Funded pensions, labor market participation, and economic growth 1

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1 Funded pensions, labor marke paricipaion, and economic growh 1 Mark A. Robers Universiy of Noingham Eric O N. Fisher The Ohio Sae Universiy Keywords: social welfare sae, labor force paricipaion, economic growh Absrac. This paper analyses a model of overlapping generaions in which agens who do no paricipae in he labor marke are unable o borrow. Thus an increase in a fully funded pension raises aggregae savings even wih a fixed paricipaion rae since privae savings are no crowded ou one-for-one. When labor force paricipaion is deermined endogenously, a rise in he level of fully funded pensions increases he aggregae labor supply. This in urn increases aggregae savings and growh, direcly by raising per capia savings and indirecly hrough ax and ineres rae effecs. 1. Inroducion 1 This paper is par of he research projec, "Social securiy iniiaives and economic growh", which is financed by he ESRC under he Evolving Macroeconomy Programme. The auhors would like o hank he Economic Policy Research Uni a he Universiy of Copenhagen for he hospialiy ha made par of his research possible. They also hank seminar paricipans a he 2000 Mancheser Conference on Growh and Business Cycles and a The Ohio Sae Universiy for commens on earlier drafs.

2 The reform of sae pensions, namely he abandonmen of he radiional unfunded plans, is very much on he agenda. One quesion is wheher he alernaive should be a fully funded public scheme or one where individuals are encouraged o make privae savings and borrowing decisions. These wo possibiliies are imperfec subsiues if some agens are unable o obain loan finance. We consider he implicaions of household borrowing consrains in an endogenous growh model and show moving o a fully funded sae pension may enhance growh. The general effecs of borrowing consrains on growh are ambiguous. Jappelli and Pagano (1994) presen a model where household borrowing consrains enhance growh because hey decrease consumpion and hus free loanable funds for invesmen. DeGregorio (1996) shows ha he same consrains may reduce growh by resricing invesmen in human capial. Is sign will depend in general on he exen o which individuals borrow in order o finance consumpion insead of invesmen in human capial. We consider he former, where borrowing consrains are beneficial for growh. In modern economies, however, he empirical relevance of financing consrains on he growh process may acually be small. Jappelli (1990) repors he consensus ha only weny percen of he households in he Unied Saes are credi consrained. We show ha even if only a small share of households are consrained in financial markes, here may be a significan effec on he growh process. Alhough only a small share of households bear he full brun of credi consrains, heir inframarginal effecs are significan for he enire economy. The paper models aspecs of he financial marke and he labor marke in an exended version of he Diamond (1965) overlapping generaions model. Alhough he labor-leisure radeoff and labor union effecs are someimes analyzed wihin his

3 framework, i is less common o model labor force paricipaion. 2 An imporan aspec of our model is ha, while he demand for funds derives as usual from he corporae secor s invesmen decisions, heir supply is derived from only households who are employed. This fac hinges on he key assumpion ha households ha do no paricipae in he labor marke are unable o borrow. There is boh a sociological and an economic raionale for he assumpion of discriminaory borrowing consrains. Firs, no paricipaing in he labor marke may lead o social exclusion and a loss of saus, perhaps a form of financial collaeral. Second, consumpion smoohing implies ha he lower relaive incomes of non-paricipans early in he life cycle will give hem a endency o borrow. Household borrowing consrains affec he individual s paricipaion decision. This choice is based on a comparison of he uiliy of paricipaing--including an idiosyncraic dis-uiliy of effor--wih ha of oping ou of he labor force. A person ouside he labor force incurs boh a lower income early in he life cycle and an inabiliy o borrow agains fuure social welfare paymens. Thus he inabiliy o borrow has repercussions for he aggregae supply of labor. The cenral concern of our paper, however, is he effec of a fully funded social securiy plan on economic aciviy and growh. Of course, if financial markes were complee, a fully funded reiremen program would have no effec on capial accumulaion and growh. Bu in a model wih borrowing consrains, an increase in fully funded old-age benefis does influence economic growh. An increase in such benefis raises oal savings. Since people ou of he labor force canno offse 2 Individual labor supply is considered in Homburg (1990), Breyer and Sraub (1993) and Raffelhueschen (1993), and labor union effecs are discussed in Demmel and Keuschnigg (2000). The

4 increased old-age benefis by borrowing, crowding ou is less han complee. Indeed, he increase in aggregae savings is relaed in a very simple way o he proporion of non-paricipans in he household secor. Furher, an increase in old-age benefis will acually raise aggregae labor supply. Fully funded social securiy is effecively a form of forced savings ha canno be offse by individuals who are consrained from borrowing. Thus increased old-age benefis raise he cos of no paricipaing in he labor marke. Increasing labor force paricipaion will in urn raise aggregae savings. Since hose ou of work face a finance consrain, a rise in he labor supply is anamoun o a rise in he number of savers. Also, savings per paricipan may increase. Indeed, here are wo posiive mechanisms and a negaive one. A rise in paricipaion or employmen raises he marginal produc of capial and hus he rae of ineres. This will increase savings. Also, greaer labor force paricipaion lowers axes since hey are used in par o fund unemploymen benefis. This second effec raises savings since i increases disposable incomes. The hird effec is ha he increased supply of labor drives down he curren real wage. Neverheless, aggregae savings mus rise, since he adverse wage effec is dominaed by he employmen effec because firms demand for labor is elasic. The res of he paper is organized as follows. The model and is equilibrium are given in Secion 2, while Secion 3 describes some properies of a balanced growh pah. Secion 4 gives a brief hisory of he adven of he social welfare sae in Europe a he end of he nineeenh cenury, and Secion 5 calibraes he model o German daa from ha period. Secion 6 offers a brief summary. common focus of hese papers is on how pensions reform may alleviae he labor marke disorions

5 2. The model and is equilibrium There is a measure of M agens in generaion 0, wih exogenous populaion growh a he rae n per generaion. The uiliy of a ype-j agen born in period 1 is given by his funcion: σ (1) σ 1 σ 1 σ 1 j j j j 1 j j U (c, c +1,φ ) = c σ + c +1 σ φ 1 +θ where c j is consumpion a ime by a ype-j agen and φ j 0 is ha agen s (perhaps ime-dependen) fixed cos of working. 3 The index j [0, M ] and agens j are uniformly disribued on his suppor, and we assume haφ is increasing in j; hus agens are ranked according o heir idiosyncraic (perhaps ime-dependen) dis-uiliy of effor. The decision o paricipae in he labor marke involves a fundamenal nonconvexiy: eiher he agen is in he labor force and incurs he fixed uiliy loss φ j or he is no and incurs no such loss. 4 The parameer σ > 0 is he iner-emporal elasiciy of subsiuion, and he parameer θ > 0 is he subjecive discoun facor measured a he lengh of a working life. If an agen j [0, M ] is no consrained in his savings decision, hen he uiliy funcion (1) gives rise o he corresponding savings funcion: caused by pay-as-you-go sysems. 3 The uiliy of an agen born in generaion 0 is jus U (c ) = c This assumpion is akin o he Rogerson s (1988) noion ha a job is lumpy. Eiher one works a whole job or one does no work a all.

6 σ (2) j j σ 1 σ 1 j 1 +θ j s( y, y +1,1 + r +1 ) = (1 + (1 +θ ) (1 + r +1 ) ) y y r +1 where y j is income a ime and r is he real rae of reurn on savings held from +1 period hrough period +1. Since he dis-uiliy of effor is separable, his savings funcion does no depend upon an agen s ype wihin a generaion. Le he indirec uiliy of a ype j agen who is in he labor force be j j j V ( y, y +1,1 + r +1,φ ). This is he maximal value of (1) subjec o c + (1+ r ) c y + (1+ r ) y. The indirec uiliy of an agen who is j 1 j j 1 j ~ j j j j consrained in his savings decision is jus V ( y, y +1 ) = U ( y, y +i ), where we have imposed implicily ha he agen gives up no leisure, as he is no in he labor force. An agen who is in he labor force earns he going wage w and pays income and payroll axes in he amoun τ. The governmen earmarks b of hese axes for his pension. An agen who does no paricipae in he labor force receives a ne benefi of d τ in he firs period, and b of his axes is also pu ino a fully funded pension scheme. All agens reire in he second period of heir lives and receive a pension benefi of (1+ r )b. Thus an agen j [0, M ] paricipaes in he labor force if and +1 only if ~ V (w τ,(1+ r +1 )b,1+ r +1,φ j ) V (d τ,(1+ r +1 )b ). (3)

7 Thus here will be a criical value 0 ~ j M such ha all ypes j ~ j are in he labor ~ force and all ypes j > j are no. Since he ypes are uniformly disribued, he ~ fracion of he populaion ha is in he labor force is j / M. saisfies The governmen runs a balanced budge in each generaion. Thus is policy τ = b + (1 ~ j / M )d. (4) Noe ha d τ + b is necessary for agens receiving public benefis o cover heir income and social insurance axes. Also, a simple manipulaion of (2) shows ha agens ouside he labor force are consrained in heir borrowing decisions only if 1 σ σ (d τ ) / b < (1+ r +1 ) (1+θ ), which is rue if real ineres raes are posiive and public subsidies o hose ouside he labor force are no oo generous. I is possible o show ha a higher labor force paricipaion rae enails a lower ax rae since fewer people are on he dole. This fac implies ha a represenaive individual will be less inclined o borrow because disposable income is higher earlier in he life cycle. The privae and social reurns o capial differ because here is an economywide exernaliy as in Romer (1988). Le firms be indexed by i [0,1] ; hen he oupu of he i h firm is: 1 α β α β Y (5) (i) = [AK M ][K (i)] [L (i)].

8 where Y (i) is he firm s oupu, K = K (i)di is he aggregae capial sock, K (i) is firm s inpu of capial and L (i) is inpu of labor. We impose α > 0, β > 0, and α + β = 1, hus assuming consan reurns o scale a he firm level. The firs erm in brackes capures he economy-wide growh exernaliy, and he second and hird erms are he firms own privae inpus. Noice ha he growh exernaliy depends upon he size of he poenial labor force. Also, he parameers have been chosen so ha aggregae oupu is linear in he aggregae sock of capial in an economy wih a coninuum of idenical firms. If all he firms employ he same number of workers and use he same amoun of capial as inpu, hen (5) implies ha per capia oupu is: ~ y = [Y (i) / L (i)]di = Ak [ j / M ]β where k = K / M is he per capia capial sock. If he labor force paricipaion rae is consan, hen oupu per person rises a he rae of growh of he capial sock per worker. The members of generaion 0 are endowed wih he economy s iniial capial sock, and members of any oher generaion are endowed wih one uni of labor when young and nohing when old. Thus agens in he workforce save in order o smooh consumpion during he course of he life imes. This is he source of funds for privae invesmen; he governmen uses is social insurance revenues o purchase capial as well. Le Π = (d,b,τ ) =1 be a sequence saisfying (4) and le he iniial capial sock k 1 be given. Then equilibrium in he economy is a lis of facor prices (w,r +1 ) = 1, a labor force paricipaion rule ( j =1, and corresponding aggregae ~ )

9 quaniies ( y,k ) such ha: (i) agens j [0, ~ +1 =1 j ] maximize uiliy subjec o he usual iner-emporal budge consrain; (ii) firms maximize profis aking he ~ aggregae capial sock as given; (iii) agens j [ j, M ] are consrained in heir borrowing decisions; and (iv) goods markes and facor markes clear in each period. There are wo immediae implicaions of his definiion. Firs, each firm has he same capial-labor raio. Second, he sum of privae and public savings deermines invesmen and hus nex period s capial sock per person: 1 ~ k = (1+ n) [( j / M )s(w τ,(1+ r )b,1+ r ) + b ]. (6) Equaion (6) is perhaps he single bes descripion of equilibrium. I shows ha here is a balanced growh pah if he labor force paricipaion rae is consan and if axes and benefis are all indexed o he wage rae. 3. Properies of he equilibrium ~ β 1 Profi maximizaion implies ha he real wage is w = βa( j / M ) k and he ~ / β real ineres rae is r = αa( j M ). Thus he real wage is decreasing in he labor force paricipaion rae, and he real ineres rae is increasing in i. Also, if he labor force paricipaion rae is consan, hen he real ineres rae is consan, and he real wage, he capial sock and gross domesic produc all grow a he same rae. Wrie he sum of public and privae savings as ~ S = ( j / m )s(w τ,(1+ r )b,1+ r ) + b. Using he governmen budge balance (4), we can derive anoher imporan aspec of he equilibrium:

10 S / b = (M ~ j ) / M. (7) Thus increasing he pension benefi wihou changing any oher aspec of governmen policy will raise aggregae savings by he unemploymen rae. Since he pension benefi is fully funded and pays he marke rae of reurn, marginal changes in is level have no effec on he savings of unconsrained households. Bu such a change raises economy-wide savings precisely in proporion o he number of households who do no paricipae in he credi marke. The labor supply decision is he cenral aspec of he model. We assume ha he dis-uiliy from working is uniformly disribued across he populaion wih suppor [0,Φ ]. Thus people in each generaion are ranked from hose who incur no psychic fixed cos upon enering he labor force o hose who incur he maximal fixed cos Φ. The maximal elemen of his suppor depends upon ime because agens aiudes owards work may have sociological componens inheren in hem. We are fully cognizan of he fac ha we are breaking an economis s aboo in mixing echnological parameers wih agens preferences, bu we hink ha his specificaion is warraned by hisorical experience. Indeed, in he simulaions described below, we index Φ o w = βak, he wage ha occurs if here is maximal paricipaion in he labor force. Since he real ineres rae depends upon fuure labor force paricipaion, here is a forward-looking dynamic in he model. Equaion (2) shows ha curren savings and hus invesmen depend upon nex period s ineres rae. Thus he paricipaion rae-- and by exension all oher endogenous variables--canno be solved independen of he behavior of he economy on is ransiion o a balanced growh pah. Sill, i is easy o

11 see ha if Φ Aβk hen all agens will paricipae in he labor marke. Thus in a growing economy, any specificaion of he dis-uiliy of having a job ha does no rise a he rae of growh of he economy will enail complee labor force paricipaion asympoically. Assume ha public policy is such ha d = dw and b = bw, and assume furher ha he upper bound for he disribuion of he fixed coss of working is Φ = Φw. Then here is a balanced growh pah for his economy. Finally, i is convenien o wrie u = (M ~ j ) / M as he share of people ou of he work force; is value on a balanced pah is jus u, and he concomian paricipaion rae is 1 u. Using (2) and (6), we see ha on such a pah he per capia growh rae is: (1 u)(1 ud) (8) 1 β 1 1+ g = (1+ n) βa(1 u) + bu. σ β 1 σ 1+ (1+θ ) (1+αA(1 u) ) Several commens abou (8) are warraned. Firs, he growh rae increases wih he size of he economy, an arifac of he assumpion ha he marginal privae and social producs of capial differ. Second, he growh rae depends posiively upon labor s share of oupu, since wages are he source of savings. Third, he growh rae depends posiively upon labor force paricipaion rae. Thus increasing he fixed psychic cos of having a job will lower he growh rae. Fourh he per capia growh rae is negaively relaed o populaion growh and o he discouning parameer. And finally, he growh rae depends posiively upon he pension benefi, since ha is he only way ha people ouside he labor marke can save. 5 5 Alhough an increase in fully funded pensions may raise he growh rae, his will no be Pareoimproving. For example, individuals who sill choose no o paricipae will be made worse-off.

12 4. Brief Elemens of Social Welfare Policies in Several European Counries There is a remarkable coincidence beween he increase of he growh raes of he major indusrial counries in he 1870 s and beginnings of he Welfare Sae. Maddison (1982) idenifies hree major phases of capialis developmen and emphasizes ha he growh rae of he indusrial economies acually acceleraed during each shif of regime. 6 The nineeenh cenury also winessed he beginnings of he roos of he social welfare sae; many auhors cie he direc connecion beween he Briish Poor Laws and Bismarck s firs policies concerning social insurance. 7 A simplisic explanaion for he rise of he welfare sae is ha he poliical economy of redisribuion is a luxury ha an increasing affluen body poliic purchases a he ballo box. The Bismarckian policies were insiued of course no as fully funded bu as pay-as-you-go plans. One migh hink ha he concomian crowding ou would reduce he long-erm growh rae, bu he model suggess ha increased pension benefis migh acually miigae his effec o some exen, especially if he increased benefis offse he poenially deleerious effecs of social insurance on long-run laborforce paricipaion. The model has only wo policy variables ha summarize a more complicaed array of acual social welfare programs. Hansen (1997) idenifies six salien aspecs of hese programs: illness insurance, unemploymen insurance, paymens for injuries susained a work, reiremen insurance, family allowance, and maerniy leave. In our sylized model, all bu one of hese is capured by he policy parameer d. Thus, 6 During he period from 1750 unil 1785, Holland was he produciviy leader and world growh was essenially sagnan. From 1785 o 1890, he Unied Kingdom was he produciviy leader, and he leading counry grew a abou 1.0% per man-hour per annum. Afer 1890, he Unied Saes became he leader and he analogous rae acceleraed o 2.3%. 7 See Mommsen and Mock s (1981) The Emergence of he Welfare Sae in Briain and Germany.

13 while we speak loosely of unemploymen benefis, his parameer capures any aspec of he social welfare sysem ha ends o lower labor-force paricipaion permanenly. Indeed, no unemploymen insurance scheme in Denmark, Sweden, Finland, Germany, he Neherlands, or Grea Briain has provisions for permanen paymens. Some counries do have unemploymen benefis ha las as long as seven years, and he replacemen raes for hese benefis are quie high, much more generous han he parameer we use in he simulaion below. Sill, i is perhaps bes o inerpre he policy parameer d as an amalgam of income mainenance paymens and oher social welfare benefis ha end o decrease he long-run rae of paricipaion in he labor force. The policy parameer b capures reiremen insurance or a public pension. In all of all of he above counries bu Germany, every person is eniled o a public pension regardless of work hisory. And hese pension benefis can be quie generous: he maximal pensions enail replacemen raes ha cluser around 55% of he income of he average working person. In he simulaion below, we chose a fairly conservaive public pension benefi of 20% of he average working person s income. Again, in he calibraion below, i is bes o hink of hese public pension benefis as a combinaion of income mainenance and oher benefis for people who have a very checkered work hisory. 5. Calibraing he model We fied he model o daa for he economy of Germany from Maddison (1982). I is worh emphasizing ha we are calibraing our model o daa from an economy ha insiued a pay-as-you-go scheme of social welfare benefis. I is likely ha hese programs crowd ou capial accumulaion and hus slow long-run growh. Hence he calibraions in his secion underesimae he growh raes ha would have occurred if

14 he Bismarckian reforms had been fully funded. In a model wih increasing reurns o capial in he aggregae, his fac implies ha we are perhaps being conservaive abou he long-run effecs of changing pension benefis. The base case simulaes a social welfare sae wih boh moderae unemploymen and pension benefis. We se d =.4 and b =.2 ; he corresponding ax rae was 21.2%. Thus his configuraion of policy parameers implies ha he ne (permanen) social benefis accruing o a person of working age ouside he labor force were abou 19% of he full employmen wage. The base year was 1870, and we considered each generaion o be a period of 25 years. The rae of populaion growh was se a 10.3% per generaion, maching he increase from 39.2 millions o 61.4 millions beween 1870 and Maddison repors ha 61.4% of he oal populaion was beween 15 and 64 years old in We assumed ha he female labor force paricipaion rae was zero in 1870, and hus calibraed he iniial size of he labor force a 12,043,00 workers. We assumed ha he subjecive discoun rae was θ = 1.7, implying an annual discoun rae of 4%, and we se he iner-emporal elasiciy of subsiuion a σ = 2, in keeping wih he middle value suggesed by Lucas (1988). Capial s share in oupu was se a α =.33, and labor s share was hus β =.67. These numbers reflec he fac ha measured facor shares in he indusrial economies has been fairly consan over a long horizon, and many oher sudies use hese shares. I is of course imporan o describe he disribuion of he idiosyncraic dis-uiliy j of work. We assumed ha he φ s were uniformly disribued on he inerval [0,0.935βAk ]. This suppor was chosen wih he inen of replicaing a long-erm unemploymen rae of 3%, a figure ha is perhaps a bi low for he German economy.

15 Sill, unemploymen is very cyclical, and we waned o have a conservaive base case. Thus he calibraed labor force paricipaion rae was 97%. The wo mos difficul numbers o calibrae in his class of growh models are he iniial capial sock and he value of A, he consan relaing he oupu wih he corresponding capial sock. Maddison esimaes ha he sock of gross nonresidenial fixed capial in Germany in 1976 was 808 billions of 1970 dollars. Using his index numbers, 8 we find ha he analogous sock of capial in 1870 was 31.2 billion 1970 dollars. Maddison also esimaes ha he German gross domesic produc per capia in 1870 was dollars. 9 In our model, his fac implies ha A =.66, bu ha number is much oo small for he calibraed economy because he real ineresed rae is oo low. Maddison calculaes ha he German economy grew abou 2.47% per annum per capia beween 1870 and Seing A = 11.5, we see ha he model fis he long-run growh rae inheren in he daa well. In paricular, he annual growh rae is 2.45% and he real ineres rae is 5.4%. 10 Finally, we can ge a sense of he imporance of pension benefis in he secondbes economy wih axes by raising benefis from b =.2 o b =.21, while keeping he dole rae unchanged. This policy happens o be ax-neural, so he ne unemploymen benefis are unchanged. The one-percen rise in he pension rae increases labor force paricipaion from 97% o 99.5%. Also, here is a rise in he long-run growh rae, from 2.45% o 2.56% per annum. As Lucas (1988) has emphasized, seemingly small 8 The index for Germany is calculaed for ne non-residenial fixed capial, and we are hus assuming ha he depreciaion rae is consan. 9 Indeed, he raio beween he measured sock of capial and gross domesic produc per capia has been remarkably consan, and Maddison s esimaes for his raion in he Germans economy is abou Unforunaely, he value A =11.5 significanly oversaes he level of GDP in And o complicae maers furher, he value A = 130 arises from he usual Solow growh accoun in he base year This leads us o believe ha he economy-wide growh exernaliy ha is inheren in his class of models makes heir calibraion very sensiive o he possibiliy ha he base-year aggregae capial sock is mis-measured.

16 changes in he growh rae can have enormous effecs in he long run. I is worh emphasizing again ha his increase in growh is affeced hrough wo channels. Firs, he higher pension benefis induce an increase in worker paricipaion raes because he effec of being consrained in he credi marke is now more onerous. And second, higher pension benefis increase economy-wide savings. 6. Conclusion We have analyzed an imporan aspec replacing a pay-as-you-go social securiy plan wih a fully funded one. Should policy makers resor o a funded public scheme or o a privae one? Our model has shown ha a fully funded scheme may raise he raes boh of labor paricipaion and of growh. Counries wih more generous schemes are prediced o have lower unemploymen raes and faser growh. The calibraion suggess ha here can be a significan empirical effec of increasing a fully funded social securiy sysem, even when he level of nonparicipaion is fairly small. A modes rise in pension benefis increases he labor force paricipaion rae in a plausibly calibraed economy by more han wo percen. I also increases he long-run growh rae by abou one-enh of a percen. The analysis in his paper occurs in a second-bes world where some agens are unable o borrow. I should be sressed ha he acual incidence of credi consrains need no be high for he model's resuls o hold; i is only necessary ha heir discriminaory naure affecs incenives a he margin. Consequenly, he model is able o capure he characerisics of a developed economy in which here is a role for public policy. 15

17 References Breyer, F. and Sraub, M. "Welfare Effecs of Unfunded Pensions Sysems when labor supply is endogenous." Journal of Public Economics, 50 (1993), DeGregorio, J. "Borrowing Consrains, Human Capial Accumulaion and Growh." Journal of Moneary Economics, 37 (1996), Demmel, R. and Keuschnigg, C. "Funded Pensions and Unemploymen", Finanzarchiv 57 (2000), Diamond, P. A. Naional Deb in a Neoclassical Growh Model. American Economic Review 55 (1965), Hansen, H. Elemens of Social Securiy in Six European Counries. Danish Insiue of Social Research: Copenhagen, Homburg, S. "The Efficiency of Unfunded Pension Schemes", Journal of Insiuional and Theoreical Economics 146 (1990), Jappelli, T. "Who is Credi Consrained in he US Economy?" Quarerly Journal of Economics, 105 (1990), Jappelli, T. and Pagano, M. "Savings Growh and Liquidiy Consrains." Quarerly Journal of Economics, 109 (1994), Lucas, R. E. On he Mechanics of Economic Developmen. Journal of Moneary Economics 22 (1988), Mommsen, W. J. and W. Mock (eds.). The Emergence of he Welfare Sae in Briain and Germany: Croom Helm: London, Maddison, Angus. Phases of Capialis Developmen. Oxford Universiy Press: Oxford, 1982.

18 Raffelhueschen, B. "Funding Social Securiy hrough Pareo-opimal Conversion Policies", Journal of Economics 7, Supplemen (1993), Rogerson, Richard. Indivisible Labor, Loeries, and Equilibrium. Journal of Moneary Economics 21 (1988), Romer, P. M. Increasing Reurns and Long-run Growh. Journal of Poliical Economy 94 (1986),