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Dilemmas About Pensions
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DILEMMAS ABOUT PENSIONS
Peter Sinclah· 1 Director of Central Bank Studies Bank of England and Department of Economics University of Birmingham United Kingdom
This paper looks at the general principles underlying pensions systems, and the relative merits of different kinds of system of state superannuation payments. A'pay as you go system is. it is argued, usually inferior to a fully funded one. The paper presses the case for the view that redistribution is a cogent argument- perhaps the most cogent argument- for state provision, in a practical context where earnings opportunities differ between individuals. Perfect capital markets are a-;sumed, and labour supplies are endogenous. There is some merit in a unifonn state pension supported by a proportional tax on wage earnings, and its implications under two different social welfare functions are considered. But outcomes are Pareto-dominated, under each social welfare function, by a self-selection system from a continuous menu of contribution and pension rates. The least able opt for a large pension and a high tax rate, the abler for less of both. So far from state pensions being proportional to earnings, they should in fact be negatively associated with them.
l.
INTRODUCTION
This paper looks at two features of pension systems- whether they are fully funded or not, and at their redistributive impact. It argues that full funding has important general advantages. Turning to the second issue, I ask why governments provide pensions, why governments should provide pensions. The short answer to the first question is that pension systems are simply inherited from the past, and their longterm character, and the problem of vested interests make them very hard to change quickly. There are several possible answers to the second question. But perhaps the most compelling is that people differ greatly in their capacity to earn. It would seem outrageous that very low earners should be left to starve if they survive into old age. If a key motive for state pension provision is redistribution, then it should be viewed The author thanks a referee for helpful suggestions, and participants at seminars and conferences at City, Leicester and Warwick universities, Lisbon, the Economic Society of Austmlia, the Centml Bank of Argentina, the Reserve Bank of Australia and the Hong Kong Monetary Authority for valuable comments on associated work. Any opinions expressed are those ofthe author
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as an aspect of optimum tax policy. The implications of this are examined in later sections of this paper. The structure of the paper is as follows. Section 2 of this paper examines five arguments that may be used to justify the provision of state pensions, and argues that income redistribution is the most cogent of these. In section 3, two key sets of features of pension schemes are explored and various criteria for assessing arrangements for pensions are discussed. The background to current difficulties faced by pension schemes is analysed in section 4, while section 5 looks at some proposed solutions to them. Section 6 lays down certain desirable properties for a simple model for examining pension issues. Section 7 then looks at such a model and at its policy implications. Some qualifications and conclusions are discussed in the final eighth section of the paper.
2.
WHY DO GOVERNMENTS PROVIDE PENSIONS FOR THE OLD?
There are many possible reasons for the public provision of pensions. First, private capital markets for pensions may be undeveloped, thin or subject to monopolistic mispricing. The monopolistic mispricing may emerge as a result of increasing returns in fund management, which, if ubiquitous, would imply that there was room for only one private sector provider. Second, saving for old age may be a merit good, which is valued more highly by the government, and in the grey light of hindsight by the old person, than by the young who have to choose how much to save. Third, externalities may be involved: the rest of society may be upset to think of old people in a state of destitution, and derive positive pleasure from transferring resources to them. Fourth, life insurance markets may be bedevilled by problems of asymmetric information, giving rise to market failure due to moral hazard or adverse selection for example. Fifth. poverty among the aged may represent unequal opportunities to earn that the individuals enjoyed when they were younger. All these five arguments may help to explain why states began, first in Germany, and later in the Netherlands, Scandinavia, Britain and elsewhere, to provide pensions some twelve decades ago. But none of the first four is really compelling. Arguments one and four really constitute cases for regulating private providers, or perhaps for a (temporarily) state-owned pension company to establish standards and compete with them. But they do not amount to a cogent justification · for state provision as such. Adverse selection and moral hazard would appear, furthermore, to be much more of an issue with certain other kinds of insurance, particularly relating to income. Individuals have negligible knowledge of the timing of their deaths, and can rarely exercise that much influence upon it. Arguments two and three can be made the basis of a persuasive case for subsidizing voluntary savings, to internalize the externality (in the third case) or maximize the individual's true welfare (in the second). But argument five is different. Disparity in earnings ability, in a population of individuals with similar preferences, will lead to inequality in incomes. Abler people will typically consume more in their youth and old age than people with lower ability. With diminishing marginal utilities of consumption, this implies distributive inefficiency: the sum of all young people's utilities will, for example,
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be lower than they would be if unevenness in consumption by the young could be reduced or removed. · Ideally, when all individuals' lifetime preferences are similar, and the marginal utility of consumption is declining, it will be best to equalize consumption across all members of a given age group. This will be true under any social welfare function that treats individuals symmetrically. Achieving this ideal may be well-nigh impossible, however. What it calls for is a system of lump-sum taxes that vary by ability (more exacting on the abler, light or even negative on those with less talent). That way the distortionary effects of taxing labour income at the margin can be avoided. The able, with their large lumpsum tax demands, respond by supplying a large amount of labour (presumably, leisure is a nonnal good). The less able work less time, and may not even work at all. The consumption of everyone at a given stage of life will be the same. The key problem here is that the individual is surely likely to have a much better idea of his ability than the fiscal authority. The state agency responsible for · redistribution will have to rely on individuals' own reports of their own abilities. So the able have a strong incentive to lie. It is in their interest to claim to have lower talent than they truly have. That way they can enjoy a lower tax demand, and either more leisure or higher consumption or both. So if we assume that people will tell the truth if and only if it suits them, a sad but probably realistic premise, the ideal ability tax system is infeasible. If the tax authority can observe earnings, it will be forced to tax them instead, and this implies inevitable inefficiency. A wedge is driven between the worker's marginal rate of transforming labour into a produced good and his marginal rate of substitution between leisure and that good. In such a context, optimum taxation of incomes and redistribution becomes an intricate second-best problem. The issue of optimum pensions is perhaps best thought of, then, as an intertemporal variant of on the theme of optimal income taxation. In much of what follows, the classic insights of Mirrlees ( 1971 ), the pioneering paper that provided the basis for modem optimum income tax analysis, will be applied later on in .this paper in a simple model of overlapping generations. 3,
TYPES OF PENSION SYSTEM ANDY ARDSTICKS TO JUDGE THEM BY
There are many types of pensions system, but one key factor differentiating pension systems in practice is the extent to which contributions on the one side, and benefits on the other, are related to earnings. Count von Bismarck, the Prussian (and later, German) Chancellor in much of the late Nineteenth Century; introduced a system where both contributions and benefits were proportional to earnings. These characteristics are still apparent in the state pension systems ruling in contemporary Germany and many of its neighbours. Pension benefits and contributions are quite close to being proportional to earnings in Belgium, France, Germany, Italy and Sweden for example. In Austria and Portugal, they are exactly proportional. William Beveridge, architect of Britain's welfare state after the Second World War, is associated with quite a different system, where, at least initially, both contributions and benefits were absolute sums
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of money, unrelated to earnings. Neither the Biscmarckian nor the Beveridge pension system, in their pure forms, achieves any degree of income redistribution. But a combination of Bismarckian contributions and Beveridge benefits is
clearly redistributive. This is the system currently operating in Denmark, Ireland, the Netherlands and the U.K. If the absolute benefits are the same for all, and all contributions are equiproportional to earnings, the combination of the two is
definitely progressive. It enriches the aged poor at the expense of the better-paid young. In the United States, contributions are a fixed proportion of earnings, while pensions paid increase slightly with earnings- still progressive, but less so.
A second fundamental distinction is between fully funded and pay as you go pension systems. In the latter case, pensions paid to the current old are financed by levies upon the current young; in the former, by contributions that the current old had themselves made in their youth. With minor qualifications, state pension systems
tend to be pay as you go, while private systems are (approximately) fully funded. Countries differ widely in the size of private pension provision. There is no private pension financing in Luxembourg. At the end of 1996, it amounted to less than I 0 per cent ofGDP in Austria, Belgium, France, Germany, Greece, Italy and Spain. In Japan it was 22 per cent, and the European Union average was 21 per cent, as against over 60 per cent in the United States and Britain, and 89 per cent in the Netherlands. 2 There are five tests one could apply to a pensions system: i. Is it fair between generations? ii. Is it fair within generations? iii. Does it generate an efficient trade-off between an individual's consumption at different stages of life? iv. Does it generate an efficient trade-off between an individual's consumption and labour? v. Does it maximize utility in the long run? The first criterion depends upon the planner's perception of social welfare. For example, one needs to ask, are the welfare levels of all generations weighted equally, or is there discounting of future generations' welfare? Are different
generations' welfare levels perfect substitutes, less than perfect substitutes, or even perfect complements, for instance? In the limit, if they were perfect complements, the planner would never be prepared to make the poorest generation worse off by any amount at all, no matter how much other, better-off generations might gain as a result. With different generations' utilities regarded as perfect or reasonably good substitutes, however, the planner would be quite prepared to see some limited suffering for some generations for the greater good of others. Fairness within generations is an irrelevant issue if every member of a generation is in the same position as regards resources. But individual differences imply that one cannot consider the "welfare of a particular generation" without stipulating exactly how these individuals' utility levels are aggregated or related from the planner's viewpoint. In quite a wide group of cases, fairness within
generations is interpretable, ideally, as perfect equality in consumption. Miles and Timmerman (1999), Table 2, p.256.
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One of the many trade-offs that economic agents face is that between jam today and jam tomorrow. If an allocation of resources is to be Pareto-efficient, it must not be possible, by rearranging it, to increase the welfare of one person without bringing loss to someone else. Conditions for Pareto-efficiency include equality between marginal rates of substitution and transformation between any pair of produced goods, among them that between consumption in youth and consumption in old age. Satisfying this condition implies that the ratio of the marginal utilities of these two equals one plus the (real) rate of interest. If this condition is infringed, by taxation levied on pensions or interest on savings for example, just for one generation atone set of dates, it is in principle possible to abolish it and make everyone in that generation, and everyone else in every other generation, better off by some set of appropriate changes. Another Pareto efficiency condition relates to the trade-offbetween consumption and leisure. The young individual's marginal rate of substitution between leisure and consumption needs to equal the marginal product of that labour. An infringement would imply that more could be produced with reallocation and no extra call on labour. In general, this condition calls for the absence of any marginal taxes on labour income. Consider a pension system that ensures that each young person pays in a sum exactly equal to the discounted value of benefits to be received in old age. This system will honour the Pareto's efficiency condition. But it will achieve no redistribution of income. A Beveridge system with common pensions benefits, but contributions that varied with ability to earn, would be redistributive and Paretoefficient. But, as we have seen, it runs into serious snags concerning feasibility. So criteria (ii) and (iv) are very likely to conflict in practice. Criterion (v) is of c'onsiderable interest too. Suppose that everyone is alike, there is no technical progress, and that there is no role for depletable natural resources. This means that levels of lifetime consumption and utility should be stationary in any long run equilibrium (as well as common within every generation). Consumption by one generation's young workers will be the same as the next generation's; and the same should go for consumption in old age, labour supply, wage rates, interest rates and other macroeconomic variables. So the natural question to ask is whether a long run equilibrium established by voluntary saving will generate the highest stationary level of utility. It will, provided that it so happens th.at the (real) rate of interest equals the rate of population growth. In this Golden Rule outcome, stationary utility will be maximized.' Now consider a state pension system. A fully funded system, where I
This result holds for the traditional, representative agent model of overlapping generations models with exogenous labour supply by youths. It also extends to the case where utility may be written U(c,C,-h) where c and C denote consumption in youth and old age respectively, and his labour supply in youth. The constraint here is C=(!+r)[ wh-cJ. First maximize U with respect to c, C. h and the Lagrange multiplier on the constraint; then differentiate the first order conditions totally. The implicit equation for next period's capital per worker in the next period, a restriction to steady states and the properties of a well-behaved production function linking the factor prices to the capital-labour ratio (k) will then suffice to establish the result when utility is at a maximum against k.
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individuals are free to lend or borrow by themselves on the same terms as the state, has no impact on long run equilibrium; private saving adjusts one-to-one for any official saving. But a pay as you go system, all else equal, can only involve lower long run values of capital relative to labour, and hence lower wage rates, and higher interest rates. If and when the rate of inferest is less than the rate of population growth, a move towards a pay as you go system can only lead to a rise in steady state utility. The economy suffers from excess capital, and the pay as you go system is a very efficient way of destroying surplus capital. But if and where the rate of interest exceeds the rate of population growth - a condition known as "dynamic
efficiency" -a move from a pay as you go to a fully funded system, whatever its initial disadvantages, can only raise utility in the steady state. Ifendogenous population growth, altruism and technical progress are introduced, however, it is conceivable that the long run superiority of fully funded pensions under dynamic efficiency is open to reversal. Adapting Becker and Murphy's ( 1990) model of fertility and human capital building could imply this; Zhang (1995) argues that pay as you go pensions can be favourable to growth. 4.
DIMENSIONS OF THE PENSIONS PROBLEM
The average age of most countries' populations has been increasing, and looks set to continue growing for several decades to come. From the pensions standpoint, the "pensioner dependency ratio", the ratio ofthose eligible to draw pensions to those in paid work, is now rising quite sharply almost everywhere. Several factors contribute to this development. Seven of the main ones are:
a. b. c.
increasing life expectation female employment is now rising more slowly improved contraception, and more widespread availability of abortion, since
the 1960s d. e.
later marriage, and parents choosing to ~ostpone children or reduce family size men tending to retire earlier
f.
elongation of education
g.
post-war baby bulge is soon to stop contributing and draw pensions
On (a), life expectation increases have been pronounced, on all definitions, in many countries- especially in Western Europe and East Asia. In the European Union, it has been rising on average by some 33 days per year for the past quartercentury. Greek males now display the fastest rate of increase within this group. Dietary improvements and lifestyle changes (such as lower incidence of smoking)
appear to be the driving force. Only in some sub-Saharan countries badly afflicted by AIDS, and some parts of the former Soviet Union, is there any current evidence of falling expectation of life. If improving life expectation merely reduces the proportion of workers that dies before reaching retirement, its effect upon pensions finances could even be favourable. Problems arise from this standpoint when
average retirement spells increase, as indeed they have. Half a century ago, West European men could expect some six or seven years of life at age 65. Now they can expect to live twice as long on attaining this age.
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Increasing life expectation ,is not a new phenomenon, although the rate has
quickened somewhat in the 1980s and 1990s. For a long period, it was maskedfrom the standpoint of underfunded state pensions- by rising female labour force participation. More women at work, plus some switch from part-time to full-time work, led to increasing pension contributions in most countries. But from the 1970s
onward, first in Northern and Eastern Europe, and then, later on, elsewhere, women's share in total employment has tended to converge towards a plateau.
Taken together with (a) and other phenomena, this phenomenon, factor (b) above, has begun to yield adverse implications for pension financing arrangements.
At the same time as people tending to live longer, births have tended to fall. Many factors explain this. The contraceptive pill was invented in 1951, and its · widespread use began to be authorized in many countries in and after 1960. Shortly afterwards, abortion became legal in much of Northern Europe and North America. The number of life births fell in many countries by between 25 per cent and 35 per cent between the late 1950s and the mid-1970s. Most of the change followed smartly upon the availability of abortion and the pill. Nowhere have fertility rates recovered to previous leVels (although there have been some recent increases in for
example France and Sweden). In the European Union as a whole, the annual fertility rate was 1.5 per cent in 1995. In 1960, it had been 2.6 per cent. 4 · Turning to (d), we may note that a tendency to later marriage has reinforced these developments. In the OECD area, brides on first marriage are some four years older now than they were two generations ago. A trend towards later marriage is
accompanied by a broadly parallel trend towards starting families later. Since there is no evidence of any change in the range of ages at which women cease to be
capable of bearing children, families postponed become families reduced. Reductions in family size may have been the outcome of conscious choices, tooresponses, for example, to improved labour market opportunities for mothers, or to the movements, often downwards for quite protracted periods, in the urban-space-
purchasing power of labour earnings. One factor that has aggravated the position is (e), the growing tendency for some men, in particular, to cease participating in the labour force before reaching the formal age of retirement. Belgium is a particularly interesting case here. Three
decades ago, most all Belgian men continued working until well into their sixties. Now the labour force participation of men in the 60-64 age range has fallen to barely one quarter, and many Belgian men are retreating from the world of work even
younger. Britain displays the same phenomenon, although the trend is less pronounced. In the British case, Nickell (2001) shows that early retirement due to sickness is the main culprit, with back pain and depression the most frequently cited causes of ill health. In the context of increasing life expectation, one might anticipate increases in the age of retirement as a way of balancing the accounts. Unfortunately, the reverse has -happened. Part of the reason is that, in many
countries, policy was directed to protecting younger and middle aged workers from
Boldrin era/. ( 1999), Table 2, p.294.
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the threat of unemployment during the 1980s in particular. Encouraging earlier retirement, often funded by sickness insurance schemes, was a device that helped to achieve this, while at the same time removing these workers frOm the politically embarrassing unemployment count. Frorri the pensions viewpoint, this matters
primarily because the growing numbers of sick older wofkers under the retirement age are no longer making any contribution (or at least as large a contribution as
before) to pension fund revenues. Boldrin et a/. (1999) observe that falling employment for the old is "the single most damaging factor for the financial sustainability of pay as you go pension schemes". Interestingly they find no empirical support for the view that early retirement lowers unemployment among the young. If the effective age of retirement for many men was actually slipping, rather than rising in line with life expectation, the taxable base for pension contributions
was also under attack from another quarter. Spells of secondary and higher education were lengthening. This is phenomenon (f). The minimum age for leaving secondary school was raised in several countries, Britain among them. More
important, the proportion staying on till age I 8, rather than leaving earlier, increased. On top of this came a rise in the take-up of graduate education (average university enrolments have approxim'ately doubled in relation to cohort size in
Western Europe between 1980 and 2000). The only factor of note to operate in the opposite direction, nowhere powerful enough to offset these developments, was the reduced incidence and duration of military conscription. So there are more retired people, tending to live longer; more people ceasing
to work before the retirement age; a flattening off of women's employment share; a seemingly enduring tendency to later, smaller families; and the duration of the working career is being squeezed from below by the elongation of education. In concert, these factors pose awkward challenges for the public purse when pensions are provided by the State. One phenomenon that makes them urgent is factor (g). This is the fact that the great bulge of babies born in North America and Western Europe shortly aftyr the end of the Second World War are now within a decade or two of retirement. In I 995, the European Union average elderly dependency ratio (the ratio of those aged 60 and over to those aged between 20 and 59) was 37 per cent. Eurostat official demographic projections based on current trends suggest it will reach 72 per cent in 2050 (Boldrin eta/. (1999), Table 3, p.295). Any pension system is open to strain as a result of demographic developments. Longer life expectation, for example, is problematical for all systems, private or public, fully funded or pay as you go. Benefits have to be trimmed, or contributions raised, or both, to keep the books in balance. With changes in births, however, there is a difference. These pose no direct problem for fully funded systems, but can create havoc when pension arrangements are of the pay as you go variety. (In a
closed economy there is still an indirect difficulty even with fully funded systems, since undulations in population growth rates are liable to create complex disturbances in the values of wage rates and real interest rates).
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5. POLICY RESPONSES TO PENSION UNDERFUNDING Underfunding of fUture pension liabilities can be countered in three main ways:
(i) raising the age at which individuals quality for pensions; (ii) raising contributions levied on the young; and
(iii) reducing the value of pensions paid. None are easy to apply in practice. The first of these three responses is the natural reaction to increasing life expectation. Two decades ago men in most OECD economies could look forward, on average, to ten years in retirement, after a career spanning about 45 years. This
gives a ratio of two to nine. Now career length is shortening somewhat, while the average retirement spell for men has risen by about two years, and sometimes more,
in many countries. In retrospect, the age of pension eligibility should probably have been increased by perhaps eighteen months - to keep the ratio of retirement to career spells constant.
One problem here is that workers' productivities may still fall with age, on average, much as they have always done. Dietary and lifestyle improvements may postpone death with little if any impact on individuals' abilities to continue working effectively late middle age. One reply would point out that older workers' comparative advantages may change as they age: they may become completely unsuited to some types of work, but remain quite proficient in others. A worker's final career stage could therefore involve a change in role and tasks, and quite possibly a less senior and lower-paid position. If so, private pension arrangements,
which are usually tilted towards immediate pre-retirement earnings, may need revision.
A second difficulty is the fact that age eligibility for pensions should only be revised with adequate notice, to permit employees and employers plan ahead appropriately. This is a more telling point in the context of the third policy (lowering the pension paid). But even in relation to raising the pension eligibility age, it implies that the transition to a better system can hardly be immediate. The second policy response, raising contributions by the young, has certain attractions. It shields the current old from what could otherwise be a drastic and
presumably completely unanticipated reduction in their consumption in old age. It increases the next period's stock of capital, because although the young are likely to reduce their voluntary saving somewhat, total saving, public and private, will rise. And it represents a step in the direction of the key principle that future pensions
should be funded: when the current young generation retires, it will be their own pensions that will be financed by the investment of their contributions.
There is, however, a snag. The current young will suffer a serious fall in lifetime consumption and utility, if it is they that are called upon to finance not just the previous generations pensions but their own as well. Why should the burden of adjustment fall only upon this generation? Intergenerational fairness arguments
suggest that the changeover to a fully funded system should be gradual. Indeed, perhaps the current old should share some of the burden too. One consideration that reinforces this is the fact that the prices of factors of production will take time to converge on the new steady state equilibrium. The real
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wage rate will start to climb, and the rate of interest will fall. But for the current young, the wage rate will actually drop iftheir labour is endogenous. They will react to additional tax burdens by working longer. This will increase the rate of interest faced by the current old on their voluntary saving giving them a windfall gain, which should presumably merit some compensating reduction in pension benefits. The third policy reaction involves a cutback in the value of pensions paid. This can be achieved in a variety of ways. Perhaps the simplest involves breaking or 'suspending the link, if there is one, between state pensions and wage rates. Real wage rates display a positive time trend of between I per cent and 2 percent per year in most advanced economies. Full pension- real wage linkage meanS uprating the nominal Value of pensions, annually or perhaps more frequently, to cover both inflation and the growth rate of real wages. It also implies ·that two retired individuals, who differ only in age, will receive the same pension in the same year. Ifreal wages grow, for example, by 1.5 per cent per year, a complete suspension of the wages link for twenty years - so that pensions were indexed to prices only would reduce pension liabilities by some 23 per cent. This is a major saving, achieved quite speedily. Alternatively, pension payments could be inflation proofed and uprated by some fraction of real wage rises. In favour of either of these moves is the point that the pensioner does not suffer an absolute reduction in the real value of the pension. If poverty is absolute, delinking pensions from earnings, and tying them instead to the relevant price index for pensioners, is completely innocuous. Delinking also offers a relatively rapid escape route from pension underfunding problems. On the other hand, there are difficulties. One is that the pensioner's real income stream is presumably lowered below what had been previously expected. So he is being asked to make a sacrifice in that sense; and indeed, had he known about this long enough ahead, he could and perhaps would have offset many of its effects by saving more when he was working. Furthermore, there are familiar and powerful arguments for thinking that poverty is at least in part a relative concept. Delinking pensions from real wages, in a context where labour productivity and real wage rates climb over time, can only widen the income gap between one generation and its successor- and the all too visible gap between the old and the comparatively better off young. Optimal redistribution in a situation like this would seem more appropriately from the relatively affluent young towards the poorer old. Wage-delinking actually has the opposite effect. Lastly delinking pensions from pay is certainly not a substitute for achieving a fully funded system. It is only a device for making the pensions system less generous. So the most that could be said for it is that it may have its place in a general programme of transition to that superior system ..
6. HELPFUL FEATURES OF A MODEL FOR PENSIONS For many purposes a model of overlapping generations. with its pattern of discrete time. is a simpler and more appropriate framework than a continuous time set-up. In the former, people can live for two periods, work only in the first, and consume, presumably, in both periods of their lives.
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This approach has one or two drawbacks, however, of which perhaps the most telling is that it forces an individual's retirement to be a fixed (and rather implausibly large) portion of his or her economic life. One way round this difficulty is to assume that everyone is certain to live for the first working period, and faces
a probability of, say, q of surviving into old age. In such circumstances, one may assume the existence of assets that can be bought by youths, with gross returns of in the event of survival, and zero otherwise. Private saving in the fortn of such instruments restores the intertemporal trade-off condition that the ratio of the marginal utilities of consumption in youth and old age should equal the gross rate of interest, I + r. This set-up also has the merit of allowing one to examine changes in life expectation by altering the parameter q. Within the (at most) two-period lives set-up, it is highly desirable to assume that the intertemporal utility function treats old age consumption, C, in an additively separable and logarithmic fashion. The advantage of this is that, because C can be defined as the product of two numbers- the sum of private saving and discounted pension on the one side, and the gross rate of interest (I +r) on the other, this last
number plays no role in the agent's optimisation decisions. Just why this is so
helpful stems from the fact that the rate of interest here is the rate expected to hold in the next period, which will depend on next period's ratio of capital to worker's labour supply. With any other set-up, a closed fortn solution for next period's capital-labour ratio will be unavailable for this reason. Another possible characteristic of an overlapping generations model is homotheticity as regards consumption at different stages of life. This becomes important when people are allowed to differ, for example in ability to earn. Homotheticity for consumption is youth, c, and old age, C, is the critical condition pertnitting aggregation. This was first established by Flemming ( 1977). When utility is log-linear in C, for reasons examined above, homotheticity for c and C requires utility to be log-linear inc as well. Most models of overlapping generations with production exogenise labour
supply: the young are typically assumed to work for a period of unit length, while the old do not work at all. But the labour supplies of individuals are not in practice uniform or constant over time. More generally, it is natural to ask how equilibrium is affected when labour is endogenous. This is especially so in the context of taxes and transfers. The easiest way of making labour supply endogenous in the overlapping generations framework is to make utility linear (and decreasing) in
labour supply in the period of youth, as well as log-linear inc and C, consumption levels in youth and old age. This quasi-linear utility function is highly tractable; this merit is particularly valuable once individual differences are introduced. Quasilinearity does not infringe Flemming's aggregability condition of (c, C) homotheticty, because it does not relate specifically to labour supply. The utility function with which it is easiest to work is therefore
U = -b lnb- (1-b)ln(l-b) +blnc + (1-b) InC -mh
(I)
The first two terms are constants whose presence removes unnecessary clutter from the associated indirect utility functions.
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ANALYSIS
Agents maximise (I) with respect to h, c and C, subject to two,constraints. These are first that h be non-negative, and second that p + (I +r)(wh( I -t)-c)- C be nonnegative. Here, pis the pension and t the tax rate facing the individuaL The first order conditions imply that any individuals facing a wage rate less
than mpi( I +r )(I-t) will not participate in the labour force. They will consume bpi (1+r) in youth and (1-b)p in old age, financing the former by borrowing against their future pension. The utility of such people will equal In p- bln(l +r). Those with sufficiently high wage rates will supply labour of (Jim)- piw(/+r)(l-t), consuming bw(J -t)im in youth and (1 +r)w(/ -t)( I -b)im in old age. Their saving in youth will equal w(l-t)( I -b)im- pi(/ +r), This will be positive if their wage rate is high enough. In general, there will be three groups in the young population: the unemployed; employed dissavers; and employed savers. The utility of those who do work will equal , U = In w(/-t)im +(/-b)ln(J +r) -1 + mpiw(l +r)( I-t).
The issue of redistribution only arises once wage rates are allowed to differ. It is simplest to assume that the wage rate each person faces is a product of two numbers- the real wage rate for someone with unit ability, and their own ability level, a variable taken to be uniformly distributed on the interval from 0 to I. In the numerical results below, b is set to one half, and m to unity. We shall assume that the pension system is fully funded. The natural place to begin is with a system that is pure Bismarckian in contributions and pure Beveridge in benefits. In this case p and the earnings contribution rates faced by everyone are the same. Later both parameters may be
allowed to vary, in order to obtain optimal non-linear benefit and contribution rates. If the social welfare maximand is mean utility, the optimum earnings contribution rate is 0.336, which finances a universal pension with a discounted present value
to a youth of0.0574. With minimum utility the maxim and- as prescribed by Rawls -the common pension goes up to 0.0674, and the tax rate to finance it to 0.544. In the first case, 17.3 percent of workers are unemployed; in the second, 29.6 percent. A superior pension and contribution system can easily be identified. Suppose that t and p are available, but that everyone can choose a different pension-
contribution rate package if they prefer. Suppose that the set of packages is given by P = QT- X. You can opt between a generous pension p, and a high contribution rate t, or lower values of both as given by that general equation. Each person first chooses savings and labour supply, then maximizes resulting indirect utility with
respect to the contribution rate for them. Higher wage individuals will go for lower pensions and lower contribution rates. The idea is that out of the continuum of
pension-contribution rate packages, each person picks the package best for them. Preferences given by ( 1) satisfy the "single-crossing condition" that ensures a unique optimum package for each individual who works. The Flemming aggregation condition ensures that if pensions are fully funded, the steady state pattern of factor prices is unique. Coulter eta/. (1997) argue in favour of opt outs. Arguments in
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favour of this are attractive. But one can go further, and make the size of the pension a continuous variable, negatively related to the size of earnings. In this case, Rawlsian social welfare is maximized when t, the contribution rate
chosen by the unemployed, is some 68 per cent. Everyone in work opts for a lower value of the contribution rate, which falls progressively to reach about for the ablest person working. High earners do not receive a state pension in old age: instead they
pay a lump-sum tax, as given by the formula P=QT -X. If mean utility is the maximand, the marginal contribution rate selected by the ablest will vanish, so that there is a zero marginal tax rate on earnings, but to earn this privilege they face a
really steep lump sum tax demand. The marginal tax rate confronting the least able worker is 0.65. Unemployment rates are 34.3 per cent in the latter case, and about 419 in the Rawlsian optimum. One notable feature of these results is that the marginal contribution rates associated with the biggest pension are quite close in these two very different optima, and the difference in unemployment rates is quite small. Where the two optima differ most is in the speed with which contribution rates fall as earnings rise,
but they fall quite steeply in both cases. These observations imply that there may well be rather less political dispute about the general shape of an ideal pension system than might appear from the traditional optimum tax literature. There is another striking feature, too. The Raw Is-optimal non-linear pension system does
not just yield higher minimum utility than the Rawls-optimal linear system - it Pareto-dominates it, in the sense that everyone's utility is higher in the first optimum than the second. Similarly, the utilitarian-optimal non-linear system Pareto-dominates the utilitarian-optimal linear one.
8.
QUALIFICATIONS AND CONCLUSIONS
This paper has abstracted from a number of considerations. First, it has neglected problems of uncertainty. There may be randomness is birth and death rates, technological progress and preferences; unforeseen political changes may also lead to uncertainty in the future path of pension benefits and contributions. The rate and character of technological progress determine the growth rate of real wage rates and
the rate of return on capital. As Miles and Timmerman ( 1999) emphasize, the net present value of future state pension liabilities is highly sensitive to assumptions made about these two rates. It has omitted government spending on public goods or debt service, assuming instead that pension provision is the sole fiscal activity
· undertaken by the State. The economy under consideration has been closed to trade, perfectly competitive, innocent of any Keynesian difficulties, and devoid of money. It has been assumed that all agents fully understand the pension and benefit system confronting them, despite some rather worrying evidence (eg Bouri eta/.
(2001)) to the contrary. There is no altruism towards children or parents, no bequests, no education, private or public (a factor stressed by Boldrin eta/. (1999) which may go some way to mitigate the disadvantages of a pay-as-you-go system). Unlike Becker and Murphy (1990) there is no endogeneity of fertility or human capital building. It has concentrated upon steady state,solutions, and selected a
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convenient if less than fully plausible assumption about the distribution of abilities. Preferences have been common and deliberately modelled in a shape that permits aggregation across heterogeneous workers and yields a closed form solution for · factor prices and associated variables.
The conclusion to which this paper points is that the strongest case for a government role in pension provision is based upon unequal earning opportunities. Pensions need not be uniform. Greater redistribution is achieved if they are absolute
and uniform, as opposed to proportional to earnings. But still greater redistribution can be attained by making the size of the pension decline as earnings increase. Indeed, the pension for high earners can, and probably should, be negative. To compensate, the marginal pension contribution rate needs to decline, too, as
earnings rise, and should in fact be zero at the top at least when social welfare is utilitarian. In the circumstances considered in this paper, a pay-as-you-go pension system
is inferior to a fully funded one. It is natural to ask how quickly, if at all, one should make the transition from the former to the latter, in a country where pensions are unfunded. Here again, the social welfare function· is of vital importance. If it is
Rawlsian between the generations, the answer is that you should stick to the bad system you have inherited, because the transition would bring pain to at least one generation (the poorest generation), which no amount of subsequent gains by later generations could compensate. But if, at the other extreme, social welfare is utilitarian- the (discounted) sum of the stream of all generations' utilities- the transition is worth undertaking. And if the discount rate for social welfare is low enough, it appears that the correct course of action is to withdraw pay-as-you-go
pensions immediately and in full forthe current young. But detailed analysis of this issue must await further research.
REFERENCES Becker, G., K. Murphy and R. Tamura (1990), Human Capital, Fertility and Economic Growth, Journal of Political Economy, 98, S 12-37. Boeri, T., A. Boersch-Supan and G. Tabellini (2001), Would You Like to Shrink the Welfare State? A Survey of European Citizens, Economic Policy, April, 950. . Boldrin, M., J. Dolado, J. Jimeno and F. Perrachi (1999), The Future of Pensions in Europe, Economic Policy, November, 289-320. Coulter, F., C. Heady, C. Lawson and S. Smith (1997), Social Security Reform for Economic Transition: the Case of the Czech Republic, Journal of Public Economics, 66,313-26. Feldstein, M. (1996 ), The Missing Piece in Policy Analysis: Social Security Reform, American Economic Review papers and proceedings, 86, 1-14.
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Flemming, J.S (1977), Optimal Payroll Taxes and Social Security Funding: Some Transitional Problems fora Closed Economy,Joumal of Public Economics, 7, 329-50. Miles, D. and A. Timmermann (1999), Risk Sharing and Transition Costs in the · Reform of Pension Systems in Europe, Economic Policy, November, 233-64 Mirrlees, J.A. (1971), An Exploration in the Theory of Optimal Income Taxation, Rcl'icw of Economic Studies, 38, 175-208. Nickell, S.J. (2001), UK Labour Market Performance 1997-2001, Presidential Address to the British Association for the Advancement of Science, Section F, Glasgow, September. Zhang, J. (1995), Social Security and Endogenous Growth, Journal of Public Economics, 58, 185-213.
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DILEMMAS ABOUT PENSIONS
Peter Sinclah· 1 Director of Central Bank Studies Bank of England and Department of Economics University of Birmingham United Kingdom
This paper looks at the general principles underlying pensions systems, and the relative merits of different kinds of system of state superannuation payments. A'pay as you go system is. it is argued, usually inferior to a fully funded one. The paper presses the case for the view that redistribution is a cogent argument- perhaps the most cogent argument- for state provision, in a practical context where earnings opportunities differ between individuals. Perfect capital markets are a-;sumed, and labour supplies are endogenous. There is some merit in a unifonn state pension supported by a proportional tax on wage earnings, and its implications under two different social welfare functions are considered. But outcomes are Pareto-dominated, under each social welfare function, by a self-selection system from a continuous menu of contribution and pension rates. The least able opt for a large pension and a high tax rate, the abler for less of both. So far from state pensions being proportional to earnings, they should in fact be negatively associated with them.
l.
INTRODUCTION
This paper looks at two features of pension systems- whether they are fully funded or not, and at their redistributive impact. It argues that full funding has important general advantages. Turning to the second issue, I ask why governments provide pensions, why governments should provide pensions. The short answer to the first question is that pension systems are simply inherited from the past, and their longterm character, and the problem of vested interests make them very hard to change quickly. There are several possible answers to the second question. But perhaps the most compelling is that people differ greatly in their capacity to earn. It would seem outrageous that very low earners should be left to starve if they survive into old age. If a key motive for state pension provision is redistribution, then it should be viewed The author thanks a referee for helpful suggestions, and participants at seminars and conferences at City, Leicester and Warwick universities, Lisbon, the Economic Society of Austmlia, the Centml Bank of Argentina, the Reserve Bank of Australia and the Hong Kong Monetary Authority for valuable comments on associated work. Any opinions expressed are those ofthe author
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as an aspect of optimum tax policy. The implications of this are examined in later sections of this paper. The structure of the paper is as follows. Section 2 of this paper examines five arguments that may be used to justify the provision of state pensions, and argues that income redistribution is the most cogent of these. In section 3, two key sets of features of pension schemes are explored and various criteria for assessing arrangements for pensions are discussed. The background to current difficulties faced by pension schemes is analysed in section 4, while section 5 looks at some proposed solutions to them. Section 6 lays down certain desirable properties for a simple model for examining pension issues. Section 7 then looks at such a model and at its policy implications. Some qualifications and conclusions are discussed in the final eighth section of the paper.
2.
WHY DO GOVERNMENTS PROVIDE PENSIONS FOR THE OLD?
There are many possible reasons for the public provision of pensions. First, private capital markets for pensions may be undeveloped, thin or subject to monopolistic mispricing. The monopolistic mispricing may emerge as a result of increasing returns in fund management, which, if ubiquitous, would imply that there was room for only one private sector provider. Second, saving for old age may be a merit good, which is valued more highly by the government, and in the grey light of hindsight by the old person, than by the young who have to choose how much to save. Third, externalities may be involved: the rest of society may be upset to think of old people in a state of destitution, and derive positive pleasure from transferring resources to them. Fourth, life insurance markets may be bedevilled by problems of asymmetric information, giving rise to market failure due to moral hazard or adverse selection for example. Fifth. poverty among the aged may represent unequal opportunities to earn that the individuals enjoyed when they were younger. All these five arguments may help to explain why states began, first in Germany, and later in the Netherlands, Scandinavia, Britain and elsewhere, to provide pensions some twelve decades ago. But none of the first four is really compelling. Arguments one and four really constitute cases for regulating private providers, or perhaps for a (temporarily) state-owned pension company to establish standards and compete with them. But they do not amount to a cogent justification · for state provision as such. Adverse selection and moral hazard would appear, furthermore, to be much more of an issue with certain other kinds of insurance, particularly relating to income. Individuals have negligible knowledge of the timing of their deaths, and can rarely exercise that much influence upon it. Arguments two and three can be made the basis of a persuasive case for subsidizing voluntary savings, to internalize the externality (in the third case) or maximize the individual's true welfare (in the second). But argument five is different. Disparity in earnings ability, in a population of individuals with similar preferences, will lead to inequality in incomes. Abler people will typically consume more in their youth and old age than people with lower ability. With diminishing marginal utilities of consumption, this implies distributive inefficiency: the sum of all young people's utilities will, for example,
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be lower than they would be if unevenness in consumption by the young could be reduced or removed. · Ideally, when all individuals' lifetime preferences are similar, and the marginal utility of consumption is declining, it will be best to equalize consumption across all members of a given age group. This will be true under any social welfare function that treats individuals symmetrically. Achieving this ideal may be well-nigh impossible, however. What it calls for is a system of lump-sum taxes that vary by ability (more exacting on the abler, light or even negative on those with less talent). That way the distortionary effects of taxing labour income at the margin can be avoided. The able, with their large lumpsum tax demands, respond by supplying a large amount of labour (presumably, leisure is a nonnal good). The less able work less time, and may not even work at all. The consumption of everyone at a given stage of life will be the same. The key problem here is that the individual is surely likely to have a much better idea of his ability than the fiscal authority. The state agency responsible for · redistribution will have to rely on individuals' own reports of their own abilities. So the able have a strong incentive to lie. It is in their interest to claim to have lower talent than they truly have. That way they can enjoy a lower tax demand, and either more leisure or higher consumption or both. So if we assume that people will tell the truth if and only if it suits them, a sad but probably realistic premise, the ideal ability tax system is infeasible. If the tax authority can observe earnings, it will be forced to tax them instead, and this implies inevitable inefficiency. A wedge is driven between the worker's marginal rate of transforming labour into a produced good and his marginal rate of substitution between leisure and that good. In such a context, optimum taxation of incomes and redistribution becomes an intricate second-best problem. The issue of optimum pensions is perhaps best thought of, then, as an intertemporal variant of on the theme of optimal income taxation. In much of what follows, the classic insights of Mirrlees ( 1971 ), the pioneering paper that provided the basis for modem optimum income tax analysis, will be applied later on in .this paper in a simple model of overlapping generations. 3,
TYPES OF PENSION SYSTEM ANDY ARDSTICKS TO JUDGE THEM BY
There are many types of pensions system, but one key factor differentiating pension systems in practice is the extent to which contributions on the one side, and benefits on the other, are related to earnings. Count von Bismarck, the Prussian (and later, German) Chancellor in much of the late Nineteenth Century; introduced a system where both contributions and benefits were proportional to earnings. These characteristics are still apparent in the state pension systems ruling in contemporary Germany and many of its neighbours. Pension benefits and contributions are quite close to being proportional to earnings in Belgium, France, Germany, Italy and Sweden for example. In Austria and Portugal, they are exactly proportional. William Beveridge, architect of Britain's welfare state after the Second World War, is associated with quite a different system, where, at least initially, both contributions and benefits were absolute sums
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of money, unrelated to earnings. Neither the Biscmarckian nor the Beveridge pension system, in their pure forms, achieves any degree of income redistribution. But a combination of Bismarckian contributions and Beveridge benefits is
clearly redistributive. This is the system currently operating in Denmark, Ireland, the Netherlands and the U.K. If the absolute benefits are the same for all, and all contributions are equiproportional to earnings, the combination of the two is
definitely progressive. It enriches the aged poor at the expense of the better-paid young. In the United States, contributions are a fixed proportion of earnings, while pensions paid increase slightly with earnings- still progressive, but less so.
A second fundamental distinction is between fully funded and pay as you go pension systems. In the latter case, pensions paid to the current old are financed by levies upon the current young; in the former, by contributions that the current old had themselves made in their youth. With minor qualifications, state pension systems
tend to be pay as you go, while private systems are (approximately) fully funded. Countries differ widely in the size of private pension provision. There is no private pension financing in Luxembourg. At the end of 1996, it amounted to less than I 0 per cent ofGDP in Austria, Belgium, France, Germany, Greece, Italy and Spain. In Japan it was 22 per cent, and the European Union average was 21 per cent, as against over 60 per cent in the United States and Britain, and 89 per cent in the Netherlands. 2 There are five tests one could apply to a pensions system: i. Is it fair between generations? ii. Is it fair within generations? iii. Does it generate an efficient trade-off between an individual's consumption at different stages of life? iv. Does it generate an efficient trade-off between an individual's consumption and labour? v. Does it maximize utility in the long run? The first criterion depends upon the planner's perception of social welfare. For example, one needs to ask, are the welfare levels of all generations weighted equally, or is there discounting of future generations' welfare? Are different
generations' welfare levels perfect substitutes, less than perfect substitutes, or even perfect complements, for instance? In the limit, if they were perfect complements, the planner would never be prepared to make the poorest generation worse off by any amount at all, no matter how much other, better-off generations might gain as a result. With different generations' utilities regarded as perfect or reasonably good substitutes, however, the planner would be quite prepared to see some limited suffering for some generations for the greater good of others. Fairness within generations is an irrelevant issue if every member of a generation is in the same position as regards resources. But individual differences imply that one cannot consider the "welfare of a particular generation" without stipulating exactly how these individuals' utility levels are aggregated or related from the planner's viewpoint. In quite a wide group of cases, fairness within
generations is interpretable, ideally, as perfect equality in consumption. Miles and Timmerman (1999), Table 2, p.256.
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One of the many trade-offs that economic agents face is that between jam today and jam tomorrow. If an allocation of resources is to be Pareto-efficient, it must not be possible, by rearranging it, to increase the welfare of one person without bringing loss to someone else. Conditions for Pareto-efficiency include equality between marginal rates of substitution and transformation between any pair of produced goods, among them that between consumption in youth and consumption in old age. Satisfying this condition implies that the ratio of the marginal utilities of these two equals one plus the (real) rate of interest. If this condition is infringed, by taxation levied on pensions or interest on savings for example, just for one generation atone set of dates, it is in principle possible to abolish it and make everyone in that generation, and everyone else in every other generation, better off by some set of appropriate changes. Another Pareto efficiency condition relates to the trade-offbetween consumption and leisure. The young individual's marginal rate of substitution between leisure and consumption needs to equal the marginal product of that labour. An infringement would imply that more could be produced with reallocation and no extra call on labour. In general, this condition calls for the absence of any marginal taxes on labour income. Consider a pension system that ensures that each young person pays in a sum exactly equal to the discounted value of benefits to be received in old age. This system will honour the Pareto's efficiency condition. But it will achieve no redistribution of income. A Beveridge system with common pensions benefits, but contributions that varied with ability to earn, would be redistributive and Paretoefficient. But, as we have seen, it runs into serious snags concerning feasibility. So criteria (ii) and (iv) are very likely to conflict in practice. Criterion (v) is of c'onsiderable interest too. Suppose that everyone is alike, there is no technical progress, and that there is no role for depletable natural resources. This means that levels of lifetime consumption and utility should be stationary in any long run equilibrium (as well as common within every generation). Consumption by one generation's young workers will be the same as the next generation's; and the same should go for consumption in old age, labour supply, wage rates, interest rates and other macroeconomic variables. So the natural question to ask is whether a long run equilibrium established by voluntary saving will generate the highest stationary level of utility. It will, provided that it so happens th.at the (real) rate of interest equals the rate of population growth. In this Golden Rule outcome, stationary utility will be maximized.' Now consider a state pension system. A fully funded system, where I
This result holds for the traditional, representative agent model of overlapping generations models with exogenous labour supply by youths. It also extends to the case where utility may be written U(c,C,-h) where c and C denote consumption in youth and old age respectively, and his labour supply in youth. The constraint here is C=(!+r)[ wh-cJ. First maximize U with respect to c, C. h and the Lagrange multiplier on the constraint; then differentiate the first order conditions totally. The implicit equation for next period's capital per worker in the next period, a restriction to steady states and the properties of a well-behaved production function linking the factor prices to the capital-labour ratio (k) will then suffice to establish the result when utility is at a maximum against k.
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individuals are free to lend or borrow by themselves on the same terms as the state, has no impact on long run equilibrium; private saving adjusts one-to-one for any official saving. But a pay as you go system, all else equal, can only involve lower long run values of capital relative to labour, and hence lower wage rates, and higher interest rates. If and when the rate of inferest is less than the rate of population growth, a move towards a pay as you go system can only lead to a rise in steady state utility. The economy suffers from excess capital, and the pay as you go system is a very efficient way of destroying surplus capital. But if and where the rate of interest exceeds the rate of population growth - a condition known as "dynamic
efficiency" -a move from a pay as you go to a fully funded system, whatever its initial disadvantages, can only raise utility in the steady state. Ifendogenous population growth, altruism and technical progress are introduced, however, it is conceivable that the long run superiority of fully funded pensions under dynamic efficiency is open to reversal. Adapting Becker and Murphy's ( 1990) model of fertility and human capital building could imply this; Zhang (1995) argues that pay as you go pensions can be favourable to growth. 4.
DIMENSIONS OF THE PENSIONS PROBLEM
The average age of most countries' populations has been increasing, and looks set to continue growing for several decades to come. From the pensions standpoint, the "pensioner dependency ratio", the ratio ofthose eligible to draw pensions to those in paid work, is now rising quite sharply almost everywhere. Several factors contribute to this development. Seven of the main ones are:
a. b. c.
increasing life expectation female employment is now rising more slowly improved contraception, and more widespread availability of abortion, since
the 1960s d. e.
later marriage, and parents choosing to ~ostpone children or reduce family size men tending to retire earlier
f.
elongation of education
g.
post-war baby bulge is soon to stop contributing and draw pensions
On (a), life expectation increases have been pronounced, on all definitions, in many countries- especially in Western Europe and East Asia. In the European Union, it has been rising on average by some 33 days per year for the past quartercentury. Greek males now display the fastest rate of increase within this group. Dietary improvements and lifestyle changes (such as lower incidence of smoking)
appear to be the driving force. Only in some sub-Saharan countries badly afflicted by AIDS, and some parts of the former Soviet Union, is there any current evidence of falling expectation of life. If improving life expectation merely reduces the proportion of workers that dies before reaching retirement, its effect upon pensions finances could even be favourable. Problems arise from this standpoint when
average retirement spells increase, as indeed they have. Half a century ago, West European men could expect some six or seven years of life at age 65. Now they can expect to live twice as long on attaining this age.
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Increasing life expectation ,is not a new phenomenon, although the rate has
quickened somewhat in the 1980s and 1990s. For a long period, it was maskedfrom the standpoint of underfunded state pensions- by rising female labour force participation. More women at work, plus some switch from part-time to full-time work, led to increasing pension contributions in most countries. But from the 1970s
onward, first in Northern and Eastern Europe, and then, later on, elsewhere, women's share in total employment has tended to converge towards a plateau.
Taken together with (a) and other phenomena, this phenomenon, factor (b) above, has begun to yield adverse implications for pension financing arrangements.
At the same time as people tending to live longer, births have tended to fall. Many factors explain this. The contraceptive pill was invented in 1951, and its · widespread use began to be authorized in many countries in and after 1960. Shortly afterwards, abortion became legal in much of Northern Europe and North America. The number of life births fell in many countries by between 25 per cent and 35 per cent between the late 1950s and the mid-1970s. Most of the change followed smartly upon the availability of abortion and the pill. Nowhere have fertility rates recovered to previous leVels (although there have been some recent increases in for
example France and Sweden). In the European Union as a whole, the annual fertility rate was 1.5 per cent in 1995. In 1960, it had been 2.6 per cent. 4 · Turning to (d), we may note that a tendency to later marriage has reinforced these developments. In the OECD area, brides on first marriage are some four years older now than they were two generations ago. A trend towards later marriage is
accompanied by a broadly parallel trend towards starting families later. Since there is no evidence of any change in the range of ages at which women cease to be
capable of bearing children, families postponed become families reduced. Reductions in family size may have been the outcome of conscious choices, tooresponses, for example, to improved labour market opportunities for mothers, or to the movements, often downwards for quite protracted periods, in the urban-space-
purchasing power of labour earnings. One factor that has aggravated the position is (e), the growing tendency for some men, in particular, to cease participating in the labour force before reaching the formal age of retirement. Belgium is a particularly interesting case here. Three
decades ago, most all Belgian men continued working until well into their sixties. Now the labour force participation of men in the 60-64 age range has fallen to barely one quarter, and many Belgian men are retreating from the world of work even
younger. Britain displays the same phenomenon, although the trend is less pronounced. In the British case, Nickell (2001) shows that early retirement due to sickness is the main culprit, with back pain and depression the most frequently cited causes of ill health. In the context of increasing life expectation, one might anticipate increases in the age of retirement as a way of balancing the accounts. Unfortunately, the reverse has -happened. Part of the reason is that, in many
countries, policy was directed to protecting younger and middle aged workers from
Boldrin era/. ( 1999), Table 2, p.294.
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the threat of unemployment during the 1980s in particular. Encouraging earlier retirement, often funded by sickness insurance schemes, was a device that helped to achieve this, while at the same time removing these workers frOm the politically embarrassing unemployment count. Frorri the pensions viewpoint, this matters
primarily because the growing numbers of sick older wofkers under the retirement age are no longer making any contribution (or at least as large a contribution as
before) to pension fund revenues. Boldrin et a/. (1999) observe that falling employment for the old is "the single most damaging factor for the financial sustainability of pay as you go pension schemes". Interestingly they find no empirical support for the view that early retirement lowers unemployment among the young. If the effective age of retirement for many men was actually slipping, rather than rising in line with life expectation, the taxable base for pension contributions
was also under attack from another quarter. Spells of secondary and higher education were lengthening. This is phenomenon (f). The minimum age for leaving secondary school was raised in several countries, Britain among them. More
important, the proportion staying on till age I 8, rather than leaving earlier, increased. On top of this came a rise in the take-up of graduate education (average university enrolments have approxim'ately doubled in relation to cohort size in
Western Europe between 1980 and 2000). The only factor of note to operate in the opposite direction, nowhere powerful enough to offset these developments, was the reduced incidence and duration of military conscription. So there are more retired people, tending to live longer; more people ceasing
to work before the retirement age; a flattening off of women's employment share; a seemingly enduring tendency to later, smaller families; and the duration of the working career is being squeezed from below by the elongation of education. In concert, these factors pose awkward challenges for the public purse when pensions are provided by the State. One phenomenon that makes them urgent is factor (g). This is the fact that the great bulge of babies born in North America and Western Europe shortly aftyr the end of the Second World War are now within a decade or two of retirement. In I 995, the European Union average elderly dependency ratio (the ratio of those aged 60 and over to those aged between 20 and 59) was 37 per cent. Eurostat official demographic projections based on current trends suggest it will reach 72 per cent in 2050 (Boldrin eta/. (1999), Table 3, p.295). Any pension system is open to strain as a result of demographic developments. Longer life expectation, for example, is problematical for all systems, private or public, fully funded or pay as you go. Benefits have to be trimmed, or contributions raised, or both, to keep the books in balance. With changes in births, however, there is a difference. These pose no direct problem for fully funded systems, but can create havoc when pension arrangements are of the pay as you go variety. (In a
closed economy there is still an indirect difficulty even with fully funded systems, since undulations in population growth rates are liable to create complex disturbances in the values of wage rates and real interest rates).
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5. POLICY RESPONSES TO PENSION UNDERFUNDING Underfunding of fUture pension liabilities can be countered in three main ways:
(i) raising the age at which individuals quality for pensions; (ii) raising contributions levied on the young; and
(iii) reducing the value of pensions paid. None are easy to apply in practice. The first of these three responses is the natural reaction to increasing life expectation. Two decades ago men in most OECD economies could look forward, on average, to ten years in retirement, after a career spanning about 45 years. This
gives a ratio of two to nine. Now career length is shortening somewhat, while the average retirement spell for men has risen by about two years, and sometimes more,
in many countries. In retrospect, the age of pension eligibility should probably have been increased by perhaps eighteen months - to keep the ratio of retirement to career spells constant.
One problem here is that workers' productivities may still fall with age, on average, much as they have always done. Dietary and lifestyle improvements may postpone death with little if any impact on individuals' abilities to continue working effectively late middle age. One reply would point out that older workers' comparative advantages may change as they age: they may become completely unsuited to some types of work, but remain quite proficient in others. A worker's final career stage could therefore involve a change in role and tasks, and quite possibly a less senior and lower-paid position. If so, private pension arrangements,
which are usually tilted towards immediate pre-retirement earnings, may need revision.
A second difficulty is the fact that age eligibility for pensions should only be revised with adequate notice, to permit employees and employers plan ahead appropriately. This is a more telling point in the context of the third policy (lowering the pension paid). But even in relation to raising the pension eligibility age, it implies that the transition to a better system can hardly be immediate. The second policy response, raising contributions by the young, has certain attractions. It shields the current old from what could otherwise be a drastic and
presumably completely unanticipated reduction in their consumption in old age. It increases the next period's stock of capital, because although the young are likely to reduce their voluntary saving somewhat, total saving, public and private, will rise. And it represents a step in the direction of the key principle that future pensions
should be funded: when the current young generation retires, it will be their own pensions that will be financed by the investment of their contributions.
There is, however, a snag. The current young will suffer a serious fall in lifetime consumption and utility, if it is they that are called upon to finance not just the previous generations pensions but their own as well. Why should the burden of adjustment fall only upon this generation? Intergenerational fairness arguments
suggest that the changeover to a fully funded system should be gradual. Indeed, perhaps the current old should share some of the burden too. One consideration that reinforces this is the fact that the prices of factors of production will take time to converge on the new steady state equilibrium. The real
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wage rate will start to climb, and the rate of interest will fall. But for the current young, the wage rate will actually drop iftheir labour is endogenous. They will react to additional tax burdens by working longer. This will increase the rate of interest faced by the current old on their voluntary saving giving them a windfall gain, which should presumably merit some compensating reduction in pension benefits. The third policy reaction involves a cutback in the value of pensions paid. This can be achieved in a variety of ways. Perhaps the simplest involves breaking or 'suspending the link, if there is one, between state pensions and wage rates. Real wage rates display a positive time trend of between I per cent and 2 percent per year in most advanced economies. Full pension- real wage linkage meanS uprating the nominal Value of pensions, annually or perhaps more frequently, to cover both inflation and the growth rate of real wages. It also implies ·that two retired individuals, who differ only in age, will receive the same pension in the same year. Ifreal wages grow, for example, by 1.5 per cent per year, a complete suspension of the wages link for twenty years - so that pensions were indexed to prices only would reduce pension liabilities by some 23 per cent. This is a major saving, achieved quite speedily. Alternatively, pension payments could be inflation proofed and uprated by some fraction of real wage rises. In favour of either of these moves is the point that the pensioner does not suffer an absolute reduction in the real value of the pension. If poverty is absolute, delinking pensions from earnings, and tying them instead to the relevant price index for pensioners, is completely innocuous. Delinking also offers a relatively rapid escape route from pension underfunding problems. On the other hand, there are difficulties. One is that the pensioner's real income stream is presumably lowered below what had been previously expected. So he is being asked to make a sacrifice in that sense; and indeed, had he known about this long enough ahead, he could and perhaps would have offset many of its effects by saving more when he was working. Furthermore, there are familiar and powerful arguments for thinking that poverty is at least in part a relative concept. Delinking pensions from real wages, in a context where labour productivity and real wage rates climb over time, can only widen the income gap between one generation and its successor- and the all too visible gap between the old and the comparatively better off young. Optimal redistribution in a situation like this would seem more appropriately from the relatively affluent young towards the poorer old. Wage-delinking actually has the opposite effect. Lastly delinking pensions from pay is certainly not a substitute for achieving a fully funded system. It is only a device for making the pensions system less generous. So the most that could be said for it is that it may have its place in a general programme of transition to that superior system ..
6. HELPFUL FEATURES OF A MODEL FOR PENSIONS For many purposes a model of overlapping generations. with its pattern of discrete time. is a simpler and more appropriate framework than a continuous time set-up. In the former, people can live for two periods, work only in the first, and consume, presumably, in both periods of their lives.
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This approach has one or two drawbacks, however, of which perhaps the most telling is that it forces an individual's retirement to be a fixed (and rather implausibly large) portion of his or her economic life. One way round this difficulty is to assume that everyone is certain to live for the first working period, and faces
a probability of, say, q of surviving into old age. In such circumstances, one may assume the existence of assets that can be bought by youths, with gross returns of in the event of survival, and zero otherwise. Private saving in the fortn of such instruments restores the intertemporal trade-off condition that the ratio of the marginal utilities of consumption in youth and old age should equal the gross rate of interest, I + r. This set-up also has the merit of allowing one to examine changes in life expectation by altering the parameter q. Within the (at most) two-period lives set-up, it is highly desirable to assume that the intertemporal utility function treats old age consumption, C, in an additively separable and logarithmic fashion. The advantage of this is that, because C can be defined as the product of two numbers- the sum of private saving and discounted pension on the one side, and the gross rate of interest (I +r) on the other, this last
number plays no role in the agent's optimisation decisions. Just why this is so
helpful stems from the fact that the rate of interest here is the rate expected to hold in the next period, which will depend on next period's ratio of capital to worker's labour supply. With any other set-up, a closed fortn solution for next period's capital-labour ratio will be unavailable for this reason. Another possible characteristic of an overlapping generations model is homotheticity as regards consumption at different stages of life. This becomes important when people are allowed to differ, for example in ability to earn. Homotheticity for consumption is youth, c, and old age, C, is the critical condition pertnitting aggregation. This was first established by Flemming ( 1977). When utility is log-linear in C, for reasons examined above, homotheticity for c and C requires utility to be log-linear inc as well. Most models of overlapping generations with production exogenise labour
supply: the young are typically assumed to work for a period of unit length, while the old do not work at all. But the labour supplies of individuals are not in practice uniform or constant over time. More generally, it is natural to ask how equilibrium is affected when labour is endogenous. This is especially so in the context of taxes and transfers. The easiest way of making labour supply endogenous in the overlapping generations framework is to make utility linear (and decreasing) in
labour supply in the period of youth, as well as log-linear inc and C, consumption levels in youth and old age. This quasi-linear utility function is highly tractable; this merit is particularly valuable once individual differences are introduced. Quasilinearity does not infringe Flemming's aggregability condition of (c, C) homotheticty, because it does not relate specifically to labour supply. The utility function with which it is easiest to work is therefore
U = -b lnb- (1-b)ln(l-b) +blnc + (1-b) InC -mh
(I)
The first two terms are constants whose presence removes unnecessary clutter from the associated indirect utility functions.
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ANALYSIS
Agents maximise (I) with respect to h, c and C, subject to two,constraints. These are first that h be non-negative, and second that p + (I +r)(wh( I -t)-c)- C be nonnegative. Here, pis the pension and t the tax rate facing the individuaL The first order conditions imply that any individuals facing a wage rate less
than mpi( I +r )(I-t) will not participate in the labour force. They will consume bpi (1+r) in youth and (1-b)p in old age, financing the former by borrowing against their future pension. The utility of such people will equal In p- bln(l +r). Those with sufficiently high wage rates will supply labour of (Jim)- piw(/+r)(l-t), consuming bw(J -t)im in youth and (1 +r)w(/ -t)( I -b)im in old age. Their saving in youth will equal w(l-t)( I -b)im- pi(/ +r), This will be positive if their wage rate is high enough. In general, there will be three groups in the young population: the unemployed; employed dissavers; and employed savers. The utility of those who do work will equal , U = In w(/-t)im +(/-b)ln(J +r) -1 + mpiw(l +r)( I-t).
The issue of redistribution only arises once wage rates are allowed to differ. It is simplest to assume that the wage rate each person faces is a product of two numbers- the real wage rate for someone with unit ability, and their own ability level, a variable taken to be uniformly distributed on the interval from 0 to I. In the numerical results below, b is set to one half, and m to unity. We shall assume that the pension system is fully funded. The natural place to begin is with a system that is pure Bismarckian in contributions and pure Beveridge in benefits. In this case p and the earnings contribution rates faced by everyone are the same. Later both parameters may be
allowed to vary, in order to obtain optimal non-linear benefit and contribution rates. If the social welfare maximand is mean utility, the optimum earnings contribution rate is 0.336, which finances a universal pension with a discounted present value
to a youth of0.0574. With minimum utility the maxim and- as prescribed by Rawls -the common pension goes up to 0.0674, and the tax rate to finance it to 0.544. In the first case, 17.3 percent of workers are unemployed; in the second, 29.6 percent. A superior pension and contribution system can easily be identified. Suppose that t and p are available, but that everyone can choose a different pension-
contribution rate package if they prefer. Suppose that the set of packages is given by P = QT- X. You can opt between a generous pension p, and a high contribution rate t, or lower values of both as given by that general equation. Each person first chooses savings and labour supply, then maximizes resulting indirect utility with
respect to the contribution rate for them. Higher wage individuals will go for lower pensions and lower contribution rates. The idea is that out of the continuum of
pension-contribution rate packages, each person picks the package best for them. Preferences given by ( 1) satisfy the "single-crossing condition" that ensures a unique optimum package for each individual who works. The Flemming aggregation condition ensures that if pensions are fully funded, the steady state pattern of factor prices is unique. Coulter eta/. (1997) argue in favour of opt outs. Arguments in
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favour of this are attractive. But one can go further, and make the size of the pension a continuous variable, negatively related to the size of earnings. In this case, Rawlsian social welfare is maximized when t, the contribution rate
chosen by the unemployed, is some 68 per cent. Everyone in work opts for a lower value of the contribution rate, which falls progressively to reach about for the ablest person working. High earners do not receive a state pension in old age: instead they
pay a lump-sum tax, as given by the formula P=QT -X. If mean utility is the maximand, the marginal contribution rate selected by the ablest will vanish, so that there is a zero marginal tax rate on earnings, but to earn this privilege they face a
really steep lump sum tax demand. The marginal tax rate confronting the least able worker is 0.65. Unemployment rates are 34.3 per cent in the latter case, and about 419 in the Rawlsian optimum. One notable feature of these results is that the marginal contribution rates associated with the biggest pension are quite close in these two very different optima, and the difference in unemployment rates is quite small. Where the two optima differ most is in the speed with which contribution rates fall as earnings rise,
but they fall quite steeply in both cases. These observations imply that there may well be rather less political dispute about the general shape of an ideal pension system than might appear from the traditional optimum tax literature. There is another striking feature, too. The Raw Is-optimal non-linear pension system does
not just yield higher minimum utility than the Rawls-optimal linear system - it Pareto-dominates it, in the sense that everyone's utility is higher in the first optimum than the second. Similarly, the utilitarian-optimal non-linear system Pareto-dominates the utilitarian-optimal linear one.
8.
QUALIFICATIONS AND CONCLUSIONS
This paper has abstracted from a number of considerations. First, it has neglected problems of uncertainty. There may be randomness is birth and death rates, technological progress and preferences; unforeseen political changes may also lead to uncertainty in the future path of pension benefits and contributions. The rate and character of technological progress determine the growth rate of real wage rates and
the rate of return on capital. As Miles and Timmerman ( 1999) emphasize, the net present value of future state pension liabilities is highly sensitive to assumptions made about these two rates. It has omitted government spending on public goods or debt service, assuming instead that pension provision is the sole fiscal activity
· undertaken by the State. The economy under consideration has been closed to trade, perfectly competitive, innocent of any Keynesian difficulties, and devoid of money. It has been assumed that all agents fully understand the pension and benefit system confronting them, despite some rather worrying evidence (eg Bouri eta/.
(2001)) to the contrary. There is no altruism towards children or parents, no bequests, no education, private or public (a factor stressed by Boldrin eta/. (1999) which may go some way to mitigate the disadvantages of a pay-as-you-go system). Unlike Becker and Murphy (1990) there is no endogeneity of fertility or human capital building. It has concentrated upon steady state,solutions, and selected a
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convenient if less than fully plausible assumption about the distribution of abilities. Preferences have been common and deliberately modelled in a shape that permits aggregation across heterogeneous workers and yields a closed form solution for · factor prices and associated variables.
The conclusion to which this paper points is that the strongest case for a government role in pension provision is based upon unequal earning opportunities. Pensions need not be uniform. Greater redistribution is achieved if they are absolute
and uniform, as opposed to proportional to earnings. But still greater redistribution can be attained by making the size of the pension decline as earnings increase. Indeed, the pension for high earners can, and probably should, be negative. To compensate, the marginal pension contribution rate needs to decline, too, as
earnings rise, and should in fact be zero at the top at least when social welfare is utilitarian. In the circumstances considered in this paper, a pay-as-you-go pension system
is inferior to a fully funded one. It is natural to ask how quickly, if at all, one should make the transition from the former to the latter, in a country where pensions are unfunded. Here again, the social welfare function· is of vital importance. If it is
Rawlsian between the generations, the answer is that you should stick to the bad system you have inherited, because the transition would bring pain to at least one generation (the poorest generation), which no amount of subsequent gains by later generations could compensate. But if, at the other extreme, social welfare is utilitarian- the (discounted) sum of the stream of all generations' utilities- the transition is worth undertaking. And if the discount rate for social welfare is low enough, it appears that the correct course of action is to withdraw pay-as-you-go
pensions immediately and in full forthe current young. But detailed analysis of this issue must await further research.
REFERENCES Becker, G., K. Murphy and R. Tamura (1990), Human Capital, Fertility and Economic Growth, Journal of Political Economy, 98, S 12-37. Boeri, T., A. Boersch-Supan and G. Tabellini (2001), Would You Like to Shrink the Welfare State? A Survey of European Citizens, Economic Policy, April, 950. . Boldrin, M., J. Dolado, J. Jimeno and F. Perrachi (1999), The Future of Pensions in Europe, Economic Policy, November, 289-320. Coulter, F., C. Heady, C. Lawson and S. Smith (1997), Social Security Reform for Economic Transition: the Case of the Czech Republic, Journal of Public Economics, 66,313-26. Feldstein, M. (1996 ), The Missing Piece in Policy Analysis: Social Security Reform, American Economic Review papers and proceedings, 86, 1-14.
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Flemming, J.S (1977), Optimal Payroll Taxes and Social Security Funding: Some Transitional Problems fora Closed Economy,Joumal of Public Economics, 7, 329-50. Miles, D. and A. Timmermann (1999), Risk Sharing and Transition Costs in the · Reform of Pension Systems in Europe, Economic Policy, November, 233-64 Mirrlees, J.A. (1971), An Exploration in the Theory of Optimal Income Taxation, Rcl'icw of Economic Studies, 38, 175-208. Nickell, S.J. (2001), UK Labour Market Performance 1997-2001, Presidential Address to the British Association for the Advancement of Science, Section F, Glasgow, September. Zhang, J. (1995), Social Security and Endogenous Growth, Journal of Public Economics, 58, 185-213.