THREE ESSAYS ON THE ENDOGENOUS GROWTH OF A REGIONAL ECONOMY UNDER THE IMPACTS OF DEMOGRAPHIC CHANGES TAE-JEONG KIM DISSERTATION

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1 THREE ESSAYS ON THE ENDOGENOUS GROWTH OF A REGIONAL ECONOMY UNDER THE IMPACTS OF DEMOGRAPHIC CHANGES BY TAE-JEONG KIM DISSERTATION Submied in parial fulfillmen of he requiremens for he degree of Docor of Philosophy in Economics in he Graduae College of he Universiy of Illinois a Urbana-Champaign, 2010 Urbana, Illinois Docoral Commiee: Professor Geoffrey J.D. Hewings, Chair and Direcor of Research Professor Werner Baer Professor Anil K. Bera Professor Anne P. Villamil

2 ABSTRACT The impac of an ageing populaion on he economy is one of he key issues in mos developed counries. I is a generally acceped noion ha an ageing populaion could cause negaive effecs, including a decrease of per-capia oupu and economic welfare, on he economy mainly due o he decline of he labor force and aggregae saving rae. The firs chaper adops he wo-secor overlapping generaion (OLG) model o capure he impac of populaion ageing on he regional economy and compares he effeciveness of governmen policy in an endogenous growh perspecive. Comparing he compuaional resuls of a one-secor OLG model where agen s produciviy is given exogenously, he simulaion resul confirms ha endogenously deermined invesmen in human capial significanly offses he negaive effecs of he ageing populaion on he regional economy. The chaper also aemps o check if here is room for he governmen o weaken and preven he negaive effecs of he ageing populaion. For his, his chaper examines he effecs of wo kinds of governmen ransfer sysems on he regional economy: money ransfer and educaional ransfer sysems. The money ransfer, which is redisribued o agens by he governmen, could be used for an individual s consumpion, saving and educaional invesmen. Educaional ransfer is given direcly o he individual proporional o his or her opporuniy cos semming from educaion invesmen. The resul shows ha he educaional ransfer sysem is superior o money ransfer sysem in he long-run in erms of growh of per-capia income, aggregae welfare and sabilizing he facor prices. However, he resuls imply ha here exiss a ii

3 rade-off relaionship in implemening an educaional ransfer sysem beween economic growh and equiy of income and wealh. The second chaper seeks o examine he effecs of he ageing populaion in Illinois wih inclusion of he household s ex-ane inra-generaional heerogeneiy across race and migraion saus. For his, his chaper empirically shows ha here are significan gaps in reurns o educaion beween race and migraion saus in Illinois; and here exiss significan relaionships beween a residen s demographics and he probabiliy of in- and ou- migraion around Illinois. These empirical resuls, including heerogeneous properies across race and migraion saus and demographic- relaed migraion endency, are calibraed ino he wo-secor OLG model. Using his wo-secor OLG model incorporaed wih he inra-generaional heerogeneiy over race and migraion saus, his chaper proecs he economic growh of Illinois will decelerae subsanially unil he mid 2020s due o populaion ageing. Afer ha ime, he growh of Illinois will parially recover. The maor economic problems of he ageing era sem from he deficiency of he labor force. Also he Black s unemploymen rae ends o be subsanially high in Illinois. Taking he wo labor marke- relaed problems of ageing populaion and high Black s unemploymen ino consideraion, he governmen could implemen a labor policy measure aiming a increasing he employmen rae of he Black o he level of he oher races hrough he absorpion of he unemployed Blacks by offering indusry subsidies or incenives. However, he resul shows ha an indirec educaional policy, argeing he upgrading of he ransmission channel of human capial sock from he old generaion o he young generaion of he Black, is more preferable han he direc employmen policy in erms of iii

4 long-run effecs on per-capia income and social welfare. Also, his chaper shows ha he effecs of he governmen s immigraion policy, which aims a replacing lowproducive inernaional immigrans wih naive, relaively high-producive unemployed individuals who have been unemployed, are very limied in erms of per-capia income, welfare and aggregae produciviy. On he conrary, ax and ransfer policy inducing inernaional immigrans o inves more in heir educaion works relaively beer. Furhermore, under his policy scheme, he naive s human capial sock also improves significanly because of posiive spillover effecs even hough he ransfer sysem s direc beneficiary is he inernaional immigran group. The hird chaper aemps o proec he economic pahs for he individual Midwes saes (Illinois, Indiana, Michigan, Ohio and Wisconsin, as well as he Res of he US) in he fuure when he populaion ageing becomes more pronounced. To accomplish his ask, a dynamic general equilibrium model is developed so ha i could incorporae he iner-regional ransacions and endogenous growh mechanisms wihin he framework of an OLG model. Key parameer values associaed wih he regional inerconnecions were assigned by using muli-regional Social Accouning Marix (SAM) of he Midwes saes. Two differen seady-sae resuls were presened wih he wo differen age-cohor populaion srucures corresponding o year 2007 and These seady-sae resuls imply ha here should be considerable negaive impacs on he regional economies in he sense of declining per-capia oupu. The rae of declining of per-capia oupu are proeced o be heerogeneous across he regions due o he differen developmens of age-cohor populaion srucures and consequenly differen levels of iv

5 endogenously deermined educaional invesmen of workers. Furhermore, he regions could be grouped separaely according o he levels of average human capial sock of workers: high-skilled and low-skilled regions, being roughly consisen wih acual labor produciviy saisics. I is inuiive ha he supply-demand ineracions beween he regions should be affeced by developmens of demographics in each region. This inuiion is consisen wih he simulaion resuls in he sense ha he resul revealed he developmen of oupu price in a cerain region reflecs he dynamics of demographics of every region. Meanwhile, according o he dynamic simulaion, he negaive impacs of populaion ageing will no be so severe unlike wha was presened in he seady-sae resuls. This miigaion of negaive effecs could be aribued mainly o he growh of human capial sock of workers. The dynamic simulaion resuls reveal ha he percapia oupu of every region is proeced o grow posiively in he near fuure when he populaion ageing will be pronouncing. However, he growh rae of he per-capia oupu is proeced o be heerogeneous across he regions: he regions wih high-skilled workers hold he poenial hrea ha populaion ageing could give more negaive impacs on he economy due o he relaively sluggish growh of human capial sock. Also, he dynamic simulaion resuls show ha cerain regions in Midwes will experience heir erms-of-rade deeriorae in he near fuure, implying ha careful aenion should be given o heir fuure rade condiions. v

6 To my faher and moher vi

7 ACKNOWLEDGEMENTS Firs of all, my special and sincere graiude goes o my advisor, Geoffrey J.D. Hewings. If i had no been for his srong encouragemen and insighful guidance, I could no have arrived a his desinaion. I have been also benefied by collaboraing and discussing wih he promising graduae sudens a he Regional Economics Applicaions Laboraory (REAL) under he direcion of Geoffrey J.D. Hewings. I would also like o express my graiude o Professor Werner Baer, Professor Anil K. Bera and Professor Anne P. Villamil for heir valuable advices and commens as my hesis commiee members. Also, I am deeply graeful o my family members. I wish his hesis could be one of my humble ribues o my parens. Also I would like o hank o my wife, who has always sood by me during his long and difficul period. Finally, his research could no have been iniiaed wihou he help and suppor of he Bank of Korea. However, he conens of his hesis represen he resuls of my own research; and do no reflec he view of he Bank a all. Also, any errors appearing here are enirely my responsibiliy. vii

8 TABLE OF CONTENTS Chaper 1: Endogenous Growh of Ageing Economy: Evidence and Policy Measures...1 Chaper 2: Endogenous Growh of he Ageing Economy wih Inra-Generaional Heerogeneiy over Race and Migraion Saus...40 Chaper 3: Iner-Regional Endogenous Growh under he Impacs of Demographic Changes...78 References Appendix A: Esimaion of he Iniial Human Capial Sock Disribuion over Age-Cohors in Chaper Appendix B: Key Variables from Dynamic Simulaion Resuls in Chaper viii

9 Chaper 1 Endogenous Growh of Ageing Economy: Evidence and Policy Measures 1.1 Inroducion The impac of an aging populaion on economy is one of he key issues in mos developed counries. In paricular, he dependency raio 1 of he US is expeced o rise rapidly unil mid 2030 s. Table 1.1 shows ha he raio in he US is proeced o increase from 19% in 2004 o 33% in 2035 and hen level off a around 33%. The growh of dependency raio is proeced o peak in 2025 and hen slow down (figure 1.1). This change of rend reflecs he impac of baby boomers born in he pos-world War II period from 1946 hrough 1964 who will be approaching reiremen age sequenially over he nex wo decades; he oldes baby boomers urn 60 in lae 2000s and he younges urn 60 in lae 2020s. The sae of Illinois 2 also shows similar rends excep ha he dependency raio of Illinois is anicipaed o be less han naional raio (see able 1.1). An aging populaion could cause negaive effecs on he economy, including a decrease of per-capia oupu and economic welfare, mainly due o he decline in he supply of he labor force and he saving rae: he dissaving of he old should increasingly offses he saving of he young during he ageing era. Therefore, i becomes imporan o 1 Dependency raio = number of populaion over 65 / number of populaion beween 15 and U. S Census Bureau proeced populaion s age srucure of each sae up o 2030 and naional populaion s age srucure up o

10 forecas he impacs of an aging populaion on he economy and o assess he opions for governmen policies ha migh be needed o address he challenge. A wo-secor overlapping generaion (OLG) model is developed o capure he impac of populaion ageing on Illinois and compare he effeciveness of governmen policy in an endogenous growh perspecive. The endogenous growh model has aemped o endogenize he underlying source of susained growh. In he case of a wosecor endogenous growh model, producion of human capial is supposed o be relaively inensive in human capial. Consequenly, each individual s educaion aciviy plays a key role in economic growh. For example, in he Uzawa (1965) model, here is no physical capial involved in producion of human capial while in he Lucas (1988) model, he oal facor produciviy in he final good secor depends on he average level of human capial in an economy. Sadahiro and Shimasawa (2002) developed he overlapping generaion model (OLG) based on wo-secor endogenous growh heory in order o proec he effecs of populaion ageing impac on he economy. They endogenized he individual s choice in human capial invesmen a he workplace; and found ou ha endogenously deermined invesmen in human capial offses significanly he negaive effecs of ageing populaion. However, hey did no apply heir model o an acual populaion srucure; and also paid lile aenion o he role of governmen policy. Ludwig e al. (2007) exended Sadahiro and Shimasawa (2002) wih differen formaions of human capial accumulaion. 2

11 This chaper is organized as follows. In secion 2, he model descripion and he numerical algorihm will be demonsraed. In secion 3, he compuaional resuls of he baseline model are presened, compared o hose wih a one-secor OLG model, which does no ake endogenous growh of human capial ino consideraion (his kind of model will be referred o as an exogenous model laer). In secion 4, he governmen s policy o address he negaive effecs of ageing populaion on he regional economy will be simulaed. In he final secion, he conclusion will be drawn and he furher research subec will be briefly discussed. 1.2 Baseline Model There are hree ypes of agens in he baseline model: represenaive households, firms and governmen. The households maximize uiliy, subec o he usual budge consrain. Firms hire labor and ren physical capial o produce physical goods in he compeiive marke. Governmen levies pension ax on he workers and operae he social pension sysem of pay-as-you-go ype wih he ax revenue. A wo-secor economy is proposed wih physical goods and human capial secors. The arge period is 2001 hrough 2050 when he ageing phenomenon is proeced o deepen in Illinois as well as he U. S. I is assumed ha here is no uncerainy in he economy. There exis J generaions in every single year and he generaions are overlapped every sample period Households 3 Thus, we could call his paper s model as perfec foresigh OLG model. 3

12 A he beginning of age 1 4, each individual makes a decision on allocaing resources on consumpion and savings as well as spliing he endowmen ime ino schooling and working for a whole life-ime o maximize his/her life-ime welfare. I is assumed ha he individual eners ino he labor marke a age 1 and reire a age *. Every agen is supposed o live unil age J. The insananeous uiliy funcion has wo argumens, consumpion and invesmen in human capial: c u( c, e ) =,, + θe 1 γ 1 γ,, 1 γ γ > 1, 0 < θ < 1 (1.1) where c, is consumpion and e, is ime fracion of invesmen in human capial 5 a ime and age while θ is he parameer of he degree of educaional invesmen moive and γ is he parameer of he inverse of he iner-emporal elasiciy of subsiuion. Therefore, he individual s life-ime uiliy funcion is as follows: J J 1 γ 1 γ c , + θe + 1, U = β u( c + 1,, e + 1, ) = β = 1 = 1 1 γ (1.2) 1 U denoes he life-ime uiliy of he individual who is born in he year and β denoes he parameer of subecive discoun rae. The individual who was born in ime has a following life-ime budge consrain: J + 2 * p c + 1, (1 τ + 1) h + 1, w + 1(1 e + 1, ) = 1 k = 1 r = + k = 1 k = 1+ r k + 4 Noe ha age 1 in he model corresponds o age 20 in realiy. 5 In he model, he individual whose age is beween 1 and * allocaes his/her endowmen ime (=1) ino 0 1 for = 1,..., *. labor and educaion invesmen. Therefore,, e 4

13 1 + J + 2 pen + 1, (1.3) = * + 1 k = 1+ r k where r is he real ineres rae, w is he wage rae and p τ is he social securiy ax rae a ime while h, is he human capial sock and pen, is he level of pension benefi a ime and age. Every new generaion in each year maximizes he life-ime uiliy funcion (1.2) under he budge consrain (1.3). The Euler equaions (1.4) and (1.5) could be derived by compuing he firs order condiions wih regard o consumpion, saving and educaion invesmen ime: ( β ( 1 )) 1/ c = + r c (1.4) + 1, , γ e θ = 1/ γ, p, (1 τ ) w h, c if *. (1.5) 6 Noe ha, in his model, spending ime in educaional invesmen is supposed o affec agen s uiliy in hree channels: (1) educaional invesmen ime uiliy (shor-run direc channel), (2) educaional invesmen ime labor ime labor income consumpion uiliy (shor-run indirec channel) and (3) educaional invesmen ime human capial sock labor produciviy labor income consumpion uiliy (long-run indirec channel). As for he 3 rd channel, Heckman e. al (1998) revealed ha pos-school learning, including ob search, learning-by-doing and workplace educaion, accouns for 1/3 o 1/2 of all skill formaion in a modern economy. 6 Noe ha we have a boundary condiion e, 1. 5

14 An individual s wealh, which comprises accumulaed personal saving over ime, a ime and age a (=, ) evolves as follows: a + + = (1 τ ) h w (1 e ) + (1 + r ) a c p 1, 1,,,, if 1 * (1.6) a = 1, 1 pen +, (1 + r ) a + +, c, if > *. Aggregae supply of physical capial sock a ime is: = J s,, = 1 K a N (1.7) N, where denoes populaion size of age-cohor in ime. The aggregae consumpion a ime is: J =,, = 1 C c N. (1.8) Firm The firm produces a composie good by rening physical capial and hiring labor in order o maximize is profi each year. The Cobb-Douglas producion funcion is used wih he following specificaion: Y A K L d α e d 1 α = ( ) ( ) (1.9) where d K he demand of physical capial and e d L is he demand of effecive labor a ime while A is he parameer of oal facor produciviy and α is he parameer of physical capial income share. Facor prices are deermined in he compeiive marke: r = α A( K ) ( L ) δ (1.10) d α 1 e d 1 α 6

15 d α e d α and w = (1 α) A( K ) ( L ) (1.11) where δ is physical capial depreciaion rae Governmen The governmen in he baseline economy us operaes he social securiy sysem; he governmen levies a social securiy ax on labor income and ransfers he pension benefi o reirees. The governmen s budge is assumed o be balanced every period: τ * J N, ((1 e, ) w h, ) = N, pen,. (1.12) p = 1 = * + 1 The magniude of annual pension benefi of a reiree is dependen on his/her average yearly (gross) labor income before reiremen. The governmen ransfers a pension benefi o a reiree which amouns o his/her yearly average labor income muliplied by replacemen raio (ξ ) Human capial Generally an individual s human capial sock is embodied privaely so i has a propery of rivalry and exclusiveness; he use of embodied skills in one aciviy precludes heir use in anoher aciviies ( rivalry ) and people have propery righs in heir own skills ( exclusiveness ). Therefore, o mainain and improve aggregae human capial sock in he economy, here should be a ransferring mechanism of human capial sock from generaion o generaion; his ransferring mechanism is referred o as educaion. 7

16 Following he human capial producion funcion of Sadahiro and Shimasawa (2002), he process may be presened as: h (1 δ ) h B( mk ) ( h e ) φ 1 φ + 1, + 1 = h, +,, (1.13) where k is he physical capial/labor raio while B is he parameer for accumulaion efficiency of human capial, m is he porion of physical capial sock for producing he human capial sock, δ h is he parameer of depreciaion rae of human capial sock and φ is he parameer of elasiciy of human capial formaion funcion. This human capial producion funcion includes he physical capial raio and he degree of accumulaion efficiency of human capial sock so ha he model could reflec he efficiency of educaion sysem of he corresponding economy. Noe ha here is a need o develop a rule of assigning a human capial sock of age 1 individuals of each year. The proposal of Sadahiro and Shimasawa (2002) is adoped so ha he new generaion is born wih a porion of human capial sock of he previous generaions: * * hc h,1 = π h 1, N 1, / N 1, = 1 = 1 (1.14) hc where π is he parameer of efficiency of human capial ransmission beween generaions. Aggregae human capial sock a ime is defined as: H * = h, N,. (1.15) = 1 Then, aggregae supply of effecive labor can be compued as shown in (1.16): * e s = (1, ),, = 1 L e h N. (1.16) 8

17 1.2.5 Marke clearing Facor and goods marke clearing condiions hold a every period as follows: ( ) L = L L (1.17) e s e d e ( ) K = K K (1.18) s d Y = C + I + G (1.19) 7 where I = K (1 δ ) K Calibraion Parameers This chaper adops he relevan parameers from he relaed previous lieraure (see able 1.2). In paricular, he parameers associaed wih he human capial producion are from Sadahiro and Shimasawa (2002). The oher parameers are mainly from Park and Hewings (2007). Also noe ha i is for he period 2001 hrough 2050 ha simulaion resuls are presened in he nex secion. Age-cohor srucure As for he age-cohor disribuion, calibraed o our model, he U. S. Census Bureau (USCB) s proecions ha are available up o 2030 are used. The USCB s proecion are exended o 2050, assuming ha he correlaion of age-cohor srucures beween Illinois 7 In his model, G =0. 9

18 and he U. S will be equivalen as for he previous period. Figure 1.2 shows he changes of age-cohor srucures of Illinois from 2010 hru 2030 o The impacs of his demographic change will be explored in he nex secion. Iniial disribuion One of he difficulies his sudy should address is how o se he iniial disribuion of wealh and human capial sock in 2001, which is he beginning year of economy of our model. The economy of Illinois was no a a seady sae in 2001; hence, his chaper shows he anoher way o address his issue, insead of adoping a seady sae disribuion of wealh and human capial sock as a disribuion in Firs, for he disribuion of human capial sock in 2001, he produciviy age profile 8 adoped by Park and Hewings (2007) was used so ha i would be possible o compare he simulaion resuls beween he one-secor model ( exogenous model ) and he wo-secor model ( endogenous model ), ha have differen views on human capial and is role on economic growh. Secondly, he iniial wealh disribuion migh be calibraed empirically. However, he impacs of facors 9 oher han ageing populaion and governmen s fiscal policies should be excluded in proecing he economic variables. Thus, he iniial wealh disribuion in an endogenous approach can be generaed like he following. I was 8 Park and Hewings (2007) assumed an individual s labor produciviy o be an exogenous funcion of his/her age: e λ λ λ 2 = and calibraed he parameers: 1, 2, 3 λ λ λ. 9 For example, uncerainies surrounding he economy affec he saving moive of he consumers remarkably in realiy. We do no wan hese uncerainies, which exis ouside he model, affec our simulaion resuls. 10

19 assumed ha he cross-secional wealh disribuion in 2001 was exacly he same as he life-cycle wealh profile of age 1 generaion in Saring wih he arbirary iniial wealh disribuion hen he life-cycle wealh profile of each generaion in each period can be calculaed. Our ineres is in wheher he wealh disribuion across generaions in 2001 is idenical o he life-cycle profile of age 1 generaion in The fixed-poin ieraion mehod is used o ge he convergence of wealh disribuion. Wealh disribuion across generaions in 2001 ha is developed by he mehod menioned above has a usual life-cycle paern: wealh is accumulaed unil he reiremen age and hen decreases close o zero since here is no beques moive in consumer s uiliy funcion in he model (figure 1.3). Again, noe ha, by assumpion and for comparison purposes, he iniial wealh disribuion in 2001 is idenical in boh of models: he exogenous produciviy model and he endogenous human capial model. 1.3 Compuaional Resuls In his secion, he simulaion resul of baseline model will be presened. The resuls from he endogenous human capial model will be compared o he simulaion resuls of he exogenous model in order o derive he implicaions of he roles of human capial during he era of an ageing populaion. As menioned before, he exogenous produciviy model assumes ha he individuals devoe his/her whole endowmen ime ino working. On he conrary, he individuals in he oher model have an incenive of spliing his/her endowmen ime ino working and human capial invesmen. 11

20 1.3.1 Per-capia oupu During our sample period, i.e., 2001 hrough 2050, per-capia oupu coninues o grow under he endogenous human capial model. In conras, under he exogenous produciviy model, per-capia oupu increases for he early sage bu begins o decrease in he early 2010s and hen levels off in he lae 2030s (see figure 1.4). Therefore, he per-capia oupu of endogenous human capial model is 24% larger han ha of he exogenous produciviy model in Noe ha he per-capia oupu of he exogenous case is larger han ha of he endogenous case for he early years of our sample period since he individuals do no devoe heir whole endowmen ime ino working. However, he increasing produciviy of he endogenous case dominaes he relaive deficiency of labor conribuions a an early sage. Figure 1.2 showed ha he impac of he ageing phenomenon is forecas o be mos profound during he 2010s and 2020s. According o he simulaion resuls of he endogenous human capial model, per-capia oupu grows 0.44 and 0.12 percen on average during he 2010s and 2020s and hen recovers relaively quickly by he 2030s. As able 1.3 shows, he improvemen of oal produciviy dominaes he negaive effec of decreases in he labor force in he case of endogenous human capial model. The scarciy of labor decreases he growh of per-capia oupu by 0.27 percen poin and 0.29 percen poin during 2010s and 2020s respecively, while increasing oal produciviy acceleraes he oupu growh by 0.47 percen poin and 0.37 percen respecively. On he conrary, he exogenous produciviy model forecass ha he economy will suffer he 12

21 negaive growh of per-capia oupu during 2010s and 2020s and hen recover slowly from he impac of an ageing populaion Facor prices The exogenous produciviy model forecass ha facor prices such as ineres and wage raes will go hrough considerable change during he phase of ageing populaion. In he ageing economy, he labor (physical capial) becomes relaively scarce (abundan), herefore he facor price of labor (physical capial) moves higher (lower). However, according o he endogenous human capial model, he agens deermine his/her life-cycle profile of working and ime shares of human capial invesmen, based on his/her expecaion abou fuure pah of each facor prices. The implicaions are ha he agens in he endogenous model end o increase his/her ime share of invesmen in his/her human capial since he/she knows he wage rae (ineres rae) will become higher (lower) in he fuure and his/her human capial sock will grow proporionally o his/her invesmen ime. 10 This kind of mechanism, in he endogenous human capial model, makes he facor prices o show relaively sable movemens during he ageing period, compared o hose of he exogenous produciviy model. Figure 1.5 shows he simulaion resuls confirming hese conecures. Since ageing does no cause a considerable drop in he ineres rae or a rise in he wage rae, he aggregae saving rae 11 does no decline sharply during he ageing period in spie of he same proecion of he demographic ransiion (figure 1.6). The 10 See Saving rae (%) = aggregae saving / aggregae disposable income. 13

22 endogenous model implies ha he aggregae saving rae will drop by 6.6 percenage poins from 2007 o On he conrary, he exogenous model implies ha i will decline by 11.7 percenage poins during he same period Welfare In his secion, he simulaion resuls for social welfare will be presened. Figure 1.7 shows he consumpion level corresponding o aggregae social welfare. 12 Social welfare grows gradually in he case of he endogenous model, bu i seems o sagnae in he case of he exogenous model. However, i akes a long ime for he social welfare of endogenous model o cach up wih he social welfare of he exogenous model. This resul may be ascribed o he fac ha he wage rae of he endogenous model does no surge as in he case of he exogenous model. On he oher hand, a relaively high ineres rae in he endogenous model canno cancel he negaive effec of low wage raes since young agens ener he labor marke wihou any asse holdings. Also, noe ha i akes some ime o build up he human capial sock o he level ha could dominae he low wage rae effec. Thus, he raio of average welfare of working cohors o he reired cohors in he endogenous model is relaively low, compared o ha of exogenous model (able 1.4). 12 Due o he uiliy funcional forma, welfare is compued o be a negaive value. Noe ha magniude of uiliy does no maer: ha is uiliy should be considered as ordinal, no as cardinal. 14

23 1.3.4 Sensiiviy analysis Maoriy of he parameers are acceped from he previous relevan lieraure. In his secion, he resul of sensiiviy analysis associaed wih he key parameer values will be presened. One parameer which will be aken ino consideraion is he elasiciy of ineremporal subsiuion (EIS: 1/γ ), which measures he exen o which household agens subsiue heir consumpion iner-emporarily in response o he expeced changes in he real ineres rae in he fuure. The oher parameers of ineres are he efficiency of human capial formaion ( B ) and reiremen age ( * ). The resuls show ha he per-capia oupu and is growh are subsanially influenced wih he magniude of γ and B. Firs, he lef panel in figure 1.8 shows ha he lower EIS (case of γ =2.6) increases he growh rae of per-capia oupu during he ageing era. However, he effec of lowering EIS aenuaes gradually along he years. On he conrary, under he higher EIS (case of γ =1.2), he growh rae was negaive mos of years during 2001 hrough This is mainly because he endency o defer less consumpion o he fuure, which was riggered by he expecaion ha ineres rae declines during he ageing era, is promoed by increasing he EIS. This in urn induce he individuals o pu less weigh on he schooling since he schooling us help he individuals o consume more in he fuure and make consume less in he curren period; hus he average produciviy of he workers (human capial sock) falls, compared o he model economy wih he lower EIS (righ panel in he figure 1.8). Second, he parameer ( B ) conneced direcly o he efficiency of human capial formaion significanly affecs he performance of he model economy. When parameer 15

24 B is se o be.38, which is.10 poins higher han baseline, he growh rae of per-capia oupu becomes subsanially higher (figure 1.9). This maches he inuiion quie well since he individuals pu more weigh on heir schooling when he reurn o educaion is higher when every hing is held consan. However, he whole dynamic paern of growh of per-capia oupu are similar each oher regardless of magniude of his parameer value. Third, as he individuals expec o live longer, hey plan o exend heir reiremen age since hey need more income o suppor heir lenghened life ime unless hey raionally expec a favorable change in he public pension sysem. Also in a poin view of governmen, exension of reiremen age seem o be desirable since he prime source of negaive effecs of populaion ageing is he deficiency of labor force. The simulaion resuls reveal ha he effecs of exending he reiremen age canno be ignored in erms of boosing he per-capia oupu: he per-capia oupu was increased abou.5 percen from he baseline when exending one more year of reiremen age (lef panel in figure 1.10). However he effecs are no enlarged along he years; hus he growh rae of per-capia oupu was no affeced by exending he reiremen age (righ panel in he figure 1.10). Furhermore, he growh rae ges he downward pressure in he long erm by exending he reiremen age 13. The main reason why he impacs on he economic performance are no accumulaed iner-emporarily could be raced o he way how he human capial forms in he model (see 1.13). If he reiremen age is exended, he young should share he 13 More specifically, afer mid 2020s when he ageing phenomenon is forecas o be subdued, he growh rae under he model of exending he reiremen age is lower han he growh rae of baseline model. 16

25 educaional sysem, which is he consan porion of physical capial sock according o he model specificaion 14, wih he old who were no supposed o have paricipaed in he educaion sysem unless he reiremen age was exended; and more condensed educaional environmen lowers he efficiency in building up he human capial sock of younger workers. Furhermore, he elderly who belong o he age-cohor over han previous reiremen age are less efficien in developing heir produciviy; and hey will reire soon. Therefore, he average labor produciviy in he economy ges he negaive pressure by exending he reiremen age. This negaive pressure on he average produciviy is accumulaed generaion o generaion hrough he human capial ransmission mechanism. In case of exending 5 years of reiremen age, he average produciviy declines by.86 percen in he iniial year (2001) and decrease by 3.42 percen in 2050 (able 1.5). 1.4 Governmen policies This secion ries o answer he following quesion: Which governmen policy is effecive o miigae he effec of ageing populaion? In he las secion, we have seen ha simply exending he reiremen age does no guaranee he susainable growh during he ageing era. One opion for effecive governmen policy should be o aler individual s choices so ha he equilibrium oucomes should be ones ha susain he higher economic growh and social welfare wih he same amoun of budge. 14 In our model, he physical capial which is used for he educaion is denoed by mk in (13). 17

26 In his chaper, he focus is resriced o he ax and ransfer policy, more specifically, money ransfer and educaional ransfer. For reference, Seshadri and Yuki (2003) explored he effecs of a governmen s redisribuive policy on he equiy and efficiency in he model economy. Using he simple wo-period sochasic OLG model, hey showed ha he educaional ransfer enhances he efficiency and reduces he inequaliy in he seady sae equilibrium. Money ransfer is a kind of redisribuion of wealh. In he simulaion used here, a lump-sum money ransfer is given o each household who is in he working age-cohor regardless of is income, produciviy and wealh levels. I could be used as a source for consumpion, saving and educaion invesmen. 15 Educaional ransfer is given o an individual proporionally o his/her opporuniy cos of educaion invesmen. In oher words, he primary purpose of educaional ransfer policy is o encourage he agens o inves in heir human capial. The background of his policy should be ha he average workers who are older han before (hanks o he populaion ageing) should be less acive in increasing heir invesmen in heir human capial due o he low marginal reurn o schooling; on he conrary he worker s skill a he workplace are rapidly made obsolee under he populaion ageing. Grip and Loo (2001) classifies skill obsolescence ino wo caegories according o is cause: echnical and economic skill obsolescence. The cause of echnical obsolescence is found a he naural wear of skills; while economic skill obsolescence is aribued o he 15 In our endogenous model, educaion expendiure is no a direc argumen in household s budge consrain, bu educaion ime is an argumen of uiliy funcion. Noe ha increasing consumpion, hanks o money ransfer, could weaken he incenive of laboring so ha agen will increase his/her educaion ime fracion. 18

27 exernal causes such as echnological developmens and shifs of he demand for skill levels from he indusries. Firs, i should be obvious ha populaion ageing may cause rapid echnical skill obsolescence in he aggregae level. Also, here are increasing empirical sudies showing ha he demand for he low skilled is rapidly declining mainly due o he fas echnical progress (Goldin and Kaz, 1998 and Bresnahan el al., 2002). Thus, he purpose of educaional ransfer should be undersood as help o decelerae he speed of obsolescence of he aggregae skill level in he corresponding economy, caused by populaion ageing, as well as o aach he low-skilled persons o he fas changing indusrial skill demand. Now, he seup of each secor under each scheme of governmen policy will be presened. Noe ha firm and human capial secors are idenical o our baseline model and marke clearing condiions are sraighforward enough o be omied in his secion Households Educaional ransfer When he governmen implemens an educaional ransfer sysem, an agen who was born in year has a following iner-emporal budge consrain: J + 2 J c = pen + + 1, e + 1, = 1 k = 1 + rk = * + 1 k = (1 τ + 1) rk (1 τ ) r * p e 1, 1 ((1 1 1)(1 1, ) e h + w + τ + τ + e + + µ e + 1, ) (1.20) = 1 k = + 1 k 19

28 where µ is he reimbursemen rae, which represens how much porion of opporuniy cos of an individual s educaional invesmen is covered by he governmen s e educaional ransfer, and τ is he educaion ax rae a ime. The Euler equaions (1.4) and (1.5) should be modified as follows: ( β ( 1 (1 τ e ) )) 1/ c = + r c (1.21) + 1, , γ e θ = p e ((1 τ τ ) µ ) 1/ γ,, w h, c if *. (1.22) 16 An individual s wealh, ha is accumulaed personal savings over ime, a ime and age (= a, ) evolves by he following equaions: ( ) a = h w (1 τ τ )(1 e ) + µ e + ( (1 τ ) r ) a c if 1 * (1.23) p p e 1, 1,,,,, a + + = pen + (1 + (1 τ ) r ) a c if > *. (1.24) e 1, 1,,, Money ransfer When he governmen operaes he money ransfer sysem, household s iner-emporal budge consrain is as follows: J + 2 J c = pen + + 1, e + 1, = 1 k = 1 + rk = * + 1 k = (1 τ + 1) rk (1 τ ) r * + 2 p e ( h 1, w 1(1 τ 1 τ 1)(1 e 1, ) χ e , ) (1.25) = 1 k = + 1 k τ + τ < µ. 16 p e Noe ha 1 20

29 where χ, is he money ransfer from governmen o individual whose age is a ime. The individual s dynamic opimizaion problem can be solved as: ( β ( 1 (1 τ e ) )) 1/ c = + r c (1.26) + 1, , γ e θ = p e ( 1 τ τ ) 1/ γ,, w h, c if *. (1.27) The individual s wealh a ime for workers evolves by he following equaion while he wealh for he reired agens evolves by (1.24): a + + = (1 τ τ ) h w (1 e ) + (1 + (1 τ ) r ) a + χ c if 1 * (1.28) p e e 1, 1,,,,, Governmen When he governmen operaes he educaional ransfer sysem, i levies an educaional ax on household s income and reimburses proporionally o his/her opporuniy cos semming from ime spen on educaional invesmen. I is assumed ha he governmen s social securiy sysem and educaional ransfer sysem are operaed independenly from each oher. Also he assumpion ha governmen s budge is balanced every period is mainained. Therefore, he budge consrain corresponding o he educaional ransfer sysem is as follows while he consrain of social securiy sysem is same as (1.12): τ µ * J * N, ((1 e, ) w h, ) + N, ( r a, ) = N, ( e, w h, ). (1.29) e = 1 = 1 = 1 21

30 When he governmen operaes he money ransfer sysem, i also levies a ax on household s income and ransfers he lump-sum amoun o each worker. Furher, he governmen s social securiy sysem and money ransfer sysem are operaed independenly from each oher. The budge consrain of money ransfer sysem is as follows: τ * J * N, ((1 e, ) w h, ) + N, ( r a, ) = N, χ,. (1.30) e = 1 = 1 = 1 Noe ha he economy is simulaed under wo differen governmen policy schemes: educaional ransfer and money ransfer sysems. However, i is assumed ha he budge volumes of hese wo sysems are idenical a every period for comparison purpose Compuaional resul Per-capia oupu In he shor-run, boh of he governmen policy sysems decrease per-capia oupu since hese ransfer sysems weaken he incenive o work. Figure 1.11 implies ha he shorrun negaive effec is much larger when he governmen operaes an educaional ransfer sysem han when i operaes money ransfer sysem. For example, he educaional ransfer sysem which reimburses 30% (20%, 10%) of opporuniy cos of educaional invesmen decreases per-capia oupu by 1.99% (1.16%, 0.52%) in 2001, compared o he per-capia oupu of baseline model in On he conrary, he money ransfer 22

31 sysem whose budge volume is equivalen o ha of he educaional ransfer sysem lowers us he oupu by 0.21% (0.12%, 0.06%) in However, he governmen s ransfer sysem booss he economy in a long-run. In paricular, he posiive effec of educaional ransfer is noeworhy whereas money ransfer sysem barely increases he per-capia oupu even hough governmen expends same amoun of budge every single year. For example, educaional ransfer sysem whose reimbursemen rae is 30% (20%, 10%) increases per-capia oupu by 3.78% (2.39%, 1.14%) in 2050, compared o he per-capial oupu of baseline model in However, he money ransfer sysem increases per-capia oupu by 0.28% (0.17%, 0.08%) in The governmen s ransfer policy increases he incenive of invesmen in human capial. This increasing incenive causes an improvemen in oal produciviy in he economy and finally booss he economy during he ageing period. Table 1.6 shows ha he educaional ransfer encourages individuals o allocae more ime o schooling han he money ransfer opion does even hough he money ransfer consumes he equivalen governmen s budge as he educaional ransfer sysem every year. The educaional ransfer sysem whose reimbursemen rae is 30% (20%, 10%) increases he average ime share of educaional invesmen by 27.87% (16.04%, 7.10%), compared o he baseline model where no ransfer policy is involved. On he oher hand, he money ransfer sysem increases he ime share of educaion invesmen only by 3.08% (1.80%, 0.81%), compared o he baseline model. I should be also noiced ha individuals devoe more 23

32 ime ino invesing in his/her human capial as he reimbursemen rae is higher or governmen ransfer more lump-sum money amoun o he individuals Facor prices In he las secion, noice ha when he governmen implemens a ransfer policy regardless of educaional or money ransfer, he individuals are encouraged o allocae more ime ino his/her human capial invesmen. From his resul, i can be assumed ha he relaive scarciy of labor (or relaive abundance of physical capial) during he demographic ransiion would be miigaed due o furher improvemen of produciviy if he governmen implemens ransfer policies. Table 1.7 confirms hese conecures. The educaional ransfer sysem soohes he phenomenon of relaive scarciy of labor (or relaive abundance of physical capial) more effecively han money ransfer sysem does alhough i consumes he same budge volume as he educaional ransfer sysem. Also, he miigaing effec is larger as he governmen ransfers more. During 2010 hrough 2030, when he ageing phenomenon peaks, he rise of he wage rae (decrease of ineres rae) resuling from he scarciy of labor force could be weakened if governmen implemens a ransfer sysem o counerac ageing phenomenon (figure 1.12). However, i should be noed ha in an early sage of he governmen s policy implemenaion, he economy could receive a emporary labor shorage shock since agens begin o allocae more ime ino educaion han before and oal produciviy is no ye high enough o cover his shorage of labor ime. 24

33 The educaional ransfer sysem is more effecive han he money ransfer sysem in miigaing less-saving endency during ageing periods. Furhermore, he aggregae saving rae could be increased more as governmen reimburses more under he educaional ransfer sysem (figure 1.13). On he conrary, here is no noable posiive effec of he money ransfer sysem regardless of is magniude. Again, i should be noed ha aggregae saving rae could be lower han in he baseline case in an early sage of governmen s policy implemenaion because household s saving drops mainly due o decrease of income semming from he shorage of working hours and he immaure saus of human capial sock Welfare The educaional ransfer increases social welfare significanly while money ransfer s effec is rivial regardless of he magniude of ransfer. Educaional ransfers affec social welfare hrough wo channels: educaion and consumpion. Individuals are encouraged o spend more ime in schooling and his increase in educaional invesmen posiively affecs direcly he individual s welfare. Furhermore, rising schooling ime promoes an individual s human capial sock so ha he/she could enoy more consumpion in he fuure. Since human capial sock has o be accumulaed, his posiive effec is acceleraed as ime passes unless governmen changes is policy schemes. Table 1.8 shows ha a persisen educaional ransfer sysem acceleraes growh of social welfare. The educaional ransfer sysem ha reimburses 30% (20%, 10%) of he opporuniy cos of human capial invesmen promoes 2.70% (1.73%, 0.83%) compared o he baseline 25

34 case during 2000 s. During he 2040 s, he educaional ransfer whose reimbursemen rae is 30% (20%, 10%) improves social welfare by 6.29% (3.92%, 1.84%) Economic equiy The simulaion resuls show ha he governmen s ransfer policies do no improve equaliy of income and wealh disribuion. Insead, boh of he educaional ransfer and money ransfer policies worsen equaliy of income disribuion. Also, he educaional ransfer policy even deerioraes he equaliy of wealh disribuion. Noe ha he money ransfer improves he equaliy of wealh disribuion bu he degree of improvemen seems o be very small (figure 1.14). I can be seen ha he Gini coefficien of income rises more as governmen increases is reimbursemen rae and ransfers more money. In he case of he Gini coefficien of wealh, he coefficien becomes higher as he governmen s reimbursemen rae of educaional ransfer sysem increases while he money ransfer lowers he coefficien a lile. These resuls imply ha he governmen ransfer regime does no work so effecively for he agen wih low human capial sock while he policy encourages efficien agens o inves more effecively in his/her human capial sock. 1.5 Conclusions The ageing phenomenon is forecas o peak from 2010 o 2030 in case of Illinois; and i has been shown ha he populaion ageing is expeced o affec Illinois economy negaively. Neverheless, he negaive effecs of an ageing populaion are smaller in he 26

35 endogenous model han he forecass from an exogenous model. This gap may be aribued o he fac ha he exogenous model overlooks he roles of human capial sock. An individual has a moive o inves in his/her human capial wih a sacrifice of curren loss of labor income since individuals expec ha his/her curren invesmen in educaion will pay off more in he fuure han a curren sacrifice. Two kinds of ransfer sysem as governmen policy measures were explored under he same scale of budge: money ransfer and educaional ransfer sysems. The educaional ransfer sysem is superior o money ransfer sysem in he long-run in erms of growh of per-capia income, welfare and sabilizing he facor prices. However, i should be noed ha, in he shor-run, he drawbacks of he educaional ransfer sysem, ha is decrease of labor ime-share, dominaed he posiive effecs of his ransfer sysem (promoion of human capial sock) since i akes ime for human capial sock o be buil up enough o cover he impac of he policy s drawbacks. Also, policy-makers should noe ha here exiss a rade-off in implemening ransfer policies beween economic growh and equaliy of income and wealh disribuion. The analysis has shown ha here is room for governmen o help weaken and preven he negaive effecs of ageing populaion. Thus, governmen should pay careful aenion o is curren fiscal condiion so ha i could play acive role in addressing he challenge of populaion ageing in he near fuure. Also he long-erm cos/benefis and appropriaeness of volumes of direcly redisribuive policies should be sensibly reexamined ahead of he era of populaion ageing. 27

36 Several poins should be menioned for furher sudy regarding he subecs his chaper ried o deal wih. Firs of all, uncerainy facor should be included in he model so ha we could draw more realisic implicaions for governmen s policy. For example, in las secion where here is a ransiion of inequaliy measures, i was assumed ha human capial sock, asse holding, consumpion and ime-shares of labor and schooling are idenical if he agens are in he same age-cohor in he same year. If individual uncerainy facors such as produciviy shock and lay-off risks had been included in he model (hen, we can call his model as heerogeneous sochasic general equilibrium model), he individual s reacion o he policy would have been differen from hose presened. Also, he specificaion of governmen policy could be modified o reflec acual policy scheme 17 so ha i would be possible o derive more applicable resuls. Secondly, anoher simulaion could be implemened o find ou he opimal mixure of educaional ransfer and money ransfer for miigaing he negaive effecs on economic growh 18 and enhancing he equiy of he economy as well. Thirdly, he model should be developed ino one ha incorporaes he changes of migraion paern and he produciviy-heerogeneiy of agens. I was assumed ha he produciviies of agens in he same generaion group are idenical in his chaper. However, in realiy, he produciviy, ha is called human capial sock in his chaper, is exensively differen across races and immigraion saus even hough hey are in he same generaions. Also, when governmen s policy is expeced o increase he economic 17 For example, money ransfer could be given proporionally o agen s (revealed) produciviy and income and ax could be imposed progressively o he agens according o he income level. 18 Of course, he obecive of economic policy should be differen, for example, he obecive of ransfer sysem could be decreasing of deep concenraion of wealh. However, in his paper, we supposed ha he governmen s primary obecive is o boos he economy growh in erms of per-capia oupu. 28

37 growh, he populaion srucure will become differen from ha of baseline proecion we exensively adoped in his sudy since he impac of governmen policy could cause changes of dynamic migraion paern. 29

38 Figures and Tables Figure 1.1: Growh of dependency raio of he U. S reiremen age (20) (65) Figure 1.2: Demographic change of Illinois: change of age-cohor srucure 30

39 age age Figure 1.3: Iniial disribuion of wealh (lef) and human capial sock (righ) oupu under exogenous produciviy model (lef) oupu under endogenous human capial model (lef) endogenous case/exogenous case (righ) Figure 1.4: Per-capia oupu of Illinois in wo differen model specificaions 31

40 ineres rae in he exogenous produciviy model ineres rae in he endogenous human capial model Figure 1.5: Transiion of ineres rae (upper) and wage rae 25% aggregae saving rae in he exogenous model 20% aggregae saving rae in he endogenous model 15% 10% 5% 0% Figure 1.6: Transiion of aggregae saving rae 32

41 2.5 endogenous model exogenous model Figure 1.7: Consumpion level corresponding o aggregae social welfare Baseline: gamma=1.91 Higer EIS: gamma=1.2 Lower EIS: gamma= Figure 1.8: Growh rae of per-capia (lef) and ransiion of average produciviy (human capial sock) of workers under differen EIS (1/ γ ) value assignmen Baseline: B=.28 B=.18 B= Figure 1.9: Growh rae of per-capia oupu under differen parameer values B 33