ETLA ELINKEINOELÄMÄN TUTKIMUSLAITOS

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1 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. 765 Jukka Lassla Tarmo Valkonen AGEING, DEMOGRAPHIC RISKS, AND PENSION REFORM * Ths sudy was fnancally suppored by he ageng programme of he Academy of Fnland and by he Cenral Penson Secury Insue. We have grealy benefed from he dscussons wh he Insue s research saff. We also hank Elsa Fornero, Florence Legros and Jorgen Morensen for commens and Eja Kaupp for model programmng. We are also graeful o Juha Alho for provdng us wh realsaons of sochasc populaon smulaons. ISSN

2 LASSILA, Jukka VALKONEN, Tarmo, AGEING, DEMOGRAPHIC RISKS, AND PENSION REFORM. Helsnk: ETLA, Elnkenoelämän Tukmuslaos, The Research Insue of he Fnnsh Economy, 2, 34 p. (Keskuseluahea, Dscusson Papers, ISSN ; No. 765). ABSTRACT: Ageng wll ncrease penson expendure and conrbuon raes. There s also ncreasng awareness ha he rsks conneced o moraly, ferly, and mgraon are consderable. In penson reforms one mus decde how hese rsks are o be shared beween workers and pensoners, and also ake no accoun ha n he ranson phases dfferen cohors may gan or lose. We dscuss he rsk-sharng and nergeneraonal dsrbuon aspecs of hree penson polcy measures ha eher have already been adoped or are beng proposed n Sweden and Fnland. Each of hese mehods, lnkng benefs o lfe expecancy, ndexng benefs o he oal wage bll, and usng ferly-dependen prefundng, has s own advanages and weaknesses. Usng a numercal OLG model, and realsaons from sochasc populaon smulaons, we demonsrae ha hese mehods grealy enhance he susanably of a penson sysem n unfavourable demographc oucomes bu have praccally no effecs f he demographcs reman sable. Thus he allocaon of rsks can be mproved whou fundamenally changng he sysems. KEY WORDS: Demographc uncerany, penson benefs, longevy adjusmen, ndexng, paral prefundng, vong JEL Classfcaon: H 55, J LASSILA, Jukka VALKONEN, Tarmo, AGEING, DEMOGRAPHIC RISKS, AND PENSION REFORM. Helsnk: ETLA, Elnkenoelämän Tukmuslaos, The Research Insue of he Fnnsh Economy, 2, 34 s. (Keskuseluahea, Dscusson Papers, ISSN ; No. 765). TIIVISTELMÄ: Tavoeena on uka, men eläkepolslla omlla vodaan asaa väesön käänymsen aheuamaa eläkemaksujen nousupanea. Lähökohana on, eä väesön käänymsen määrää e eukäeen edeä: synyvyyeen, kuolevuueen ja srolasuueen lyy kakkn merkävää epävarmuua. Tarkaselava omenpeä ova yöeläkkeden ndekson, elnajanodoeen nousun huomomnen eläkkessä, ja rahasonnn somnen synyvyyeen. Arvonkreerenä käyeään vakuuksa kansanaloudellsn muuujn, yönanajan ja yönekjän eläkemaksuhn, eläkejärjeselmän okeudenmukasuueen ja koalouksen hyvnvonn. Jos väesökehys on vakaaa, e omenpellä ole juurkaan vakuuksa. Jos aas väesökehys osoauuu epäsuousaks, nämä omenpee asaava väesön käänymsen kusannuksa ehokkaas er sukupolven kesken. Täen ne paranava väesörsken kohdenumsa er sukupolvlle. Tuloksa on laajemmn esely julkasussa Työeläkkeden ndekson, elnakakorjaus ja väesön käänymnen, Eläkeurvakeskuksen ukmuksa 2:2 ja ETLA B 72. ASIASANAT: yöeläkkee, väesöepävarmuus, elnajanodoe, ndekson, rahason

3 Conens I Inroducon II Quanfyng demographc uncerany 2 III Three mehods of redsrbung demographc rsks 5 IV Smulaon resuls 6 4. The smulaon model Adjusng pensons o lfe expecancy Indexaon of pensons o oal wages Lnkng prefundng o he ferly rae 4.5 The aggregae effecs of he measures 3 V Vong for a penson reform 5 5. Lessons from prevous vong leraure Indcaors of polcal suppor 6 VI Conclusons 9 References 2 Appendx. Acuary and welfare effecs 23 Appendx 2. The FOG model 27

4 2

5 I INTRODUCTION Mos curren publc penson sysems are defned benef PAYG sysems. Followng he defned benef prncple n he deermnaon of pensons means ha he conrbuon rae manly absorbs he shocks generaed by unexpeced economc or demographc rends. Hence, s mosly he curren young and fuure workng-age populaon ha s affeced by hese shocks. I s very unlkely ha, as defned, he nergeneraonal redsrbuon rule s opmal. Fnancng pensons wh he pay-as-you-go prncple mples ha prevous generaons have already creaed an mplc penson deb, whch mus be fnanced by fuure workers. In some cases, he fnancng of he pensons s suppored by paral prefundng. In Fnland s mplemened so ha he success of he nvesmen polcy only affecs fuure conrbuons, no benefs. Hence, he arsenal of polcy measures for mproved nergeneraonal redsrbuon also ncludes prefundng rules, n addon o he deermnaon of benefs. Observng he exsence of large baby-boom generaons rerng soon, he low ferly rae and ncreasng longevy, one fnds easy o forecas ha he populaon wll age markedly durng he nex hree decades. I s far less noced ha here s large uncerany nheren n he populaon forecass, akng no accoun ha he relevan horzon for nergeneraonal rsk smoohng by penson polcy s very long. The uncerany s revealed, for nsance, by he sudes of Alho (998) and Lee (2), whch show ha sochasc populaon forecass gve large confdence nervals o ferly, moraly and mgraon. We sudy hree mehods of redsrbung he economc mpacs of populaon rsks nergeneraonally. The frs mehod s o lnk he prefundng rules o ferly, mplyng ha new fundng reacs o he number of fuure workers. The oher wo mehods, famlar from he Noonal Defned Conrbuon (NDC) penson sysems, are o lnk pensons o longevy and o changes n oal wages. These approaches can be appled n curren penson sysems, whou fundamenally changng he rules. In he comparson of hese mehods we use four crera. These are he coss and acuaral farness of he penson sysem, he aggregae economc mplcaons and household welfare. We also perform a prelmnary analyss of he polcal economy aspecs of mplemenng hese measures. The man queson s wheher here exss a any pon of me a majory of voers who are n favour of one of he reforms. The mpacs of he redsrbuon mehods are evaluaed usng a numercal general equlbrum model. The overlappng generaons model (FOG) smulaes he neracon of populaon rends, penson sysem rules and he res of he economy durng he nex years. The model also gves a number of wnners and losers of any polcy measure. One of he jusfcaons for a PAYG-fnanced defned benef penson sysem s ha redsrbues hese rsks beween generaons. In hs dscusson s compared o a fully funded defned conrbuon penson sysem. One of he oucomes of he dscusson s ha a parally funded sysem s lkely o be bes (see e.g. Dua e al. 999). Our approach s ed o me and place: we smulae he dynamc effecs of changng some rules n he curren Fnnsh prvae-secor penson under chosen demographc pahs. We look a fuure penson benefs and conrbuons and also he welfare of household generaons. The laer requres ha he general equlbrum repercussons are also aken no accoun.

6 2 We quanfy n he nex secon he magnude of demographc uncerany and explan how s appled n he FOG model. Secon 3 descrbes he new polcy measures and he jusfcaons gven for hem. The fourh secon presens he model used and he smulaon resuls. Secon 5 ncludes he vong analyss. Conclusons and polcy recommendaons are oulned n he sxh secon. II QUANTIFYING DEMOGRAPHIC UNCERTAINTY 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. Each smulaon produces annual populaon daa for he comng fve decades. The followng fgures presen some dsrbuonal sascs descrbng he daa mass. Fgure presens he medan of he sze of he Fnnsh populaon, and he frs and nnh decle and he frs and hrd quarle. The wdh of nervals spreads rapdly n me. In 23, n 8 of smulaons he populaon wll be beween 4.7 mllon and 6 mllon people, and he correspondng fgures for 25 are 3.8 mllon and 6.7 mllon. Fgure 2 shows he uncerany n he number of brhs, and Fgure 4 shows ha longevy ncreases for boh males and females, and ha women wll probably connue o lve longer han men bu s no oally mprobable ha men wll cach up. In prncple, all he 5 alernave populaon pahs could be used as npus n a numercal OLG model, such as he FOG model used n hs sudy. Evaluang dfferen penson polcy measures wh he model would hen provde a dsrbuon of he effecs, reflecng he demographc uncerany n he background. In pracce, however, ha has been well beyond our me resources, and a shor cu was chosen nsead. Alho provded wo sample pahs for he sudy by 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 2 dvded by he number of people beween ages From hs orderng, he wo samples closes o he lms of he 8 confdence nerval n 23 were chosen. Fgure 4 shows hese realsaons as well as he baselne (Kela-Eurosa) scenaro. The 8 confdence nerval n he age rao n 23 s wde: he lms are.63 and.787 (Fgure ). 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 does no ncrease subsanally. 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. 2 The average reremen age n Fnland s 59 years.

7 3 Fgure. Fnnsh populaon Mll. nh. Mll. nh s decle s quarle Medan 3 rd quarle 9 h decle Source: calculaons by J. Alho ETLA Fgure 2. Number of chldren under year of age by year-end nh. 8 s decle s quarle Medan 3 rd quarle 9 h decle nh Source: calculaons by J. Alho ETLA

8 4 Fgure 3. Newborn s lfe expecancy n Fnland, 5 confdence nervals years years 85 Females Males Source: calculaons by J. Alho ETLA Fgure 4. 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 four fgures clearly demonsrae ha here s huge uncerany n demographc projecons. Thus s proper o consder he consequences of hs uncerany for penson polcs and oher ageng polces. No all ageng research recognses hs. Bovenberg and van den Lnden (997), for example, downplay demographc rsks among he relevan rsks:

9 5 Demographc rends can be foreseen wh some degree of accuracy, even over he long erm. Bu here s consderable uncerany abou non-demographc rends (such as employmen, wage growh, he reurn on capal, famly formaon and dssoluon) ha wll affec sysems of old-age nsurance. III THREE METHODS OF REDISTRIBUTING DEMOGRAPHIC RISKS The well-known problems caused by populaon ageng o he curren pay-as-you-go sysems have generaed a lvely dscusson abou possble reforms. The Anglo-Amercan dscusson s concenraed manly on he ssue of prvasaon,.e. he pros and cons of shfng o a fully funded defned conrbuon sysem. The ams of reforms n Europe are more modes, bu nclude many smlar elemens. The NDC scheme, whch has recenly been adoped n Sweden, Ialy, Poland and Lava, seems o offer an alernave, whch provdes effcency-mprovng elemens whou large ranson coss. The conrbuon rae promses o be sable and here are no nvesmen rsks. How s hs scheme supposed o keep he promses? The soluon s wo-dmensonal. Frsly, he benefs are lnked more closely o conrbuons. Secondly, here are rules, whch generae an endogenous adjusmen of benefs o demographc or economc shocks. The new way of dealng wh ncreased lfe expecancy s o lnk penson benefs o average longevy. The hgher he expeced number of penson years, he smaller s he penson. Snce lfe expecancy s lkely o ncrease que slowly and seadly n ndusral counres, ndvduals already know early durng her workng age he probable amoun of he reducon n pensons. Therefore hey can adjus n advance by shfng labour supply and prvae savng correspondngly. Sweden has also adoped a flexble reremen age, whch makes he adjusmen even easer. The fnal oucome s ha pensons are gradually cu, bu n a way whch s well jusfed. The new Swedsh pay-as-you-go earnngs-relaed penson sysem also allocaes he producvy growh rsks ncreasngly owards he penson age. Penson rghs generaed durng workng age are ndexed o per capa growh of ncomes. Afer reremen he ndexaon s based on he long-erm average growh assumpon. Therefore, f he growh s hgher, he pensons are rased, bu he conrbuon base s also larger. If growh s slower han assumed, he real value of pensons dmnshes and so he solvency of he sysem s supposed o be guaraneed. Several observers (e.g. Valdes-Preo 999 and Scherman 999) have noed ha he adoped growh adjusmen does no solve he problems caused by ageng. I does no ake no accoun he effec of a dmnshng labour force, snce s based on per capa ncomes. The planners of he sysem were aware of hs defcency and have suggesed he use of a "brake" n ndexaon f he solvency of he sysem s endangered. In pracce, hs brake would behave as f he pensons were ndexed o he growh of oal wages. We smulaed he effecs of ageng usng he Swedsh ype of growh adjusmen. I urned ou ha whou he brake he ndexaon rule markedly weakens he solvency of he penson sysem compared o, for example, ndexaon o prce nflaon, see Lassla and Valkonen (2). Ths s because he shrnkng labour force mples hgher per capa wages (due o a hgher capa/labour rao) and so ndexaon rases pensons more, he faser he

10 6 labour force falls. The resul holds even n a case n whch he employers' conrbuon rae s allowed o adjus o hgher expendures, hereby creang pressure on wages o fall. The oher ndexaon rule also consdered n Sweden, bu hen rejeced, s o lnk he pensons drecly o oal wages. Indexaon o oal wages well maes he changes n he conrbuon base, hereby provdng good means of adjusmen boh o long-erm rends n producvy growh and populaon and o shor-erm varaon n he parcpaon rae and unemploymen. A shf o a full ndexaon of pensons o oal wages has, however, wo apparen weaknesses. The frs s ha he mehod shfs almos all earnngs rsks o reremen age, and hese rsks mgh be large owng o, for example, exceponally srong busness cycles. Anoher problem s ha he new penson level and conrbuons would be much hgher afer he shf. We show ha boh he problems can be mgaed wh an adjused oal wage ndex (PasTEL), whch sll manans he desred propery of followng he rends n he conrbuon base. The hrd mehod, presened nally n Lassla and Valkonen (999), s o lnk he penson prefundng rule o ferly. 3 The sarng pon s he curren Fnnsh earnngs-relaed old age penson sysem, whch s parally funded. Curren prefundng rules provde some auomac smoohng of penson conrbuon raes due o shfs n demographc rends. As fundng akes place for each worker, he more rered workers here are, he more funds here are. These funds are used o pay a par of he penson benefs afer he worker reres. Thus, he conrbuon raes need no rse n full proporon o he number of rerees. The remanng problem s ha a major share of he penson coss s sll fnanced by he PAYG prncple, whch means ha he conrbuon rae s sensve o he sze of he workng-age populaon. Our am was o modfy he prefundng rule so ha would ake no accoun he number of fuure workers. Forunaely, he number of new enrans n he labour force can be accuraely forecas 2 years earler, when nformaon abou brhs s avalable. We amend curren old-age penson fundng rules so ha, for each fundng cohor, he amoun funded also depends on he sze of he fundng cohor relave o he sze of recenly born cohors. I s mporan o noe ha he ferly-lnked prefundng rule can also be appled n cases n whch here are no ye exsng penson funds. The benefs n hese cases are, however, less mpressve. IV SIMULATION RESULTS 4. The smulaon model FOG s an Auerbach-Kolkoff ype, perfec foresgh numercal overlappng generaons model. I descrbes Fnland as an open economy. 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 plan her whole fuure when hey are young. They choose he allocaon of me beween labour and lesure n each perod, he 3 See also Orszag and Orszag (2). Snn (2) noes ha generaons wh low ferly nves less n human capal. Therefore s far ha hey are forced o save and nves more and hereby fnance he mssng par.

11 7 mng of consumpon beween perods, and he amoun of bequess gven. The penson sysem affecs hese decsons by changng he resources avalable durng varous perods and he relave prces. Any polcy measure generaes a need o revse he lfe span plan. The model s descrbed n more deal n Appendx 2. We use, as he baselne, a recen populaon forecas made by he Socal Insurance Insue, Fnland. The alernave pahs were chosen so ha hey corresponded o he lower and upper pons of he 8 predcon nerval of he age-dependency rao n 23. The use of dfferen demographc scenaros, produced by sochasc populaon smulaons, as npus n an overlappng-generaons general equlbrum smulaon model s echncally sraghforward. Inellecually, here s a gap: here s no uncerany n our 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. Alhough would be more sasfacory o have uncerany ncluded, we feel, however, ha no essenal changes n resuls could be expeced. Prefundng changes he mng of conrbuons, no he rsks relaed o benefs nor hose relaed o dsably or oulvng one s savngs. I s, however, possble ha changng he prefundng rule would also reduce precauonary savng, f credbly of he penson sysem ncreased. Longevy adjusmen and PasTEL ndexng also affec he sze of he PAYG sysem by affecng he benef levels, and even f people wsh o compensae for hs by savng hey canno buy asses wh exacly he same properes. Sll, he nergeneraonal dsrbuon effecs domnae, and s hard o see why he resuls would change f uncerany were explcly ncluded. Includng uncerany properly n our model would also be dffcul. Compuaonal models of socal secury have developed very rapdly durng he las few years, see, for example, Imrohorogly e al. (999) and Rus (999). Sll, as far as we know, even he mos sophscaed curren numercal OLG models (see e.g. De Nard e al. (999)) can handle only dosyncrac ncome and longevy uncerany. 4.2 Adjusng pensons o lfe expecancy When he penson sysem was creaed n he begnnng of he 96s, he average lfe expecancy of a 65-year-old Fnn was 3 years. Accordng o curren forecass, he correspondng fgure for 25 s 2-2 years (Lndell 999). Ths means ha he me spen as a rered person s ncreased by a half. If we add o ha he effecs of generous early reremen sysems, he rend n he suppor rao s even more ousandng. When PAYG fnancng s used, fuure workers pay he burden, whch means ha he sysem creaes a large nergeneraonal ransfer of resources from he fuure. If hs s consdered unfar, here s a need o neuralse, whch can be done by adjusng pensons. Snce n each pon of me here s sgnfcan uncerany abou he fuure longevy (see Fgure 3), a polcy rule mus be creaed whch deermnes he sze of he adjusmen needed. Observed v. forecas moraly n longevy adjusmen The Swedsh applcaon of longevy adjusmen o penson benefs s based on observed moraly. Each year, he laes avalable sascs on age-specfc moraly s used o calculae he expeced remanng lfeme of hose reachng he age of 65. An alernave

12 8 would be o use forecas moraly specfc o he cohor reachng 65. Wh ncreasng lfe expecancy, he forecas-based esmae of he lengh of he remanng lfeme exceeds ha based on he laes observed moraly. One mgh hen hnk ha a longevy adjusmen based on forecass would yeld bgger cus n monhly pensons han an adjusmen based on observed moraly. Ths s no lkely o be rue, however. The adjacen graph (5) shows hree longevy adjusmen coeffcens for Fnland from 2 onwards. All are based on he KELA-Eurosa demographc scenaro. A coeffcen based on observed moraly s used n hs sudy. Observed means here ha as he scenaro acualses perod by perod, he coeffcen s calculaed from he prevous perod s age-specfc morales. The forecas-based coeffcen s calculaed from he cohors forecas longeves, whch requre, n each perod, he use of fuure perods forecas moraly raes. Each perod s longevy s compared o he base perod s longevy; he coeffcen s he nverse of hs comparson. Longevy adjusmen o each cohor s pensons s done only once, when he cohor sars o receve old-age pensons (see p. 39). The coeffcen based on observaons goes below ha based on forecass, and hus resuls n greaer reducons n monhly penson benefs. The reason s ha he ncrease n longevy has already aken place n he base perod s forecass, bu no n he observaons. The cohor reachng 65 n he base perod s already expeced o lve que long, bu he observed age-specfc moraly raes n he perod precedng he base perod show a much shorer lfe expecancy. Fgure 5. Longevy adjusmen coeffcens.5 Based on observed moraly Based on forecas moraly Based on forecas moraly n relaon o nally observed ETLA.8 Only f he forecas-based longeves are compared o he observaon-based longevy n he base perod wll he coeffcen based on forecass resul n larger savngs n penson expendure. The hrd lne n he graph llusraes hs. The problem s ha produces a downward jump n he base perod, creang a bgger dfference beween wo adjacen cohors han eher of he oher wo coeffcens.

13 9 Fgure 6. Penson conrbuon raes and longevy adjusmen Curren sysem Longevy-adjused ETLA When he observed numbers are used n he longevy adjusmen, he FOG model gves he followng smulaon resuls. The reducon s abou per cen n he real value of he ndvdual pensons durng he nex 25 years. Afer ha he adjusmen ncreases slowly and reaches 3-4 per cen n 5 years (see Fgure 5). When consderng he scale of he cus, s useful o remember ha even a modes yearly growh of.5 per cen would more han double pensons n 5 years. The longevy adjusmen reduces aggregae pensons relaed o oal wages, as well as he conrbuon rae, abou 3 per cen n he long erm (see Fgure 6). A measure ha descrbes he farness of he penson sysem, he acuary rae, shows ha s he curren workers whose reurn from he new sysem s lower (see Fgure 4 n Appendx ), whereas he fuure workers consder he sysem farer. If he populaon scenaro wh a hgh age-rao s used, he declne n expendures s wce as large. The polcy measure generaes reacons n he labour and capal markes. The reducon n penson conrbuon raes leaves room for hgher wages, hereby creang posve ncenve effecs and labour supply ncreases. On he oher hand, he cu n fuure pensons promoes addonal prvae savng for old age. The fnal creron for he goodness of he polcy s he welfare of households. As Fgure 5 n Appendx shows, he curren workng-age generaons lose, bu fuure ones gan. The mplcaon s ha for fuure households, he posve ne wage effec domnaes he reducon n pensons. If we calculae a dscouned sum of lump-sum ncome ransfers/axes necessary o compensae for all he mpacs of he measure, shows ha here s a slgh mprovemen n overall welfare. 4.3 Indexaon of pensons o oal wages The recen reforms n penson ndexaon have had wo conflcng ams. The frs s o cu he penson expendures. I s acheved by decreasng he wegh of wages and ncreasng he wegh of some cos-of-lvng measure n he penson ndex. The second am s o sa-

14 blse he penson conrbuon rae. Tha requres ha he ndex reacs o changes n he conrbuon base,.e. n he oal wages. The conflc follows from he expecaon ha ageng wll rase wages more han prces. As noed n he prevous secon, ndexaon of pensons drecly o oal wages s expeced o proec he conrbuon rae effcenly agans varaon n he conrbuon base. Bu f he sarng pon s he curren penson sysems, n whch almos always here s less han complee ndexaon n wages, he shf o he new ndexaon ncreases penson expendures and rases conrbuons. Snce he measure affecs he sock of pensons gradually, he ranson perod s long. Expandng he PAYG sysem hs way creaes negave ncenve effecs and ransfers resources from fuure generaons by rasng he conrbuon rae. Currenly, he Fnnsh publc penson sysem apples a combnaon of he wage-level ndex and he cos of lvng ndex n he ndexaon of pensons. Durng workng-age he weghs of wages and consumer prces are boh.5 n hs TEL-ndex. Afer reremen he wegh of consumer prces rses o.2 and he wegh of wages falls o.8. We modfy TEL-ndex by subsung he oal wages for he wage-level ndex. The use of hs new ndex (PasTEL) elmnaes he nal jump n he pensons and conrbuons, ndependenly of he fuure rends n demographcs. I also shelers he elderly from large varaons n oal wages. For echncal deals, see p. 4. Ineresng resuls emerge f he populaon follows he hgh age rao pah. In hs case, he srong reducon n he labour force produces a hgher wage rae, bu smaller oal wages. Therefore ndexaon o he wage rae reacs, from he pon of vew of he solvency of he penson sysem, n he wrong drecon. Even n he Fnnsh case, n whch he above descrbed adjusmen dampens he effec, he rend n he TEL-ndces s evden (see Fgure 7). Alernavely, f he PasTEL-ndex s used, he long-erm conrbuon rae can be nearly per cen lower (see Fgure 8). Correspondngly, he acuary rae s smooher (Fgure 6 n Appendx ) and he welfare of fuure households larger (Fgure 7). Fgure 7. Changes n oal wages and n curren penson ndces, hgh age rao 2.5 Toal wages Index for workng age Index for reremen age ETLA

15 4 Fgure 8. Penson conrbuon raes and PasTEL-ndex, hgh age rao Curren sysem PasTEL-ndex ETLA 4.4 Lnkng prefundng o he ferly rae The sochasc populaon forecass by Alho (998) and Lee and Tuljapurkar (998) mply ha, compared wh moraly and wh mmgraon, changes n ferly have been more dffcul o foresee. Therefore, s hs rsk whch endangers he solvency of he PAYG penson sysems mos. 4 On he oher hand, he oucome of hs rsk s revealed earler han n he oher cases. Hence, f he ferly nformaon s ulsed fully, allows more me for nergeneraonal redsrbuon of he fnancal burden. Ferly-lnked prefundng even akes place much earler han prefundng n a fully funded scheme, whch s parcularly mporan when he curren demographc oulook s consdered. The man prvae-secor earnngs-relaed penson sysem n Fnland, he so-called TEL scheme, s parally funded. Fundng does no affec penson benefs. I only affecs he level and me pah of conrbuons. A par of he 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. 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 (see Appendx 2, pp.39-4, and Lassla and Valkonen 2a). In he upper par of Fgure 9 he prefundng perod refers o a cohor, n he FOG model, born n and enerng he labour force n 995. When ha cohor receves old-age pensons, n , he money prefunded n her workng years wll be whdrawn, wh he neres accrued o hose funds, and used o pay a par of her pensons (he res comes from he PAYG par). 4 If pensons are nally fully prefunded, he problem s, of course, avoded. Bu when he sarng pon s an exsng PAYG penson scheme, no even a ranson o a fully funded sysem solves he problem of fnancng he already accrued penson rghs, and he demographc rsks nvolved.

16 2 We amend he curren old-age penson fundng rules so ha, for each fundng cohor (a cohor beween ages 2 54 n our model), he amoun funded also depends 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 s rered. Ths ferly effec vares beween cohors, and for each cohor vares over me. If he fundng cohor s bgger han he younger cohors, fundng s ncreased. If ferly ncreases and younger cohors were bgger, fundng would declne compared wh curren rules, bu neher of he scenaros n he lower par of Fgure 9 has ha feaure. Fgure 9. Prefundng of old-age pensons Example: cohor born Wage ncome Penson prefundng perod whdrawng perod Number of brhs h. pers Kela-Eurosa h. pers wll be n workng age n hgh age rao 3 2 ETLA In model smulaons he new rule was calbraed so ha does no change markedly he amoun of prefundng n he case of he baselne populaon forecas. Bu when he hgh age rao wh low ferly occurs, prefundng ncreases, requrng a somewha hgher conrbuon rae durng he nex 3 years (see Fgure 9). Afer ha he conrbuon rae sablses o a level ha s nearly percenage pons lower han n he case of he curren penson sysem. The oucome s based on wo facors. The frs s he ncreased nvesmen ncomes from he markedly hgher penson fund. The oher s ha he generaons whch

17 3 benef from prefundng are much smaller han he payng ones. Boh he jusfcaons mply ha s mporan o sar o apply he new rule as soon as possble. The acuary raes descrbed n Fgure 8 llusrae ha he farness of he penson sysem decreases less when he new rule s followed. A rough smplfcaon says ha n erms of he farness of he penson sysem, all unborn generaons wll benef from he measure, and he curren workers wll lose. The welfare mplcaons are smlar (see Fgure 9). Fgure. Penson conrbuon raes and ferlydependen prefundng, hgh age rao 4 Curren sysem Ferly-dependen prefundng ETLA 4.5 The aggregae effecs of he measures Unexpeced changes n ferly, lfe expecancy and mgraon are very dfferen knds of rsks from he pon of vew of penson sysems. Table lss he polcy measures amed a redsrbung hese rsks beween generaons. Table. Demographc rsks and assocaed penson polcy measures Measure Rsk ype Ferly Longevy Mgraon Lnk beween lfe-expecancy and benefs - effecve - Wage bll ndexaon effecve - effecve Ferly-adjused prefundng effecve - -

18 4 Fgure. Penson polcy effecs on conrbuon raes and funds, hgh age rao Toal conrbuons Funds, of wages 5 A+B A+B A+C A+C A+B+C A+B+C Curren sysem Polces: A = Longevy adjusmen B = PasTEL-ndex C = Ferly-dependen prefundng ETLA As we have learned from he prevous secons, here are many choces o be made when mplemenng hese rules. For example, adjusmen for changes n lfe expecancy can be defned usng eher observed or forecased numbers. Also, some adjusmen should be used n he ndexaon of pensons o oal wages, a leas f consumer prces have heavy wegh n he nal ndex. Furhermore, he opmal weghs of he ferly of varous co-

19 5 hors n he prefundng rule are no well defned. Our smulaon expermens wh alernave specfcaons of he rules (no repored here) show, however, ha he nsurance role of hese rules s no very sensve o he deals. Fgure below shows he aggregae effecs of he hree measures on penson conrbuons and funds. Combnng longevy adjusmen and PasTEL-ndexaon does no markedly change he rao of penson funds o oal wages, bu markedly lowers conrbuons by adjusng pensons and expandng he wage bll. The second presened alernave s he nroducon of he PasTEL ndex ogeher wh a lnk beween ferly and prefundng. The me pah of conrbuons now clmbs more rapdly unl he year 23 and falls hereafer. Ths s due o he accumulaon and depleon of he penson fund and he larger nvesmen ncomes. The hrd case suded s a combnaon of all he hree measures. As expeced, lowers he conrbuon rae mos. Moreover, he knk n he conrbuon rae s more eye-cachng. If he objecve s o smooh he pah of he conrbuon rae, he chosen combnaon of rules s no opmal n hs demographc scenaro. Ths observaon s verfed by nong ha he acuary rae of fuure generaons s markedly hgher han he rae of hose cohors whch wll sar her workng lfe durng he nex decade. The fnal evaluaon of he measures s ha he combnaon of he measures effcenly redsrbues he negave consequences of he hgh age rao shock. The deals and he opmal scale of he measures used reman o be solved n fuure sudes. V VOTING FOR A PENSION REFORM 5. Lessons from prevous vong leraure Dfferen facors n nroducng, mananng and srucurng penson sysems have been analysed n he publc choce leraure. Verbon (993) fnds four facors ha explan he exsence of publc penson schemes. The frs s ha he young generaons perceve a posve relaonshp beween her conrbuons o he sysem and he benefs hey expec o ge hemselves when hey are old. Ths relaonshp can be modelled n varous ways. In Brownng (975) and Boadway and Wldasn (989a,b) voers beleve ha he penson sysem decson wll reman unchanged ndefnely. The assumpon s explaned by nfrequen vong or nong ha he analyses apply only o seady saes. Anoher possbly s o assume a socal conrac ha es he hands of he nex vong majory. Kolkoff, Persson and Svensson (988) suded how a socal conrac, whch benefs boh young and old, can be formulaed. Verbon (987) and van Dalen and van Praag (993) relae he fuure levels of socal secury posvely o he curren level wh declnng weghs. In Hu's (982) analyss he lnk beween he curren and fuure levels of socal secury s unceran, bu posve. The second facor explanng publc pensons s nergeneraonal alrusm. Cuckerman and Melzer (989) show how he exen of nergeneraonal dsrbuon n a polcal equlbrum depends on he srengh of he voer's beques move and on he general equlbrum effecs of he polcy. If a voer s oblged o leave negave prvae bequess, he s n favour of publc ransfers from young o old. The majory of penson sysems generae nrageneraonal redsrbuon. In Tabelln's (99) model, poor alrusc young people, as well as he elderly, also suppor he publc

20 6 penson sysem because helps hem o suppor her parens 5. Conesa and Crueger (998) noe ha he suppor for PAYG socal secury depends largely on he dosyncrac ncome rsks ha he heerogeneous ndvduals face. Verbon's fourh facor explanng penson sysems s ha he elderly force he young o manan he sysem by polcal power. One can hen ask where he lms of such behavour are f here s no alrusm. In smple wo-perod models, where here are no prce effecs, a majory vong rule leads o corner soluons of havng no penson sysem or o a sysem where he rered use all he naonal wealh, dependng on whch generaon s larger. One soluon s o assume a represenave democracy, n whch governmen weghs a dfferen generaon's ules dfferenly n decson-makng. The use of an ad hoc wegh funcon s no, however, a preferable soluon. Büler (2) analyses he majory vong aspec of several penson polcy opons usng a compuable OLG model, whch descrbes a small open economy. The suded (permanen) reforms are cus n benefs and ncreases n payroll axes, n he earmarked consumpon ax rae and n he reremen age. The smulaons show ha a hgher reremen age domnaes he oher opons. The closng rule of he res of he publc secor s shown o be mporan, snce he amoun of ax dsorons generaed by he penson sysem depends on hs rule. The penson conrbuons pad by ndvduals do no affec her benefs n he model. Ths assumpon s, consequenly, also mporan for he resuls. One feaure of he economy, whch mgh se lms o he nergeneraonal redsrbuon, and s absen from Büler s sudy, s he general equlbrum prce effecs. Lassla and Valkonen (995) show ha f a small economy jons a currency unon, he voed replacemen rae would be hgher, snce he neres rae reacon generaed by he expanson of he PAYG sysem s mssng. These sudes reveal ha smulaon models have many advanages over he heorecal wo-perod OLG approach. Compuable models can ncorporae a much more dealed descrpon of, for example, he household lfecycle decsons, of socal secury rules and of he macroeconomc feaures of he economy. 5.2 Indcaors of polcal suppor A numercal OLG model allows one o calculae he uly consequences of polcy changes for all cohors, curren and fuure. These uly gans and losses can be used n formng ndcaors of polcal suppor for varous possble polces. We call hese vong ndcaors. Techncally, we compare he baselne developmen wh an alernave penson polcy choce o see whch s preferred by curren households. Preferred refers o lfeme uly calculaons beween he wo alernaves, where n boh cases he fuure pah of polcy varables s beleved wh cerany. Nex we ask wheher he baselne pah wll be preferred n he nex perod, agans he alernave of choosng he oher polcy opon and sayng on ha pah hereafer. Then we move on o he followng perod, and repea he exercse. By calculang he share of wnners we ge a seres of numbers, one for each pe- 5 See, however, Mullgan and Sala-I-Marn (999) for a crcal assessmen of he Tabelln s approach.

21 7 rod. Ths s one vong ndcaor. I s only defned agans an alernave, whch consss of a se of fuure pahs each sarng from he baselne pah bu a dfferen pons n me. I s no clear wheher we should consder he voes of he oal adul populaon or jus he workng-age populaon. If penson polcy decsons are acually made n labour marke nsuons, may well be ha he opnons of he workng-age people coun much more han hose of pensoners. Ths may well be he case n Fnland, where he sauory earnngs-relaed penson sysem was creaed n co-operaon wh labour marke organsaons, and hey are represened n he admnsrave bodes. They also negoae ogeher wh he represenaves of he cenral governmen abou he fuure developmen of he penson scheme (see Lassla and Valkonen 2b). We calculae he vong ndcaors also for hose n workng age. The polcy measures n he vong analyss have been mplemened unexpecedly; he voers had no ancpaed hem. The sze of welfare changes s measured by compensaed varaons. In he FOG model, relave compensaed varaons by generaons are measured by ( ln Es ln E c ), where E denoes dscouned lfeme consumpon expendure, s refers o he smulaon run and c s consumpon necessary o acheve he baselne uly a smulaon prces. Summary of resuls Longevy adjusmen: In he Kela-Eurosa populaon scenaro lfe expecancy ncreases. Thus s no surprsng ha mos people alve a presen lose due o he longevy adjusmen. Older workers realse hey wll ge lower pensons han hey have prevously hough. They have only a few more years o work, and he conrbuon rae wll no declne noably durng ha me. Mddle-aged workers face bgger cus n pensons, bu also slghly lower conrbuon raes n he fuure. Young workers wll face he bgges cus of hose workng durng he change, bu hey wll also have me o see large reducons n conrbuons. Thus, s a queson of balancng he losses from benef cus and he gans from lower conrbuons. For voers a he me of he change, he balance s negave. All fuure generaons wll gan. The case s he oppose o ha of creang a PAYG penson sysem, where nal generaons gan and fuure generaons pay ha nal gan. Here a (mosly) PAYG sysem s slghly reduced, curren generaons pay ha bll, and fuure generaons jonly enjoy he resul. Lfe expecancy s also ncreasng n Sweden. Thus s lkely ha he above analyss, f appled o Swedsh voers, would yeld smlar resuls. How could he Swedes decde o mplemen he longevy adjusmen? Where does he suppor come from? Or, s here somehng wrong wh he analyss? One possbly s ha he uly funcon n he model s badly flawed. Inergeneraonal alrusm may be more common han n he chosen specfcaon. Anoher possbly s ha he decson-makers have gnored he uly analyss. The emphass may be solely on publc fnances. Thrdly, he reference scenaro may be wrong. Dong nohng may no be a

22 8 relevan opon; he expeced ncrease n conrbuon raes mus be deal wh somehow. We should compare alernave measures of prevenng he rse n conrbuons. Fourhly, he resul may be rgh. Makng penson reforms may be oo dffcul n many counres, or a leas reforms are posponed as far as possble. In our low age rao scenaro lfe expecancy, n fac, decreases. Voers expec ha o happen, and here s suppor for he polcy whch would ncrease he benefs (Fgure 2). Fgure 2. Suppor for mplemenng longevy adjusmen, low age rao Share of wnners n oal populaon Share of wnners n workng populaon ETLA Ferly-dependen prefundng: All voers lose boh n he base scenaro and n he hgh age rao alernave. The losses are 4 5 mes larger n he laer. In boh scenaros ferly s declnng, whch requres more fundng and hgher conrbuons. Ths polcy s very unpopular. PasTEL-ndexng: Almos all voers lose n he base scenaro; only old pensoners may gan a lle. Agan, he losses are much larger n he hgh-age rao where he wage bll grows much more slowly han n he base scenaro. Bu afer 22 some suppor also urns up, sarng from young workers. In 25 a majory of workers would suppor he change (Fgure 3). The fases declne n he workng-age populaon s passng, and workers sar o gan more from he reduced conrbuons. Moreover, he oal wage ndex gves larger pensons han he curren ndex afer he year 275. One general feaure emerges. The opposon o measures s he sronger he more effecs he measures wll have. Ferly-dependen fundng would be very unpopular f ferly were expeced o declne rapdly. The longevy adjusmen would be easer o agree upon, f longevy were no expeced o rse. Alhough hs s unsurprsng, carres a lesson: he

23 Fgure 3. Suppor for changng o he PasTEL ndex, hgh age rao Share of wnners n oal populaon Share of wnners n workng populaon ETLA polcy rules should be mplemened well n advance of he acualsaon, or he general expecaon of fuure acualsaon, of he problems. VI CONCLUSIONS Our wo sarng pons were ha he demographc rsks are larger han generally realsed and ha he curren PAYG penson sysems redsrbue he rsks manly o he fuure workng-age czens. Afer ha we presened hree mehods for mproved nergeneraonal redsrbuon and smulaed her effecs. A lnk beween longevy and penson benefs mpresses us as beng well-jusfed and easy o mplemen. If nformaon abou he lkely reducon n pensons s gven early enough, ndvduals can already adjus durng workng age. The same apples o ferlyadjused prefundng, snce he fnancal burden s dsrbued o he whole workng lfe. The wage bll ndexaon has wo faces. The long-run rends n demographcs and producvy are easer o foresee and adjus, bu he shor-erm varaons are no, whch mgh be a problem n some cases (f he busness cycles are srong, he pensoner s credconsraned and he mnmum ncome ransfers are low). Anoher problem s he markedly hgher benefs and coss generaed by a shf o a pure oal wage ndex. We solve boh he problems by usng he PasTEL-ndex, whch combnes he oal wage ndex wh a cos-oflvng ndex. Penson polces n Fnland am, que correcly, a posponng he acual reremen age and ncreasng he raes of reurn on funds. One canno, however, coun on he success of hese polces. And even f hey succeed, unfavourable demographc oucomes may resul n very hgh conrbuon raes. The mechansms and rules suded here would reac auomacally o demographc developmens. If no demographc surprse ook place, he measures would have no effecs, excep he longevy adjusmen, whch would reac o he n-

24 2 crease n lfe expecancy. If demographcs urned ou o be very unfavourable, he measures would effecvely allevae he consequences o he penson sysem. The overall oucome of hs sudy s ha f curren penson sysems use all he nformaon ncluded n he populaon forecass more effcenly, he allocaon of rsks can be mproved whou fundamenally changng he sysems. As many of he benefs requre ha he measures are carred ou early enough and planned usng a very long horzon, s beer ha he reacons are based on rules raher han on dscreon. The vong analyss also suppors he dea of early mplemenaon. Furhermore, as each of he above menoned measures has s own advanages and weaknesses, some combnaon mgh be opmal.

25 2 References Alho, J.M. (998): A sochasc forecas of he populaon of Fnland. Sascs Fnland, Revews 998/4. Helsnk. Auerbach, A. J. and J. L. Kolkoff (987): Dynamc Fscal Polcy. Cambrdge Unversy Press. Cambrdge Boadway, R.W. and D. Wldasn (989a): A Medan Voer Model of Socal Secury. Inernaonal Economc Revew, Vol. 3, pp Boadway, R.W. and D. Wldasn (989b): Vong Models of Socal Secury Deermnaon. In B.A. Gusafsson and N.A. Klevmarken (eds.), The Polcal Economy of Socal Secury (Amserdam, Norh Holland), pp Bovenberg, L. and A. van der Lnden (997): Penson Polces and he Agng Socey. The OECD Observer, No. 25 Aprl/May. Brownng, E. K. (975): Why he Socal Insurance Budge s oo Large n a Democracy. Economc Inqury, Vol. 3, pp Büler, M. (2): The polcal feasbly of penson reform opons: he case of Swzerland. Journal of Publc Economcs, Vol. 75, pp Conesa, J.C. and D. Krueger (999): Socal Secury Reform wh Heerogeneous Agens. Revew of he Economc Dynamcs, Vol. 2, pp Cuckerman, A. and A.H. Melzer (989): A Polcal Theory of Governmen Deb and Defcs n a Neo-Rcardan Framework. Amercan Economc Revew, Vol. 79, pp De Nard, M. S. Imrohoroglu and T. J. Sargen (999): Projeced U.S. Demographcs and Socal Secury. Revew of Economc Dynamcs, Vol. 2-3, Dua, J., S. Kapur and J.M. Orszag (999): How o fund pensons: ncome uncerany and rsk averson. Paper presened a he Royal Economc Socey Conference 999. Hu, S.C. (982): Socal Secury, Majory-Vong Equlbrum and Dynamc Effcency. Inernaonal Economc Revew, Vol. 23, pp Imrohoroglu, A., S. Imrohoroglu and D. Jones (999): Compuaonal Models of Socal Secury, n R. Marmon and A. Sco (eds.) Compuaonal Mehods for he Sudy of Dynamc Economes. Oxford Unversy Press, pp Kolkoff, L.J., T. Persson and L.A.O. Svensson (988): Socal Conracs as Asses: A Possble soluon o he Tme Conssency Problem. Amercan Economc Revew, Vol. 78, pp Lassla, J. (2): Wage Formaon by Majory Vong and he Incenve Effecs of Pensons and Taxaon. Fnnsh Economc Papers, Vol.3, pp Lassla, J. and T. Valkonen (995): Polcy Credbly n Numercal Overlappng Generaons Models. ETLA Dscusson Paper No Helsnk. Lassla, J. and T. Valkonen (999): Penson prefundng and ageng n Fnland (n Fnnsh) ETLA, B 58 and The Cenral Penson Secury Insue, Sudes 999:2. Helsnk.

26 22 Lassla, J. and T. Valkonen (2): Penson ndexng, longevy adjusmen and ageng n Fnland (n Fnnsh). ETLA, B 72 and The Cenral Penson Secury Insue, Sudes 2:2. Helsnk. Lassla, J. and T. Valkonen (2a): Penson Prefundng, Ageng and Demographc Uncerany. Inernaonal Tax and Publc Fnance, Vol. 8, pp Lassla, J. and T. Valkonen (2b): Prefundng n a Defned Benef Sysem - he Fnnsh Case. In M. Feldsen and H. Seber (eds.): Socal Secury Penson Reform n Europe. NBER conference volume, forhcomng from The Unversy of Chcago Press. Lee, R.D. (2): The Lee-Carer mehod of forecasng moraly, wh varous exensons and applcaons. Norh Amercan Acuaral Journal, 4, Lee, R.D. and S. Tuljapurkar (998): Deah and Taxes: How Longer Lfe Wll Affec Socal Secury. Demography 34 no., (February 998). Lndell, C. (999): Lfe expecancy ncreases how abou reremen age? (n Fnnsh). The Cenral Penson Secury Insue, Repors 999:8. Helsnk. Mullgan, C.P. and X. Sala-I-Marn (999): Socal secury n heory and pracce (I): facs and polcal heores. NBER Workng Paper No. 78. Cambrdge. Nemelä, H. (994): The developmen of Fnland's overall penson sysem (n Fnnsh, wh an 8- page Englsh summary). 2nd edon. Publcaons of he Socal Insurance Insuon. 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 Annual Bank Conference on Developmen Economcs, The World Bank, Aprl 2, 2. Rus, J. (2): Sraeges for Incorporang Rsks, Uncerany, and Prvae Insurance Mechansms n Models of Socal Insurance. In Long Term Model Developmen for Socal Secury Polcy Analyss, Urban Insue. Scherman, K.G. (999): The Swedsh Penson Reform. ILO, Issues n socal proecon, dscusson paper No. 7. Geneve. Snn, H-W. (2): Why a Funded Penson Sysem s Useful and Why I s No Useful. NBER Workng Paper No Cambrdge. Tabelln (99): A Posve Theory of Socal Secury. NBER Workng Paper No Cambrdge. Valdés-Preo, S. (2): The fnancal sably of noonal accoun pensons. Scandnavan Journal of Economcs, Vol. 2, pp Van Dalen, H.P. and B.M.S. van Praag (993): Publc Pensons, Marke Power and Inergeneraonal Confdence. In Wolfe, B.L. (ed.) Proceedngs of he 48h Congress of he Inernaonal Insue of Publc Fnance, Seoul 992. Supplemen o Publc Fnance, Vol. 48, pp Verbon, H.A.A. (987): The Rse and Evoluon of Penson Sysems. Publc Choce, Vol. 52, pp Verbon, H.A.A. (993): Publc pensons: he role of expecaons and he role of publc choce. Journal of Populaon Economcs, Vol.6, pp

27 23 Appendx. Acuary and welfare effecs of he polcy measures Some addonal effecs of he above-suggesed polcy measures are presened n he followng pages wh fgures. The crera used for varous polces requre more explanaon. Fgures 3, 5 and 7 gve nformaon abou he generaon-specfc acuary raos. Fgures 4, 6 and 8 descrbe he changes n welfare. 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 Α R = Z + l s R zr / τ gr = = TW + = The measure s closely relaed o he money s worh calculaons famlar from he penson reform dscusson n Uned Saes. The uly measure shows relave compensaed varaons by generaons. They are measured as logarhmc dfferences beween he new dscouned lfeme consumpon expendures and he consumpon necessary o acheve he baselne uly a he new prces. Therefore, posve numbers express a welfare gan.

28 24 Fgure 4. Acuary rae Curren sysem Longevy-adjused Cohors denoed by he year of enerng he labour force. ETLA Fgure 5. Welfare effecs of longevy adjusmen Cohors denoed by he year of enerng he labour force. ETLA

29 25 Fgure 6. Acuary rae, hgh age rao Curren sysem PasTEL-ndex Cohors denoed by he year of enerng he labour force. ETLA Fgure 7. Welfare effecs of PasTEL ndexaon, hgh age rao Cohors denoed by he year of enerng he labour force. ETLA

30 26 Fgure 8. Acuary raes, hgh age rao Curren sysem Ferly-dependen prefundng Cohors denoed by he year of enerng he labour force. ETLA Fgure 9. Welfare effecs of ferly-dependen prefundng, hgh age rao Cohors denoed by he year of enerng he labour force. ETLA