ( )( ) ( ) β F β F β β F = A εk + ε ν L, (2) K = d ) K + I (, K (22) B = bp K and (23) 2 I G = ξ. K The equaons (8) and (9) have been smplfed by leavng ou he capal ncome ax F K d erms. The prce varables p, p descrbe he prces of value added and capal un. r s he domesc neres rae, whch generaes neres flows o be dsrbued durng perod. The ypcal CES producon funcon parameers are as follows: A F s he scale parameer, ε s he share parameer and β s he subsuon parameer. ν descrbes he rae of producvy growh of labour. The accumulaon of capal K s explaned by usng he deprecaon rae d and he amoun of new nvesmens I. The parameer b descrbes he collaeral value of he capal sock. In he las equaon, he parameer ξ deermnes he scalng of he nvesmen adjusmen coss. Three of he four frs-order condons of he consraned opmsaon are used as model equaons, he fourh beng he ransversaly condon. Markes The model ncludes four markes, whch clear every perod. In he labour marke, frms demand labour accordng o he margnal producvy of labour rule. Households' aggregae labour supply s dvded beween publc and prvae employmen. The wage rae s deermned by equang supply and demand n he labour marke.

13 Frms are sole supplers n he marke of he domesc good. The produc s used by oher frms as par of he compose nermedae and nvesmen goods, by households as par of he compose consumpon good and by foregn agens. The demand of domesc agens and he prces of he compose goods are deermned by a cos mnmsng procedure. The domesc demand of he fxed-prce mpored good s also deermned by mnmsng he coss of he compose goods. The perfecly elasc supply adjuss o demand n hs marke. The fourh marke s he capal marke, n whch savng and nvesmen are balanced by he domesc neres rae r d. Toal savng s he sum of domesc savng and foregn porfolo nvesmens. The presenaon above descrbes only he relevan pars of he model. The acual model ncludes e.g. he governmen wh an neremporal budge consran, and rade and capal flows wh he res of he world 4. The modelled penson sysem ncludes employee s conrbuon rae and prefunded dsably and oher early pensons, whch are no mporan for our resuls. The model s un perod s fve years, and he annual fundng rules have been modfed accordngly. The model s descrbed n more deal n Valkonen (999) and Lassla (2). Acuary rao As an nergeneraonal measure of he connecon beween benefs and conrbuons we defne he followng. The acuary rao s he rao of a cohor s dscouned benefs from he penson sysem o s dscouned sum of paymens o he penson sysem. The benefs nclude old-age pensons, denoed by z, and, combned no s Z, dsably and unemploymen pensons and all oher pensons from he earnngs-relaed penson sysem. T T T W (24) Α R = Z + l s R zr / τ gr = = TW + = If he acuary rao equals, he cohor ges he same rae of reurn on penson conrbuons han would have go from fnancal markes. A rao less han descrbes a usual suaon n PAYG penson schemes, afer he nal generaons who have go a rao n exceed of uny. Acuary rao s closely relaed o he money s worh calculaons famlar from he penson reform dscusson n he Uned Saes. 4 The amoun of labour marke effcency losses due o he hgher penson conrbuons depends on boh he deals of he penson sysem and on he ax srucure of he economy. In he Fnnsh case, he overall axaon of earned ncomes s hgh even before he ageng sars o have effec. The dual ncome ax sysem allows he capal ncomes o be much less axed. These feaures emphasze he benefs of labour ncome ax smoohng, whch could be acheved va prefundng of pensons.

14 4. BASELINE SCENARIO Our baselne smulaon ncludes he neracon beween populaon, he penson sysem and he res of he economy. The ageng of he populaon s due o he connuous ncrease n lfe expecancy and he low brh rae. Accordng of he offcal forecas, he Fnnsh populaon reaches he maxmum n he begnnng of he 22'es. The man pon s, however, ha he workng age populaon sars o dmnsh already afer a few years and he amoun of pensoners ncreases srongly, snce he baby-boom generaons rere. The low reremen age and he maurng of he penson sysem magnfy he economc burden. The forward-lookng frms reac o he expeced reducon n labour force by lowerng he growh rae of nvesmens and by developng labour-savng producon mehods. The excess demand of labour acceleraes he growh of wages, even hough also he employer's penson conrbuon rae rses. The wages are suppored by he dampened growh of expors, whch mproves he erms of rade of he economy. From he pon of vew of he workers, he oucome s, however, negave, snce he hgher consumer prces and he hgher employee's conrbuon rae lowers he growh rae of he purchasng power of wages. In he capal markes, here s nally an excess supply of fnancal capal due o fallng nvesmen rae and he sll hgh penson savng. The generaed surplus s nvesed abroad. The penson savng dmnshes, however, gradually and also he aggregae household savng reduces due o ageng. The nsuffcen savng fnally urns he curren accoun surplus o a permanen defc. Wh lower margnal produc of capal he marke value of he frms drops from he nal growh pah. In he case of open capal markes, hs s compensaed o he nvesors by hgher dvdends, whch can be dsrbued due o reduced need for nvesmen fnance. An alernave vew of he capal marke developmen suggess ha snce he ageng s common o larges counres, he nal hgh savng rae lowers he neres rae. Ths fallng rend urns afer wo decades and he neres rae clmbs gradually afer ha, bu does no reurn o he nal level before he end of hs cenury. Accordng o he baselne scenaro, he prvae secor penson expendures rse abou 2 percenage pons and average penson conrbuon rae rses abou percenage pons of he correspondng aggregae wages durng he frs half of he cenury. The gap s explaned by he fac ha he penson fundng ncreases. The larger nvesmen reurns of he fund mgaes he needed long-erm hke n he penson conrbuon rae. Whle he benef deermnaon rules reman nac, he hgher conrbuon rae neverheless weakens sgnfcanly he acuaral farness of he penson sysem. 5. EFFECTS OF CHANGING THE PREFUNDING RULES 5. Increasng he degree of prefundng We sudy he effecs of rasng he degree of prefundng (parameer a n equaon ) of he prvae secor old-age pensons from one hrd o wo hrds ( p.a.) and o one (.5 p.a.) from 25 onwards. Fundng sll akes place only beween ages and he dsably penson fundng remans unaffeced.

15 2 The developmen of he oal conrbuon rae depends on he demographc rends. In he base alernave (KELA-Eurosa), ncreasng fundng o wo hrds resuls n a roughly horsonal pah for he conrbuons. A hgher degree of fundng would be over-reacng: conrbuon rae could be lowered afer 225. Ths overshoong would be even more pronounced n he low age rao scenaro. Bu n he low ferly (hgh age rao) case a 2/3 degree of fundng would no suffce o yeld sable conrbuon raes, see Fgure 2. Smlar developmens can be seen n acuary raes (Fgure 3). Increasng he degree of prefundng could yeld a more even oucome and make fuure generaons poson beer, bu s que possble o overshoo and unnenonally harm curren generaons oo much. The prefundng degree s no an easy polcy nsrumen o use. 5.2 Addng ferly o he deermnans of prefundng Curren prefundng rules provde some auomac smoohng of penson conrbuon raes n he case of changng demographcs. As fundng akes place for each worker, he more here are rered workers he more here are also funds. And hese funds are used o pay a par of he penson benefs of hese rered workers. Thus he conrbuon raes need no rse n full proporon o he number of rerees. If we hnk of he rao of pensoners o workers, curren prefundng rules reac o he numeraor. To sablze he conrbuon rae more, also he denomnaor should be aken no accoun. Ths s he subjec of hs secon. Table. Toal conrbuon rae and asses of he penson funds n Toal conrbuon rae, Asses, per cen of oal wages Curren rules Prefundng rae 2/3 Prefundng rae Curren rules Ferly dep. prefundng Prefundng rae 2/3 Prefundng rae Ferly dep. Prefundng Kela- Eurosa Low age rao

16 3 Hgh age rao We amend curren old-age penson fundng rules so ha, for each fundng cohor ( a cohor beween ages 23 55), he amoun funded depends also on he sze of he fundng cohor relave o he sze of recenly born cohors. The dea s ha we can esmae from he sze of recenly born cohors he sze of he work force n hose fuure perods when he fundng cohor wll be rered. Ths ferly effec vares beween cohors, and for each cohor vares n me. The ferly correcon changes equaon () no ( ): M h j,, S, j /( + r ) j= 65 IN ( ) h = ab, kg where b n f ( n,..., n ), =, /, +, The share of he presen value of benefs ha s prefunded s no longer a, bu nsead a mulpled by he erm b, whch depends on he sze of he fundng cohor (a s brh year), compared o he brh szes of he younger cohors. If he fundng cohor s bgger han he younger cohors, b exceeds uny and hus fundng s ncreased. If ferly ncreases and younger cohors are bgger, fundng declnes compared o curren rules. If he fundng cohor and younger cohors are equal n sze, b equals. The funcons f are formulaed so ha, n effec, he fuure generaons are represened wh weghs correspondng o her presence n he labour force durng he years when he now fundng cohor s rered. All hose fuure generaons canno be ncluded n he ferly correcon: fundng ends a age 54, and he younges cohor ncluded s hus 53 years younger han he fundng cohor. Bu when he cohor reaches e.g. he age 9, here are persons 72 years younger payng penson conrbuons. Sll, he ferly correcon capures a szeable fracon of he fuure labour force. Deals of he f -funcons are presened n Lassla and Valkonen, 999.

17 4 Table 2. Toal conrbuon rae and asses of he penson funds n 27, baselne and wh hgher neres rae Toal conrbuon rae, Baselne scenaro Hgher neres rae Asses, per cen of oal wages Baselne scenaro Hgher neres rae Kela-Eurosa - curren rules prefund. rae 2/ ferly depend Low age rao - curren rules prefund. rae 2/ ferly depend Hgh age rao - curren rules prefund. rae 2/ ferly depend Fgure 4 shows ha ferly-dependen prefundng would no make much dfference n he basc populaon scenaro and n he low age rao case. Bu would make a huge dfference f ferly would declne, as n he hgh age rao case. The conrbuon rae would hen be somewha hgher han wh curren rules for abou 3 years, bu afer ha he rae would sablze below 4 per cen nsead of rsng o 5 per cen. From fgure 4 seems ha a raher modes ncrease n conrbuon raes, alhough for a longsh perod, faclaes a very szeable declne laer. Ths s precsely wha happens. The smple explanaon s ha, wh declnng ferly, here are much more people payng he modesly ncreased conrbuons han here wll be n he fuure payng as conrbuons he PAYG par of curren large cohors. Wh many payers he funds accumulae and wll be huge n relaon o he wage blls of smaller fuure cohors Ferly-dependen prefundng also makes acuary raes more even, especally n he case of hgh age rao, see Fgure 5. Macroeconomc and welfare effecs In all he polces descrbed above he pre-fundng rae s nally acceleraed. Therefore he macroeconomc oucomes are smlar and s suffcen o descrbe he overall rends. Shfng he mng and scale of pre-fundng nvolves necessarly adjusmens n he conrbuon rae. From he pon of vew of aggregae economy, does no maer wheher he employer's or employee's rae s shfed, he mpac on ne wages s dencal. In a

18 5 defned benef sysem, a hke n he conrbuon rae due o ncrease n pre-fundng represens a pure ax. Consequenly, lowers he ncenves o supply of labour durng he acve fundng phase. The overall effcency oucome s, however, lkely o be margnally posve, snce he larger nvesmen ncomes cu he fuure op rae of conrbuons. The nal reducon n he labour supply due o he jump n he conrbuon rae reduces margnal producvy of capal and spurs frms o lower somewha he nvesmen rae. Laer hs rend reverses. Household savng reacs n a smlar way o he varaon n he penson conrbuon rae. The ncrease n penson savng domnaes n he capal markes cung he curren accoun defc permanenly. The overall mpacs are, as expeced, n he case hgher fundng degree polces more promnen han n he case of brh rae adjusmen polcy, when he demographc rends follow he offcal forecass. The benefcal macroeconomc oucomes of he laer polcy are evden only n he hgh age rao scenaro. In hs case he gans of acve pre-fundng really srke ou boh because of he srongly reduced dsorons n labour supply and he markedly lower foregn ne deb, whch would oherwse burden heavly he small fuure household generaons. Any ncrease n pre-fundng reduces he welfare of he curren workers due o he lower ne wage. Correspondngly, he fuure households gan. For he fnal evaluaon, one should herefore o be able o add he gans and losses of varous household generaons. Ths procedure s, however, subjec o many objecons. The man feaures can anyhow be observed from he fgures descrbng he relave compensaed varaons by generaons (see Fgure 6). They show ha a gan from acve pre-fundng s possble also n he baselne case, bu n he low ferly rae scenaro he mprovemen n welfare s large. Ths apples especally o he polcy of lnkng he fundng rae o ferly. 6. CONCLUSIONS We have consdered he performance of penson prefundng rules n a defned-benef sysem and n an envronmen where here s consderable uncerany concernng fuure demographc developmens. In he rules, new fundng and whdrawals from exsng funds are relaed o accrued ndvdual penson rghs, as s currenly he suaon n he Fnnsh penson sysem, and o ferly. Penson prefundng can smoohe conrbuon raes n economes where ageng wll ncrease penson expendure. Bu funds ha are suffcen n one demographc oucome are oo small n anoher and may be oo hgh n a hrd one. Increasng he degree of prefundng, n relaon o accrued penson rghs, n he Fnnsh earnngs-relaed penson sysem could yeld a more even nergeneraonal oucome and make fuure generaons poson beer. The lkelhood of demographc scenaros n whch hs would happen s large wh small ncreases n fundng bu ges smaller wh larger ncreases fundng. I s que possble o overshoo and harm curren generaons oo much. Thus, a fxed degree of prefundng s hardly he bes choce. Makng he degree of prefundng ferly-dependen would no make much mpac n he basc populaon scenaro bu f ferly would declne, a raher modes ncrease n conrbuon raes would faclae a very szeable declne laer. Wh declnng ferly, here are more people payng he modesly ncreased conrbuons han here wll be

19 6 people n he fuure payng as conrbuons he PAYG par of curren large cohors. Wh many payers he funds do accumulae and wll be huge n relaon o he wage blls of smaller fuure cohors. Fundng rules ha combne accrued penson rghs and ferly seem o be worhy of furher nvesgaons. Desgnng prefundng rules ha work well n unceran demographc envronmen s no a rval maer. Tha should no be used as an argumen no o prepare for he fuure, bu nsead as a sarng pon o sudy alernaves and compare her performance by e.g. smulaon sudes. Alhough he ools for such sudes are no deal ye, hey provde valuable nsghs no he properes of varous prefundng rules under dfferen demographc oucomes. REFERENCES Dsney, R. (999): Noonal Accouns as a Penson Reform Sraegy: An Evaluaon Socal Proecon Dscusson Paper No. 9928, World Bank, Washngon DC. Lassla, J. (2): Wage Formaon by Majory Vong and he Incenve Effecs of Pensons and Taxaon. Fnnsh Economc Papers (forhcomng). Lassla, J. and T. Valkonen (999): Penson prefundng and ageng n Fnland (n Fnnsh), Helsnk: ETLA B 58. Lassla, J. and T. Valkonen (2a): Prefundng n a Defned Benef Sysem - he Fnnsh Case. In Marn Feldsen and Hors Seber (edors): Socal Secury Penson Reform n Europe. NBER conference volume, forhcomng from The Unversy of Chcago Press. Lassla, J. and T. Valkonen (2b): Penson Polces and Demographc Rsks. Paper presened a he Year 2 Inernaonal Research Conference on Socal Secury, organzed by he Inernaonal Socal Secury Assocaon (ISSA) on Sepember 2 n Helsnk. Orszag, J. M. and P. R. Orszag (2): The Benefs of Flexble Fundng: Implcaons for Penson Reform n an Unceran World. Paper presened a he World Bank ABCDE 2 Conference. Palacos, R. and M. Pallares-Mrallès (2): Inernaonal paerns of penson provson. Socal Proecon Dscusson Paper No. 9. World Bank, Washngon DC. Scherman, K.G. (999): The Swedsh Penson Reform. ILO, Issues n socal proecon, dscusson paper nro 7. Geneve. Snn, H.-W. (998a): The Pay-As-You-Go Penson Sysem as a Ferly Insurance and Enforcemen Devce. CES Dscusson Paper No. 54. Unversä München. Snn, H.-W. (998b): Commen on Persson, eoksessa Seber, H. (om.) Redesgnng Socal Secury. Insu für Welwrschaf an der Unversä Kel. Snn, H.-W. (2): Why a Funded Penson Sysem Is Useful and Why I Is No Useful. NBER Workng Paper No 7592, March 2. Sundén, A. (2): How wll Sweden s new penson sysem work? An Issue n Bref, Cener for Reremen Research a Boson College, March 2, No. 3. Valkonen, T. (999): The Fnnsh Corporae and Capal Income Tax Reform: A General Equlbrum Approach. ETLA A 29. Helsnk. Avalable onlne a

20 7 Fgure 2. Effecs of ncreasng old-age penson prefundng on penson conrbuons and funds Toal conrbuons Funds, of wages 5 KELA-Eurosa KELA-Eurosa Low age rao Low age rao Hgh age rao Hgh age rao ETLA Base case Fundng degree 2/3 Fundng degree

21 8 Fgure 3. Effecs of ncreasng old-age penson prefundng on acuary rae KELA-Eurosa Low age rao Hgh age rao Base case Fundng degree 2/3 Fundng degree Cohors denoed by he year of enerng labour force ETLA

22 9 Fgure 4. Effecs of ferly-dependen prefundng on penson conrbuons and funds Toal conrbuons Funds, of wages 5 KELA-Eurosa KELA-Eurosa Low age rao Low age rao Hgh age rao Hgh age rao Base case Ferly-dependen prefundng ETLA

23 2 Fgure 5. Effecs of ferly-dependen prefundng on acuary raes KELA-Eurosa Low age rao Hgh age rao Base case Cohors denoed by he year of enerng labour force. Ferly-dependen prefundng ETLA

24 Fgure 6. Welfare effecs Increased fundng degree Ferly-dependen prefundng Low age rao KELA-Eurosa Hgh age rao Cohors denoed by he year of enerng labour force ETLA

25 E L I N K E I N O E L Ä M Ä N T U T K I M U S L A I T O S (ETLA) THE RESEARCH INSTITUTE OF THE FINNISH ECONOMY LÖNNROTINKATU 4 B, FIN-2 HELSINKI Puh./Tel. (9) 69 9 Telefax (9) 6753 In In hp:// KESKUSTELUAIHEITA - DISCUSSION PAPERS ISSN No 73 No 74 No 75 No 76 No 77 No 78 No 79 JUKKA LASSILA ROMAS LAZUTKA AUDRONE MORKUNIENE SVEND E. HOU- GAARD JENSEN, Lhuanan Penson Sysem: Alernaves and Proposals for he Fuure A Summary Repor by The Phare Sudy Group. Helsnk p. HANNU PIEKKOLA PETRI BÖCKERMAN, On Whom Falls he Burden of Resrucurng? Evdence from Fnland. Helsnk p. KARI E.O. ALHO, The Sably Pac and Ineffcences n Fscal Polcy Makng n EMU. Helsnk p. PETRI BÖCKERMAN MIKA MALIRANTA, Regonal Dspares n Gross Job and Worker Flows n Fnland. Helsnk p. RITA ASPLUND REIJA LILJA, Employmen and Unemploymen n Fnnsh Manufacurng s Technologcal Progress he Cause or he Cure? Helsnk p. JUHA HONKATUKIA, Komasen pääsökaupan kokonasaloudellse vakuukse Suomessa s. JUHA HONKATUKIA, Arvoa energaverouksen aloudellssa vakuukssa Suomessa s. No 72 RITA ASPLUND, Prvae Reurns o Educaon n Fnland: Back o Bascs p. No 72 RITA ASPLUND, Inhmllnen pääoma ja palka Suomessa: Paluu perusmalln s. No 722 HANNU HERNESNIEMI, Evaluaon of Esonan Innovaon Sysem p. No 723 MARKUS PAUKKU, European Unon and Uned Saes Trade Relaons p. No 724 No 725 No 726 HELI KOSKI, Regulaors and Compeon Spurrng or Reardng Innovaon n he Telecommuncaons Secor? p. HELI KOSKI, Feedback Mechansms n he Evoluon of Neworks: The Insalled User Base and Innovaon n he Communcaons Secor p. KARI E.O. ALHO, Implcaons of EMU on Indusral Relaons The Counry Repor on Fnland p. No 727 ESA VIITAMO, Mesäklusern palvelu klpalukykyanalyys s.

26 No 728 ERKKI KOSKELA MARKKU OLLIKAINEN, Opmal Fores Conservaon: Compeveness versus Green Image Effecs p. No 729 SINIMAARIA RANKI, Does he Euro Exchange Rae Maer? p. No 73 No 73 TOPI MIETTINEN, Pokkeavako valonyhö yksyssä? Valonyhöden avoeden kehys ja veralu yksysomseuhn yryksn s. ERKKI KOSKELA RONNIE SCHÖB HANS-WERNER SINN, Green Tax Reform and Compeveness p. No 732 MATTI VIRÉN, Fnancng he Welfare Sae n he Global Economy p. No 733 LAURA PAIJA, ICT Cluser The Engne of Knowledge-drven Growh n Fnland p. No 734 STEFAN NAPEL MIKA WIDGRÉN, Inferor Players n Smple Games p. No 735 No 736 No 737 No 738 KARI E.O. ALHO, Opmal Fscal and Moneary Polces n a Recesson: Is There a Way Ou of he Trap n an Open Economy? p. ERIK PLUG WIM VIJVERBERG, Schoolng, Famly Background, and Adopon: Is Naure or s Nurure? p. ERKKI KOSKELA MATTI VIRÉN, Is There a Laffer Curve beween Aggregae Oupu and Publc Secor Employmen? p. PASI HUOVINEN, Työhön ja vapaa-akaan lyvä makalu Helsnkn. Analyys majouslasosa s. No 739 HANNU PIEKKOLA, Unobserved Human Capal and Frm-Sze Premum p. No 74 No 74 No 742 No 743 No 744 JOHANNA ALATALO JUHA HONKATUKIA PETRI KERO, Energaurpeen käyön aloudellnen merkys Suomessa s. JUKKA LASSILA TARMO VALKONEN, Penson Prefundng, Ageng, and Demographc Uncerany p. PENTTI SYDÄNMAANLAKKA, The New Challenges, Roles and Compeences of Human Resource Managemen p. EVA M. MEYERSSON TROND PETERSEN RITA ASPLUND, Pay, Rsk, and Producvy. The Case of Fnland, p. MATTI VIRÉN, Fscal Polcy, Auomac Sablsers and Polcy Coordnaon n EMU p. Elnkenoelämän Tukmuslaoksen julkasema "Keskuseluahee" ova raporeja alusavsa ukmusulokssa ja välraporeja ekellä olevsa ukmukssa. Tässä sarjassa julkasuja monsea on mahdollsa osaa Talouseo Oy:sä kopon- ja omuskuluja vasaavaan hnaan. Papers n hs seres are repors on prelmnary research resuls and on sudes n progress. They are sold by Talouseo Oy for a nomnal fee coverng copyng and posage coss. d:\raapalo\dp-julk.sam/2.2.2