Postponing Retirement, Endogenous Fertility, Social Security. and Welfare. Gen Zhixiang. Tanggang Yuan

Transcription

1 Pspning Reiremen, Endgenus Ferili, Scial Securi and Welfare Gen Zhixiang Tanggang Yuan Absrac Based n an exended verlapping generains mdel wih endgenus ferili, his paper sudies he effecs f raising he mandar reiremen age n he ferili rae, scial securi benefi, and welfare in a neclassical grwh mdel The sud shws ha a small amun f he pspnemen f he reiremen age can imprve he ferili rae a minr exen in he lng run When he upu elasici f capial is n less han 5, he pspnemen f he reiremen age will have a negaive effec n scial securi benefi and als a negaive effec n welfare in he lng run When, hwever, he upu elasici f capial is small enugh, bh f he scial securi benefi and welfare increase in delaing reiremen age in he lng run Kewrds Reiremen Ferili PAYG scial securi Welfare Inrducin Man develping and develped cunries are experiencing rapid ppulain aging and a decline in labr suppl Due ppulain aging, he susainabili f exising scial securi ssems is increasingl challenged, especiall wih he pa-as-u-g (PAYG) pensin ssem In rder reduce he burden f pensin paus, he usual pracice is cuing per-capia pensin benefis, increasing cnribuin raes r pspning reiremen Man expers prpse pspne he mandar reiremen

2 age, and i is suppred ha pspning reiremen ma becme feasible because f he pliical push f aging (Galass and Prfea, 4; Galass, 8) Currenl, man cunries are prepared raise r have raised he mandar reiremen age r he fficial pensin age Fr example, in 983, he Unied Saes Cngress implemened an increase in he Nrmal Reiremen Age (NRA) f mnhs per ear, an increase ha sared in (Masrbuni, 9) Japan will pspne he reiremen age frm 6 65 in 6, German passed he law in 6 ha he reiremen age wuld be exended 67 ears frm 9, Ial k flexible plic f exending he reiremen age bh in 995 and 4, and China will raise he mandar reiremen age in prgressive seps in he nex few ears Thrugh he plic f pspning he reiremen age in prgressive seps, sme cunries expec alleviae he srain f he gvernmen budge wihu decreasing he scial securi benefi increasing he cnribuin rae Hwever, sme sudies shw ha he pspnemen f he reiremen age ma be harmful fr scial securi benefi in he lng run (Miazaki 4; Fani 4) Bu in hese sudies, he end ake he ferili rae as exgenusl given In reali, he ferili rae is affeced b man facrs, such as wage incme, ime and mne cs f child-rearing ec, as a cnsequence, i changes ver ime Therefre, i is likel prduce inaccurae cnclusins under he assumpin f exgenus ferili Ms f he sudies have been cnduced wih endgenus ferili (Becker and Barr 988; Barr and Becker 989; Zhang and Zhang 998; Wigger 999; Omri 9; Miazaki 3; Wang 5; Smmer, 6) In he mdel wih endgenus ferili, much aenin has been paid he relainship amng scial securi, ferili, incme and grwh (Wang e al, 994; Zhang, 995; Blackburn and Cipriani, 998; Kremer and Chen, 999; Grezen e al, 3; Rsai, 4; Fani and Gri, ; Varvarigs and Zakaria, 3) T he bes f ur knwledge, here are n relevan lieraure invesigae he effecs f raising he mandar reiremen age n he ferili, PAYGO scial securi benefi, and welfare geher in he lng run In his paper, we will sud he effecs f endgenus ferili in a neclassical grwh mdel Malhus was he firs ecnmis wh sudied demgraph and k ferili as an endgenus variable

3 As an alernaive he radiinal wa f reling n children, he pspnemen f he reiremen age is cnsidered decrease he ferili rae because i reduces he parens maerial dependence n children Hwever, i is fund ha, in sme OECD cunries, he ferili rae is n decreasing ver ime afer exending he reiremen age Fr insance, Fig shws he al ferili raes f several cunries frm OECD Frm he Fig, we can see a lile rise in al ferili raes afer pspning he reiremen age Therefre, he decreasing ferili due delaing reiremen needs furher sud Surce: OECD Daa (ferili raes) Fig Tal ferili raes The aim f his paper is hus invesigae hw he pspnemen f he mandar reiremen age affecs he ferili rae, PAYG scial securi benefi, and welfare in he lng run We use he exended verlapping generains (OLG) mdel b Diamnd (965) in a neclassical grwh framewrk, and find ha a small amun f he pspnemen f he mandar reiremen age decreases precauinar saving, and hus increases dispsable incme, which encurages he ung have mre children Therefre, i can imprve he ferili rae in he lng run, bu he degree f he imprvemen is ver limied I is shwn ha he ferili rae is mainl affeced b he cs f child-rearing The ferili rae f he Unied Saes decrease fr her reasns in 8 Fr example, he financial crisis had greal reduced he wealh f peple and had risen he unemplmen rae, which decreased he ferili desire amng peple (Lvenheim and Mumfrd, 3) 3

4 As scial securi benefi, in he sead sae, pspning reiremen has w effecs n he agen s scial securi benefi One is ha i can imprve he ferili Hence, here are mre ung wrkers suppr ld pensiners, s i increases he agen s scial securi benefi Mrever, a small amun f he pspnemen f he reiremen age increases he cnribuin raes, which als increases he scial securi benefi The her is ha he rising ferili rae and delaing reiremen decrease he capial f per wrker, hus decreases he real wage As a cnsequence, i decreases he agen s scial securi benefi When he upu elasici f capial is n less han 5, he laer dminaes he frmer, s he agen scial securi benefi decreases in a small amun f he pspnemen f he reiremen age in he lng run When he upu elasici f capial is less han a given value, which is he funcin f discun facr and preference weigh fr he number f children relaive he ung agen s cnsumpin, he frmer dminaes he laer, s he agen s scial securi benefi increases in he lng run When he upu elasici f capial is mre han he given value and less han 5, a a lw parll ax rae, he agen s scial securi benefi decreases in he lng run, while a a high parll ax rae, he agen s scial securi benefi increases in he lng run An agen s welfare depends n a ung agen s cnsumpin, an ld agen s cnsumpin afer reiremen, and he number f children in he sead sae We find ha a small amun f he pspnemen f he reiremen age decreases he ung agen s cnsumpin When he upu elasici f capial is less han r equal 5, he ld agen s cnsumpin increases in he lng run The agen s welfare increases in a small amun f he pspnemen f he reiremen age when he upu elasici f capial is small, herwise i decreases in he lng run The res f his paper is rganized as fllws Secin describes he mdel Secin 3 analzes he effecs f he pspnemen f he mandar reiremen age n he Ferili, PAYG scial securi benefi, and welfare in he lng run Secin 4 cncludes The mdel 4

5 Agens Time is discree and cninues frever, =,, Cnsider a w-perid general equilibrium OLG mdel in a clsed ecnm, he adulhd f an agen is separaed in w perids: uh and ld age Each perid is ne uni f ime Yung agens in perid in elasicall suppl ne uni f labr and earn a wage f w while paing a scial securi ax, which is dened bτ (,) In he secnd perid, +, he pspnemen f he mandar reiremen age is x, which is a plic variable deermined b he gvernmen, hen s/he has wrk a fracin x [,) f he ime and pas he ax xτ w + Fr he res f her r his ime, x, she r he is reired When x = implies ha he agen wrks full ime in he firs perid f life and reires in he whle secnd perid f life, which is he radiinal assumpin f he OLG mdel f Diamnd (965) The relainship beween ppulains f adjacen n generains is linked b he endgenus ferili as / = N+ N If a ung agen a dae has δ n w, n children, we assume ha he phsical cs f rearing hem is where δ (,) 3Thus, a ung agen s budge cnsrain is c + s = ( τ δ n ) w () Where c and s are he ung agen s cnsumpin and savings, respecivel When she r he becmes ld a +, she r he receives he ineres incme, R s = ( + r ) s + + ( τ ) xw ne wage incme f + r,where + is he ne ineres rae In addiin, she r he receives a ( x) P, and a scial securi benefi f + Therefre, in he secnd perid, +, an ld agen s budge cnsrain is c = R s + ( τ ) xw + ( x) P () 3 We d n cnsider he ime spen rearing ne child, because we can lk fr a persn lk afer ur children in he labr marke and pa he wage, he ime cs can be cnvered in mne cs an exen This seing will n affec ur resuls 5

6 P Where + is he per uni f ime pensin An agen cares abu n nl ver cnsumpin bu als in relain he number f children she r he has Thus an agen brn dae has he fllwing lifeime uili: U = ln c + β ln c + γ ln n + (3) Where β (,) is a subjecive discun facr and γ > is a preference weigh have children relaive c Under he cnsrains () and (), ne can maximize he lifeime uili and achieve he fllwing funcins: β ( τ ) ( + γ )[( τ ) xw + + ( x) P + ] s = w + β + γ ( + β + γ ) R + γ ( τ ) γ[( τ ) xw + + ( x) P + ] n = + δ ( + β + γ ) ( + β + γ ) δ w R Firms + (4) As regards prducin secr, we assume ha firms are idenical and ac cmpeiivel A each dae, a firm uses aggregae capial K and al labr suppl L prduce cnsumpin gds, where L = N + xn The prducin echnlg is Cbb-Duglas funcin, and he al facr prducivi (TFP) is nrmalized Therefre, he prducin funcin is Y = F( K, L ) = K L α α, where α (,) is he capial share f al upu We suppse ha he capial sck per wrker and upu per wrker are dened b k = K / L and = Y / L, respecivel, s he inensive frm f prducin funcin ma be wrien as = k α Fr simplici, i is assumed ha phsical capial all depreciaes a he end f each perid 4Cnsequenl, under he cmpeiive marke, we can ge he fllwing marginal cndiins fr capial and labr in equilibrium: R r k w k α α = + = α, = ( α ) (5) 4 Since ne perid in his mdel crrespnds abu 3 ears, i is reasnable assume ha phsical capial depreciaes full wihin ne perid 6

7 3 Gvernmen We assume ha he Fllwing PAYG scial securi budge is balanced b he gvernmen in ever perid: τ N w + τ xn w = ( x) N P (6) Where he lef-hand side f he abve equain represens he scial securi ax receips and he righ-hand side represens he pensin expendiure Furhermre, we can wrie he equali as fllws: τ w + n + x = x P + ( ) ( ) (7) 4 Equilibrium The phsical capial accumulain f a firm a ever perid cmes frm he previus agens saving, s he marke-clearing cndiin in gds as well as in capial K markes is expressed b he ideni: = + Ns We can wrie i in he fllwing frm in erms f capial sck per wrker: k s = + n + x (8) Expliing (4), (5), (7) and (8), we can bain he fllwing dnamic evluin equain: k + αβ ( α)( τ ) = k α( + β + γ )( x + n ) + ( α )( + γ )( x + τ n ) α (9) and α γα( τ ) k + γ xk+ n = α ( + β + γ ) δαk γτ k + Plugging equain (9) in equain () wih arrangemen, we have () γ ( τ )[ α( + β + γ )( x + n ) + ( α)( + γ )( x + τ n )] + γ xβ ( α)( τ ) n = δ ( + β + γ )[ α( + β + γ )( x + n ) + ( α)( + γ )( x + τ n )] γτβ ( α)( τ ) () 7

8 The equain () is quadraic in n and i has a ms w real rs Accrding he lemma 9 in Abel (3), he psiive and higher r is sable Then he ferili rae cnverges he fllwing sead sae n afer ne perid () [ γ ( τ )( τ τα + α ) δ x( + αβ + γ )] + γ ( τ )( τ τα + α ) δ x( + αβ + γ ) + 4 δ[ α ( + β + γ ) + ( α)( + γ ) τ ] γ ( τ ) x n = δ[ α ( + β + γ ) + ( α )( + γ ) τ ] Equain (9) guaranees a unique sead sae, and he capial sck per wrker cnverges he fllwing sead sae k, we have αβ ( α)( τ ) k = α ( + β + γ )( x + n) + ( α )( + γ )( x + τ n) (3) α Therefre, he scial securi benefi f he agen in equilibrium is p = ( x) P = τ ( α )( n + x) k α (4) Where p represens he scial securi benefi in equilibrium 3 Ferili, PAYG scial securi benefi, and welfare in he lng run 3 Ferili Prpsiin 3 The capial sck per wrker decreases as he reiremen age increases, and privae savings decreases as well in he lng run A small amun f he pspnemen f he mandar reiremen age x can imprve he ferili rae in he lng run Prf We knw ha all variables are cninuus in he parameer values α, β, γ and τ Taking he derivaive f n wih respec x and rearranging i a x =, we have 8

9 n = δ ( αβ γ )( τ τα α ) δ[ α( β γ ) ( α )( γ ) τ ] x δ[ α( + β + γ ) + ( α)( + γ ) τ ]( τ τα + α ) αβ ( α)( τ ) = > [ α ( + β + γ ) + ( α )( + γ ) τ ]( τ τα + α) Therefre, his implies ha a small amun f he pspnemen f he mandar reiremen age can increase he ferili rae in he lng-run Obviusl, accrding he equain (3), we have k x < Frm he equain (8), in he sead sae, we have s = ( n + x) k Taking he derivaive f s wih respec x and rearranging i b using he firs rder cndiins a x =, we have 3 α α x n = s αβ ( α)( τ) ( α) ( + γ) τ ( α)( α+ α )( + γ) τ α[( + γ)( α+ α ) + αβ ] = x α( + β+ γ) + ( α)( + γ) τ ( α)[ α( τ) + τ][ α( + β+ γ) + ( α)( + γ) τ] > > Therefre, accrding he abve equain, he sign f s x x = depends n he sign f he funcin h( τ ),which is he numerar f he hird erm n he righ-hand side Thus, we have h τ α γ τ α α α γ τ α γ α α αβ 3 ( ) = ( ) ( + ) ( )( + )( + ) [( + )( + ) + ] Nice ha h() = α[( + γ )( α + α ) + αβ ] <, and h α γ α α () = ( + )( + ) < Because because f h( τ ) is quadraic in τ, i is a parabla, which is pening he p ( α)( α + α ) τ = > 3 α + γ >, and he axis ( α) This implies 3 ( ) ( ) 9

10 ha h( τ ) < fr all τ (,) Therefre, a small amun f he pspnemen f he mandar reiremen age x decreases privae savings In rder sud he impac f raising he mandar reiremen age n he ferili, we use differen parameers verif is rbusness f resul Here, we enumerae several parameer seings We assume ha he lengh f each perid is 3 ears5 The reiremen age is increased frm 5 ears ld, s x is /3 /6 Oher parameers are se as fllws: α = 3,4, 3 β = 98 = 55 r β = = , γ = β, δ =,5, τ =, α=3 α=4 7 n x γ=β=55,δ=,τ= α=3 α= n x β=γ=74,δ=,τ= 5 Accrding Feldsein (985), a generain is 3 ears

11 5 4 3 α=3,δ=5 α=4,δ=5 n x β=γ=55,τ= α=3,τ=5 α=4,τ=5 4 n x β=γ=74,δ= Fig Effecs f pspning he reiremen age n he ferili rae Fig nl gives several resuls I shws ha he lng-run ferili rae increases as x increases Of curse, he cnclusin sill hlds wih her parameer seings The effecs f pspning he reiremen age n ferili can be explained b life-ccle cnsumpin mdel When he reiremen age is raised, he agen can ge exra wage incme in he secnd perid, s she r he des n need mre saving suppr he life afer reiremen in he firs perid The reducing saving can be used rear children Therefre, peple wuld like raise mre children, he ferili rae increases as he reiremen age increases Furhermre, due he pspnemen f he reiremen age, he increase f he fuure incme ma reduce he credi cnsrains faced b he parens in he ung, which can als cnribue increasing he ferili rae Frm Fig, ne ha he expansin f pa-as-u-g scial securi decreases he ferili rae in he lng run, bu he effec is limied Hwever, he phsical cs f child-rearing greal affecs he ferili rae The resuls ma have impran implicains fr ppulain plic

12 3 PAYG scial securi benefi The secnd effec is he agen s scial securi benefi We cnsider hw he pspnemen f he mandar reiremen age affecs he scial securi benefi, in he lng run, ha is he p Prpsiin 3 () If β + β + β ( + γ ) < α < + γ, hen he scial securi benefi p increases in a small amun f x fr ever τ [,) ; () If β + β + β ( + γ ) < α < + γ, hen here exiss a uniqueτ (,), such ha fr ever τ (, τ ), p f x fr ever decreases in a small amun f x and increases in a small amun τ ( τ,) ; (3) If α, p decreases in a small amun f x fr ever τ (,) Prf Taking he derivaive f p wih respec x and rearranging i, we have p α n k = τ ( α) k + + ( n + x) αk x x x A x =, we have n k γ ( τ )( τ τα + α) = δ[ α( + β + γ ) + ( α)( + γ ) τ ], αβ ( α)( τ ) α x n α = = α( + β + γ ) + ( α)( + γ ) τ, [ ( )( )] α x n α = + α k αβ α τ αβ ( α )( τ ) = + αβ + γ +, x α τ τα + α [ α ( + β + γ ) + ( α )( + γ ) τ ]

13 p n k x x x α = τ ( α) k + + n αk = τ ( α ) k > α γ τ α α α γ τ αβ α α γ ( α )[ α( + β + γ ) + ( α )( + γ ) τ ]( τ τα + α) α ( ) ( + ) + ( )( )( + ) + ( ) ( + ) > Therefre, he sign f p x = x depends n he sign f he funcin g( τ ), g( τ ) is he numerar f he secnd erm f he abve equain n he righ-hand side Thus, 3 3 g( τ ) : = ( α) ( + γ ) τ + α( α )( α )( + γ ) τ + αβ ( α) α ( + γ ) If < α < /, g α γ α α α γ αβ α α γ 3 3 () = ( ) ( + ) + ( )( )( + ) + ( ) ( + ) = α + γ α + γ + α α α + γ + αβ α > ( ) ( ) ( ) ( )( )( ) ( ) > > If 3 β + β + β ( + γ ) g() = αβ ( α) α ( + γ ) > < α < < + γ, in his case, accrding he shape f his funcin, g( τ ) > fr ever τ (,) Therefre, p x > fr ever τ (,) Which implies a small amun f pspnemen f he mandar reiremen age can imprve he scial securi benefi in he lng run If 3 β + β + β ( + γ ) g() = αβ ( α) α ( + γ ) < < α < + γ, hen here is a unique τ (,) such ha g( τ ) = and g( τ ) < fr ever τ (, τ ) Oherwise, g( τ ) > fr ever τ ( τ,) Therefre, under he β + β + β ( + γ ) < α < cndiin + γ,we have p x < fr ever τ (, τ ) and p x > fr everτ ( τ,) The frmer implies ha a small amun f raising he mandar reiremen age can decrease he scial securi benefi, and he laer can 3

14 imprve i in he lng run If α =/, g( τ ) = / 8( + γ )( τ ), hen g( τ ) < fr ever τ (,) Hence, he agen s scial securi decreases in he lng run Ifα > /, hen Nice ha g αβ α α γ () = ( ) ( + ) < < < g α γ α α α γ αβ α α γ 3 3 () = ( ) ( + ) + ( )( )( + ) + ( ) ( + ) = α α + γ + α α α + γ + αβ α < [( ) ]( ) ( )( )( ) ( ) < < Hence, accrding he shape f g( τ ), we knw ha g( τ ) < fr everτ (,) Therefre, under he assumpinα /, we have p < x fr everτ (,) I implies ha a small amun f pspnemen f he mandar reiremen age can decrease he scial securi benefi in he lng run The inuiin behind his resul is ha he pspnemen f he mandar reiremen age has w effecs n he agen s scial securi benefi One is ha a small amun f he pspnemen f he mandar reiremen age can decrease he precauinar savings, and hus increases dispsable incme, which encurages he ung have mre children Therefre, i can imprve he ferili rae in he lng, bu he magniude is ver limied Hence, i causes mre wrkers suppr he PAYG scial securi ssem In addiin, he pspnemen f reiremen age has prlnged he pensin cnribuin perid, which als can increase he scial securi benefi As a cnsequence, i can increase he scial securi benefi The her is ha he rising ferili rae and a small amun f he pspnemen f he mandar reiremen age can decrease he capial f per wrker, and hen decrease he real wage As a cnsequence, i can decrease he scial securi benefi in he lng run When he upu elasici f capial is small enugh, he firs effec dminaes he secnd effec, s p increases Hwever, when he upu elasici f capial is mre 4

15 han 5, he secnd effec dminae he firs effec, s p decreases In addiin, when he upu elasici f capial is in a small range, he dminance f he effec depends n he cnribuin rae f he scial securi 33 Welfare A small amun f he pspnemen f he mandar reiremen age can decrease he saving rae, and hus decrease he real wage level in he equilibrium Hwever, i increases he lng-run ferili rae The decreasing wage will reduce he agen s well being, bu i will increase welfare b imprving he ferili rae Therefre, we wan invesigae hw i affecs he agen s welfare In he sead sae, he agens welfare is defined b (5) U x Lnc β c γ n ( ) : = + ln + ln, where c =( τ δ n )( α) k α ( n + x) k, and α τ ατ c =[( + ) n + x] k α Firs, we wan knw he effecs f raising he mandar reiremen age n an adul agen s cnsumpin and n an ld agen s cnsumpin in he sead sae We have he fllwing prpsiin: prpsiin 33 ()The ung agen s cnsumpin c decreases in a small amun f x fr ever τ (,) ;()If < α /, he ld agen s cnsumpin c increases in a small amun f x fr ever τ (,) ; (3)If + β + γ ( + β + γ )( + β + γ ) β < α <, he ld agen s cnsumpin c decreases in a small amun f x fr ever τ (,) ; If + β + γ ( + β + γ )( + β + γ ) / < α < β, hen here exis a unique ) τ (,), c increases in a small amun f x fr ever 5 τ (, ) τ ), and decreases in a small

16 amun f x fr ever τ ( ˆ τ,) Prf i is eas shw ha c n k [ ( ) ( )( ) x c x x n k ( + ) k n ] x x = k c [ α ( + β + γ ) + ( α )( + γ ) τ ]( τ τα + α)( α ) α α = δ α k + τ δ n α αk > ( α( τ ) + τ )( α β + α ( β ( + γ ) + ( + γ )( τ )) + ( + γ ) τ ) < β Therefre, The ung agen s cnsumpin c decreases in a small amun f x fr ever τ (,) In rder invesigae hw he ld agen s cnsumpin changes as he mandar reiremen age increases, I ake he derivaive f c wih respec x Then, a x =, we ge c α α + γ αβ α τ + α α + β + γ + α β x ( α )[ α ( + β + γ ) + ( α )( + γ ) τ ] ( )[( )( ) ( )] [( )( ) ] α = k > Frm he abve equain, i shws ha he sign f c x depends n he numerar f he firs erm n he righ-hand side f his equain Le h( τ ) : = α α γ αβ α τ α α β γ α β ( )[( )( + ) ( )] + [( )( + + ) + ] If < α < /, hen, h() = α[( α)( + β + γ ) + α β ] >,and h() = ( α )( + αβ + γ ) > This funcin is linear in τ This implies h( τ ) > fr ever τ (,) Therefre, in his case, he ld agen s cnsumpin increases in a small amun f x fr everτ [,) If α = /, hen h( τ ) = β ( τ ) > 8 fr allτ (,) Therefre, he ld agen s 6

17 cnsumpin c increases in a small amun f x fr everτ (,) If α > /, he firs erm f h( τ ) is negaive Accrding he shape f he funcin, is sign depends n he sign f he erm l( a) = ( α)( + β + γ ) + α β When l( a ) <, he sluin f he inequali is + β + γ ( + β + γ )( + β + γ ) β < α < Furhermre, h() = ( α)( + αβ + γ ) < Hence, h( τ ) is negaive fr all τ (,) In his case, he ld agen s cnsumpin c decreases in a small amun f x fr ever τ (,) When l( a ) >, he sluin is + β + γ ( + β + γ )( + β + γ ) / < α < β In his case, here is a unique ) τ (,) such ha h( τ ) > fr ever τ (, ) τ ), and h( τ ) < fr ever τ ( ˆ τ,) Therefre, a a lw parll ax rae, he ld agen s cnsumpin increases in a small amun f x, while a a high rae, he ld agen s cnsumpin decreases in a small amun f x Nw, we wan invesigae hw he pspnemen f he saur reiremen age affecs he agen s welfare Since i is difficul use mehds f cmparaive saics deermine he sign, we prvide a numerical illusrain analze he effec f raising he mandar reiremen age n he agen s welfare Le us se he upu elasici f capial α = 3,/ 3,4, 5 A generain is 3 ears (Feldsein, 985) Hence, fr he values f β and γ,we se β = γ = = Fr he cs f childrearing, Apps and Rees () argue ha each child s cs f rearing accuns fr -3 f he famil s incme, which is als suggesed b Dean and Muellbauer (986), while i is 5 in Miazaki (3) We se i as and 5 Fr he value f he parll ax rae, we se i as 5, which is used b Fani (4) We ne ha he mandar reiremen age will be increased b 5 ears Therefre, able belw displas he effecs f raising he mandar reiremen age n welfare 7

18 Table Effecs f raising he saur reiremen age upn welfare Parameer seings Delaing reiremen age α = 3, β = γ =74, τ = 5, δ = α = / 3, β = γ =74, τ = 5, δ = α = 4, β = γ =74, τ = 5, δ = α = 5, β = γ =74, τ = 5, δ = α = 3, β = γ =74, τ = 5, δ = α = / 3, β = γ =74, τ = 5, δ = α = 4, β = γ =74, τ = 5, δ = α = 5, β = γ =74, τ = 5, δ = Frm he able, when he upu elasici f capial is less han 4, he welfare increases as reiremen age increases Oherwise, he welfare decreases as reiremen age increases Of curse, he magniude is ver small This has an impran plic implicain fr sme develping cunries In rder reduce he burden f pensin paus, man cunries wan implemen he plic f raising he mandar reiremen age, such as China Hwever, i shws ha, in sme develping cunries wih higher upu elasici f capial, he delaing reiremen age has a negaive 8

19 effec n he individual welfare and als a negaive effec n pensin benefis Hence, hese cunries shuld reduce he upu elasici f capial b imprving labr prducivi fr he individual well being and pensin benefis 4 Cnclusin This paper uses a neclassical grwh mdel wih endgenus ferili and sudies hw he pspnemen f he mandar reiremen age affecs he ferili rae, scial securi benefi, and welfare in he lng run I is shwn ha a small amun f raising he reiremen age can increase he ferili rae in he lng run Daa analsis indicaes ha he ferili rae is a limied imprvemen as he reiremen age increases, bu he reducin f cs f child-rearing can greal imprve he ferili Hwever, i will n necessaril lead he imprvemen f he scial securi benefi in he lng run When he elasici f capial is n less han 5, he agen scial securi benefi decreases in a small amun f he pspnemen f he reiremen age in he lng run Onl when he elasici is small enugh, he scial securi benefi increases in he reiremen age in he lng run Oherwise, i depends n he cnribuin rae As he welfare, when he upu elasici f capial is small, he welfare increases as reiremen age increases Oherwise, he welfare decreases as reiremen age increases Bu he magniude is ver small 9

20 References Abel AB (3) The effecs f a bab bm n sck prices and capial accumulain in he presence f scial securi Ecnmerica, 7: Apps P, Rees R () Husehld prducin, full cnsumpin and he css f children Labur Ecn 8:6-648 Blackburn, K, G P Cipriani, 998, Endgenus ferili, mrali and grwh, Jurnal f ppulain Ecnmics, : Barr RJ, Becker GS (989) Ferili chice in a mdel f ecnmic grwh Ecnmerica 57:48-5 Becker GS, Barr RJ (988) A refrmulain f he ecnmic her f ferili Q J Ecn 3:-5 Cremer, H, P Pesieau, 3, The duble f dividend f pspning reiremen, : Dean AS, Muellbauer J (986) On measuring child css: wih applicains pr cunries J Pli Ecn 94:7-744 Diamnd PA (965) Nainal deb in a neclassical grwh mdel Am Ecn Rev 55:6-5 Fani L, Gri L () Ferili and PAYG pensins in he verlapping generains mdel J Ppul Ecn 5: Fani L (4) Raising he mandar reiremen age and is effecs n lng-run incme and pa-as-u-g pensins Merecnmica 65: Galass, V, Prfea, P, 4, Lessns fr an aging scie: he pliical susainabili f scial securi ssems Ecnmic Plic, 9:64-5 Galass, V, 8, Pspning reiremen: he pliical effec f aging Jurnal f Public Ecnmics, 9:57-69 Grezen, B V, T Leers, L Meijdam, Scial Securi and endgenus ferili: pensins and child allwances as Siamese wins, Jurnal f Public Ecnmics, 87:33-5 Feldsein M (985) The pimal level f scial securi benefis Q J Ecn :33-3 Kremer, M, D L Chen, 999, Incme Disribuin Dnamics wih Endgenus Ferili, Jurnal f ecnmic grwh, 7:7-58 Lvenheim, M F, K J Mumfrd, 3 D Famil Wealh Shcks Affec Ferili Chices? Evidence frm he Husing Marke, Review f Ecnmics and Saisics, 95: Masrbuni, G, 9, Labr suppl effecs f he recen scial securi benefi cus: Empirical esimaes using chr discninuiies Jurnal f Public Ecnmics, 9, 93:4-33 Miazaki K (3) Pa-as-u-g scial securi and endgenus ferili in a neclassical grwh mdel J Ppul Ecn 6:33-5 Miazaki K (4) The effecs f he raising-he-fficial-pensin-age plic in an verlapping generains ecnm Ecn Le 3:39-33 Omri T (9) Effecs f public educain and scial securi n ferili J Ppul Ecn :585-6 Rus, J, C Phelan, 997, Hw scial securi and Medicare affec reiremen behavir in a wrld f incmplee markes Ecnmerica, 65(4):78-83 Rsai, F C, 4, Scial Securi in a nn-alruisic mdel wih uncerain and endgenus ferili, Jurnal f Public Ecnmics, 4, 6:83-94 Saubli, S, Zweimüller, J 3, Des raising he earl reiremen age increase

21 emplmen f lder wrkers? Jurnal f Public Ecnmics, 8:7-3 Smmer, K, 6, Ferili chice in a life ccle mdel wih idisncraic, Jurnal f Mnear Ecnmics, 83:7-38 Wang, P, C K Yip, CA Scese, Ferili chice and ecnmic grwh The Review f Ecnmic and Saisics, 76:55-66 Wang L (5) Ferili and unemplmen in a scial securi ssem Ecn Le 33:9-3 Wigger BU (999) Pa-as-u-g financed public pensins in a mdel f endgenus grwh and ferili J Ppul Ecn :65-64 Varvarigs, D, I Z Zakaria, Endgenus ferili in a grwh mdel wih public and privae healh expendiures, Jurnal f Ppulain Ecnmics, 6:67-85 Zhang, J 995, Scial Securi and endgenus grwh, jurnal f Public Ecnmics, 58:85-3 Zhang J, Zhang J (998) Scial securi, inergenerainal ransfers, and endgenus grwh Can J Ecn 3:5-4