PAYG pensions, public education and growth

Transcription

1 PAYG pesios, puli eduaio ad groh Mihael Kagaovih * ad Volker Meier Asra: We osider a small ope eoomy i hih people voe o he size of puli eduaio. I is sho ha groh ad elfare a e ehaed y he iroduio of pay-as-you-go pesios eve if he groh rae of aggregae ages falls shor of he ieres rae. The reaso lies i he fa ha idividuals parially ake io aou posiive exeraliies of puli eduaio hrough is impa o heir o pesio. Keyords: Pay-as-you-go pesios; puli eduaio; groh; exeraliies JEL lassifiaio: D 90, H 23, H55, I28 * Deparme of Eoomis, Idiaa Uiversiy, Wylie Hall, Bloomigo, IN 47405, USA, E- mail: mkagaov@idiaa.edu Ifo Isiue for Eoomi esearh, Poshigersr. 5, D-8679 Muih, Germay, meier@ifo.de

2 . Iroduio Puli pay-as-you-go (PAYG) pesio shemes i hih pesios are fiaed y urre oriuios of orkers have ofe ee riiized as eig derimeal for groh (Feldsei, 974). Capial aumulaio is redued sie oh he puli pesio ad he oriuio o he pesio sheme ill rig do savigs. Ad ulike he siuaio i a fuded pesio sheme, he missig savigs o he persoal level are o replaed y savigs ihi he pesio sheme. Moreover, he implii rae of reur o oriuios o a PAYG sheme ypially falls shor of he ieres rae. As a osequee, iome per apia ill e redued afer he iroduio of a PAYG pesio sheme. This argume, hoever, fails o ake oie of he impas orkig i he opposie direio hrough puli eduaio. Primary ad seodary eduaio is oadays o a overhelmigly large exe pulily fiaed i all OECD ouries, ad uiversiies also reeive los of fuds from puli soures. If a PAYG pesio sheme is irodued, voers ill ake io aou he posiive impa of maroeoomi huma apial aumulaio o heir pesios he voig o he size of he eduaio ax. Wage iome groh arisig hrough huma apial aumulaio may more ha offse groh gaps due o missig physial apial aumulaio. This seems pariularly likely i a orld of iegraed apial markes, here apial ouflos redue he impa of apial aumulaio o faor pries susaially. To illusrae his argume i is simples form, e aalyze a small ope eoomy i hih savigs do o a all affe he ieres rae. We demosrae for he ehmark seig of homogeous households ha age groh ill e sroger uder a PAYG sheme. This is also rue he lifeime iome per apia is redued due o a loer reur o PAYG oriuios relaive o he ieres rae. As lifeime iome gros a he same rae as ages, i ill exeed he orrespodig value uder a fuded sheme afer a fiie umer of periods. Furher, eve uder he PAYG sheme, puli eduaio may remai elo he effiie level. We proeed y osiderig more realisi searios ih a ueve disriuio of iome. As he iome of he media voer falls shor of mea iome, his hildre are susidized hrough puli eduaio. A he same ime, he loer iome redues he demad for eduaio. Wih logarihmi preferees, he ax prie effe ad he iome effe offse eah oher. Havig a PAYG sheme ih a defied oriuio rae ireases he demad for eduaio. O op of ha, he media voer may eefi hrough

3 a puli pesio sheme if is redisriuive. This pesio susidizaio effe a idue him o voe for eve more puli eduaio. The lieraure has maily deal ih groh impas of PAYG shemes ih privae eduaio. Oe srad of researh is oered ih he impa of pesio formulas o huma apial formaio here eduaio is fiaed ihou iergeeraioal rasfers. Kemiz ad Wigger (2000) sress ha PAYG pesios a irease groh ad elfare he he pesio of a idividual rises oh ih his ork iome ad his ime spe o huma apial aumulaio. By providig addiioal ieives for huma apial formaio, posiive iergeeraioal exeraliies i he huma apial aumulaio proess ill e ake io aou. Doquier ad Paddiso (2003) fous o aleraive pesio formulas ad sho ha a Beveridgea fla pesio sheme disourages ivesme i huma apial, hereas Bismarkia oriuio-relaed formulas ased oly o a parial earigs hisory se he sroges ieives. For eviromes i hih pares fiae he eduaio of heir hildre, i has ee argued repeaedly ha posiive groh effes of iroduig PAYG shemes a e expeed oly hrough overomig liquidiy osrais (Kagaovih ad Zilha, 999; Lamreh e al., 2005). I a loyig model of a represeaive demoray Kemiz (2000) already oies ha orkers may ake a ieres i promoig puli eduaio due o is impa o pesios. His mai fous lies o he impas of hagig moraliy ad feriliy, hoever. Aoher srad of he lieraure is oered ih ormaive aspes of likig puli eduaio ad PAYG shemes. Oe effiiey argume for providig shoolig pulily lies i he impossiiliy o efore rasfer paymes y hildre i exhage for fiaig eduaio ihi he family (Si, 2004). Bu if alruism oard he youg is eak, he level of puli eduaio may e hose here he margial reur o ivesme i huma apial exeeds he ieres rae. I suh a siuaio, PAYG pesios ill ehae effiiey y foserig huma apial aumulaio. agel (2003) sudies a iergeeraioal ora ih puli eduaio ad PAYG pesios o resore effiiey. Boldri ad Moes (2005) argue ha hese o pars of goverme ierveio a e used o replae he missig marke for fiaig ivesme i huma apial i a effiie fashio. The oriuio mos losely relaed o ours is Kagaovih ad Zilha (2007). I a losed eoomy seig ih voig o puli eduaio i urs ou ha egaive groh effes of iroduig are PAYG sheme via a reduio i physial apial aumula- 2

4 io ill geerally oueigh posiive groh effes via a aeleraio of huma apial aumulaio. The prese oriuio shos ha his resul may e ured aroud he e allo for ieraioal moiliy of apial. 2. The asi model We osider a overlappig geeraios eoomy i hih eah idividual lives for he hree periods hildhood, orkig age, ad reireme. I his firs period of life -, every idividual reeives puli eduaio e, he volume eig hose y he pare geeraio. Eduaio yields a huma apial edome h i i he ex period, he orkig age. The produio ehology of huma apial is desried y σ ( σ h h e ), () i i ih 0 < σ <, here hi is he pare s huma apial, expressig ha huma apial aumulaio akes plae oh a shool ad i he family. Durig orkig age, every idividual ielasially supplies her huma apial, here oal age iome is i hiw, ih W deoig he age relaed o a effiiey ui of laor. Every idividual has hildre, eig or a he egiig of he orkig age period. The oriuio o he puli pesio sheme is i, ih he oriuio rae eig fixed, ad he payroll ax rae for fiaig shools is θ. Ne iome is divided io orkig age osumpio i ad savigs s i y : y i ( ) i si θ (2) I her las period, he old age, he idividual osumes o i, eig equal o he sum of he puli pesio π ad savigs iludig ieres, here he ieres faor is. o i π i si (3) Preferees are represeed y a uiliy fuio U (,, e) eig srily ireasig ad srily oave i all argumes, here he hird argume is eduaio of he hil- y o 3

5 dre of he idividual. Pares are alruisi oard heir hildre, here havig he level of puli eduaio as a eleme of he uiliy fuio may e ierpreed as joy of givig. For derivig more speifi resuls, e use a example ih addiivelyseparale logarihmi uiliy, y o y o U (,, e) l l l e, (4) ih,, > 0. Savigs are deermied y he firs-order odiio U U 0. 2 Assumig ha expediures o eduaio are fiaed y a proporioal payroll ax, he shool udge equaio is give y e θ, (5) here is he average age i he pare geeraio. Whe voig, eah idividual hooses her preferred eduaio ax rae θ. For simpliiy, he urrely old do o voe. This assumpio is jusified y reallig ha hey are o affeed y he deisio o he eduaio ax. The puli pesio sheme a eiher osis of a fuded sysem ih a pesio formula f i π, (6a) i or of a pay-as-you go sheme, here e a disiguish eee a oriuio-relaed pesio i ( ) π / (6) i ad a fla sheme ih a lump-sum pesio l i π. (6) We osider a small ope eoomy seig i hih he faor pries ad W are deermied i he orld marke. For simpliiy, hese pries are saioary. 4

6 3. Homogeous populaio As a ehmark seario e aalyze he ase i hih all idividuals ihi a geeraio are ideial. The o PAYG shemes are ideial i his siuaio. Movig from a fuded pesio sysem o a PAYG sheme raises age groh. The PAYG sheme is irodued y makig he old geeraio a prese, hih has o ee aiipaed y hem: Proposiio : Wih a homogeous populaio, he iroduio of a PAYG pesio sheme raises age groh if iome effes i he hoie of he eduaio ax a e egleed. Proof. Cosider a eoomy ih average age. The preferred eduaio ax rae is deermied y U e π e i i U 3 U 2 θ e θ 0. (7) π i Noie ha π i 0 uder a fuded sheme ad > 0 uder a PAYG sheme. e e If iome effes a e egleed, he sri oaviy of he uiliy fuio i θ esures ha he hose ax raes ill saisfy θ < θ. Cosequely, e have f e > e ad f >. f The iuiio ehid his resul is easily udersood. Whe a PAYG sheme is i plae, a addiioal moive o fiae puli eduaio apar from alruism oards hildre arises. Puli eduaio ireases average ages i he ex geeraio, ad he pesioers ill reeive some share of he age groh. Iroduig a PAYG sheme a redue or irease lifeime iome a a give eduaio ax, hih may affe he relaive sizes of margial uiliies. If he assoiaed iome effes o he eduaio ax are suffiiely small, he addiioal moive for ivesig i puli eduaio ill osiue he domiaig effe. Empirial esimaes of iome ad susiuio elasiiies sugges ha a Co-Douglas speifiaio of he uiliy fuio is a reasoale approximaio (Gradsei e al., 2005, h. 4), implyig ha he preferred eduaio ax varies lile aross iomes. 5

7 The resulig ieremporal alloaio is o effiie if h e W > holds a he margi. Whe he margial produ of puli eduaio exeeds he margial produ of apial, a iergeeraioal Pareo improveme a e ahieved y ivesig more i puli eduaio raher ha i physial apial, here he goverme de a e repaid y axig he aive geeraio i he ex period. A ovious quesio is hy he goverme does o pursue suh a poliy ayay. I real orld eoomies, may govermes eig resposile o fiae puli eduaio fae de osrais. These osrais are geerally less igh oly if ivesme i puli physial apial is fiaed. h The ehologially effiie level of eduaio saisfies W. If oras ih e miors ould e efored, pares ould simply rasfer he eessary amou o fiae he effiie level amou of eduaio. The hildre ould repay heir de ih ieres i he ex period. Alruisi pares ould he add some addiioal rasfer i erms of physial apial or he oupu good, hih ould e made eiher ier vivos or as a eques. Therefore, if pares are idiffere eee givig he same amou of moey as eduaio or i ash, overivesme i eduaio ao our. Sie he alruisi moive may ell e oo eak o esure a suffiiely high level of puli eduaio, he PAYG sheme a a as a devie o ehae elfare y promoig ivesme i huma apial. 4. Heerogeeous populaio Whe osiderig he example of a Co-Douglas ype logarihmi uiliy fuio, he resulig osumpio levels are y i o i ( θ ) π i i ( θ ). i i π, (8) The preferred eduaio ax a e rie as 6

8 7 ( ) ( ). * π π θ i i i i i e e (9) While θ geerally also deermies e ad i π, i a easily e heked ha a uique soluio saisfyig (9) alays exiss. Wih a fuded pesio sheme, here is a uaimous voe, resulig i a ax rae. θ f (0) The uaimiy voe is a osequee of he speifiaio of he uiliy fuio. eplaig he Co-Douglas speifiaio y a more geeral CES form ould allo for preferred ax raes dereasig or ireasig i he age, depedig o he elasiiy of susiuio eee o osumpio ad eduaio (Gradsei e al. (2005), h. 4). Proposiio 2: Wih a give pesio oriuio rae, a skeed iome disriuio ad logarihmi preferees, he eduaio ax ad he age groh rae uder a fla PAYG pesio sheme are higher ha uder a oriuio-relaed PAYG sheme. Proof. If e have a oriuio-relaed PAYG pesio sheme, he hose eduaio ax rae is agai idepede of iome, saisfyig ( ) ( ). ) ( σ θ () Wih a fla pesio sheme, here are idividualized preferred eduaio ax raes equal o ( ) ( ), ) ( * σ θ i i i (2)

9 hih derease i age iome i. As he preferees of he idividuals are siglepeaked, he media voer heorem applies. Wih a skeed iome disriuio, mea * iome exeeds media iome. Sie θ i ( ) θ holds, he hose eduaio ax rae uder a fla pesio sheme exeeds he orrespodig ax rae uder a oriuiorelaed sheme. The groh faor of average huma apial is h h θw σ (3) As he groh rae rises ih he ivesme rae i puli eduaio, age groh ill e permaely faser ih a fla PAYG sheme ha ih a oriuio-relaed PAYG sheme. Hee, sarig a a give iome disriuio ad a fixed oriuio rae, age groh ill e faser ih a pesio sysem ha redisriues ihi a geeraio. The media voer ops for a eve higher eduaio ax ha uder he oriuio-relaed sheme eause her addiioal pesio is higher. This resul sads i oras o Kemiz ad Wigger (2000) ad Doquier ad Paddiso (2003) ho sho ha oriuio-relaed PAYG pesios offer a sroger ieive for privae eduaio. I our seig of puli eduaio, he media voer has a addiioal ieive ih fla pesios, as some reurs from puli huma apial ivesme are redisriued oards him. Ulike he ase of homogeous households, i ao e exluded ha his redisriuio idues overivesme i puli eduaio. Equaio (3) also implies ha age groh ill e permaely faser uder a PAYG sheme ha uder a fuded sheme. Hee, eve if lifeime iome is redued y a move o a PAYG sheme he he ieres rae exeeds he rae of groh of aggregae ages (a a give eduaio ax), iome per apia uder a PAYG sheme ill exeed he resulig levels uder a fuded sheme afer a fiie umer of periods. 8

10 5. Choie of pesio sheme The las osideraio idiaes ha a majoriy of voers may e illig o move from a fuded sheme o a PAYG sheme eve if his ould redue heir lifeime iome a a give eduaio ax. As hey foresee he assoiaed move o a higher eduaio ax, hey ake io aou he suseque higher pesio. Cosequely, a iergeeraioal Pareo improveme a e ahieved. This is summarized i Proposiio 3, dealig ih a move from a fuded sheme o a Bismarkia PAYG sheme. Proposiio 3: A uaimous voe i favor of a posiive PAYG ax eig expeed a he same size i he ex period a our eve if uder he fuded pesio sheme he ieres rae exeeds he groh rae of aggregae ages, ha is, if >. Proof. Curre pesioers alays prefer a posiive PAYG ax o a PAYG ax of zero due o a irease i old age osumpio. As ireases i he PAYG ax ill e assoiaed ih a higher level of puli eduaio, a voer i he orkig age ill suppor he move o a higher PAYG ax eig i plae also i he ex period if his expeed lifeime iome ireases. If a oriuio-relaed PAYG formula is i plae, lifeime iome of a idividual ih age i is give y I i i i ( θ ( ) ) θ ( ) i π i θ ( ) σ W (4) Ireasig he oriuio rae hages lifeime iome as follos: I i ( σ ) θ i i θ (5) Noie ha ih 0, he hose eduaio ax is θ ( σ ). For his I example, i urs ou ha i 0 a 0 ad θ. Moreover, as > 0 uder 9

11 I he PAYG sheme, i follos ha i > 0 for κ for almos ay κ > 0. Therefore, sarig a a siuaio ih ( ε for suffiiely small ε > 0, a 0, θ ( )) exiss for hih I, θ ( )) > I (0, (0)) holds. i ( i θ Whe he ieres rae is equal o he groh rae of he sum of ages uder a fuded pesio sheme ad alruism is egligile, a move oard a oriuio-relaed PAYG sheme ill e suppored y all voers. As he groh rae of ages ill irease ih he risig ivesme i puli eduaio, lifeime iome of eah idividual rises ih a ireasig PAYG ax. As a osequee, lifeime iome uder some posiive PAYG ax a exeed lifeime iome uder a fuded sheme eve if he margial impa of iroduig he PAYG ax o lifeime iome is egaive. If people a voe o oh he PAYG oriuio rae [ 0, ] ad he eduaio ax rae θ, a oudary soluio ih respe o he former ill geerally ur ou, ha is, voers ill eiher hoose 0 or. This resul oviously holds a a give eduaio ax ad arries over o he ase of eduaio axes ireasig i he soial seuriy oriuio rae. If i does make sese o have some posiive PAYG ax for a majoriy of voers, heir uiliy ill furher irease y exedig he sheme. Wih a ireasig ivesme rae i puli eduaio, he rae of reur o soial seuriy oriuio rises ih a ireasig oriuio rae. This resul is similar o Kolmar s (997) seig here people voe o he PAYG oriuio rae ad he share of pesios ha are paid aordig o he umer of hildre. Sie hese hild eefis irease ih he oriuio rae, drivig up feriliy ad he rae of reur o oriuios, voers ill hoose o se he PAYG ax eiher o zero or o he maximum level. I praie, a PAYG sheme ill e assoiaed ih a oriuio rae elo he maximum eause apial markes are imperfe. As idividuals are ypially uale o orro agais fuure pesio laims, hey ao apure he full eefis of exedig he PAYG sheme. 6. Colusios The idespread fear ha PAYG shemes harms groh due o a delie i physial apial formaio is halleged y our oriuio. If huma apial aumulaio is largely pulily fiaed, hih seems o e a valid desripio of he siuaio i OECD ouries, iroduig ad exedig PAYG pesio shemes have a posiive 0

12 effe o ages ad iome groh. Voers are illig o pay higher axes for fiaig puli eduaio oday as hey a reasoaly expe o reeive higher pesios omorro as a reur o heir ivesme. I his ay, PAYG pesios a e used o overome edeies oard uderivesme i puli eduaio. I oras o frameorks i hih he idividuals fiae heir o eduaio, a PAYG sheme ha redisriues from he rih o he poor may lead o a eve faser age groh. As he media voer eefis from redisriuio, ivesme i puli eduaio eds o e eve higher. The mai avea of he aalysis oviously lies i he assumed asee of egaive effes hrough a smaller level of physial apial aumulaio. Eve if eah eoomy uder osideraio is small ompared o he res of he orld, a symmeri poliy i all ouries ill have a egaive impa o physial apial formaio as predied y he losed eoomy model. Ad he egaive effes may e more prooued if redisriuio i he puli pesio sheme disourages privae savig.

13 eferees Boldri, M. ad Moes, A. (2005) The iergeeraioal sae: eduaio ad pesios. evie of Eoomi Sudies 62, Doquier, F. ad O. Paddiso (2003) Soial seuriy eefi rules, groh ad iequaliy. Joural of Maroeoomis 25, Feldsei, M. (974) Soial seuriy, idued reireme ad aggregae apial aumulaio. Joural of Poliial Eoomy 82, Gradsei, M., M. Jusma ad V. Meier (2005) The poliial eoomy of eduaio, MIT Press: Camridge MA ad Lodo. Kagaovih, M. ad I. Zilha (999) Eduaio, soial seuriy ad groh. Joural of Puli Eoomis 7, Kagaovih, M. ad I. Zilha (2007) Aleraive pesio sysems ad groh. Mimeo. Kemiz, A. (2000) Soial seuriy, puli eduaio, ad groh i a represeaive demoray. Joural of Populaio Eoomis 3, Kemiz, A. ad B. U. Wigger (2000) Groh ad soial seuriy: he role of huma apial. Europea Joural of Poliial Eoomy 6, Kolmar, M. (997) Iergeeraioal redisriuio i a small ope eoomy ih edogeous feriliy. Joural of Populaio Eoomis 9, Lamreh, S., P. Mihel ad J.-P. Vidal (2005) Puli pesios ad groh. Europea Eoomi evie 49, agel, A. (2003) Forard ad akard iergeeraioal goods: hy is soial seuriy good for he evirome? Ameria Eoomi evie 93, Si, H.-W. (2004) The pay-as-you-go sysem as a feriliy isurae ad eforeme devie. Joural of Puli Eoomis 88,