Chapter 10 Social Security 1

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1 Chaper 0 Social Securiy 0. Inroducion A ypical social securiy sysem provides income during periods of unemploymen, ill-healh or disabiliy, and financial suppor, in he form of pensions, o he reired. Alhough he generosiy of sysems varies among counries, hese elemens are presen in all developed economies. The focus of his chaper is he economic implicaions of financial assisance o he reired. The overlapping generaions economy provies o be ideal for his purpose. In economic erms, he analysis of he apr of he social securiy sysem ha provides assisance during umemploymen or ill-healh is concerned wih issues of uncerainy and insurance. Specifically, unemploymen and ill-healh can be viewed as evens ha are fundamenally uncerain, and he provision of social securiy is insurance cover agains bad oucomes. In conras, reiremen is an ineviable oucome, or a leas an opion, once he reiremen age has been reached. Insurance is herefore no he main issue (excep for he problem of living for longer han accumulaed wealh can finance). Insead, he issues ha are raised wih pensions are he poenial ransfers of resources beween generaions and he effec on savings behavior in he economy. Boh of hese issues require a reamen ha is se wihin an explicily ineremporal framework. The pensions sysems in many developed economes are coing under pressure in a process ha has become known as he pensions crisis. The roos of his crisis can be found in he design of he sysems and he process of change in populaion srucure. The poenial exen of his crisis provides srong gound for holding he view ha reform of he pension sysem is currenly one of he mos pressing economic policy challenges. Afer describing alernaive forms of pension sysems, he naure of he pensions crisis is described. This inroduces he concep of he dependency raio and how his raio links pensions and pension conribuions. The economic analysis of social securiy begins wih a sudy of heir effec on he equilibrium of he economy. We will inroduce he overlapping generaions economy and showed how is compeiive equilibrium may be inefficien. The poenial for inefficiency opens up he possibiliy of efficiency-enhancing policy inervenions. From his perspecive we consider wheher social securiy can be used o secure a gain in efficiency. The fac ha a social securiy program may enhance efficiency can be undersood This chaper draws from Hindriks and Myles (2006, Chper 20). Lecures on Public Finance Par _Chap0, 2008 version P. of 34

2 from he effec of social securiy on he level of he capial sock. If a social securiy program has he form of forced saving, so ha consumers are provided wih greaer second-period income han hey would naurally choose, hen he program will raise he capial sock hrough he increased savings i generaes. This will be beneficial in an undercapialized economy. Conversely, if he program simply ransfers earnings from hose who are working o hose who are reired, savings will fall and hence he level of capial. These observaions moivae he search for a social securiy program ha can guide he economy o he Golden Rule. The fall in he birh rae is one of he cuases of he pensions crisis. I is an ineresing quesion o consider how a change in he birh rae affecs he level of welfare a he seady sae of an overlapping generaions economy. We pursue his issue by considering how he birh rae affecs he srucure of he consumpion possibiliy fronier, boh in he absence and in he presence of a social securiy program. Social securiy may be beneficial for he economy, bu here are issues of poliical economy conneced wih he coninuaion of a program. The inroducion of a program wih he srucure observed in pracice resuls in a ransfer of resources oward he firs generaion of reired (hey receive bu do no conribue) and away from some of he generaions ha follow. This raises he quesion of how such a program is ever susained, since each generaion has an incenive o receive bu no o conribue. The final analyical issue is o review he concep of Ricardian equivalence and is implicaions for social securiy. Ricardian equivalence is he observaion ha by changing heir behavior, consumers are able o offse he acions of he governmen. We show he consequences his can have for social securiy and address he limiaions for he argumen. Finally, afer having compleed he analyical maerial, we reurn o address some of he proposals ha have been made for he reform of social securiy programs. 0.2 Types of Sysem One defining characerisic of a social securiy sysem is wheher pensions are paid from an accumulaed fund or from curren ax conribuions. This feaure forms he disincion beween fully funded and pay-as-you-go social securiy sysems. The economic effecs, boh in erms of efficiency and disribuion, beween hese wo polar forms of sysem are markedly differen. In a pay-as-you-go social securiy program he curren conribuions hrough axaion of hose in employmen provide he pensions of hose who are reired. A any poin in ime he conribuions o he sysem mus mach he pension paymens made by he sysem. The social securiy sysems presenly in operaion in he Unied Saes, he Unied Kingdom, and numerous Lecures on Public Finance Par _Chap0, 2008 version P.2 of 34

3 oher counries are broadly of his form. The qualifier broadly is used because, for example, alhough he US sysem owns some asses and could afford a shor-erm defici, he asses would fund only a very shor period of paymens. A each poin in ime a pay-as-you-go sysem saisfies he equaliy Benefis received by reired = Conribuions of workers () This equaliy can be expressed in erms of he number of workers and pensioners by β R = τe (2) where τ is he average social securiy conribuion of each worker, β is he average pension received, E he number of workers in employmen, and R he number of reired. If here is a consan rae of growh of populaion, so ha he workforce is a consan muliple of he reired populaion, hen E = [ + n] R. Using his in (2) yields β R =τ[ + n] R or β = [ + n]τ (3) This relaionship implies ha he ax paid when young earns ineres a rae n before being reurned as a pension when old. Hence in a pay-as-you-go pension sysem he reurn on conribuions is deermined by he growh rae of populaion. In a fully funded sysem each worker makes conribuions oward social securiy via he social securiy ax, and he conribuions are invesed by he social securiy program. The program herefore builds up a pension fund for each worker. The oal pension benefis received by he worker when reired are hen equal o heir conribuion o he program plus he reurn received on he invesmen. Such a program saisfies he equaliies Pensions = Social securiy ax plus ineres = Invesmen plus reurn (4) The implicaion of his consrain is ha he fund earns ineres a rae r, so he pension and he ax are relaed by β = [ + r]τ (5) Lecures on Public Finance Par _Chap0, 2008 version P.3 of 34

4 A fully funded social securiy sysem forces each worker o save an amoun a leas equal o he ax hey pay. I remains possible for workers o save more if hey choose o do so. If, in he absence of social securiy, all workers chose o save an amoun in excess of he axed levied by he program hen, holding all else consan, a fully funded sysem will simply replace some of he privae saving by an equivalen amoun of public saving. In his case a fully funded syem will have no effec on he equilibrium oucome. We explore his observaion furher when we discuss Ricardian equivalence in secion 0.8. In more general seings wih a variey of invesmen opporuniies, he possibiliy mus be considered ha he rae of reurn on privae savings may differ from ha on public savings. When i does a fully funded sysem may affec he equilibrium. This poin arises again in he analysis of pension reform. Conrasing hese wo forms of sysem, i can be observed ha a pay-as-you-go sysem leads o an inergeneraional ransfer of resources, from curren workers o curren reired, whereas a fully funded sysem can a mos cause an ineremporal reallocaion for each generaion. This observaion suggess ha he wo sysems will have raher differen welfare implicaions; hese will be invesigaed in he following secions. In addiion he pay-as-you-go sysem has a reurn of n on conribuions and he fully funded sysem has a reurn of r. These reurns will differ unless he economy is a he Golden Rule allocaion. Sysems ha fall beween hese wo exremes are ermed non-fully funded. Such sysems make some invesmens, bu he paymens made in any given period may be greaer han or less han he revenue, composed of ax paymens plus reurn on invesmen, received in ha period. The difference beween paymens and revenue will comprise invesmen, or disinvesmen, in he pension fund. 0.3 The Pensions Crisis Many counries face a pensions crisis ha will require ha heir pensions sysems be significanly reformed. This secion idenifies he naure and consequences of his crisis. Once he analysis of social securiy is compleed, we reurn in secion 0.9 o review a range of proposals for reform of he sysem in he ligh of his crisis. The basis of he pensions crisis is hreefold. Firs, he birh rae has fallen in mos developed economies. Alhough immigraion has parially offse he effec of his in some counries, here has sill been a ne effec of a seady reducion in he addiion of new workers. The second effec is ha longeviy is increasing, since people are one average living longer. For Lecures on Public Finance Par _Chap0, 2008 version P.4 of 34

5 any given reiremen age, his is increasing he number of reired. Third, here is also a endency for he reiremen age o fall. Table Dependency Raio (populaion over 65 as a proporion of populaion 5-64) Ausralia France Japan Unied Kingdom Unied Saes Source: OECD (hp:// The ne effec of hese hree facors is ha he proporion of reired in he populaion is growing, and i is his increase ha is problemaic. In general erms, as he proporion of he populaion ha is reired rises, he oupu of each worker mus suppor an ever larger number of people. Oupu per capia mus rise jus o keep consumpion per capia consan. If oupu does no rise quickly enough, hen produciviy gains will be dilued and oupu per capia will fall. Furhermore, supporing he reired a a given sandard of living will impose an increasing burden on he economy. The size of his effec can be seen by looking a forecass for he dependency raio. The dependency raio measures he relaive size of he reired populaion and is defined as he size of he reired populaion relaive o he size of he working populaion. Table repors he dependency raio for a range of counries over he recen pas and forecas for is developmen ino he fuure. The counries in he able are ypical wih he dependency raio forecas o increase subsanially in all cases he raio more han doubles from 980 o This means ha hose working have o suppor an increasing proporion of reired. In some cases, for insance, Japan, he forecas increase in he dependency raio is dramaic. The consequence of he increase in he dependency raio can be expressed in more precise erms by looking a he relaionship beween he conribuions o pay for social securiy and he resuling level of social securiy. Using he ideniy (2) for a pay-as-you-go sysem and dividing hrough by E, he relaionship beween social securiy ax, pension, and dependency raio is given by τ = βd (6) Lecures on Public Finance Par _Chap0, 2008 version P.5 of 34

6 where D is he dependency raio, R E. Hence as D rises, τ mus increase if he level of he pension β is o be mainained. Alernaively, he pension decreases as D increases if he ax rae is held consan. If some combinaion of such changes is no made, hen he social securiy sysem will go ino defici if he dependency raio increases. Neiher a defici, a falling pension, or an increasing ax are aracive opions for governmens o presen o heir elecors. To avoid such deficis, wha hese facs imply is ha governmens face a choice beween mainaining he value of pension paymens bu wih an ever-increasing ax rae, or hey mus allow he value of pensions o erode so as o keep he ax rae broadly consan. For example, he UK governmen has reaced o his siuaion by allowing he real value of he sae pension o seadily erode. As shown in Table 2 he value of he pension has fallen from almos 40 percen of average earnings in 975 o 26 percen in 2000, and i is expeced o coninue o fall, especially since he pension is now indexed o prices raher han earnings. These reducions have aken he value of he pension well below he subsisence level of income. Consequenly pensioners wih no oher source of income receive supplemenary sae benefis o ake hem o he subsisence level. This reducion in he sae pension has been accompanied by governmen encouragemen of he use of privae pensions. Table 2 Forecass for UK basic sae pension Dae Rae as percenage of average earnings Source: UK, Deparmen of Work and Pensions (hp:// In conclusion, he basis of he pensions crisis has been idenified, and i has been shown haw his impacs on he sae pensions ha will be paid in he fuure. The deph of his crisis showns why social securiy reform is such an imporan policy issue. The chaper now proceeds o look a he economic effecs of social securiy as a basis for undersanding more abou he argumens behind he alernaive reforms ha have been proposed. 0.4 The Simples Program Lecures on Public Finance Par _Chap0, 2008 version P.6 of 34

7 Having se ou he issueses conneced wih social securiy programs, he focus is now placed on heir economic effecs. The fundamenal insigh ino he effec of social securiy upon he economy can be obained using he simple model. In his economy here is no producion bu only he exchange of endowmens. Alhough simple, his economy is sill capable of supporing a role for social securiy. In he economy under analysis, each consumer receives an endowmen of one uni of he single consumpion good in he firs period of heir life bu receives no endowmen in he second period. To simplify, he populaion is assumed o be consan. The equilibrium of his economy wihou any governmen inervenion has he endowmen enirely consumed when young so ha here is no consumpion when old. This has o be he equilibrium, since he old have nohing o offer he young in rade. This auarkic equilibrium is no Pareo-efficien, since all consumers would prefer a more even disribuion of consumpion over he wo periods of life. How can a social securiy program improve on he auarkic equilibrium? Consider a pay-as-you-go program ha axes each young consumer half a uni of consumpion and ransfers his o an old consumer. The lifeime consumpion plan for every consumer hen changes from he auarkic equilibrium consumpion plan of {,0} o he new consumpion plan of,. 2 2 Provided ha he preferences of he consumers are convex, he new allocaion is preferred o he original allocaion. Since his applies o all generaions, he social securiy sysem has achieved a Pareo improvemen. This argumen is illusraed in Figure 2. The Pareo improvemen from he social securiy sysem is represened by he move from he lowes indifference curve o he cenral indifference curve. Lecures on Public Finance Par _Chap0, 2008 version P.7 of 34

8 Figure 2 Consumpion when old Pareo Improvemen and Social Securiy /2 {x *, x 2* } /2 Consumpion when young In fac a far sronger conclusion can be obained han jus he abiliy of social securiy o achieve a Pareo improvemen. To see his, noe ha he assumpion of a consan populaion means ha he per capia consumpion possibiliies for he economy lie on he line joining o { 0,}. In he same way ha he Golden Rule was defined for he economy wih producion, he Golden Rule allocaion can be defined for his economy as ha which maximizes uiliy subjec o he firs- and second-period consumpion levels summing o. Denoe his {,0} allocaion by { x *, x 2* }. The Golden Rule allocaion can hen be achieved by a pay-as-you-go social securiy program ha ransfers 2* x unis of he consumpion good from he young consumer o he old consumer. These argumens show how social securiy can achieve a Pareo improvemen and, for he simple exchange economy described, even achieve he Golden Rule allocaion. The social securiy program is effecive because of he inergeneraional ransfer ha i engineers and he consequen revision in he consumpion plans. The opimaliy resul was buil upon he use of a pay-as-you-go program. In conras, a fully funded program canno be employed, since here is no commodiy ha can be used as an invesmen vehicle. The form in which hese conclusions exend o he more general overlapping generaions economy wih producion is now discussed. 0.5 Social Securiy and Producion Lecures on Public Finance Par _Chap0, 2008 version P.8 of 34

9 I has already been shown haw social securiy can obain a Pareo improvemen in an overlapping generaions economy wih no producion. When here is producion, a wider range of effecs can arise, since social securiy affecs he level of savings and hence capial accumulaion. These addiional feaures have o be accouned for in he analysis of social securiy. The concep of he Golden Rule and is associaed capial labor raio is well known. This showed ha he opimal capial sock is he level which equaes he rae of ineres o he rae of populaion growh. If he capial sock is larger han his, he economy is dynamically inefficien and a Pareo improvemen can be made by reducing i. When i is smaller, he economy is dynamically efficien, so no Pareo improvemen can be made, bu he economy is no in an opimal posiion. These observaions hen raise he quesions: How does social securiy affec capial accumulaion? Can i be used o move a nonopimal economy closer o he Golden Rule? To answer hese quesions, consider a social securiy program ha axes each worker an amoun τ and pays each reired person a pension β. The program also owns a quaniy s K of capial a ime s. Equivalenly, i can be said o own k, s s K k =, of capial per uni of L labor. A social securiy program will be opimal if he combinaion of τ, β, and feasible for he program and ensures he economy achieves he Golden Rule. A feasible social securiy program mus saisfy he budge ideniy s k is s s s = [ + + β L τl + r k L k L k L ] (7) which saes ha pension paymens mus be equal o ax revenue plus he reurn on capial holdings less invesmen in new capial. Since he populaion grows a rae n, in a seady sae he ideniies L L = + n, L = [ + n] L generae he seady-sae budge ideniy s + s + and k = k k can be used in (7) o s β = τ + [ r n] k + n s (8) Lecures on Public Finance Par _Chap0, 2008 version P.9 of 34

10 Nohing ha he pension, β, which is received in he second period of life, is discouned in a consumer s budge consrain (since + s = w τ and [ + r ] s + β = x, i follows ha x 2 2 x β s = ), he budge consrain under he program can be wrien + r x 2 β x = = w τ + (9) + r + r The condiion describing consumer choice remains U( x, x ) = + r 2 U ( x, x ) 2 2 (0) Equilibrium on he capial marke requires ha privae savings are equal o oal capial less he capial owned by he social securiy program. This condiion can be expressed as s w x τ = [ + n][ k k ] () The choices of he represenaive firm do no change, so he condiions relaing facor prices o capial sill apply wih f '( k) = r (2) f ( k) kf '( k) = w (3) The seady-sae equilibrium wih he pension is he soluion o equaions (8) o (3). The aim now is o invesigae he effec ha he social securiy policy can have on he equilibrium. To see why i may be possible o design a program ha can achieve he Golden Rule, i should be noed ha he failure of he compeiive equilibrium wihou inervenion o achieve efficiency resuls from he savings behavior of individuals leading o over- or under-accumulaion of capial. Wih he correc choice of social securiy program he governmen can effecively force-save for individuals. This alers he seady-sae level of he capial sock and hence he growh pah of oupu. Lecures on Public Finance Par _Chap0, 2008 version P.0 of 34

11 In equaions (8) o (3) here are five privae-secor choice variables ( k, x, x, w, and 2 r ) ha are reaed as endogenous, plus he hree variables ( β, τ and s k ) ha describe he social securiy program. Given ha here are six equilibrium condiions, he pension sysem can choose any wo of he variables describing he program wih he hird deermined alongside he endogenous variables. To analyze he sysem, i is simples o rea β as endogenous and τ and s k as exogenous. The mehod of analysis is o assume ha he Golden Rule is achieved and hen o work back o he implicaions of his assumpion. Consequenly le r = n. From he firm s choice of capial, he Golden Rule is consisen wih a capial sock ha solves * f '( k ) = n and hence a wage rae ha saisfies * * * w = f ( k ) k f '( k ). The imporan observaion is ha wih r = n, he budge consrain for he social securiy program collapses o β = τ + [ r n] k + n s = τ (4) so a program aaining he Golden Rule mus have he form of a pay-as-you-go sysem wih β = [ + n]τ. I is imporan o observe ha any value of k is consisen wih (4) when r = n, including posiive values. This observaion seems o conflic wih he definiion of a pay-as-you-go-sysem,i does no add o or subrac from his level of capial. Insead, he reurn on he capial i owns is jus sufficien o mainain i a a consan level. I remains rue ha along any growh pah, including he seady sae, a pay-as-you-go sysem canno increase is capial holdings. The value of he ax and capial sock of he program required o suppor he Golden Rule can now be found by using he fac ha he program is pay-as-you-go o reduce he consumer s budge consrain o s 2 x x + = w + r (5) Combining his consrain wih he condiion describing consumer choice indicaes ha he demand for firs-period consumpion mus depend only on he wage rae and he ineres rae, so x = x ( w, r). Using he condiions for he choice of he firm, we have ha he wage rae and Lecures on Public Finance Par _Chap0, 2008 version P. of 34

12 ineres rae depend on he level of capial, so demand for firs-period consumpion can be wrien as x = x ( w, r) = x ( f ( k) kf '( k), f '( k)) = x ( k) (6) The capial marke-clearing condiion can hen be wrien as s w x ( k) τ = [ + n][ k k ] (7) Using he condiions for he choice of he firm and evaluaing a he Golden Rule level generaes * * * * * τ = [ f ( k ) k f '( k ) x ( k ) [ + n] k ] + [ + n] k (8) s Condiion (8) deermines pairs of values {, k s } Any pair {, k s } τ ha will achieve he Golden Rule. τ ha saisfies (8) will generae he Golden Rule, provided ha he capial sock held by he program is no negaive. For insance, if he program holds no capial, so ha s k = 0, hen he value of he social securiy ax will be * * * * * τ = f ( k ) k f '( k ) x ( k ) [ + n] k (9) Alhough he discussion o his poin has implicily been based on he ax, τ, being posiive, i is possible ha he opimal program may require i o be negaive. If i is negaive, he social securiy program will generae a ransfer from he old o he young. As an example, if w x ( w, r) = and f ( k) = k, hen 2 he deails of his derivaion). Subsiuing hese values ino (9) gives α [ α ] * α k = (see exercise (3) for n α τ = n [ α ] [ α] n [ + n] 2α (20) If he rae of populaion growh is 5 percen, hen he ax will be negaive whenever Lecures on Public Finance Par _Chap0, 2008 version P.2 of 34

13 < α 43 (2) For his example he ax rae is posiive only for very small values of α. The resuls have shown ha aainmen of he Golden Rule requires a pay-as-you-go social securiy sysem. By implicaion, a fully funded program will fail o aain he Golden Rule. In fac an even sronger resul can be shown: a fully funded program will have no effec on he equilibrium. To demonsrae his resul, observe ha a fully funded program mus saisfy he ideniy ha he value of pension paid mus equal he value of ax conribuions plus ineres, or s β L = τl [ + r ] = k L [ + r ] (22) Evaluaed a a seady sae, s β =τ[ + r] = k [ + n][ + r] (23) The subsiuion of (23) ino he equilibrium condiions (8) o (3) shows ha hey reduce o he original marke equilibrium condiions. The fully funded sysem herefore replaces privae saving by public saving and does no affec he consumpion choices of individual consumers. I herefore has no real effec on he equilibrium and, if he iniial seady sae were no a he Golden Rule, he fully funded social securiy program would no resore efficiency. This analysis has demonsraed how a correcly designed social securiy program can generae he Golden Rule equilibrium, provided ha i is no of he fully funded kind. A fully funded sysem does no affec he growh pah. In conras, a pay-as-you-go sysem can affec he aggregae levels of savings and hence he seady-sae capial-labor raio. This allows i o achieve he Golden Rule. 0.6 Populaion Growh The fall in he rae of populaion growh is an imporan facor in he pensions crisis. While operaing a simple pay-as-you-go program, a decreasing populaion size makes i harder o susain any given level of pension. Observing his fac raises he general quesion of how he level of welfare is relaed o he rae of populaion growh. This secion addresses his issue boh wih and wihou a social securiy program. Lecures on Public Finance Par _Chap0, 2008 version P.3 of 34

14 Assume firs ha here is no social securiy program in operaion. Recall ha he consumpion possibiliy fronier is defined by a pair of consumpion levels x 2 and x ha saisfy he condiions x = f ( k) kf '( k) [ + n] k (24) and 2 x = [ + n] k[ + f '( k)] (25) Figure 3 Populaion growh and Consumpion Possibiliies x 2 Fronier afer increase in n Gradien [+n] Iniial Fronier x The effec of a change in he populaion growh rae can be deermined by calculaing how i modifies his consumpion possibiliy fronier. For a given value of k, i follows ha 2 x = k n and x = k[ + f '( k n )]. Consequenly, holding k fixed, an increase in he growh rae of populaion reduces he level of firs-period consumpion bu raises he second-period level. This moves each poin on he consumpion possibiliy fronier inward and upward. Furhermore, when evaluaed a he Golden Rule capial-labor raio, hese changes in he consumpion levels saisfy x x 2 / * n = [ + / n f '( k )] = [ + n] (26) Lecures on Public Finance Par _Chap0, 2008 version P.4 of 34

15 Hence, for a small increase in n, he poin on he fronier corresponding o he Golden Rule equilibrium mus shif upward along a line wih gradien [ + n]. The consequence of hese calculaions is ha he shif of he consumpion possibiliy mus be as illusraed in Figure 3. How he level of welfare generaed by he economy is affeced by an increase in n hen depends on wheher he iniial equilibrium level of capial is above or below he Golden Rule level. If i is below, hen welfare is reduced by an increase in he populaion growh rae he capial sock moves furher from he Golden Rule level. The converse occurs if he iniial equilibrium is above he Golden Rule. This is illusraed in Figure 4 where he iniial equilibrium is a 0 e wih a capial labor raio below he Golden Rule. The equilibrium moves o e following an increase in n. I can also be seen in he figure ha if he iniial equilibrium had been a a poin on he fronier above he Golden Rule, hen he upward shif in he fronier would imply ha he new equilibrium moves ono a higher indifference curve. Now inroduce a social securiy sysem and assume ha his is adjused as populaion growh changes o ensure ha he Golden Rule is saisfied for all values of n, he Golden Rule allocaion moves along he line wih gradien However, for large increases in n. For a small change in [ + n], as noed above. n, he gradien of his line becomes seeper. This moves he Golden Rule equilibrium as shown in Figure 5 o a poin below he original angen line. As a consequence he increase in populaion growh mus reduce he per capia level of consumpion x x 2 +. Therefore, even wih an opimal social securiy scheme in operaion, an increase in + n populaion growh will reduce per capia consumpion. Figure 4 Populaion growh and Consumpion Possibiliies x 2 e 0 e x Lecures on Public Finance Par _Chap0, 2008 version P.5 of 34

16 The effec of changes in he rae of populaion growh are no as clear as he simple equilibrium ideniy for a pay-as-you-go program suggess. As well as he mechanics of he dependency raio, a change in populaion growh also affecs he shape of he consumpion possibiliy fronier. How welfare changes depends on wheher a social securiy program is in operaion and on he locaion of he iniial equilibrium relaive o he Golden Rule. If an opimal program is in operaion, hen an increase in populaion growh mus necessarily reduce he level of per capia consumpion. Figure 5 Populaion growh and Social Securiy x 2 New fronier New Golden Rule allocaion Iniial Golden Rule allocaion Iniial Fronier x 0.7 Susaining a Program In he simple economy wihou producion, a social securiy program involving he ransfer of resources beween generaions achieves a Pareo improvemen. This raises he obvious quesion of why such a program will no always be inroduced. The basic naure of he pay-as-you go pension program described above is ha he young make a ransfer o he old wihou receiving anyhing direcly from hose old in reurn. Insead, hey mus wai unil heir own old age before receiving he compensaing paymen. Alhough hese ransfers do give rise o a Pareo improvemen, i can be argued ha i is no in he young consumer s privae ineres o make he ransfer provided hey expec o receive a ransfer (Think of he generaions playing a game. Giving a ransfer canno be a Nash equilibrium sraegy). If he young consumers do no give heir ransfer bu sill expec o receive heir pensions, hen heir consumpion level will be increased. Clearly, his makes hem beer off, so hey will no wish o make he ransfer. Since he social securiy sysem is no individually Lecures on Public Finance Par _Chap0, 2008 version P.6 of 34

17 raional, how can he young be persuaded o consen o he imposiion of he social securiy program? Two differen answers o his quesion will be considered. The firs answer is based on alruism on he par of he young hey are willing o provide he ransfer because hey care abou he old. This raionalizes he exisence of a social securiy program bu only by making an assumpion ha moves ouside he sandard economic framework of individual self-ineres. The second answer works wih he sandard neoclassical model of self-ineres bu shows how he program can be susained by he use of punishmen sraegies in an ineremporal game. I should be sressed ha he fac ha paricipaion in a social securiy program is mandaory is no by iself a valid explanaion of he exisence of he program. All programs have o have willing paricipans o iniiae hem (so hey mus be individually raional a heir inroducion) and need coninuing suppor o susain hem. Alruism refers o feelings of concern for ohers beside oneself. I is naural o hink ha alruism applies o close family members, bu i may also apply o concern for people generally. Alhough he exisence of alruism akes us ouside he sandard perspecive of behavior driven by narrow self-ineres, i need no affec he ools we employ o analyze behavior. Wha is mean by his is ha alruism alers he naure of preferences bu does no affec he fac ha a consumer will wan o achieve he highes level of preference possible. Consequenly, given a se of alruisic preferences, he consumer will sill choose he acion ha bes saisfies hose preferences subjec o he consrain placed on heir choices. The sandard ools remain valid bu operae on differen preferences. There are numerous ways o represen alruism, bu one of he simples is o view i as a consumpion exernaliy. Wriing he uiliy of a consumer in generaion in he form U + ( = U x, x, x ) (27) gives an inerpreaion of alruism as concern for he consumpion level,, achieved by a member of he earlier generaion (which is usually inerpreed as he paren of he consumer). A very similar alernaive would be o assume ha x + = ( U U x, x, U ) (28) so ha alruism is refleced in a concern for he uiliy of he member of he earlier generaion. Lecures on Public Finance Par _Chap0, 2008 version P.7 of 34

18 Boh of hese forms of alruism provide a moive for a social securiy program ha ransfers resources from he young o he old. Consider (27). A consumer wih his uiliy funcion can be hough of as choosing heir personal consumpion levels x, x, and a ransfer, τ, o + he old consumer. The effec of he ransfer is o arise he consumpion level budge consrain of he old consumer is x, since he = [ ] x + r s + τ (29) Provided ha he marginal uiliy generaed by an increase in is sufficienly high, he consumer will willingly choose o make a posiive ransfer. In his sense he provision of social securiy has become individually raional because of alruism. The second reason why ransfers may be susained is now considered. A raional explanaion for paricipaing in a social securiy program can be found in he fac ha each young person expecs a similar ransfer when he is old. Young persons can hen be hreaened wih having his removed if hey do no hemselves ac in he appropriae manner. This punishmen can someimes (bu no always) be sufficien o ensure ha compliance wih he social securiy program is mainained. To give subsance o hese observaions, i is bes o express he argumen using he language of game heory. The analysis so far has shown ha he sraegy o provide a ransfer is no a Nash equilibrium. Recall ha in he deerminaion of a Nash equilibrium each individual holds he sraegies of all ohers consan as hey consider heir own choice. So, if all ohers are providing ransfers, i will be a beer sraegy no o do so bu o sill receive. If ohers are no ransferring, hen i is also bes no o do so. Therefore no providing a ransfer is a dominan sraegy, and he individually raional Nash equilibrium mus be for no ransfers o ake place. These simple Nash sraegies are no only ones ha can be played. To moivae wha else can be done, i is bes o hink abou repeaed games and he more sophisicaed sraegies ha can be played in hem. A repeaed game is one where he same sage game is played once each period for an endless number of periods by he same players. The Prisoner s Dilemma given in he marix in Figure 6 has he general feaures of he social securiy model. I is no exacly he same, since he social securiy model has many generaions of consumers and no jus he wo given in he game. x Figure 6 Social Securiy Game Lecures on Public Finance Par _Chap0, 2008 version P.8 of 34

19 Player Conribue Don Conribue Conribue 5, 5 0, 0 Player 2 Don Conribue 0, 0 2, 2 If boh players conribue o social securiy, hen a payoff of 5 is aained. If neiher conribues, he payoff is only 2. This reflecs he fac ha he social securiy equilibrium is Pareo-preferred o he equilibrium wihou. However, he highes payoff is obained if a player chooses no o conribue bu he oher does. When played a single ime, he unique Nash equilibrium is for boh players o choose Don conribue if he oher conribues, hen i pays no o. This reasoning applies o boh players and hence he equilibrium. This equilibrium is inefficien and is Pareo-dominaed by {Conribue, Conribue}. The siuaion is compleely changed if he game is repeaed indefiniely. Doing so allows he efficien equilibrium {Conribue, Conribue}. The siuaion is compleely changed if he game is repeaed indefiniely. Doing so allows he efficien equilibrium {Conribue, Conribue} o be susained. The sraegy ha suppors his is for each player o choose Conribue unil heir opponen chooses Don conribue. Once his has happened, hey should coninue o play Don conribue from ha poin on. To evaluae he payoffs from his sraegy, assume ha he discoun rae beween periods is δ. The payoff from always playing Conribue is hen 5 + 5δ + 5δ 2 + 5δ 3 + L = 5 (30) δ Alernaively, if Don conribue is played unilaerally a emporary gain will be obained bu he payoff will hen fall back o ha a he Nash equilibrium of he single-period game once he oher player swiches o Don conribue. This gives he payoff Lecures on Public Finance Par _Chap0, 2008 version P.9 of 34

20 0 + 2δ + 2δ 2 + 2δ 3 δ + L = (3) δ Conrasing hese, playing Conribue in every period will give a higher payoff if δ 5 = (32) δ δ or 5 δ > (33) 8 Tha is, {Conribue, Conribue} will be an equilibrium if he players are sufficienly paien. The reason behind his is ha a paien player will pu a high value on payoffs well ino he fuure. Therefore he reducion o a payoff of 2 afer he firs period will be very painful. For a very impaien player, only he payoff of 0 will really maer and hey are driven o Don conribue. The sraegy jus described is known as a punishmen sraegy : he deviaion from Conribue is punished by reversion o he inefficien Nash equilibrium. Alhough he punishmen will hur boh players, he poin is ha i will no happen in equilibrium, since he opimal play wih hese sraegies is always o choose Conribue when players are paien. In summary, in an infiniely repeaed game, punishmen sraegies can be used o suppor efficien equilibria. The same line of reasoning can be applied o he analysis of social securiy. Wha is differen in his conex is ha he same players do no inerac every period. Insead, i is a differen pair of old and young consumers ha mee in each period. However, he punishmen sraegy can sill be employed in he following way: Each consumer when young will provide a ransfer of size x o he old consumer ha overlaps wih hem only if ha old person alive a he same ime provided a ransfer in he previous period; oherwise no ransfer is provided. If all generaions of consumers play according o his sraegy, hen he ransfers can be made self-supporing. There remains one imporan limiaion o his use of punishmen sraegies in he social securiy environmen. To implemen he sraegy, each young consumer mus know wheher Lecures on Public Finance Par _Chap0, 2008 version P.20 of 34

21 he ransfer was made in he period before hey were alive. This issue does no arise in he sandard applicaion of punishmen sraegies, since he players are alive in all periods hey need only remember wha happened in he previous period. Consequenly some form of verificaion device is necessary o suppor he punishmen sraegy. Wihou he verificaion he only equilibrium is for here o be no ransfers which is a Pareo-inferior oucome. This discussion of pay-as-you-go social securiy has shown how such a sysem can be susained even when here is a shor-run incenive for consumers no o make he required ransfers. The basis for his claim is ha social securiy in an overlapping generaions economy has he naure of a repeaed game so ha sraegies ha punish he failure o provide a ransfer can be employed. Wha his analysis shows is ha an apparen ac of generosiy he gif of a ransfer o he older generaion can be made o be raional for each individual. So he provision of social securiy may occur no hrough alruism bu hrough raionaliy. 0.8 Ricardian Equivalence Ricardian equivalence refers o he proposiion ha he governmen can aler an economic policy and ye he equilibrium of he economy can remain unchanged. This occurs if consumers can respond o he policy by making off-seing changes in heir behavior ha neuralize he effec of he policy change. In erms of he presen chaper, Richardian equivalence holds when he governmen inroduces, or changes, a social securiy sysem and ye he changes in individual behavior render he policy change ineffecual. Such equivalence resuls have already feaured wice in he ex. On he firs occasion, in he analysis of he privae purchase of public goods, i was shown ha by changing heir purchases, he individuals could offse he effec of income redisribuion. Furhermore i was also reional for he individuals o make he off-seing changes. The second case of equivalence arose in he derivaion of he opimal social securiy program where i was noed ha a fully funded sysem would no affec he capial labor raio. The explanaion for his equivalence was ha consumers reac o a fully funded social securiy program by making a reducion in heir privae saving ha ensures ha oal savings is unchanged. The common feaure of hese examples is ha he effec of he policy change and he off-seing reacion involves he same individuals. I is his ha provides hem wih a direc incenive o modify heir behavior. Clearly, his is rue only of a social securiy sysem ha is fully funded wih a reurn equal o ha on privae savings. If social securiy is anyhing bu fully funded, a change in he sysem will affec a number of generaions, since he sysem mus Lecures on Public Finance Par _Chap0, 2008 version P.2 of 34

22 be redisribuive over ime. In he case of pay-as-you-go, social securiy involves purely ineremporal redisribuion. A change in a program can herefore affec consumers in differen generaions who need no be alive a he ime he program is changed nor even be alive a he same ime. A firs sigh, his would seem o mean ha i canno be possible for equivalence o hold. This argumen is in fac correc given he assumpions made so far. To obain a basis for eliminaing he effec of policy, i is necessary o link he generaions across ime so ha somehing ha affecs one generaion direcly somehow affecs all generaions indirecly. The way ha his can be done is o reurn o he idea of alruism and inergeneraional concern. Inuiively we can hink of each consumer as having familial forebears and descendens (or parens and children in simple language). This ime we assume ha each paren is concerned wih he welfare of heir children, and ha heir children are concerned wih he welfare of he grandchildren. Indirecly, alhough hey are no alive a he same ime in he model, his makes he parens concerned abou he grandchildren. Wha effec does his have? I makes each family ac as if i was a dynasy sreching hrough ime, and is decisions a any one momen ake ino accoun all laer consequences. A change in a social securiy program hen causes a reacion righ hrough he decision process of he dynasy. To provide some deails, le he uiliy of he generaion born a ime be + ~ U U x, x, U ) (34) = ( + ~ ~ I is he erm U ha represens he concern for he nex generaion. Here + as he maximum uiliy ha will be obained by he children, who are born a +, of he U + is defined paren born in. The fac ha he family will ac as adynasy can hen be seen by subsiuing ~ for U o give + + ~ ~ U U x, x, U ( x, x, U )) (35) = ( If his subsiuion is coninually repeaed, hen he single paren born a ulimaely cares abou consumpion levels in all fuure ime periods. By his fac i is now possible o demonsrae ha Ricardian equivalence applies o social securiy in hese circumsances. Consider an iniial posiion wih no social securiy program and no populaion growh (so n = 0 ). The consumer a reflecs his concern for he Lecures on Public Finance Par _Chap0, 2008 version P.22 of 34

23 descenden by making a beques of value of life is b. Hence he consumpion level in he second period x + = s [ + r + ] b (36) and ha of his descenden is + + = w + + b s+ x (37) Assume ha a social securiy program is now inroduced and ha each consumer has one descenden. Under he erms of he program, young consumers are axed an amoun τ o pay a pension of equal value o old consumers. Then he consumpion level of each paren saisfies x + = s [ + r + ] + τ bˆ (38) and ha of his descenden x ˆ τ (39) + + = w+ + b s+ Bu noe ha if he beques is changed so ha bˆ = b + τ, he same consumpion levels can be achieved for boh he paren and he child as for he case wih no pension. Furhermore, since hese consumpions levels were he opimal choice iniially, hey will sill be he opimal choice. So he old consumer will make his change o heir beques, and he social securiy scheme will have no effec. The conclusion of his analysis is ha he change in he beques can offse he ineremporal ransfer caused by a social securiy sysem. Alhough his was only a wo-period sysem, i can easily be seen ha he same logic can be applied o any series of ransfers. All ha he dynasy has o do is adjus each beques o offse he effec of he social securiy sysem beween any wo generaions. The oucome is ha he policy has no effec. This is he basic poin of Ricardian equivalence. I mus be noed ha here are limiaions o his argumen. Firs, i is necessary ha here be acive inergeneraional alruism. Wihou his here is no dynasic srucure, and he offseing changes in bequess will no occur. In addiion he argumen only works if he iniial beques Lecures on Public Finance Par _Chap0, 2008 version P.23 of 34

24 is sufficienly large ha i can be changed o offse he policy wihou becoming negaive. Does i apply in pracice? We clearly observe bequess bu many of hese may be uninenional and occur due o premaure deah. The concep of Ricardian equivalence can be exended ino oher areas of policy. Closely relaed o social securiy is he issue of governmen deb, which is also an inergeneraional ransfer (bu from children o parens), and is effecs on he economy. This was he iniial area of applicaion for Ricardian equivalence, wih changes in bequess offseing changes in governmen deb policy. Furhermore, if links are made across households, i becomes possible for changes in household choices o offse a policy ha causes ransfers beween households. This has lead o he quesion of wheher everyhing is neural. The answer depends on he exen of he links. 0.9 Social Securiy Reform The basic naure of he pensions crisis facing a range of economies was idenified in secion 3: increasing longeviy and he decline in he birh rae are combining o increase he dependency raio. Wihou major reform or an unaccepably high increase in ax raes, he pension programs will eiher go ino defici or pay a much reduced pension. A variey of reforms have been proposed in response o his crisis. Some of hese are now briefly reviewed. Underlying he crisis is he fac ha he pension sysems are essenially of he pay-as-you-go form. Wih such a srucure an increase in he dependency raio will always pu pressure on he pension sysem. The reform mos ofen discussed in he Unied Saes is for he social securiy sysem o move oward a fully funded srucure. Once he sysem reaches he poin of being fully funded, pensions are paid from he pension fund accumulaed by each worker. This breaks he ideniy relaing pensins o he dependency raio. A fully funded sysem can operae eiher as a governmen-run scheme or on he basis of privae pensions. We commen on his choice below. For now, we noe ha as well as reducing he real value of he pension, he UK governmen has moved in he direcion of a fully funded program by encouraging he use of privae pensions. The difficuly wih his approach is ha i relies on workers making adequae provision for heir reiremen and here is much evidence ha his is no he case. If an economy were o reform is pension sysem, i would ake some ime o ransi from he pay-as-you-go sysem o he fully funded sysem. The reform requires ha a capial fund be esablished ha akes a period of invesmen. Furhermore he pay-as-you-go sysem canno be erminaed abruply. Those already reired will sill require he provision of heir pensions, and Lecures on Public Finance Par _Chap0, 2008 version P.24 of 34

25 hose close o reiremen will have oo lile ime o inves in a pension fund and so will require he coninuaion of he pay-as-you-go elemen. These facs imply ha hose who are in work during he ransiion process will have o boh pay he pensions of he reired and pay o finance heir own pension fund. In simple erms, hey are paying for wo ses of pensions and fare badly during he reform process. A he very leas, his suggess ha here could be significan poliical pressure agains he proposed reform. I is ineresing o consider he exen o which social securiy provision is deermined by poliical consideraions. Evidence on his is provided by Mulligan, Gil, and Sala-i-Marin in heir analysis of social securiy and democracy. Their key finding is ha social securiy has lile o do wih he voing process because counries wihou voing sill supply public insurance in he same way. They even observe for Chile ha mos of he growh in social securiy spending occurred under nondemocraic regimes, and payroll axes reached exremely high levels under General Pinoche. In fac hey repor on nine dynamic case sudies Greece, Porugal, Spain, Ialy, Argenina, Brazil, Chile, Peru, and Uruguay for he period 960 o 990. The counries were seleced on he basis of heir exreme poliical changes over his period. Wih he excepion of Greece, i is found ha formerly nondemocraic counries do no, relaive o heir democraic neighbors, change heir social securiy programs afer experiencing democracy (in erms of he amoun of public insurance spending, and he design of ax and benefi formulas). Similarly formerly democraic counries do no change heir program when hey become nondemocraic. Furhermore muliple regression sudies fo he deerminans of public insurance spending, conrolling for populaion age and per capia income, find neiher a significan parial correlaion beween democracy and social insurance spending (relaive o GDP), nor a significan ineracion beween democracy and he oher variables in a spending regression. These resuls sugges ha he role of poliical consrains on social securiy may someimes be oversaed. I is useful o sress a classical error ha ofen accompanies discussion of swiching o a fully funded sysem. The error arises from comparing he likely raes of reurn on personal accouns wih hose paid under he curren pay-as-you-go sysem. The proposiion ha suggess swiching o he fully funded sysem o benefi from he opporuniy for higher raes of reurn is a fallacy. Compare firs he real rae of reurn delivered by he exising social securiy over he las decades (abou 2 percen per year) wih he risk-free rae of reurn of 3 o 4 percen ha personal accouns could guaranee by holding inflaion-indexed US Treasury securiies. The reurn in he exising sysem is only 2 percen because of he arihmeic of he pay-as-you-go sysem. Lecures on Public Finance Par _Chap0, 2008 version P.25 of 34

26 Suppose ha all workers conribue a fixed fracion of heir income o social securiy. The key poin is ha oday s conribuions cover he pension benefis of oday s reirees, who were he previous generaion of workers ha conribued. The oal reurn corresponds o he growh of overall wage income (populaion plus produciviy growh rae). Thus he real rae of reurn in an ongoing sysem is 2 percen if he economy grows a ha rae in he long run. There is a fallacy o he argumen ha 3 o 4 percen yield on personal accouns is beer. The fallacy is ha he reurn on he exising sysem is low because workers sar wih a liabiliy o provide for he reirees of he previous generaion. If he workers could defec from heir liabiliy o he curren elderly, hey could earn a rae much higher han 2 percen, even if no personal accouns were inroduced. Bu, of course, no one wans o cu he benefis of he elderly who conribued o he sysem hroughou all heir working lives. To pu i differenly, he opporuniy of a higher rae of reurn wih personal accouns comes from he misleading feaure ha hey come wih no obligaion o raise he pensions of he curren elderly. This is he feaure ha accouns for he differences in reurns. Moreover he higher expeced reurn is offse by a leas he percepion of greaer risk. This is no o say ha he reurns in he exising sysem are risk-free. The major risk in he presen sysem is probably ha pension benefis paid in he fuure are subjec o he poliical whims of fuure governmens. The disribuional effecs of a reform from a pay-as-you-go sysem o a fully funded sysem are illusraed by he simulaion repored in Table 3. This simulaion deermines he growh pah of an economic model for a reference case in which he sae pension is held consan. Applied o he Unied Kingdom, he model assumes ha he value of he pension is 20 percen. A reform is hen considered where an announcemen is made in 997 (he year he research was conduced) ha he sae pensin will be seadily reduced from he year 2020 unil being phased ou in The aim of he long period beween announcemen and reducion is o allow for adjusmen in privae behavior. The removal of he sae pension implies ha privae savings will have o increase o compensae. The negaive ages in he firs column of Table 3 refer o consumers who had no ye been born in 997, so a consumer wih age 0 in 997 will be born in The numbers in he second and hird columns shows he percenage by which he lifeime wage of ha age group would need o be changed in he reference case o give he same level of welfare as in he reform case. Hence he value of. for he age group 40 o 50 in he Unied Kingdom shows ha his group is worse off wih he reform a reducion of. percen of heir wage in he base case would give hen he same walfare level as in he reform case. Lecures on Public Finance Par _Chap0, 2008 version P.26 of 34

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