Coping with Spain s Aging: Retirement Rules and Incentives

Transcription

1 WP/07/22 Coping wih Spain Aging: eiremen ule and Incenive Mario Caalán, Jaime Guajardo, and Alexander W. Hoffmaier

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3 2007 Inernaional Moneary Fund WP/07/22 IMF Working Paper European Deparmen Coping wih Spain Aging: eiremen ule and Incenive Prepared by Mario Caalán, Jaime Guajardo, and Alexander Hoffmaier * Auhorized for diribuion by Jame Daniel May 2007 Abrac Thi Working Paper hould no be repored a repreening he view of he IMF. The view expreed in hi Working Paper are hoe of he auhor() and do no necearily repreen hoe of he IMF or IMF policy. Working Paper decribe reearch in progre by he auhor() and are publihed o elici commen and o furher debae. Thi paper evaluae he macroeconomic and welfare effec of exending he averaging period ued o calculae penion benefi in a pay-a-you-go yem. I alo examine he complemenariie beween reform exending he averaging period and hoe increaing he reiremen age under alernaive ax policie. The analyi i baed on a model in he Auerbach-Kolikoff radiion applied o he Spanih economy. Wihou reform, he imulaion ugge ha aging-relaed pending a a hare of oupu will increae 6 percenage poin by 2050, which are wice a much a in European Commiion (2006) projecion due o general equilibrium effec. Alo, reform exending he averaging period o he enire work life limi expendiure preure a he peak of he demographic hock a much a increaing he reiremen age in line wih life expecancy (4 percenage poin of GDP). Thee reform and prefunding he demographic hock miigae he advere macroeconomic effec of aging and improve welfare. JEL Claificaion Number: E, H2, and J22 Keyword: penion reform, dynamic general equilibrium model, and Spanih penion yem Auhor Addree: mcaalan@imf.org, jguajardo@imf.org, ahoffmaier@imf.org * We are graeful for ueful commen received on earlier verion of hi paper from eminar and conference paricipan a IMF Iniue (2007); NBE Summer Iniue (2006); John Hopkin Univeriy, SAIS (2006); Naional Univeriy of Tucumán, Argenina (2006); IMF European Deparmen (2004); and Spanih Miniry of Finance (2004).

4 2 Conen Page I. Inroducion...4 II. The Model...7 A. Model Overview...7 B. Houehold...8 C. Firm... D. The Governmen...2 E. Equilibrium...2 F. Balanced Growh Equilibrium and Calibraion...4 G. Houehold Labor, Conumpion, and Ae Holding in he Iniial Seady Sae...5 III. Baeline Simulaion...6 A. Demographic Traniion...6 B. Baeline Macroeconomic Scenario...7 IV. Simulaion of Penion eform...9 A. Effec of Penion eform in he Final Seady Sae...9 B. Effec of Penion eform in he Demographic Traniion...2 C. Effec of Tax-Smoohing Policie...25 D. Welfare Analyi...25 V. Concluion...27 Table. Variable Definiion and Noaion Fir Order Condiion Houehold Opimizaion Problem Balanced Growh Pah Calibraion of he Baeline Model (Iniial Seady Sae) Demographic Traniion: Model Time Line Decompoiion of he Change in Penion Expendiure ( ) Macroenomic Effec of Penion eform and Fical Policie During he Demographic Traniion Decompoiion of Penion Expendiure Increae Tax-a-you-go and Low Immigraion...43 Figure. Houehold' Ae Holding ( A ), Labor Effor ( n ), and Conumpion ( c ) Model Dependency aio Baeline and Penion eform Macroeconomic Scenario Tax-a-you-go and Low Immigraion Houehold' Ae Holding ( A ), Labor Effor ( n ), and Conumpion ( c ) Welfare and Macroeconomic Effec of Penion eform in he Final Seady Sae...48

5 3 6. Baeline and Penion eform Macroeconomic Scenario Tax-Smoohing and Low Immigraion Welfare Effec of Penion eform and Fical Policie Houehold' Ae Holding ( A ), Labor Effor ( n ), and Conumpion ( c )...5 Appendixe I. Value Funcion a eiremen...29 II. Calibraion Daa Source...33 III. Comparaive Saic in he Final Seady Sae...35 eference...36

6 4 I. INTODUCTION The andard view in he penion lieraure i ha pay-a-you-go (PAYG) yem dior labor marke incenive a reurn on penion conribuion are lower han hoe on oher form of aving (Samuelon (958)). Thu, parameric reform dicuion of PAYG yem focu prominenly on ighening he conribuion-benefi linkage, and hereby increaing acuarial fairne (Lindbeck and Peron (2003) and reference herein). In hi connecion, exending he averaging period of conribuion ued o calculae penion benefi ha received a fair amoun of aenion in he lieraure bu no in he conex of quaniaive aemen uing applied dynamic general equilibrium (DGE) model. Thi paper evaluae he macroeconomic and welfare effec of exending he averaging period of conribuion ued o calculae penion benefi in a PAYG yem. I alo examine he complemenariie beween reform exending he averaging period and hoe increaing he reiremen age under alernaive ax cenario. The evaluaion i baed on a DGE framework in he Auerbach-Kolikoff (987) radiion applied o he Spanih economy. Spain erve a a valuable cae udy due o i penion rule, ocial agreemen, and demographic profile. Fir, he Spanih public PAYG yem calculae penion benefi baed on average, inflaion-indexed, gro wage earning in he correponding averaging period. Moreover, reform implemened in 997 doubled he averaging period o he la 5 year of an individual work life wih he view of enhancing he conribuion-benefi linkage. Second, Spain reached a broad poliical and ocial conenu known a he Paco de Toledo on he need o preerve he public PAYG yem hrough reform geared o enuring i uainabiliy, including by improving he alignmen of benefi and conribuion; he Paco ruled ou privaizaion and reform oward compulory fully funded cheme. Third, even conidering Spain remarkable immigraion phenomenon, he demographic hock i expeced o be larger and hu poe a more ubanial challenge for long-run fical uainabiliy han elewhere in Europe. The imulaion of he baeline cenario highligh he fical challenge: penion expendiure increae a a hare of oupu by 6 percenage poin, and he conumpion ax rae rie by more han 30 percenage poin by Thee eimae reflec an unchanged reiremen age and averaging period, wih aging-relaed expendiure financed by conumpion ax rae adjumen (ax-a-you-go). The projeced fical preure reflec increae in he dependency raio and wage rae a labor become carcer and he effec of hee increae on individual penion benefi. Alo, penion expendiure preure are The Paco wa eablihed hrough a broad poliical agreemen raified by he Spanih Congre by virual unanimiy in April, 995 eeking o preerve he public PAYG naure of he old-age penion yem hrough parameric reform; labor union joined he call for reform a year laer. The Paco wa updaed in 2003 and coninue o re he need o align penion benefi and conribuion.

7 5 9 percenage poin and 3 percenage poin higher han hoe projeced, repecively, by he European Commiion (EC, 2006) and oja (2005). 2 Addreing he demographic hock hrough parameric reform o he PAYG yem deliver izeable macroeconomic and welfare benefi. Two penion reform cenario under ax-ayou-go policie highligh hee benefi. Fir, a parial penion reform cenario gradually increaing he reiremen age 3 and holding conan he averaging period aenuae expendiure preure and he needed increae in axe, while booing he aggregae capial ock and oupu. Thi reform will reduce he increae in penion expendiure a a hare of oupu by 4 percenage poin, and he conumpion ax rae increae by 7 percenage poin over he nex 40 year. Furhermore, i induce a bu-boom cycle in he aggregae labor upply: aggregae effecive labor decline over he nex wo decade, bu increae hereafer, reflecing grandfahering claue and houehold ineremporal labor ubiuion effec. Second, a full penion reform cenario ha in addiion exend gradually he averaging period o he enire work life will furher reduce he increae in penion expendiure a a hare of oupu by 4 percenage poin, and he conumpion ax rae increae by 7 percenage poin over he nex 40 year. Thu, exending he averaging period i a imporan in miigaing he aging-relaed pending and ax preure a increaing he reiremen age in The labor upply repone o he reform involve a rade-off: exending he averaging period increae houehold labor effor, paricularly a high-kill age by removing ineremporal diorion, bu i dicourage labor effor by reducing penion benefi a real wage driven by echnological progre increae over ime. The analyi illurae ha, in conra o increaing he reiremen age, exending he averaging period condiional on raiing he reiremen age rigger a boom-bu cycle in aggregae effecive labor, making i carcer a he demographic orm inenifie. Overall, boh reform deliver ignifican welfare gain. Thee gain arie from he lower and flaer pah of conumpion ax rae, which reduce diorion in houehold conumpionaving deciion, and he exenion of he averaging period, which remove labor marke diorion. 2 Along wih oher general equilibrium effec, he effec of riing wage rae on individual penion benefi accoun o a large exen for he difference beween hi paper imulaed penion expendiure preure and he correponding EC projecion. In he baeline cenario dicued below, individual penion benefi rie faer han oupu per capia a he peak of he demographic hock. In conra, he EC projecion aume ha individual penion benefi rie in line wih oupu per capia. 3 Specifically, he reiremen age of generaion reiring in he 2050 increae by wo year, and for laer generaion, i increae wo year every decade up o a maximum increae of eigh year. On average, he reiremen age in he populaion increae in line wih life expecancy during he demographic raniion.

8 6 Prefunding he fical impac of he demographic hock, in eiher penion reform cenario, by ax moohing a once-and-for-all increae in he conumpion ax rae in 2008 can furher aenuae he advere macroeconomic effec in he demographic raniion. However, prefunding hif he ax burden from generaion ha are acive when he dependency raio peak o curren and fuure generaion. The combined effec of penion reform and prefunding creae ne welfare loe for ome curren generaion and ne gain for all fuure generaion (relaive o he baeline cenario). Thu, addiional compenaing mechanim are needed o enure a Pareo improving package of reform. Thee may include delaying he increae in he conumpion ax rae or argeing ranfer o ne loer financed wih deb. The imulaion alo reveal wo broader implicaion of exending he averaging period. Fir, exending he averaging period limi he increae in individual penion benefi a he peak of he demographic raniion when wage rae rie faer more han in he long run. 4 In oher word, wih a ax-a-you-go policy, he exenion conribuion o limi ax rae increae varie over ime. Second, in he long run, exending he averaging period o he enire work life reul in he highe welfare gain when echnological progre i high. Wih no echnological progre, long-run welfare gain are large when he averaging period i horer han he enire work life. While hi paper i more comprehenive in aeing he effec of exending he averaging period, previou paper have alo udied hee effec. Diamond (200) dicued he labor marke diorion ariing from he hor averaging period and advocaed exending i o he enire work life bu did no quanify hi reform. Wihou employing a DGE approach, Jimeno (2000 and 2003) concluded ha exending he averaging period reul in penion expendiure reducion beween and 2 percenage poin of oupu, ignificanly maller han hoe repored in hi paper. Uing DGE approache, Sánchez Marín (200) found ha exending he averaging period reduce penion expendiure a a hare of oupu by abou.8 percenage poin by 2050, while Díaz-Saavedra (2005) aee hoe reducion o amoun o 2.5 percenage poin. In he laer, however, he (endogenou) reiremen age decreae when he averaging period i exended, and hu, hoe reul are no comparable o hoe dicued below. The re of he paper i organized a follow. Secion II dicue he model and i calibraion. Secion III dicue he baeline reul. Secion IV aee he effec of penion reform. Secion V conclude. 4 A he peak of he demographic raniion, exending he averaging period accoun for half of he ax rae reducion obained from a full penion reform in Spain. In he long run, however, exending he averaging period accoun for a enh of he ax rae reducion.

9 7 II. THE MODEL A. Model Overview The model follow he Auerbach-Kolikoff radiion. 5 The (cloed) economy i populaed by overlapping generaion of finiely lived houehold, aomiic firm, and an infiniely lived governmen. Houehold conume and accumulae ae during heir lifeime, work during heir youh, and reire when old. Firm produce he ingle good in he model uing labor and capial, and he governmen collec income, conumpion and payroll axe o finance governmen expendiure and penion benefi, and redeem he iniial governmen deb. Alhough he general equilibrium rucure i andard, he model incorporae pecific feaure of he Spanih penion yem. In paricular, i incorporae a ylized verion of he Spanih penion rule whereby he old-age benefi i calculaed baed on average gro wage earning in he correponding averaging period; in he baeline cenario below, he averaging period i he la 5 year of he individual work life. 6 In addiion, o capure he effec on houehold behavior of demographic aging and penion reform, he model include he following elemen. Houehold reire a an exogenouly given age, bu labor upply i endogenou a houehold chooe he amoun of labor and leiure ime during heir work life. Houehold labor kill (produciviy) vary exogenouly wih age o accoun for he oberved hump-hape in wage rae over year of employmen. Labor-augmening produciviy growh caue real wage growh over ime, hu allowing he model o capure he rade-off noed above: exending he averaging period dicourage labor effor by reducing average wage earning and penion benefi, bu i encourage labor effor by eliminaing ineremporal diorion, paricularly when kill are high. Life expecancy i exogenou bu increae over ime o mach demographic projecion. Finally, he model explicily accoun for he effec of populaion aging on public healh-relaed expendiure. Thee feaure allow he model o meaningfully quanify he effec of reforming he penion rule on labor marke incenive and macroeconomic oucome, including complemenariie wih alernaive ax policie o finance old-age relaed pending. The model i preened in aionary form and, for he reader convenience, i noaion i ummarized in Table. 5 A urvey of he lieraure exending back o Auerbach and Kolikoff (987) can be found in Kolikoff (2000). The numerical oluion mehod involved are decribed in Heer and Maußner (2005), and Judd (999). 6 The model i real, ha i, money and inflaion play no explici role. Thi i conien wih he paper focu on he long-erm effec of aging. Alo, he inflaion indexaion of penion conribuion and benefi implie ha inflaion i neural wih repec o he penion yem.

10 8 B. Houehold The lifeime uiliy of a houehold born a ime i deermined by i lifeime conumpion (c) and leiure (l), and i given by T+ T = β + = { + γ + } U log( c ) log( l ), () where he houehold life i characerized by wo diinc phae: a work life laing T period or year ( =,..., T ) and a mandaory reiremen laing T year ( = T +,..., T + T ). Noe ha he model allow he houehold life expecancy and reiremen age o vary acro generaion, and henceforh, hee are aumed o be nondecreaing over ime. The houehold i endowed wih a fixed number of hour per year, which i normalized o ha work (n) and leiure (l) add up o one: n =,..., T + + = = T +,... T + T l. (2) A houehold accumulae ae (A) during i work life according o he following budge conrain: ( + ξ) A = [ + r ( τ )] A + ( τ τ ) W e n ( + τ ) c, (3) + I I c where nex year ae are deermined by adding o hi year ae he houehold aving, which are obained by adding ne reurn on ae o ne wage income and ubracing gro conumpion. A noed above, he houehold labor produciviy per hour varie wih age according o a kill premium ( e ). The premium i defined a he relaive produciviy of an -year old houehold o ha of a one-year old (unkilled) houehold; he laer i normalized o, and hu, W denoe he wage per uni of labor ime of an unkilled worker. In equaion (3), he houehold ake a given he payroll (τ), income (τ I ), and conumpion (τ c ) ax rae, and he inere (r) and wage (W) rae. 7 7 Income axe are levied on labor income and ae earning; for impliciy, hee ax rae are aumed o be he ame.

11 9 During reiremen, he houehold wage income i replaced by an old-age penion (b) in he budge conrain, a follow: T + b + I + T c ( + ξ) A+ = [ + r+ ( τ+ )] A+ + ( + τ ) c. T + + ( + ξ ) (4) Noe ha he old-age penion for a houehold born a ime and reiring a ime expreed a follow: + T can be W b e n, (5) T T + + j j j + T = ψ T j μ j + j T ( ) μ ξ + = + + where he average (gro) wage in he averaging period (covering he la µ year before reiremen) i caled down by he replacemen raio (ψ). 8 Noe ha penion benefi and real wage earning are dicouned by labor augmening produciviy growh (ξ ) in he aionary-ranformed equaion (4) and (5). Thi dicouning reflec he fac ha he houehold penion benefi (equaion (4)) and he pa nominal wage earning ued o compue he iniial penion benefi (equaion (5)) are adjued by inflaion, bu no by produciviy growh. 9 The model aume ha here are no inergeneraional beque or inheriance: he houehold i born (ener he labor force) wih zero ae a age =, and die wihou ae a age = T + T +, T T = = 0. (6) A A + + The houehold problem i o chooe he pah of conumpion, leiure and ae holding { c+, l+, A+ } T+ T = o maximize i lifeime uiliy () ubjec o conrain (2) (6). 8 The penion benefi formula, before applying aionary ranformaion i given by: ˆ b W e n T T + ˆ j j + T = ψ j j μ + + j= T + μ real erm hroughou reiremen, ha i bˆ. Noe ha he penion benefi, once deermined, remain conan in = bˆ for = T + 2,..., T + T. T + + T + 9 Conien wih he majoriy of old-age penion in Spain, penion are aken a no axed.

12 0 The houehold problem can be expreed a a equence of wo dynamic opimizaion problem, a follow: { } T T+ T+ Max β log( c ) log( ) (, ) T + + γ l+ + β V A+ T b + T + { c+, l+, A+ } = = T ubjec o (2), (3), (5) and (6). T+ T+ where V( A+ T, b ) + T i he houehold value funcion or dicouned indirec uiliy when i reire a ime + T having reached he age of T + year. Upon reiremen, he houehold opimizaion problem can be expreed recurively, and a cloed-form oluion for he value funcion (V ) follow from he log uiliy aumpion. 0 Two e of condiion olve he houehold problem under andard dynamic opimizaion echnique; Table 2 conain boh e of fir order condiion where V A(.) and V b(.) denoe T he parial derivaive of V (.) wih repec o A + T + T and b + + T. The fir e equaion (7), (9) and () refer o a houehold conumpion-leiure choice a pecific age (inraemporal fir order condiion). In each period, he houehold equae he marginal uiliy of conumpion (caled by wage) o he marginal uiliy of leiure. The econd e equaion (8), (0), (2) and (3) govern he houehold conumpion-aving deciion over ime (ineremporal fir order condiion or Euler equaion). In hi cae, houehold equae he marginal uiliy of curren conumpion o he dicouned marginal uiliy of fuure conumpion (caled by he ne reurn on aving). Thee equaion reflec he peculiariie of he Spanih penion rule averaging period and inflaion indexaion of conribuion and benefi and wheher a houehold i working or reired. Specifically, while he houehold i in he labor force he penion rule inroduce hree ubperiod in he houehold opimizaion problem. The fir comprie he iniial year in he labor force prior o he averaging period (µ) ( =,..., T μ), when he houehold annual wage earning do no affec i fuure penion benefi. The econd correpond o he fir µ- year of he averaging period ( = T μ+,..., T, ) when he conumpion-leiure choice 0 Noe ha he houehold value funcion V (.) depend no only on i ock of ae a reiremen ( T b + T T A + + T) and i fuure annual penion benefi ( + ) bu alo on fuure inere rae and income ax rae. A deailed derivaion of he value funcion (V ) can be found in Appendix I. When he houehold reire, i face only he iner-emporal fir order condiion a i no longer upplie labor.

13 (inraemporal fir-order condiion) alo reflec he fac ha wage earning accrued in hi ubperiod provide addiional uiliy during reiremen becaue of heir effec on he penion benefi; 2 however, he conumpion-aving deciion remain unchanged. In he final year of he averaging period ( = T ), he conumpion-aving deciion reflec, nonehele, he reiremen of he individual in he following period ( V A ). When he houehold reire ( = T+,..., T+ T ), however, here i no labor upply choice and only he conumpion-aving deciion remain. 3 h h h Aggregae houehold conumpion ( C ), effecive labor upply ( N ), and ae ( A ) are obained by aggregaing individual houehold variable a each poin in ime, a follow: 4 T T+ T T+ T h P h P h P = = = = P = P = P N e n, A A, C c. C. Firm f Firm maximize a (aionary-ranformed) profi funcion ne of capial depreciaion Π. They do o ubjec o a conan-reurn-o-cale Cobb-Dougla producion funcion wih labor-augmening echnological progre, α ( ) ( ) α K N ( r δ ) K W N, Π =Ζ + f f f f f where δ i he rae of capial depreciaion. Boh oupu and facor marke are perfecly compeiive, and herefore, individual firm face given wage ( W ) and renal rae ( r ). The 2 All ele equal, he houehold increae he upply of labor during he reference period becaue of hi added benefi o work. 3 The analyi ar wih a full e of generaion, T0 + T, a ime = 0. Thu, during he fir 0 T0 + T year 0 a number of runcaed opimizaion problem are aociaed wih hoe houehold of age = 2,..., T0 + T0 ha were born before = 0. Noe ha we are auming ha all runcaed generaion have he ame work life and reiremen period. 4 h Noe he conra beween he definiion of he aggregae effecive labor upply ( N ) and he aggregae labor effor. The aggregae effecive labor upply i he um of he ime devoed o work by all he generaion in he labor force in a given year, where each generaion working ime i weighed by i kill and populaion ize. By conra, he aggregae labor effor ( n h ) i he weighed (by populaion ize) um of he ime devoed T o work by all generaion in he labor force, wihou accouning for kill difference: h P n = n. P =

14 2 fir order condiion require ha labor and capial: W and r + δ equal, repecively, he marginal produc of W α ( α) f f K K =Ζ ( α), r δ α. + =Ζ N N D. The Governmen The governmen e axe o enure long-run fical uainabiliy. A noed before, he governmen collec payroll, income, and conumpion axe from houehold. Tax revenue are ued o finance public conumpion (G), penion benefi, and redeem governmen deb (D). Public conumpion ha wo componen: healh-relaed public conumpion which i driven by change in he populaion age rucure (ee Appendix II for deail); and non healh-relaed public conumpion which remain conan a a hare of aggregae oupu. Thu, he governmen budge conrain i a follow: 5 P D r D G r A W N C + I h h c h + ( + ξ) = ( + ) + [ τ ( + ) τ ] P b + T + T T + + T + P h τ T W N = T ( ξ ) P + +, where he (nonocial ecuriy) primary defici (erm in bracke), and he ocial ecuriy defici (la wo erm) are hown eparaely. E. Equilibrium An equilibrium imulaneouly place all houehold and firm on heir maximizing pah, eablihe he olvency of he governmen, and clear marke. Conider an iniial 5 The budge conrain, before aionary ranformaion, i given by h h h h I c D + = ( + r) D + [ G τ ( r A + W N ) τ C ] + b P τ W N. Noice ha he (aionary-ranformed) old-age penion for a houehold born a ime T and reiring a ime i given by W T T + T + j j = n T T j + j + μ j= T ( ) + μ + ξ b ψ T + T = T + T. Uing he equaliy b = b + + T + for,..., = T + T + T, i can be T b + b+ T + hown ha =. The dicoun of he aionary-ranformed penion benefi by produciviy T ( + ξ) ( + ξ) growh reflec he fac ha nominal benefi are adjued only by inflaion.

15 3 populaion of ize 0 { } P wih work live { } = D0 0, capial ock 0 0 T0+ T0 h P = 0 = 0 = 0 D K A A P P wih age rucure { P } T + T = T and life expecancie = { T T } = K >, and diribuion of ae { A } 0 0 houehold born during he period of analyi ( 0 ),, a given equence of newborn cohor +, iniial governmen deb 0 T + T =, uch ha. The equilibrium i a collecion of lifeime plan for boh, + { c +, l+, A+ } T+ T =, for = 0,,...,, and hoe born before hen ( < 0 ) houehold of age 2 hrough T0 + T0 a = 0 ha face runcaed lifeime plan + T {,, } 0 + T c l A 0, for = 2,..., T 0 + T, 0 + = f f a equence of allocaion for he firm { K, N } = 0 and capial { } 0, a equence of relaive price of labor W, r, and a equence of governmen policy variable including payroll, = income, and conumpion ax rae, and governmen conumpion and deb, {, I c τ τ, τ, G, D} = 0, uch ha: f f he equence of allocaion { K, N } = 0 olve he firm opimizaion problem; he lifeime plan for houehold born during he period of analyi + { c +, l+, A+ } T+ T =, for 0, olve heir opimizaion problem; and he lifeime plan for houehold of age = 2,..., T0 + T a ime 0 0 heir runcaed opimizaion problem; he governmen budge conrain i aified for 0 ; T + T c, l, A olve + = { } = f h he labor marke clear, N = N = N, for 0 ; he ae marke clear, f h A = D + K = A, for 0 ; and he oupu marke clear,

16 4 P K + = + K + Y C G, for 0, where f Y = Y and + ( ξ) ( δ) P he equilibrium aggregae oupu and conumpion level. 6 F. Balanced Growh Equilibrium and Calibraion C = C are h To calibrae he model, a balanced growh equilibrium i defined. The economy exhibi a balanced-growh equilibrium auming conan populaion growh rae (p), work life ( T = T ), and reiremen period ( T = T ) when he governmen implemen a fical policy characerized by a conan governmen expendiure-o-oupu raio, conan ax rae, and a conan deb-o-oupu raio. 7 Along he balanced growh equilibrium pah, all endogenou variable grow a conan rae (Table 3). The balanced-growh equilibrium can be expreed a a eady ae in derended variable in he aionary-ranformed model. The model i calibraed o mach ome ylized fac and relevan feaure of he Spanih economy a follow: Sandard parameer value in he real buine cycle lieraure are ued o e he houehold dicoun facor ( β ) and he depreciaion rae (δ ). The hare of capial in producion (α ) i obained from previou Spain-pecific calibraion and economeric udie. The oal facor produciviy parameer ( Ζ ) i e o ha he capial-oupu raio in he iniial eady ae i conien wih he Spanih daa. The rae of labor-augmening echnological progre i e o be conien wih long-erm oupu per capia growh. The value of (p) mache he average populaion growh rae for The leiure parameer i calibraed o ha he fracion of ime worked by a repreenaive houehold in he populaion i The economy aggregae conrain P K ( + ξ) + + ( δ) K Y C G P = + i obained from he aggregae conrain of he houehold ecor, he fir-order condiion of firm, he marke equilibrium condiion, and he governmen budge conrain. The aggregae conrain of he houehold ecor a ime i given by T + T T + h P b I h I h T P c h A ( ξ + ) [ r ( )] A ( ) W N ( ). T C P τ τ τ + + ( ξ ) P τ + + = = T + 7 The age rucure of he populaion remain invarian over ime, and hu, boh componen of public conumpion (healh-relaed and non healh-relaed) are conan a a hare of oupu. 8 Auming ha a houehold or individual leep 8 hour per day, he leiure-work deciion i made for he remaining 6 hour. Thi ranlae ino a oal of 2 (=7x6) hour per week. Auming 40 working hour per week, he individual work 35.7 (=40/2) percen of he non-leep ime. Adjuing he fracion of ime worked by labor force paricipaion abou 77 percen for hoe beween he age of 6-64 yield

17 5 Tax rae are calibraed o mach effecive rae oberved in Specifically, he payroll ax rae (τ ) mache he oberved raio of ocial ecuriy conribuion o wage income, and he conumpion ( τ c I ) and income ax rae ( τ ) mach he raio of indirec ax revenue o privae conumpion and direc ax revenue o GDP. The penion replacemen raio value i e o Becaue of recen change o he ocial ecuriy yem in Spain, he replacemen raio for new penioner differ from hoe of penioner reired under previou regime. The parameer choice mache raio for he mo recen cohor of penioner. The value of he work life and reiremen period are e o ha houehold ener he labor force when hey are on average 22 year old, reire a age 62 and live 80 year wih cerainy, which i he implici life expecancy a birh. The houehold labor kill profile by age ( e ) wa calibraed o mach he Spanih worker average hourly wage profile by age (Appendix II). Thi profile i imilar o ha of US worker a repored by Hanen (993) in ha kill are low a he beginning of he work life, peak a abou 50 year of age, and decline o inermediae level by he end of he work life. Given hee value, he calibraion exercie verifie ha he reuling value of he endogenou variable in he iniial eady ae and he fical raio mach cloely hoe of he Spanih daa (Table 4). G. Houehold Labor, Conumpion, and Ae Holding in he Iniial Seady Sae A anicipaed, he 5-year averaging period inroduce a dicree jump in he houehold labor effor profile preciely 5 year before reiremen (Figure ). Noe ha a he beginning of work life, houehold are relaively unkilled and hu work few hour; however, a hey age, and labor kill improve, ime devoed o work increae. Sill, houehold labor effor peak before he beginning of he averaging period even hough kill are ill increaing. 9 Thi i becaue houehold reduce labor effor before he averaging period o compenae for he higher labor effor hey will exer during he averaging period. Inuiively, he deire o anicipae leiure before he averaging period dominae he incenive o increae labor effor provided by he gain in kill. Alo, upon enering he averaging period he number of hour worked jump, and remain high unil reiremen, becaue houehold inernalize he effec of heir labor effor on he fuure penion. Sill, houehold labor effor implie increaing wage earning hroughou heir worklife. Accordingly, houehold incur deb a he beginning of heir live o parially mooh conumpion which ill increae over ime becaue he houehold rae of ime preference i lower han he ne rae of reurn on ae. During he averaging period, 9 Noe in Appendix II ha he houehold kill peak a abou 25 year of employmen, wherea in Figure, he labor effor peak afer 2 year of employmen.

18 6 houehold inenify heir ae accumulaion o upplemen heir penion income and boo conumpion during reiremen. In reiremen, conumpion i highe and ae are depleed. III. BASELINE SIMULATIONS The ime line for he imulaion correpond o a 370-year period divided ino hree unequal ubperiod. In he fir cenury, he economy i in he eady ae decribed in Secion II. The middle egmen cover he demographic raniion from a high o a low feriliy rae, ime-varying immigraion, and increaing life expecancy ha ake 70 year o work ielf ou. In he final 00 year, he economy i in a new eady ae characerized by lower populaion growh and higher life expecancy han in he fir cenury. 20 The beginning of he hree ubperiod correpond, repecively, o he year 857, 957, and 227. A. Demographic Traniion Among he exogenou elemen in he imulaion, he demographic hock and immigraion meri pecific aenion. The one of he demographic raniion pecifically, o higher life expecancy i aken o be 957, wih houehold (22 year of age) enering he labor force ha year and dying 59 year laer (8 year old) in 205 (Table 5). Life expecancy i aumed o increae one year per decade aring in 957 o ha houehold enering he labor force nine decade laer (in 2047) die a 90 year of age (in 24). From 2047, he life expecancy of houehold enering he labor force remain fixed a 90 year. The number of labor force enran reflec he combined effec of feriliy and immigraion and i e o ha he endogenou rajecory of he model dependency raio he raio of populaion aged 62 year and older over populaion beween 22 and 6 year of age mache ha of he available official projecion hrough 2060 (Figure 2). 2 Accordingly, he annual growh rae of labor force enran in he period i higher han in he iniial eady ae, decline beween 2006 and 2059, and i conan aferward. Noe ha he generaion enering he labor force in 2060 die in 227, he year marking he end of he demographic raniion and he beginning of he final eady ae. Following he Spanih Naional Saiic Iniue (INE), a low- and a high-immigraion cenario are conidered. In he low immigraion cenario, he dependency raio i able a abou 35 percen unil 985, decline lowly for he nex weny year due o immigraion and oher emporary facor, boom ou a 34 percen by 2004 and hen rie lowly o reach abou 35.5 percen by 200. From 200, and for he nex fory year, however, he raio increae harply o over 85 percen in In he high immigraion cenario, he dependency raio alo rie harply, bu i ill imilar o he low immigraion cenario. 20 Specifically, he annual rae of populaion growh in he la cenury i equal o 0.5 percen he average oberved in he decade ending in 200 reflecing a moderae rebound from he minimum (0.3 percen per annum) oberved in he decade ending in Noe ha if he growh rae of labor force enran and life expecancy are conan a in he eady ae he growh rae of he oal populaion i equal o ha of he labor force enran.

19 7 Noe ha in he model afer peaking, he dependency raio decline for he nex hree decade ( ) a labor force enrance recover. However, he raio increae again when he growh of labor force enrance abilize, reflecing he coninued improvemen in life expecancy. Only when boh labor force enrance and life expecancy abilize doe he dependency raio gradually converge (from above) o i eady ae value of 59 percen. Alhough he exac number vary, he evoluion of he dependency raio i qualiaively he ame acro he immigraion cenario. B. Baeline Macroeconomic Scenario Several aumpion are made regarding governmen policie and immigraion. Fir, he parameer of he ocial ecuriy yem reiremen age and averaging period remain unchanged over he 370 year of analyi. Second, a fical preure arie during he demographic raniion, he governmen implemen a ax-a-you-go policy: conumpion ax rae are adjued o ha he governmen budge conrain hold while oher ax rae and he governmen nonhealh expendiure-o-oupu and deb-o-oupu raio remain conan. 22 Third, a noed above, ince he low- and high-immigraion cenario reul in imilar rajecorie of he dependency raio, he imulaion dicued below are for he lowimmigraion cenario. The baeline imulaion ugge ha penion expendiure, a a hare of oupu, increae by 6 percenage poin by 2050 wih evere macroeconomic conequence (Figure 3 and Table 7). The conumpion ax rae peak a 5 percen in 2050 more han 30 percenage poin higher han in 2007 o finance he ocial ecuriy defici. A a reul, oupu and conumpion per capia (derended by echnological progre) are 8 percen lower han in he iniial eady ae. 23 Moreover, a axe ar riing in 200, oupu per capia deeriorae long before he peak of he demographic hock in 2050, bu remain uncahed for a couple of decade (hrough 2025). Thi reflec he fac ha capial per capia increae due o he riing hare in he populaion of old working houehold whoe ae holding peak a reiremen. In addiion, aggregae effecive labor i alo uained by he riing hare of old high-killed working houehold and a higher marginal produciviy of labor. The change in he populaion age rucure alo accoun for he increae in conumpion per capia, which i reinforced by he anicipaion of conumpion by young generaion foreeeing ax rae increae. Afer 2025, however, capial, labor, oupu and conumpion per capia fall harply unil abou Thi 22 Auerbach and Kolikoff (987) and De Nardi and oher (999) how ha financing he demographic hock in he US economy wih conumpion axe i le diorionary han financing i wih oher axe payroll and income axe a he ax burden i hared by more generaion. Caalán and oher (2005) confirm hi reul for he Spanih economy. Noe ha he raio of governmen conumpion-o-oupu varie over ime according o he evoluion of he populaion age rucure, reflecing he proviion of healh-care ervice, a decribed in Appendix II. 23 Noe ha in Figure 3 and Table 7, oupu (conumpion) i aionary-ranformed a indicaed in Table adjued by echnological progre and populaion growh. Accordingly, hee variable can alo be inerpreed a oupu (conumpion) per capia deviaion from heir long erm rend.

20 8 urnaround come abou a he hare of newer generaion le able o accumulae ae becaue hey have been axed heavily ince birh increae relaive o previou, more affluen, generaion. In addiion, he recenly reired affluen generaion ar depleing heir izeable ae holding, which reinforce he downurn in oupu and he capial ock. Noe ha facor price rack he evoluion of he dependency and he capial-oupu raio: he reurn on capial fall, and he wage rae (derended by echnological progre) increae unil abou Alo, he wage rae increae imply ha he (derended) average penion rie by 4 percen and exacerbae he expendiure preure. The general equilibrium effec (average penion and oupu) accoun for abou half of he penion expendiure preure and alo explain he difference wih he EC aemen of he fical impac of aging. Decompoing penion expendiure increae hrough percenage poin a a hare of oupu how ha: he average penion increae accoun for 3 percenage poin, he decline in oupu per capia accoun for 4.5 percenage poin, and he change in he populaion age rucure accoun for he remaining 8.6 percenage poin (Table 8). Furher inigh ino he baeline imulaion can be gleaned from houehold behavior (Figure ). In hi connecion, i i ueful o conider wo generaion of houehold: one enering he labor force in 990 and he oher enering in 200. The former generaion i among he mo heavily axed generaion a i die in 2053, when axe peak. The laer generaion i among hoe living hrough he wide ax rae wing a i die in 2074, and hu face boh he harp ax increae aociaed wih he demographic hock and he ubequen decline a he hock diipae. Conider fir he hypoheical cae when facor price are conan o ha hee houehold only face change in conumpion axe. The pah of conumpion ax rae noed above a harp increae during , and ubequen decreae hrough 2080 generae wealh and ubiuion effec affecing houehold lifeime plan. In paricular, an ineremporal conumpion ubiuion effec arie from houehold foreeeing higher (lower) fuure conumpion ax rae, which hu anicipae (delay) conumpion. 24 Noe ha boh generaion hif conumpion away from he high ax rae period, bu heir conumpion profile differ. The 990 generaion anicipae conumpion in repone o heavy ax rae a he end of i life (around 2050), reinforcing he aggregae conumpion boom prior o The 200 generaion, however, end o popone conumpion unil he end of i life, when ax rae have already declined. Their behavior, hu, reinforce he collape in aggregae conumpion around Change in facor price provide an addiional ource of ineremporal ubiuion. Specifically, he riing wage rae before 2050 induce an ineremporal delay of work effor in he lifeime of he 990 and 200 generaion whoe work live end in he year An increaing pah of conumpion ax rae would alo induce houehold o anicipae labor effor if wage rae remained conan, a he conumpion-leiure raio in each period i inverely relaed o he conumpion ax rae (equaion (7) in Table 2). However, wage rae vary over ime in he imulaion.

21 9 and 2050 relaive o generaion born in he iniial eady ae. 25 Boh elemen, higher wage rae and higher houehold labor effor in he averaging period, increae individual penion benefi, and hu in addiion o he increaed dependency raio pu furher preure on public finance. In he final eady ae, he dependency raio and he conumpion ax rae are higher han in he iniial eady ae due o a longer reiremen period a life expecancy increae and he working life remain fixed and a maller rae of populaion growh (Figure 4). The negaive wealh effec aociaed wih higher axe implie lower lifeime conumpion, and higher lifeime work effor (for he repreenaive houehold), becaue of he need o accumulae more ae and enhance he penion income o finance a longer reiremen period. 26 Indeed, ae holding coninue increaing during he iniial year of reiremen, in conra wih he iniial eady ae. IV. SIMULATIONS OF PENSION EFOMS A dicued above, wo reform cenario are conidered. A parial penion reform increae houehold reiremen age bu leave he averaging period unchanged. Addiionally, a full penion reform exend he averaging period ued o compue he penion benefi o he enire work life. Before dicuing he demographic raniion, i i ueful o fir underand he long run impac of hee reform. A. Effec of Penion eform in he Final Seady Sae In a nuhell, reforming he penion yem improve welfare in he final eady ae. In oher word, he benefi aociaed wih lower axe including lower ineremporal diorion in conumpion and labor more han offe he welfare co of penion benefi cu in he final eady ae. A deailed dicuion of hi reul follow. Parial penion reform Increaing he reiremen age from 47 o 49 year and he work life from 46 o 48 year lower he dependency raio and boo he aggregae effecive labor upply by increaing he 25 iing wage increae penion benefi for a given labor effor a poiive wealh effec ha provide an incenive o conume more bu work and ave le. However, hi effec i mall compared o he oppoie negaive wealh effec induced by high conumpion axe. 26 Noe ha he longer life expecancy fully accoun for he higher work effor. Our uiliy aumpion imply ha he wealh and ubiuion effec on leiure of higher conumpion ax rae cancel ou; hu, lifeime work effor would no change if populaion growh were lower bu life expecancy remained conan.

22 20 number of cohor working each period (Figure 5). 27, 28 The greaer lifeime labor income reul in a higher capial accumulaion, which in urn increae he capial-labor raio and he wage rae. Even hough he wage rae i higher, individual penion decline becaue he hump-haped kill imply a reducion in houehold average labor kill (and wage income earned) in he averaging period. Sill, welfare improve a he lower individual penion and dependency raio imply a reducion in conumpion ax rae and an increae in conumpion. Full penion reform Exending he averaging period o he enire work life increae welfare monoonically depie he decline in penion benefi due o he concomian decline in conumpion ax rae (Figure 5). The ineracion of he hump-haped kill and echnological progre play a cenral role in explaining why aggregae effecive labor and oupu per capia increae when he averaging period i horer han 5 year, bu decreae when i i longer. Specifically, When he averaging period i horer han 5 year a i wa prior o he 997 reform exending i reul in a higher aggregae effecive labor upply, which reflec he higher average kill of houehold in he averaging period and enhanced labor effor during high-kill age. 29 Penion benefi decreae, however, a hi effec i more han offe by he impac of echnological progre, a high wage earning year are more heavily dicouned by growh in produciviy. 30 When he averaging period i 5 year a i i currenly or longer, exending i decreae he aggregae effecive labor upply a i reul in lower average kill in he averaging period. Thi and echnological progre reduce he penion benefi. In eiher cae, he decline in he penion benefi allow a reducion in he conumpion ax rae ha boo houehold conumpion and welfare. 27 Wih a work life of 48 year and a reiremen period of 20 year, he model dependency raio in he final eady ae i he ame a in he iniial eady ae (0.35). Alo, wih a work life of 48 year, he raio of working-o-reiremen year for a given houehold in he final eady ae i lighly higher (2.4) han in he iniial eady ae (2.2) an unchanged raio would reul from a work life of 47 year and a reiremen period of 2 year. 28 Since houehold ener he labor force wih 22 year of age, hi correpond o increaing he reiremen age from 68 o 70 year. Compared o he iniial eady ae, increaing he model reiremen age from 40 o 48 year correpond o increaing he naural reiremen age from 62 o 70 year. 29 Figure 4 doe no how labor profile by age for hi paricular reform; however, i i ill ueful o illurae why exending he averaging period induce houehold o exer more effor when hey are highly killed, hu increaing aggregae effecive labor. 30 Labor-augmening echnological progre increae real wage over ime, wherea he penion calculaion i baed on inflaion-adjued wage earning during he houehold averaging period. In equaion (5), an increae T in ξ reduce, ceeri paribu, he penion benefi b +. + T

23 2 Thee imulaion alo ugge ha a full penion reform increae welfare in he final eady ae. A noed above, increaing he reiremen age while holding conan he averaging period (parial reform) increae welfare, and o doe exending he averaging period while holding conan he reiremen age (full reform). Combining hee parial effec improve welfare unambiguouly. A word of cauion regarding he welfare effec of exending he averaging period: he monoonic improvemen depend on he rae of echnological progre. 3 Specifically, when here i no echnological progre, welfare i maximized when he averaging period i horer han he enire work life (ee Appendix III). Thi i becaue when he averaging period i already long and i exended furher, he penion benefi rie a he decline in effecive labor induce higher wage ha, in conra o he dicuion above, are no deflaed by echnological progre. Conumpion ax rae, in urn, increae o finance he higher penion benefi, reducing houehold welfare. B. Effec of Penion eform in he Demographic Traniion Before urning o he imulaion reul in he demographic raniion, i i imporan o clarify he aumpion made regarding houehold expecaion of reform, and he announcemen and implemenaion of he reform. Specifically, reform are unanicipaed: before hey are announced, houehold enviage he baeline cenario o unfold. And reform are imulaneouly announced and implemened a he beginning of 2008; he announcemen i credible and include he parial grandfahering claue for raniional generaion a deailed below. Grandfahering claue The principle guiding he deign of grandfahering claue in hi udy i o provide more grandfahering o houehold nearing reiremen wih le ime o adju o he new penion rule and gradually le grandfahering o houehold furher away from reiremen (Table 6). 32 Houehold ha are 48 year of age or older in 2008 including hoe already reired and hoe ha have enered he averaging period are fully grandfahered. 3 Alo, in hee eady ae imulaion, houehold welfare improve when penion benefi and he conumpion ax rae fall. Thi i becaue houehold ue ax reducion o ave on heir own for reiremen earning a marke rae of reurn. We do no model myopia or elf-conrol problem ha could preven houehold from aving in hi raional, forward looking way. If hee addiional diorion were preen, he welfare analyi and he policy implicaion could change ignificanly for inance, in order o replicae he welfare implicaion of our analyi, a par of he reform raegy, he governmen could place he ax reducion in individual reiremen accoun o deal wih he elf-conrol problem. 32 Only a parial grandfahering i conidered a a complee grandfahering would no yield penion expendiure aving unil he lae 2040 when he fir generaion of he reformed yem reire, oo lae o miigae he advere macroeconomic effec of aging.

24 22 Younger houehold face, o a varying degree, he parameric reform aring in Specifically, The reiremen age of houehold wih year of age in 2008 i increaed by one year (and heir work live exended o T = 4 year) relaive o he baeline. The reiremen age of generaion aged year in 2008 and of hoe enering he labor force in i increaed by wo year (and heir work live exended o T = 42 year). Saring in 207, he reiremen age increae wo year every decade unil work live reach 48 year generaion born in have work live laing 44 year, and all generaion born afer 2046 have work live laing 48 year. The averaging period of each generaion 47 year of age, or younger, in 2008 i exended o he whole period beween 2008 and reiremen. The averaging period of houehold born in 2008 and laer i exended o heir enire work live. 33 Parial penion reform A parial penion reform aenuae he expendiure preure and conumpion ax rae increae ha are needed, while booing he aggregae capial ock and oupu. I parially offe he advere effec of aging and limi he increae in penion expendiure and ax rae in he period Comparing he pah of aggregae variable in he parial penion reform holding he averaging period a 5 year wih hoe in he baeline cenario reveal he effec of increaing he reiremen age (Figure 3 and Table 7): Penion expendiure, a a hare of oupu, increae by abou 2 percenage poin beween 2008 and percenage poin le han in he baeline. The conumpion ax rae peak in 2053 a 44 percen up 25 percenage poin from Sill, hi i abou 7 percenage poin lower han in he baeline. In he final eady ae he conumpion ax rae i 9 percen, 8 percenage poin lower han in he baeline. The capial ock per capia i conienly higher han in he baeline, albei ignificanly o afer 205. The aggregae labor upply per capia i ignificanly higher han in he baeline afer 2023, bu lighly lower han in he baeline before 2023, reflecing he grandfahering rule and houehold behavior. Oupu per capia i ignificanly higher han in he baeline only ince he early By 2050, when he dependency raio peak, oupu per capia i 4 percen higher han in he baeline 4 percen lower han in he iniial eady ae. 33 Noe ha he generaion aged 47 year old 26 year old in he model ener he averaging period in Before he penion reform (in he baeline), he generaion aged 47 in 2008 wih 26 year in he workforce reire in 2023 and ha a 5 year averaging period. Afer he penion reform, hi generaion reire in 2024 and ha a 6 year averaging period.

25 23 Capial-labor raio and wage rae are conienly higher han in he baeline; rae of reurn on ae are lower han in he baeline, excep for a brief period ( ). Conumpion per capia i coniderably higher han in he baeline afer Penion benefi are lower han in he baeline, paricularly afer A in he baeline imulaion, however, he (derended) average penion increae by 9 percen unil 2055, and fall harply hereafer. Alo, he reform reduce he reiredo-oal populaion raio from 43 percen (baeline) o 26 percen. The decompoiion of he penion expendiure preure hrough 2050 how ha he average penion, he populaion age rucure, and oupu per capia have imilar conribuion o limiing expendiure increae relaive o he baeline beween.3 and.5 percenage poin of oupu (Table 8). A bu-boom cycle in aggregae effecive labor i aociaed wih he parial reform cenario: aggregae effecive labor decline before he 2020, bu increae hereafer, reflecing he grandfahering claue and houehold ineremporal labor ubiuion effec. The mall decline in he effecive labor upply in (Figure 8) can be explained by houehold behavior. A houehold work longer (wih an unchanged averaging period) hey ubiue labor ineremporally: working more a older age, when heir kill have already declined, while exering le effor during heir middle work live, when heir kill are highe. A he oue of he reform, hi ubiuion reul in a mall reducion in he aggregae labor upply. A ime goe by, however, more houehold ener he upper age range and exer high labor effor, which ogeher wih a larger number of working cohor, reul in aggregae labor gain. Full penion reform A full penion reform deliver more ignifican macroeconomic improvemen: i furher limi he increae in penion expendiure, a a hare of oupu, beween 2008 and 2050 o 8 percenage poin of oupu, ha i, 8 percenage poin le han in he baeline; ax rae increae are alo furher limied o 37 percen or abou 4 percenage poin lower han in he baeline. Thu, exending he averaging period condiional on increaing he reiremen age i a imporan in miigaing he macroeconomic effec of aging a increaing he reiremen age a he peak of he demographic hock, By comparing he full and parial penion reform cenario (Figure 3 and Table 7), he pure effec of exending he averaging period from 5 year o he enire work life can be aeed. Specifically, exending he averaging period: educe he penion expendiure preure: penion expendiure increae, a a hare of oupu, 8 percenage poin beween 2008 and percenage poin lower han in he parial reform. The conumpion ax rae peak in 2050 a 37 percen 7 percenage poin lower compared wih he parial reform, bu ill 8 percenage