Child Benefit and Fiscal Burden: OLG Model with Endogenous Fertility

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1 Modern Economy, 2011, 2, doi: /me Published Online Sepember 2011 (hp:// Child Benefi and Fiscal Burden: OLG Model wih Endogenous Feriliy Absrac Kazumasa Oguro, Junichiro Takahaa, Manabu Shimasawa Associae Professor, Hiosubashi Universiy, Tokyo, Japan Research Associae, JICA Research Insiue, Tokyo, Japan. Associae Professor, Akia Universiy, Akia, Japan Received May 31, 2011; revised July 12, 2011; acceped July 22, 2011 In his paper, we presen an OLG simulaion model wih endogenous feriliy o analyze he relaionship beween child benefi and fiscal burden. Our simulaion resuls show ha expansion of he child benefi will improve he welfare of curren and fuure generaions. On he oher hand, our findings show ha we canno expec a significan long-erm improvemen in welfare solely from he increase of he consumpion ax. If boh he fiscal susainabiliy and he improvemen of he welfare of curren and fuure generaions are requiremens, we will need a policy-mix ha includes boh child benefi expansion and addiional fiscal reform. Keywords: Compuable General Equilibrium (CGE) Model, Overlapping Generaions (OLG), Child Benefi, Endogenous Feriliy 1. Inroducion Developed counries currenly face unprecedened demographic changes which require exensive reform in fiscal sysems, social securiy sysems, and oher relaed programs. However, due o conflicing ineress beween younger and older generaions, reform may be resriced. As an example of a pay-as-you-go pension, in order o improve he susainabiliy of he sysem, he governmen has he opion of reducing he benefis o he elderly or increasing he burden on he working generaion. Obaining agreemen on reform by boh generaions is ofen oo difficul for he governmen o achieve. In his siuaion, some developed counries such as France have proceeded wih he expansion of child benefi programs. These programs are expeced o increase he populaion of he younger generaion as a ax resource and, as resul, o reduce he per capia fiscal burden in he fuure. In his paper we analyze he relaionship beween child benefi and he fiscal burden in he seing of an overlapping generaions (OLG) model. In he process of his analysis, i is imporan for us o disinguish beween an exogenous feriliy model and an endogenous feriliy model. The reason is ha recen sudies have clarified ha he Pareo-efficiency condiion of he exogenous feriliy model differs from ha of he endogenous feriliy model. Firs, for an exogenous feriliy model, we use he OLG model inroduced by Diamond [1]. Three ypes of seady saes exis in he model: under-accumulaion, golden rule, and over-accumulaion. The firs wo seady saes are Pareo-efficien, bu he hird is no. In addiion, an empirical sudy by Abel e al. [2] repors ha in indusrialized counries dynamic efficiency is saisfied. In a seady sae, dynamic efficiency corresponds o under-accumulaion (or golden rule). Therefore, he possibiliy ha developed counries are in a sae of under-accumulaion seems high. In an exogenous feriliy seing, an allocaion is said o be Pareo-efficien if i is impossible o make some individuals beer off wihou making oher individuals worse off. For his reason, in an exogenous case, we canno improve any generaion s uiliy while a he same ime sacrificing anoher generaion s uiliy. However, recen sudies clarify he properies of he compeiive equilibrium wih an endogenous feriliy seing. Rau and Srinivasan [3] and Charkrabari [4] analyze he properies of ineremporal equilibrium wih endogenous feriliy. Conde-Ruiz e al. [5] and Golosov e al. [6] presen he definiion of Pareo-efficiency crieria in an endogenous feriliy framework. Copyrigh 2011 SciRes.

2 K. OGURO ET AL. 603 As a developmen of hese sudies, Michel and Wigniolle [7] 1 poin ou he possibiliy ha under-accumulaion may no be efficien in an endogenous feriliy seing. This implies ha some policies could effec improvemen in one generaion s welfare wihou sacrificing anoher generaion s welfare, even when i is in an underaccumulaion sae near he seady sae. Moreover, he remarkable poin made by Michel and Wigniolle [7] is o clarify ha he Represenaive-Consumer efficien (RCefficien) condiion, which is a concep developed in heir sudy, has a profound connecion wih he sign-of-inequaliy relaionship beween he child-rearing cos and wage rae. 2 Tha is, if some policies do provide effecs o his relaionship, improvemen in RC-efficiency becomes possible. Michel and Wigniolle [7] provide proof ha, by uilizing an OLG model wih endogenous populaion growh, he possibiliy o improve RC-efficiency also exiss in he case of under-accumulaion. Bu hey did no analyze an economy model wih public deb. Therefore, Oguro and Takahaa [13] analyze he relaionship beween child benefi and fiscal burden, in he seing of an OLG model wih boh endogenous feriliy and public deb, and provide he condiion of RC-efficiency. However, hey also could no analyze he relaionship beween child benefi and fiscal burden in a real economy. The reason is ha he overlapping generaions of heir OLG model amoun o only wo: he working generaion and he reired generaion. To analyze he relaionship in a real economy, i is necessary o build an OLG model wih more overlapping generaions: e.g., a model wih 85 overlapping generaions and endogenous feriliy. To his end, we consruc a large-scale numerical dynamic equilibrium OLG model wih endogenous feriliy, which is calibraed o he Japanese economy. And we quaniaively evaluae he effecs of child benefi change: e.g., he effecs on he welfare of muliple generaions. By doing his, we aemp o answer wheher a fundamenal change in child benefi policy resuls in significan posiive effecs on he Japanese economy, especially in erms of he governmen fiscal siuaion. The srucure of his paper is as follows. In Secion 2, we describe he model srucure; Secion 3 presens he calibraion sraegy and he findings; Secion 4 describes simulaion resuls, and Secion 5 conains concluding remarks and policy implicaions. 1 Alhough here have been several approaches ha endogenize feriliy decisions, Michel and Wigniolle [7] depend on he benchmark framework, which assumes ha children are consumpion goods ha appear in he uiliy funcion of he parens. The basic aricles are Becker [8], Willis [9], and Ecksein and Wolpin [10]. Oher approaches depend on he lieraure based on he addiional assumpion of descendan alruism as in Becker and Barro [11] or he assumpion of ascendan alruism and sraegic behavior of parens, as in Nishimura and Zhang [12]. 2 The definiion of RC-efficiency can be seen in Michel and Wigniolle [7] or Oguro and Takahaa [13]. 2. The Model Srucure In his secion, we describe he demographic and economic srucure of our model. The model used here is a compuable general-equilibrium OLG model wih perfec foresigh agens, muliple periods, and endogenous feriliy. In our model, here is a represenaive individual for each generaion in he households secor. Each individual a age 20 maximizes his/her ineremporal uiliy funcion wih consumpion and number of children. The represenaive compeiive firm has a sandard Cobb-Douglas producion echnology and maximizes is profis. In our model, no only he goods marke bu also facor markes are perfecly compeiive. The model has five main building blocks: 1) household behavior, 2) firm behavior, 3) he Governmen, 4) he public pension, and 5) marke equilibrium. Deails of each block follow Household Behavior There is a represenaive individual for each generaion in he household secor. We assume ha preferences forms are he same for all agens in all generaions. Moreover, each individual lives for a fixed number of periods. In each period of he model, he oldes generaion dies and a new one eners. And he represenaive individuals maximize heir ineremporal uiliy funcion wih consumpion and number of heir children subec o heir lifeime income. They are also assumed o be raional, having perfec foresigh. Each generaion eners he labor marke a age 21, bears and brings up heir children a ages 21 o M + 20, reires a age Q 1, is graned a pension a Q, and dies a age Z. In addiion, each supplies labor inelasically. The wihin-period uiliy funcion exhibis consan relaive risk aversion, and preferences are addiive and separable over ime. In each region, he uiliy funcions of he h generaion born in year are specified as: Z 20 1 c, n U (1) 1 1 where refers o he weigh beween number of children and consumpion, 1 he preference parameer of number of children, he h period of life, he pure rae of ime preference, and 2 he reverse of he elasiciy of ineremporal subsiuion of consumpion. The argumens of he uiliy funcion are he number of children ( n ) and he consumpion per period ( c, ). Leisure does no ener he uiliy funcion since he individual s labor supply is assumed o be exogenous. 3 This is he expansion of he uiliy funcion provided by Groezen e al. [14]. If σ 1 = σ 2 = 1 and Z = 22, i.e. only wo periods (working period and reired period), his uiliy funcion becomes he same form as ha of Groezen e al. [14]. Copyrigh 2011 SciRes.

3 604 K. OGURO ET AL. In addiion, we assume ha he number of children ( n, ) whom he h generaion bears a he h period of life is he following: n p n, where p 0 if 1 M 20 and p 0 if M 20 where p refers o he possibiliy ha each generaion bears he children a he h period of life and his parameer is assumed o be exogenous. Moreover, he echnological progress is assumed o be exogenous and labor embodied. We model agespecific labor produciviy by assuming a hump-shaped age-earnings profile, i.e., a quadraic form of is age, so is age-wage profile e akes he following form: 2 e 0 12 (3) 0, 1 0 and 2 0 The ineremporal budge equaion of each generaion is described as follows: 1 n M g1 k Z g 1g20, 1 g 1 r 20 1 k R k20 c 20, NW r 20 1 k R k k20 20 Q21 (1 w 20 w 20 ) w 20(1 ) e 1 (1 r 1 k 20 ) R k k20 (1 p ) q Z Q20 (1 r ) k 1 k 20 R k20 c (2) (4) 1 1 r R refers o he facor of he presen discouned value which is driven from he gross ineres rae R and he capial ax r in year, g is he child rearing cos a he g h period of life, is he governmen subsidy in year, c is he consumpion ax rae in year, w is he labor income ax rae in year, w is he public pension conribuion rae in year, NW is he ne lifeime income of generaion, is w he wage rae in year, p is he ax for pension benefi in year, and q sands for pension benefi in year. In addiion, child rearing cos is assumed o be proporional o ne lifeime income, i.e., NW g g, where g is he consan parameer. Each generaion maximizes is uiliy funcion (1) under he budge consrain (4). When 1 2, he maximizaion procedure differeniaing he household uiliy funcion (2) wih respec o n and c,, subec o he individual s lifeime budge consrain (4), yields he following equaions concerning consumpion per period and number of children. where c, 1 1 c r k 1 n and 20 R k20 k20 1/ 1/ M g 1 1g20 p 1, 1 g1 g k 1 1 r R k20 k20, (5) 1/ 1/ Z 20 1 M g 1 1g20 p 1c 20 1 g1 1 g 1r k 1 k Rk r k 1 k R k20 / 1/ 1 1/ 1 NW If he parameer is sable, hese equaions dicae he following wo relaionships: 1) as in any life-cycle model, he rade-off beween curren and fuure consumpion is deermined by he raio of he ineres rae and he ime preference rae, and by he degree of risk aversion, and 2) he number of children declines, when he child rearing cos increases or he governmen subsidy decreases. Moreover, from hese equaions, he following forms can be shown: where C Z20 M20 (6) C N c, N N n 20, 20, 1 1 is he aggregaed consumpion in year, and N measures he number of he generaion born in year. In addiion, we can also derive he following physical wealh accumulaion equaion: a a 1r R,, w 20 w 20 w, 1 1 c c n and 20, g 1 g 20, g1 Z 20 Na 20, 1 PA, (7) where a, is physical wealh asse of generaion a he h period of life, and PA is he aggregaed privae Copyrigh 2011 SciRes.

4 K. OGURO ET AL. 605 asse in year Firm behavior The inpu/oupu srucure is represened by he Cobb- Douglas producion funcion wih consan reurn o scale. The firm decides he demand for physical capial and effecive labor in order o maximize is profi wih he given facor prices of wage and ren, which are deermined in he perfec compeiive markes. 1 Y AK L e, L Q20 e, 1 e N K I, (8) K (9) where Y is oupu, sands for capial income share, A is a scale parameer, K is he physical capial sock, and Le, is he effecive labor. We can derive wo facor prices, he rae of reurn r and he wage rae per uni of effecive labor w, by he firs-order condiions for he firm s maximum profi: 1 1 R 1r AK Le, 1 (10) w 1 AK L where e, is he depreciaion of physical capial The public pension The pension secor grans a pension o he reiremen generaions while pension conribuion is colleced from he working generaions. P w wl e, (11) where P sands for he aggregaed pension conribuion. The aggregaed pension benefis in year is given by he produc of he populaion of reiremen age, replacemen rae, and average earnings of each generaion during he working period W. Z20 Z20 B q N W N (12) Q19 Q19 where denoes replacemen rae and B is he aggregaed pension benefi. We explicily model he public pension sysem as payas-you-go. The budge consrain of he pension secor can be shown as follows: P 1sp B (13) where spdenoes public subsidy o pension, which is financed by governmen expendiure G. Moreover, we assume ha he public pension secor mainains a fixed replacemen rae exogenously. As a resul, in our model, he pension conribuion rae is endogenously deermined in order o keep he budge consrain (13) The Governmen The governmen secor has four ypes of axes: wage ax, consumpion ax, capial ax, and pension benefi ax, and he public deb issue income as is revenue and pays he consumpion, invesmen, and ineres paymens as expendiures. T w wl e, c C r R PA p B (14) We keep all ax raes consan. The role of he governmen is o endogenously deermine he rae of he public deb issue as a residual of governmen expendiure and revenue. D G T 1 rd 1 (15) where G sands for governmen expendiure in year, T denoes ax revenue in year, D denoes public deb in year. The public deb issue Bond D 1 rd 1 is se endogenously due o he difference beween expendiure and ax revenue. I should be noed ha he public deb issue o GDP raio will change over ime as a resul of possible imbalances beween revenues and expendiures. Thus we don know wheher he fiscal policy of a counry is susainable and wheher he governmen s ineremporal budge consrain mus be saisfied Marke Equilibrium Finally, in our model of a closed economy, we require he equilibrium in he financial marke, i.e., he aggregae value of asses equals he marke value of he capial socks plus he value of ousanding governmen bonds: PA K D (16) 3. The Daa, Calibraion, and Scenarios 3.1. Daa and Calibraion Firs, we presen he values of he main parameers and exogenous variables of he model in Table 1. The parameer values for he households and firms behaviors are derived from Auerbach and Kolikoff [15] and various early OLG simulaion sudies in Japan. 4 These parameers, such as echnological and preference parameers excep he weigh parameer, are assumed o be consan. 4 See Sadahiro and Shimasawa [16,17]; Uemura [18]; and Ihori e al. [19]. Copyrigh 2011 SciRes.

5 606 K. OGURO ET AL. Table 1. Parameer Values of he Model. PARATER VALUE Uiliy funcion Time preference rae 0.01 Ineremporal elasiciy of subsiuion Weigh parameer beween children number and consumpion 0.84 * Producion funcion Technology progress Capial share in producion 0.3 Physical capial depreciaion 0.05 Tax policy parameers Wage ax w 20.0% Capial ax r 20.0% Consumpion ax c 5.0% Pension benefi ax p 10.0% Pension policy parameers Naional subsidy o pension sp 25.0% Replacemen raio 50.0% Oher parameers 0 o % Child rearing cos o ne lifeime income 6 o % 11 o % 16 o % Child bearing possibiliy 1 o 5 3.0% 6 o % 11 o % 16 o % Governmen subsidy o child rearing cos 0.1 Limi age of bearing child M 40 Age of reiremen Q 65 Average life expecancy Z 85 * This parameer is fixed afer year The exogenous variables such as he macroeconomic, fiscal, and public pension variables are derived mainly from OECD [20] Tax Daabase, and Whiehouse [21] Pensions Panorama. In addiion, he child bearing possibiliy parameer is derived from he daa of Age-specific feriliy rae, which is provided by he Naional Insiue of Populaion and Social Securiy Research [22], and he parameer values of he child rearing cos and he governmen subsidy are derived from he special research repor abou social cos of rearing children, which is provided by he Cabine Office Direcor-General for Policies on a Cohesive Sociey, Japan [23]. Second, by conrolling he weigh parameers in years , we calibrae our demographic proecion o fi he daa s rend in Populaion by Age (generaion born in ), which is provided by he Saisics Bureau, Minisry of Inernal Affairs and Communicaions wih he collaboraion of oher Minisries and Agencies in Japan. Figure 1 repors he acual values and he compued values of demographic proecion. Noe ha acual and calculaed values correspond closely. Nex, in order o analyze he relaionship beween child benefi and fiscal burden, we sar our calculaions Copyrigh 2011 SciRes.

6 K. OGURO ET AL. 607 Figure 1. Demographic Proecion of Each Generaion. wih a phase-in period of abou 200 years in order o relax he unrealisic assumpion of a seady sae in he 2007 base year of our simulaion. Moreover, since he model is simulaed over 500 periods, we ensure a sufficienly long period for a seady sae o be achieved. Table 2 repors he acual values of some key variables in 2007 and he compued values in he model. Also, noe ha acual and calculaed values correspond closely Scenarios Nex we presen simulaion scenarios (See Table 3). The scenarios are classified ino four caegories. Scenario 1 assumes he baseline case wih no expansion of child benefi, and Scenarios 2 and 3 assume 100% increase of child benefi afer Scenario 4 assumes 50% increase of child benefi afer Scenarios 5 and 6 assume no expansion of child benefi bu an increase in he consumpion ax o 10% and 15% (consumpion ax reform), respecively. Finally, Scenario 7 is he policy-mix of Scenario 2 (permanen expansion) and Scenario 6 (15% consumpion ax reform). In Scenarios 2 and 4, he increase of child benefi is permanen from In Scenario 3, he increase of child benefi is emporal for Simulaion Resuls We now urn o describe he simulaion resuls repored in Figures 2 o 5 and Table 4. Here we presen he scenarios of resuls of he child benefi expansion in comparison o he cases of no expansion, he case of consumpion ax reform, and he case of policy-mix (permanen expansion and consumpion ax reform) Demographic Proecion and Macroeconomic Variables Figure 2 shows he populaion proecion of fuure generaions born in The proecion of Scenario 1 and official esimaion, which is provided by he Naional Insiue of Populaion and Social Securiy Research [23], closely correspond. In Scenario 2 (100% permanen child benefi increase), compared wih Scenario 1, he populaion of he generaion born in 2030 increases by 143,000, in Scenario 3 (100% emporally child benefi increase) by 11,000, in Scenario 4 (50% permanen child benefi increase) by 66,000, in Scenario 5 (10% consumpion ax reform) by 4,000, in Scenario 6 (15% consumpion ax reform) by 19,000, and in Scenario 7 (policy-mix) by 166, Figure 3 also shows he reired populaion raio. The raio of Scenario 1 and official esimaion, which is provided by he Naional Insiue of Populaion and Social 5 Consumpion ax reform may conribue o he increase of populaion of fuure generaions hrough he mechanism in ha he fall in ne lifeime income decreases he child rearing cos, e.g., he opporuniy cos which is he ne los income when parens bring up a child. Copyrigh 2011 SciRes.

7 608 K. OGURO ET AL. Naional Income (% of GDP) Table 2. Year 2007 of he Baseline Scenario. OFFICIAL MODEL Privae consumpion 74.1% 81.3% Governmen purchases of goods and services 21.0% 24.3% Saving rae 3.1% 6.1% Governmen Indicaors Pension premium o wage 14.9% 14.9% Gross public deb (% of GDP) 170.6% 170.6% Primary balance (% of GDP) 2.4% 4.5% Tax revenues (% of GDP) 18.4% 19.8% Oher Indicaors Capial oupu raio Ineres rae 1.7% 2.6% Daa source: Official values are derived from OECD Economic Oulook No. 84, 2008 and Annual Repor on Naional Accouns, he Japanese SNA saisics (Cabine Office). Child benefi Table 3. Scenarios. Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7 No increase 100% increase afer % increase for % increase afer 2015 No increase No increase 100% increase afer 2015 Consumpion ax 5% 5% 5% 5% 10% 15% 15% Figure 2. Simulaion Resuls-Demographic Proecion of Fuure Generaion. Copyrigh 2011 SciRes.

8 GDP K. OGURO ET AL. 609 Table 4. Simulaion Resuls-Macro Economic Proecion. GDP per employee Saving rae Capiallabor raio Ineres rae Wage rae Deb-GD P raio Deb per employee Pension premium o wage Scenario % % 6.17% % 2.61% % % % 14.90% % % 5.59% % 2.51% % % % 15.83% % % 5.82% % 2.37% % % % 17.37% % % 0.69% % 2.32% % % % 25.99% % % 1.16% 95.61% 2.85% 98.66% % % 26.45% Scenario % % 6.17% % 2.61% % % % 14.90% % % 5.59% % 2.51% % % % 15.83% % % 6.06% % 2.36% % % % 17.37% % % 0.95% % 2.32% % % % 25.99% % % 1.49% 95.27% 2.87% 98.56% % % 26.48% Scenario % % 6.17% % 2.61% % % % 14.90% % % 5.59% % 2.51% % % % 15.83% % % 6.05% % 2.37% % % % 17.37% % % 0.93% % 2.33% % % % 25.99% % % 1.24% 95.30% 2.87% 98.57% % % 26.48% Scenario % % 6.17% % 2.61% % % % 14.90% % % 5.59% % 2.51% % % % 15.83% % % 5.94% % 2.37% % % % 17.37% % % 0.81% % 2.32% % % % 25.99% % % 1.31% 95.45% 2.86% 98.61% % % 26.46% Scenario % % 6.17% % 2.61% % % % 14.90% % % 5.59% % 2.51% % % % 15.83% % % 6.86% 97.14% 2.76% 99.13% % % 17.37% % % 0.43% % 2.50% % % % 26.38% % % 2.02% 96.93% 2.78% 99.07% % % 26.65% Scenario % % 6.17% % 2.61% % % % 14.90% % % 5.59% % 2.51% % % % 15.83% % 99.60% 7.84% 90.56% 3.15% 97.07% % % 17.37% % % 1.65% 98.84% 2.67% 99.65% % % 26.74% % % 5.45% 97.71% 2.73% 99.31% % % 26.89% Scenario % % 6.17% % 2.61% % % % 14.90% % % 5.59% % 2.51% % % % 15.83% % 99.63% 8.14% 90.63% 3.15% 97.09% % % 17.37% % % 1.31% 98.80% 2.67% 99.64% % % 26.74% % % 4.99% 97.37% 2.75% 99.20% % % 26.92% Copyrigh 2011 SciRes.

9 610 K. OGURO ET AL. Securiy Research [24], closely correspond. In Scenario 2, compared wih Scenario 1, he raio in 2030 decreases by 0.3%, in Scenario 3 by 0.03%, and in Scenario 4 by 0.14%. Thus i can be seen ha hese child benefi expansions slighly decrease he progress of populaion aging. As we adop he lifecycle hypohesis, he saving rae is severely affeced by he rise of he rae of elderly populaion, which is srongly correlaed wih he demographic rend. In Scenarios 1 o 7, here is no significan change in he rend of he saving rae during he simulaion periods. Bu is level differs in each scenario. In Scenario 1, he saving rae shows a endency o decrease from 6.17% in 2007 o 1.16% in Table 4 shows ha he child benefi expansions basically raise he saving rae in 2007 o 2030 years. On he oher hand, he reform wih higher consumpion ax reduces he saving rae more in he years from 2007 o Because of he assumed echnology and lifecycle hypohesis, he GDP is deermined mainly by working-age populaion dynamics. In he baseline scenario, he GDP level grows sagnan. I declines markedly from 2020 o 2030, reflecing he declining labor force. And hen, in each scenario, he GDP declines o 80.66% % in 2030 from he base year Bu, in Scenarios 1 o 5, GDP per employee increases from 2007 o On he oher hand, in Scenarios 6 and 7, GDP per employee emporally decreases in 2015 and increases afer Figure 3. Simulaion Resuls-Reired populaion raio. nario, due o he capial marke equilibrium, he ineres rae (wage rae) flucuaes wihin a narrow range, e.g., 2.32% % (98.56% %) over hree decades Fiscal Variables Generally, he child benefi expansion can be expeced o give he fiscal balance ambivalen effecs hrough several channels. If he expansion is financed by new public bond issues, i iniially increases public deb. Bu he increase in he number of children also increases ax bases, and hen changes he rend of governmen revenue and expendiure. As a resul, he fuure governmen deb will be eiher reduced or increased. Table 4 shows ha in Scenario 2, compared wih Scenario 1, he Deb-GDP raio slighly increases by 6.99% in In Scenario 3, he raio increases by 5.05% in 2030, and in Scenario 4 by 3.30%. Figure 4 also shows ha in Scenario 2 compared wih Scenario 1, he deb per employee slighly increases by 0.01 in 2030, in Scenario 3 by 0.02 in 2030 and in Scenario 4 by 0.01 in On he oher hand, in Scenarios 5 o 7 (consumpion ax reform or policy-mix), he Deb-GDP raio is reduced by 58.80% % in 2030, and he deb per employee is reduced by in Welfare Finally, we briefly valuae facor prices. In each sce- Figure 5 shows generaional welfares of Scenarios 1 o 7. Copyrigh 2011 SciRes.

10 K. OGURO ET AL. 611 Figure 4. Simulaion Resuls-Deb per employee. Figure 5. Simulaion Resuls-Welfare wih Equivalen Variaion. These are welfares of subsequen cohors measured in erms of lifeime uiliy level agains he cohor born in The long-run increase in he pension premium o wage rae caused by he progress of aging decreases he amoun of resources available wihin heir lifeime. The long-run increase in he public deb o GDP raio also reduces privae capial sock available and possibly decreases fuure growh. Curren and fuure generaions suffer a severe welfare loss. In Scenarios 1 o 7 in Figure 5, we measure he welfare of each generaion wih equivalen variaion. The welfares of Scenario 5 and 6 gradually decline and he Copyrigh 2011 SciRes.

11 612 K. OGURO ET AL. boom for his scenario doesn occur unil birh year 2030, bu Scenarios 1 o 4 have a welfare boom a he generaion born in 2025, and he boom for Scenario 7 is in In addiion, in Scenarios 2 o 4, compared wih Scenario 1, all generaions born afer 1990 obain a welfare gain: e.g., in Scenario 2, he welfare of he generaion born in 2030 dramaically increases by 4.6%, in Scenario 3 by 0.2%, and in Scenario 4 by 2.2%. This means ha he welfare condiions in Scenarios 2 o 4 correspond o he concep of RC-improvemen developed by Michel and Wigniolle [7]. On he oher hand, in Scenarios 5 o 7, compared wih Scenario 1, mos generaions born afer 1940 suffer a welfare loss whose burden is covered by an increase in consumpion ax. However, if Scenario 6 is an ineviable choice in order o mainain he susainabiliy of fiscal budge, we should change he baseline scenario from Scenario 1 o Scenario 6. Then, in Scenario 7, compared wih Scenario 6, all generaions born afer 1990 obain a welfare gain. This means ha Scenario 7 also becomes an RC-improvemen. Therefore, from he comparison beween he child benefi scenarios, he consumpion ax reform scenarios, and he policy-mix scenario, we draw he following conclusions: 1) if we can ignore he susainabiliy of he fiscal budge in Scenarios 2 o 4, he child benefi expansions are expeced o make some conribuions o he improvemen of he welfare of curren and fuure generaions, and 2) if boh he susainabiliy of he fiscal budge and he improvemen of he welfare of curren and fuure generaions are requiremens, we will need o promoe a policy such as a policy-mix wih he child benefi expansion and addiional fiscal reform, i.e. increasing he consumpion ax. Then, he policy-mix can be expeced o provide a higher level of welfare for curren and fuure generaions han only consumpion ax reform. 5. Concluding Remarks In his paper, we presened an OLG simulaion model wih endogenous feriliy in order o analyze he relaionship beween child benefi and fiscal burden in Japan. Our simulaion resuls show ha expansion of he child benefi will improve he welfare of curren and fuure generaions. On he oher hand, our findings show ha we canno expec a significan long-erm improvemen in welfare solely from implemening a policy of increasing he consumpion ax. If boh he susainabiliy of he fiscal budge and he improvemen of he welfare of curren and fuure generaions are requiremens, we will need o promoe a sraegy consising of such componens as a policy-mix ha includes boh child benefi expansion and addiional fiscal reform, i.e. increasing he consumpion ax. Implemenaion of such a he policy-mix can be expeced o provide a higher economic level in he welfare of curren and fuure generaions could be expeced solely from consumpion ax reform. In addiion, he Japanese governmen is currenly rying o develop a model for esimaing he direcion of he populaion of fuure generaions, which has economic underpinnings. Therefore, if our model can be made more robus, i may prove o have a grea impac on he mehod for esimaion of he Japanese populaion, by which we analyze he relaionship beween fuure populaion and changes in he economic environmen. Finally, in an era of populaion aging, Japan will face enormous difficulies. Even given he difficuly of he ask, Japan, like oher developed counries, mus confron hese and oher obsacles and solve he relaed issues o char a producive and viable fuure for is fuure generaions. 6. References [1] P. A. Diamond, Naional Deb in a Neoclassical Growh Model, American Economic Review, Vol. 55, No. 5, 1965, pp [2] A. B. Abel, N. G. Mankiw, L. H. Summers and R. J. Zeckhauser, Assessing Dynamic Efficiency: Theory and Evidence, Review of Economics Sudies, Vol. 56, No. 1, 1989, pp [3] L. K. Rau and T. N. Srinivasan, Dynamics of Endogenous Growh, Economic Theory, Vol. 4, No. 5, 1994, pp [4] R. Chakrabari, Endogenous Feriliy and Growh in a Model wih Old Age Suppor, Economic Theory, Vol. 13, No. 2, 1999, pp [5] J. I. Conde-Ruiz, E. L. Gimenez and M. Perez-Nievas, Millian Efficiency wih Endogenous Feriliy, Review of Economic Sudies, Vol. 77, No. 1, 2010, pp [6] M. Golosov, L. E. Jones and M. Teril, Efficiency wih Endogenous Populaion Growh, Economerica, Vol. 75, No. 4, 2007, pp [7] P. Michel and B. Wigniolle, On Efficien Child Making, Economic Theory, Vol. 31, No. 2, 2007, pp [8] G. S. Becker, An Economic Analysis of Feriliy. In: Naional Bureau of Economic Research, Ed., Demographic and Economic Change in Developed Counries, Naional Bureau of Economic Research, Inc., Princeon, 1960, pp [9] R. Willis, A New Approach o he Economic Theory of Feriliy Behavior, Journal of Poliical Economy, Vol. 81, No. 2, 1973, pp [10] Z. Ecksein and K. Wolpin, Endogenous Feriliy and Opimal Populaion Size, Journal of Public Economics, Vol. 27, No. 1, 1985, pp Copyrigh 2011 SciRes.

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