Pension Systems and their Meaning for Welfare

Transcription

1 Pension Sysems and heir Meaning for Welfare A Comparison of PAYG and FF Pension Sysems Inauguraldisseraion zur Erlangung des akademischen Grades eines Dokors der Wirschafswissenschafen der Universiä Bielefeld vorgeleg von Diplom-Volkswirin Wencke Böhm Bielefeld, Juni 2012

2 Pension Sysems and heir Meaning for Welfare A Comparison of PAYG and FF Pension Sysems Inauguraldisseraion zur Erlangung des akademischen Grades eines Dokors der Wirschafswissenschafen der Universiä Bielefeld vorgeleg von Diplom-Volkswirin Wencke Böhm Bielefeld, Juni Die Arbei wurde auf alerungsbesändigen Papier lau ISO 9706 gedruck.

3 Firs Advisor: Second Advisor: Dean: Prof. Dr. Bernhard Eckwer Prof. Dr. Izhak Zilcha Prof. Dr. Herber Dawid

4 Recenly he news repored ha Germany has he lowes birh raes in he world and he balance beween young and old ciizens will overurn from 2030 on. Therefore, he quesion wheher a pay-as-you-go pension sysem or a fully funded one provides suiable pension benefis for he reirees becomes even more urgen. During my docoral sudies I had he chance o analyze his quesion deeply. I wan o hank my professor Bernhard Eckwer for his rus and his professional commens hroughou my work. Alhough I had already found a opic for my hesis, which is no closely relaed o his own field of research, when I sared o work wih him he gave me he freedom and his uncondiional suppor o pursue my own research. I benefied a lo from his deep knowledge of economic heory and his inuiion for economic mechanism. Furher, my supervisor Prof. Izhak Zilcha was of grea imporance for me. He gave me he possibiliy of a research visi o Tel Aviv and suppored my work srongly wih fruiful discussions. Many ideas for my work were developed during debaes wih him and via paper recommendaions. Also, I wan o hank Prof. Böhm for giving me he chance o sar my academical career. My colleagues Andreas Szczukowski, Nikolai Brand, Beina Fincke and many more have been of grea value for me and for my research. During numerous discussion sessions hey helped me o find my way and always provided an open ear. Las bu no leas I wan o hank my family and friends for heir uncondiional love and suppor. Bielefeld, Ocober 2012 I

5 Conens 1 Inroducion 1 2 Growh and Welfare Inroducion The basic model Individual decisions Decisions under PAYG Decisions under Fully Funded Deerminaion of τ - social planner Comparison of he capial in efficiency unis Welfare Comparison Impac of human capial on welfare Concluding remarks Appendix Endogenous Feriliy and Welfare Inroducion Model Decisions under PAYG Decisions under FF Analysis of birh raes Welfare Comparison Transfer Paymens Decisions under PAYG II

6 CONTENTS Decision under FF Comparison of birh raes Welfare comparison wih/wihou ransfer paymens Conclusion Influence on Educaion Decisions Inroducion The benchmark model Decisions under PAYG Decision under FF Comparison of Welfare under PAYG and FF Dynasies of heerogenous agens Inequaliy and Growh Welfare Comparison Conclusion Conclusion 86 III

7 Chaper 1 Inroducion Hisory of he Pension Sysem in Germany Unil Oo von Bismarck inroduced a law concerning he old-age reiremen coverage in Germany in 1889 people were working unil heir deah or hey were suppored by heir children. Some years earlier he governmen inroduced an acciden and a disabiliy insurance. During his process i became aware ha old people should be prevened from life-long work and povery as well. The implemenaion of an old-age pension sysem wen hand in hand wih enormous discussions. Finally, parlamenarians agreed on a pension sysem which pension paymens were relaed o he agens conribuions. Pension benefis were no organized in a fla way as he aim was no o augmen care agains povery 1. Deerminaion of he individual pension paymens were no made according o he individual average wage income. For simpliciy reasons workers were divided ino four income groups insead. Workers received an enilemen o pension paymens a he age of 70 years (in 1916 his age was reduced o 65 years). In he period 1881/90 life expecancy a birh for men was and for women years 2. This makes clear ha he number of agens reaching he necessary age for reiremen benefis was very low. Workers and employers paid he same amoun as conribuions and he governmen graned a so-called Reichszuschuss (governmenal allowance). Alhough Bismarck claimed ha he sae and is insiuion would live forever and, herefore, pensions would be 1 For furher informaion see U. Haerendel (2000). 2 Daa aken from G. Wiesner (2001). 1

8 1. Inroducion safe, he pension sysem was organized in a fully funded way since a pay-as-you-go sysem was acceped as unreliable 3. During he firs world war he capial sock of he pension sysem was used for financing miliary aciviies. The hyper-inflaion aferwards worsened he problem of missing financial ressources of he sysem. To fulfill he public pension obligaions he governmen swiched o a PAYG sysem. Alhough he public saw hose risks of a fully funded sysem, he common opinion sill believed in he reliabiliy of his scheme 4. Fosered by he srong economic growh in he 1920 s, Germany reurned o a funded pension sysem. Under he regime of Hiler hey changed some componens of he social policy. A governmenal allowance o pension benefis was no longer given on an individual level bu for he general public. The amoun of allowance increased significanly. Furher, a guaranee for pension benefis was no longer given by he federal saes bu by he counry (Reichsgaranie). A his ime, one aim was ha pension benefis should no deviae o much from he wage income. In conras o he habi during he Firs World War, during he Second World War i was communicaed ha resources of he pension sysem were used o finance he acs of war. Hence, he sysem de faco used curren conribuions o fulfill is obligaions agains old-age pensioners, alhough a PAYG sysem was no officially implemened ye. In 1957 a grea pension reform ook place. The governmen inroduced a modified pay-as-you-go sysem 5. This means ha conribuion raes were defined, consan for a en years coverage period, in such a way ha a he end of he period a capial sock exised which was as high as he aggregae pension obligaions for one year. A ha ime pension paymens were no an allowance o old-age welfare insead hey should more or less subsiue wage income. This led o an increase of he conribuion rae from 11% o 14% in 1957 and was furher increased for he second coverage period o 16.25% and for he hird o 18.25%. A he ime 3 Under a pay-as-you-go (PAYG) sysem pension benefis are payed by curren conribuions, hence symbolyzes a pure reallocaion of wage income from he working generaion o he reired generaion. Under a fully funded (FF) sysem agens receive he reurns on heir conribuions as pension benefis. 4 For furher informaion see P. Manow (2000). 5 For furher informaion see W. Schmähl (2007). 2

9 1. Inroducion of he pension reform, he governmen assumed a consan life-expecancy of he agens, which had already been discussed criically by Georg Heubeck (1956) in his survey. Through his reform, pension benefis go a dynamical componen. Benefis were no longer deermined a a fixed poin of ime insead hey were deermined coninuously over he conribuion period so ha he developmen of wage income over he work-life was respeced. Over he following years muiple changes of he pension law occured and in 1989/92 and 2001 small reforms of he pension sysem ook place 6. This has led o oday s effecive pension law and he srucure of he pension sysem. Pension benefis are sill payed according o he own conribuions and o he relaive posiion of he own wage income compared o he average wage income. Furher, he pension benefis are relaed o he wage developmen of he conribuors, so ha pensioners benefi from he economic developmen. In 2009 he governmen decided ha pension benefis are bounded from below, meaning ha hey can only increase or remain consan bu never decrease in case of a negaive wage developmen. For susainabiliy reasons a so-called susainabiliy facor was inroduced in 2002, which relaes he number of conribuors o he number of pensioners. Owing he demographic change he age a enry was increased from 65 o 67 (adjusable over he nex 20 years), he conribuion rae raised o 19.9% and due o he decreasing pension level he governmen decided o boos occupaional and privae pension insurances. While he occupaional pension scheme is boosed only by axaional savings, he privae pension scheme, in form of a Rieser-Rene, is promoed wice. The governmen gives allowances (if agens save he minimum amoun 4% of he gross wage income) and ax benefis o he privae scheme. Boh addiional precauion insrumens are no mandaory and while a high number of agens save in form of a Rieser-Rene, he occupaional scheme is no widely spread. 6 For furher informaions see F. Ruland (2007). 3

10 1. Inroducion Overview of differen European Pension Sysems In differen European counries old-age reiremen welfare is arranged in various ways. A pure fully funded or a pure pay-as-you-go pension sysem is implemened in none of he European counries. In general, he accommodaion in reiremen is based on more han one pillar. Three pillars of old-age provisions are well-known: a) he public pension sysem b) an occupaional pension scheme and c) a privaely organized old-age provision. The firs pillar is ypically organized in form of a PAYG sysem whereas he laer wo are funded sysems. Counries are divided in wo ypes: a liberal and a conservaive welfare sae 7. Counries belonging o he firs ype are for example Grea Briain, Ireland, he USA and o some exend he Neherlands. Germany, France and Ausria are examples for a conservaive welfare sae. Such saes wan o ensure he living sandard of heir ciizens whereas a liberal welfare sae is anxious o preven is ciizens from old-age povery by graning a minimum level of pension paymens. In his conex wo ypes of paymen schemes are o be menioned: Bismarck and Beveridge. A Beveridge scheme disburses a fla pension paymen o every agen wih no regard o his own conribuions. This is conrary o a Bismarck scheme where agens receive pension paymens according o heir own conribuions. This scheme is based on he social insurance law inroduced by Oo von Bismarck, which we menioned above. The Beveridge scheme relies on he Briish naional insurance, which was designed mainly by Lord William v. Beveridge. While Bismarck already inroduced a social securiy sysem in 1881, Beveridge s ideas from 1942 led o he Briish social legislaion in In liberal welfare saes each agen is graned a minimum pension paymen, which is no sufficien o ensure one s living sandard. Hence, he governmen of hese counries expec heir ciizens and companies o ake measures for an appropriae welfare in reiremen. This precauion can be carried ou eiher in he second or he hird pillar. Conservaive welfare saes insead inend o guaranee heir ciizens an appropriae living sandard already by he firs pillar, i.e. public pension sysem. Due o demographic changes i has become harder o fulfill his aim by focussing on he firs pillar only. Therefore, conservaive welfare saes need o enlarge heir effor 7 Facs provided in his paragraph are aken from H. Söger (2011). 4

11 1. Inroducion owards he second and hird pillar. In he end, his means ha agens ake more responsibiliy for heir welfare in he reiremen period. Ofen counries gran ax reliefs or fringe benefis o give incenives for an appropriae prevenion. The firs pillar is ofen encouraged by governmenal grans o indemnify pension paymens. The OECD values his pracice as criical since i slows down he economic growh and conradics he principle of fairness regarding fuure generaions. Nex, we wan o give a small overview how pension sysems are srucured in differen counries. Grea Briain inroduced he so-called Basic Sae Pension (BSP) in 1946, which supplies a fla pension benefi o all agens who conribued o he sysem for a leas he minimal required ime span. All employees are covered by his BSP. The pension benefis are low and do no achieve he level of he Briish social welfare benefis. In he 1970 s Briain inroduced a mandaory public addiional sysem (SERPS) wih he aim o ensure he living sandard of agens while reired. This sysem was replaced by he Sae Second Pension (S2P). Iniially, a conribuion-relaed pension sysem, he S2P was resrucured in 2007 now following he concep of Beveridge, hence disburses fla pension paymens. The Briish governmen subsidizes he second pillar and allows o compensae he S2P sysem by an occupaional pension scheme. This scheme is no mandaory for companies and only 54% of all employees are covered by such a sysem. The hird pillar is he privae pension insurance fund. Furher, a so-called Sakeholder Pension (STP) exiss. This sysem was inroduced o cover agens who do no have an occupaional or a privae pension scheme and earn beween 9000 and GBP per year. Alogeher he Briish pension sysem is hardly able o guaranee is ciizens heir living sandard. The Neherlands implemened a pension sysem based on he hree pillars as well. In 1956 hey inroduced a conribuion-financed public pension sysem, he so-called Allgemene Ouderdomswe (AOW). The conribuion rae was increased from 6.7% in 1957 o 18% in Facing he problems of increased coss and a decreased raio of conribuors o beneficiaries, he Duch govermen esablished a fund in he lae 1990 s, financed by ax money, wih he aim o guaranee susainabiliy of he pension sysem. This sysem should no ensure living sandards bu preven agens 5

12 1. Inroducion from old-age povery. Pension paymens are no graned according o conribuions insead according o he imespan an agen has lived in he Neherlands. To achieve he highes possible pension paymen, a ciizen mus live for a leas 50 years in he Neherlands. This paymen is 70% of he ne wage floor for singles and 50% for couples. The second pillar consiss of secoral agreemens and is par of he labor pac. Hence, i is mandaory for companies o conribue o an occupaional pension scheme. As a resul 94% of he employees are covered by such a sysem. The 6% non-covered employees work for companies which are no liable o secoral agreemens. One disincive feaure of he Duch second pillar is ha conribuions are payed alhough here migh be breaks in he occupaion. The hird pillar, privae pension insurance, plays a minor role bu is a complemenary sysem for high-wage earner and is promoed by axaional governmenal grans. The aim of he French pension syem is o ensure he living sandard of he ciizens. I is divided ino wo pars: he public pension sysem regime de base which provides 50% of he average income and an addiional mandaory occupaional pension scheme. In 2003 he governmen raised he minimal conribuion ime from 37.5 o 41 years and in 2010 o 41.5 years. Afer he long conribuion period agens receive 50% of heir average wage income. The governmen uses he bes 25 years o deermine he average income. In France, families wih more han hree children benefi from an income-relaed pension increase. Hence, large families are financially promoed. Maerniy leaves are added o he conribuion period up o wo years per child. Agens whose income is very low or conribue only for a shor period o he pension sysem are graned wih a minimal paymen, he so-called minimum vieillesse. These benefis are much lower han he minimal wage income. Agens are differeniaed in he public as well as in he occupaional pension scheme by heir professional caegory. A big difference o Grea Briain or he Neherlands is ha benefis ou of he occupaional pension sysem are no funded bu insead based on a pay-as-you-go sysem. Their benefis are conribuion relaed according o a Bismarck scheme. Privae pension insurance is more or less crowded ou as agens already receive a high percenage of heir ne wage income by combining firs and second pillar. 6

13 1. Inroducion Recen Developmens Nowadays he level of pension benefis approximaely lies a 70% of he las ne wage income and he conribuion rae a 19.9% in Germany. Forecass say ha he level of pension benefis will decrease while he conribuion rae will increase up o 22% in 2030 (according o he Alergrenzenanpassungsgesez) 8. There are several reasons for his developmen. Demographic change is one. In many indusrialized wesern counries he populaion grows old. Real world daa demonsraes a median age of he populaion in several European counries and Japan above 40 years. In Germany he median age is , in Ialy i is 43.5 years. For a comparison, he populaion of India has a median age of The share of old agens (65 years and older) in he enire populaion will increase over ime in many European counries. In 1995 he share of old agens wihin he populaion was for example in Germany 15.4%, in he Neherlands 13,2% and in France 15.0%. The forecas for 2050 predics he share o be: in Germany 27.7%, in he Neherlands 24.4% and in France 26.8% 10. A ime series visualizes he developmen of he shares of agens under 20 years and he shares of agens above 65 years in he enire populaion of Germany in a ime period from 1890 o From his i becomes clear ha he share of he young populaion is decreasing (from 44.9% in 1890 o 21.2% in 2000) and he share of he old populaion is increasing (from 5.1% in 1890 o 16.2% in 2000). The share of he working generaion (age 20 o 65) increased from 50% in 1990 o 62.6% in 2000 and is supposed o sabilize around 60% in he fuure 11. In agens of he working populaion faced 9 reirees while forcecass guess ha in working agens will face 56 reirees, which is a dramaic change. The number of reirees increased from 1960 o 2005 from 7.8 o 19.4 million in he old Wes German saes and if we include he newly-formed Eas German saes o 24.5 million. The lengh of he reiremen period increased from 9.9 years up o Informaion is aken from Ruland (2007). 9 All daa is aken from he World Facbook 2011 by CIA, USA and demonsraes esimaed values for Compare G. Wiesner (2001). 11 Daa aken from he Saisisches Bundesam in G. Wiesner (2001). 7

14 1. Inroducion years. All hese numbers visualize ha fuure solvency of he implemened public pension sysem in Germany is dispuable. I is no clear wheher a PAYG sysem will be able o suppor reirees wih suiable pension benefis. Therefore, i is ofen discussed o swich o a fully funded pension sysem. Such a sysem is independen of he demographic developmen, of he unemploymen rae and of he economic progress. Also i is ofen claimed ha an FF sysem earns higher reurns for is reirees han a PAYG sysem. If an FF sysem is implemened, agens have o ake more responsibiliy o ensure hemselves a sufficien old-age wealh. Many papers claim ha an FF sysem leads o higher economic growh due o higher capial accumulaion bu ofen neglec he effecs on he wage rae and he ineres rae. Neverheless, hese wo values have a big impac on he welfare of agens. Before a swich of he sysems is implemened i should be clearified wheher a PAYG or an FF sysem leads o higher welfare. This work ries o shed ligh on he comparison of hese wo differen pension sysems in heir pure form (no ax benefis or any allowances). The effecs of differen pension sysems on he economy are manifold. Pension sysems do no only influence economic growh hrough higher or lower physical capial accumulaion bu have an impac on agens decisions for children and on invesmens in educaion of children. This again are facors which favor economic growh. Hence, an analysis which compares pension sysems bu disregards he impac on individual decisions besides savings neglecs an imporan aspec. The relaion beween economic growh and individual welfare (measured in individual life-ime uiliy) is ambiguous. In some economic siuaions i may be possible o draw conclusions direcly from his sylized fac bu his is no necessarily he case. Also, i migh be ha one pension sysem leads o higher inequaliy (regarding human capial, i.e. wage income) wihin he economy. Beside he poliical implicaion (insabiliy of poliical formaions, rios, ec.) i is no clear wheher his prohibis higher welfare. Alhough he inequaliy is higher under one sysem, i migh be ha he agen s welfare is superior if each agen earns higher wage income under his sysem. 8

15 1. Inroducion The main quesions, which we ry o answer in his work, are: Does higher economic growh go hand in hand wih higher individual welfare? Do differen pension sysems have diverse impac on he feriliy rae? Is he decision on invesmens in educaion of children influenced by differen pension sysems in various ways? Can he feriliy of agens be increased by ransfer paymens? And does his lead o higher economic growh? Which sysem leads o higher inequaliy? Is his necessarily welfare lowering? While he second chaper mainly addresses he firs quesion, chapers 3 and 4 consider various addiional quesions. Chaper 2 uses a closed economy and elaboraes he crucial relaion beween he sae of developmen of (various) economies, growh and welfare. I incorporaes effecs of physical capial accumulaion on he rae of reurn which may reduce welfare. The las wo chapers employ a small open economy o focus on addiional quesions like feriliy (chaper 3) and educaion (chaper 4) wihou he effecs on wage and ineres raes. In all hree following chapers we use an OLG-Model. This allows us o analyze ineremporal effecs and dynamic processes over ime. We consider closed as well as small open economies. Alhough he small open economy assumpion is a sric simplificaion, i offers he possibiliy of clear saemens on he regarded effecs of he pension sysems. All agens face a cerain non sochasic lifespan, i.e. we absrac from he risks of an early demise. Model Overview In he second chaper we analyze economic growh and individual welfare (measured as life-ime uiliy) and show ha higher economic growh does no necessarily lead o higher individual welfare. Using he srucure of a wo-period OLG-Model we 9

16 1. Inroducion presen a general equilibrium model of a closed economy populaed by homogenous agens. Decisions on educaion and he number of children are negleced. To accomodae he demographic change, observable in many developed economies, we implemen a sochasic process for he developmen of he populaion size. In our model he populaion is shrinking over ime. Alhough agens do no make decisions regarding heir schooling, we implemen an exogenously given human capial formaion process in which human capial is growing by a consan facor over ime. Our model coincides wih he common resul ha FF leads o higher physical capial accumulaion and, herefore, o higher economic growh. Tesing wheher higher economic growh goes hand in hand wih higher welfare, we find ha here is no necessarily a posiive link. We show ha differen economies, endowed wih differen capial inensiy facors, do no all benefi (in erms of welfare) from he same pension sysem. This means ha he pension sysem, which leads in a highly developed economy o higher welfare, may resul in lower welfare in a non-developed economy. A saemen on higher welfare under one pension sysem can, herefore, no be given wihou knowing he capial inensiy facor of he economy. The model considered here concenraes on a comparison of pension sysems implemened in wo idenical economies a he same ime. Therefore, we neglec he ransiion from one sysem o he oher. The hird chaper considers he impac of pension sysems and paymen schemes on he welfare of heerogenous agens, measured in erms of individual life-ime uiliy. One resul is ha PAYG as well as FF can be he pension sysem ha ensures he higher possible welfare depending on economic parameers. The wo major pension sysems are considered, each in combinaion wih wo differen paymen schemes: Beveridge (fla) and Bismarck (conribuion relaed). Heerogeneiy of agens is one addiional aspec which disinguishes our work from many oher papers which ofen assume homogeneiy of agens. For simpliciy, we inroduce wo differen ypes of agens: low-skilled (low individual human capial) and high-skilled (high individual human capial). The agens differ according o heir human capial endowmen, bu are equipped wih he same preferences. Depending on heir individual ypes agens prefer differen paymen schemes regarding heir individual welfare. Their 10

17 1. Inroducion birh raes also differ under differen schemes. High-skilled agens will have a mos he same number of children as he low-skilled agens under all four possible combinaions of pension sysems and paymen schemes. Excluding a learning process, his leads o a decrease of average human capial over ime. As his resuls in a lowering of oupu per capia, which is ofen used as a measuremen of welfare, we ask wheher incenives can be inroduced o raise feriliy of high-skilled agens. By inroducing ransfer paymens i is possible o raise feriliy and hrough his o increase average human capial. As hese incenives work in he inended direcion we furher analyze wheher addiional advanages like an increase of individuals welfare go hand in hand. The fourh chaper presens an equilibrium model of a small open economy wih iner-generaional alruism. In a benchmark model we analyze how differen pension sysems influence he human capial formaion of agens. Agens decide wheher and how much (we exclude credi consrains) o inves in he educaion process of heir children. The aim is o show ha agens behave differenly (concerning educaion expendiures) under he wo differen pension sysems. Furher, a PAYG pension sysem leads o higher human capial formaion and higher economic oupu han an FF sysem under cerain condiions. We ry o figure ou wheher his is valid in general or wheher cerain condiions exis under which a PAYG sysem leads o higher economic growh. As his model uses a small open economy wih mobile physical capial and immobile human capial, he only source for economic growh is aggregae human capial. We inroduce wo differen families of agens who are homogenous wihin he family bu heerogenous concerning heir human capial endowmen beween he families. Regarding heir preferences and heir abiliy parameer he agens of he wo families do no differ. The influence of he pension sysems is differen on he wo families. I is shown ha he family which is iniially wealhier (higher human capial leads o higher wage income) will remain he wealhier family over ime. We analyze under which pension sysem he inequaliy concerning he allocaion of human capial wihin a generaion is larger and wheher higher economic oupu goes hand in hand wih higher inequaliy or no. The model shows ha under cerain condiions a posiive link beween inequaliy and economic 11

18 1. Inroducion oupu exiss. In conras, Galor and Zeira (1993) show ha higher inequaliy goes hand in hand wih lower economic oupu. The main difference o our work is he exisence of imperfec credi markes and he exisence of wo differen producion funcions which eiher employ unskilled or skilled labor. Our work does no compare he economy under he wo differen pension sysems in a seady sae analysis bu poinwise in each period. Small Lieraure Overview In a closed economy wihou pension sysems Fani and Gori (2007) and (2010) analyze he effecs of child allowance on endogenous feriliy. They claim in boh papers ha child benefis have an ambiguous effec on he feriliy rae since opposing effecs exis. They figure ou a direc posiive effec due o reduced coss of child-rearing bu as well a negaive effec due o he reduced wage rae. In heir paper from 2010 hey add schooling expendiures which are financed by all agens in he economy. While child grans are consan over ime, expendiures on schooling may vary over ime. One resul is ha an increase of schooling expendiures leads o higher feriliy and o higher economic growh. Alhough we use a small open economy, we see he posiive effec of increased human capial on economic growh and as well welfare in chaper 3 and 4. In he paper by Fenge and Weizsäcker (2009) agens divide heir ime o work and o have children, assuming ha each child reduces he labor ime by a cerain fracion. Implemening a PAYG pension sysem, he coss of having children remain privae while he benefis become public. They inroduce a wofold pension sysem consising of a Bismarck pension benefis are payed proporionally o conribuions and a child pension benefis according o he number of own children. While a Bismarck pension helps o minimize he labor-leisure (child ime) disorion of he PAYG sysem, a child pension minimizes he feriliy disorion. They figure ou ha child pensions and child benefis (in our work: ransfer paymens) are perfec subsiues. Wigger (1999) assumes inergeneraional care, meaning ha old reired agens re- 12

19 1. Inroducion ceive pension paymens and presens from heir children. Hence, having children is kind of an insurance of fuure wealh. Presens depend negaively on he conribuion raes as higher conribuions imply higher pension benefis. One of his resuls is ha higher conribuion raes lead o lower feriliy raes since agens know ha children make less presens and, herefore, lose heir significance as an insurance of old-age wealh. Soares (2006) as well as Lambrech e al (2005) explore implicaions of a learning process on economic growh under PAYG pension sysems. Due o alruism as well as egoism (higher pensions) parens finance he learning process of heir children and, herefore, improve heir human capial which leads o higher economic growh and o higher pension paymens. Kaganovich and Zilcha (2012) presen a general equilibrium model in which hey implemen a human capial formaion rule. Public educaion expendiures are deermined by a majoriarian voe. They show ha an FF pension leads o higher ax raes for educaion expendiures han a PAYG sysem and hrough his o higher human and physical capial accumulaion and o higher economic growh. Kaganovich and Meier (forhcoming) show ha he opposie is rue in a small open economy. The fourh chaper of his work is similar o hose wo papers. While using a small open economy we draw our aenion o privae invesmens in schooling of children insead of publicly deermined educaion expendiures. Our model uses privae schooling as an addiional opional par in he human capial formaion. I shows ha parens inves in educaion if heir preferences for childrens human capial are srong enough, i.e. if he inergeneraional alruism is srong enough. Glomm and Kaganovich (2008) implemen a model of heerogenous agens in which he governmen funds wo programs: public educaion and social securiy. Agens conribue a proporional ax o boh programs while he benefis which hey receive are fla. Parenal ime and public schooling expendiures are complemenary goods in he human capial formaion. They show ha an increase of he social securiy ax rae has a reducing effec on he income inequaliy and on he same ime a posiive effec on he economic growh. A comparison of he effecs under FF and PAYG pension sysems is negleced. Differences o our resuls in chaper 4 can be explained by differen human capial formaions and he assumpion of a 13

20 1. Inroducion closed economy. Galor and Zeira (1993) analyze he relaion beween inequaliy and growh as well bu wihou he exisence of any pension sysem. One resul of heir work is ha higher inequaliy goes hand in hand wih lower economic oupu. The main difference o our resuls in chaper 4 arises hrough he exisence of imperfec credi markes and he exisence of wo differen producion funcions which eiher employ unskilled or skilled labor. Why is a Swich of Pension Sysems so difficul? The difficuly of a ransiion from a PAYG pension sysem o an FF one lies in he fac ha agens who have already conribued during heir whole work-life o he PAYG pension sysem will no receive any pension paymens ou of he new implemened FF sysem. The swich of he pension sysems is a clear cu. So far, reirees received pension paymens ou of he conribuions from working agens. Afer he ransiion heir pension paymens will be he reurn on heir own conribuions. Therefore, agens, who conribued only o he PAYG sysem, do no receive anyhing ou of he FF sysem. Of course, i is a huge social problem how o compensae he generaions who conribued (parly) o he PAYG sysem and face no (or low) public pension paymens afer he swich. A compensaion mus assure ha hese generaions are no worse off afer he ransiion. As a PAYG sysem is jus a pure reallocaion of wage-income from he working populaion o he reired populaion, here are no financial reserves, which could be used for compensaing he ransiion generaion. A swich from one sysem o he oher always includes a srucural break and i is no reasonable ha his can be done wihou lowering he welfare of a leas some generaions. There are wo possible szenarios for financing a compensaion of he ransiion generaion supposably. The firs would be o ax agens by a higher rae unil he ransiion period. The governmen would save/inves hese ax revenue and would finance he compensaion paymens ou of he reurns in he crucial period. This would lead o a lowering of he welfare of all agens who would face he higher ax burden. The advanage of his szenario is ha afer he ransiion no addiional paymens are necessary 14

21 1. Inroducion and only a pure FF pension sysem exiss. The second possibiliy would be ha he governmen pays he compensaion paymens financed by a deb and increases he ax rae afer he ransiion for some generaions. The compensaion paymens would have o be high enough so ha he ransiion generaion would receive he same welfare as if a PAYG pension sysem would sill be implemened. The ax rae would have o be adjused in such a way ha he generaions facing he higher ax burden would no be worse off compared o he case of a PAYG sysem. This could be achieved if an FF pension sysem led o higher welfare in general. Then i is possible o compensae he ransiion generaion wihou seing any generaion worse off in erms of life-ime uiliy. In 2000/2001 he German governmen inroduced he so-called Rieser-Rene. This is a privaely financed pension sysem wih he srucure of an FF sysem. Under cerain condiions (minimal conribuions 4% of he ne wage income) he governmen advances conribuions o his privae pension sysem by graning fringe benefis and ax reliefs. The German governmen inroduced his kind of privae pension sysem because he ne-pension-sandard was reduced from 70% o 67% during he pension-reform. Since 2005 he German govermen has advanced he Rürup-Rene by graning ax benefis as well. 15

22 Chaper 2 Pension Sysems and heir Meaning for Welfare Absrac: The implemenaion of a fully funded (FF) pension sysem in an economy leads o higher economic growh han he implemenaion of a pay-as-you-go (PAYG) sysem. Bu i is no clear how pension sysems influence he uiliy of he populaion hrough heir effec on wage-raes and raes of reurn on capial. This chaper shows ha PAYG leads o higher welfare under specific condiions. Economies, which vary in heir capial inensiy facors, generae higher welfare of heir agens under differen pension sysems. Using a closed economy wih sochasic populaion growh we presen a general equilibrium model and analyze he relaion beween economic growh and individual agens welfare. 16

23 2. Growh and Welfare 2.1 Inroducion As he populaion of mos indusrialized counries becomes older and older over ime, he quesion of how o ensure heir old-age wealh becomes more imporan. In hese counries we observe a demographic change and he old generaion will become he dominan fracion of he populaion. Real world daa demonsraes a median age of he populaion in several European counries and in Japan above 40 years of age. In Germany he median age is , in Ialy i is 43.5 years for insance. For a comparison, he populaion of India has a median age of The World Facbook 2011 provides ime series which indicae ha he populaion in many counries grows old. This may be due o beer healh care, healhier ways of life, less hard work and many more. In mos European counries, excep he Neherlands, he old-age securiy sysem is organized in he form of a pay-as-you-go (PAYG) pension sysem. In his case, he young working par of he populaion pays for he pension paymens of he old and reired par of he populaion. Hence a PAYG sysem is a pure reallocaion of income from young working agens o old reired agens. As he fracion of young working individuals is shrinking, hey have o conribue indivually more from heir wage income or he reirees will receive a lower pension paymen by consan conribuion raes. Due o he demographic change, doubs arise wheher a PAYG pension sysem will remain susainable. Ofen discussed is a ransiion from PAYG o a fully funded (FF) pension sysem o solve he problem of less conribuors and more beneficiaries. The PAYG sysem is no suied o provide an adequae level of reiremen paymen a accepable coss for he conribuors. Some observers hink ha he exising pension sysem has o be changed in a drasic way as hey see i already on he verge o collapse Börsch- Supan (1998). The healh of he pension sysem is of major ineres, as Diamond, Orzag (2005) exposed for he USA ha for wo-hirds of he elderly beneficiaries he pension paymen is he majoriy of income and for 20 percen of he beneficiaries i is heir only income. 1 All daa is aken from he World Facbook 2011 by CIA, USA and demonsraes esimaed values for

24 2. Growh and Welfare Before aking he difficul ask of a ransiion from a PAYG pension sysem o an FF one, i should be clear wheher an FF sysem is he favorable opion. One aspec is economic growh under boh pension sysems, which is considered by many papers in he exising lieraure. A differen aspec is individual welfare. In his paper we analyze boh and show ha higher economic growh does no necessarily lead o higher individual welfare, which is scaled as life-ime uiliy. Using he srucure of a wo-period OLG-Model we presen a general equilibrium model in which we use a closed economy populaed by homogeneous agens. Decisions on educaion and he number of children are negleced. To accomodae he demographic change we implemen a sochasic process for he developmen of he populaion size. In our model he populaion is shrinking over ime. Alhough agens do no make decisions regarding heir schooling, we implemen an exogenously given human capial formaion process in which human capial is growing by a consan facor over ime. Our model coincides wih he common resul ha FF leads o higher physical capial accumulaion and, herefore, o higher economic growh. Analyzing wheher higher economic growh goes hand in hand wih higher welfare shows no necessarily a posiive correlaion. Differen economies, endowed wih differen capial inensiy facors, do no all benefi (in erms of welfare) from he same pension sysem. This means, ha he pension sysem which leads in a highly developed economy o higher welfare, may resul in lower welfare in a non-developed economy. A saemen on he dominance of one pension sysem can, herefore, no be given wihou knowing he capial inensiy facor of he economy. Our consideraions focus on a comparison of pension sysems implemened in wo idenical economies a he same ime. Therefore, we neglec he ransiion from one sysem o he oher. 2.2 The basic model We consider an overlapping generaions economy in which perfecly compeiive firms produce a homogeneous good, which can be used for consumpion and for invesmen. They use physical and human capial as inpus in a consan reurns neoclassical producion echnology F (K, H). As we assume a closed economy, physical and human capial are immobile and remain wihin he economy. The popula- 18

25 2. Growh and Welfare ion lives for exacly wo periods adulhood and reiremen and each generaion consiss of a number of homogeneous agens, who are all endowed wih a cerain amoun of human capial. As we wan o sudy he effecs of demographic change and human capial, he size of each generaion does no remain consan over ime, hence we assume populaion growh. The producion echnology can be described by a classical Cobb-Douglas producion funcion: Y = F (K, H ) = A K δ H 1 δ = A K δ (N h ) 1 δ (2.2.1) wih A > 0, 0 < δ < 1. Y describes oal oupu in period, K is he aggregae sock of physical capial financed by he savings of he previous generaion (depending on he ype of pension sysem). H denoes he aggregae sock of human capial. All agens supply inelasically one uni of labor in heir firs period of life. The aggregae sock of human capial H = N h used for producion is given by he number of young/adul agens (N ) imes heir individual endowmen of human capial (h ). The aggregae sock of physical capial is deermined in differen ways under he wo ypes of pension sysems. Capial is assumed o depreciae compleely from one period o he nex. Hence aggregae capial never conains old capial. In case of a PAYG pension sysem he aggregae capial in + 1 consiss of he aggregae savings s of he young agens in period. Therefore, K G +1 = N s G. (2.2.2) Variables belonging o he PAYG sysem are indexed by G, variables belonging o he fully funded sysem by F. The characerisic of a fully funded pension sysem is ha he conribuions are invesed/saved in he producion process and are no only reallocaed from young o old agens like under a PAYG sysem. Hence, aggregae capial consiss of privae savings and public savings (from he pension sysem): K F +1 = N s F + N τ w F h, (2.2.3) where τ denoes he conribuion rae. Since he FF pension sysem is assumed o wihold no par of he conribuions o cover any coss or o gain proceeds, aggregae 19

26 2. Growh and Welfare conribuions are complely invesed. Facor markes are compeiive so ha prices of physical and human capial are given by heir marginal producs: where k = K N h w = F (K, H ) H R +1 = F (K +1, H +1 ) K +1 = (1 δ) A K δ H δ = (1 δ) A k δ (2.2.4) = δ A K δ 1 +1 H 1 δ +1 = δ A k δ 1 +1 (2.2.5) denoes capial in efficiency unis. The homogeneous agens live exacly for wo periods, i.e. here is no risk of an early demise. In heir firs period of life, i.e. adulhood, hey inelasically supply one uni of labor. In he second period hey are reired and do no work, herefore, gain no wage income. Each member of a generaion, adul in period, is endowed wih idenical individual human capial denoed by h. We assume ha he individual human capial grows by an exogenously given facor from one generaion o he nex. The human capial formaion is described by: h +1 = β h (2.2.6) where β > 1 denoes he exogenously given growh facor of human capial. direcly follows ha a generaion + 1 is more skilled han is preceding generaion. Hence, he qualiy of labor, offered by he young agens, is higher han he one of heir ancesors. If he populaion size would remain consan over ime, i would resul in a coninuosly growing aggregae sock of human capial. As he populaion does no remain consan over ime bu insead decreases, i is no clear wheher he aggregae sock of human capial is increasing, decreasing or remains consan over ime. The populaion is growing wih a sochasic growh facor, denoed by n +1. The size of he populaion is given by: N +1 = (1 + n +1 ) N. (2.2.7) n +1 is i.i.d. and uniformly disribued over an inervall [a, b] for all, wih a < b. If we wan o simulae a decreasing populaion (demographic change in he wesern indusry economies), a leas he parameer a has o be negaive and is absolue value has o be greaer han ha of b. The size of he fuure generaion N +1 is no known by he generaion in period. I 20

27 2. Growh and Welfare 2.3 Individual decisions In his secion our focus lies on he single agen and his decisions regarding savings and consumpion. Since he lives for exacly wo periods bu receives wage income (which can be consumed or invesed) only in he firs period, he has o ensure consumpion in boh periods via savings and/or pension paymens. As his wage income is non-sorable (for laer consumpion), he invess par of i in he producion process. In he second period of his life he receives reurns on his invesmen and pension paymens, which he consumes complely as we do no assume any beques moives Decisions under PAYG The PAYG pension sysem is he predominan sysem in mos indusrialized counries. I is characerized by a reallocaion of wage income. Young working agens are forced by he governmen o conribue a fixed par of heir wage income (conribuions) o he pension sysem. The PAYG sysem akes hese conribuions bu does no inves hem in he producion process. Insead i gives i direcly o he living old-age reirees (beneficiaries). The agens receive uiliy ou of consumpion in boh periods. As hey have o make heir decision regarding oday s and omorrow s consumpion (e.g. savings) a he beginning of heir firs period, we describe heir expeced uiliy by he following equaion: [ E U G (c,, c +1, ) ] = ln c G, + E [ln c G +1,] (2.3.1) where c, denoes consumpion in period of an agen born/adul in and c +1, is his consumpion in + 1. As consumpion in adulhood depends on common variables only, i is no necessary o regard he expeced value of oday s consumpion. The resuling uiliy ou of fuure consumpion is uncerain in period because of he uncerain developmen of he populaion. All variables of period + 1 are random a he poin of ime. The young working agens allocae heir afer-ax (afer conribuion) wage income W 1 beween curren consumpion and privae savings. 21

28 2. Growh and Welfare Hence hey face he following budge consrain in heir firs period: c G, = W G 1 s G (2.3.2) = (1 τ) w G h s G where w is he curren compeiive wage rae per uni of effecive labor. Effecive labor means labor muliplied by he individual human capial which symbolizes how producive one uni of labor is. τ is he uniform and fla conribuion rae, which agens ake as given. Their decision regarding privae savings is no limied o posiive values. Tha means, hey are allowed o borrow agains heir fuure wealh. The ineres rae is assumed o be he same for borrowing as well as for lending. Negaive savings are equal o credi aking and can be caused by appreciaing oday s consumpion more han omorrows. Each agen of he same generaion is supposed o receive an equal amoun of benefis from he pension sysem while reired. These benefis as well as reurns on privae savings are no objecs of axaion. The oal amoun of conribuions from he new working generaion is colleced by he pension sysem and passed o he old generaion wihou any deducions for adminisraion coss. Our agens are assumed o be self-concerned and only value heir own consumpion, i.e. here are no beques moives. Therefore, we wrie he individual budge consrain of an old-age reiree in he following way (which is random a he poin of ime ) c G +1, = R G +1 s + W G 2 (2.3.3) = R G +1 s G + N +1 N τ w G +1 h +1 = R G +1 s G + (1 + n +1 ) τ w G +1 β h, where W2 G are he benefis an old-age reiree receives from he pension sysem. The gross rae of reurn on savings is given by R+1s G G. w+1 G denoes he wage rae of he fuure generaion (born in + 1) and h +1 is fuure individual human capial. Each agen derives his decision belonging o his decision variables s G, c G,, c G +1, by maximizing his expeced uiliy of life-ime consumpion given in (2.3.1) wih respec o he budge consrains given by (2.3.2) and (2.3.3). [ max E U G (c,, c +1, ) ] = max ln c G, + E [ln c G s,c,,c +1, s,c,,c +1, +1,]. (2.3.4) 22

29 2. Growh and Welfare Solving he sysem we obain from he FOC 2 : s G = 1 τ 2 + τ (1 δ) δ 1 wg h. (2.3.5) Due o he logarihmic form of he uiliy funcion, he demography facor n +1 is cancelled ou and, herefore, he insecuriy belonging o he benefi paymens from he ye unknown group of conribuion payers plays no role in he decision process. If we subsiue opimal savings, given by (2.3.5), in equaion (2.3.2), we receive consumpion in adulhood as: c G 1 + τ (1 δ) δ 1, = 2 + τ (1 δ) δ (1 τ) 1 wg h (2.3.6) 1 + τ (1 δ) δ 1 = 2 + τ (1 δ) δ (1 τ) (1 δ) A 1 (kg ) δ h. By plugging (2.3.5) in equaion (2.3.3) and hen applying formula (2.2.5), we receive consumpion in he second period of life as c G +1, = R+1 G 1 τ 2 + τ (1 δ) δ 1 wg h + (1 + n +1 ) τ w+1 G h +1 (2.3.7) = δa(k+1) G δ 1 1 τ 2 + τ(1 δ)δ 1 wg h + (1 + n +1 )τ(1 δ)a(k+1) G δ h +1. Knowing (2.3.5), we now deermine he aggregae sock of capial under a PAYG regime, which is given by he aggregae savings of he previous generaion: K+1 G 1 τ = N 2 + τ (1 δ) δ 1 wg h (2.3.8) k+1 G 1 (1 τ) (1 δ) = 1 + n +1 β(2 + τ (1 δ) δ 1 ) A (kg ) δ. (2.3.9) The deerminaion of K G +1 and k G +1 uses a Markovian process. Hence, by knowing oday s variables w G, h, N, k G we can deermine omorrow s capial sock. This relaionship shows ha omorrow s aggregae sock of capial, used in he producion echnology, is uniquely deermined. Using his expression for capial in efficiency 2 To receive s in his form, we use he equaliy k +1 G N = s G (1+ñ +1) N β h which is he capial in efficiency unis in period + 1. k +1 is a random variable in period 23

30 2. Growh and Welfare unis in equaion (2.3.7), we calculae omorrow s consumpion by ( ) δ 1 ( ) δ 1 (1 τ)(1 δ) c G +1, = h 1 + n τ(1 δ)δ 1 A δ+1 β 1 δ δ ( 1 + τ(1 δ)δ 1) (k G ) δ2. (2.3.10) Laer we will compare he expeced life-ime uiliy of an agen under PAYG and under FF. I is more ineresing o compare uiliies in he long-run insead of direcly afer inroducing he appropriae pension sysem, as i is possible o achieve flucuaions of oucome hrough he inroducion process. These flucuaions are supposed o be cancelled ou in he long run. Hence we need a condiional equaion which deermines he capial in efficiency unis for an arbirary period. The law of moion of k G is given by k G = 1 ( ) δ ( ) δ 1( ) 1 1 (1 δ)(1 τ) n 1 + n n 1 β(2 + τ (1 δ) δ 1 ) A i=1 δi 1 k0 δ. (2.3.11) Iniial capial in efficiency unis is given by k 0 = K 0 H 0. We assume ha he iniial endowmen of physical and human capial and he iniial size of he populaion is he same under boh pensions sysems, hence we drop he superscrip G in equaion (2.3.11). In he case of a fixed demographic facor n he prefacor would be simplified o ( 1 1+n ) i=1 δi Decisions under Fully Funded There is a significan dissimilariy in he way he wo differen ypes of pension sysems work. While he PAYG sysems collecs conribuions from he young agens and ransmis hem direcly o he reirees, he FF sysem collecs he conribuions, bu hen saves hem for one period. The savings of he FF pension sysem are invesed in he producion echnology and earn a reurn. The single agen is equipped wih he same logarihmic and addiively separable uiliy funcion as under he PAYG sysem. Bu as he FF sysems works in a varied way, he pension benefi paymens are defined differenly. So he individual budge consrains differ: 24