A Perfect Marriage: Child-related Pensions and Public Education *

Transcription

1 A Prfc Marriag: Child-rlad Pnsions and Public Educaion * Michal Voigländr I I Dparmn of Economic Policy, Univrsiy of Cologn, Albrus-Magnus Plaz, Cologn, Grmany (Fax: , -mail: voiglandr@wiso.uni-koln.d) Absrac In h prsn papr h ffcs of a radiional and a child-rlad pay-as-you-go pnsion sysm on friliy dcisions of a rprsnaiv houshold ar xamind. Thrby, h analysis focuss spcially on h inrplay of parnal dcisions on uaniy and ualiy, inroducd by Bckr (1960). As i will b shown, a radiional pay-as-you-go sysm in ihr cas disors dcisions of parns. By conras, h child-rlad pnsion sysm is a mans o rsor opimaliy, providd ha a dvic lik public ducaion is in plac. Morovr, as ducaion is financd collcivly, axpayrs gain pnsion nilmns according o hir involvmn in h accumulaion of human capial. JEL classificaions: D10, I20, H55 Ky words: Pay-as-you-go, child-rlad pnsion, uaniy and ualiy of childrn A. Inroducion All Europan pay-as-you-go sysms (PAYGO) ar on h vrg of collaps. As birh ras dclin and lif-xpcancis sadily ris h burdn on h forhcoming gnraions rachs a lvl which is unsusainabl for various rasons. Among conomiss i is, hrfor, common sns ha h dominanc of unfundd sysms has o b rducd by a largr shar of funding. Y, hr is a livly dba in Grmany as wll as in ohr Europan counris abou how pnsion nilmns should b cappd. In gnral, wo possibiliis hav bn proposd: On h on hand on can lowr nilmns ually for all mmbrs of a gnraion. This proposal is widsprad among conomiss and was vry rcnly advancd by a commission on h long-rm susainabiliy of h Grman social-scuriy sysm (Kommission zur Nachhaligki dr Finanzirung dr sozialn Sichrungssysm 2003). On h ohr hand, a group of conomiss, rcnly Sinn (2000), proposs o I grafully acknowldg h suppor of h Oo Wolff Insiu for Economic Sudis, Cologn. Addiionally, I lik o hank Barbara Hnman, Kai Mnzl, Philipp Paulus and Ann Zimmrmann for usful commns. 1

2 diffrnia nilmns according o h gnraiv conribuion. Thus, h lar group aims a inroducing a child-rlad pay-as-you-go pnsion sysm (CPAYGO) in which pnsions ar prdominanly drmind by h numbr of childrn. Evn a firs glanc, h advanags of such a sysm sm o b complling. Firs of all, a child-rlad pnsion sysm prvns a social dilmma which can occur in a radiional PAYGO. According o h social scuriy hypohsis a PAYGO sysm diminishs friliy ras bcaus of growing opporuniy coss of childrn. 1 As coss hav o b born by parns bu rvnus (pnsions) ar disribud collcivly, parns adjus hir dcisions and bar fwr childrn. This is infficin as h pnsion sysm sill rlis on populaion growh. 2 This infficincy can b ovrcom by graning pnsions only o parns. Scondly, and his is an xnsion o h prvious ida, a CPAYGO is sabl vn if h dmography changs. In such a pnsion sysm hos who do no hav childrn ar forcd o sav individually in ordr o scur hir old-ag incom. Hnc, as soon as friliy changs,. g. bcaus of changd prfrncs, individual savings will adjus. On a macroconomic lvl h combinaion of human capial, hr man as fuur conribuion payrs, and ral capial is always sufficin o scur a fixd lvl of pnsions for h ldr gnraion. In spi of hs advanags h suppor for a CPAYGO is only minor. On major problm of his schm is rfrrd o as h ualiy-uaniy rad-off. I is fard ha a CPAYGO may ngaivly affc h ualiy of child-raring, as Cigno (1993, p. 515) and Folbr (1994, p. 89) poind ou. Wih rfrnc o Bckr (1960) h ualiy of childrn involvs invsmns in h wll-bing of childrn. Expndiurs on h ducaion or halh car of childrn ar h mos prominn xampls for hos kinds of invsmns. As i is assumd ha a highr lvl of ualiy will incras h probabiliy of highr incom and hnc highr conribuions o h pnsion sysm, a CPAYGO migh caus a nw social dilmma if ualiy is subsiud by uaniy (i.. h numbr of childrn). Thus, a nw infficincy would occur. Bsids, povry and inualiy migh incras in fuur gnraions. This papr is aimd a xamining his rad-off in grar dail. Using a simpl microconomic modl in h radiion of Bckr (1960) h dcisions of a rprsnaiv houshold concrning h ualiy and uaniy of childrn undr a radiional PAYGO and a CPAYGO ar highlighd. Morovr, h analysis will b xpandd by inroducing a public ducaion sysm. I will b dmonsrad ha h combinaion of such an insiuion and a CPAYGO is a mans o rsor opimaliy. Thus, hs wo insiuions consiu a prfc marriag. Finally, h policy implicaions and h main conclusions ar summarisd. 1 For mpirical work suid o back his viw s for xampl Cigno and Rosai (1996) or Cigno, Casalaro and Rosai (2003). 2 For a formal ramn s Prinz (1990), Bnal (1990), Kolmar (1997) or Ehrlich and Lui (1998). 2

3 B. Th Modl Th following microconomic modl highlighs h ffcs on h uaniy-ualiy dcision of housholds undr a PAYGO and a CPAYGO. Thr will b no amp o clos h modl by inroducing a producion scor. Thus, h following idas can b considrd as parial analysis or as h dcisions of a houshold in a small counry whr prics ar fixd. W assum a rprsnaiv houshold of gnraion ha drivs uiliy from h consumpion of goods and from h uaniy and ualiy of childrn. Hnc, h houshold is no alruisic owards is childrn bu i rgards childrn and hir wll-bing (ualiy) as consumpion goods. Th uiliy funcion of h rprsnaiv houshold is hrfor dfind as follows: U = U(c,,) (1) whr N (2) * = N +1 c : Lif-cycl consumpion : Numbr of childrn of h houshold : Expndiurs for h ualiy of childrn N : Siz of gnraion in priod Th uiliy funcion U( ) is assumd o b sricly monoonically incrasing and sricly uasiconcav. Thus, consumpion, childrn and h ualiy of childrn ar rgardd as normal goods. Th houshold rcivs a fixd labour incom w _ which i can us for consumpion and raising and ducaing childrn. Th horizonal lin abov h variabl for labour incom indicas ha h dcision abou is lvl was akn by h prvious gnraion. W assum ha labour incom dpnds on invsmns in ualiy rcivd whil bing a child. This is a ui common xpcaion: Th br childrn ar ducad and h halhir hy say, h grar should b hir incom prospcs, a las on avrag. As a consunc of his srucur h individual labour incom is xognous for h workr bu ndognous for his offspring. W assum ( ), rprsning h prsn valu of h fuur incom of h w + 1 3

4 2 w ) offspring, o b wic diffrniabl wih + 1( w+ 1( ) > 0 and < 0. Furhrmor, h 2 houshold facs a mandaory PAYGO sysm wih a fixd conribuion ra of 0<α <1 and a promisd pnsion wih a prsn valu of p >0. Th rprsnaiv houshold, hus, maximiss is uiliy funcion which is subjc o h following lif-cycl budg rsricion: _ g(c,,) c *(z *z) p w*(1 ) = + + = α (3) z : Fixd cos pr child, z >0. z : Pric of on uni of ualiy, z >0. Th budg consrain consius a convx s as w can show ha for wo disinc poins u = (u,u,u) and v g(v)(v j j u) j 0. Thrby, j j1 = = (v,v,v) wih g(v) g(u) h following inualiy holds: g(v) rprsns h parial drivaiv, rspcivly. In a firs sp w wan o driv an opimal soluion for h dscribd dcision problm. Such a soluion could b rgardd as h dcision of an alruisic social plannr wih prfc forsigh. Alrnaivly, his can b inrprd as h common maximisaion of h uiliy of all individuals of gnraion in h sociy. In such an opimal soluion i would b akn ino accoun how a PAYGO sysm is financd. As i is common, h pnsion nilmns of gnraion dpnd on h conribuions of h following gnraions. Assuming a rprsnaiv houshold, h pnsion nilmn is dircly drmind by h conribuions of is offspring. Thrfor, w obain p = w ( )* α * (4) + 1 Euaion (4) sipulas ha h prsn valu of h individual pnsion nilmn uals h prsn valu of h conribuions paid by h offspring of h rprsnaiv houshold. Thrfor, a houshold ha dos no bar, rar and duca childrn canno gain pnsion nilmns from a PAYGO. Hnc, as in a fully fundd sysm, individuals hav o ak prcauions in ordr o rciv a pnsion. Childrn and hir ualiy ar hus no only consumpion bu invsmn goods. 4

5 If w now subsiu (4) ino (3), rarrang and opimis h uiliy funcion w rciv h following rsuls: U/ c =λ U/ =λ *(z + z * w ( )* α) + 1 U/ =λ*(z * w ( )/ * * α) + 1 (5) (6) (7) Th rm λ is h common Lagrang muliplir and displays h marginal uiliy of mony incom. Assuming z + z * w ()* α 0 and + 1 z * w ( )/ * α 0 h budg + 1 consrain of h common maximisaion problm consius a convx s, oo. Hnc, h firs ordr condiions ar sufficin and ncssary for an absolu maximum. As w ar spcially inrsd in parnal dcisions concrning h numbr and ualiy of childrn, w can focus our analysis on uaions (6) and (7). Firs of all, on should no ha z, and appar in boh uaions. Hnc, h chosn lvl of dircly affcs h shadow pric of, and vic vrsa. Such an oucom is ypical for non-linar budg consrains and has an imporan ffc on h considrd ualiy and uaniy dcision. A shif of h rlaiv pric of ihr uaniy or ualiy will lad o rlaivly larg adjusmns rlaiv o ohr consumpion goods - wih rspc o h chosn lvl of and. B awar ha his dos no ruir uaniy and ualiy o b br subsius han any ohr consumpion goods chosn a random. 3 Thrfor, dviaions from h opimal condiions can hav normous ffcs du o h inrplay of hs wo variabls. 4 Scondly, i bcoms apparn ha a social plannr would ak h coss as wll as h rvnus of childrn ino accoun. Euaion (6) displays h fac ha in uilibrium h marginal uiliy of has o ual h marginal coss pr child, which consis of h fixd cos pr child ( z ) plus h ualiy cos pr child ( z * ), minus h rvnus pr child, which ar drmind by h fuur conribuions o h pnsion sysm pr child ( w + 1( )* α ). Th sam logic applis o uaion (7). Th marginal coss of ualiy ar drmind by h numbr of childrn and h pric pr uni of ualiy ( z * ) whras h marginal rvnus of ualiy ar consiud by h fuur xra conribuions o h pnsion sysm ha aris from an addiional marginal xpndiur on ualiy ( w + 1()/ ** α). In h following w will xamin how a rprsnaiv houshold will adjus is dcisions facing diffrn yps of PAYGO. As w know ha in ach PAYGO, ihr a radiional or a 3 S Bckr and Lwis (1973), p For furhr dails s Bckr (1991), ch. 5 and Razan and Sadkin (1995), ch. 3. 5

6 child-rlad sysm, pnsions hav o b financd by h conribuion paymns of fuur gnraions, h jus drivd opimal condiions mus hold in ordr o guaran fficincy. C. PAYGO vs. CPAYGO Th main diffrnc bwn h common and h individual maximisaion problm is h prcpion of h pnsion nilmn. For an individual, p is no ndognous bu xognous bcaus hr individual dcision dos no sm o affc h financial siuaion of h PAYGO. Espcially in larg sociis which consis of many housholds, h individual gnraiv conribuion sms o bcom lss imporan (for h pnsion). Thus, rvnus ha corrspond o baring and raising childrn vanish and h pnsion nilmn bcoms a bnfi which from h poin of viw of an individual houshold canno b influncd. If his is h cas h firs-ordr condiions for U(. ) wih rspc o and chang as follows: U / U / = λ *( z = λ *( z + z * ) * ) (8) (9) In comparison wih h opimal condiions h shadow prics of boh and ris. Thrfor, h houshold chooss a lowr lvl of boh goods, bu spnds mor incom on ohr consumpion. Whn pnsions ar prcivd as fixd h fuur conribuions of childrn o h PAYGO sysm ar ignord. Hnc, h invsmn moiv for raising childrn vanishs, probably wih svr consuncs for h susainabiliy of h pnsion sysm. Dpnding on h prfrncs h adjusmns of h houshold will mor havily affc h ualiy han h uaniy dcisions, or vic vrsa. Howvr, h ovrall ffc wih rspc o uaion (4) is clar. If α is fixd, pnsion nilmns hav o b lowrd compard o h opimal siuaion. A dclin of h prsn valu of pnsion nilmns, in urn, has h sam ffc as a dclin of incom. Assuming all goods o b normal goods his inducs a fall in ovrall consumpion which includs friliy and ualiy xpndiurs. Thrfor, furhr and furhr pnsion cus bcom ncssary. Of cours, his ffc could b compnsad by priva funding. Y, his is no fficin as wlfar could b incrasd if dcisions abou h numbr and ualiy of childrn ar rvisd. If α is no fixd bu p, possibly bcaus of a guarand minimum pnsion or bcaus of prfrncs of h mdian vor (Browning 1975), h sam logic applis. Each ris in h conribuion ra, hus a fall in disposabl incom, will lad o fwr childrn and lss xpndiurs on hir wll-bing. 6

7 No mar if α or p is affcd, h siuaion can b rgardd as a social dilmma. As coss of childrn hav o b born individually bu rvnus ar disribud collcivly, individual coss of childrn ar highr han social coss. Thrfor, dcisions ar subopimal and hr ar possibiliis for improvmn. Of cours, if all individuals could bargain in his siuaion fficincy could b rsord, bu ha soluion can b xcludd bcaus of ransacion coss and a lack of commimn as on can asily comprhnd. So a diffrn soluion is ndd o ovrcom his problm of insiuional xrnaliis 5. Two possibiliis hav bn advancd. Firsly, h PAYGO sysm could b abandond. 6 Scondly, fficincy could b rsord by rdfining propry righs. Th firs soluion is vry popular among conomiss. Howvr, a ransiion o a fully fundd sysm is difficul o dsign as h nilmns of h ldr gnraions hav o b prsrvd. Thrfor, h currn workrs hav o cop wih a doubl burdn which mos possibly hamprs wlfar improvmns. In addiion and rgardlss of h doubl burdn, a PAYGO sysm islf can b a dvic o rach fficincy. For insanc, Radka and Razin (1995, ch. 10) show ha, in absnc of ngaiv buss, such an inrgnraional ransfr sysm is fficin. Furhrmor, h mixur of human capial and ral capial migh b a mor fficin way o scur old ag pnsions wih rfrnc o h porfolio slcion hory (s Mron 1984). Morovr, in mos wsrn Europan counris policy makrs discuss only a frzing of conribuion ras which lads o a diminishd siz of h PAYGO bu no is aboliion. This also applis o currn proposals in Grmany as i was mniond in h inroducion. Hnc, h social dilmma will sill xis, only h magniud of h problm is rducd. Having oulind hs argumns shall b sufficin o xplain why spcial anion is paid o h scond alrnaiv which is rfrrd o as a child-rlad pay-as-you-go sysm (CPAYGO). By diffrniaing pnsions according o h numbr of childrn such a sysm is aimd a mrging social and individual coss of child baring. Alrnaivly, on could say ha h propry righs wih rgard o conribuions of h working gnraion ar r-dfind, i.. according o h involvmn in baring and ducaing childrn. W assum ha h rprsnaiv houshold rcivs a pnsion b pr child. Iniially, h oal amoun of pnsions shall no chang so ha h following uaion holds: b* = p (10) Thn, h lif-cycl budg consrain changs as follows: 5 Th rm insiuional xrnaliy is usd as his siuaion dos no rsul from a mark failur bu from h insiuional framwork of a PAYGO. 6 S for xampl Fldsin (1996) for his proposal. 7

8 _ w*(1 α ) = c + *(z b + *z) (11) By opimising (1) wih rspc o (11) w obain h following rsuls for and : U/ =λ*(z b + z * ) U/ =λ*(z * ) (12) (13) Th ransiion of a PAYGO ino a CPAYGO has wo simulanous ffcs. Firsly, h aboliion of h fixd pnsion p has h sam ffc as a dclin of incom. Hnc, h xpndiurs on uaniy, ualiy and ohr consumpion will b rducd. Scondly, h inroducion of a CPAYGO dircly affcs h shadow pric of childrn. Compard o ualiy and ohr consumpion raising childrn bcoms rlaivly mor araciv. Consunly, h houshold will choos mor childrn whil fwr rsourcs ar usd for consumpion and xpndiurs on ualiy. Morovr, h fall in ualiy will lad o a furhr drop in h shadow pric of childrn lading o addiional adjusmns. A h nd of his procss, h rlaivly larg ris in h lvl of uaniy will b accompanid by a rlaivly sharp dclin in h lvl of ualiy. Dspi h firs ffc, hus, on can obsrv a subsiuion of ualiy by uaniy. Agains his background, Cigno s (1993, p. 515) and Folbr s (1994, p. 89) samns abou an undsirabl subsiuion ffc can b confirmd. By comparing uaions (6) and (7) wih (12) and (13) on can sipula ha h houshold aks ino accoun h fuur rvnus pr child (b ), bu no h marginal rvnus of xpndiurs on ualiy. So no all drminans of fuur conribuions ar considrd simulanously, which implis ha h pnsion schm is no adua o allow for fficincy. D. Th rol of public ducaion So far w hav implicily assumd ha only parns financ xpndiurs ha ar rlad o h ualiy of childrn. Y his is no h cas. In almos all modrn sociis bnfis for familis ar widsprad, spcially concrning ducaion, halh car and child car. For Grmany, h advisory council of h Fdral Minisry for Family Affairs, Snior Ciizns, Womn and Youh (Wissnschaflichr Bira für Familinfragn 2002) assrs ha approximaly bwn 20.8 % and 35.8 % of oal xpndiurs on childrn (xcp for opporuniy coss) ar born by axpayrs. Similar rsuls apply o h majoriy of Europan counris. 8

9 Prdominanly hs bnfis aim o improv h wll-bing of childrn, hnc hir ualiy. As a consunc, ransfrs in kind ouwigh ransfrs in cash by far. As w will s, such masurmns affc h favourabiliy of boh pay-as-you-go sysms in usion considrably. In h following w rsric our analysis o a public ducaion sysm as an xampl for such public xpndiurs. A las hr diffrn rasons can b advancd for his rsricion. Firsly, public ducaion is common in almos all counris and hrfor h mos prominn xampl for public xpndiurs rlad o childrn. Scondly, i is wihou usion ha hs xpndiurs dircly affc h ualiy dcisions akn by parns. Ohr bnfis, lik subsidis for day car, migh hav ohr goals dpnding on h circumsancs. For xampl, publicly financd child car could b rgardd as a mans o nhanc womn s mploymn. Thirdly and finally, h raional for public ducaion is byond dispu whil ohr mans of collciv invsmn in h ualiy of childrn, lik fr halh car, ar mor ofn usiond. 7 As ducaion involvs an xrnaliy problm islf, a corrsponding ransfr is a mans o nhanc conomic fficincy. Furhrmor, public ducaion is h major dvic o improv ual opporuniis. According o Homann and Pis (1996, p. 221), i is a prmis for h approval of a social conrac. Bhind a Rawlsian vil of ignoranc, hus, individuals would mos probably sl for such an insiuion. In spi of our focus on public ducaion i should b srssd ha h analysis could b applid o ohr yps of bnfis as wll. Thn, howvr, i would b rasonabl o discuss guidlins for a raional family policy which is byond h scop of his papr. In a firs sp w wan o xamin h ffc of h inroducion of public ducaion whil a radiional PAYGO sysm is in plac. From a hisorical prspciv his can b rgardd as a ypical dvlopmn. W assum ha a shar τ of all coss rlad o h ducaion of childrn is publicly financd. This can dno ha parns sill hav o pay a f pr child owards h school or ha addiional srvics hav o b born individually. Th provision of h public good shall b financd by an incom ax. Thus, w gain h following condiion: τ * z * = * w (14) Du o h inroducion of public ducaion h budg consrain of h houshold changs as follows: _ w*(1 α)*(1 ) + p = c + *(z + (1 τ )**z) (15) 7 For an ovrviw and assssmn of Europan family policis s for xampl Wrding (2001). 9

10 If w now rarrang and opimis (1) wih rspc o (15) w can driv h marginal ra of subsiuion of wih rspc o : U / U / = z + (1 τ )* z (1 τ) * z * * (16) U / Diffrniaing his xprssion wih rspc o τ yilds / τ > 0. U / As h sign of his xprssion is posiiv w can conclud ha h shadow pric of ualiy dclins compard o h shadow pric of uaniy and ohr consumpion. Thrfor, h houshold spnds mor mony on ualiy which in urn incrass h shadow pric of uaniy. Hnc, h mor coss a sociy bars ha rfr o h ualiy of childrn h fwr childrn will b born. Du o h changs in h insiuional framwork i bcoms mor araciv for housholds o rais fwr bu br ducad childrn. Th ffc of h incom ax is du o h rlaivly larg subsiuion ffc only of minor rlvanc. Wih rfrnc o our opimal soluion h rproducion ra is far oo low. Rmmbr ha h inroducion of a PAYGO alrady lad o a subopimal choic rgarding friliy. By adding a sysm of public ducaion his problm worsns bcaus rlaiv prics ar disord. Agains his background i is no surprising ha spcially counris which focus on graning bnfis o familis ha aim a improving h wll-bing of childrn, lik Grmany, Ialy or Spain, hav lowr friliy ras han hos counris who aim o lowr coss for boh uaniy and ualiy, lik Franc (s Eurosa 2003). So far w can conclud ha a pur CPAYGO disors dcisions in favour of h numbr of childrn whil a radiional PAYGO in combinaion wih public ducaion disors dcisions in favour of xpndiurs on ualiy. I is, hrfor, slf-vidn o xamin whhr hs cass of sub-opimaliy can b ovrcom by sling for boh, a sysm of public ducaion and a child-rlad pnsion sysm. In ordr o do so, w combin uaion (15) wih a child-rlad pnsion. Hnc, hr ar now wo dvics, b and τ, which affc h uaniy and ualiy dcisions of h houshold in diffrn ways. For h corrsponding opimisaion problm w gain h following soluions: U/ =λ*(z b + (1 τ)*z *) U/ =λ*(1 τ)*(z * ) (17) (18) 10

11 Now w ar abl o rsor opimaliy as on can ac on boh condiions simulanously. By uaing (17) and (6) as wll as (18) and (7) and solving for b w gain h opimal lvl for h child-rlad pnsion. w ( ) b =α*w ( ) α* * (19) This rsul nds a brif xplanaion. Th firs rm on h righ-hand sid rfrs o h oal sum of conribuions a workr pays for h ldr gnraion. I rprsns, hrfor, h maximum pnsion which an adul could rciv pr child. This sum of conribuions has o b diminishd by h scond rm. Th drivaion of w +1 ( ) wih rspc o allgoriss h ra of rurn of xpndiurs on ualiy. Thus, h las rm has o b rgardd as h oal amoun of rvnus ha can b achivd by xpndiurs on h ualiy of childrn. Of cours, hs rvnus hav o b muliplid by α as only his shar of rvnus is disribud among h pnsionrs. As a rsul, pnsion nilmns should no only b grand according o h numbr of childrn raisd bcaus xpndiurs on ualiy hav o b rwardd, oo. For τ w obain h following condiion: τ=α w ( ) * * z (20) Subsiuing τ in (14) and rarranging w can idnify h scond moiv for obaining a pnsion in such an opimal CPAYGO. w ( ) + 1 w* =α* * (21) In uilibrium h sum of axs uals h prsn valu of rvnus which corrsponds o h xpndiurs on h ualiy of childrn. Th significanc of (21) is as follows. Taxpayrs gain pnsion nilmns by invsing in h ualiy of childrn. Thrfor, w obain a raional for graning childlss housholds a pnsion, oo. Obviously, individual xpndiurs of parns on h ualiy of childrn ar no rwardd in opimum. Y, if τ is chosn corrcly invsmn and consumpion wih rspc o ar sparad from ach ohr. Th shar τ of coss rprsns hos xpndiurs which ar aimd o scur old ag pnsions whil h shar (1-τ) rfrs o consumpion by parns. Likwis on migh say ha h social and individual coss of ualiy ar brough oghr by subsidising h pric pr uni of ualiy. 11

12 Baring his in mind h assssmn of h subsiuion ffc has o b rvisd. I is obvious ha a subsiuion ffc will occur if a sociy which subsidiss public ducaion convrs a radiional PAYGO sysm ino a CPAYGO. In his cas, howvr, h subsiuion ffc is inviabl in ordr o nhanc wlfar. By mploying ransfrs for public ducaion and inroducing a child-rlad pnsion an fficin unfundd pnsion sysm can b dvlopd. Agains his background, boh dvics consiu a prfc marriag as hy idally supplmn ach ohr. E. Policy Implicaions Alhough h analyical framwork is kp simpl, i is possibl o driv som imporan policy implicaions. Firs of all, by using a framwork in h radiion of Bckr h inrplay of parnal dcisions wih rspc o ualiy and uaniy has bn highlighd. In ordr o mploy an fficin pay-as-you-go sysm i is ncssary o ak simulanously ino accoun h ncssiy of h shr xisnc of a forhcoming gnraion and h accumulaion of human capial. In som Europan counris hr is a rnd o gran only ransfrs ha aim o nhanc h ducaion of childrn. For xampl, in Grmany child car bnfis (Erzihungsgld) hav bn cappd rcnly whil i is plannd o nlarg h provision of public child car insiuions, spcially kindrgarn. Howvr, such a policy is inadua o offs h infficincy of a radiional PAYGO. In conras, whn bing subsidisd for h xpndiurs on ualiy housholds will choos fwr childrn. As a conclusion, monary ransfrs o parns of h yp of a child-rlad pnsion ar an ssnial dvic in ordr o provid an fficin unfundd pnsion sysm. Of cours, his dos no imply abolishing xising ualiy improving dvics bu o combin hm wih a child-rlad pnsion. In addiion, vn if on assums ha dvics lik h provision of subsidisd day car hav a prdominan ffc on h uaniy dcisions as h opporuniy coss of childrn fall, hy ar no adua o subsiu child rlad pnsions, ihr. Th rason is ha only a fracion of all parns rly on, and hrfor bnfi from, such possibiliis. Bsids, h rsricions for an unimly provision of child-rlad bnfis hav o b akn ino accoun. Scondly, h modl highlighs ha a pur CPAYGO is as infficin as a pur radiional PAYGO. Taxpayrs should gain pnsion nilmns according o hir shar of invsmn in human capial. Hnc, childlss individuals will rciv a pnsion vn afr h ransiion o CPAYGO, alhough on a lowr lvl. As conribuions o h xising pay-as-you-go sysms ar ihr ax financd or rlad o h incom of h individuals, i is rasonabl o link h conribuions o h pnsion nilmns according o h invsmns in human capial. Thrfor, h basic srucur of h xising pnsion sysms can a las b parially mainaind. 12

13 Thirdly, and his is an xnsion o h prvious poin, as a parial ransiion is sufficin, h ransiion procss is much asir o implmn compard o ohr rform opions. As a rsul, h odds for such a rform ar favourabl. Espcially in Grmany, whr ruls for nonconribuory pnsion claims for mohrs (Erzihungszin) ar alrady in plac, h ransiion procss can b asily implmnd. 8 If h significanc of hs non-conribuory pnsion claims will b nhancd sp by sp whil conribuory pnsion claims ar a las hld consan, h ransiion procss will b paricularly smooh. Th dcras in conribuory pnsion nilmns will auomaically forc housholds wih only on child or wihou childrn o sav individually. By combining h CPAYGO wih priva savings counris will obain a pnsion sysm ha is susainabl and indpndn of dmographic dvlopmns. As h pak of dmographic crisis is alrady in sigh, howvr, h firs sp owards a nw pnsion sysm should b mad righ now. Finally, on could ask whhr i would b mor usful o gran h child-rlad pnsion whil parns acually rais childrn. For insanc, liuidiy consrains of parns could back h prfrnc for child allowancs. Alhough his discussion shall no b h opic of his papr a las wo argumns can b pu forward for rsricing h bnfi o h rirmn ag. Firsly, in h ral world h avrag fuur incom of childrn, and hus h avrag conribuion, is difficul o sima. Hnc, i is vn mor difficul o achiv opimaliy. Nvrhlss, his would no b h main caus. Scondly and mor imporan, vn wih a CPAYGO in plac h dominanc of unfundd pnsion sysms has o b rducd. Whn child rlad pnsions ar paid ou as child allowancs whil parns ar young, hy will solly rciv an old-ag pnsion ha corrsponds o hir invsmns in h ualiy of childrn. As a consunc, h rplacmn ra would b rlaivly low so ha a pnsion abov h minimum living sandard could no b guarand. Thn vn parns hav o b obligd o sav individually in ordr o prvn fr-riding. As on can s, h child-rlad pnsion nilmn disburdns parns from mandaory saving which in urn has h sam ffc as an addiional ransfr whil bing young. To sum up, only whn h minimum sandard of living is guarand an unimly provision of h child-rlad pnsion is an opion. For insanc, on could allow parns wih mor han wo childrn o op for a child allowanc for ach addiional child insad of an addiional pnsion nilmn. F. Conclusion This papr dal wih h inrplay of friliy dcisions and diffrn yps of pay-as-you-go sysms. Thrby, spcially h possibiliy of undsirabl subsiuion ffcs accompanying 8 Currnly h pnsion nilmns according o h gnraiv conribuion ar only of minor imporanc. S for xampl Hnman and Voigländr (2004). 13

14 h inroducion of a CPAYGO has bn xamind. As i urnd ou, a subsiuion ffc is inviabl bu opimal providd ha a public ducaion sysm is in plac. By acing simulanously on boh variabls, uaniy and ualiy of childrn, infficincy can b prvnd. Thrfor, hs wo insiuions idally supplmn ach ohr so ha hy can b calld a prfc marriag. In addiion, on major objcion agains h inroducion of a CPAYGO, h far of an undsirabl subsiuion ffc, can b rjcd. Of cours, furhr rsarch, horical as wll as mpirical, would b bnficial. Th prsnd modl could b xndd in many dircions. For xampl, mor yps of pnsion sysms or a diffrn insiuional framwork could b considrd. On h mpirical sid, h rurn on xpndiurs on ualiy should b simad in ordr o gran pnsions adualy. For forhcoming pnsion rforms h prsnd rsul is, nonhlss, rally promising. In mos wsrn counris a sysm of public ducaion is in plac so ha h ransiion of h PAYGO sysm ino a CPAYGO is wlfar nhancing. In addiion, as only a parial ransiion is ncssary, h odds for such a rform ar favourabl compard o ohr rform opions. Howvr, h prruisi for such a rform would b ha h imporanc of child-rlad bnfis for unfundd pnsions sysms is rckond by acadmics as wll as poliicians. Rfrncs Bckr, Gary S. (1960), An conomic analysis of friliy, in: Coal, A. J. (d.), Dmographic and Economic Chang in Dvloping Counris, Princon Univrsiy Prss, Princon (NJ) Bckr, Gary S. and H. Grgg. Lwis (1973), On h Inracion bwn h Quaniy and Qualiy of Childrn, Journal of Poliical Economy 81, Bckr, Gary S. (1991) A rais on h family (nlargd diion), Cambridg, Mass. Bnal, Bnjamin (1989), Th old-ag scuriy hypohsis and opimal populaion growh, Journal of Populaion Economics 1, Browning, Edgar K. (1975) Why h social insuranc is oo larg in a dmocracy, Economic Inuiry 13, Cigno, Alssandro (1993), Inrgnraional ransfrs wihou alruism. Family, mark and sa, Europan Journal of Poliical Economy 9,

15 Cigno, Alssandro and Furio C. Rosai (1996), Joinly drmind saving and friliy bhaviour: Thory and simas for Grmany, Ialy, UK and USA, Europan Economic Rviw 40, Cigno, Alssandro; Casolaro, Luca and Furio C. Rosai (2003), Th Impac of Social Scuriy on Saving and Friliy in Grmany, Finanzarchiv 59, Ehrlich, Isaac and Francis T. Lui (1998), Social scuriy, h family, and conomic growh, Economic Inuiry, 36, Eurosa (2004), Firs dmographic simas for 2003, Populaion and Social Condiions, Thm 3 1/2004 Fldsin, Marin (1996), Th missing pic in policy analysis: Social scuriy rform, Amrican Economic Rviw 86, 1-14 Folbr, Nancy (1994), Childrn as public goods, Amrican Economic Rviw 84, Hnman, Barbara und Michal Voigländr (2004), Unzurichnd Brücksichigung dr Kindrrzihung als Ursach dr Rnnkris, Wirschafsdins 84, Homann, Karl and Ingo Pis (1996), Sozialpoliik für dn Mark: Thorisch Prspkivn konsiuionllr Ökonomik, in: Pis, Ingo. and Marin Lschk (ds.), Jams Buchanans konsiuionll Ökonomik, Tübingn Kolmar, Marin (1997), Inrgnraional rdisribuion in a small opn conomy wih ndognous friliy, Journal of Populaion Economics 10, Kommission für di Nachhaligki in dr Finanzirung dr Sozialn Sichrungssysm (2003), Abschlussbrich, Bundsminisrium für Gsundhi und Sozial Sichrung, Brlin Mron, Robr C. (1984) On h rol of social scuriy as a mans for fficin risk-baring in an conomy whr human capial is no radabl, in: Bodi, Zvi and John B. Shovn (ds.), Financial Aspcs of h U.S. Pnsion Sysm, Prinz, Aloys (1990), Endognous friliy, alruisic bhaviour across gnraions, and social scuriy sysms, Journal of Populaion Economics 3, Razin, Assaf and Efraim Sadka (1995), Populaion Economics, Cambridg, Mass. Sinn, Hans-Wrnr (2000), Pnsion rform and dmographic crisis. Why a fundd sysm is 15

16 ndd and why i is no ndd, Inrnaional Tax and Public Financ 7, Wrding, Marin (2001), Child-rlad bnfis hroughou h family lif-cycl: Lssons from h cas of Grmany, Ifo-Sudin 47, Wissnschaflichr Bira für Familinfragn (2002): Grchigki für Familin. Zur Bgründung und Wirnwicklung ds Familinlasn- und Familinlisungsausglichs, Bundsminisrium für Famili, Sniorn, Fraun und Jugnd, Brlin 16