Immigration, Fiscal Policy, and Welfare in an Aging Population

Transcription

1 Immigraion, Fiscal Policy, and Welfare in an Aging Populaion S. Nuray Akin Universiy of Miami Deparmen of Economics Coral Gables, FL May 2011 Absrac I evaluae he welfare effecs of exogenous changes in immigraion policy by consrucing a heerogeneous agen overlapping generaions model wih agens differing in age, origin, and skills. Calibraing he model o Germany, I mach he main feaures of he social securiy and ax sysems, and accoun for differences in iner-generaional ransmission of skills and feriliy beween immigrans and naives. I find ha a prohibiion on immigraion reduces welfare for he naives, whereas a policy ha allows an annual inflow equal o 0.4 percen of he populaion increases welfare for all agens on he new balanced growh pah (by 0.1 o 2.8 percen depending on he ype of he agen). Ineracions beween he social securiy sysem, axes, and equilibrium prices are crucial: immigraion reduces wages, bu raises he renal rae of capial and he number of workers per reiree, allowing for higher pension benefis and a lower consumpion ax rae. JEL Classificaion: D6, D58, E62, F22, J11 Key Words: Immigraion Policy, Social Securiy, Aging, Overlapping Generaions Model, Welfare

2 Immigraion, Fiscal Policy, and Welfare in an Aging Populaion 1 Inroducion Does immigraion reduce or increase he welfare of curren and fuure generaions when an economy experiences rapid aging of is populaion? Many sudies in he lieraure provide mixed evidence by focusing on individual aspecs of he problem, such as fiscal susainabiliy hrough immigraion or he labor marke effecs of immigrans. This paper quanifies he effecs of changes in immigraion policy on individual welfare by consrucing a five-period life-cycle general equilibrium model. I conribues o he lieraure by explicily accouning for he ineracions beween he labor marke and he hree pillars of fiscal policy: he ax sysem, he social securiy sysem, and he immigraion policy. The model is calibraed o he German economy, which provides a naural experimen. Germany has hisorically been he major desinaion for immigrans in Europe and i provides rich micro-daa on immigrans and naives ha is necessary o idenify main characerisics of he wo groups, such as differences in skills and feriliy. Moreover, Germany is one of he mos prominen cases of aging: he raio of he populaion aged 65 and older o hose aged 15 o 65 (he dependency raio) is esimaed o increase from 28 percen o 50 percen in he nex 45 years. 1 Perhaps Germany is he mos ineresing economy o sudy due o recen changes in ax and social securiy policies in response o aging. Firs, marginal ax raes on labor income were reduced dramaically o increase he supply of labor (he op and boom raes fell by 11 percen). Conemporaneously, immigraion policy was reformed o favor inflow of high-skilled workers. Finally, he pension benefi formula was modified o include a susainabiliy facor, which reduces paymens o reirees when he dependency raio increases. The model presened here incorporaes hese elemens. We ake each model period o be 20 years. Agens differ in origin (immigran or naive), age, and skill level (low or high). Life span is uncerain. The model replicaes key feaures of ax and pension sysems. In paricular, here are marginal labor income 1 Börsch-Supan and Wilke (2003) repor ha before he pension sysem was reformed in 2001 and 2005, projecions indicaed ha he payroll ax rae needed o finance German pensions would increase from oday's 19.5 percen o more han 28 percen in 2040, if he benefi levels and labor force paricipaion raes were mainained. 2

3 and payroll axes, and pensions are indexed o lifeime earnings via a benefi calculaion formula. A key elemen of he model is he number of people of each ype in each period. To make he evoluion of he disribuion of populaion precise, I calculae skill- and origin-specific feriliy from he daa as well as a Markov skill ransiion marix, which shows he probabiliy ha a child of a paricular ype of paren will have high or low skill. The model is calibraed by using individual level micro-daa from he German Socio- Economic Panel. In he baseline, I assume ha he economy is on he balanced growh pah wih annual inflow of low- and high-skilled immigrans equal o 0.1 and 0.01 percen of he populaion, respecively. Combined, his corresponds o an iniial annual ne inflow of 83,000 people, which is in line wih he daa in 2005 provided by he German Saisical Insiue. 2 I solve for he equilibrium ransiion pah of he economy and repor resuls from six differen experimens in which eiher he skill composiion or he oal inflow of he immigrans change. There are hree imporan conclusions. Firs, higher immigran inflows increase welfare by causing a decline in he dependency raio, which allows he governmen o balance is budge wih a lower consumpion ax rae. For example, when annual inflows of young working-age immigrans of each skill level are 0.2 percen of he populaion, welfare of iniial young naives is 2.8 percen higher compared o welfare under he baseline economy. The increase is around 2.0 percen for year old naives, 0.9 percen for year old naives, and 0.1 percen for he iniial old generaion. Second, increases in life-expecancy make he reurns from immigraion higher: under he same immigran inflow, when he survival probabiliy o age 80+ is doubled, welfare increases by a bigger facor (3.1 percen for he iniial young). Third, keeping he oal inflow consan, reversing he skill composiion of immigrans improves welfare by he same order of magniude. In his paper, increased immigraion no only raises he size of he labor force, bu also lowers real wages. This negaively affecs pension benefis, as benefis are srongly linked o pas wages. However, here are wo oher impacs of immigraion. The firs is he rise in reurn o capial, which raises he reurn on savings. The second effec comes 2 Genesis (The Federal Saisical Office of Germany daabase sysem). 3

4 hrough he susainabiliy facor in he pension benefi calculaion formula. Specifically, when aging leads o an increase in he reiree-conribuor raio, he susainabiliy facor reduces he value of each pension poin earned, which in urn reduces he pension benefi. Hence, when he economy experiences a higher immigran inflow, pension benefis rise, as he number of pensioners per worker declines. In equilibrium, hese wo posiive effecs dominae he negaive effec of declining wages, and herefore he consumpion of a reiree increases. This sudy conribues o a large lieraure in public finance ha focuses on he relaionship beween demographic ransiion, fiscal susainabiliy, and immigraion. Soresleen (2000) and Bonin, Raffelhueschen, and Walliser (2000) ask wheher immigrans can help susain fiscal policy, wihou a specific emphasis on individual welfare. The former uses a calibraed dynamic general equilibrium model and concludes ha a policy ha admis 1.6 million year-old high-skilled immigrans annually could resolve he fiscal problems associaed wih he aging of he baby boom generaion in he U.S. The laer uses he generaional accouning framework (Auerbach, Gokhale, and Kolikoff, 1994) and finds ha immigraion can only parially decrease he fiscal burden of fuure generaions induced by aging in Germany. Ohers sudy labor-marke effecs of immigrans wih an emphasis on wages. Pischke and Velling (1997) finds no evidence of derimenal effecs on naive wages by using daa on Germany, while Borjas (2003) concludes ha a 10 percen increase in supply reduces wages by 3 o 4 percen in he U.S. Krueger (1999), Fehr (2000), Imrohoroglu, Imrohoroglu, and Joines (1995), Imrohoroglu, Imrohoroglu, and Fuser (2003) focus on quanifying welfare effecs of social securiy wihou explicily modeling immigraion policy. A hree-region world economy (U.S., Japan, and he Euro-region) model wih labor immobiliy appears in Fehr, Jokisch, and Kolikoff (2005), which concludes ha, independen of he skill level, an expansion of immigraion will no aler he capial shorage, ax hikes, and he reducion in real wages expeced along he demographic ransiion. My approach in his paper is unique, as he impac of immigraion on welfare is sudied by incorporaing he deails of he social securiy sysem and he ax policy in he model, which are necessary o idenify he ineracion among differen componens of fiscal policy. 4

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6 2 The Model The economy consiss of hree secors: heerogeneous individuals wih elasic labor supply, a perfecly compeiive represenaive firm wih consan reurns o scale producion echnology, and a governmen ha balances is budge. 2.1 Individuals Individuals live for a maximum of five periods and differ wih respec o age, origin, and working abiliy. A model period is 20 years. In period one (youh), individuals do no work or save. They derive consumpion from he ransfer income paid by he governmen. In periods wo and hree (adulhood), individuals choose opimal consumpion c, working hours n, and end-of-period wealh holding a, aking he axes, facor prices, and he immigraion policy as given. They pay payroll and labor income axes wih marginal raes τ p and τ, respecively. Consumpion and capial income are axed a fla raes τ c and τ k. Individuals can have children only in he second period, beween he ages of 20 and 39. The feriliy rae is exogenous. In periods four and five (reiremen), individuals do no work. Hence, consumpion is derived from governmen ransfers χ and proceeds from asses. There is longeviy uncerainy. The condiional probabiliy of surviving from age i o i+1 is λ i. In case of accidenal deah, individual wealh becomes a par of he governmen's revenue. The ype of an agen alive in is denoed by (, o, s) is origin, o = n for naives and m age; o { m, n} working abiliy (or produciviy), s i, where { 1, 2,3, 4,5} i is o = for immigrans; and s { l, h} = l for low-abiliy, s= h for high-abiliy. is Figure 1: The Life-cycle of an Individual Age 1 (0-19) Age 2 (20-39) Age 3 (40-59) Age 4 (60-79) Age 5 (80-99) A child is born Becomes a paren and working-age adul Reires Dies wih probabiliy 1 6

7 An agen's efficiency unis, e ios,,, is exogenously given. Wage per efficiency uni is w. Therefore, we i, o, sn i, o, s, is he oal labor income of an agen who supplies n unis of labor a. A ax funcion T compues oal axes paid on labor income (he sum of payroll and income axes). A pension funcion P compues he benefi for an individual as a funcion of his labor earnings and average earnings y in he economy during adulhood. Tables 1 and 2 show he main variables and funcions used in he model The Individual s Problem An individual born a chooses {,, } subjec o n c a + o maximize expeced uiliy ios,,, ios,,, i 1, os,, ios,,, c c n E + λ k 1 γ j= 1 k = 2 1 γ c (1 + τ ) = χ 1, os,, c, 1, o, α 1 γ j 1 j α α γ + 1, os,, β j+ 1, os,, + j(1 j+ 1, os,, + j) c (1 + τ ) + a w e n + χ T( w e n ) 2, os,, + 1 c, + 1 3, os,, , os, 2, os,, + 1 2, o, , os, 2, os,, + 1 c (1 + τ ) + a w e n + χ T( w e n ) 3, os,, + 2 c, + 2 4, os,, , os, 3, os,, + 2 3, o, , os, 3, os,, + 2 +(1 + (1 τ ) r ) a k + 2 3, o, s, + 2 c (1 + τ ) + a (1 + (1 τ ) r ) a + χ 4, o, s, + 3 c, + 3 5, o, s, + 3 k + 3 4, o, s, + 3 4, o, + 3 c (1 + τ ) (1 + (1 τ ) r ) a + χ n + P( w e n, w e n, y, y ) 5, os,, + 4 c, + 4 k + 4 5, os,, + 3 4, o, + 3 4, os,, + 2 = n5, os,, + 3 = , os, 2, os,, , os, 3, os,, P( w e n, w e n, y, y ) + 1 2, os, 2, os,, , os, 3, os,, Skill Transmission and he Measure of Newborns I assume ha children of immigrans are naives and ha individuals can have children only in he second period of heir lives. Transmission of skills from parens o children follows a Markov process. Le ϕ os, denoe he number of children per person of origin-o and skill-s. Le μ 2, os,, denoe he number of child-bearing individuals a ime. Le π os, 7

8 be he probabiliy ha a paren of origin-o and skill-s will have a high-skilled child. Then, he number of newborns of each skill level is: ( ) μ = ϕ μ π + ϕ μ π 1, nh,, ns, 2, ns,, ns, ms, 2, ms,, ms, s { l, h} ( ( ) ( )) μ = ϕ μ 1 π + ϕ μ 1 π. 1, nl,, ns, 2, ns,, ns, ms, 2, ms, ms, s { l, h} Skills are assumed o be exogenous and fixed during an agen s lifeime. 2.2 The Firm s Problem The represenaive firm hires labor ( N ) and capial ( K ) o produce oupu. The producion funcion is Cobb-Douglas: θ 1 ( z N ) θ Y = K, (1) where z is an exogenous labor augmening produciviy process wih deerminisic growh rae Γ. The aggregae labor inpu each agen in he economy: ios,, ios,,, ios,,, i {2,3} o { m, n} s { l, h} N is he sum of efficiency unis supplied by N = e n μ. (2) The aggregae capial inpu K is he sum of oal privae wealh: K a μ =. (3) ios,,, ios,,, i {3,4,5} o { m, n} s { l, h} Le δ be he depreciaion rae of he capial sock. Given he renal rae of capial r and he wage rae w, he firm maximizes profis: { K, N } θ { ( ) 1 θ K zn r δ K wn } max ( + ). (4) 2.3 The Governmen Fiscal policy consiss of fla ax rae τ k on capial income and τ c on consumpion; marginal labor income ax rae τ and payroll ax rae τ p ; per-capia age-specific public expendiures g i ; per capia pension benefi P ha is condiional on a worker s 8

9 produciviy, and public ransfers (excluding pensions) χ ha are age- and originspecific. 3 Age-specific per-capia governmen expendiures grow a he growh rae of he per-capia Gross Naional Produc, Γ. 4 Hence, aggregae public expendiures are: G ( 1 ) g μ,,, = +Γ. (5) i i o s ios,, Le i, o, s i, o, s, T( we n ) denoe he oal income and payroll axes paid ou of labor income by a ype ( i, o, s) individual. Denoe he aggregae ax revenues of he governmen by Rev, aggregae non-pension relaed ransfers by pension benefis as Pen. Then, Rev = T( we,, n,,,) μ,,, + τ c μ,,,,,, + r τ K ios ios ios c ios ios k ios,, ios,, TR, and aggregae (6) ( 1 ),,,, TR = +Γ χ μ (7) i o i o s io, Pen = Pios,,, μios,,,. (8) ios,, Governmen balances budge in each period. The consumpion ax adjuss o mainain balance. Hence, G + TR + Pen = Rev. (9) 2.4 Immigraion Policy Immigraion policy ψ { ψ2, l, ψ2, h} = deermines he number of immigrans of age (model age 2) of each abiliy level (low and high) as a fixed fracion of he size of he populaion in he previous period. I do no consider an inflow of immigrans aged 40 o 59. Akin (2006) shows ha such a policy will no be welfare improving because hose agens, on average, conribue for fewer years o he social securiy sysem compared o he longer years of reiremen benefis hey receive. Therefore, I analyze a class of immigraion policies ha allow he enry of younger workers. 3 The cos of bringing one more agen o he economy is i g. This parameer depends only on he age of an agen. I is crucial o consider differen coss of immigrans and naives on he governmen s budge; however such disaggregaed daa on governmen expendiures is no available. 4 See Auerbach, Kolikoff, Hagemann, and Nicolei (1989). 9

10 2.5 Law of Moion for Populaion Le μ denoe he oal populaion in he economy a ime. Given he immigraion policy ψ, children per person { ϕ os }, skill ransiion probabiliies, o { m, n } { π } os, o { m, n }, s { l, h } survival probabiliies { i} i { 1,2,3,4} λ, populaion evolves according o: ( ) μ = ϕ μ π + ϕ μ π 1, nh,, ns, 2, ns,, ns, ms, 2, ms,, ms, s { l, h} ( ( 1 ) ( 1 )) μ = ϕ μ π + ϕ μ π μ 1, nl,, ns, 2, ns,, ns, ms, 2, ms,, ms, s { l, h} { } { } = λμ i+ 1, n, s, i i, n, s, 1, for i 1,2,3,4 and s l, h { } μ, for, 2, ms,, = ψ2, sμ 1 s l h μ μ { } { } = λμ i+ 1, m, s, i i, m, s, 1, for i 2,3,4 and s l, h = μ. (10) 1 i, o, s, 1 ( ios,, ), and The skill ransiion probabiliies are imporan in deermining he number of agens who are high- or low-skilled a any ime in he economy. Several sudies in he lieraure esablished ha many counries experience a low inergeneraional mobiliy in schooling and income. For example, by using German micro-daa, Dusmann (2005) repors ha parenal background is srongly relaed o he school choice and school achievemen of he child. He also finds lile convergence for individuals from differen parenal backgrounds. Acemoglu and Pischke (2001) find ha a 10 percen increase in family income generaes a 1.4 percen increase in he probabiliy of aending a four-year college in he U.S. This rigidiy is incorporaed o he model. 3 Compeiive Equilibrium Definiion (Compeiive Equilibrium) Given he iniial disribuion of asses a 0, populaion 0 μ, governmen ransfers { χ } io. io, and τ, feriliy raes and skill ransiion probabiliies {, } and expendiures g i ; ax raes τ c, τ k, τ p, ϕ π, survival probabiliies os, os, os, 10

11 { λ } i i, and immigraion policy ψ, an equilibrium is a sequence { w, r, N, K, Rev, Pen, G, TR, τ,{ n, c, a, μ } } c, ios,,, ios,,, ios,,, ios,,, ios,, = 0 (i) {,, } n c a + solves he individual s problem, ios,,, ios,,, i 1, os,, ios,,, such ha (ii) {, } K N solves he firm s problem, (iii) The goods marke clears: ( ) 1 θ K z N = K + 1 (1 δ) K + G + μ,,, c,,,, θ ios ios ios,, (iv) The labor marke clears (Equaion (2) holds.), (v) Aggregae capial equals aggregae privae wealh (Equaion (3) holds.), (vi) The consumpion ax rae balances he governmen's budge (Equaion (9) holds.), (vii) Populaion evolves according o (10). 4 Calibraion I calibrae preference and producion funcion parameers using he necessary condiions of he derended version of he model. Efficiency unis, children per person, skill ransiion probabiliies, age-origin disribuion of non-pension ransfers, and oal working hours are calculaed using he German Socio-Economic Panel Daa (GSOEP) ha is published by he German Insiue for Economic Research (DIW Berlin). I used he European Commission s Economic and Financial Affairs repor on he German pension sysem (2005) o replicae he pension sysem. The income and social securiy ax schedule informaion comes from OECD s 2006 repor on axing wages. 4.1 The daa The GSOEP is a represenaive longiudinal micro-daa on persons and households in Germany ha sars in I conains informaion on educaion levels, sources of income (labor income, ransfers from he governmen and oher sources of income), number of children, naionaliy, and work hours for he differen groups ha consiue he German populaion. Individuals over age 16 are inerviewed every year. For he purposes of his paper, I use hree sub-samples of he daa: Sample A Residens in he Federal Republic of Germany, Sample B Foreigners in he Federal Republic of Germany, and Sample C German residens in he German Democraic Republic. 11

12 Sample A (he Wes-German sample) includes daa on persons in privae households wih a household head who does no belong o he main foreigner groups of guesworkers (Turkish, Greek, Yugoslavian, Spanish, or Ialian). Sample B has informaion on persons in privae households wih a household head from main foreigner guesworker groups. This sample consiss of five auonomous samples for he five numerically larges foreign naionaliy groups living in Wes-Germany as immigrans in Sample C, he Eas-German sample, covers persons in privae households where he household head was a German Democraic Republic ciizen. An immigran in he model is an individual who belongs o he main foreigner guesworker groups. The disribuion of aggregae public ransfers among differen ransfer caegories, as well as public expendiures oher han ransfers, is published by he German Saisical Insiue (Saisisches Bundesam). In his paper, I use he 2005 daa. 4.2 Preference parameers. The coefficien of relaive risk aversion, γ, is assumed o be 2.0 in he main calibraion, which is commonly used in he lieraure for overlapping generaions models. 5 The ime preference parameer β is chosen so ha he seady sae equilibrium of he model replicaes he capial-oupu raio in he German economy. The consumpion share parameer α is chosen so ha he seady sae average annual working hours of individuals beween he ages 20 and 59 are consisen wih he GSOEP. On average, annual working hours are I suppose ha he maximum working hours of an individual is 100 hours per week and 5200 hours per year. 4.3 Efficiency unis. The efficiency unis for working-age individuals are esimaed from he annual labor income profiles of immigrans and naives of each skill level and age. For he purposes of his paper, individuals wih a leas 15 years of schooling (he equivalen of hree or more years of college educaion) are assumed o be high-skilled. Condiional on paricipaion in he labor marke (more han 450 hours a year), I calculae he average hourly wage for boh immigrans and naives of working age for each skill level. Noe ha individuals in he model work only in he second and hird periods of heir lives, ages 20 o 59. Table 4 liss he esimaed average hourly wages in Euros in For example, see Nishiyama and Smeers (2003, 2007). 12

13 4.4 Skill Transiion. In order o calculae skill ransiion probabiliies, I idenify parens and children in he firs sample of he micro panel daa, I hen divide parens ino four groups: low-skilled naives, high-skilled naives, low-skilled immigrans, and highskilled immigrans. In order o find he skill level of heir children, I follow he children in he daa each year unil he las sample in Children and parens wih incomplee informaion on years of schooling over ime are dropped from he sample. Given a caegory of parens, I find he skill ransiion probabiliies by calculaing he number of children of each skill level as a fracion of he oal number of children who belong o hose parens. Findings are presened in Table Feriliy Raes and he Iniial Disribuion of he Populaion Feriliy raes. Children per person are esimaed from he GSOEP for boh immigrans and German naives of each skill level. Individuals can have children only in he second period of life in he model. Hence, he esimaes in Table 6 correspond o children per person of ages in he daa. The challenge in calculaing feriliy across origins and skill levels is how o allocae children wih one high-skilled and one low-skilled paren, or children who have one German and one immigran paren. In his sudy, all children who have a leas one immigran paren are reaed as children of immigrans. Once children have been allocaed o German naive or immigran caegories, he allocaion of children o skill levels is done in accordance wih he skill inensiy in he household. The following seps give he deails of he procedure o calculae he number of children per ferile-age adul of each skill-s and origin-o: 1. Link children and aduls by maching heir household numbers. Allocae children who are mached wih boh naive and immigran aduls o he immigran aduls. This maching process forms pseudo-households consising of ferile-age aduls and he children who are allocaed o hem on he basis of origin. 2. For each pseudo-household compue he proporion of aduls who are of skill-s and muliply his by he number of children in he pseudo-household. 3. Sum he resuls in Sep 2 across pseudo-households in he daa. This sum is he oal number of children allocaed o skill-s and origin-o. 4. Divide he oal number of children from Sep 3 by he number of ferile-age aduls of skill-s and origin-o in he micro-daa. 13

14 The numbers in Table 6 are calculaed as an average of figures beween 1984 and The Iniial Disribuion of he Populaion. The German Saisical Office Populaion Saisics summarizes he disribuion of populaion across ages and naionaliies. Daa by educaion groups is no available. Therefore, I assume ha he disribuion of aggregae populaion across skills mimics he corresponding disribuion from he micro-daa, which is a represenaive sample of he whole populaion. Table 7 shows he calculaed disribuion of populaion for Survival Probabiliies. I use daa published by he Human Moraliy Daabase a he Universiy of California Berkeley. The las daa available for Germany is for he year Therefore, I assume ha he survival probabiliies are fixed a heir 2005 levels. Calculaed probabiliies are shown in Table Depreciaion rae of fixed capial. Le η be he populaion growh rae on he balanced growh pah. The depreciaion rae of fixed capial, δ, is chosen such ha: Toal Gross Invesmen δ = Γ η. Fixed Capial In 2001, gross fixed capial formaion (invesmen), GDP and oal ne capial sock for Germany were 420.8, , billion Euros in curren prices, respecively. 6 Given hese values, I mach a seady sae capial-oupu raio of 3.2 and and invesmen-oupu raio of Hence, he raio of gross invesmen o fixed capial is 6.5 percen. I assume ha he GDP per capia growh rae, Γ, is 1.89 percen, which is he average annual growh rae of GDP per capia in Germany for he las wo decades. 7 Noe ha he populaion growh rae on he balanced growh pah depends on he immigraion policy. For he baseline economy on a balanced growh pah wih 0.2 percen immigraion of each age-skill caegory annually, η is approximaely 1 percen per year. Y 4.7 Share of capial in he producion funcion: θ is chosen such ha δ + r = θ. K Given Y K = 0.31, r = 4.16 percen, δ = 4.66 percen, we ge θ = Table 8 shows he values of he calibraed parameers oher han hose of ax schedule, fixed ransfers, and social securiy. 6 See Kamps (2005). 7 SourceOECD, Online Daabase, Naional Accouns Daa (2006). 14

15 4.8 Taxes, Pensions, and Fixed-ransfers Taxes. All axes in he model are colleced a he individual level. The ax sysem includes progressive axes on labor income as well as a capial income ax and a consumpion ax. The capial income ax rae is assumed o be a fla-rae of 15 percen, which is he sandard rae of corporae ax in Germany. The consumpion ax adjuss in each period in order o balance he governmen budge. Therefore, i is a variable ha is deermined in equilibrium. The labor income ax rae replicaes he income ax schedule in Germany in The basic ax allowance is 7,664. The marginal ax rae increases linearly from 15 percen o 24 percen unil 12,739. Beween 12,740 and 52,151, i increases linearly o 42 percen. 8 For incomes higher han 52,152, he ax rae is consan a 42 percen (See Figure 2.). More specifically, le X be he axable income rounded o he nex full euro amoun. Define Y = (X 7,664)/10,000; Z = (X 12,739)/10,000. The income ax liabiliy (in Euros) is calculaed according o he following formula: 0 if X 7,664 (883.7Y + 1,500) Y if 7,665 X 12,739 Tax liabiliy = (228.7Z + 2,397) Z if 12,740 X 52, X 7,914 if X 52,152. Compulsory social securiy conribuions also replicae he marginal raes in They consis of a ax for pension and unemploymen benefis (26 percen) up o a gross income ceiling 62,400, and ax for sickness and long-erm care (14.7 percen) up o a gross income ceiling of 42,300 (See Figure 3.). Boh he employer and he employee pay equal shares of he payroll ax. Since he incidence of he payroll ax does no affec he equilibrium resuls, I assume ha i is fully paid by he employee. Figure 4 shows he sum of income and social securiy ax raes on income. Since all hese raes are yearly and one period in he model is 20 years, he ax schedule in he calibraion is adjused o be compaible wih he model. 8 See OECD (2006). 15

16 Pension Benefis. The general pay-as-you-go, earnings-relaed sauory pension scheme covers around 85 percen of he employed populaion. 9 For each year of conribuions, a worker in he sauory pension scheme receives pension poins ha reflec his relaive earnings posiion. The average wage in a paricular year is equal o one pension poin. The individual pension benefi a (denoed as P ) is calculaed as he produc of he sum of pension poins earned hrough working-lifeime (pp) and he value of one pension poin, ppv, measured in Euros per monh. Tha is, P = pp* ppv. Pension poin in working-year j is deermined by he earning of an individual in ha year ( we j jos,, n ios,,, j) relaive o he average earnings of all he workers in he economy ne of axes ( earned is: y j ). Therefore, for an individual who works for I years, he sum of pension poins I we pp = j= 1 j j, o, s i, o, s, j y j n. As an example, a person reiring wih a conribuion period of 40 years based on an average income earns 40 pension poins over his working years. These pension poins are muliplied by he curren pension poin value ( for pensioners from Wesern Germany), which gives a gross pension of 40 * = 1,045.2 per monh. The pension poin value is adjused annually. The adjusmen facor depends on growh rae of gross earnings and "he susainabiliy facor," which reduces benefis if he number of conribuors o he sysem decreases relaive o he number of pensioners. 10 In he model, each individual works for 40 periods (beween he ages of 20 o 59) and reires a age I approximae he Susainabiliy Facor by he change in he raio of pensioners o conribuors from one period o anoher. Therefore, in he calibraion, value of one pension poin a ime is calculaed as: 9 See Börsch-Supan and Wilke (2003). 10 The adjusmen formula also includes he "Rieser Facor," which considers ransiion o a muli-pillar pension sysem in which conribuions o ax subsidized volunary privae pension scheme (second pillar) reduce benefis in he public scheme (firs pillar). However, Bonin (2001) and Börsch-Supan (2002) repor ha since he labor-marke assumpions underlying he Rieser Facor are unrealisic, is effecs on he susainabiliy of he pension sysem will be minimal. Hence, I absrac away from i. 11 In 2005, he average effecive age of reiremen in Germany was 61.7 for men and 60.7 for women. (See Saisics on Average Age and Official Age of Reiremen in OECD Counries, OECD, 2006.) 16

17 vpp y pensioners conribuors conribuors = vpp 1 + y pensioners 2 The consan, 0.25, ha muliplies he Susainabiliy Facor is called he "allocaion facor" in he German Pension Sysem. Non-pension Transfers per Person. Age-origin profiles of oal ransfers per capia are esimaed from he GSOEP. The daa includes quesions abou monhly old-age and disabiliy benefis, child benefis, maerniy benefis, general welfare, healh and longerm care benefis, housing allowances, subsisence allowances, and unemploymen benefis. Since he pension, healh and long-erm care benefis are specifically modeled, ransfers per person exclude hose iems. Table 9 summarizes he resuls. 5 Resuls 5.1 Experimens I assume ha he economy is iniially on a balanced growh pah (in 2005) wih an annual inflow of year old low- and high-skilled immigrans equal o 0.1 percen and 0.01 percen of he German populaion, respecively. This corresponds o an annual ne inflow of around 83,000 immigrans, which is in line wih he daa of 2005 and 2005 published by he German Saisical Insiue. I invesigae he resuling effecs on allocaions, prices, and welfare of an exogenous one-ime change in immigraion policy. I repor welfare resuls from six differen experimens in which eiher he skill disribuion of immigrans or he oal size of immigran inflows change. All simulaions are execued by derending he model. The algorihm used o solve for he ransiion pah is given in he Appendix. 5.2 Equilibrium allocaions and prices To se he background for he welfare resuls, I firs summarize he effecs on allocaions and prices of a new immigraion policy under which annual inflow of immigrans of each 17

18 ype is 0.2 percen of he oal populaion. 12 Figures 5-10 show he movemen of he economy on he ransiion pah. The year 2005 is he iniial balanced growh pah, 2025 is he firs period afer he policy change, and 2165 is he year in which he economy reaches he new balanced growh pah. Consumpion: This policy increases he consumpion of individuals of every age, origin, and skill group. The main facor ha affecs equilibrium consumpion is he decline in he consumpion ax rae. Alhough immigrans increase governmen expendiures and pensions in he aggregae, governmen's ax revenue goes up by a bigger facor. Thus, he consumpion ax rae ha balances he budge goes down, allowing for an increase in consumpion. For reirees, he increase in pension benefis generaed hrough a lower dependency raio is anoher facor ha conribues o higher consumpion. Labor supply: Labor supply is quie robus o he change in immigraion policy. We observe a sligh increase (0.1 percen) in hours worked for individuals aged on he new balanced growh pah year old workers experience a decline in he working hours by 0.2 percen. Noe ha year old agens face wo opposie effecs. Firs, he rise in he renal rae increases he asse income, which reduces incenive o work. Second, he decline in wages provides incenive o work more. Here, he firs effec dominaes he second. 13 Prices: Wih increased immigraion, he rae of reurn on capial increases from 5.4 percen in 2005 o 5.7 percen in The wage rae is lower on he ransiion pah. An increased inflow of immigrans reduces he capial-labor raio, which causes a decrease in he wage rae and an increase in he ineres rae. Pensioner-conribuor raio: The raio on he new balanced growh pah (0.57) is smaller relaive o is iniial value (0.41). As more working-age immigrans are allowed, he imbalance creaed by rapid aging improves. Individual pensions: In his experimen, pension benefis increase. Two opposing facors conribue o his behavior hrough he indexaion formula. Firs, declining wage earnings on he ransiion pah push pension benefis down. Second, he reducion in he 12 I only repor he welfare resuls for all experimens. The graphs for he oher five experimens are available upon reques. 13 Individuals do no have asse income in he second period of he lifecycle. Hence, for hem, he only relevan effec is he second one. 18

19 pensioner-conribuor raio due o increased immigraion creaes a rise in benefis hrough he susainabiliy facor. In his experimen, he second effec dominaes. In summary, here are hree ineresing resuls. Firs, he exac modeling of he social securiy sysem enables us o assess he opposing ineracions beween changes in wages and changes in he pensioner-conribuor raio. The inclusion of he susainabiliy facor raises pension benefis via increasing he pension poin value, compensaing for a decline in benefis caused by declining wage earnings. 5.3 Welfare In order o measure he change in welfare, I calculae percenage change in real income ha is needed o achieve lifeime uiliy under he new immigraion policy. Since individual preferences are of consan elasiciy of subsiuion ype, he change in real income is a perfec index of change in welfare. Table 10 summarizes he resuls for he new balanced growh pah. There are wo main conclusions. Firs, when here is a prohibiion on immigraion (Experimen 1 in Table 10), naive welfare goes down by 3 percen. Second, an increase in welfare may be achieved regardless of he skill ype of immigrans. Keeping he oal inflow consan, we see ha policies admiing more low-skilled immigrans achieve a similar welfare improvemen as policies admiing more high-skilled immigrans. The resuls indicae ha he main channel hrough which immigraion influences equilibrium allocaions is he pensioner-conribuor raio. Bigger inflows, independen of he skill level, improve he dependency raio by allowing more workers o ener he labor marke. Low-skilled immigrans help slighly more, as heir feriliy rae is he highes among all ypes of agens in he economy. On he new balanced growh pah, relaive o he iniial pah, we observe ha consumpion is higher. Labor supply is slighly higher for agens aged and is lower for hose aged The increase in consumpion is mosly due o a decline in he consumpion ax rae. As an example, under Experimen 2, consumpion ax rae goes down from is iniial level of 20 percen o 9 percen. Similar welfare conclusions hold on he ransiion pah. Table 11 shows he resuls for cohors alive a he firs period of he policy change (2025). Figures 5 o 10 19

20 illusrae he behavior of some of he key equilibrium variables on he ransiion from he iniial balanced growh pah o he new one under Experimen 2. Welfare of all ypes of agens goes up under increased immigraion scenarios. 5.4 The Role of he Susainabiliy Facor To isolae he role of he susainabiliy facor in he resuls, I consider wha would occur if he allocaion facor were se o zero. Hence, he indexaion formula becomes: y vpp = vpp 1 y 1 2, where he pension poin value a depends only on is value a 1 and he growh rae of earnings. I evaluae he resuls from wo experimens. Firs, I consider a shif o a policy ha prohibis immigraion. Second, I change he immigraion policy such ha annual inflow of each skill ype of immigrans is 0.2 percen of he populaion. For each experimen, I firs calculae wo differen equilibrium balanced growh pahs - one wih he susainabiliy facor in effec, and one wihou i. Then, I compare he oucomes. Under a shif o a policy ha prohibis immigraion, consumpion and welfare of each agen decline, regardless of wheher or no he susainabiliy facor is included in benefi calculaions. The reason is he rise in he pensioner-conribuor raio due o low naive feriliy. However, when he benefi formula includes he susainabiliy facor, he rise in he dependency raio causes a decline in individual pensions. Hence, in he aggregae, governmen expendiures on pensions are lower compared o a nosusainabiliy-facor scenario, which makes i possible for he budge o balance wih a lower consumpion ax rae. As a resul, when he wo balanced growh pahs are compared, he one ha incorporaes he susainabiliy facor delivers lower individual pension benefis and consumpion ax rae, bu higher consumpion and welfare. In he case of posiive immigran inflows, he conclusion is reversed: individual consumpion and welfare are higher in he absence of he susainabiliy facor. Wih more immigrans in he economy, he pensioner-conribuor raio declines. Hence, when he susainabiliy facor is included, he value of each pension poin goes up, increasing he benefi for each individual. However, his also raises aggregae governmen spending on 20

21 pensions, necessiaing a higher consumpion ax rae o balance he budge. Therefore, he new balanced growh pah consumpion as well as welfare are lower compared o heir levels when he susainabiliy facor is excluded from calculaions. In his experimen, exclusion of he susainabiliy facor improves welfare 0.5 percen more relaive o he oucome wih he susainabiliy facor. In summary, he inclusion of a susainabiliy facor is beneficial for an economy ha ries o minimize immigraion; bu derimenal o one ha would like o pursue a more liberal immigraion policy. 5.5 An increase in life-expecancy In he developed world, life-expecancy has increased subsanially over ime. For example, over he las cenury, U.S. life-expecancy a birh rose from 48 o 75 years among men, and 51 o 80 years among women. 14 In Germany, beween 1962 and 2002 he average life expecancy has increased from 67.1 years o 75.6 years among men, and 72.7 o 81.3 among women. 15 Therefore, i is imporan o undersand he implicaions of immigraion in an economy where individuals live longer. To achieve his, I double he condiional probabiliy of surviving from age 60+ o 80+, ha is, I se λ 4 = in he new experimen. I is no surprise ha increased life expecancy resuls in higher posiive influence of immigraion. As more people reach older ages, number of elderly relaive o hose of he working-age rises. Therefore, more immigraion helps he economy by increasing he size of he conribuors. On he ransiion pah, welfare of each ype increases by 0.1 o 0.3 percen relaive o he level observed when λ 4 = Sensiiviy Analysis In he model, he only parameer ha is no calibraed is he coefficien of relaive risk aversion γ, whose value is assumed o be 2. The values ha are used in he lieraure range from 0.5 o 4 for life-cycle models. To evaluae he robusness of he resuls o he degree of risk aversion, I solve for equilibrium where risk aversion is equal o 0.5, 1, or 3 14 Cener for Disease Conrol and Prevenion (2005). 15 See Klenk, Rapp, Buchele, Keil, and Weiland (2007). 21

22 and repor he percenage change in welfare on he new balanced growh pah relaive o Under he new policy, he annual inflow of each ype of immigrans is 0.2 percen of he populaion (Experimen 2). The resuls are presened in Table 13. Alhough lower degrees of risk aversion lead o a smaller increase in welfare on he new balanced growh pah, he behavior of he equilibrium allocaions do no change. For all values of γ, consumpion and welfare increase for all ypes, labor supply is seady, he wage rae declines, and he ineres rae rises. 6 Concluding Remarks In his paper I analyzed how a change in immigraion policy would affec governmen finances and individual choices by incorporaing key elemens of he German social securiy and income ax sysems in an overlapping generaions model. One of he main findings is ha allowing an annual immigran inflow equal o 0.4 percen of he populaion will increase consumpion and welfare. This is due o a rise in he reurn o savings and a decrease in he consumpion ax rae. There are wo opposie effecs of immigraion on an individual's pension benefis. Firs, a decline in he wage rae reduces benefis, as he laer is srongly linked o he former hrough he indexaion formula. Second, immigraion leads o an improvemen in he reiree-conribuor raio, which raises benefis hrough he susainabiliy facor. The ne effec on pensions is posiive. Anoher ineresing resul is he improvemen in welfare regardless of he skill composiion of immigrans. Many heaed debaes on immigraion in he developed world are based on he argumen ha low-skilled immigrans lower he well-being of naives because hey bring wages down. This paper proves oherwise. Alhough naive wages decline afer an immigran inflow, he improvemen in he dependency raio no only leads o a rise in pension benefis; bu also reduces axes on consumpion. Finally, he paper delivers a clear policy recommendaion. Naions wih aging populaions would benefi from opening borders o young, working-age immigrans, as long as hose individuals conribue o he sysem as ax-payers. 22

23 References Acemoglu, Daron and J.-S. Pischke (2001). "Changes in he Wage Srucure, Family Income, and Children's Educaion," European Economic Review 45, Akin, S. Nuray (2006). Populaion Aging, Public Expendiures, and Immigraion Policy in Germany, Ph.D. Disseraion, Universiy of Minnesoa, Deparmen of Economics. Auerbach, Alan, and L. Kolikoff (1987). Dynamic Fiscal Policy. Cambridge Universiy Press. Auerbach, Alan, L. Kolikoff, R. Hagemann, and G. Nicolei (1989). The Dynamics of an Aging Populaion: The Case of Four OECD Counries. NBER Working Paper Auerbach, Alan, J. Gokhale, and L. Kolikoff (1994). Generaional Accouning: A Meaningful Way o Evaluae Fiscal Policy, Journal of Economic Perspecives 8, Bonin, Holger (2001). "Will i Las? An Assesmen of he 2001 German Pension Reform," IZA Discussion Paper 343, Germany. Bonin, Holger, B. Raffelhueschen, and J. Walliser (2000). Can Immigraion Alleviae he Demographic Burden? FinanzArchiv 57, Borjas, George (2003). The Labor Demand Curve is Downward Sloping: Reexamining he Impac of Immigraion on he Labor Marke, Quarerly Journal of Economics 118, Börsch-Supan, Axel (2000). "A Model Under Siege: A Case Sudy of he Germany Reiremen Insurance Sysem," The Economic Journal 110, Börsch-Supan, Axel (2002). "A Blue Prin for Germany's Pension Reform," Mannheim Insiue for he Economics of Aging Discussion Paper 02002, Mannheim Universiy. Börsch-Supan, Axel, A. Reil-Held, and C. B. Wilke (2003). "How o Make a Defined Benefi Sysem Susainable: he 'Susainabiliy Facor' in he German Benefi Indexaion Formula," MEA Disscussion Paper 03037, Mannheim Universiy. Börsch-Supan, Axel, and R. Schnabel (1998). "Social Securiy and Declining Labor Force Paricipaion in Germany," American Economic Review 88,

24 Börsch-Supan, Axel, and C. Wilke (2003). "The German Public Pension Sysem: How i Was, How i Will Be?," MEA Discussion Paper 34003, Mannheim Universiy. Cener for Disease Conrol and Prevenion (2005). Healh, Unied Saes, 2005, wih Charbook on Trends in he Healh of Americans, Conesa, Juan C. and D. Krueger (1999). "Social Securiy Reform wih Heerogenous Agens," The Review of Economic Dynamics 2, Dusman, Chrisian (2005). "Parenal Background, Secondary School Track Choice, and Wages," Oxford Economic Papers 56, European Commission, Economic and Financial Affairs (2005). Modelling he Impac of Aging Populaions on Public Spending: Counry Fiche on he German Pension Sysem, Fehr, Hans (2000). Pension Reform during he Demographic Transiion, Scandinavian Journal of Economics 102, Fehr, Hans, S. Jokisch, and L. Kolikoff (2005). The Role of Immigraion in Dealing wih he Developed World s Demographic Transiion, NBER Working Paper Friedberg, Rachel M., J. Hun (1995). "The Impac of Immigrans on Hos Counry Wages, Employmen, and Growh," The Journal of Economic Perspecives 9, Genesis-Online (The Federal Saisical Office of Germany daabase sysem.) The Federal Saisical Office of Germany, Wiesbaden, Germany. German Federal Minisry of he Inerior (2005). Immigraion Law and Policy, Berlin, Germany. Human Moraliy Daabase. Universiy of California, Berkeley and Max Planck Insiue for Demographic Research. Available a Imrohoroglu, Ayse, S. Imrohoroglu, and D. Joines (1995). "A Life-Cycle Analysis of Social Securiy," Economic Theory 6, Imrohoroglu, Ayse, S. Imrohoroglu, and L. Fuser (2003). "A Welfare Analysis of Social Securiy in a Dynasic Framework," Inernaional Economic Review 44, Judd, Kenneh, F. Kubler, and K. Schmedders (2003). Compuaional Mehods for Dynamic Equilibria wih Heerogeneous Agens, in M. Dewaripoin, L. P. Hansen, and S. J. Turnovsky, eds, Advances in Economic Theory and Economerics III, New York. 24

25 Kamps, Crisophe (2005). New Esimaes of Governmen Ne Capial Socks for 22 OECD Counries , IMF Working Paper 0467, Inernaional Moneary Fund. Klenk, Jochen, K. Rapp, G. Buchele, U. Keil, and S. Weiland (2007). "Increasing life expecancy in Germany: Quaniaive Conribuions from Changes in Age- and Disease- Specific Moraliy," European Journal of Public Healh 17, Nishiyama, Shinichi, and K. Smeers (2003). Consumpion Taxes and Economic Efficiency in a Sochasic OLG Economy, NBER Working Paper Nishiyama, Shinichi, and K. Smeers (2007). Does Social Securiy Privaizaion Produce Efficiency Gains? Quarerly Journal of Economics 122, OECD (2006). Taxing Wages, 2005/2005 Special Feaure: Par-ime Work and Taxing Wages, , Paris, France. OECD (2006). Saisics on Average Age and Official Age of Reiremen in OECD Counries, Paris, France. Pischke, Jörn-Seffen, and J. Velling (1997). Employmen Effecs of Immigraion o Germany: An Analysis Based on Local Labor Markes, The Review of Economics and Saisics 79, Raffelhueschen, Bernd, and J. Walliser (1999). Unificaion and Aging in Germany: Who Pays and When? In Alan J. Auerbach, L. Kolikoff, and W. Leibfriz, eds., Generaional Accouning around he World, Chicago: The Universiy of Chicago Press. Rios-Rull, J. Vicor (1997). Compuaion of Equilibria in Heerogeneous Agen Models, Federal Reserve Bank of Minneapolis Saff Repor 231. SourceOECD - Online Daabase (2006). OECD Naional Accouns Daa, Paris, France. Soresleen, Kjeil (2000). Susaining Fiscal Policy hrough Immigraion, The Journal of Poliical Economy 108, The German Socio-Economic Panel (2005). A Represenaive Longiudinal Sudy of Privae Households in he Enire Federal Republic of Germany, The German Insiue for Economic Research (DIW), Berlin, Germany. 25

26 Appendix An Equilibrium Transiion Pah I solve he derended version of he model. I assume ha he economy is in he corresponding iniial seady sae in period 0, and he new immigraion policy { 2, l, 2, h, 3, l, 3, h} ψ% = ψ% ψ% ψ% ψ% is announced. I use he fixed poin ieraion algorihm (Judd, Kubler, and Schmedders 2003; Rios-Rull, 1997) o compue a ransiion pah o he new seady-sae equilibrium (hereafer, he final seady-sae equilibrium) is as follows: 1. Assume ha he economy reaches he new seady sae wihin a large number of periods, 20 in his case Se he iniial guess on he ineres rae sequence { r } 20 0 consumpion ax rae { τ } 20, and average earnings o c, { y } 201 = 1 = 2. For periods = 1, 2,...,19, compue forward he measure of individuals according o he law of moion for populaion. Given he iniial guesses, compue he new equilibrium 1 ineres rae { r } 20, ax rae 1 { τ } 20, and 1 = c, { y } 20 = = ha would prevail if { r } 20, 0 { τ } 20, and o = 1 c, { y } 201 = 1 =, = 1 sequences implied by he decision rules were he rue equilibrium sequences. 3. New guesses of he ineres raes, he consumpion ax, and he average earnings are generaed as an average of he previous guesses and he sequences implied by he individual and firm decision rules and he governmen s budge consrain. 4. Sop when r 1 0 ( 0 ) 1 0 ( 0 ) 1 0 ( 0 r 1 r, τc, τc, 1 τc,, y y 1 y ) is less han Updae guesses of ineres rae, consumpion ax, and average earnings by { r } = λ{ r } + λ { r } { τc, } = λ{ τc, } + λ { τc, } (1 ), (1 ), = 1 = 1 = 1 = 1 = 1 = { y } λ{ y } (1 λ) { y} = +, where λ ( ) = 1 = 1 = 1 0,1. 16 Afer 7 periods, which corresponds o 140 years, he annualized rae of reurn on capial is 0.001percen away from is seady sae value. 26

27 Figure 2. Marginal Income Tax Raes, Taxable income in housand euros Figure 3. Marginal Payroll Tax Raes, Taxable income in housand euros Figure 4. Toal Marginal Tax on Labor Income, Taxable income in housand euros 27

28 Figure 5. Consumpion per Capia (consumpion of year old high-skilled naive in 2005=100) year olds year olds high-skilled naive high-skilled naive 170 high-skilled imm high-skilled imm. low-skilled naive low-skilled imm low-skilled naive low-skilled imm year olds year olds high-skilled naive high-skilled naive 280 high-skilled imm low-skilled naive low-skilled imm. 240 high-skilled imm. low-skilled naive low-skilled imm Figure 6. Labor Supply (Percenage of Time Worked) year olds year olds high-skilled imm. 42 high-skilled naive 20 high-skilled naive 40 low-skilled naive high-skilled imm low-skilled imm low-skilled naive low-skilled imm