FACULTEIT ECONOMIE EN BEDRIJFSKUNDE TWEEKERKENSTRAAT 2 B-9000 GENT Tel. : 32 - (0)9 264.34.61 Fax. : 32 - (0)9 264.35.92 WORKING PAPER Pension reform in an OLG model wih heerogeneous abiliies Tim Buyse a,b, Freddy Heylen a and Renaa Van de Kerckhove a a SHERPPA, Ghen Universiy b Research Foundaion Flanders (FWO) Firs version : Augus 2012 This version : December 2014 2012/810 D/2012/7012/43
Pension reform in an OLG model wih heerogeneous abiliies Tim Buyse a,b, Freddy Heylen a and Renaa Van de Kerckhove a a SHERPPA, Ghen Universiy b Research Foundaion Flanders (FWO) 29 December 2014 Absrac We sudy he effecs of pension reform on hours worked, human capial, income and welfare in an open economy populaed by four overlapping generaions: hree acive generaions (he young, he middle aged and he older) and one generaion of reired. Wihin each generaion we disinguish individuals wih high, medium or low abiliy o build human capial. Our simulaion resuls prefer an inelligen pay-as-you-go pension sysem above a fully-funded privae sysem. This pay-as-you-go sysem condiions pension benefis on pas individual labor income, wih a high weigh on labor income earned when older and a low weigh on labor income earned when young. Uncorreced, however, such a sysem implies welfare losses for curren low-abiliy generaions and rising inequaliy. Complemening or replacing i by basic and/or minimum pension componens is negaive for aggregae employmen and welfare. Beer is o mainain he igh link beween individual labor income and he pension also for low-abiliy individuals, bu o srongly raise heir replacemen rae. An addiional correcion improving he welfare of low-abiliy individuals would be o mainain for hese individuals equal weighs on pas labor income. Keywords: employmen by age; reiremen; pension reform; heerogeneous abiliies; overlapping generaions JEL Classificaion: E62; H55; J22; J24 Corresponding auhor: Tim Buyse, SHERPPA, Ghen Universiy, Sin-Pieersplein 6, B-9000 Gen, Belgium, Phone: +32 9 264 34 87, Fax: +32 9 264 89 96, e-mail: Tim.Buyse@UGen.be. 1
0. Inroducion Growing concern for he long-run financial viabiliy of public pension sysems has pu pension reform high on he agenda of policy makers and researchers. Many counries legislaed changes o heir pension sysem during he las wo decades. A he same ime, he lieraure on pension economics expanded rapidly. To face he pension challenge, here now seems o be general agreemen on he need for higher employmen, especially among older individuals, and higher produciviy and growh. Several insiuional and policy variables may play a role here. The design of he pension sysem is cerainly one of hem. Anoher concern is o provide adequae reiremen benefis for everyone, so as o avoid old-age povery. Opimal pension design should herefore no only serve he objecive of higher employmen and produciviy, bu also safeguard he welfare of households wih low earnings capaciy. A huge lieraure has sudied he influence of he pension sysem on employmen and/or growh (see e.g. Lindbeck and Persson, 2003, and he many papers ha we refer o below). In Buyse e al. (2013) we ook his lieraure as far as we could. We sudied he effecs of pension reform in an OLG model for an open economy where hours worked by young, middle aged and older individuals, educaion of he young, he reiremen decision of older workers, and aggregae per capia growh, are all endogenous. The model also conains a rich fiscal block o assess he effecs of pension reform on he public budge. Simulaing he model, our resuls preferred an inelligen pay-as-you-go (PAYG) sysem above a fully-funded privae sysem. We found posiive effecs on employmen, growh and welfare o be he sronges in a PAYG sysem ha condiions pension benefis on pas individual labor income, wih a high (low) weigh on labor income earned when older (young) o compue he pension assessmen base. Pension reform in his direcion encourages young individuals o sudy and build human capial, which promoes produciviy and per capia income. Furhermore, i encourages older workers o pospone reiremen. Srenghening he link beween one s fuure old-age pension, on he one hand, and one s human capial and labor supply when older, on he oher, inroduces srong financial incenives which may bring abou imporan changes in behavior. An imporan weakness of our model in Buyse e al. (2013), however, is ha i assumes equal abiliy and capaciy o learn for all people. Realiy is differen, however. Daa reveal ha in 2010 26% of he 25-64 year old populaion in he OECD had no upper secondary degree. Abou 44% had an upper secondary degree bu no eriary degree. The fracion of people wih a eriary degree was 30%. Among young cohors (age 25 o 34), educaional aainmen is higher. Ye, he fracion ha does no complee upper secondary educaion is sill close o 20% on average (OECD, Educaion a a Glance, 2012, Tables A1). The simple fac ha innae abiliy as for example refleced by IQ varies across people, implies ha one can never expec everyone o succeed a he secondary, le alone he eriary level. The challenge ha emerges from hese facs is clear. If an inelligen pension reform requires a igher link beween one s fuure pension and one s individual human capial and labor income (especially labor income earned a older age), welfare losses for individuals wih low innae abiliy may be unavoidable. The incidence of old-age povery among hese individuals can be expeced o rise. A he same ime, individuals wih high innae abiliy will experience welfare gains. 2
One may hus expec a subsanial increase in welfare inequaliy. Our main research quesions in his paper arise from hese expecaions. Wha pension reform is opimal if he objecive is no only o improve employmen and aggregae produciviy and efficiency, bu also o avoid welfare losses for low-abiliy individuals and rising inequaliy in welfare? If some redisribuion in he pension sysem is necessary, should his hen be achieved by a minimum pension, a basic pension or by an earnings relaed pension paired wih a higher replacemen rae for he low educaed? To answer hese quesions we sudy opimal pension reform and he induced income and welfare disribuion in a general equilibrium OLG model wih endogenous employmen and human capial ha also incorporaes heerogeneiy in abiliy. More precisely, we exend our model in Buyse e al. (2013) by defining in each generaion individuals ha are born wih high, medium or low innae abiliy. Individuals wih higher abiliy ener he model wih more human capial. They are also more producive in building addiional human capial when hey allocae ime o (eriary) educaion. Calibraing and simulaing he model, our findings highligh he major imporance of accouning for heerogeneous abiliies and for he disribuional consequences of pension reform. We confirm he aggregae efficiency of he inelligen PAYG sysem advocaed in Buyse e al. (2013) compared o a fully-funded privae sysem, bu also demonsrae he significan welfare losses ha moving o his sysem would impose on curren generaions of low-abiliy individuals who canno sudy and who earn low wages. Inrageneraional welfare inequaliy would rise srongly. To avoid his, addiional policy measures argeing low-abiliy individuals will be necessary. Invesigaing various alernaives, we learn he following. Firs, he inroducion of a minimum pension does promoe he welfare of he curren and fuure low-abiliy generaions. I is negaive, however, for aggregae welfare, employmen and per capia oupu. The main reason is ha labor supply and employmen among low-abiliy individuals would fall sharply. Eligibiliy o a pension above he level ha hese individuals can ever collec from heir own labor kills an imporan incenive o work. Togeher wih a rise in public pension expendiures, hese negaive employmen effecs undermine he public budge, and force he governmen o raise axes. Second, he alernaive of inroducing a basic or fla pension for all ciizens has even worse effecs. Fla pensions imply a reducion in he reurn o working for all individuals and o educaion for individuals wih higher and medium abiliy. Overall negaive effecs on employmen, human capial and produciviy would in he end make everyone worse off in absolue erms, including he individuals wih low abiliy. The only posiive effec may be ha inequaliy declines. Third, a much more efficien response o he disribuional challenge imposed by he PAYG sysem advocaed in Buyse e al. (2013) is o mainain he igh link beween individual labor income and he pension also for low-abiliy individuals, bu o significanly raise heir replacemen rae. Moreover, since hese individuals canno sudy (a he eriary level), i makes much less sense for hem o reduce (raise) he weigh aached o labor income earned as a young (older) worker o compue he pension assessmen base. Many sudies have documened how he pension sysem may affec he incenives of individuals of differen ages o work (e.g. Sheshinski, 1978; Auerbach e al., 1989; Gruber and Wise, 2002; Sommacal, 2006; Cigno, 2008; Fisher and Keuschnigg, 2010; Jaag e al., 2010; de la Croix e al., 2013; 3
Fehr e al., 2013). Ohers have invesigaed he relaionship beween he pension sysem and invesmen in human capial, as a major deerminan of produciviy and growh (e.g. Zhang, 1995; Kemniz and Wigger, 2000; Docquier and Paddison, 2003; Zhang and Zhang, 2003; Le Garrec, 2012). Mos recenly, Ludwig e al. (2012), Buyse e al. (2013) and Kindermann (2015) made progress by sudying pension reform in OLG models where boh employmen by age and human capial are endogenous. Alhough hese hree sudies differ in he way hey model growh (exogenous or endogenous), each of hem demonsraes he imporance of modelling he many muual relaionships beween key variables. For example, if policy can make people pospone reiremen and work longer, he reurn o invesmen in educaion will rise, and so may human capial and produciviy. Conversely, policies ha promoe invesmen in human capial will also encourage people o work longer since hey will hen ge a higher reurn from heir invesmen. Also, if pension reform discourages employmen of he young, i may sill be efficien if his conribues o educaion. For a proper assessmen of he effecs of pension reform i is imporan o ake such ineracions ino accoun. As we have menioned above, we ake he model developed in Buyse e al. (2013) as our saring poin, bu exend i by modeling individuals wih heerogeneous abiliies. Many researchers have inroduced heerogeneous abiliies in OLG models before. Some have done his o sudy he effecs of he pension sysem on inequaliy, as one of he dependen variables. The way in which heerogeneiy is inroduced differs, however. Some auhors model individuals wih differen human capial (or skill) levels when hey ener he model (e.g. Sommacal, 2006; Fehr e al., 2013). Ohers inroduce individuals wih he same iniial human capial, bu differen learning abiliies (e.g. Docquier and Paddison, 2003; Kindermann, 2015). Anoher assumpion o make is wheher or no human capial and produciviy are subjec o idiosyncraic shocks during life, as for example in Fehr e al. (2013). In our model individuals wih higher abiliy will have boh higher iniial human capial and be more producive in building addiional human capial when hey allocae ime o (eriary) educaion. Individuals wih low abiliy will ener he model wih low human capial and have zero produciviy o sudy and build addiional human capial. We absain, however, from shocks o individual human capial and produciviy during individuals life. This se of assumpions may offer he bes mach o recen findings by Hugge e al. (2006, 2011) and Keane and Wolpin (2007) ha heerogeneiy in human capial endowmen a young age and learning abiliies, raher han shocks o human capial, accoun for mos of he variaion in lifeime uiliy. Our approach also maches findings ha innae learning abiliy and human capial a he age of 23 are srongly posiively correlaed (Hugge e al., 2011). A final imporan elemen is he relaionship beween he human capial of subsequen generaions. In he main par of his paper, we follow Ludwig e al. (2012) and Kindermann (2015) among ohers, and assume ha human capial is predeermined and generaion-invarian. Growh will hen be exogenous. In a shor robusness secion we will, however, assume ha when people ener he model, hey inheri a fracion of he human capial of he previous generaion, as in Azariadis and Drazen (1990) and Buyse e al. (2013). Individuals wih higher abiliy inheri a larger fracion. Differen generaions hen sar wih differen (abiliy-specific) human capial, and growh becomes endogenous. 4
The srucure of his paper is as follows. In Secion 1 we documen differences in employmen by age, educaion of he young, he effecive reiremen age of older workers, and per capia growh across 13 OECD counries before he financial crisis (1995-2007). Secion 2 ses ou our basic model wih predeermined and generaion-invarian human capial. Nex o he pension sysem, we inroduce a fiscal policy block. The governmen in he model ses ax raes on labor, capial and consumpion. I spends is revenue on (non-producive) goods, non-employmen benefis (including early reiremen benefis), old-age pensions, and ineres paymens on ousanding deb. In Secion 3 we calibrae he model on acual daa. Secion 4 gives more insigh ino he realiy behind he key pension policy parameers and he key fiscal policy parameers in our model. We repor daa for he same 13 OECD counries. In Secion 5 we confron he model s predicions (using he counry-specific policy parameers) wih he facs described in Secion 1. Secion 6 includes he resuls of a range of model simulaions. We invesigae he seady sae employmen, educaion, oupu and welfare effecs of various reforms of he pension sysem. We sudy effecs per generaion and per abiliy group. In Secion 7 we invesigae (and confirm) he robusness of our findings o allowing an inergeneraional ransfer of human capial and endogenous growh. Secion 8 concludes he paper. 1. Cross-counry differences in employmen, eriary educaion and per capia growh Table 1 conains key daa on employmen, educaion and growh in 13 OECD counries in 1995-2007. One would like a reliable model o mach he main cross-counry differences repored here. The employmen rae in hours (n) indicaes he fracion of poenial hours ha are acually being worked by he average person in one of hree age groups (20-34, 35-49, 50-64). Comparable daa for hours worked by abiliy ype (skill level) are no available. Poenial hours are 2080 per person per year (52 weeks imes 40 hours per week). The observed employmen rae rises if more people in an age group have a job, and if he employed work more hours. The employmen rae in he age group of 50 o 64 is also affeced by he average age a which older workers wihdraw from he labor force. We include he effecive reiremen age as he fourh daa column in he Table. In mos counries, his age is well below he official age o receive old-age pensions (65 in mos counries, 60 in France and Ialy). The educaion rae (e) is our proxy for he fracion of ime spen sudying by he average person of age 20-34. I has been calculaed as he oal number of sudens in full-ime equivalens, divided by oal populaion in his age group. Our daa for (average annual) real per capia growh concern real poenial GDP per person of working age. We refer o Appendix A for deails on he calculaion of our daa, and on he assumpions ha we have o make. As is well known, middle aged individuals work mos hours, followed by he young. The older generaion works he lowes number of hours. Average employmen raes across counries in hese hree age groups are 55.0%, 63.7% and 43.6% respecively. Furhermore, he daa reveal srong cross-counry differences. We observe he highes employmen raes in each age group in he US. Employmen raes are much lower in he core counries of he euro area. The Nordic counries ake inermediae posiions, alhough hey are close o he core euro area for he younger generaion. The laer, however, seems o be relaed o educaion. Young people s effecive paricipaion in 5
educaion is also by far he highes in he Nordic counries. These counries also show he highes poenial per capia growh raes. On average, growh in he core euro area and he US was more han 0.5 percenage poins lower in he period under consideraion. The US and he oher Anglo- Saxon counries end o have he lowes paricipaion in educaion among people of age 20 o 34. Finally, we noe ha he effecive reiremen age also varies across counries. The reiremen age is quie low in Belgium (57.9) and France (58.8). By conras, individuals in Nordic or Anglo-Saxon counries paricipae longer. Unsurprisingly, correlaion beween he effecive reiremen age and he employmen rae among older workers (n 3 ) is very high (0.89). Table 1 Employmen rae in hours (n) by age, effecive reiremen age, educaion rae (e) and per capia growh in OECD counries (1995-2006/7) n 1 (20-34) n 2 (35-49) n 3 (50-64) Effecive reiremen age e Annual real per capia growh Ausria 59.9 64.3 34.7 59.5 12.5 2.06 Belgium 51.1 56.8 29.3 57.9 14.1 1.77 France 48.7 60.3 38.0 58.8 14.9 1.54 Germany 49.7 55.2 34.9 61.1 17.2 1.56 Ialy 50.1 61.9 33.8 60.1 12.6 1.30 Neherlands 50.8 54.6 34.2 60.0 14.7 2.20 Core euro area average 51.7 58.8 34.2 59.6 14.3 1.74 Denmark 56.2 66.7 49.6 62.2 21.7 1.81 Finland 55.6 69.0 47.3 60.2 23.1 2.72 Norway 51.9 60.9 50.6 63.1 18.1 2.29 Sweden 53.6 66.1 55.4 63.4 17.7 2.18 Nordic Average 54.3 65.6 50.7 62.2 20.2 2.25 US 65.6 74.2 59.6 64.2 12.8 1.54 UK 60.8 68.4 49.4 62.0 12.3 2.13 Canada 60.9 69.5 50.4 62.1 13.6 1.68 All counry 55.0 63.7 43.6 61.1 15.8 1.91 Average Daa sources: OECD (see Appendix A); daa descripion: see main ex and Appendix A. The daa for employmen and growh concern 1995-2007. The daa for educaion and he effecive reiremen age are averages for 1995-2006. All daa are in percen, excep he reiremen age. 6
2. The model wih exogenous growh Our analyical framework borrows heavily from Buyse e al. (2013). I consiss of a compuable fourperiod OLG-model for a small open economy wih endogenous employmen and human capial. New in his paper is ha we realisically ake ino accoun differences in individuals innae abiliies. 2.1. Basic seup and demographics We consider hree acive adul generaions, he young, he middle aged and he older, and one generaion of reired agens. Individuals ener he model a age 20. Each period of life is modeled o las 15 years. Wihin each generaion we assume hree ypes of individuals wih differen abiliy: a group H wih high abiliy, a group M wih medium abiliy and a group L wih low abiliy. We normalize each abiliy group o 1, so ha he size of a generaion is 3, and oal populaion is 12, and consan. Differences in abiliy are refleced boh in he amoun of human capial wih which individuals ener he model and in heir produciviy of schooling (a he eriary level) when young. Low abiliy individuals ener wih he lowes human capial and will never go ino eriary educaion. They only work or have leisure (including oher non-marke aciviies). High and medium abiliy young people ener he model wih more human and will also inves a fracion of heir ime in eriary educaion. Middle aged and older individuals do no sudy anymore. Whaever heir innae abiliy, hey only work or have leisure. The sauory old-age reiremen age in our model is 65. Individuals may however opimally choose o leave he labor force sooner in a regime of early reiremen. Oupu is produced by domesic firms acing on compeiive markes. These firms employ physical capial ogeher wih exising echnology and effecive labor provided by he hree acive generaions. In he spiri of Buier and Klezer (1993), physical capial is inernaionally mobile, whereas labor and human capial are immobile. In wha follows, we concenrae on he core elemens of he model: he opimizing behavior of individuals, he formaion of human capial, he behavior of domesic firms and he deerminaion of aggregae oupu, capial and wages. 2.2. Individuals: preferences and ime allocaion An individual wih abiliy a (a = H, M, L) reaching age 20 in period maximizes an ineremporal uiliy funcion of he form: U 4 a = β j 1 (ln c ja + j ) 1 θ j=1 ) a = H, M, L (1) 1 θ (l ja wih 0 < < 1, j > 0, θ > 0 (θ 1). Superscrip indicaes he period of youh, when he individual comes ino he model. Subscrip j refers o he jh period of life and a refers o abiliy. Lifeime uiliy depends on consumpion (c ja ) and enjoyed leisure (l ja ) in each period of life. The parameers, and θ define he discoun facor, he relaive value of leisure versus consumpion, 7
and he inverse of he ineremporal elasiciy o subsiue leisure. These parameers are common across abiliy ypes. The preference parameer may, however, be differen in each period of life. Excep for he laer assumpion, our specificaion of he insananeous uiliy funcion is quie common in he macro lieraure (e.g. Rogerson, 2007; Erosa e al., 2012). Figure 1 shows he individuals ime allocaion over he life-cycle. Equaions (2)-(5) describe how his is refleced in enjoyed leisure l ja. Time endowmen in each period is normalized o 1. l 1a = 1 n 1a e 1a, wih e 1L = 0. (2) l 2a l 3a = 1 n 2a = Γ (μ(r a (1 n 3a )) 1 1 ζ + (1 μ)(1 R a ) 1 1 ζ) ζ ζ 1 (3) (4) l 4a = 1 (5) Figure 1. Life-cycle of an individual of generaion and abiliy a 20 35 50 65 80 R a Period +1 +2 +3 Work Sudy n 1a n 2a n 3a = R a n 3a 0 e 1a 0 0 0 Leisure ime 1 n 1a e 1a 1 n 2a R a (1 n 3a ) + (1 R a ) 1 Noe: e 1L = 0. In he firs period of acive life (Equaion 2), leisure falls in labor supply (n 1a ) and in educaion ime (e 1a ). Only he low abiliy individuals do no sudy (e 1L = 0). In he second and hird period, no one sudies. Individuals only work or have leisure (Equaions 3 and 4). Following he approach in Buyse e al. (2013), par of he individuals opimal choice of leisure in he hird period of heir life concerns he deerminaion of early reiremen. Individuals choose R a which relaes o he opimal effecive reiremen age and which is defined as he fracion of ime beween age 50 and 65 ha he individual paricipaes in he labor marke; (1 R a ) is he fracion of ime in early reiremen. Assuming ha labor marke exi is irreversible and pos-reiremen employmen is no allowed, he relaionship beween he fracion of ime devoed o work beween 50 and 65 (n 3a ) and he fracion of ime devoed o work before early reiremen bu afer 50 (n 3a ), is as follows: n 3a = R a. n 3a. Leisure ime in he hird period herefore consiss of wo pars: non-employmen ime before he effecive reiremen age R a (1 n 3a ), and ime in early reiremen afer i (1 R a ). Equaion (4) hen describes composie enjoyed leisure of an older worker as a CES-funcion of boh pars. Like 8
Buyse e al. (2013), we assume imperfec subsiuabiliy beween he wo leisure ypes. The idea is ha leisure ime afer and beween periods of work is no he same as leisure ime in periods when individuals are no economically acive anymore. 1 Equaion (4) expresses ha individuals prefer o have a balanced combinaion of boh raher han an exreme amoun of one of hem (and very lile of he oher). In his equaion ζ is he consan elasiciy of subsiuion, µ is a usual share parameer and Γ is added as a normalizaion consan such ha he magniude of l 3a corresponds o he magniude of oal leisure ime (1 n 3a ). The laer assumpion allows us o inerpre 3 as he relaive value of leisure versus consumpion in he hird period, comparable o 1 and 2. The main resuls in his paper are no in any way influenced by he magniude of μ, Γ or ζ. 2.3. Individuals: budge consrains Equaions (6)-(10) describe he budge consrains ha individuals are subjec o. We briefly explain hese consrains, paying paricular aenion o he deerminans of he old-age pension benefi ha individuals receive, and is relaionship o employmen and human capial in earlier periods. (1 + τ c )c 1a (1 + τ c )c 2a (1 + τ c )c 3a (1 + τ c )c 4a + Ω 1a + Ω 2a + Ω 3a = w a, h 1a n 1a = w a,+1 h 2a (1 τ w ) + bw a, h 1a (1 τ w )(1 n 1a e 1a ) (6) n 2a +(1 + r +1 )Ω 1a = w a,+2 h 3a R a n 3a (1 τ w ) + bw a,+1 h 2a (1 τ w )(1 n 2a ) (7) (1 τ w ) + bw a,+2 h 3a (1 τ w )R a (1 n 3a ) +b er w a,+2 h 3a (1 τ w )(1 R a ) + (1 + r +2 )Ω 2a (8) = (1 + r +3 )Ω 3a + pp a (9) pp a = ρ wa 3 j=1 (p j w a,+j 1 h ja n ja (1 τ w )) wih: 0 p j 1 3 j=1 p j = 1 n 3a = R a n 3a +ρ fa ( 1 ) 3 (w 9 a,+3h +4 j ja n +4 j j=1 a=h,m,l ja (1 τ w )) (10) The LHS of Equaions (6)-(9) shows ha individuals allocae heir disposable income o consumpion (including consumpion axes, τ c ) and o he accumulaion of non-human wealh. We denoe by Ω ja he sock of wealh held by a ype a individual of generaion a he end of he jh period of his life. Individuals sar adul life wih zero asses. As is clear from Equaion (9), hey also finish life wih zero asses. During he hree periods of acive life, disposable income a he RHS includes afer-ax labor 1 The former may be paricularly valuable from he perspecive of relaxaion and ime o spend on personal aciviies of shor duraion. The laer may be valuable o enjoy aciviies ha ake more ime and ask for longer erm commimen (e.g. long journeys, non-marke aciviy as a voluneer). 9
income and non-employmen benefis. From he second o he fourh period, i may also include ineres income. We denoe by w a,k he real wage per uni of effecive labor supplied a ime k by an individual wih abiliy a and by r k he exogenous (world) real ineres rae a ime k. Effecive labor of an individual wih abiliy a depends on hours worked (n ja ) and human capial (h ja ). Given he ax rae on labor income τ w, young individuals earn an afer-ax real wage equal o w a, h 1a n 1a (1 τ w ). Afer-ax labor income of middle aged and older workers in Equaions (7) and (8) is deermined similarly. For he fracion of ime ha young, middle aged and older individuals are inacive, hey receive a non-employmen benefi from he governmen. Older individuals may be eligible o wo kinds of benefis: sandard non-employmen benefis (analogous o wha young and middle aged workers receive) as long as hey are on he labor marke, and early reiremen benefis afer having wihdrawn from he labor marke. All benefis are defined as a proporion of he afer-ax wage of a full-ime worker. The ne replacemen rae for sandard nonemploymen benefis is b, for early reiremen benefis i is b er 2. Afer he sauory reiremen age (65) individuals have no labor income and no nonemploymen benefis anymore. They earn ineres income from accumulaed non-human wealh, and hey receive an old-age pension benefi (pp a ). We assume a public PAYG pension sysem in which pensions in period k are basically financed by conribuions from he acive generaions in ha period k (see below). As described by Equaion (10), individual ne pension benefis consis of wo componens. A firs one is relaed o he individual s earlier ne labor income. I is a fracion of his socalled pension base, i.e. a weighed average of ne labor income in each of he hree acive periods of life. The ne replacemen rae is ρ wa. The parameers p 1, p 2 and p 3 represen he weighs aached o each period. This par of he pension rises in he individual s hours of work n ja and his human capial h ja. I will be lower when he individual reires early (lower R a ). The second componen of he pension is a fla-rae or basic pension. Every reiree receives he same amoun relaed o average ne labor income in he economy a he ime of reiremen. Here, he ne replacemen rae is ρ fa. Noe ha we allow abiliy-specific pension replacemen raes ρ wa and ρ fa. This specificaion is in line wih he daa in many counries. The imporance of own-income relaed versus fla componens may be very differen depending on people s earned income, and herefore abiliy (see Secion 4 and Table 5 below). For oher policy variables like labor ax raes such differences are much smaller (Heylen and Van de Kerckhove, 2013). The inroducion of abiliy-specific pension replacemen raes also allows a richer policy analysis. 2.4. Individuals: human capial formaion Individuals ener our model a he age of 20 wih a predeermined level of human capial. This level is generaion-invarian, bu i rises in innae abiliy. The laer reflecs for example ha higher innae 2 As explained in greaer deail by Buyse e al. (2013, foonoe 5), he approach o model early reiremen benefis as a funcion of a worker s las labor income, similar o sandard non-employmen benefis, reflecs regulaion and/or common pracice in many counries. 10
abiliy makes i easier for individuals o learn and accumulae knowledge a primary and secondary school. In Equaion (11) we normalize he human capial of a young individual wih high abiliy o h 0. A young individual wih medium abiliy eners he model wih only a fracion ε M of his. A young worker wih low abiliy eners wih an even lower fracion ε L. These fracions will be calibraed. h 1a = ε a h 0 a = H, M, L (11) wih 0 < ε L < ε M < ε H = 1. During youh, individuals wih high and medium abiliy will inves a fracion of heir ime o expand heir human capial, making hem more producive in he second and hird period. We adop in Equaion (12.a) a human capial producion funcion similar o Lucas (1990), Glomm and Ravikumar (1998), Bouzahzah e al. (2002) and Docquier and Paddison (2003). The producion of new human capial by hese individuals rises in he amoun of ime hey allocae o educaion (e 1a ) and in heir iniial human capial (h 1a ). We assume a common elasiciy of ime inpu (σ) and a common efficiency parameer (φ) for boh abiliy ypes. Individuals wih low innae abiliy do no sudy. In Equaion (12.b) heir human capial remains consan. Finally, we assume in Equaion (13) ha he human capial of all individuals remains unchanged beween he second and he hird period. We have in mind ha learning by doing in work may counerac depreciaion. The same assumpion explains he lack of depreciaion in Equaion (12). In no way does his assumpion affec our main resuls in his paper. h 2a h 2L h 3a wih 0 < σ 1, φ > 0. = h 1a (1 + φ(e 1a ) σ ) a = H, M (12.a) = h 1L (12.b) = h 2a, a = H, M, L (13) 2.5. Individuals: opimizaion and he role of he pension sysem Individuals will choose consumpion, labor supply in each period of acive life, educaion when young (for he medium and high abiliy individuals), and heir effecive reiremen age o maximize Equaion (1), subjec o Equaions (2)-(13). Subsiuing Equaions (2)-(5) for l ja 11 and (6)-(9) for c ja ino (1), and maximizing wih respec o Ω 1a, Ω 2a, Ω 3a, n 1a, n 2a, n 3a, R a and e 1a, yields eigh firs order condiions for he opimal behavior of an individual wih abiliy a enering he model a ime. Equaion (14) expresses he law of moion of opimal consumpion over he lifeime. Equaions (15.a), (15.b) and (15.c) describe he opimal labor-leisure choice in each period of acive live. Individuals supply labor up o he poin where he marginal uiliy of leisure equals he marginal uiliy gain from work. The laer consiss of wo pars. Working more hours in a paricular period raises addiional resources for consumpion boh in ha period and when reired. The marginal uiliy gain from work rises when he marginal uiliy of consumpion (1/c ja ) is higher, and when an exra hour of work yields more exra consumpion. Higher human capial (and is underlying
deerminans), lower axes on labor, lower axes on consumpion and lower non-employmen benefis conribue o he gain from work. Exra consumpion during reiremen rises in he ownincome- relaed pension replacemen rae (ρ wa ) and in he weigh aached o he relevan period when compuing he pension base (p j ). Equaions (15.a)-(15.c) highligh posiive subsiuion effecs from he pension replacemen rae ρ wa. To he exen ha higher replacemen raes raise individuals consumpion possibiliies (c ja ), hey also cause adverse income effecs on labor supply. Basic pensions (ρ fa ) do no direcly occur in Equaions (15), bu hey do affec employmen via his income effec. c j+1,a = β(1 + r +j ), j = 1,2,3 (14) c ja γ 1 l 1a (l 1a ) θ n 1a = w a,h 1a (1 τ w )(1 b) c 1a (1+τ c ) + β³ ρ wa p 1w a, h 1a (1 τ w ) c 4a (1+τ c ) (15.a) γ 2 l 2a (l 2a ) θ n 2a = w a,+1(1+φ(e 1a c 2a σ ) )h1a (1+τ c ) (1 τ w )(1 b) + β² ρ wa p 2w a,+1 (1+φ(e σ 1a) )h1a (1 τ w ) c 4a (1+τ c ) (15.b) γ 3 l 3a (l 3a ) θ n 3a = w a,+2(1+φ(e 1a σ ) )h1a c 3a (1+τ c ) Ra (1 τ w )(1 b) + β ρ wa p 3w a,+2 (1+φ(e σ 1a) )h1a Ra (1 τ w ) c 4a (1+τ c ) (15.c) Equaion (16) describes he firs order condiion for he opimal effecive reiremen age. The LHS represens he uiliy loss from posponing reiremen. Laer reiremen reduces enjoyed leisure as early reiree, bu raises enjoyed leisure in beween periods of work for given work ime n 3a. The RHS shows he marginal uiliy gain from posponing reiremen. This marginal gain follows from consuming he exra labor income (vis-à-vis he early reiremen benefi) in he hird period, and he higher fuure old-age pension afer 65. The laer effec rises in ρ wa and p 3. γ 3 l 3a (l 3a ) θ R a = w a,+2(1+φ(e 1a σ ) )h1a (1 τ w )(n 3a +b(1 n 3a ) ber ) c 3a (1+τ c ) +β ρ wa p 3w a,+2 (1+φ(e σ 1a) )h1a n 3a (1 τ w ) c 4a (1+τ c ) (16) Finally, Equaion (17) imposes for high and medium abiliy individuals ha he marginal uiliy loss from invesing in human capial when young equals he oal discouned marginal uiliy gain in laer periods from having more human capial. Individuals will sudy more he higher fuure versus curren afer-ax real wages and he higher he marginal reurn of educaion (σφ(e 1a ) σ 1 ). Labor axes 12
during youh herefore encourage individuals o sudy, whereas labor axes in laer periods of acive life discourage hem. Noice also ha high benefi replacemen raes in laer periods, and a high income-relaed pension replacemen rae (ρ wa ), combined wih high weighs p 2 and p 3, will encourage young individuals o sudy. The reason is ha any fuure benefis and he fuure pension rise in fuure labor income, and herefore human capial. A final ineresing resul is ha young people sudy more all oher hings equal if hey expec o work harder in laer periods (n 2a, n 3a = R a. n 3a ). γ 1 l 1a (l 1a ) θ e 1 c 1a 1a c 1a e 1a = β 1 c 2a c 2a e 1a + β 2 1 c 3a c 3a e 1a + β 3 1 c 4a c 4a e 1a a = H, M (17) wih: c 1a e 1a c 2a e 1a c 3a e 1a c 4a e 1a = bw a,h 1a (1 τ w ) 1+τ c = σφ(e 1a = σφ(e 1a = ρ wa σφ(e 1a ) σ 1 w a,+1h 1a (1 τ w )[n 2a 1+τ c ) σ 1 w a,+2h 1a (1 τ w )[R a (n 3a 1+τ c +b(1 n2a )] (1 b)+b b er )+b er ] ) σ 1 3 (p j=2 jn jawa,+j 1 h 1a (1 τ w )) 1+τ c The pension sysem in our model is of he PAYG ype as we see i in mos OECD counries. Expendiures are basically financed by conribuions from workers (labor axes). However, since we do no define a sricly separae budge for he pension sysem, he governmen may also suppor i using oher resources from is general budge (see Secion 2.7.). I will be obvious from our discussion of Equaion (10) and he firs order condiions in his secion ha for a given way of financing he specific organizaion of pension benefis may have srong effecs on behavior in earlier periods of life. We summarize hem here. Boh income and subsiuion effecs occur: - A higher replacemen rae ρ wa raises he reurn o working (n, for all abiliy groups) and o building human capial (e, h, for high and medium-abiliy individuals) in earlier periods. I will encourage individuals o work and o inves in educaion. - Changes in he paricular weighs of he periods ha consiue he pension assessmen base o which ρ wa applies, may modify hese incenive effecs. The reurn o working in a paricular period rises in he weigh aached o ha period. A shif in weigh from p 1 o p 3 brings srong incenives o work less when young, and o work more and longer when old. This shif also includes a srong incenive o inves in human capial. The ne reurn o educaion rises in p 2 and p 3, bu falls in p 1. - Pension sysems ha encourage individuals o work more when middle aged or older, also simulae hem o sudy when young (a leas when hey have medium or high innae abiliy). The reason is ha an increase in n 2 or n 3 raises he reurn o educaion. Conversely, individuals who 13
inves more in human capial when young will also prefer o work more and longer a higher age. The reason here is ha a higher level of human capial raises wages and he reurn o working. - Higher replacemen raes ρ wa do no only bring abou subsiuion effecs, however. Raising individuals consumpion possibiliies, hey also cause adverse income effecs on labor supply. - The sory is differen when old-age benefis are of he basic pension ype (ρ fa ). These cause no subsiuion effecs, and hus no incenive effecs o work or sudy. They only affec employmen (negaively) via he income effec. Since lower employmen in laer periods affecs he reurn o educaion, a basic pension sysem would also discourage invesmen in educaion. Shifing from an own-earnings relaed o a basic pension sysem is bad for efficiency. Obviously, for a proper assessmen of he effecs of pension sysems and reforms, one canno disregard he issue of financing. In his respec, i has been shown in he lieraure ha if an increase of he replacemen rae ρ wa and he fuure pension benefi is associaed wih an increase in he ax rae on labor, he posiive effec on labor supply disappears. In mos cases, i.e. when he presen discouned value of benefis is lower han he value of he conribuions, he effec may urn negaive (see e.g. also Cigno, 2008; Fisher and Keusschnigg, 2010). The posiive effec on educaion will no disappear, however. A pension sysem wih earnings-relaed benefis will always encourage individuals o inves in educaion when young. The reason is ha when he presen value of fuure benefis is lower han he value of he conribuions, an implici ax srucure resuls ha has high ax raes on labor income in he firs period of acive life and lower ax raes owards he end. This subsidizes human capial formaion (see also Kindermann, 2015). Raising individuals fuure wages, a higher level of human capial will hen recreae posiive incenive effecs for individuals o work when middle aged and older. All hese ineracions beween endogenous labor and endogenous human capial, supplied by individuals of differen generaions and abiliy, clearly highligh he need for a larger scale numerical analysis of pension reform. We carry ou his analysis in Secion 6. 2.6. Domesic firms, oupu and facor prices Firms ac compeiively on oupu and inpu markes and maximize profis. All firms are idenical. Toal domesic oupu (Y ) is given by he producion funcion (18). Producion exhibis consan reurns o scale in aggregae physical capial (K ) and labor in efficiency unis (A H ), so ha profis are zero in equilibrium. Technology A is growing a an exogenous and consan rae x: A +1 = A (1 + x). Equaion (19) defines oal effecive labor as a CES aggregae of effecive labor supplied by he hree abiliy groups. In his equaion s is he elasiciy of subsiuion beween he differen abiliy ypes of labor and η H, η M and η L are he inpu shares. We will impose ha η H = 1 η M η L. Y = K α (A H ) 1 α (18) 1 1 1 1 H = (η H H s H, + η M H s M, + η L H L, s 1 1 s 1 s ) (19) 14
Equaion (20) specifies effecive labor per abiliy group. Wihin each abiliy group we assume perfec subsiuabiliy of labor supplied by he differen age groups. H a, = n 1a h 1a + n 1 2a h 1 2a + n 2 2 3a h 3a = (n 1a 1 + n 2a ψ 1 2 a + n 3a ψ 2 a )ε a h 0 a = H, M, L (20) To derive Equaion (20) we make use of Equaions (12) and (13) where we define: 1 + φ(e 1a ) σ ψ a, where ψ L = 1 (21) I hen follows ha: h j 3a = h j 2a = ψ j j a h 1a a = H, M, L. Furhermore, we exploi he resul ha h 1a = h 1 1a = h 2 1a = ε a h 0 (22) Subsiuing Equaion (20) for a = H, M and L ino (19), and recognizing differences in he capaciy ε a o inheri human capial as indicaed by Equaion (11), yields Equaion (23). H = [ 1 1 η a ε s 1 a (n 1a + n 2a ψ 1 2 a + n 3a ψ 2 a ) 1 1 s 1 s h0 (23) a=h,m,l ] s Compeiive behavior implies in Equaion (24) ha firms carry physical capial o he poin where is afer-ax marginal produc ne of depreciaion equals he world real ineres rae. Physical capial depreciaes a rae δ k. Capial axes are source-based: he ax rae k applies o he counry in which he capial is used, regardless of who owns i. The (world) real ineres rae being given, firms will insall more capial when he amoun of labor in efficiency unis increases or he capial ax rae falls. In ha case he ne reurn o invesmen in he home counry rises above he world ineres rae, and capial flows in. Furhermore, perfec compeiion implies equaliy beween he real wage and he marginal produc of effecive labor for each abiliy ype (Equaion 25). Workers of a paricular abiliy ype will earn a higher real wage when heir supply is relaively scarce, when he level of echnology is higher, and when physical capial per uni of aggregae effecive labor is higher. [α ( A H K ) 1 α δk ] (1 τ k ) = r (24) (1 α)a 1 α ( K H ) α η a ( H H a, ) 1 s = wa, a = H, M, L (25) Our assumpions of consan populaion and of individuals enering he model wih a predeermined and generaion-invarian level of human capial imply ha in seady sae effecive labor will be consan. Physical capial, oupu and real wages by conras will all grow a he exogenous echnology growh rae x. 2.7. Governmen 15
Equaion (26) describes he governmen s budge consrain. Demand for goods G, benefis relaed o non-employmen B (including early reiremen benefis), old-age pension benefis PP, and ineres paymens r D are financed by axes on labor T n, axes on capial T k, and axes on consumpion T c and/or by new deb ΔD +1. We define D as ousanding public deb a he beginning of period. ΔD +1 = D +1 D = G + B + PP + r D T n T k T c (26) wih: G = gy B = a=h,m,l ((1 n 1a e 1a )bw a, h 1a (1 τ w ) + (1 n 1 2a )bw a, h 1 2a (1 τ w ) +R 2 a (1 n 3a 2 )bw a, h 2 3a (1 τ w ) + (1 R 2 a )b er w a, h 2 3a (1 τ w )) PP = a=h,m,l (ρ wa j=1 (p j w a,+j 4 h ja 3 3 n ja +ρ fa ( 1 ) (w 9 a=h,m,l a,h ja 3 T n, = τ w a=h,m,l ( n +1 j ja w a, h ja T k = τ k (αy δ k K ) T c = τ c 4 j=1 (c jh 3 (1 τ w )) 3 +1 j n +1 j j=1 ja (1 τ w ))) +1 j j=1 ) +1 j + c +1 j jm + c jl +1 j ) Noe our assumpion ha he governmen claims a given fracion g of oupu. Goods bough by he governmen have no effec on privae secor produciviy, nor do hey direcly affec individuals uiliy. Non-employmen benefis (B ) are an uncondiional source of income suppor relaed o inaciviy (leisure) and non-marke household aciviies as in Rogerson (2007) and Dhon and Heylen (2009). Alhough i may seem srange o have such ransfers in a model wihou involunary unemploymen, here is clear pracical relevance. Uncondiional or quasi uncondiional benefis o srucurally non-employed people are a fac of life in many European counries. Noe also our assumpion ha he pension sysem is fully inegraed ino governmen accouns. We do no impose a specific financing of he PAYG pension plan. The governmen can use resources from he general budge o finance pensions. 2.8. Aggregae equilibrium and he curren accoun Opimal behavior by firms and households and governmen spending underlie aggregae domesic demand for goods in he economy. Our assumpion ha he economy is open implies ha aggregae domesic demand may differ from supply and income, which generaes inernaional capial flows and imbalance on he curren accoun. Equaion (27) describes aggregae equilibrium as i can be derived from he model s equaions. The LHS of (27) represens naional income. I is he sum of domesic oupu Y and ne facor income from abroad r F, wih F being ne foreign asses a he beginning of. The aggregae sock of wealh Z accumulaes wealh held by individuals who enered he model in -1, -2 and -3. A he RHS of (27) CA sands for he curren accoun in period. Y + r F = C + I + G + CA (27) 16
wih: F = Z K D CA = F +1 F = ΔZ +1 ΔK +1 ΔD +1 I = ΔK +1 + δ k K 3. Parameerizaion The economic environmen described above allows us o simulae he effecs on employmen, educaion, oupu and welfare of various changes in he pension sysem. Our main conribuion in his paper is ha we model and assess differenial effecs for individuals wih differen abiliy. This simulaion exercise requires us firs o parameerize and solve he model. Table 2 conains an overview of all parameers. Many have been se in line wih he exising lieraure. Ohers have been calibraed o mach key daa. We se he rae of ime preference a 1.5% per year, he (exogenous and consan) world real ineres rae a 4.5% per year and he physical capial depreciaion rae a 8% per year. Considering ha periods in our model las 15 years, his choice implies a discoun facor β = 0.8, an ineres rae r = 0.935 and physical capial depreciaion δ k = 0.714. In he producion funcion for goods we assume a capial share coefficien α equal o 0.3. The elasiciy of subsiuion s beween he differen abiliy ypes of effecive labor is se equal o 1.5. Our values for he rae of ime preference, he capial share and capial depreciaion are well wihin he range of values imposed in he lieraure (e.g. Alig e al., 2001; Heijdra and Romp, 2009; Ludwig e al., 2012). So is he value for s. The empirical labor lieraure consisenly documens values beween 1 and 2 (see Caselli and Coleman, 2006). For he value of he ineremporal elasiciy of subsiuion in leisure (1 θ) we follow Rogerson (2007, p. 12). He pus forward a reasonable range for θ from 1 o 3. In line wih his, we impose θ o be equal o 2. This choice implies an elasiciy of labor supply which is much higher han he very low elasiciies ypically found in micro sudies. Given our macro focus, however, hese micro sudies may no be he mos relevan ones (see Rogerson and Wallenius, 2009; Fiorio and Zanella, 2012). Four parameers relae o human capial producion. For he elasiciy wih respec o educaion ime (σ) we choose a conservaive value of 0.3. This value is wihin he range considered by Bouzahzah e al. (2002) and Docquier and Paddison (2003), bu much lower han he elasiciy of 0.80 ha we see in Lucas (1990) or Glomm and Ravikumar (1998). The choice of a conservaive value for σ excludes ha our main findings in he nex secions migh be due o an overesimaion of he reurns o educaion 3. The lieraure provides much less guidance for he calibraion of he relaive iniial human capial of medium and low abiliy individuals (relaive o he iniial human capial of high abiliy individuals, ε M and ε L ). To deermine hese parameers we rely on PISA science scores. These scores leave no doub. In abou all OECD counries he science es score of sudens a he 17 h percenile varies beween 65% and 69% of he es score of sudens a he 83 h percenile, while he science es score of sudens a he 50 h percenile varies beween 82.5% and 85.5% of he es 3 Imposing higher values for σ would only reinforce our main conclusions in his paper. 17
score of sudens a he 83 h percenile 4. The differences across counries in hese relaive scores are exremely small. We can ake hem as objecive indicaors of he relaive cogniive capaciy of low and medium abiliy individuals, and will correspondingly se L equal o 0.67 and M equal o 0.84. Las bu no leas, he efficiency parameer φ in he human capial producion funcion has been deermined by a calibraion procedure ha we discuss now. We deermined eigh parameers by calibraion. Nex o he efficiency parameer in human capial producion (φ), hese are he exogenous echnology growh rae (x), wo share parameers in aggregae effecive labor (η M and η L, where η H follows as 1 η L η M ), hree ase for leisure parameers (γ 1, γ 2, γ 3 ) and he elasiciy of subsiuion (ζ) in he composie leisure funcion in Equaion (4). The calibraion arge values are repored a he boom of Table 2. Six of hem concern Belgium: hree employmen raes, he effecive reiremen age, aggregae paricipaion in eriary educaion, and growh. We choose Belgium since i is a small open economy (and herefore maches key assumpions of our model) and since in Belgium public pension benefis are calculaed exacly as we model hem 5. The oher wo arge values are he relaive wages of young workers wih below upper secondary educaion or wih upper secondary educaion in he US compared o workers wih eriary educaion. Alhough in pracice a whole sysem of simulaneous equaions is solved in which each arge value is imporan for each parameer o be calibraed, i may be useful for our exposiion here o bring some more srucure. Cerain parameers are clearly more han ohers linked o cerain arge values. The calibraed growh rae of echnology (x) reflecs oal per capia oupu growh over a period of 15 years, annual growh in Belgium being 1.77%. The leisure parameers, including he elasiciy of subsiuion in he composie leisure funcion (4), are basically deermined so ha wih observed levels of he policy variables (ax raes, non-employmen benefi replacemen raes, pension replacemen raes, ec.) in Belgium, he model correcly predics Belgium s employmen raes by age (n 1, n 2, n 3 ) and effecive early reiremen age (R). By he same approach he efficiency parameer in human capial producion (φ) is mainly deermined o correcly predic paricipaion in educaion (e). We find ha he ase for leisure rises wih age (γ 1 = 0.074, γ 2 = 0.147, γ 3 = 0.258) and observe a sronger degree of subsiuabiliy han in he Cobb- Douglas case beween he wo ypes of leisure for older workers (ζ = 1.54). The efficiency parameer φ urns ou o be 1.21. Finally, calibraion of he share parameers η M and η L is mainly driven by he values for relaive wages of young workers in he US. They are deermined so ha wih observed levels of he policy variables in he US, and given he whole se of oher parameers, he model correcly predics hese relaive wages. As shown by Equaion (25), he share parameers are imporan deerminans of he relaive produciviy of labor. Acual wages are informaive if a close 4 The daa ha we repor are averages of he PISA resuls for he years 2000, 2003 and 2006. Ideally, for our parameerizaion, we dispose of PISA es scores for sudens aged 19. The available daa concern sudens aged 15. 5 Public pensions are proporional o average annual labor income earned over a period of 45 years, wih equal weighs o all years. In our model his comes down o ρ wa > 0, wih p 1 = p 2 = p 3 = 1/3. Only individuals wih labor income below abou 75% of he mean receive an addiional social assisance benefi, which in our model can be expressed as a basic pension for he low abiliy individuals. So, ρ fl > 0, while ρ fm = ρ fh = 0. We provide more deails in he nex secion. 18
link can be assumed beween wages and produciviy. This condiion is much more likely fulfilled in he US han in Europe, which explains he inroducion here of US relaive wages raher han Belgian ones. We provide more deail on our calibraion procedure o obain η L and η M in Appendix B. The resuls imply η L = 0.19, η M = 0.33 and η H = 0.48. Finally, we had no ex ane indicaion on he remaining parameers in he composie leisure funcion in Equaion (4). We impose equal weigh for boh leisure ypes (µ=0.5). The normalizaion parameer Γ equals 2. The size of his parameer has no impac a all on our resuls. Table 2. Parameerizaion and benchmark equilibrium Technology and preference parameers Goods producion (oupu) α = 0.30, s = 1.5, η H = 0.48, η M = 0.33, η L = 0.19 Exogenous echnology growh x = 0.301 Human capial φ = 1.21, σ = 0.3 Iniial human capial ε M = 0.84, ε L = 0.67 Preference parameers β = 0.80, θ = 2, γ 1 = 0.074, γ 2 = 0.147, γ 3 = 0.258 World real ineres rae r = 0.935 Capial depreciaion rae δ k = 0.714 μ = 0.5, ζ = 1.54, Γ = 2 Fiscal policy and pensions policy parameers (a) τ w = 67.2%, τ c = 13.4%, τ k = 27.1%, b = 59.6%, b er = 79.0%, ρ wl = 55.4%, ρ wm = 63.1%, ρ wh = 42.7%, ρ fl = 17.2%, ρ fm = ρ fh = 0% Targe values for calibraion Employmen, educaion and growh (b) n 1 n 2 n 3 R e Annual per capia growh 51.1% 56.8% 29.3% 57.9 14.1% 1.77% Relaive wages of young workers, US (c) w L h 1L /w H h 1H w M h 1M /w H h 1H 0.43 0.63 Noes: (a) Values for Belgium. For a deailed descripion of hese policy parameers, see Secion 4 in his paper; (b) Values for Belgium, see Table 1 and Appendix A. (c) As a proxy for he relaive wage of low-abiliy (medium-abiliy) young workers, we use available daa on earnings of workers of age 25-34 wih below upper secondary educaion (wih secondary educaion) in he US relaive o earnings of workers wih a eriary degree. The daa concern 2007. Daa source: OECD Educaion a a Glance, 2009, Table A7.1a. 4. Fiscal policy and pension policy in 13 OECD counries Tables 3 and 4 describe key characerisics of fiscal policy in 1995-2001/2004. Our proxy for he ax rae on labor income concerns he oal ax wedge, for which we repor he marginal rae in %. The daa cover personal income axes, employee and employer social securiy conribuions payable on 19