Public pensions as optimal social contracts

Journal

of Public

PUBLIC

Economics

31 (1986) 237-251.

PENSIONS

AS OPTIMAL Michael

Department of Economics,

Received

North-Holland

February

McMaster

SOCIAL

CONTRACTS

R. VEALL* University, Hamilton, Canada Lb’s 4M4

1985, revised version

received July 1986

A simple overlapping generations model is modified to allow for an externality experienced by the young from consumption by the elderly. This sets up a game between generations in which one generation’s strategy may be to save too little and rely on gifts from the young (e.g. public assistance) for retirement income. Social security can therefore be viewed as a Pareto-optimal contract to restore efficient intertemporal allocation. A funded public pension plan corresponds to forced saving but is vulnerable in that the next young generation may stop contributing, rely on its children for retirement assistance and meanwhile reap the consumption externality from the current elderly’s social security benefits. This suggests a forced-giving or pay-as-you-go type of compulsory pension plan (such as exists in most nations) which also has the advantage of aiding the initial old generation and therefore generating an immediate consumption externality for the initial young. The approach can also be used to explain other aspects of existing social security.

1. Introduction One reason that it is difficult to draw conclusions from the vast literature on the effects of social security is that there is no consensus as to why the programme exists at all. For example, in the well-known work of Barro (1974), pay-as-you-go social security is completely neutral, making the reasons for its creation difficult to understand. Of the reasons that have been advanced to explain the existence of government-mandated pensions, there is no agreement as to whether or not such a programme might be socially efficient. One explanation for the existence of social security is provided by Browning (1975). In his model, government-mandated pensions are not socially efficient, but are a result of the voting process, with the old outvoting the young. While instructive, there are a number of shortcomings with this approach. Probably most importantly, the model requires that social security be the only Peter Diamond, Deb Fretz, Ignatius *Sam Bucovetsky, John Burbidge, Jim Davies, Horstmann, Glenn Hubbard, Greg Huffman, Peter Kuhn, members of workshops at McMaster University and the University of Western Ontario, Nicholas Stern and two anonymous referees have provided useful comments on earlier versions. Financial support has been provided by the Social Sciences and Humanities Research Council of Canada. 0047-2727/86/%3.50

0

1986, Elsevier Science Publishers

B.V. (North-Holland)

238

M.R. Veall, Public pensions as social contracts

method of redistributing wealth. If there are other instruments such as taxes, there is the so-called ‘cycling’ problem of shifting coalitions in majority voting models as the young could join forces with some of the older workers, using tax concessions to ‘bribe’ them away from supporting pension transfers to the elderly. Even if pensions are the only instrument, it is not clear in the Browning model why older individuals do not use their political power to raise pensions still further. 1 Finally, for what it is worth, polling evidence suggests that the current young (who are clear financial losers from social security)2 in fact strongly support the programme. This paper provides an explanation for the existence of social security in which it is Pareto improving. Current such explanations fall into two basic categories [see Diamond (1977)]. The first type might be called ‘market failure’ explanations. For example, there could be economies of scale in pension provision and government operation of pensions would be an alternative to private sector monopoly. Also, there might be adverse selection/moral ‘Perhaps the labour supply distortion explanation of Meltzer and Richard (1981) might be applicable, although in this case if the elderly have power to maximize their revenue it would appear to imply an aggregate labour supply elasticity of at least 1.0, which is much larger than is commonly estimated. Browning’s model also predicts that social security should benefit only potential voters, but in most countries legal immigrants who are not citizens and hence not eligible to vote, nevertheless are eligible for social security. Also, in some nations, women received pension transfers long before they were eligible to vote. For example, in Switzerland women (including unmarried women) were granted full pension rights in 1948 (which implied an initial transfer benefit to the elderly) and did not receive the right to vote until 1971. Elderly women, both single and married, also received substantial benefits from the German pension system developed in 1889 and expanded in 1911. German women did not receive the vote until 1919. [See Kirkpatrick (1979).] ‘For the United States, see, for example, Thompson (1983, p. 1456, footnote 62). 3While many economists dismiss polling evidence, it appears to be conceded that politicians do use polls to aid in decision making and certainly the market supports extensive polling activity. Polls in the United States and Canada consistently indicate that the degree of support for social security is high and it does not vary much by age, in contrast to the voting model prediction. In the United States, a Gallup Poll in December 1982 considered alternatives by which the social security deficit could be reduced. The approval rates were very similar across age groups. In particular, when it was suggested that the exemption from income tax of social security benefits should be removed (which was, interestingly, as close as the surveyors came to suggesting a benefit reduction), the approval rate was 28 percent of those aged 18-29, 14 percent of those 30-49, 17 percent of those 50-64 and 18 percent of those 65 and older. An increase in the payroll taxes used to support social security was approved by 33 percent of those 18-29, 28 percent of those 30-49, 39 percent of those S&64 and 40 percent of those 65 and older. A different Gallup Poll 2-5 February, 1979 found that only 5 percent of those under 30 thought social security should be cut to balance the government budget, which wab exactly the same percentage as those over 50. In Canada, a Gallup Poll on 9 October, 1974 found that those aged 18-29 and 3@49 would be substantially more generous in increasing pensions than those 50 and over, with, for example, 40 percent of those aged 18-29 in favour of pensions over $400 per month, compared to 30 percent of those aged 3049 and 22 percent of those 50 and over. A poll on 11 July, 1970 found only 1 percent of individuals thought pensions were too high. It may be possible, however, that workers do not realize that current benefits are essentially current contributions [see Browning (1975)].

M.R. Veall, Public pensions as social contracts

239

hazard problems in the provision of retirement income insurance that could be alleviated by compulsory participation [e.g. Diamond and Mirrlees (1978), Eckstein, Eichenbaum and Peled (1986)]. While such insurance market issues are undoubtedly important in determining specific features of existing plans, they have a major flaw. The introduction of social security has generally involved a massive transfer of wealth to the elderly and to older workers. 4 Market failure justifications cannot explain this transfer, but can only explain government operation of funded pensions.’ The second type of explanation for the existence of social security in Diamond (1977) involves paternalism. In exploring this possibility he suggests that individuals if left alone may not save ‘enough’ for their old age because of irrationality in decision-making or because of a lack of good information about their future incomes or expected lifetimes. The approach in this paper is related to this in that individuals may save insufftciently from a social perspective. But it differs in that the results here are based on perfect rationality and no uncertainty. The key assumption is that there is a positive externality received by the young with respect to the elderly’s consumption. It is shown in section 2 that because of this, some individuals may rationally undersave, relying in retirement on gifts from the young, for example in the form of public assistance. Social security could then be thought of as a forced-savings programme as, for example, in Musgrave (1968). The problem with the explanation so far is that it justifies a funded social security plan, not a pay-as-you-go system. The discussion of sections 3 and 4 therefore illustrates that a forced-giving system may be preferable to a system of forced savings. This is essentially because a funded plan (a) does not generate the benefits of increased consumption by the initial old generation and (b) will always be vulnerable in the sense that any current young generation may not contribute, relying on the next generation for retirement assistance while still enjoying the externality from the social security savings of its parents. In section 4 some additional insights provided by the model are also discussed. It suggests why there are so many individuals whose wealth consists almost entirely of social security entitlements and why relatively few individuals appear to have borrowed against their social security wealth.6 There is also some discussion as to why, if altruism is the basic motivation for social security, there might be different levels of pension support for different contribution levels. The reason suggested is that for a pension plan 4Thompson (1983, p. 1445) cites research that only three industrial countries, Canada, Japan and Sweden, have had substantial reserves and in all cases funding is only partial. ‘Market failure explanations also cannot explain why men and women receive equal rights in most public pension plans, rather than being treated actuarially. %ee Diamond (1977) and Hurd and Shoven (1982) for U.S. evidence.

M.R. Veall, Public pensions as social contracts

240

funded by a payroll tax, labour supply effects will be lessened if there is some link between contributions and eventual pension entitlements [as in Burkhauser and Turner (1983)]. Section 5 presents the summary and conclusions of the research.

2. The model 2.1. The utility function A very simple model is employed to illustrate the basic point as clearly as possible. Assume the economy consists of an infinite chain of generations, with an older and younger generation living in each period t and exogenous population growth at rate n. Only the young receive income M. (The extension to variable labour supply is straightforward.) They then must survive in the second period on their savings or on gifts from the next generation. Saving is in the form of stored goods, where storage yields to the owner a natural, exogenous interest rate r, which may be positive or negative. The utility function of a generation is

where superscripts denote time of birth, and subscripts the.time of consumption, so that C: is current per capita consumption by the young, C:+I is their per capita consumption next period and C:- ’ is current per capita consumption by the current old. The utility function is assumed to have everywhere positive first derivatives Ui and to be quasiconcave. A generation is treated throughout the paper as consisting of one decision-maker. The withingeneration ‘public-good’ issue associated with pensions and altruism is treated, for example, by Sen (1967). (A referee points out that since each generation is effectively one individual, perhaps setting n = 0 would be more consistent; the reader can do this in the following without any essential loss.) It is worthwhile to discuss the third argument of (1) which represents an externality experienced by the young with respect to consumption by the old. [See Hochman and Rodgers (1969) or Pauly (1973) for discussion and application of this type of effect.] Alternatively, the Barro (1974) gift model could be used’ [see also Becker (1974), Buiter (1979), and Carmichael (1982)], yielding:

U’= U(Ci, c:,

=~(c:,c:+l,

1,

u’- ‘) u(c:x

:, c:-‘,

lr2).

(2)

‘Right from the beginning it is probably worthwhile to note that the Barro (1974) result of social security neutrality will not hold because there will not always be operative generational transfers.

M.R. Veall, Public pensions as social contracts

From the perspective of optimization at time t, C:I: and U’-’ can both omitted, as they depend on choices already made in earlier periods [see, example, Burbidge (1983)J Therefore in this sense, formulations (1) and are equivalent, although as will be seen their implications are different for welfare evaluation of the eventual outcome.

2.2. Optimization Generation

241

be for (2) the

with exogenous gift receipts

t’s optimization

problem then corresponds to the Lagrangian:

u,= U(Ci,(l +@,+(I

+n)g,+,,(l

+rP-I

+(I +n)gJ (3)

+&(M-C:-S,-g,),

where non-negativity constraints on all variables are implicit, g, is the gift during period t by the younger generation born in period t to the older generation and S, is savings by the generation born in period t. Secondperiod consumption is first-period savings plus interest plus the gift from the next generation (multiplied by 1 +n, since there are n percent more givers than receivers). The young cannot borrow against future gifts, as there is no one who will lend. Therefore, assuming g,, 1 is exogenous, the first-order conditions are: au =U,(Ci,(l IX:

2

+r)S,+(l

+n)g,+,,(l

+r)S,_,

(44

+(l +n)g,)-I,=O,

au,_ --(I +w*(c:,(l as

+r)S,+(l +nk,+,,(l

++-I

I

+(l +n)g,)-&=O,

av,_ -(I +W,(G(l ag

f

+$%+(l +nk,+,,(1 +rP-,

+(l +n)g,)-&=O,

au

-.-!

a4

=M-C;-S,-g,=O

(W

(4c)

(44

There are multiple solutions to these conditions. However, make the reason-

242

M.R. Veall, Public pensions as social contracts

able ‘charity-begins-at-home’

assumption

U,(C,,C,,C,)>RU,(C,,C2,C2),

about

U that for given n and r:

(5)

for all C, and CZ, where R =( 1 + n)/( 1 +r). (In words, if an individual’s own retirement consumption will equal consumption by the current elderly, the marginal utility of saving exceeds that of giving.) Also, follow Samuelson (1958) and make the steady-state assumption. Under these conditions there exists a unique solution. As the steady-state values of the second and third arguments of the Ui above are equal, Assumption (5) implies that in a steady state with saving, (4b) will exceed (4~) and there will be no gifts; the solution will be simply private allocation between current consumption and saving given r and M. This solution is also locally stable in the sense that perturbations in either gifts or savings by a generation will not increase its utility and can have no effect on subsequent generations. It is also straightforward to show that the steady-state utility corresponding to (1) will not be maximized. For example, if to abstract from other issues comparison is done at ~=n (so that R= l), the steady-state solution to (4a)-(4d) will involve too little retirement consumption because each generation disregards the positive externality associated with its own saving. That same solution with r= n is however the optimal steady state under the Barro intergenerational altruism interpretation, as the steady-state maximum of (2) is equivalent to individual t’s maximization of utility U’.’

2.3. Relying on gifts for retirement In any case, as a starting point assume that a steady state with savings and therefore no gifts has held up to the end of period t- 1. If this is viewed as a game between the generations, this is a Nash equilibrium as each generation takes the next generation’s gifts as fixed. However, generation t may decide to play as a Stackelberg leader and realize its first move advantage: it may be able to increase its utility by not saving at all and relying on gifts from generation t + 1 to survive the second period, Solving first-order conditions (4a)44d) yields a gift function,

g,=~(M+S,-t/R+Rg,+1)--S,-1IR,

(6)

‘The maximum steady state of (1) is the maximum of U= U(C,,C,,C2) subject to M= C, + CJ(1 + n), the economy budget constraint. It is straightforward to calculate the tirst-order conditions of this optimization problem and show that the optimum C, will necessarily exceed that in the steady-state solution to (4a)<4d) which, as noted, is also the steady-state optimum of (2).

M.R.

Veall, Public pensions as social contracts

243

if g, is positive. The function 4 expresses the optimal C:-’ from (1) (the optimal consumption by the current elderly from the perspective of the young generation t); the &JR and Rg,+I are added to M as they expand generation t’s opportunity set by reducing required g, and S,, as long as these latter are interior solutions. If generation t were at a zero-savings corner solution, the g,, 1 term in (6) would be omitted. In any case, provided all goods are normal, 0 < $i < 1, so - 1 < 8g,/%_ 1 ~0, i.e. the more the elderly have saved, the less they receive in gifts. Increases in savings are not completely offset as savings by one generation effectively contribute to the resources available to be allocated (partially as gifts) by the next generation. If generation t plays Stackelberg and exploits rule (6) a new set of lirstorder conditions can be obtained by substituting the expression implied for g,, 1 by (6) into (3) and reoptimizing. These conditions are identical to (4a)(4d) except

g

=(l +n)4,U,-1,=0, I

(4’b)

which as 4, < 1, implies (again at r=n) that saving will be lower than in the previous steady-state Nash equilibrium. This result is strongly intuitive as if g,, 1 is positive, any increase in saving tends to be offset by a reduction in gifts so that the incentive to save is reduced. There are two important points to re-emphasize at this stage. First, it is possible that the utility-maximizing solution to generation t will not occur with g,+r ~0; instead generation t may prefer to remain in the steady-state solution with gifts always zero. To receive the gifts, generation t has to reallocate its consumption intertemporally; this may not be worthwhile if the consumption externality and hence the gift is small. Second, if generation t does exploit the externality by reducing its savings and relying on gifts, subsequent generations may suffer. Specifically, if there is a new steady state (see next section), retirement consumption will necessarily be lower and again evaluating at n = r, further from the steady state welfare optimum using either the consumption externality approach (1) or the Barro altruism approach (2). It is this inefficiency in intertemporal allocation that a social security programme may be used to remedy.

3. Social security: An example 3.1. The zero gifts solution versus the zero savings solution Solving for the precise actions of generation t and its descendants is very complicated, because of the complex nature of the dynamics. For example, because of the forward-looking nature of the dynamics in gift rule (6), the

J.P.E.-

E

244

M.R. Veall, Public pensions as social contracts

actions of any generation depend on all of its successors. To complicate matters even further, there is the possibility of a generation switching to a corner solution, not only at time t but at any time in the future. To abstract from these technical complications a simplified example will be used. The motivation is to demonstrate that social security is consistent with the model although, as will be clear, the social security solution is not inevitable. The simplification is attained by employing a logarithmic utility function, U;=cclnC:+filnC:+,+,lnC:P1,

(7)

@>P/R>Y,

(8)

where

with the first part of (8) representing a condition on the discount rate and the second part being the ‘charity-begins-at-home’ Assumption (5). This simplifies the dynamics greatly as there are only two possibilities for generation t: either the no-gift steady state of: C, = MM/(X + B),

S, = BMl(a + 0)

(9)

(which is also the Nash steady state) will continue forever or generation t will break the pattern by saving nothing at all, and no subsequent generation will save either. To see this latter point, consider that the first-order conditions (4a)+4d) solve for a gift rule analogous to (6) of K, + I

=

X(M + WW(~ + 141-St/R

(10)

in the logarithmic case.’ Substituting this rule into tion problem yields first-order conditions:

where

au;jac:= a/c;-

A, = 0,

dU;/aS, = fl/( R M

+ S,) - i, =

generation

t’s optimiza-

(114 0,

(1lb)

aUl/ag,=y/((S,~,/R)+g,)--i,=O,

(llc)

aU;/a;l,=M-c:-St-g,=o,

(114

again

non-negativity

constraints

have

been

left out.

From

(llb)

the

‘Applying (6) directly would imply a Rg,+2 term in the first part of (lo), but as discussed below (6), this only applies if S,,, >O. Here it can be shown that if such a term is included in (lo), the only change will be that the marginal utility of saving (1 lb) will be smaller. Therefore savings will still be zero after time t and so there is no g, + 2 term.

M.R. Veall, Public pensions as social contracts

245

maximum marginal utility of saving is /l/RM which by (8) must always be less than the minimum marginal utility of consumption a/M. Therefore if g,, I >O, generation t (and by extension every generation thereafter) will not save but rely on retirement support from their children. There will then be a new steady state in which all future young support their elderly with a gift of yM/(a+ y) while saving nothing and consuming the remainder. As is intuitive, the standard of living under retirement is lower when the resources come from gifts and not from saving. This intertemporal allocation is inefficient as compared under n=r to the optimal steady state.” It is also locally stable as a generation cannot improve its welfare by changing its gift level or by saving. Moreover, perturbations in gifts will not affect subsequent generations and small positive savings by a generation will simply lead to a reduction in the gifts it receives with no change in the next generation’s desired savings (of zero) and hence no lasting effect.

3.2. Choosing between the solutions Under what conditions will generation t make the jump? Clearly it will change from the no-gift solution only if its own utility will increase, which depends on the generosity of the retirement gift it will receive if it spends everything and hence on the consumption externality parameter y. It can be shown that generation t will not save if Y>

@(4(~ + B))“‘“lC(~ + PM - P(d(@+ B))“‘pl.

(12)

If y is less than the right-hand side of (12) the no-gift steady state will prevail. Possible parameters which satisfy (8) and (12) are R = 1, a =OS, B=O.4 and y = 0.2.

3.3. Models of social security There are a number of possible ways to view social security in this model, depending on the equilibrium concept chosen. Two will be discussed here. In each case the assumption is that generation t has spent its entire income and is now relying on its children for retirement support. While generation t+ 1 must supply this gift, it is possible by the development of some sort of government institution that it can improve its own welfare and that of every generation thereafter. “The optimal steady for (7) is obtained by maximizing aln C, +pln C,+yln CZ subject to M=C, +C,/(l+n) as in footnote 8. This implies C, =aM/(a+p’+y) and C,=(l+n)(p+y)M/ (a+b+r). This second-period consumption exceeds the (1 +n)yM/(a+ y) received in gifts under the no-savings steady state from (1 la)-(l Id). If (7) is treated as a form of (2), the optimal steady state would then be (9). again implying a different intertemporal allocation than (1 la)+ 1 Id).

246

M.R. Veall, Public pensions as social contracts

First, suppose that generation t + 1 supplies the gift of yM/(a+ y), but by legislation it can bind future generations to this same ‘social security’ gift. Because it does not have to behave strategically to receive this gift, the generation t + 1 can now have positive savings and will in fact attain the same steady state consumption pattern that held before period t if n = r.’ ’ However, it seems more reasonable that even by legislation generation t + 1 cannot bind a transfer level on all subsequent generations. In that case, the pension plan just described would be vulnerable in that generation t+ 2 could reduce its support of the elderly in recognition that generation t+ 1 made some savings. The problem of ‘binding’ future generations in an overlapping generations model first arose in the original contribution of Samuelson (1958) and has received extensive discussion since [see, for example, Hammond (1975), Shubik (1981), and Holler (1984)]. Some of the most prominent work has been in overlapping generations models of money with no natural storable good where money improves welfare as an ‘artificial’ storable good. Each young generation has an incentive to repudiate the money of the current old; in fact this is a competitive equilibrium [see, for example, Shell (1971), Wallace (1980)]. However, it seems reasonable to impose a different equilibrium concept in which the repudiation of its parents’ money by a generation will mean its own money will be repudiated in turn, and this concept in fact lies at the heart of all such models [e.g. de Vries (1985)]. Suppose the same equilibrium concept, which Samuelson (1958, p. 480) refers to as Kant’s Categorical Imperative (‘enjoining like people to follow the common pattern that makes each best off’) and Hammond (1975) calls ‘cooperative egoism’, is adopted here. Therefore suppose that generation t+ 1 calculates the optimal gift such that each generation gives exactly what it receives and no generation has an incentive to change the size of the gift.” In other words, the equilibrium concept does not allow a generation to reduce its social security transfer to its elders without having its own retirement income cut similarly. It is straightforward to show in this case the optimal social contract is for all generations after t to give (b-t- y)M/(cc+ /Y+r) to their predecessors. There will be no saving. This attains the steady-state optimum under consumption externality approach (1) (even if n #r)13 and the plan is not vulnerable as there are no savings and each generation has the incentive to continue the plan unchanged.14 It is also consistent with the “Perhaps interestingly, under this view social security leads to an increase in savings, unlike in Feldstein (1974). “Using another terminology, if the rule is that a generation receives a gift only if it gives a similar gift, the resulting equilibrium is ‘perfect’ in the sense of Selten (1965). “C, will be aM/(a+fl+y) and C, will be (1 +n)(fl+y)M/(u+fl+y). See footnote 10. 14Becuase of the equilibrium concept that each generation matches its predecessors gifts, the equilibrium is obviously not stable with respect to perturbations in gifts but correction of that instability is part of the role of the social security contract. There is stability with respect to perturbations in savings.

M.R. Veall, Public pensions as social contracts

247

observation that the current old are the wealthiest elderly generation ever, both absolutely and as compared to the current young [Hurd and Shoven (1982)].

3.4. The initial conditions for social security Why might it be generation t that is the first to play the strategy of consuming its entire income in the first period? At least three possible explanations consistent with the model can be briefly sketched. One possibility is that the gift or transfer technology is developed in period t, and therefore generation t is the first to exploit it by relying on transfers for retirement income. For the United States, Roberts (1984) has suggested that public transfer programmes began crowding out private charities in the 1930s as a means of support of the poor. Social security, which embodies a similar transfer technology, also appeared in the United States about that time, with legislation passed in 1935 and the first payment in 1939. A second possibility is that, within the context of the model, the right-hand side of (12) initially exceeds y. Then in period t, a once-and-for-all increase in n or fall in r pushes this expression below y and triggers the reduction in saving and the subsequent creation of social security. (There is a ratchet effect such that the return of n and r to their original values would not lead to the collapse of social security although abandonment is possible for small enough n or large enough r.) Another possibility is that the fall in savings might not be due to a strategy at all, but instead to an event like the Depression wiping out the value of saved assets. In this model it does not matter whether generation t has no savings deliberately or accidentally; in either case generation t+ 1 must support it and if it in turn can expect similar retirement support, it will create social security.

3.5. A two-way

consumption

externality

As a final modification of the model, consider the possibility of a two-way consumption externality: suppose the elderly also experience an externality with respect to consumption by the young. In this circumstance, perhaps the young could attempt to coax a gift from the elderly by not consuming in the first period but this is unlikely to be credible as the young have endowment M: the elderly can exploit the young more effectively as they can precommit by not saving. Once we have ruled out gifts from the old to the young, a two-way consumption externality need not make the zero-savings strategy less likely. While this may seem counterintuitive, note in the example that consumption

248

M.R. Veall, Public pensions as social contracts

when young by generation t + 1 if it makes gifts to its parents is at least equal to its first period consumption in the no-gifts steady state. If generation t receives a gift, it will not diminish the externality it receives, as generation t+ 1 provides the gift from its savings.” 4. Social security issues The model is instructive on some general issues respecting social security. For example, why is social security in most countries on an unfunded, payas-you-go basis? It is sometimes questioned whether such a plan is viable, in that subsequent generations may not contribute and end the plan. However, the model here suggests that a funded plan may be more vulnerable. Any current young generation would have the temptation to stop contributing to the plan and let the fund support the current elderly while relying on gifts from its own children for its own retirement support. But as long as indioidual utility functions do not change, a pay-as-you-go plan is essentially invulnerable16 (under Kant’s Categorial Imperative equilibrium concept), as the incentive for any young generation to reduce payments to the elderly must be tempered first by the loss of the consumption externality and second by the realization that it too will receive the reduced payment when elderly. Another important question is why is it that social security primarily takes the form of old age pensions? Would not some individuals reallocate their consumption by appropriate borrowing, regardless of when income is actually received? However, complete reallocation cannot be achieved because individuals are typically entitled by bankruptcy law to enough of their earnings or assets to maintain some minimum standard of living. Lenders accordingly do not allow extensive borrowing against old age pensions. The model of this paper provides an explicit justification for this bankruptcy law and hence the associated ‘capital market imperfection’. Individuals are not allowed to risk too much of their retirement income because of the same consumption externality effect on which the paper’s model of social security creation is based. While the simple model here has all individuals within a generation saving identically, a simple extension to allow income to vary by individual would leave some individuals at the no-savings point bound to a certain minimum level of retirement consumption while richer individuals choose a higher consumption level in retirement and hence save. That zero savings are not required to get retirement assistance is in fact one of the advantages of social security. Moreover, as the analysis here suggests, the rich are not generally “This result does not hold under a Barro-type altruism, where parents will value their children’s utility and hence the utility of all their descendants. In that case the zero-savings strategy will be less likely. ‘Wnless n and r change sufficiently.

M.R. Veal/, Public pensions as social contracts

249

given an exemption from social security participation because (a) they share in the consumption externality and (b) they also can potentially run their savings to zero. The analysis so far also does not explain why the benefits may vary by contribution level. If the model is generalized slightly to allow a labour/ leisure choice and if the gift level is first set and then paid for by revenues raised within a generation by a payroll tax, then obviously there is a labourjeisure distortion. But if future benefits are tied directly to contributions, there are no adverse labour supply effects [as in, for example, Burkhauser and Turner (1983)]. With heterogeneous individuals, the closeness of the link between contribution and benefit is presumably related to the same sort of equity versus efficiency tradeoff that must be resolved for all government revenue and expenditure programmes.” Finally, it should be emphasized that the model is based on the strong assumption that the interest rate is fixed, an assumption that cannot be relaxed without seriously complicating the analysis. However, even with endogenous r it would appear that the basic point is preserved. An externality experienced by the young from the consumption of the elderly may be exploited through individuals not saving sufficiently and then relying on the assistance of others for retirement support. Programmes like social security may help to remedy the resulting inefficiency in the intertemporal allocation of consumption, although additional intervention such as government debt or government investment policy may be required to solve the Golden Rule problem. This is an important area for future research.

5. Summary and conclusions The basic motivation of this paper is to provide a positive-economics explanation for the existence of compulsory old-age pensions as observed in the United States and other industrial nations. Of the existing explanations, those based on moral hazard/adverse selection problems in insurance markets are incomplete as they do not explain why in almost every country social security has been initiated with a large transfer to the older generation. While this can be explained by voting models, these in turn suffer from the “While there is some weak link between contributions and benefits in the United States, in most countries the connection is even weaker. Summarizing from Myers (1981) the plans of the Netherlands, Israel, Australia and New Zealand approximate a demogrant, while those of the United Kingdom and Sweden reflect contributions only very weakly. The only pension plans of which the author is aware that have a close relationship between benefits and contributions are the Provident Funds of nations such as India, Malaysia, Sri Lanka and Singapore which, except in the last case, do not have high coverage. Another explanation for the link between contributions and benetits advanced by Merton (1982) is that the altruistic effect might be in terms of the ratio of second-period to tirst-period consumption, i.e. society feels sorrier for a poor person who was once rich than for a person who was always poor.

250

M.R. Veall, Public pensions as social contracts

‘cycling’ shortcoming of median voter analysis; these models also seem to imply that the elderly could use their voting power to acquire even bigger pensions. This paper explores the approach based on altruism or, more precisely, a positive consumption externality. Previous research along these lines is largely informal and often argues that individuals optimize incorrectly or have misleading information. Social security is then described as a paternalistic ‘forced-savings’ programme. Here a simple but formal optimizing model with perfect information is used to illustrate a rationale for the pay-as-yougo, unfunded type of social security generally observed, which is more correctly thought of as a ‘forced-giving’ programme. The model is consistent with the altruism models of Hochman and Rodgers (1969) and Pauly (1973) or the gifts version of the Barro (1974) model. The basic idea is that if the current young derive some sort of benefit from consumption by the elderly, the elderly may exploit this and not save, instead relying upon gifts from the young for retirement support. This can lead to an inferior steady state, where no one is consuming ‘enough’ in retirement. A compulsory social security programme can reallocate consumption and be Pareto optimal. The social security programme will be unfunded so that the initial old generation receives additional retirement income and the initial young receive the associated consumption externality. In addition a funded plan would be vulnerable in that any young generation could stop saving and end the plan, still reap the consumption externality from the elderly’s savings and rely on the next generation for retirement support. The approach is also consistent with laws that guarantee subsistence to a bankrupt, and hence prevent individuals from borrowing fully against their anticipated pensions. This seems important, as one characteristic of pensions by definition is that they are received only after a certain age has been attained, which would not affect retirement consumption if perfect capital and insurance markets allowed unlimited borrowing. The general approach is also consistent with the disability payments usually associated with social security as well as progressive income [Hochman and Rodgers (1969)] and welfare assistance programmes. The conclusion is that a relatively simple model with either a consumption externality or altruism is sufficient to explain many of the essential features of public pension programmes, without reliance on assumptions of suboptimal behaviour or imperfect information. Additional refinement of such models of social security seems worthwhile.

References Barro, R.J., 1974, Are government bonds net wealth? Journal of Political Economy 82. 10951117. Becker, G., 1974, A theory of social interactions, Journal of Political Economy 82, 1063-1093. Browning, E.K., 1975, Why the social insurance budget is too large in a democracy, Economic Inquiry 13, 373-388.

M.R. Veall, Public pensions as social contracts

251

Buiter, W., 1979, Government finance in an overlapping-generations model with gifts and bequests, in: G.M. von Furstenberg, ed., Social security versus private saving (Ballinger, Cambridge, Ma.) 395429. Burbidge, J.B., 1983, Government debt in an overlapping-generations model with gifts and bequests, American Economic Review 73, 222-227. Burkhauser, R.V. and J.A. Turner, 1983, Is the social security payroll tax a tax?, Mimeo. Carmichael, J., 1982, On Barro’s theory of debt neutrality: The irrelevance of net wealth, American Economic Review 72, 202-213. de Vries, CC., 1985, Legal tender and the value of money, Institute for Economic Research, Discussion paper 8504/G/M (Erasmus University, Rotterdam). Diamond, P.A., 1977, A framework for social security analysis, Journal of Public Economics 8, 2755298. Diamond, P.A. and J.A. Mirrlees, 1978, A model of social insurance with variable retirement, Journal of Public Economics 10, 295-336. Eckstein, Zvi, M. Eichenbaum and D. Peled, 1986, Uncertain lifetimes and the welfare enhancing properties of annuity markets and social security, Journal of Public Economics, forthcoming. Feldstein, MS., 1974, Social security, induced retirement and aggregate capital accumulation, Journal of Political Economy 82, 9055926. The Gallup Report, The Canadian Institute of Public Opinion, July 11, 1970 and October 9, 1974. The Gallup Poll, Public opinion poll 1979 and public opinion poll 1982, Scholar Resources Incorporated, Wilmington, Delaware. Hammond, P., 1975, Charity: Altruism or cooperative egoism? in: ES. Phelps ed., Altruism, morality and economic theory (Russell Sage Foundation, New York) 115-131. Hochman, H.M. and J.D. Rodgers, 1969, Pareto optimal redistribution, American Economic Review 59, 542-557. Holler, M.J., 1984, Intergenerational solutions to the social security dilemma, Mimeo. (University of Munich, Munich). Hurd, M. and J.B. Shoven, 1982, The economic status of the elderly, in: Z. Bodie and J. Shoven, eds., Financial aspects of the U.S. pension system (University of Chicago Press, Chicago) 3599397. Kirkpatrick, E.K., 1979 in: S. Ross, ed., Social security in a changing world (Social Security Administration, Department of Health, Education and Welfare, Washington, D.C.). Meltzer, A. and S.F. Richard, 1981, A rational theory of the size of government, Journal of Political Economy 89, 914927. Merton, R.C., 1982, On consumption-indexed pension plans, Working paper no. 910 (National Bureau of Economic Research, Cambridge, MA). Musgrave, Richard A., 1968, The role of social insurance in an overall program for social welfare, in: William G. Bowen et al., eds., The American system of social insurance (McGraw-Hill, New York) 23340. Myers, R.J., 1981, Social security (Irwin, Homewood, Illinois). Pauly, M.V., 1973, Income redistribution as a local public good, Journal of Public Economics 2, 35-58. Roberts, R.D., 1984, A positive model of private charity and public transfers, Journal of Political Economy 92, 136148. Samuelson, P.A., 1958, An exact consumption-loan model of interest with or without the social contrivance of money, Journal of Political Economy 66, 467-482. Selten, R., 1965, ‘Spieltheoretische Behandlung eines Oligopolmodels mit Nachfragetragheit,’ Zeitschrift fur die Gesamte Staatswissenschaft 12, 301-324 and 667-689. Sen, A.K., 1967, Isolation, assurance and the social rate of discount, Quarterly Journal of Economics 81, 112-124. Shell, K., 1971, Notes on the economics of infinity, Journal of Political Economy 79, 1002-1011. Shubik, M., 1981, Society, land, love or money: A strategic model of how to glue the generations together, Journal of Economic Behavior and Organization 2, 359-385. Thompson, L.H., 1983, The social security reform debate, Journal of Economic Literature 21, 1425-1467. Wallace, N.L., 1980, The overlapping generations model of fiat money, in: J.H. Kareken and N. Wallace, eds., Models of monetary economics (Federal Reserve Bank of Minneapolis, Minneapolis, MN) 49-82.